Answer:
3a - 2b - c + 16 = 23
Step-by-step explanation:
so we want to write an equetion which containe a, b and c so we have given
4a - 2b = 10 and a + c = 3
so we are going to differentiate 10 to 7 + 3 it will be
4a - 2b = 10
4a - 2b = 7 + 3 ...then we insert a + c in place of 3 b/c they are equal
4a - 2b = 7 + a + c .... we take to the left side of the equal sighn
4a - a - 2b - c = 7
3a - 2b - c = 7
thrn if we want to write the equetion =23 we add 16 both side 3a - 2b - c + 16 = 23 .
100%
A DVD player manufacturer shipped 960 DVD players last month. According to the manufacturer's records, 5 out of every 24 players were
repaired during the first year of ownership.
How many of the 960 DVD players were repaired in the first year?
If 5 out of every 24 players were repaired during the first year of ownership, then 200 of the 960 DVD players were repaired in the first year.
Based on the manufacturer's records, we know that 5 out of every 24 players were repaired in the first year of ownership. To find out how many out of the 960 DVD players were repaired in the first year, we can set up a proportion:
5/24 = x/960
To solve for x, we can cross-multiply:
5 * 960 = 24x
4800 = 24x
x = 200
Therefore, 200 of the 960 DVD players were repaired in the first year, which is approximately 20.8% of the total shipped.
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Given the circle below with tangent GH and secant JIH. If GH = 8 and
12, find the length of IH. Round to the nearest tenth if necessary.
JH
=
H
The value of the segment IH for the circle with secant through H which intersect the circle at points I and J is (6 + 2i√7) or (6 - 2i√7)
What are circle theoremsCircle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.
GH² = IH × JI {secant tangent segments}
JI = 12 - IH, we shall represent IH with x so that;
8² = x(12 - x)
64 = 12x - x²
x² - 12x + 64 = 0 {rearrange to get a quadratic equation}
with the quadratic formula;
x = [12 + √(-112)]/2 or x = = [12 - √(-112)]/2
√(-112) = 4i√7 {where i = √(-1)}
so;
x = (6 + 2i√7) or x = (6 - 2i√7)
Therefore, the value of the segment IH for the circle with secant through H which intersect the circle at points I and J is (6 + 2i√7) or (6 - 2i√7)
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can yall help me with this and this is due today!
a) The experimental probability of rolling an even number is given as follows: 12/25.
b) The theoretical probability of rolling an even number is given as follows: 1/2.
c) With a large number of trials, there might be a difference between the experimental and the theoretical probabilities, but the difference should be small.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The number of trials in which an even number is rolled is given as follows:
88 + 69 + 83 = 240.
Hence the experimental probability is given as follows:
240/500 = 12/25.
For each roll, 3 out of 6 numbers are even, hence the theoretical probability is given as follows:
p = 3/6
p = 1/2.
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A) Construct an appropriate tabular representation/summary of the random variable Number of years in operation and provide an interpretation.
b) Construct a cross-tabulation of the data on Daily Income and Type of service and provide an interpretation. Hint: Use a class width of N$ 500 for Daily Income.
c) Calculate and interpret relative measures of variability for the Daily Income for each of the three categories of Type of service
The following relation is a function:
{(-2, 4), (3, 0), (-4, 3), (-2, -1), (0, -4)}
true
false
The relation of function is False.
This relation is not a function because the input value -2 is associated with two different output values (4 and -1). In a function, each input can only have one corresponding output.
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The first two terms in an arthemetic progression are 2 and 9. The last term in the progression is the only number greater than 150. Find the sum of all the terms in the progression
The sum of all the terms in the arithmetic progression is 3507.
The common difference in an arithmetic progression is the difference between any two consecutive terms. Let the common difference be d. Then, the third term is 2 + d, the fourth term is 2 + 2d, and so on. Also, let the last term be n.
Since the last term is greater than 150, we can write n = 2 + (n-2)d > 150. Solving this inequality, we get d < 74. Therefore, the common difference can be 1, 2, 3, ..., 73.
Using the formula for the sum of an arithmetic progression, we get the sum of all the terms as (n/2)(first term + last term) = (n/2)(2 + n d) = (n/2)(11 + (n-1)d).
We can substitute n = (last term - first term)/d + 1 and solve for the sum. This gives us the final answer of 3507.
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Your supervisor asks you to separate 4,780 castings into 25 piles. When you complete the job, how many castings will you have left over
Answer:5
Step-by-step explanation:
4780/25=191.2
You don't want an odd amount of castings in different piles.
191*25=4755
4780-4755=5
I think i read the question wrong. Sorry if i did
When separating 4,780 castings into 25 piles, there will be 5 castings left over.
Explanation:A fraction is a numerical expression representing a part of a whole. It consists of a numerator (the top number) that indicates how many parts are considered, and a denominator (the bottom number) that shows the total number of equal parts in the whole. Fractions are typically expressed as a/b, where "a" is the numerator and "b" is the denominator. They are used in various mathematical operations, including addition, subtraction, multiplication, and division, and in real-life scenarios involving proportions and portions.
In order to determine the number of castings left over when separating 4,780 castings into 25 piles, we can use division. Divide 4,780 by 25 to find the number of castings in each pile.
The quotient is 191.2. Since we can't have a fraction of a casting, we round down to 191.
To find the number of castings left over, subtract the total number of castings in the piles from the original total. 4,780 - (191 x 25)
= 4,780 - 4,775
= 5
Therefore, when you complete the job, you will have 5 castings left over.
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A)Irene purchased some earrings that regularly cost $55 for a friend’s birthday. Irene used a "20% Off" coupon.
How much did Irene pay for the earrings?
Show your work. Highlight your answer.
B)Irene’s friend did not like the gift so she tried to return the earrings. She did not have the receipt, so the store would only give her store credit for 50% of the purchase price.
How much credit did Irene’s friend receive?
Show your work. Highlight your answer.
C)What is the percent change from what Irene paid and what her friend returned it for?
Show your work. Highlight your answer
A) Irene pays $44 for the earrings.
B) Irene’s friend received $22 as credit.
C) Percent change from what Irene paid and what her friend returned it for is 50%
A) Cost of earing = $55
Discount coupon = 20%
Total cost Irene pay = 55 - (20% of 55)
Total cost Irene pay = 55 - ( 55 × 20/100)
Total cost Irene pay = 55 - 11
Total cost Irene pay = 44
B) Credit given by store = 50%
Credit received = 50% of 44
Credit received = 44 × 50/100
Credit received = 22
C) Percent change = [tex]\frac{final - initial }{initial}[/tex] × 100
Percent change = [tex]\frac{44-22}{44}[/tex] × 100
Percent change = 50%
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On a unit circle, the terminal side of Angle 0 intersects the circle at point (x,y). ?
Underline the expressions that would make the following statements true.
A) sin θ = (x,y, the ratio of x to y, the ratio of y to x)
B) tan θ = (x,y, the ratio of x to y, the ratio of y to x)
C) cos θ = (x,y, the ratio of x to t, the ratio of y to x)
The correct expressions are:
A) sin θ = y
B) tan θ = y/x
C) cos θ = x
How On a unit circle, the terminal side of Angle 0 intersects the circle at the point?On a unit circle, the terminal side of Angle 0 intersects the circle at points (x,y). We can use trigonometric ratios to relate the coordinates (x,y) to the angle θ.
A) sin θ = the ratio of y to 1, or simply y.
B) tan θ = the ratio of y to x.
C) cos θ = the ratio of x to 1, or simply x.
Therefore, the correct expressions are:
A) sin θ = y
B) tan θ = y/x
C) cos θ = x
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Find Tn centered at x = 23 for all n for the function f(x) = ex. (Use symbolic notation and fractions where needed.)
For a function f(x) = e^x, we can find its Taylor series expansion Tn centered at x = 23 using the formula:
Tn(x) = Σ (f^(k)(23) * (x - 23)^k) / k!, for k = 0 to n
Since the derivative of e^x is always e^x, the k-th derivative evaluated at 23 is f^(k)(23) = e^23 for all k. Therefore, the Taylor series expansion becomes:
Tn(x) = Σ (e^23 * (x - 23)^k) / k!, for k = 0 to n
This is the Tn centered at x = 23 for all n for the function f(x) = e^x, with symbolic notation and fractions as requested.
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!!I need help seriouslyyy!!
The average cost per day for the four service is $3.23 per day
What is average cost?Average cost refers to the per-unit cost of production, which is calculated by dividing the total cost of production by the total number of units produced.
Therefore average cost = total cost/ number of unit
total cost = $108
average cost for the three services = $108/3
= $36
total average cost = $36+$54.30
= $90.30
therefore average cost for a day will be average cost for a month over 28day i.e 7days ×4
= 90.30/28
= $3.23 per day
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Gross Monthly Income: Jackson works for a pipe line company and is paid $18. 50 per hour. Although he will have overtime, it is not guaranteed when or where, so Jackson will only build a budget on 40 hours per week. What is Jackson’s gross monthly income for 40 hours per week? Type in the correct dollar amount to the nearest cent. Do not include the dollar sign or letters.
A. Gross Annual Income: $
B. Gross Monthly Income: $
To find Jackson's gross monthly income for 40 hours per week, follow these steps:
1. Calculate his weekly income: Multiply his hourly wage ($18.50) by the number of hours he works each week (40 hours).
2. Calculate his monthly income: Multiply his weekly income by the number of weeks in a month (4 weeks).
A. Gross Annual Income: To find this, multiply his monthly income by 12 (the number of months in a year).
B. Gross Monthly Income: This is the answer we need to find.
Step-by-step calculations:
1. Weekly income = $18.50 * 40 hours = $740
2. Monthly income = $740 * 4 weeks = $2,960
A. Gross Annual Income: $2,960 * 12 = $35,520
B. Gross Monthly Income: $2,960
The answer:
A. Gross Annual Income: $35,520
B. Gross Monthly Income: $2,960
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Three experiments investigating the relation between need for cognitive closure and persuasion were performed. Part of the study involved administering a "need for closure scale" to a group of students enrolled in an introductory psychology course. The "need for closure scale" has scores ranging from 101 to 201. For the 78 students in the highest quartile of the distribution, the mean score was x = 177. 30. Assume a population standard deviation of = 8. 19. These students were all classified as high on their need for closure. Assume that the 78 students represent a random sample of all students who are classified as high on their need for closure. How large a sample is needed if we wish to be 99% confident that the sample mean score is within 1. 8 points of the population mean score for students who are high on the need for closure? (Round your answer up to the nearest whole number. )
We need a sample size of at least n = 214 students to estimate the population mean score if we wish to be 99% confident that the sample mean score is within 1. 8 points of the population mean score for students who are high on the need for closure
We are given that the population standard deviation is σ = 8.19 and the sample mean is X = 177.30 for a sample of n = 78 students in the highest quartile of the "need for closure" scale.
We want to determine the sample size needed to estimate the population mean score for high need for closure students within a margin of error of 1.8 points, with 99% confidence.
Since we do not know the population mean score, we will use a t-distribution to calculate the margin of error. We can use the formula:
margin of error = t_(α/2) * (σ/√n)
where t_(α/2) is the critical value from the t-distribution for a 99% confidence level with (n - 1) degrees of freedom. We can find this value using a t-table or a calculator, and we get t_(α/2) = 2.64 (rounded to two decimal places) for n - 1 = 77 degrees of freedom.
Substituting the given values into the formula, we have:
1.8 = 2.64 * (8.19/√n)
Solving for n, we get:
n = [2.64 * (8.19/1.8)]^2 = 214 (rounded up to the nearest whole number)
Therefore, we need a sample size of at least n = 214 students to estimate the population mean score for high need for closure students within a margin of error of 1.8 points, with 99% confidence.
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Calculate the truth value for each compound proposition, using the given truth values for the simple statement letters. Type T or F beneath each letter and operator. Also, identify the main operator of each statement by typing a lowercase x in the box beneath it. Use the provided dropdown menu to indicate whether the compound statement is true or false, given the assigned truth values.
Given Truth Values
True False
K Q
L R
M S
Statement 1: (M ~ R { v ~ S L)
T or F:
Main Operator:
Assuming the given truth values, Statement 1 is____.
Statement 2: (~ S = M ). (L ~ K )
T or F:
Main Operator:
Assuming the given truth values, Statement 2 is____.
Statement 3: ~(R V ~ L) (~ S S)
T or F:
Main Operator:
Assuming the given truth values, Statement 3 is____.
Statement 4: ~ [(Q V ~ S). ~ (R = ~ S)]
T or F:
Main Operator:
Assuming the given truth values, Statement 4 is____.
Statement 5: (S = Q) = [(K ~ M) V ~ (R. ~ L)]
T or F:
Main Operator:
Assuming the given truth values, Statement 5 is_____
Statement 5 is True
Statement 1: (M ∧ ~R) ∨ (~S ∧ L)
T or F: T
Main Operator: ∨
Assuming the given truth values, Statement 1 is True.
Statement 2: (~S ↔ M) ∧ (L ∧ ~K)
T or F: F
Main Operator: ∧
Assuming the given truth values, Statement 2 is False.
Statement 3: ~(R ∨ ~L) ∧ (~S ∨ S)
T or F: F
Main Operator: ∧
Assuming the given truth values, Statement 3 is False.
Statement 4: ~ [(Q ∨ ~S) ∧ ~(R ↔ ~S)]
T or F: T
Main Operator: ~
Assuming the given truth values, Statement 4 is True.
Statement 5: (S ↔ Q) ↔ [(K ∧ ~M) ∨ ~(R ∧ ~L)]
T or F: T
Main Operator: ↔
Assuming the given truth values, Statement 5 is True.
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In Mr. Bui's algebra class, each pair of students was given a different system of equations to solve using any method. Julia and Charlene were assigned the following system. Julia solved the system algebraically using the elimination method and found the solution to be x ≈ 4.42 and y ≈ 4.39. Charlene graphed the system and found a solution of x ≈ 2.5 and y ≈ 5.25. Select the correct statement comparing their solutions. A. Neither Julia nor Charlene found the correct solution. The graphs of the lines do not intersect, so the system has no solution. B. Neither Julia nor Charlene found the correct solution. The graphs of the lines intersect at a different point. C. Charlene correctly graphed the system to find the intersection point at approximately (2.5,5.25). D. Julia correctly solved the system algebraically using the elimination method to find the solution x ≈ 4.42 and y ≈ 4.39.
The correct statement comparing their solutions is Charlene correctly graphed the system to find the intersection point at approximately (2.5,5.25).
option C is correct.
What is a mathematical equation ?Mathematically, an equation can be described as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
Since Charlene graphed the system and found a solution of x ≈ 2.5 and y ≈ 5.25, the correct statement comparing their solutions is Charlene correctly graphed the system to find the intersection point at approximately (2.5,5.25).
In conclusion, the three major forms of linear equations: are
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As a reward for Musa's diligence and agreement, his father decided to distribute a sum of money amounting to 5,800 dinars to him and his brothers, the one with the highest average taking the largest amount, while that the one with the third rank gets an amount that is half of what the one with the first rank takes. Translate this situation as an equation with an unknown X, where X is the amount that the first rank takes. Solve the resulting equation , Solve an exact value . Gives exclusively between two consecutive natural numbers Each of the three sums
The amount that the first rank takes is 1934 dinars, and the amounts that the second and third ranks take are 967 dinars and 483.5 dinars (rounded to 484 dinars), respectively.
Let's assume that there are three brothers, including Musa. Let X be the amount of money that the brother with the highest average takes, and let Y be the amount of money that the brother with the third rank takes.
According to the given conditions, we can write the following equations:
X + Y + (5800 - X - Y) = 5800 (The total amount of money distributed should be equal to 5800 dinars)X > Y (The brother with the highest average should take the largest amount)X is an integer valueLet's simplify equation 1:
X + Y = 2900
Also, we know that:
X = (2Y + X)/2
(The amount that the third rank takes is half of what the first rank takes)
Simplifying this equation:
2X = 2Y + X
X = 2Y
Substituting this value of X in equation X + Y = 2900:
3Y = 2900
Y = 2900/3
Y ≈ 966.67
As the amount given must be a whole number between two consecutive natural numbers, we can round Y to the nearest natural number:
Y = 967
Then, X = 2Y = 2*967 = 1934
Therefore, the amount that the first rank takes is 1934 dinars, and the amounts that the second and third ranks take are 967 dinars and 483.5 dinars (rounded to 484 dinars), respectively.
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Para medir lo largo de un lago se construyeron los siguientes triangulos semejantes, en los cuales se tiene que : AC = 215m, A 'C= 50m, A'B=112m. Cual es la longitud del lago?
using the given similar triangles, the length of the lake is approximately 26.05 meters.
We have,
In the given similar triangles, we have the following information:
Length of the longer side of the larger triangle: AC = 215m
Length of the longer side of the smaller triangle: A'C = 50m
Length of the corresponding shorter side of the smaller triangle: A'B = 112m
Let's denote the length of the lake (the longer side of the smaller triangle) as x.
Now, we can set up a proportion between the sides of the two triangles:
AC / A'C = A'B / x
Substitute the given values:
215 / 50 = 112 / x
Now, solve for x:
215x = 50 * 112
Divide both sides by 215:
x = (50 * 112) / 215
x ≈ 26.05
Thus,
The length of the lake is approximately 26.05 meters.
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The complete question:
To measure the length of a lake, the following similar triangles were built, in which it is necessary to: AC = 215m, A'C= 50m, A'B=112m. What is the length of the lake?
The point k lies on the segment JL. Find the coordinates of k so that the ratios of JK to KL is 3 to 4
After considering all the given data we conclude that the coordinates of k so that the ratios of JK to KL is 3 to 4 is (-16x₁x₂-16y₁y₂)
The two values of X and Y are the coordinates of K. Let us assume that the coordinates of points J and L are (x₁, y₁) and (x₂, y₂) respectively.
Then, the coordinates of point K can be placed as (x, y), here x and y are unknowns that we need to find.
Now, we know that the ratio of JK to KL is 3:4. This means that:
JK/KL = 3/4
We can use the distance formula to find the distances JK and KL in terms of their coordinates:
JK = √((x-x₁)²+(y-y₁²) KL = √((x-x₂)²+(y- y₂)²)
Staging these distances into the above equation, we get:
√(x-x₁)²+(y-y₁))/√((x-x₂)²+(y-y₂)²) = 3/4
Squaring both sides and simplifying, we get:
16(x-x1)²+16(y-y₁)²= 9(x-x₂)²+9(y-y₂)²
Expanding and simplifying, we get:
7x²-14xx₁-9x₂²+ 7y2-14yy₁-9y₂²= -16x₁x₂-16y₁y₂
This is a quadratic equation in x and y. We can solve this equation to find the values of x and y that satisfy the given conditions. The solution to this quadratic equation gives two values of x and y, which are the coordinates of point K.
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Let G be the center of the equilateral triangle XYZ. A dilation centered at G with scale factor -3/4 is applied to triangle XYZ, to obtain triangle X'Y'Z'. Let A be the area of the region that is contained in both triangles XYZ and X'Y'Z'. Find A/the area of XYZ.
The calculated value of the expression A/the area of XYZ is [tex]\frac{49\sqrt3}{216}[/tex]
Finding the value of A/the area of XYZFrom the question, we have the following parameters that can be used in our computation:
Center of the equilateral triangle XYZ = GDilation centered at G with scale factor = 3/4By the ratio of corresponding sides (see attachment for figure), we have
(x + 2y)/(2x + y) = 3/4
By comparison, we have
x + 2y = 3
2x + y = 4
This gives
(x, y) = (5/3, 2/3)
The triangles are equilateral triangles
So, we have
Area of XYZ = 1/2 * side length² * sin(60)
This gives
Area of XYZ = 1/2 * (2x + y)² * sin(60)
Substitute the known values in the above equation
Area of XYZ = 1/2 * (4)² * sin(60)
Evaluate
Area of XYZ = 4√3
The region A is a trapezoid
So, the area is
A = 1/2 * Sum of parallel sides * height
So, we have
A = 1/2 * (x + y) * (x² - y²)
Recall that (x, y) = (5/3, 2/3)
So, we have
A = 1/2 * (5/3 + 2/3) * ((5/3)² - (2/3)²)
Evaluate
A = 49/18
Finding A/the area of XYZ, we have
A/the area of XYZ = 49/18 ÷ 4√3
This gives
A/the area of XYZ = 49/72 ÷ √3
Rationalize
A/the area of XYZ = [tex]\frac{49\sqrt3}{216}[/tex]
Hence, the value of the expression is [tex]\frac{49\sqrt3}{216}[/tex]
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Complete question
Let G be the center of the equilateral triangle XYZ. A dilation centered at G with scale factor -3/4 is applied to triangle XYZ, to obtain triangle X'Y'Z'. Let A be the area of the region that is contained in both triangles XYZ and X'Y'Z'. Find A/the area of XYZ.
XY = 2x + y
X'Z' = x + 2y
Region A is a trapezoid with parallel sides y & x and height x² - y²
If a card never cost to ask what the first minimum payment would be for $3000 balance transfer at 4. 99% there is currently no balance on the account and the fee is 4% the minimum payment would be what
The first minimum payment would be $62.40 as it is higher than $25.
To determine the first minimum payment for a $3000 balance transfer at 4.99% with a 4% fee, you need to first calculate the balance transfer fee and add it to the initial balance. Then, you'll need to determine the minimum payment based on the credit card issuer's policy.
1. Calculate the balance transfer fee: $3000 * 4% = $120
2. Add the balance transfer fee to the initial balance: $3000 + $120 = $3120
3. The minimum payment depends on the credit card issuer's policy. Typically, the minimum payment is a percentage of the balance or a fixed amount, whichever is higher. For example, if the issuer requires a minimum payment of 2% of the balance or $25, whichever is higher:
- Calculate 2% of the balance: $3120 * 2% = $62.40
- Since $62.40 is higher than $25, the first minimum payment would be $62.40.
Please note that the actual minimum payment may vary depending on the specific credit card issuer's policy.
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A hexagon has 4 sides of length 3x +5 and the other 2 sides are each 3 units shorter than the other 4 sides. What is the perimeter, P, of the hexagon in terms of x?
The perimeter, P, of the hexagon in terms of x is 18x + 24.
To find the perimeter, P, of the hexagon in terms of x, we'll consider the given side lengths.
The hexagon has 4 sides of length 3x + 5. The other 2 sides are each 3 units shorter than the other 4 sides, so their length is (3x + 5) - 3 = 3x + 2.
Now, we can calculate the perimeter by adding the lengths of all 6 sides:
P = (4 * (3x + 5)) + (2 * (3x + 2))
First, distribute the numbers to the expressions inside the parentheses:
P = (12x + 20) + (6x + 4)
Next, combine like terms:
P = 18x + 24
So, the perimeter, P, of the hexagon in terms of x is 18x + 24.
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A dealer bought some radios for a total of $1,008. she gave away 6 radios as gifts, sold each of the rest for $14 more than she paid for each radio, and broke even. how many radios did she buy?
The dealer bought 42 radios.
How many radios did the dealer buy?Let x be the number of radios the dealer bought.
Let y be the price the dealer paid for each radio.
We know that the dealer bought x radios for a total of $1,008, so:
x * y = 1008
We also know that the dealer gave away 6 radios and sold the rest for $14 more than she paid for each radio, breaking even. This means that the total revenue from selling the remaining radios is equal to the total cost of buying them:
(x - 6) * (y + 14) = x * y
Simplifying this equation, we get:
xy + 14x - 6y - 84 = xy
14x - 6y = 84
7x - 3y = 42 (dividing by 2 on both sides)
Now we have two equations:
x * y = 1008
7x - 3y = 42
We can use substitution or elimination to solve for x and y. Let's use elimination by multiplying the second equation by y/3 and adding it to the first equation:
x * y + (7x - 3y) * (y/3) = 1008 + 42 * (y/3)
xy + 7xy/3 - y²/3 = 1008 + 14y
10xy/3 - y²/3 - 14y - 1008 = 0
Multiplying both sides by 3, we get:
10xy - y² - 42y - 3024 = 0
Now we can use the quadratic formula to solve for y:
y = (-b ± sqrt(b² - 4ac)) / 2a
where a = -1, b = -42, and c = -3024:
y = (-(-42) ± sqrt((-42)² - 4(-1)(-3024))) / 2(-1)
y = (42 ± sqrt(42² - 4*3024)) / 2
y = (42 ± 126) / 2
y = 84 or y = -42
Since the price of a radio cannot be negative, we can discard the second solution and conclude that y = 84.
Now we can solve for x using the first equation:
x * y = 1008
x * 84 = 1008
x = 12
Therefore, the dealer bought 12 radios.
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Do you best to explain how the following diagram demonstrates the Pythagorean theorem
Answer:
Step-by-step explanation:
The theorem states that the square on the hypotenuse (longest side) of a right triangle equal the sum of the squares on the other 2 sides.
Counting the small squares gives us these areas.
We see that
Sum of squares on hypotenuse = 25.
and sum of squares on the other 2 sides = 9 and 16 which equals 25.
Rewrite this equation without absolute value. y=|x-5|+|x+5| if -5
The equation y = |x - 5| + |x + 5| can be rewritten as:
y = { -2x - 10, for x < -5,
{ 10, for -5 ≤ x ≤ 5,
{ 2x + 10, for x > 5.
When -5 < x < 5, both |x - 5| and |x + 5| are non-negative. So we can rewrite y = |x - 5| + |x + 5| as follows:
If x < -5, then x - 5 < -5 and x + 5 < 0, so we have:
y = -(x - 5) - (x + 5) = -2x - 10
If -5 ≤ x ≤ 5, then x - 5 < 0 and x + 5 ≥ 0, so we have:
y = -(x - 5) + (x + 5) = 10
If x > 5, then x - 5 ≥ 0 and x + 5 > 5, so we have:
y = (x - 5) + (x + 5) = 2x + 10
Therefore, the equation y = |x - 5| + |x + 5| can be rewritten as:
y = { -2x - 10, for x < -5,
{ 10, for -5 ≤ x ≤ 5,
{ 2x + 10, for x > 5.
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Given question is incomplete, the complete question is below
Rewrite each equation without absolute value for the given conditions. y = |x-5| + |x+5| if -5 < x < 5
If theta is a first-quadrant angle in standard position with p(u, v) = (3, 4), evaluate tan1/2 theta
o 1/4
o 1/2
o 2/3
We can use the given point P(3, 4) to find the values of sin(theta) and cos(theta) as follows:
[tex]sin(theta) = opposite/hypotenuse = 4/5[/tex]
[tex]cos(theta) = adjacent/hypotenuse = 3/5[/tex]
Since theta is a first-quadrant angle, we know that tan(theta) = sin(theta)/cos(theta).
Using the half-angle formula for tangent, we have:
[tex]tan(1/2 * theta) = ±√((1 - cos(theta))/2) / (1 + √((1 - cos(theta))/2))[/tex]
We can substitute the values of sin(theta) and cos(theta) that we found earlier:
[tex]tan(1/2 * theta) = ±√((1 - 3/5)/2) / (1 + √((1 - 3/5)/2))[/tex]
[tex]tan(1/2 * theta) = ±√(1/5) / (1 + √(1/5))[/tex]
[tex]tan(1/2 * theta) = ±√5 - 1[/tex]
Since theta is in the first quadrant, tan(1/2 * theta) is positive. Therefore:
[tex]tan(1/2 * theta) = √5 - 1[/tex]
We can simplify this expression by rationalizing the denominator:
[tex]tan(1/2 * theta) = (√5 - 1) / (√5 + 1) * (√5 - 1) / (√5 - 1)[/tex]
[tex]tan(1/2 * theta) = (5 - 2√5)[/tex]
So the answer is (5 - 2√5), which is approximately 0.382. Therefore, the answer is not one of the choices given.
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HELP! WILL GIVE BRAINLIEST!
A yard stick is placed on the table during a party game. A marker is placed at 11 inches, and labeled A, one labeled B at 24 inches, another labeled C at 26 and another labeled D at 36. A marble is shot toward the yard stick. What is the probability that the marble that hits the yard stick between A and D hits it between C and D? Write your answer as a percent
The required probability 40%
To find the probability that the marble that hits the yard stick between A and D hits it between C and D, we need to find the length of the interval between C and D, and divide it by the length of the interval between A and D.
The length of the interval between C and D is
36 - 26 = 10
The length of the interval between A and D is
36 - 11 = 25
The probability that a marble will strike a yardstick between A and D and C and D is
10/25 × 100 = 40%
Therefore, the probability that a marble will strike a yardstick between A and D and C and D is 40%
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the diagram shows a polygon composed of rectangles
Answer:
210 feet
Step-by-step explanation:
Refer the attached figure
LK = 22 ft
KH=JI = 18 ft.
HG=14 ft.
CD=FE=16 ft.
AL=15 ft.
GF=CB = 5ft.
KJ=HI=10 ft.
CF=CB+BG+GF=5+15+5=25 ft. =DE
AB= LK+KH+HG=22+18+14= 54 ft.
Perimeter of polygon = Sum of all sides
Perimeter of polygon=AL+LK+KJ+JI+HI+HG+GF+FE+DE+CD+CB+BA
=15+22+10+18+10+14+5+16+25+16+5+54
=210
Hence the perimeter of the polygon is 210 feet.
PLS MARK BRAINLIEST
A company manufactures and sells x microwaves per month. The monthly price-demand equation is: p(x) = 280 – 0.4z (a) Assuming that the manufacture would like to charge between $100 and $500 for microwaves, find the price that maximizes the revenue. (b) What is the maximum revenue from selling microwaves?
The price that maximizes revenue for the given monthly price-demand equation with price range between $100 and $500 is $220.
(b) The maximum revenue from selling microwaves can be found by multiplying the price that maximizes revenue by the corresponding quantity of microwaves sold. Using the price-demand equation p(x) = 280 - 0.4x, we can find the quantity that corresponds to the price that maximizes revenue as follows:p(x) = 280 - 0.4x220 = 280 - 0.4x0.4x = 60x = 150Therefore, the quantity that corresponds to the price that maximizes revenue is x = 150. The maximum revenue can be found by multiplying the price and quantity:Revenue = Price * QuantityRevenue = $220 * 150Revenue = $33,000Therefore, the maximum revenue from selling microwaves is $33,000.
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Last month, lucy and lara sold candy to raise money for their debate team. lara sold 1/5 as much candy as lucy did. if lucy sold 3/5 of a box of candy, how many boxes of candy did lara sell?
Lara sold 3/5 of a box of candy, which is the same as 0.6 boxes of candy.
How many boxes of candy did Lara sell last month to raise money?If Lucy sold 3/5 of a box of candy, then Lara sold 1/5 of 3/5, which is:
(1/5) * (3/5) = 3/25
Therefore, Lara sold 3/25 of a box of candy.
To find the number of boxes Lara sold, we can divide 3/25 by 1/5:
(3/25) ÷ (1/5) = (3/25) * (5/1) = 15/25 = 3/5
So Lara sold 3/5 of a box of candy, which is the same as 0.6 boxes of candy.
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A plane leaves Singapore airport at 07:45 to fly to Sydney. The plane flies at an average speed of 757.2 km/h. The distance from Singapore to Sydney is 6310 km. The time in Sydney is 2 hours ahead of Singapore time. Calculate the local time when the plane arrives in Sydney. Give your answer in the form hours:minutes using the 24-hour clock.
Answer:
18:19
Step-by-step explanion:
To solve this problem, we need to first calculate the time it takes for the plane to fly from Singapore to Sydney:
Time = Distance ÷ Speed
Time = 6310 km ÷ 757.2 km/h
Time ≈ 8.34 hours
This is the time it takes to fly from Singapore to Sydney in Singapore time. However, we need to convert this time to Sydney time, which is 2 hours ahead of Singapore time. Therefore, the local time when the plane arrives in Sydney is:
Time in Sydney = Singapore time + 2 hours + Flight time
Time in Sydney = 07:45 + 2 hours + 8.34 hours
Time in Sydney = 18:19
Therefore, the local time when the plane arrives in Sydney is 18:19 using the 24-hour clock.