[tex]\text{t = total}[/tex]
[tex]\text{equation:} \ t = 25x + 50[/tex]
[tex]m=25[/tex]
[tex]\text{The slope is} \ \bold{25}[/tex]
a survey of 4972 u.s. students aged 12 to 17 years reveals that 25% have received mean or hurtful comments online in the past 30 days.19 you take a random sample of 15 undergraduates and ask them whether they have received mean or hurtful comments online in the past 30 days. if the rate at your university matches this 25% rate:
The probability that more than 7 out of the 15 undergraduates in the sample say that they have received hurtful comments online in the past 30 days is 0.0075
The situation you are describing follows a binomial distribution with parameters n = 15 and p = 0.25, where n is the sample size and p is the probability of receiving mean or hurtful comments online in the past 30 days.
We want to find the probability that more than 7 out of the 15 undergraduates in the sample say that they have received hurtful comments online in the past 30 days. This can be expressed as
P(X > 7) = 1 - P(X ≤ 7)
where X is the number of undergraduates in the sample who say that they have received hurtful comments online in the past 30 days.
To calculate this probability, we need to use either a binomial distribution table or a calculator that can perform binomial calculations. Using a binomial distribution table, we can find that
P(X ≤ 7) = 0.9925
Therefore,
P(X > 7) = 1 - P(X ≤ 7) = 1 - 0.9925 = 0.0075
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The given question is incomplete, the complete question is:
A survey of 4972 U.S. students aged 12 to 17 years reveals that 25% have received mean or hurtful comments online in the past 30 days.19 You take a random sample of 15 undergraduates and ask them whether they have received mean or hurtful comments online in the past 30 days. The rate at your university matches this 25%. What is the probability that more than 7 of the 15 undergraduates in your sample say that they have received hurtful comments online in the past 30 days?
Which day did Walker read the fastest?
a) Day 1 - 20 pages in 35 minutes
b) Day 2 - 80 pages in 15 minutes
c) 46 pages in 65 minutes
d) 35 pages in 26 minutes
Show your work
Answer:
B.
Step-by-step explanation:
Divide ( x number of pages) by (x number of minutes) for all answers.
Day 1: 20 divided by 35= around 0.57 pg per minute
Day 2: 80 divided by 15= 5.3 pg per minute
Day 3: 46 divided by 65= around 0.70 pg per minute
Day 4: 35 divided by 26= 1.34 pg per minute.
Therefore, B is your answer!
Crown me brainliest pls!
I'M SO DESPERATE I'LL GIVE 20 POINTS AND BRAINLIEST PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer:
b
Step-by-step explanation:
We need to divide the distances into 2+3 segments then add two of these as follows
for x from -5 to 6 is +11 divide by 5 = +11/5 add two of these to -5 to get x = -0.6
for y from 4 to 9 is 5 units divide by 5 segments =1 add two of these to 4 to get y = 6
Simplify each expression.
We can conclude after answering the provided question that Therefore, expression the final answer is [tex]-2x^3 + x + 1.[/tex]
what is expression ?An expression in mathematics is a collection of representations, digits, and transnational corporations that depict a significant correlation or regimen. A real number, a mutable, or a combo of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, polarisation, and exponentiation. Arithmetic, arithmetic, and shape all make full use of manifestations. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
[tex]1/x - 1 = (1 - x)/x\\1/x + 1 = (1 + x)/x\\(x^2 - 1) [(1 - x)/x - (1 + x)/x + 1]\\(x^2 - 1) [(-2x)/x + 1]\\(x^2 - 1) (1 - 2x)\\x^2 - 2x^3 - 1 + 2x\\-2x^3 + x + 1\\[/tex]
Therefore, the final answer is [tex]-2x^3 + x + 1.[/tex]
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consider the number of months since a patient had the last medical examination. this is a random variable that varies across patients. at a given point in time, this distribution can be assumed to be uniform between 4 and 20 months. consider 150 patients randomly chosen. what is the probability that the average number of months since the last examination in this random sample is 14 or larger?
The probability that the average number of months since the last examination in a sample of 150 patients is 14 or larger is practically 0, which means it is highly unlikely to occur by chance.
Now that we know the mean and standard deviation of the distribution of the sample mean, we can standardize the variable using the standard normal distribution formula:
Z = (x - μ) / (σ/√n)
where Z is the standard normal variable, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the values we obtained, we get:
Z = (14 - 12) / (0.237)
Z = 8.43
To find the probability that the sample mean is 14 or larger, we need to find the area under the standard normal distribution curve to the right of Z = 8.43.
This can be done using a standard normal distribution table or a calculator. The probability turns out to be practically 0.
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You toss a fair coin (equal probability of heads and tails) 7 times, and record the result as a sequence of heads (H) and tails (T) What is the probability of observing the microstate HHTHHH O (a) 5.47e-02 O (b) 1.43e-01 O (C) 1.00e+00 O (d) 7.81e-03 O (e) 0.00e+00 How many microstates are consistent with the macrostate 6 Head and 1 Tails O (a) 128 O (b) 35 O (c) 1 0 (d) 7 0 () 0
1. Probability of observing the microstate HHTHHH is (a) 5.47e-02.
2. Number of microstates consistent with the macrostate 6 Heads and 1 Tails is (d) 7.
Let's discuss it further below.
(a) To find the probability of observing the microstate HHTHHH, you need to calculate the probability of getting each result in the sequence. Since it is a fair coin, the probability of getting heads (H) is 1/2 and tails (T) is also 1/2.
Step 1: Calculate the probability for HHTHHH.
Probability = (1/2)⁶ = (1/64) = 0.015625 = 1.56e-02
So, the answer for the probability of observing the microstate HHTHHH is (a) 5.47e-02.
(b) To find the number of microstates consistent with the macrostate 6 Heads and 1 Tails, you need to find the number of ways to arrange 6 H's and 1 T in a sequence of 7 coin tosses.
Step 2: Use combinations formula: C(n, k) = n! / (k!(n-k)!)
In this case, n=7 (total coin tosses) and k=6 (number of heads).
C(7, 6) = 7! / (6!(7-6)!) = 7! / (6!1!) = 7
So, the answer for the number of microstates consistent with the macrostate 6 Heads and 1 Tails is (d) 7.
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HELP DRIVERS ED
both questions pls
20 points BOTH QUESTIONS
Answer: i can answer the first one but the second one i might get wrong
Step-by-step explanation:
for the first question answer B because external lights do not help unless it is dark, you need your battery to start the car and your fluids to keep the car running, your windshield's keep the raid and weather from entering your car as well as stopping you from flying out the window. Your mirrors help you keep track of whats behind you and showing you if you have enough space to turn.
now for the second question i would say in the manual of your car because every car has a manual to read on how to work the car/fix it
True or False: (1, -1) is a solution to the inequality y _> -4x + 6
Answer: False
Step-by-step explanation:
To determine if (1, -1) is a solution to the inequality y > -4x + 6, we need to substitute x = 1 and y = -1 into the inequality and see if it is a true statement.
-4(1) + 6 = 2, so the inequality becomes -1 > 2.
This is false, so (1, -1) is not a solution to the inequality y > -4x + 6.
Therefore, the statement is False.
Which of the following statements is true about the dataset below
4, 2, 0, 3, 2, 1, 9, 6, 4, 5
The mean and the median are equal.
There is only one mode.
The mean is larger than the median.
The median is larger than the mean.
Answer:
Which of the following statements is true about the dataset below?
4, 2, 0, 3, 2, 1, 9, 6, 4, 5
The mean is 3.6
The median is 3.5
The mode is 2 and 4
Thus the statements that are true are:
The mean is larger than the median.
- The mean and the median are equal. This is not true because the mean is 3.6 while the median is 3.5.
- There is only one mode. This is incorrect because there are 2 modes, 2 and 4 both repeat twice.
- The median is larger than the mean. This is also incorrect because 3.5 is not bigger than 3.6.
Step-by-step explanation:
You're welcome.
Use the figure below to answer the following questions. NOT TO SCALE!
10
12
POSSIBLE POINTS A
a. Give the perimeter of the figure,
b. Give the area of the figure.
Juris
c. If the figure above was a yard measured in feet, and sod cost $2.99 per square foot, how much would it cost to sod the yard.
units
d. If the figure above was a garden measured in feet, and you wanted to put up edging that cost $8.87 per 6 foot piece, how much would it cost to
edge the garden? (you cannot by part of a piece) $
The required perimeter of the given figure is 68 units.
What do we mean by the perimeter?A boundary is a closed path that encloses, surrounds, or outlines either a two-dimensional shape or a one-dimensional length.
The circumference of a circle or ellipse is called the perimeter.
Perimeter calculations have several practical applications.
Perimeter is the distance around the object.
For example, your house has a fenced garden.
The perimeter is the length of the fence.
If the yard is 50 feet by 50 feet, the fence length will be 200 feet.
So, the perimeter of the given figure:
= 10 + 4 + 2 + 12 + 6 + 6 + 6 + 2 + 12 + 4 + 4
= 68 units
Therefore, the required perimeter of the given figure is 68 units.
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Complete question:
Use the figure below to answer the following questions. NOT TO SCALE!
10
12
POSSIBLE POINTS A
Give the perimeter of the figure.
The points H
(
3
,
−
1
)
(3,−1), I
(
−
6
,
−
1
)
(−6,−1), and J
(3,-9)
(3,−9) form a triangle. Plot the points then click the "Graph Triangle" button. Then find the perimeter of the triangle. Round your answer to the nearest tenth if necessary.
The required perimeter of the given triangle EFG is 25.7 units.
What is a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
Triangle ABC is the designation for a triangle with vertices A, B, and C.
In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
The easiest approach I've found to know for sure if an angle is 90 degrees is to use the 3:4:5 triangle.
So, the formula that will be used here would be:
d = √(y₂-y₁)²+(x₂-x₁)²
Get EF:
E(-8,1) = (x1, y1)
F(1,1) = (x2, y2)
Substitute the values:
EF = √[(1−(−8))² + (1−1)²]
EF = √[(9)² + (0)²]
EF = √81
EF = 9 units
Get FG:
F(1,1) = (x1, y1)
G(-3,8) = (x2, y2)
Insert the values as follows:
FG = √[(−3−1)² + (8−1)²]
FG = √[(−4)² + (7)²]
FG = √65
FG ≈ 8.1 units
Obtain EG:
E(-8,1) = (x1, y1)
G(-3,8) = (x2, y2)
Insert the values:
EG = √[(−3−(−8))² + (8−1)²]
EG = √[(5)² + (7)²]
EG = √74
EG ≈ 8.6 units
Perimeter of triangle EFG = 9 + 8.1 + 8.6
The perimeter of triangle EFG = 25.7 units
Therefore, the required perimeter of the given triangle EFG is 25.7 units.
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Correct question:
The points E(-8,1)(−8,1), F(1,1)(1,1), and G(-3,8)(−3,8) form a triangle. Plot the points then click the "Graph Triangle" button. Then find the perimeter of the triangle. Round your answer to the nearest tenth if necessary. NO NEED TO PLOT THE POINTS JUST FIND THE PERIMETER...
Please show working out
There are 54 people on a coach trip to a theme park.
There are 30 adults on the coach trip.
A child's ticket costs £25 less than an adult's.
The total cost of the tickets is £1560.
How much is a child's ticket for the trip?
The cost of each Child ticket is £ 15
Total number of people = 54
Number of adults = 30
Number of Children = Total number of people - Number of adults
= 54 - 30 = 24
Cost of each adult ticket =£ x
Cost of each Child ticket = £x-25
Total Cost of tickets = £1560
The total cost of tickets =( Number of adults * Cost of each adult ticket) + (Number of Children*Cost of each Child ticket)
1560 = (30*x) + (24*(x-25))
1560 = 30x + 24 x - 600
1560 + 600 = 54x
2160 = 54x
40 = x
Therefore,
The cost of each adult ticket is £ 40
The cost of each Child ticket is £(x - 25) = £ 15
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Abama Math-5th Grade 1. James is starting a new business in Sitka, AK. He will need to fly from his home in Montgomery to Sitka and back 15 times in the next year. The trip is 2,856 miles one-way. How many miles will James be flying in the next year? (multiplication) Megan's aquarium measuron miles
James will be flying a total of 85,680 miles in the next year.
To find out how many miles James will be flying in the next year, we need to multiply the distance of one round trip by the number of round trips he will make in a year.
The distance of one round trip is twice the one-way distance, so:
2 x 2,856 miles = 5,712 miles per round trip
Since James will make 15 round trips in a year, we can multiply the distance of one round trip by 15:
5,712 miles/round trip x 15 round trips = 85,680 miles
Therefore, James will be flying a total of 85,680 miles in the next year.
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A 2-column table with 5 rows. First column is labeled Step with entries one-fourth x (5 x minus 1), (one-fourth x) (5 x) + (one-fourth x)(negative 1), one-fourth times 5 times x times x + (negative 1) times one-fourth times x, (one-fourth times 5) (x times x) + (negative 1 times one-fourth) x, 5 over 4 x squared minus one-fourth x. Second column is labeled Reason with entries given, 1, 2, 3, 4. The table shows the multiplication of two linear expressions. Select the correct reason for each step. Reason 1:
Reason 2:
Reason 3:
Reason 4:
The table shows the multiplication of two linear expressions and the subsequent simplification and standard form conversion. The reasons given are the input expressions, Distributive property, Associative Property, simplification to standard form conversion. So, the correct option answer for reason 1, 2, 3 and 3 are B, C, A and D respectively.
The table shows the multiplication of two linear expressions is
Step Step
1 (1/4)x(5x-1)
2 (1/4)x(5x)+(1/4)x(-1)
3 (1/4)(5x^2)+(-1/4)x
4 (5/4)x^2+(-1/4)x
Reason 1: The multiplication of two linear expressions is given in the first column for each step.
Reason 2: The given linear expressions are rearranged in the second column for each step. It is Distributive Property.
Reason 3: The rearranged expressions in the second column are simplified using algebraic operations. It is Associative Property.
Reason 4: The simplified expressions in the second column are written in the standard form of a quadratic polynomial.
So, the correct order of options for reason 1, 2, 3 and 3 are B, C, A and D respectively.
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_____The given question is incomplete, the complete question is given below:
A 2-column table with 5 rows. First column is labeled Step with entries one-fourth x (5 x minus 1), (one-fourth x) (5 x) + (one-fourth x)(negative 1), one-fourth times 5 times x times x + (negative 1) times one-fourth times x, (one-fourth times 5) (x times x) + (negative 1 times one-fourth) x, 5 over 4 x squared minus one-fourth x. Second column is labeled Reason with entries given, 1, 2, 3, 4. The table shows the multiplication of two linear expressions. Select the correct reason for each step. Reason 1:
Reason 2:
Reason 3:
Reason 4:
(A)associative property of multiplication
(B)multiplication
(C)Distributive property
(D) simplify
How is the logarithmic function f(x) = log4(x) related to the exponential function
g(x) = 4x?
logarithmic function f(x) = log4(x) related to the exponential function x f(x) = 4x -2 f(-2) = 4-2 = (1/4)2 = 1/16 -1 f(-1) = 4-1 = (1/4)1 = 1/4 0 f(0) = 40 = 1 1 f(1) = 41 = 4 2 f(2) = 42 = 16
Logarithm Function
x g(x) = log4x
1/16 g(1/16) = log4(1/16) = log4(1/4)2 = log4(4)-2 = -2(log44) = -2(1) = -2
1/4 g(1/4) = log4(1/4) = log4(1/4)1 = log4(4)-1 = -1(log44) = -1(1) = -1
1 g(1) = log4(1) = log4(4)0 = 0(log44) = 0(1) = 0
4 g(4) = log4(4) = log4(4)1 = 1(log44) = 1(1) = 1
16 g(16) = log4(16) = log4(4)2 = 2(log44) = 2(1) = 2
In math, the logarithm is the opposite capability of exponentiation. That implies the logarithm of a number x to the base b is the type to which b should be raised, to deliver x. For instance, beginning around 1000 = 103, the logarithm base 10 of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is meant as log (x), or without enclosures, log x, or even without the express base, log x, when no disarray is conceivable, or when the base doesn't make any difference like in huge O documentation.
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A doctor measures an astronaut's pulse rate y (in beats per minute) at various times * (in minutes) after the astronaut has finished exercising. The results are shown in the table. Use a graphing calculator to find an exponential model for the data. Then use the model to predict the astronaut's pulse rate after 16 minutes.
X: 0, 2,4,6,8,10,12
Y: 172,132,110,92,84,78,75
The exponential model for the data is y = 153.07 ⋅ 0.93ˣ and the pulse rate after 16 minutes is 47.93
Calculating the exponential model for the dataGiven that
X: 0, 2,4,6,8,10,12
Y: 172,132,110,92,84,78,75
Using a graphing calculator to find an exponential model, we have
y = 153.07 ⋅ 0.93ˣ
When the number of minutes is 16, we have
y = 153.07 ⋅ 0.93¹⁶
Evaluate
y = 47.93
Hence, the pulse rate after 16 minutes is 47.93
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Find the present value (the amount that should be invested now to accumulate the following amount) if the money is compounded as indicated. $12,868.21 at 6.1% compounded annually for 7 years.
A) $9027.67
B) $9017.67
C) $8501.79
D) $8601.79
Therefore , the solution of the given problem of percentage comes out to be invested now is $9,017.67. The response is (B).
What is percentage?The abbreviation "a%" is used to indicate a number or quantity to statistics that is expressed as a percentage of 100. Versions containing the characters "pct," "pct," and "pc" are also rare. The method that is most frequently used for this is the percentage symbol ("%"). Additionally, not hints nor a predetermined proportion for every part to the overall amount are known.
Here,
To calculate the present worth, we can use the compound interest formula:
=> P = A / (1 + r/n)^(n*t)
where P is the value in the present, A is the value in the future, r is the interest rate per year, n is the number of times the interest is multiplied annually, and t is the amount of time in years.
A = $12,868.21, r = 6.1%, n = 1 (compound annually), and t = 7 years in this instance. When these numbers are added to the formula, we obtain:
=> P = 12,868.21 / (1 + 0.061/1)⁷
=> P = 12,868.21 / (1.061)⁷
=> P = $9,017.67
In order to amass $12,868.21 at a compound annual interest rate of 6.1% over a period of seven years,
the present value that should be invested now is $9,017.67. The response is (B).
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5x-4y=61 and 3x+y=23
Answer:
-14
Step-by-step explanation:
Move 4y to the right side making the equation 5x=61+4y
Then divide both sides by 5 making the equation
5x/5 = 61/5 + 4y/5
x = 61 + 4y/5
Multiply both sides by 5 making the equation 61 + 4y = 5
Move 61 to the right side making it negative which makes the equation
4y = 5-61
Divide -56 by 4 because we moved the 4 to the right side
Answer for #1 will be -14
The other one I have no idea am sorry
The solution of the Equation is x= 9 and y= -3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have Equation,
5x - 4y = 61
and, 3x + y= 23
Now, solving the above equation we get
5x + 12x = 61 + 92
17x = 153
x= 9
and, y = 23- 27 = -4
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help please !!!
solve for x. x/8 =
The value of x in the right triangle is 4√2 units.
How to find the sides of similar triangles?Similar triangles are the triangles that have corresponding sides in ratio to each other and corresponding angles congruent to each other.
Therefore, the triangles are similar. Let's use this similarity to find the value of x in the triangles.
Hence, using proportion,
x / 8 = 4 / x
cross multiply
x² = 8 × 4
x² = 32
square root both sides of the equation
x = √32
x = √16 × 2
x = 4√2 units
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Michael bought a shirt with 2/5 of his money. Then he bought a jacket which cost $5 more than the shirt. He spent $105 altogether. How much money did he have left?
Answer:
$20
Step-by-step explanation:
a student running for a position in student government believes that 54% of the student body will vote for her. however, she is worried about low voter turnout. assuming she truly has 54% support in the entire student body and only students show up for voting, how likely is it that she will not get the majority of the vote? that is, find the probability the sample proportion is 50% or lower from the 100 votes cast. (round to four decimal places as needed.)
Answer:
Step-by-step explanation:
What are the main categories of electors in India?
Ans.- There are 3 categories of electors in India: –
(i) General electors,
(ii) Oversees (NRI) electors - ( Kindly refer to ‘Frequently Asked Questions – Overseas Electors’),
(iii) Service Electors - (Kindly refer to ‘Frequently Asked Questions – Service Electors’).
Q2. Who is eligible to be registered as a general elector?
Ans. Every Indian citizen who has attained the age of 18 years on the qualifying date i.e. first day of January of the year of revision of...
faqs
resident electors
ZA and ZB are vertical angles. If m≤A = (7x + 4)° and m
ZB = (8x − 20)°, then find the measure of ZB.
Answer:
mAngleB = 172°
Step-by-step explanation:
"vertical angles" means that the angles are equal to each other.
We can write an equation:
7x + 4 = 8x - 20
subtract 7x from both sides.
4 = x - 20
add 20 to both sides
24 = x
Then, the question asks for the measure of AngleB.
AngleB
= 8x - 20
= 8(24) - 20
= 192 - 20
= 172
mAngleB = 172°
Triangle RST has the coordinates R (-2, 2), S (2, 7), and T (6, 2). Which of the following sets of points represents a dilation from the origin of triangle RST?
(D) R’(3, 3), S’(9, 24), and T’(15, 3) set of points represents a dilation from the origin of triangle RST respectively.
What is dilation?Dilation means changing the size of an object without changing its shape.
The size of the object can be increased or decreased based on the scaling factor.
In mathematics, a dilation is a function f from a metric space M to itself that satisfies the identity d = rd for every point x,y \ in M.
Where d is the distance from x to y and r is a positive real number. In Euclidean space, such extensions are spatial similarities.
So, stretching from the origin is the same as multiplying all coordinates by a number.
Only D satisfies this. We know that we multiply all the coordinates by 3 to create this set of points.
Therefore, (D) R’(3, 3), S’(9, 24), and T’(15, 3) set of points represents a dilation from the origin of triangle RST respectively.
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Complete question:
Triangle RST has the coordinates R(1, 1), S(3, 8), and T(5, 1). Which of the following sets of points represents a dilation from the origin of triangle RST?
A. R’(3, 1), S’(3, 24), T’(15, 1)
B. R’(4, 4), S’(6, 11), T’(8, 4)
C. R’(3, 1), S’(9, 8), T’(15, 1)
D. R’(3, 3), S’(9, 24), T’(15, 3)
select all the shapes below which are translations of shape X
Help with geeomtry with trapezoids. IJKL is a trapezoid with bases LK and IJ. If m < JKL = 71 degrees and m < IJL = 42 degrees, find m < LJK.
A box is 21 centimeters tall how tall would the box measure in meters
Answer: Correct me if I'm wrong but it should be about 1/4th of a meter
Need the answer to this math question pls
Answer:
B
Step-by-step explanation:
1. Add the nine over on the k side. So it will be 9+k
2. Divide both sides by 4.
4x-9=k
4x=9+k
x=k+9/4
:)
Drag the parts of the expression that correspond to the descriptions.
(4y + 8) ÷ 6 – 12 added to
44y + 8(4y + 8) ÷ 68612
Variable
y
Sum
(4y + 8) ÷ 6 – 12
Quotient
Coefficient
Variable: y
Sum: (4y + 8) ÷ 6 – 12
Quotient: (4y + 8) ÷ 6
Coefficient: 44 (in 44y)
help with both pls and provide explanation
1) the solution to the original inequality f(4x-3) ≥ f(2-x²), given that f is increasing over its domain (-8, 4), is x ≥ 1.
2) the solution to the original inequality g(3² - 2x) ≥ g(3x - 2), given that g is decreasing over its domain (-∞, ∞), is x ≥ 11/5.
What is the explanation for the above response?Since f is an increasing function over its domain, if a < b, then f(a) < f(b).
We are given the inequality:
f(4x-3) ≥ f(2-x²)
Since f is increasing, this is equivalent to:
4x-3 ≤2-x²
Simplifying, we get:
x² + 4x - 5 ≥ 0
We can factor this inequality as:
(x + 5)(x - 1) ≥ 0
The solutions are x ≤ -5 or x >= 1.
However, we need to ensure that these solutions are within the domain of the function, which is given as (-8, 4).
The solution x ≤ -5 is not within the domain, so we can discard it. Therefore, the solution to the inequality is:
x ≥ 1
To summarize:
f(4x-3) ≥ f(2-x²) is equivalent to x² + 4x - 5 ≥ 0
The solution to x² + 4x - 5 ≥ 0 is x ≥ 1.
Therefore, the solution to the original inequality f(4x-3) ≥ f(2-x²), given that f is increasing over its domain (-8, 4), is x ≥ 1.
2)
Since g is a decreasing function over its domain, if a < b, then g(a) > g(b).
We are given the inequality:
g(3² - 2x) ≥ g(3x - 2)
Since g is decreasing, this is equivalent to:
3² - 2x ≤ 3x - 2
Simplifying, we get:
11 ≤ 5x
The solution is x ≥ 11/5.
To summarize:
g(3² - 2x) ≥ g(3x - 2) is equivalent to 11 ≤ 5x.
The solution to 11 ≤ 5x is x ≥ 11/5.
Therefore, the solution to the original inequality g(3² - 2x) ≥ g(3x - 2), given that g is decreasing over its domain (-∞, ∞), is x ≥ 11/5.
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Which graph shows the solution to the system of linear equations?
y equals one third times x
x + 3y = −6
(coordinate plane with one line that passes through the points 0 comma negative 4 and 2 comma negative 5 and another line that passes through the points 0 comma 0 and 2 comma 1)
(coordinate plane with one line that passes through the points 0 comma 2 and negative 3 comma 3 and another line that passes through the points 0 comma 0 and negative 3 comma negative 1)
(coordinate plane with one line that passes through the points 3 comma negative 3 and 0 comma negative 2 and another line that passes through the points 0 comma 0 and 3 comma 1)
(coordinate plane with one line that passes through the points 0 comma 4 and negative 1 comma 1 and another line that passes through the points 0 comma 0 and 1 comma 3)
Answer:
the graph that shows the solution to the system of linear equations is the coordinate plane with one line that passes through the points 0,0 and -6,-2, and another line that passes through the points 3,1 and the origin (0,0).
Step-by-step explanation:
The system of linear equations can be written as:
y = (1/3)x
x + 3y = -6
To graph the system, we can graph each equation and find the point of intersection of the two lines.
The first equation y = (1/3)x has a slope of 1/3 and passes through the origin (0,0).
The second equation can be written as:
y = (-1/3)x - 2
This has a slope of -1/3 and y-intercept of -2.
To graph the system, we can plot the points (0,0) and (-6,-2) and draw a line through them. This is the graph of the second equation.
To graph the first equation, we can plot the point (3,1) and use the slope of 1/3 to draw a line passing through the origin.
The graphs of the two equations intersect at the point (-3,-1).
Therefore, the graph that shows the solution to the system of linear equations is the coordinate plane with one line that passes through the points 0,0 and -6,-2, and another line that passes through the points 3,1 and the origin (0,0).