The volume of the cone is approximately 2941.6 cubic inches.
To begin with, let's recall the formula for the volume of a cone. The volume of a cone is given by the formula V = (1/3)πr²h, where V is the volume, r is the radius of the base, and h is the height of the cone.
We can see that the radius of the base of the cone is 15 inches. However, we do not know the height of the cone yet. To find the height, we can use the fact that the sphere is inscribed in the cone.
We have a right triangle with the height of the cone, the radius of the base of the cone (which is one leg of the triangle), and the diameter of the sphere (which is the hypotenuse of the triangle). Using the Pythagorean theorem, we get:
h² + 15² = 20²
Simplifying this equation, we get:
h² + 225 = 400
h² = 175
h ≈ 13.23
Now that we know the height of the cone, we can plug in the values of the radius and the height in the formula for the volume of the cone. We get:
V = (1/3)π(15²)(13.23) ≈ 2941.6 cubic inches
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Explain why all of these statements are false: (a) The complete solution to Ax = b is any linear combination of Xp and Xn. (b) The system Ax- b has at most one particular solution. (c) If A is invertible, there is no solution Xn in the nullspace.
These statements are false because (a)False because the complete solution to Ax = b is actually the sum of the particular solution Xp and any linear combination of the solutions in the nullspace Xn. (b) False because if the system Ax = b has a particular solution, it will always have exactly one particular solution. (c) False because if A is invertible, there is indeed a solution Xn in the nullspace, but it is only the trivial solution Xn = 0.
(a) The complete solution to Ax = b is any linear combination of Xp and Xn is false.
Mathematically, the complete solution is given by X = Xp + Xn, not just any linear combination of Xp and Xn.
(b) The system Ax = b has at most one particular solution.
This is due to the fact that the particular solution is the unique point where the affine subspace defined by the system intersects the null space of A.
(c) If A is invertible, there is no solution Xn in the null space.
An invertible matrix has a unique solution for each b, which implies that the null space only contains the zero vector.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answer:
Step-by-step explanation:
quit
PLEASE ANSWER!
What is the length of the line that has the coordinate pairs of (-4 1/2,5) and (8 2/3, 5) ?
The length of the line that has the coordinate pairs of (-4 1/2,5) and (8 2/3, 5) is 12.16 units.
What are distance formulae?If two points of coordinates are given then we calculate the distance between them by using the following formulae
To find the length of the line is nothing but the calculation of the distance between two points that are given in the question.
[tex]d = \sqrt{(x_{2} - x_{2} )^{2} +(y_{2} - y_{1} )^{2} }[/tex]
d is the distance between two points.
(x1, x2) and (y2, y1) are the two endpoints of the line.
We can put all the values into the distance formulae and find the length of the line segment.
x1 = -4 1/2 = -3.5, y1 = 5
x2 = 26/3 = 8.6667, y2 = 5
[tex]d = \sqrt{(8.6667-(-3.5))^{2} +(5 - 5)^{2}\\[/tex]
= 12.16
Therefore, the length of the line segment is approximately 12.16 units.
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PLEASE HELP!!
- A fisherman is measuring the amount of bait he has remaining, y, in his bucket. He puts 20 pieces of bait in his bucket at the beginning of his fishing trip and uses 2 pieces every hour, x.
What is the slope for this linear relationship, and what does it mean in this situation?
A) −2; the amount of bait decreases by 2 pieces each hour
B) 2; the amount of bait increases by 2 pieces each hour
C) −20; the amount of bait in the bucket when the fishing trip began
D) 20; the amount of bait in the bucket when the fishing trip began
From the given situation of fisherman , linear relationship is given by y= 2x + 20 the slope for the linear relationship is defined by 2 as amount of bait increases by each hour by 2 pieces.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
From the given situation of fisherman , linear relationship is given by
y= 2x +20 the slope for the linear relationship is defined by 2 as amount of bait increases by each hour by 2 pieces.
As given in the question,
Number of baits in the bucket of fisherman at the beginning of trip = 20
Amount of bait increases by 2 pieces every hour
Linear relationship is defined as :
'y' represent the total number of bait in the bucket after x hours.
y = 20 + 2x
Compare it with the general equation y =mx + c
Where 'm' is the slope.
Here slope is equal to 2.
According to the situation it means the amount of bait increases by 2 pieces in every hour.
Therefore, From the given situation of fisherman , linear relationship is given by y= 2x + 20 the slope for the linear relationship is defined by 2 as amount of bait increases by each hour by 2 pieces.
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Astronomers estimate that the diameter of the Andromeda galaxy is approximately 2.2 X 10^5 light-year. A light-year is the distance light travels in a vacuum in 1 year. One light-year is approximately 5.9 X 10^12 miles. What is the diameter of the Andromeda galaxy in miles? Write your answer in scientific notation.
Answer:
Step-by-step explanation:
To find the diameter of the Andromeda galaxy in miles, we can use the given information:
Diameter of Andromeda galaxy = 2.2 X 10^5 light-years
1 light-year = 5.9 X 10^12 miles
So, we can use dimensional analysis to convert light-years to miles:
2.2 X 10^5 light-years * 5.9 X 10^12 miles/light-year = 1.298 X 10^18 miles
Therefore, the diameter of the Andromeda galaxy in miles is approximately 1.298 X 10^18 miles.
You and your friends go to Dewar's after the movies. You can order either water or a soda to drir and either a Black & White Sundae, a milkshake, or a banana split.
a. Draw a Tree Diagram to represent the given information
b. What is the probability you choose a water and Black & White Sundae?
c. How many total different combinations could be made with these choice: them?
The probability of choosing water and Black & White Sundae is 1/6.
Define probabilityProbability is a measure of the likelihood or chance of an event occurring. It is represented as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.
a. Image is attached below.
b. The probability of choosing water and Black & White Sundae is the product of the probabilities of choosing water and Black & White Sundae given that water was chosen. This can be calculated as:
P(Water and B&W Sundae) = P(Water) * P(B&W Sundae | Water)
= 1/2× 1/3
= 1/6
Therefore, the probability of choosing water and Black & White Sundae is 1/6.
c. To calculate the total number of different combinations, we need to multiply the number of drink options by the number of dessert options. Since there are 2 drink options (water and soda) and 3 dessert options (Black & White Sundae, milkshake, and banana split) with 3 different sizes for the milkshake and banana split, we can calculate the total number of different combinations as:
Total combinations = 2×(1 + 3 + 3×3)
= 2 × 13
= 26
Therefore, there are 26 total different combinations.
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Find the value of x. *
43⁰
99°
2x°
A.28
B22.5
C.19
D.71
8. True or False: A person only pays interest on the balance remaining at the end of the
billing cycle.
لامت 2 (
Answer: True.
Step-by-step explanation: A person only pays interest on the balance remaining at the end of the billing cycle. If you carry a balance beyond the grace period, your credit card issuer will charge interest. Each month you carry a balance over from the previous month, you’ll have a finance charge added to your balance.
An Oblique prism has a square base and height of 3 centimeters (5, 5, 3)
A. 30 cm^3
B. 45 cm^3
C. 60 cm^3
D. 75 cm^3
the answer is 75 cm^3
The volume of the oblique prism is 75 cm³, which is option D.
Define Oblique prismAn oblique prism is a three-dimensional geometric shape that has two parallel and congruent bases that are connected by parallelogram-shaped lateral faces. Unlike a right prism, the lateral faces of an oblique prism are not perpendicular to the base faces.
The formula for the volume of an oblique prism is given by:
Volume = Base Area × Height
Since the base of the prism is a square, its area is given by:
Base Area = Side × Side = 5 × 5 = 25 square centimeters
Substituting this and the height given as 3 cm in the formula for the volume, we get:
Volume = Base Area × Height
= 25 × 3
= 75 cubic centimeters
Therefore, the volume of the oblique prism is 75 cm³, which is option D.
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A triangle has sides with lengths 8, 15, and 17.
Is this a Pythagorean Triple? (yes/no)
With a ratio comparing 8/15, that acute angle should measure between and degrees but closer to degrees.
Answer:
Yes, the triangle with sides 8, 15, and 17 is a Pythagorean triple. This is because 8^2 + 15^2 = 64 + 225 = 289 = 17^2. As for the acute angle between sides 8 and 15, we can use the inverse tangent function to find it. tan(theta) = 8/15 theta = arctan(8/15) Using a calculator, we find that theta ≈ 28.07 degrees. Since we know this is an acute angle, we can conclude that it measures between 0 and 90 degrees, and is closer to 28 degrees than to 62 degrees.
What number is closest to the root number 120
please answer fast will give brainliest ANSWER EVERYTHING
The given points can only be represented by an exponential function.
What is a linear function?
A linear function has the following form = y = f(x) = a bx
A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
a is a constant term or y-intercept. This is the value of the dependent variable when x = 0.
b is the coefficient of the independent variable. It is also called the slope and gives the rate of change of the dependent variable.
We can determine the type of function that can represent the given points by looking at the pattern of y values corresponding to the x values.
Linear Function: A linear function has a constant slope, which means that the difference between any two consecutive values of y must be the same as the difference between two consecutive values of x. The difference between two consecutive y values is 9/8, which is not the same as the difference between two consecutive x values (which is 1). Therefore, the given points cannot be represented by a linear function. Exponential function: an exponential function has a constant ratio between two consecutive y-values, meaning that the ratio of any two consecutive y-values must be the same as the ratio of any two consecutive x-values.
The ratio of two consecutive y values is 2, which is the same as the ratio of two consecutive x values (which is 1/2). Therefore, the given scores can be represented by an exponential function. Quadratic function: A quadratic function has a quadratic term, which means that the y-values should show an increasing or decreasing pattern of differences between successive x-values. The differences between successive y values are 9/8, 3/8, 1/2, and 9. There is no pattern of increasing or decreasing differences between successive x values, so the given points cannot be represented by a square. function
Therefore, the given scores can only be represented by an exponential function.
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Lillian and Khadija are reading the same book. At the beginning of the
month, Lillian was on page 40 and Khadija was on page 10. Lillian will read
15 pages per day and Khadija will read 20 pages per day. Let L represent the
page of the book that Lillian is on at the end of t days into the month, and let
K represent the page of the book that Khadija is on at the end of t days into
the month. Graph each function and determine whether Lillian or Khadija is
farther along in the book after 4 days.
After solving the linear equation Lillian is farther along in the book than Khadija after 4 days.
What is a linear equation?A linear equation is an algebraic equation of the form:
y = mx + b
where x and y are variables, m is the slope of the line, and b is the y-intercept. The slope represents how steep the line is, and the y-intercept is the point at which the line intersects the y-axis.
According to the given informationAs we know, Lillian was on 40 pages and Khadija was on 10 pages. So, the equation is,
And Let L represent the page of the book that Lillian is on at the end of t days into the month, and let K represent the page of the book that Khadija is on at the end of t days into the month.
[tex]L(t) = 40 + 15t[/tex] Lillian's progress after t days
[tex]K(t) = 10 + 20t[/tex] Khadija's progress after t days
After solving the linear equation, we will get the rate of the reading page.
Let's say t=4,
[tex]L(4) = 40 + 15(4) = 100[/tex]
[tex]K(4) = 10 + 20(4) = 90[/tex]
Therefore, after 4 days, Lillian is farther along in the book than Khadija.
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The Area of a Rectangle is 40. The width is 2 less than 3
times the length. Find the width.
O 10
O 12
O 15
O 14
Answer:
Let Length= x, Width= y
A.t.c.
3x-2=y ...(1)
Area = length × width
= xy = 40
from (1)
[tex]x(3x - 2) = 40 \\ 3 {x}^{2} - 2x = 40 \\ 3 {x}^{2} - 2x - 40 = 0 \\ 3 {x}^{2} - 12x + 10x - 40 = 0 \\ 3x(x - 4) + 10(x - 4) = 0 \\ (3x + 10)(x - 4) = 0 \\ x = - \frac{10}{3} \: or \: 4[/tex]
neglecting -10/3
length = 4
width = 3(4)-2=12-2
= 10
The diameter of a circle is 10 centimeters. What is the angle measure of an arc bounding a sector with area 10 square centimeters?
Answer:
72 degrees
Step-by-step explanation:
You want to buy some noodles. A 6-ounce package costs $1.98. A 14-ounce package costs $4.90. A 22-ounce package costs $7.04. Which package is the best buy?
Answer:
22-ounce package is the best buy as it has the lowest price per ounce.
Step-by-step explanation:
To determine which package is the best buy, we need to calculate the price per ounce of each package:
Price per ounce of 6-ounce package = 1.98 / 6 = $0.33 per ounce
Price per ounce of 14-ounce package = 4.90 / 14 = $0.35 per ounce
Price per ounce of 22-ounce package = 7.04 / 22 = $0.32 per ounce
Therefore, the 22-ounce package is the best buy as it has the lowest price per ounce.
a computer password consists of nine characters. replications are allowed. how many different passwords are possible if each character may be any lowercase letter or digit? enter your answer in scientific notation with two digit of accuracy after the decimal point.
To calculate the number of possible passwords, we need to find the total number of combinations of lowercase letters and digits for each character of the password.
Then raise that number to the power of 9 (since there are 9 characters in the password and replications are allowed). There are 26 lowercase letters and 10 digits (0 to 9), so the total number of options for each character is 26+10=36.
Therefore, the number of possible passwords is[tex]36^9[/tex], which is equal to 1.0333862 ×[tex]10^16[/tex] (rounded to two decimal places in scientific notation). In other words, there are over 10 quadrillion possible combinations of passwords, making it very difficult for someone to guess or hack into the system by trying different combinations.
This highlights the importance of choosing a strong and secure password that is difficult for others to guess or brute-force.
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Can I have some help with math
Answer:
B 1/4
Step-by-step explanation:
Because one coin have 1/2 to land either side, but if it was two coins then is will double it so it will be 1/4.
A comic-strip writer churns out a different number of comic strips each day. For 16 days, the writer logged the number of comic strips written each day (sorted low to high): {1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7}. If the writer writes for one more day and comes up with 8 new comic strips, how will the skew be affected?
On the other hand, if the number of comic strips produced is similar to the other values in the dataset, it will have little effect on the overall skew.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.
The skew of a dataset refers to the degree to which the distribution of values is asymmetrical. A dataset is said to be skewed if the majority of the values lie on one side of the mean.
In this case, the dataset has a right skew because there are more values on the right side of the distribution (higher values) than on the left side. We can see this by noting that the median (middle value) is 3, while the mean (average value) is slightly higher at 3.375.
If the writer writes 8 more comic strips on the next day, it will increase the maximum value in the dataset from 7 to 8. This will slightly shift the distribution to the right, but the skew will remain right because the majority of the values are still clustered on the right side of the distribution.
However, the effect on the overall skew will depend on the number of comic strips the writer produces on the next day relative to the other values in the dataset. If the writer produces a large number of comic strips relative to the other values, it could shift the distribution to a more symmetrical shape.
Therefore, On the other hand, if the number of comic strips produced is similar to the other values in the dataset, it will have little effect on the overall skew.
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in order to be correct, a line graph of the number of marriages per year in the united states must have group of answer choices number of marriages on the horizontal scale. years on the horizontal scale. either marriages or years on the horizontal scale, as long as equal intervals are used. bars of equal width.
In order to be correct, a line graph of the number of marriages per year in the United States must have years on the
horizontal scale.
It is defined as the process of adding more instances of the same type to the existing pool of resources and not
increasing the capacity of existing resources like in vertical scaling. This kind of scaling also helps in decreasing the
load on the server. This is called Horizontal Scaling
This allows for a clear representation of the number of marriages over time. To create such a graph, follow these steps:
1. Label the horizontal axis with years, making sure to use equal intervals between each year.
2. Label the vertical axis with the number of marriages.
3. Plot the data points for each year, representing the number of marriages.
4. Connect the data points with a line to show the trend over time.
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What is the rule for the following geometric sequence? 64, -128, 256, -512…
A. an = 64(-1/2)n-1
B. an = 64(2)n-1
C. an = 64(-2)n-1
D. an = 64(1/2)n-1
Thus, the following is the rule for the given geometric sequence: [tex]a = 64 * (-2)^(n-1) (n-1)[/tex]. Thus, the solution is (C) a = 64(-2)n-1.
what is sequence ?An structured of integers or objects that adhere to a particular pattern or rule is referred to as a sequence in mathematics. The name for each number or item in the sequence is. A series can be explicitly created or defined recursively, and it can be infinite or finite. A method or rule that directly expresses the n - th term of the series in terms of n defines an explicit sequence. For instance, the explicit sequence 2, 4, 6, 8, 10,... has the formula a = 2n, where n is the term's position inside the sequence. A starting value and recursive formula that determines the nth word of the series in terms of the preceding terms describe a recursive sequence.
given
The number sequence is as follows: 64, -128, 256, -512.
We must determine the common ratio between the following terms in order to get the rule for this sequence.
Any term can be divided by its previous term to obtain the common ratio (r). For instance, the result of subtracting the second term (-128) from the first term (64) is
r = (-128) / 64 = -2
The third term (256) divided by the second term (-128) results in:
r = 256 / (-128) = -2
And when the fourth term (-512) is divided by the third term (256), the result is
r = (-512) / 256 = -2
We can observe that for all pairings of following terms, the common ratio is -2.
Now we can apply the following formula to a geometric sequence's general term:
a = a1 * r^(n-1) (n-1)
where r is the common ratio and a1 is the first term.
In place of the values we hold:
[tex]a = 64 * (-2)^(n-1) (n-1)[/tex]
Thus, the following is the rule for the given geometric sequence: [tex]a = 64 * (-2)^(n-1) (n-1)[/tex]. Thus, the solution is (C) a = 64(-2)n-1.
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you have a 13 oz. bottle and a 20 oz. bottle, with which you wish to measure exactly 2 oz. however, you have a limited supply of water. if any water enters either bottle and then gets dumped out, it is gone forever. what is the least amount of water you can start with and still complete the task?
The least amount of water required to measure exactly 2 oz is 12 oz. (13 oz + 7 oz - 8 oz = 12 oz).
First, add 13 oz of water to the 20 oz bottle. The combined amount of water will now be 33 oz.
Next, pour water from the 33 oz bottle into the 13 oz bottle until the 13 oz bottle is full to the top.
The remaining amount of water in the 33 oz bottle will be 20 oz.
Now, pour out the water in the 13 oz bottle into the 20 oz bottle.
Now, the 20 oz bottle will have 13 oz of water in it. This leaves the 33 oz bottle with 7 oz of water remaining in it.
Now, pour the remaining 7 oz of water in the 33 oz bottle into the 20 oz bottle.
The 20 oz bottle will now have 20 oz + 7 oz = 27 oz of water in it.
Pour out the water in the 20 oz bottle until the amount of water in it is exactly 2 oz.
Since you started with a combined amount of 33 oz, and the amount of water remaining in the 20 oz bottle is 2 oz, the
amount of water poured out is 33 oz - 2 oz = 31 oz.
Therefore, the least amount of water required to measure exactly 2 oz is 12 oz.
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A bowl contains 3 apples, 5 bananas, 4 oranges. Mary randomly selects one piece of fruit from the bowl. What is the probability that she selects and apple out of the bowl? Give the answer in the form of a decimal.
Answer:
Step-by-step explanation:
You have a little unclear question with "selects and apple out of the bowl?" I only chose apples (there are 3 of them)
[tex]\frac{3}{12} =\frac{1}{4}[/tex] answer
Step-by-step explanation:
Given,
n(S) = 12
n(A)=3
We have,
P(A) = n(A)/n(S)
= 3 /12
= 1 /4
Determine the equation of the circle with center ( 3 , 9 ) containing the point ( 8 , − 3 )
Answer:
see the answer in the picture
Step-by-step explanation:
I don't know which equation you want. but I put both the standard and general form. but the equation should be the stander form. the radius is 13 in this case
We will see that this circle is centered at the point (-5, -49) and has a radius of 1.
What is the general circle equation?For a circle of radius R centered at the point (a, b), the equation is:
(x - a)^2 + (y - b)^2 = R^2
In this case, we have:
given the equation of the circle is
x^2 + y^2 + 10x + 14y + 73 = 0
We can rewrite this as:
(x^2 + 10x) + (y^2 + 14y) + 73 = 0
(x^2 + 2*5*x + 25) + (y^2 + 2*7*y + 49) - 25 - 49 + 73 = 0
(x + 5)^2 + (y + 49)^2 -74 + 73 = 0
(x + 5)^2 + (y + 49)^2 = 1
So we have a circle centered at the point (-5, -49) with a radius equal to 1.
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complete question:
Determine the center and radius of the following circle equation
x^2 + y^2 + 10x + 14y + 73 = 0
PLEASE ANSWER BOTH GEOMETRY WILL GIVE BRAINLIEST
Answer:
x = 90
Step-by-step explanation:
You want to know the value of x in the given diagram showing crossed chords.
Angle of Intersecting ChordsThe Angle of Intersecting Chords theorem tells you the angle where the chords cross is half the sum of the intercepted arc and the opposite arc.
Here, the angle marked x° is the supplement of the angle we can find based on the given arc measures:
180° -x° = (30° +(2x -30)°)/2
180 -x = 2x/2 = x . . . . . . . . . . divide by °, simplify
180 = 2x . . . . . . . . . . . . add x
90 = x . . . . . . . . . . . divide by 2
The value of x is 90.
a) determine an equation for the family of quartic functions with zeroes -5/2, -1, 7/2, 3.
b) write equations for two functions that belong to this family
c) determine an equation for the member of the family whose graph passes through the point (-2,25)
a. A quartic function with zeroes -5/2, -1, 7/2, and 3 can be written as
f(x) = a(x + 5/2)(x + 1)(x - 7/2)(x - 3), b) Two examples of functions that belong to this family are: f1(x) = 2(x + 5/2)(x + 1)(x - 7/2)(x - 3)
f2(x) = -0.5(x + 5/2)(x + 1)(x - 7/2)(x - 3) and the equation for the member of the family that passes through the point (-2,25) is:
f(x) = (4/275)(x + 5/2)(x + 1)(x - 7/2)(x - 3)
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x.
a) A quartic function with zeroes -5/2, -1, 7/2, and 3 can be written as the product of linear factors with those zeroes:
f(x) = a(x + 5/2)(x + 1)(x - 7/2)(x - 3)
where "a" is a constant that determines the overall scaling of the function.
b) Two examples of functions that belong to this family are:
f1(x) = 2(x + 5/2)(x + 1)(x - 7/2)(x - 3)
f2(x) = -0.5(x + 5/2)(x + 1)(x - 7/2)(x - 3)
Note that these functions differ only in the value of the constant "a".
c) To find the value of "a" that makes the graph of the function pass through the point (-2,25), we can substitute x = -2 and y = 25 into the equation for f(x):
25 = a(-2 + 5/2)(-2 + 1)(-2 - 7/2)(-2 - 3)
Simplifying this expression:
25 = a(5/2)(-1)(-11/2)(-5)
25 = a(6875/4)
a = 100/6875 = 4/275
Therefore, the equation for the member of the family that passes through the point (-2,25) is:
f(x) = (4/275)(x + 5/2)(x + 1)(x - 7/2)(x - 3)
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Q8g Chengbo Sold for 180000 (3 yaun. the amount for which he Sold the house is 24% more than the amount hepaid. for the house -work out the house. Give your 3 significant figure answer
Step-by-step explanation:
he sold the house for 180000, which is 24% more than the amount he paid.
180000 = x + 0.24x
Simplifying this equation, we get:
1.24x = 180000
x = 180000 / 1.24
x ≈ 145161.29
Chengbo paid approximately 145161.29 yuan for the house.
yes ik the picture is dark but pls help ike PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer:
a. Similar
Step-by-step explanation:
The question says the triangles are right triangles, so they can't be obtuse or equilateral.
Since they are both right triangles, they both have a 90° angle. And as stated in the question, they both have a 30° angle. By Angle-Angle (AA) they are similar. But we don't know anything about any sides in either triangle, so we don't know if they are congruent or not. Just we can only know they are similar.
Jamie was given the problem, "Find the result when the factors of 65 x 2 + 212 x − 313 65x 2 +212x−313 are multiplied together." Before she could answer, her sister, Lauren, said, "I know the answer without factoring or multiplying!" What was Lauren's answer and how did she know?
The product of the factors of [tex]65x^2 + 212x - 313[/tex] is equal to the original expression. Lauren may have recognized the expression as a difference of squares and factored it accordingly.
We can first simplify the expression [tex]65x^2 + 212x - 313[/tex] by factoring it:
[tex]65x^2 + 212x - 313 = (13x - 1)(5x + 313)[/tex]
(13x - 1)(5x + 313) = [tex]65x^2 + 212x - 313[/tex]
Therefore, the product of the factors is equal to the original expression.
To see this, we can rewrite the expression as:
[tex]65x^2 - 313 - 212x = (5x)^2 - (2\cdot 5x \cdot 7) + 7^2 - 7^2 - 212x[/tex]
= [tex](5x - 7)^2 - 7^2 - 212x[/tex]
= [tex](5x - 7)^2 - 212x - 49[/tex]
= [tex](5x - 7)^2 - 1^2\cdot 49 - 212x[/tex]
= (5x - 7 - 7)(5x - 7 + 7) - 49 = (5x - 14)(5x) - 49
= 5x(5x - 14) - 49
= 5x(5(x - 2) - 9)
= 5x(5x - 29)
Therefore, the factors of the expression are (5x - 7) and (5x - 29).
Lauren may have recognized the expression as a difference of squares by noticing that the coefficient of the x term (212) is twice the product of the square roots of the first and last terms (sqrt(65) and sqrt(313)), which is a common characteristic of a difference of squares.
To learn more about factors please click on below link
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Express the vector in component form given its magnitude is 41 and direction angle is 220 degrees
Answer:
What I myself would do is plug in the given values, and we get: x = 41 * cos(220 degrees) ≈ -22.59 y = 41 * sin(220 degrees) ≈ -33.73
Therefore, the component form of the vector is (-22.59, -33.73).
Step-by-step explanation: