Write A Formula For The Function G(x) Obtained When The Graph Of F(x)=|x| Is Shifted Down 9 Units And (2024)

The correct answer is option A which is [tex]f(x) =\dfrac{1}{(x+3)(x+5)}[/tex] this expression is showing the graph given in the question.

What is a graph?

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

In the given question we can see the graph. The function [tex]f(x) =\dfrac{1}{(x+3)(x+5)}[/tex] is showing the graph given in the question.

As we put the values of x in the function we will get this type of symmetric graph shown. I also attached the graph I made on the graphing tool in the answer below.

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Answer:

90

Step-by-step explanation:

60 % = .60 in decimal

.60 (150) = 90

Answer:

The surface area is 3140 feet².

What is Surface Area?

Surface area is the amount of space covering the outside of a three-dimensional shape.

Given that:

Diameter = 20 feet

radius = 20 ÷ 2 = 10 feet

Now, Surface area will be,

=2πr²+ 2πrh

= 2 × 3.14 × (10)² + 2 × 3.14 × 10 × 40

= 6.28 × 100 + 6.28 × 400

= 628 + 25.12 × 100

= 628+ 2512

= 3140 feet²

hence, the surface area is 3140 feet².

Step-by-step explanation:

Answer:

-75;45

Step-by-step explanation:

To start, it cant be a or b since we are multiplying a positive U times -5, therefore making it negative

-5(15)

-75

then, to find the answer u need to find the right formula

tan(v2/v1) or tan^-1(v2/v1)

for this it is the inverse tangent (tan^-1)

so you have to plug the values in

=tan^-1(sin45/cos45)

which then would equal 45

We know that pupils are students

Students = S
boys = B
Teachers = T

So....

S = 8T
Boys = 3G
T = B - 70

Since there is 8x students than teachers, I did Boys = 6x and girls = 2x

I'm going to use this next: S = 8T

8x = 8(B -70)

8x = 8(6x - 70)

8x = 4x - 560

x = 14

We know there is 8x students, so there are 112 students and we know that there is 1/8 of teachers, so there are 14 teachers.

Answer = 126.

Angles

Solve for x and then find the measurement of ∠B.

As you can see in the figure, angle a and b are corresponding angles and they have the same measurements. To solve for the value of x, equate the two angle measurement to each other and simplify.

Given:

A = 5x - 5°B = 3x + 13°

Solution:

5x - 5 = 3x + 135x - 3x = 5 + 132x = 18x = 18/2x = 9

The value of x is 9. To determine the value of b, substitute the value of x to the angle measurement of b and simplify.

Given:

B = 3x + 13x = 9

3(9) + 1327 + 1340

Proving that angle a and b have the same measurements:

5x - 5 = 3x + 135(9) - 5 = 3(9) + 1345 - 5 = 27 + 1340 = 40

Answer:

Therefore, the value of b is 40.

Wxndy~~

The population mean and standard deviation of age for males are 43.21 and 20.83, respectively

How to determine the population mean and the standard deviation?

The frequency table is given as:

Age Lower Limit Upper Limit Males Females

0-9 0 9 11 9

10-19 10 19 10 9

20-29 20 29 12 13

30-39 30 39 16 16

40-49 40 49 20 24

50-59 50 59 25 24

60-69 60 69 17 18

70-79 70 79 13 12

Rewrite the frequency table to show the class midpoints and the male frequency, only.

Midpoint (x) Male Frequency (f)

4.5 11

14.5 10

24.5 12

34.5 16

44.5 20

54.5 25

64.5 17

74.5 13

The population mean is then calculated using:

[tex]\mu =\frac{\sum fx}{\sum f}[/tex]

This gives

[tex]\mu = \frac{11 * 4.5 + 10 * 14.5 + 12 * 24.5 + 16 * 34.5 + 20 * 44.5 + 25* 54.5 + 17 * 64.5 + 13 * 74.5}{11 + 10 + 12 + 16 + 20 + 25 + 17 + 13}[/tex]

Evaluate

[tex]\mu = 43.21[/tex]

The standard deviation is calculated using:

[tex]\sigma = \sqrt{\frac{\sum f(x - \mu)^2}{\sum f}}[/tex]

So, we have:

[tex]\sigma = \sqrt{\frac{11 * (4.5 -43.21)^2+....................+ 13 * (74.5-43.21)^2}{11 + 10 + 12 + 16 + 20 + 25 + 17 + 13}}[/tex]

Evaluate the expression

[tex]\sigma = 20.83[/tex]

Hence, the population mean and standard deviation of age for males are 43.21 and 20.83, respectively

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The method used to collect data for each scenario is observational study , secondary data , simulation .

What is Data Collection ?

The accumulation of data to perform research , experiment or any other study is called data collection

It is done by different methods.

While standing in front of the school, Jace recorded the number of students who walked, rode their bikes, took the bus, and were driven there. :

Because all feasible channels and techniques were investigated in order to get accurate data, this study is known as an observational study.

Noah conducted research to learn the data pertaining to the proportion of newborns having brown eyes. Since he didn't perform this directly, it is referred to as secondary data.

Lara repeatedly flipped two coins to see how many times two heads appeared because she knew she had a 25% chance of winning a contest. This is an example of simulation because she wanted to see if she would come up with the same outcome.

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Answer:

A. observational study

B. published data

C. study

Step-by-step explanation:

Did the question in edge 2022

THE ANSWER IS x € (0,4)

First we separate this into two inequalities:

2x-3>-3

2x-3>-32x-3<5

Now we solve the inequalities:

2x-3>-3

2x>0

x>0

2x-3<5

2x<8

x<4

x € (0,4)

The solution to the given inequality is 0<x<4.

The given inequality is -3<2x-3<5.

Here, the given inequality can be divided into -3<2x-3 and 2x-3<5

Now, -3<2x-3

Add 3 to both the sides of inequality, we get

0<2x

Divide 2 to both the sides of inequality, we get

0<x

In 2x-3<5

Add 3 to both the sides of inequality, we get

2x<8

Divide 2 to both the sides of inequality, we get

x<4

So, the solution is 0<x<4

Therefore, the solution to the given inequality is 0<x<4.

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Answer:

hope you can understand

Answer

- number of hours worked and free time

- a tadpole’s age and the length of its tail

- the speed of a train and the length of time to reach the destination

Step-by-step explanation:

The more hours worked, the less free time they will have

The older a tadpole gets, the shorter its tail gets because it is turning into a frog

The faster a train. the shorter time it takes to get to a place

Answer: Sydney made $111, Cassie made $37

Step-by-step explanation:

If Cassie's money is x, then Sydney is 3x. 3x - x = $74, so x = $37.

[tex]d(x_{n} , x_{m}) + d(y_{n}, y_{m})[/tex][tex]d(x_{n} , x_{m}) - d(y_{n}, y_{m})[/tex]According to proof, the sequence ([tex]r_{n}[/tex])=(d([tex]x_{n}[/tex],[tex]y_{n}[/tex])) is Cauchy. See the proof below.

What does it mean for an expression to be Cauchy?

A Cauchy statement, in the language of mathematics, is a progression of components that are arbitrarily near to one another.

What is the proof for the above Cauchy expression?

Let ε > 0

N ∈ N in a way that

Whenever n, m > N, the result is:

|[tex]r_{n} - r_{m}[/tex]|

= |[tex]d(x_{n} , y_{n}) - d(x_{m}, y_{m})[/tex] |

= | ([tex]d(x_{n} , y_{n}) - d(x_{m}, y_{n}) + d(x_{m}, y_{n}) - d(x_{m}, y_{m})[/tex]|

≤ |[tex]d(x_{n} , y_{n}) - d(x_{m}, y_{n}) | + | d(x_{m} , y_{n}) - d(x_{m}, y_{m})[/tex] |

Answer:

The square,

Step-by-step explanation:

If you see, on the left of the square, it says 4 units. And on the right of the square it says for units Those are opposites

Answer:

centre = (- 2, 3 )

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² + 4x - 6y = 12 ( collect x/ y terms )

x² + 4x + y² - 6y = 12

using the method of completing the square

add ( half the coefficient of the x/ y terms)² to both sides

x² + 2(2)x + 4 + y² + 2(- 3)y + 9 = 12 + 4 + 9

(x + 2)² + (y - 3)² = 25 ← in standard form

with centre (- 2, 3 ) and r = [tex]\sqrt{25}[/tex] = 5

Answer:

-8x

Step-by-step explanation:

Subtract 6°x from -2x.

Answer: -8

Step-by-step explanation:

So slope of the line m is 9

We know perpendicular lines have slopes negative reciprocal to each other and their product of slopes is -1

9m2=-1m2=-1/9

If slope of m is p/q then slope of perpendicular line is -q/p and vice versa

Answer:

[tex]-\dfrac{q}{p}[/tex]

Step-by-step explanation:

Slope-intercept form of a Linear Equation:

[tex]y = mx + b[/tex]

where:

m is the slopeb is the y-intercept

If line m has a y-intercept of c and a slope of p/q, then:

[tex]\textsf{Equation of line m}: \quad y = \dfrac{p}{q}x + c[/tex]

If two lines are perpendicular to each other, the product of their slopes will be -1.

Let a = slope of the line perpendicular to line m.

[tex]\implies a \times \dfrac{p}{q}=-1[/tex]

[tex]\implies a=-\dfrac{q}{p}[/tex]

Therefore, the slope of the a line that is perpendicular to line m is:

[tex]-\dfrac{q}{p}[/tex]

Answer:

1- Ans; 47 , 40 , 33 , 26 , 19 , 12 , 5

2- Ans; 400 , 299 , 198 , 97 , - 4 , - 105

Step-by-step explanation:

[tex]47 - 40 = 7 \\ 40 - 33 = 7 \\ 5 + 7 = 12 \\ 12 + 7 = 19 \\ 19 + 7 = 26 \\ 26 + 7 = 33[/tex]

[tex]400 - 299 = 101 \\ 299 - 101 = 198 \\ 198 - 101 = 97 \\ 97 - 101 = - 4 \\ - 4 - 101 = - 105[/tex]

Answer:

Parallel

Step-by-step explanation:

Parallel lines:

The parallel lines have same slope.

y = 2x + 3

Compare with slope y-intercept form of the line: y = mx +b

m is slope and b is the y-intercept.

slope of this line = 2

y = 2x

Slope = 2

These lines have same slope. So, they are parallel.

Centre(-3,2)

diameter=6 units [0-(-6)=6units ]

radius=6/2=3

Equation of circle

[tex]\\ \rm\Rrightarrow (x-h)^2+(y-k)^2=r^2[/tex]

For centre(h,k) and radius r

So our equation

[tex]\\ \rm\Rrightarrow (x+3)^2+(y-2)^2=3^2[/tex]

[tex]\\ \rm\Rrightarrow (x+3)^2+(y-2)^2=9[/tex]

Answer:

[tex](x+3)^2+(y-2)^2=9[/tex]

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

(a, b) is the centerr is the radius

From inspection of the diagram, the center of the circle appears to be at point (-3, 2), although this is not very clear. Therefore, a = -3 and b = 2.

Substitute these values into the general form of the equation of a circle:

[tex]\implies (x-(-3))^2+(y-2)^2=r^2[/tex]

[tex]\implies (x+3)^2+(y-2)^2=r^2[/tex]

Again, from inspection of the diagram, the maximum vertical point of the circle appears to be at y = 5. Therefore, to calculate the radius, subtract the y-value of the center point from the y-value of the maximum vertical point:

⇒ radius (r) = 5 - 2 = 3

Substitute the found value of r into the equation:

[tex]\implies (x+3)^2+(y-2)^2=3^2[/tex]

Therefore, the final equation of the given circle is:

[tex]\implies (x+3)^2+(y-2)^2=9[/tex]

The coordinates of B’ is given by D. A'(2, -5)

Since point A is at (2, 5), and you are reflecting it across the x-axis, you take a look at the y-coordinate.

What is the reflecting axis?

A reflection of a point, a line, or a figure in the X-axis involved reflecting the image over the x-axis to create a mirror image. In this case, the x-axis would be called the axis of reflection.

Since it is five above the x-axis, you go five below the x-axis, or just give the opposite of 5, which is -5.

So, A' is at (2, -5).

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Answer:

c (4, -3)

Step-by-step explanation:

took the quiz

Answer:

0.01296

Step-by-step explanation:

I looked it up on this website: https://www.symbolab.com/solver/simplify-calculator/simplify%206%5E%7B-1%7D.6%5E%7B5%7D?or=input

That's the link to the solution, it shows you the steps, and you can look up other simplify questions there. It used to help me a lot.

To multiply powers with the same base, add their exponents. Add −1 and 5 to get 4.

6⁴

To calculate a power, multiply the base as indicated by its exponent. So:

The number 6 is the base.4 is the exponent.

Therefore the number 6 will be multiplied 4 times,

6 × 6 × 6 × 6 = 1296

1296 ===> Answer

Answer:

0%: Impossible

25%: Unlikely

50%: Equally likely

75%: Likely

100%: Certain

Answer:

See below ~

Step-by-step explanation:

The correct percentages matched with their likelihoods are :

⇒ 0% → c. Impossible

⇒ 25% → b. Unlikely

⇒ 50% → a. Equally likely

⇒ 75% → e. Likely

⇒ 100% → d. Certain

Rewrite the right side as √3/3 = 1/√3, and recall that tan(x) = 1/√3 when x = π/6. Then since tan is π-periodic, taking the inverse tan of both sides gives

[tex]\tan\left(x + \dfrac\pi3\right) = \dfrac1{\sqrt3} \implies \tan^{-1}\left(\tan\left(x + \dfrac\pi3\right)\right) = \tan^{-1}\left(\dfrac1{\sqrt3}\right) + n\pi[/tex]

[tex]\implies x + \dfrac\pi3 = \dfrac\pi6 + n\pi[/tex]

where n is any integer. Solving for x, we get

[tex]x = -\dfrac\pi6 + n\pi[/tex]

and the solutions in the interval [0, 2π] are x = 5π/6 and x = 11π/6 (for n = 1 and n = 2).

Answer:

[tex]area = 154 {in}^{2} \\ circumference = 44inches[/tex]

Step-by-step explanation:

The solution is in the image

Answer:

a=3

b=-5

c=2

Step-by-step explanation:

Because first arrange them in decreasing order by their variables powers like this 3x²-5x+2 after that take the the coefficients

A: it would be a rectangular prism as well! a section perpendicular to the base is parallel to the sides of the prism

B: the section would be a triangular prism!

whenever I get those questions, I always imagine a small cube of cheese, and if you have trouble imagining sections etc, I'd really suggest trying it! it sharpens your mind and helps you understand how it looks! otherwise, a great program for visualizing math problems is geogebra. it not only helps you draw everything out but solves your problems half of the time tbh