Mathematics College

## Answers

**Answer 1**

**Answer:**

first we shift it by 13 units to right

|x|→|x-13|

then 9 units down

|x-13|-9

## Related Questions

What are the values for the coefficients and constant term of 2 + 3x² - 5x?

a=

B=

C=

### Answers

**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 school logo is in the form of the letter c which is surrounded by a circle. suppose the circle is centred at (0,0) and suppose the point (-2,4) lies on the circle.

write an equation of the circle.

### Answers

a school sligo is in the form of the lette c which is sureiounded by a chord fr duopoe the circle is cents 0,0 and suppose the point -2,4 lies on the circle

Hey Sydney made three times as much as Cassie made. If the difference in their pay was $74 how much money did each make

### Answers

**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.

if a pupil has a score of 60% how many marks out of 150 did he obtain

### Answers

**Answer:**

90

**Step-by-step explanation:**

60 % = .60 in decimal

.60 (150) = 90

NO LINKS!!!! Find the equation of the circle below

### Answers

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]

Approximate the population mean and standard deviation of age for males.

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

### Answers

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 diameter of a circle is 14 inches.Fund the circumference and area.Use 22/7 for pie

### Answers

**Answer:**

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

**Step-by-step explanation:**

The solution is in the image

Suppose that (x_n) and (y_n) are Cauchy sequences in a metric space (X,d). Show that the numerical sequence a_n=d(x_n,y_n) converges.

### Answers

[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] |

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

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What’s the answer for this equation -3 < 2x - 3 < 5

### Answers

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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please help me with this problem

### Answers

**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

An image of a rectangular prism is shown below: Part A: If a cross section of the prism is cut perpendicular to the base, what would be the shape of the resulting cross section? Explain your answer. (5 points) Part B: If a cross section of the prism is cut diagonal to the base, what would be the shape of the resulting cross section? Explain your answer. (5 points)

### Answers

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

PLEASE HELP ASAP!!!!!

### Answers

**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**

If the nurse to patient ratio is 3:15, how many nurses would you expect to see in a unit with 37 patients?

### Answers

if there are 3 nurses to every 15 patients, that means there is 1 nurse to every 5 patients since we can divide by 3 to simplify the ratio.

in order to find how many nurses would care for 37 patients, we can divide by 5.

37/5 = 7.4 nurses.

however, we cannot have .4 of a nurse, so you can either say 7 nurses or 8 nurses, but 7.4 rounds down to 7.

If triangle ABC was reflected over the x-axis, what would be the coordinates of B’?

a(-3, 4)

b(3, -4)

c(4, -3)

d(-4, 3)

### Answers

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

Find the surface area of a water tower that is 40 feet tall and has a diameter of 20 feet.

### Answers

**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:**

p

Line m has a y-intercept of cand a slope of 9, where p>0, q> 0, and p + q.

What is the slope of a line that is perpendicular to line m?

-q/p

P/q

q/p

-p/q

### Answers

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]

PLSS HELPPP!! Given vector u equals 15 times open angled bracket cos 45 degrees comma sin 45 degrees close angle bracket comma what are the magnitude and direction of −5u?

75; 225°

75; 135°

−75; −135°

−75; 45°

### Answers

The answer to your question is the 2 one

**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

18) Solve for x. (-2x-6° X )

### Answers

**Answer:**

-8x

**Step-by-step explanation:**

Subtract 6°x from -2x.

**Answer: -8**

**Step-by-step explanation:**

Sequences

47, 40, 33,

,19,

,5

400, 299,

,97,-4,

### Answers

**Answer:**

*1- Ans*; 47 , 40 , 33 , **2****6** , 19 , **1****2** , 5

*2- Ans*; 400 , 299 , **1****9****8** , 97 , - 4 , **-**** ****1****0****5**

**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]

Why is it important to make sure digits and decimals line up when adding and subtracting numbers with decimals? Explain by evaluating the following problem: 320.456 - 145.73.

### Answers

when evaluating decimals, it’s important to make sure they line up because the result could lead to a completely different number. for example, 320.456-145.73 is 174.83 and not making sure the decimal is in the correct place can result in 17.483 which is obviously different

During a school event, there were 8 times as many pupils as teachers and there were three times as many boys as girls. There were 70 fewer teachers than boys. How many people were there at the school event?

### Answers

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.

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

### Answers

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~~

Which of the following rational functions is graphed below￼

### Answers

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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only answer if you know! no spams :)

### Answers

**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**

Solve the the equation tan(x+pi/3) = sqrt 3/3 over the interval [0, 2].

### Answers

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).

Use a unit multiplier to convert

$15.00 per hour to dollars per

minute. Show your work.

### Answers

$15/1 hour= $15/60 minutes= $0.25/1 minute (did this by diving 15 by 60)

Use the drop-down menus to identify the method used to collect data for each scenario.

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.

Noah researched statistics online about the percentage of babies born with brown eyes.

Lara knew that she had a 25% chance of winning a contest, so she flipped two coins repeatedly to determine how many times two heads occurred.

### Answers

The method used to collect data for each scenario is **o**bservational 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

Find the centre of the circle

x^2 + y^2 + 4x - 6y = 12

### Answers

**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

Which relationships could have a negative correlation? Select three options. number of hours worked and free time speed of a car and minimum stopping distance the speed of a train and the length of time to reach the destination adult’s head circumference and age a tadpole’s age and the length of it’s tail

### Answers

**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

The lines of the equations are parallel, perpendicular, or neither. y = 2x + 3 y = 2x 1)parallel

2)perpendicular

3)neither

### Answers

**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.