Mathematics College

## Answers

**Answer 1**

step 1

Find the slope

we need two points

we take

(-4,2) and (-2,0)

m=(0-2)/(-2+4)

m=-2/2

m=-1

step 2

Find the equation in slope intercept form

y=mx+b

we have

m=-1

point (-2,0)

substitute

0=(-1)(-2)+b

0=2+b

b=-2

so

y=-x-2

step 3

Verify option A, C and option D (because the slope is -1)

option A

y-5=-(x+3)

isolate the variable y

y-5=-x-3

y=-x+2 -------> is not the solution

option C

y-3=-(x+5)

y-3=-x-5

y=-x-2 ------> is the solution

therefore

answer is the option C

## Related Questions

Two bond funds pay interest at rates that differ by 4%. Money invested for one year in the first fund earns $600 interest. The same amount invested in the other fund earns $800. Find the lower rate of interest (in percent). %

### Answers

**Given:**

The first fund earns $600 and the second fund earns $800.

Let **x%** be the lower rate of interest.

And **x+4**% be the higher rate of interest.

The difference between the amounts is,

[tex]800-600=200[/tex]

It means,

[tex]\begin{gathered} 4\text{ percent of n =200} \\ \text{Where n is the amount invested. } \\ \frac{4}{100}\times n=200 \\ n=\frac{200\times100}{4} \\ n=5000 \\ It\text{ gives } \\ \text{x percent of }5000=600 \\ \frac{x}{100}\times5000=600 \\ x=\frac{600}{50} \\ x=12 \\ \text{Same way,} \\ \text{x percent of }5000=800 \\ \frac{x}{100}\times5000=800 \\ x=\frac{800}{50} \\ x=16 \end{gathered}[/tex]

Alternative way,

For the first fund. let a be the lower rate and a+4 be the higher rate.

[tex]ax=600[/tex]

For second fund,

[tex]\begin{gathered} x(a+4)=800 \\ ax+4x=800 \\ 600+4x=800 \\ 4x=800-600 \\ x=\frac{200}{4} \\ x=50 \end{gathered}[/tex]

So,

[tex]\begin{gathered} ax=600 \\ 50a=600 \\ a=\frac{600}{50} \\ a=12 \\ \Rightarrow a+4=12+4=16 \end{gathered}[/tex]

**Answer: The lower rate of interest is 12%**

Sixth grade > S.4 Convert between percents, fractions 3 How do you write š as a percentage? W Write your answer using a percent sign (%). | Cuhimit

### Answers

To write a fraction as a percentage, you need to obtain the result of the division of 3 by 5 (this will be a decimal expression), and then multiply the result by 100. Then, we have:

[tex]\frac{3}{5}=0.6[/tex]

Therefore:

[tex]P=0.6\cdot100\Rightarrow P=60[/tex]

That is,** 3/5 can be written as 60%. **In other words, 3 is 60% of 5.

Which of the following is the polar form of −5−12i?

### Answers

Solution

[tex]undefined[/tex]

Option B

[tex]undefined[/tex]

**The final answer**

**Option B**

nd the slope of the following graph and write your result in the empty box.01987654

### Answers

In your graphic, you can choose some points: A(5,9) and B(3,5).

To find the slope, you have to divide the difference of the y-coordinates of 2 points by the difference of the x-coordinates of those same 2 points.

[tex]\text{slope = }\frac{\Delta y}{\Delta x}[/tex]

Using the 2 points:

[tex]\text{slope = (9-5)/(5-3)}[/tex][tex]\begin{gathered} \text{slope = 4/2} \\ \text{slope = 2} \\ \end{gathered}[/tex]

The blue shape is a dilation of the black shape. The scale factor is ____. Simplify your answer and write it as a proper fraction, improper fraction, or a whole number.

### Answers

We have tjhe general rule for dilations:

[tex]D_k(x,y)=(kx,ky)[/tex]

where k is the scale factor.

In this case, we can take the points (10,0) and the dilated point (8,0) to find the scale factor like this:

[tex]\begin{gathered} D_k(10,0)=(10k,0k)=(8,0) \\ \Rightarrow10k=8 \\ \Rightarrow k=\frac{8}{10}=\frac{4}{5} \\ k\text{=}\frac{4}{5} \end{gathered}[/tex]

**therefore, the scale factor is k=4/5**

the best player on a basketball team makes 85% of all free throws. The second best player makes 75% of all free throws the third best player makes 65% of all free throws based on their experimental probabilities estimate the number of free throws each player will make in his or her next 80 attempts

### Answers

In order to get the number of free throws each player will make, we simply have to multiply each probability by the total number of attempts which is 80.

The equation for the best player would then be:

[tex]\begin{gathered} 85\%\times80=x \\ or \\ \frac{85}{100}\times80=x \\ or \\ \frac{85}{100}=\frac{x}{80} \end{gathered}[/tex]

**After multiplying, we can say that estimatedly, the best player will make about 68 free throws.**

[tex]\begin{gathered} \frac{85}{100}=\frac{x}{80} \\ Cross-multiply. \\ \frac{85\times80}{100}=x\Rightarrow\frac{6800}{100}\Rightarrow x=68 \end{gathered}[/tex]

On the other hand, for the second best player, we

set amount of carbon dioxide in moles produced in a chemical reaction is given by the function f(t) = 0.02t^2 and t is in seconds find the rate of production of carbon dioxide after two seconds￼

### Answers

We have the following function for the amount of carbon dioxide in moles produced in a chemical reaction:

[tex]f(t)=0.02t^2[/tex]

*And we also have that it is a function of time (t), and we need to find the rate of production of carbon dioxide after two seconds.*

1. To find the rate of production, we need to find the derivative for the function since it will give us the instant rate of change for the chemical reaction. Then we have:

[tex]\frac{df(t)}{dt}=\frac{d}{dt}(0.02t^2)[/tex]

2. And now, applying the derivative rules for a constant, and for a power, we have:

[tex]\begin{gathered} \frac{d}{dt}(0.02t^2)=0.02*\frac{d}{dt}(t^2)=0.02*2*t=0.04*t \\ \\ \text{ Therefore, the derivative is:} \\ \\ 0.04*t \end{gathered}[/tex]

3. Then after 2 seconds, we have that the rate of production of carbon dioxide is:

[tex]0.04(2)=0.08\frac{\text{ mol}}{s}[/tex]

**Therefore, in summary, the rate of production of carbon dioxide after two seconds is 0.08 mol/s (option c).**

Looking at the Diagram what is the correct theorem,ASA Or AAS

### Answers

In the given image, you have the following:

- side OP (first triangle) is congruent to side QR

- angle N is congruent to angle S

- angle O is congruent to angle Q

**if angles N and S, and O and Q are equal, it is necessary that angles P and R are equal**. Do to all interioir angles are equal, it is necessary that all sides of both trangles have the same length (beacuse one of such sides is equal to one side of the other triangle.)

**Hence, you can conclude that both triangles are congruent:**

**ΔOPN ≅ ΔQRS**

**moreover, the specific theorem to express the congruent of both triangles is:**

**AAS**

The students in class are building a rectangular float for a homecoming parade. The float will be 6 feet wide by 10 feet long. The students made a scale drawing of the float that is 14 inches long. What is the approximate width of the scale drawing of the float?

### Answers

The scale drawing of the float is shown to be 14 inches long. The actual float has its length as 10 feet long. That means the scale used is;

[tex]\begin{gathered} \text{Scale}=\frac{14}{120} \\ \text{Note that 10 f}eet\text{ equals (10 x 12) 120 inches } \\ \text{Scale}=\frac{7}{60} \\ \text{For the width of the scale drawing, we use the scale as follows;} \\ \text{Scale}=\frac{7}{60}\times\text{actual} \\ \text{Scale}=\frac{7}{60}\times72 \\ \text{Scale}=\frac{7}{5}\times6 \\ \text{Scale =}\frac{42}{5} \\ \text{The width of the scale drawing is 8}\frac{2}{5} \\ \text{The approx}imate\text{ width therefore is 8 inches} \\ \text{This is because }\frac{2}{5}\text{ or 0.4 cannot be approx}imated\text{ to a whole number} \end{gathered}[/tex]

Find the circumference and area of a circle with diameter 6 inches

### Answers

Given a circle with d = 6 in.

Circunference:

C = π × d

C = π × 6 in

C = 18.85 in

Area:

A = π × r²

A = π × 3²

A = 28.27 in²

**ANSWER**

**circumference = 18.85 in**

**area = 28.27 in²**

Prealgebra- Determine whether the lines passing through the pairs of points are parallel, perpendicular, or neither

### Answers

It is important to note the following:

• If the slopes of the two lines are equal, they are parallel.

,

• If the slopes of the two lines are negative reciprocal of each other, they are perpendicular.

Let's now calculate the slope of each line. Use the formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let's start with line 1.

[tex]m=\frac{1-13}{-8-1}\Rightarrow m=\frac{-12}{-9}\Rightarrow m=\frac{4}{3}[/tex]

**The slope of line 1 is 4/3.**

Let's move on to line 2.

[tex]m=\frac{\frac{5}{3}-(-1)}{5-3}\Rightarrow m=\frac{\frac{8}{3}}{2}\Rightarrow m=\frac{4}{3}[/tex]

**The slope of line 2 is also 4/3.**

**Since the slopes of the two lines are the same, then the two lines are parallel.**

How many numbers between 1 and 100 inclusive are divided by 4 or 9

### Answers

First, we find how many numbers are divided by 4:

[tex]\frac{100}{4}=25[/tex]

Now, we find how many numbers are divided by 9:

[tex]\frac{99}{9}=11[/tex]

Adding these two results:

[tex]25+11=36[/tex]

Finally, we find how many numbers are divided by both 4 and 9:

[tex]36\text{ and }72[/tex]

That is, there are two numbers. We subtract 2 from 36 and we obtain 34 numbers.

**Answer: 34 numbers**

You have $ 8,619 on a credit card that charges a 11.7 % interest rate. If you want to pay off the credit card in 1 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?

### Answers

**Answer:**

**Explanation:**

We'll use the below formula to solve the given question;

[tex]undefined[/tex]

N-(-13)=24 Find the value and explain how you found it

### Answers

*Assume the equation to solve is:*

[tex]N-\mleft(-13\mright)=24[/tex]

We distribute the minus sign and make

The four sequential sides of a quadrilateral have lengths a = 3.1, b = 6.9, c = 9.6, and d = 10.6 (all measured in yards). The angle between the two smallest sides is a = 112°. What is the area of this figure?I got 58.72 but there saying that wrong

### Answers

Step 1

see the figure below to better understand the problem

Step 2

Applying the law of sines

Find out the area of triangle ABC

[tex]\begin{gathered} A=\frac{1}{2}(3.1)(6.9)sin(112^o) \\ A=9.916\text{ yd}^2 \end{gathered}[/tex]

Step 3

Applying the law of cosines

Find out the length of the side AC

[tex]\begin{gathered} AC^2=3.1^2+6.9^2-2(3.1)(6.9(cos112^o) \\ AC=8.6\text{ m} \end{gathered}[/tex]

Step 4

Applying the law of cosines

Find out the measure of angle D

[tex]AC^2=AD^2+DC^2-2(AD)(DC)cosD[/tex]

substitute given values

[tex]\begin{gathered} 8.6^2=10.6^2+9.6^2-2(10.6)(9.6)cosD \\ solve\text{ for cosD} \\ cosD=\frac{10.6^2+9.6^2-8.6^2}{2(10.6)(9.6)} \\ \\ angle\text{ D}=50.1^o \end{gathered}[/tex]

Step 5

Applying the law of sines

Find out the area of the triangle ADC

[tex]\begin{gathered} A=\frac{1}{2}(10.6)(9.6)sin(50.1^o) \\ \\ A=39.03\text{ yd}^2 \end{gathered}[/tex]

The area of the quadrilateral is equal to

[tex]\begin{gathered} A=9.92+39.03 \\ A=48.95\text{ yd}^2 \end{gathered}[/tex]The area is 48.95 square yards (rounded to two decimal places)

Explain:What is a periodic function? And what is the period? What is the amplitude? Label them on a graph(I may show you a graph and ask you to identify period and amplitude for example)

### Answers

**Answer:**

**Define a periodic function:**

**A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which repeat at intervals o radians, are periodic functions.**

**Take for instance a sine function below**

**Step 2:**

**Define the amplitude of a function:**

The **amplitud**e of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine.

[tex]\begin{gathered} From\text{ the sine function, the amplitude is represented as} \\ =A \end{gathered}[/tex]

**Step 3:**

Define the period of a function:

The Period goes from one peak to the next (or from any point to the next matching point):

This is the time it takes complete one cycle

From the equation of a sine function,

The period is represented below as

[tex]Period=\frac{2\pi}{B}[/tex]

TAKE FOR EXAMPLE ,

The sine equation given below

[tex]\begin{gathered} y=2sin(4(x-0.5))+3 \\ Amplitude=A=2 \\ period=\frac{2\pi}{B}=4 \\ period=B=\frac{\pi}{2} \end{gathered}[/tex]

The graph will be given below as

12. The seventh and eighth grade students are selling tickets to the talent show. The eighth grade studentshave sold fifteen more than twice the number of tickets that the seventh grade students have. If theysold 486 tickets altogether, how many did the eighth grade students sell?

### Answers

If x is the number of tickets the seventh grade students sold, then you have:

tickets sold by seventh grade students = x

tickets sold by seventh grade students = x

an elevator moves at a constant rate of 18 feet in 3 seconds a second elevator moves at a rate of 40 feet in 5 seconds

### Answers

**This situation does not represent a proportionality relation because the ratios are different.**

This comes from the fact that:

[tex]\frac{18}{3}=6[/tex]

and

[tex]\frac{40}{5}=8[/tex]

Therefore the ratios are different.

The displacement function of a rock thrown straight up in the air is given by f(t)= -2t^2 + 15.7t meters, where t is measured in seconds find the total distance traveled by the rock when it reaches the ground a. 30.81 mb. 31.40 mc. 61.62 md. 92.43 m

### Answers

As the rick is thrown straight up in the air and the function of its displacement is quadratic it means that the rock traveled a distance up to its maximum and then down to the ground. Then, the function value in the maximum is half the distance traveled by the rock.

[tex]f(t)=-2t^2+15.7t[/tex]

Use the next formula to find the time (t) in the maximum point of quadratic function:

[tex]\begin{gathered} f(x)=ax^2+bx+c \\ \\ x_{max}=-\frac{b}{2a} \end{gathered}[/tex][tex]t_{max}=-\frac{15.7}{2(-2)}=-\frac{15.7}{-4}=3.925[/tex]

Evaluate the function for t=3.925 to find the maximum value:

[tex]\begin{gathered} f(3.925)=-2(3.925)^2+15.7(3.925) \\ f(3.925)\approx-2(15.4056)+61.6225 \\ f(3.925)\approx-30.8112+61.6225 \\ f(3.925)\approx30.8113 \end{gathered}[/tex]

Multiply the maximum value by 2 to get the total distance traveled by the rock:

[tex]30.8113*2\approx61.62[/tex]Then, the total distance traveled by the rock when it reaches the ground is 61.62metersAnswer: C

Graph y = (1/2)|x + 2| – 1 using transformations

### Answers

First let's start with the graph of y = x:

Then, let's apply the "absolute value" operator: y = |x|

Then, we have an horizontal translation of 2 units to the left: y = |x + 2|:

Then, a vertical stretch by a factor of 1/2: y = (1/2)|x + 2|:

Finally, a vertical translation of 1 unit down: y = (1/2)|x + 2| - 1:

What is the rate of change of the function Y =X +3?x013

### Answers

**Explanation**: The rate of change of a given function is the slope. Once we are given an equation, it is important to know the slope -ntercept form of a function that is represented below

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

As we can see above, m represents the slope of the function.

**Step 1**: To find the rate of change we just need to compare our equation to the slope-intercept form given above as follows

As we can see above rate of change = slope= m = 1

**Final answer**: So the final answer is **1**.

There were 80golfers in the first round of a tournament. Of the 80, 62.5% qualified for the next round. How many did not qualify?

### Answers

**Number of golfers that didn't qualify = 30**

Explanation:

Total number of golfers = 80

The percentage that qualified for the next round = 62.5% = 0.625

Number that qualified = 80 * 62.5%

= 80 * 0.625

**Number of golfers that qualified = 50**

**Number of golfers that didn't qualify = Total number of golfers - Number of golfers that qualified**

= 80 - 50

**Number of golfers that didn't qualify = 30**

Tom and Sally are purchasing a home. They wish to save money for 8 years and purchase a house that has a value of $210,000 with cash. They deposit money into an account paying 10.2% interest.Step 1 of 2 : How much do they need to deposit each month in order to make the purchase?Step 2 of 2 : How much money did they deposit into the account in all?

### Answers

We have to calculate the monthly deposit in order to achieve a certain amount after certain number of years.

The amount is P = $210,000 and the number of years is n = 8 years.

Each deposit will increase a capital that will be compounding the interest, which has a annual rate of r = 10.2%.

As the deposits are made monthly (and we assume this is also the compounding period), we have a number of subperiods m = 12 subperiods per year.

We can use the annuity formula to find the monthly payment M so as to have a future value of FV = 210000:

[tex]M=\frac{FV*\frac{r}{m}}{(1+\frac{r}{m})^{n*m}-1}[/tex]

We can replace with the values and calculate the amount as:

[tex]\begin{gathered} M=\frac{210000*\frac{0.102}{12}}{(1+\frac{0.102}{12})^{8*12}-1} \\ M=\frac{210000*0.0085}{(1.0085)^{96}-1} \\ M\approx\frac{1785}{2.25365-1} \\ M\approx\frac{1785}{1.25365} \\ M\approx1423.84 \end{gathered}[/tex]

2) We have to calculate how much they deposit into the account.

As they deposit monthly during 8 years, the amount of deposits will be 12*8 = 96 deposits.

We can then multiply by the deposit amount and obtain:

[tex]\begin{gathered} TP=M*(n*m) \\ TP=1423.84*96 \\ TP=136688.64 \end{gathered}[/tex]

**Answer: **

**1) Monthly payment = $1,423.84 **

**2) $136,688.64**

Logan is putting hardwood floor in his kitchen and his bedroom. The kitchenmeasures 25 ft. by 25 ft. and the bedroom is 25 ft. by 20 ft. If Logan wishes topurchase a 20% excess of the hardwood, how many sq. ft. of hardwood does he need?

### Answers

He needs 1 350 sq ft of hardwood

**Explanation:**

Data:

Kitchen's measurements: 25 ft by 25 ft

Bedroom's measurements: 25 ft by 20 ft

Excess wanting to purchase: 20% => 1.20

Formula:

Area of the kitchen: A(k) = side * side

Area of the bedroom: A(b) = side * side

Total Area: A = A(k) + A(b)

Amount of sq. ft of hardwood neede: T(h) = A + (A * 20%) = A + (A * 20 / 100) = A * 1.20

Solution:

A(k) = 25 * 25 = 625 sq. ft

A(b) = 25 * 20 = 500 sq. ft

A = 625 + 500 = 1 125 sq. ft

T(h) = 1 125 * 1.20 = 1 125 + ( 1 125 * 20 / 100 ) = 1 350 sq. ft

11.) f(x) = 2 |x + 2| + 8 Transformation 1: Transformation 2: Transformation 3: 13.) f(x) = -|x |- 5 Transformation 1: Transformation 2:

### Answers

f(x) = 2 (x + 2)^2 + 8

**Transformation 1: **If we start with y = x^2 and replace x by x + 2, it has the effect of shifting the graph 2 units to the left.

**Transformation 2: **Then if we multiply the right side by 2, it turns the parabola upside down and gives a vertical expansion by a factor of 2.

**Transformation 3: **Finally, if we add 8 to the right side, it shifts the graph to 8 units up.

For which equation would x = 12 be a solution?12 - x = 448 ÷ x = 12x + 4 = 1212 x = 144

### Answers

We need to determine which of the given equations has solution x = 12.

We can do so by replacing x with 12 on the left side of an equation and comparing the result to the right side. If they are equal, then x = 12 will be a solution to that equation.

We have:

[tex]12-12=0\ne4[/tex][tex]48\div12=4\ne12[/tex][tex]12+4=16\ne12[/tex][tex]12(12)=144[/tex]

Therefore, x = 12 is a solution to the last equation.

*Answer*: **12 x = 144**

Write an equation relating S to N and then graph your equation

### Answers

Bill monthly salary is $2100 plus an additional $100 for every copy of history is fun

We set S to represent his total monthly salary and N the total number of copies that he sells

Therefore, 2100 is an independent value and 100 depends on the number of sells

then, the equation is:

[tex]S=2100+100N[/tex]

To graph the equation, we need to find the x-intercept and y-intercept:

To find the y-intercept, set x=0:

In this case, x is represented by N, and y is represented by S:

[tex]S(0)=2100+100(0)[/tex][tex]s(0)=2100[/tex]

So the graph starts at S=2100, point (S,N) = (2100, 0)

Then,

when he sells one book

N=1

[tex]S=2100+100(1)=2200[/tex]

Y = 2200

-When he sells 2 books

N =2

[tex]S=2100+100(2)=2300[/tex]

S=2300

- When he sells 3 books

N =3

[tex]S=2100+100(3)=2400[/tex]

then, S=2400

- When he sells 4 books

N = 4

[tex]S=2100+100(4)=2500[/tex]

Then, S=2500

Therefore, his salary depends on how many books he sells, then change the N value to find all the points of the graps

The mean of the distribution is 77.3 and the standard deviation is 4.8

### Answers

In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.

Given:

[tex]\begin{gathered} \operatorname{mean}\text{ = 77.3} \\ \text{standard deviation = 4.8} \end{gathered}[/tex]

From the given curve, we can assume the extreme values are three standard deviations of the mean since the shaded area covers almost all parts of the curve i.e :

[tex]z\text{ =3 or -3}[/tex]

Using the formula for z-score, we can find the extreme points:

[tex]\begin{gathered} z\text{ = }\frac{x-\psi}{\sigma} \\ \text{where }\psi\text{ is the mean and} \\ \sigma\text{ is the standard deviation} \end{gathered}[/tex]

Substituting we have:

[tex]\begin{gathered} 3\text{ =}\frac{x_1-77.3}{4.8} \\ x_1-77.3=14.4 \\ x_1\text{ =91.7} \end{gathered}[/tex][tex]\begin{gathered} -3\text{ = }\frac{x-77.3}{4.8} \\ x-77.3\text{ = -14.4} \\ x\text{ =62.9} \end{gathered}[/tex]

**Hence, **

**The percentage of total area shaded is 99.7%**

**The left and right values are 62.9 and 91.7 respectively**

12(1+x)=4x+28solving for x

### Answers

Solve for x:

[tex]12(1+x)=4x+28[/tex]

As a first step, use distributive multiplication:

[tex]12+12x=4x+28[/tex]

Then, we can use inverse operations to solve equations:

[tex]\begin{gathered} 12x-4x=28-12 \\ 8x=16 \\ x=\frac{16}{8} \\ x=2 \end{gathered}[/tex]

which is the better buy a 12 oz box of cereal for $3 or an 8 ounce box of cereal for $4

### Answers

We determine that by calculating the cost of buying one Oz for each case, that is:

[tex]p_1=\frac{1\cdot3}{12}\Rightarrow p_1=\frac{1}{4}\Rightarrow p_1=0.25[/tex][tex]p_2=\frac{1\cdot4}{8}\Rightarrow p_2=\frac{1}{2}\Rightarrow p_2=0.5_{}[/tex]

Here p1 and p2 represent the cost of 1 Oz for the 12 Oz and 8 Oz scenarios given, from this we have that is better to buy a 12 Oz box of cereal for $3 since we would be buying 1 Oz for $0.25.