Mathematics College

## Answers

**Answer 1**

Given the system of equations :

[tex]\begin{gathered} y=-3(x+2) \\ y=-3x-6 \end{gathered}[/tex]

The shown represents the both equations

So, the equations will have the same description

The first equation :

y = -3 ( x + 2 )

y = -3x - 6

Which will be the same as the second equation

so, as shown the slope of both will be the coefficient of x = -3

And y- intercept for both will be = -6

so, the answer is the first option:

## Related Questions

Finding the greatest common factor of 14x^2+24x^3-16x^6

### Answers

**the greatest common factor is 2x²**

Explanation:[tex]\begin{gathered} The\text{ given expression:} \\ 14x^2+24x^3-16x^6 \end{gathered}[/tex]

**We find the factors common to each of the term. Then we will factorise it out:**

[tex]\begin{gathered} 14x^2\text{ = 2 }\times\text{ 7 }\times\text{ x }\times\text{ x} \\ 24x^3\text{ = }2\text{ }\times\text{ 2 }\times\text{ 2 }\times\text{ 3}\times x\text{ }\times x\times x \\ 16x^6=2^{}\text{ }\times\text{ 2 }\times\text{ 2}\times\text{ 2 }\times x\text{ }\times x\times x\times x\text{ }\times x\times x \end{gathered}[/tex][tex]\begin{gathered} we\text{ check the factors common to all thre}e\text{:} \\ 2\text{ }\times x\times x=2x^2 \end{gathered}[/tex][tex]\begin{gathered} 14x^2+24x^3-16x^6\text{ = }2\text{ }x^2(\text{7})\text{ + }2^{}x^2\text{ }\times(12x)-2\text{ }x^2(8x^4)\text{ } \\ 14x^2+24x^3-16x^6=2x^2(7+12x-8x^4) \end{gathered}[/tex]

**Hence, the greatest common factor is 2x²**

Please help me with this, I don’t understand anything and all the tutors are making it so difficult, please make it simple and easy, thank you!

### Answers

**SOLUTION **

We want to solve

moving -3/x to the other side we have

[tex]\begin{gathered} \frac{x+5}{x^2-x}=\frac{1}{x-1}+\frac{3}{x} \\ adding\text{ the other side by LCM, we have } \\ \frac{x+5}{x^2-x}=\frac{x+3(x-1)}{(x-1)x} \\ expanding\text{ we have } \\ \frac{x+5}{x^2-x}=\frac{x+3x-3}{x^2-x} \\ \frac{x+5}{x^2-x}=\frac{4x-3}{x^2-x} \end{gathered}[/tex]

Continuing we have

[tex]\begin{gathered} \frac{x+5}{x^2-x}=\frac{4x-3}{x^2-x} \\ cancelling\text{ common denominators, we have } \\ x+5=4x-3 \\ collecting\text{ like terms } \\ 5+3=4x-x \\ 8=3x \\ x=\frac{8}{3} \end{gathered}[/tex]

**Hence the answer is 8/3**

the length of a rectangle is 5 m less then three times the width and the area of the rectangle is 28 m squared. find the dimensions

### Answers

let

w = width

length = l

**l = 3w - 5**

area of the rectangle = 28 meter squared

The dimension are solved below

[tex]\text{area}=lw[/tex][tex]undefined[/tex]

What is the length of YZ?X17 cm8 cmZYa) 9 cm•b) 15cmc) 19cmd) 25 cm

### Answers

The triangle given in the problem is a right triangle. Given its hypotenuse *c* and the length of one side *a*, the other side of the triangle can be computed using the Pythagorean theorem wherein

[tex]\begin{gathered} c^2=a^2+b^2 \\ b^2=c^2-a^2 \\ b=\sqrt[]{c^2-a^2} \end{gathered}[/tex]

Just substitute the value of *c *(hypotenuse) and *a *(length of one side) on the equation above and compute, we get

[tex]\begin{gathered} b=\sqrt[]{(17cm)^2+(8cm)^2_{}} \\ b=\sqrt[]{289cm^2+64cm^2} \\ b=\sqrt[]{353cm^2} \\ b=18.79\operatorname{cm}\approx19\operatorname{cm} \end{gathered}[/tex]

Hence, the length of the other side of the right triangle is 19 cm.

**Answer: c) 19 cm**

Write the explicit formula for each sequence.-2, -10, -50, -250, -1250,….

### Answers

**Answer:**

[tex]\text{ a}_n=-2.(5)^{n-1}[/tex]

**Explanation:**

Here, we want to write the explicit formula for the given sequence

Looking at the sequence, we can see that:

[tex]\frac{-10}{-2}\text{ = }\frac{-50}{-10}\text{ = }\frac{-250}{-50}\text{ = 5}[/tex]

What this simply means is that we have to multiply the preceding term by 5 to get the succeeding term

Now, we have the explicit formula as follows:

We have deduced that the sequence is geometric. So we have the explicit formula as:

[tex]\text{ a}_n=-2.(5)^{n-1}[/tex]

where n is the term number

ΔABC is translated 4 units to the left and 8 units up, then reflected across the y-axis. Answer the questions to find the coordinates of A after the transformations.1. Give the rule for translating a point 4 units left and 8 units up.2. After the translation, where is A located?3. Give the rule for reflecting a point over the y-axis.4. What are the coordinates of A after the reflection?5. After the two transformations, has A returned to its original location?

### Answers

**PART 1**

To traslate a point 4 units to the left, we substract 4 from the x-coordinate. Similarly, to traslate it 8 units up we add 8 to the y-coordinate.

This way, the rule for translating a point 4 units left and 8 units up is:

[tex](x,y)\rightarrow(x-4,y+8)[/tex]

**PART 2**

Let's apply the traslation to each of the vertex:

[tex]\begin{gathered} A(7,5)\rightarrow(7-4,5+8)\rightarrow A^{\prime}(3,13) \\ B(2,9)\rightarrow(2-4,9+5)\rightarrow B^{\prime}(-2,14) \\ C(1,3)\rightarrow(1-4,3+8)\rightarrow C^{\prime}(-3,11) \end{gathered}[/tex]

This way, we can conclude that the new set of vertex is:

[tex]\begin{gathered} A^{\prime}(3,13) \\ B^{\prime}(-2,14) \\ C^{\prime}(-3,11) \end{gathered}[/tex]

**PART 3**

By definiton, the rule to reflect a point over the y-axis is:

[tex](x,y)\rightarrow(-x,y)[/tex]

**PART 4**

We apply this transformation to each of the new vertex:

[tex]\begin{gathered} A^{\prime}(3,13)\rightarrow A´´(-3,13) \\ B^{\prime}(-2,14)\rightarrow B´´(2,14) \\ C^{\prime}(-3,11)\rightarrow C´´(3,11) \end{gathered}[/tex]

This way, we can conclude that the new set of vertex is:

[tex]\begin{gathered} A´´(-3,13) \\ B´´(2,14) \\ C´´(3,11) \end{gathered}[/tex]

**PART 5**

We can conclude that A **HAS NOT** returned to its original location.

Which table shows the ratio of Y to X as 8:1? X Y Hours y 3 3 12 20 a. 5 20 56 2 50

### Answers

**The table that shows a ratio of y to x as 8:1 is C.**

This comes from the fact every value of y is 8 times the value of x given.

In a normal distribution, 99.7% of the data fall within how many standarddeviations of the mean?

### Answers

**The Solution:**

Given:

99.7% of the data.

Required:

By the **Empirical Rule:**

**99.7% of the data falls three standard deviations from the mean.**

Thus, **the correct answer is [option A]**

the table shows the relationship between the total cost of movie tickets y and the amount of people x who attended to movieX,5,6,7,8,9,y,35,42,49,56,63which best describes the function in the table from x = 5 to x = 9

### Answers

We have the following:

we can calculate the function as follows:

the first thing is to calculate the slope of the function

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

replacing:

[tex]\begin{gathered} m=\frac{63-35}{9-5} \\ m=7 \end{gathered}[/tex]

Therefore, the function is:

[tex]y=7x[/tex]

Therefore, the cost of movie ticket is $7

The midpoint of the complex numbers 3 - 12i and 7 + 6i is 5 + bi . What is the value of b?

### Answers

The midpoint between two complex numbers x+yi and u+vi is given by:

[tex]\frac{x+u}{2}+\frac{y+v}{2}i[/tex]

Plugging the values of the numbers given we have:

[tex]\frac{3+7}{2}+\frac{-12+6}{2}i=\frac{10}{2}-\frac{6}{2}i=5-3i[/tex]

**Therefore the value of b is -3**

find the distance between (4, 200°) and (2, 140°) to the nearest tenth. help

### Answers

Notice that the given points are in **polar coordinates.**

Recall that the distance between two points **(r₁,θ₁)** and **(r₂,θ₂)** in polar coordinates is given by the **distance formula**:

[tex]d=\sqrt[]{r^2_1+r^2_2-2r_1r_2\cos (\theta_2-\theta_1)}[/tex]

Substitute **(r₁,θ₁)=(4,200º)** and **(r₂,θ₂)=(2,140º)** into the formula:

[tex]d=\sqrt[]{4^2+2^2-2\cdot4\cdot2\cos (140-200)}[/tex]

Simplify the expression on the right:

[tex]d=\sqrt[]{16+4-16\cos(-60)}=\sqrt[]{20-16(\frac{1}{2})}=\sqrt[]{20-8}=\sqrt[]{12}=2\sqrt[]{3}[/tex]

Express the number as a decimal to the nearest tenth as required:

[tex]2\sqrt[]{3}\approx3.5[/tex]

**Hence, the distance between the points is about 3.5 units.**

x1 2 3 2 Does the table represent a function? Y 1 4 9 -4

### Answers

Function, domain and range

x = 1. 2. 3. 2

y = 1. 4. 9. -4

THEN analyze table

If in a table, x values are REPEATED, then this table does NOT represent a function

For example, in this case ,number 2 is repeated two times

Then, for this reason, this table IS NOT a function

Find the mean. If necessary, round to one decimal place.60, 57, 86, 26, 128, 82

### Answers

**EXPLANATION**

The mean formula is given by the following expression:

[tex]\text{Mean}=\frac{\sum ^{}_{}X}{N}[/tex]

Where X represents each individual value and N the number of values.

Plugging in the numbers into the expression:

[tex]\text{Mean = }\frac{60+57+86+26+128+82}{6}=\frac{439}{6}=73.1666\ldots\approx73.2[/tex]

In conclusion, the **mean** is **73.2**

I need help with this practice Question #1Does the series converge or diverge? Question 2# You conclude this because the series is ________________

### Answers

STEP - BY - STEP EXPLANATION

What to find?

Determine whether the given series converge or diverge.

**Given**:

**Step 1**

Determine the common ratio.

[tex]\begin{gathered} \frac{16}{27}\times\frac{9}{4}=\frac{4}{3} \\ \\ \frac{4}{9}\times\frac{3}{1}=\frac{4}{3} \\ \\ \frac{1}{3}\times\frac{4}{1}=\frac{4}{3} \end{gathered}[/tex]

It is enough to see that it is a **geometric series.**

**Step 2**

List out the conditions for convergence /divergence of a **geometric series**.

• If the absolute value of the ,common ration, i.e, |r| is less than 1,, the the series ,converges,.

,

• If, |r| > 1, then the series, diverges.

Clearly, 4/3 > 1

This implies |r| >1, hence the series **diverges**.

**ANSWER**

**The series diverges.**

**The series is geometric and the absolute value of the common ratio is greater than 1.**

hello I seem to be having some difficulties please help

### Answers

**Answer:**

$5904

**Explanation: **

• The purchase value of the car = $21,500

,

• The rate of depreciation = 35%.

To find the **resale value **of the car after a certain number of years, we use the **depreciation formula** below:

[tex]A(t)=A_o(1-r)^t[/tex]

• The initial value, Ao = 21,500

,

• The rate, r = 35% =0.35

,

• The time, t (in years) = 3

**Substitute these values** into the formula:

[tex]\begin{gathered} A(3)=21500(1-0.35)^3 \\ =21500(0.65)^3 \\ =5904.44 \\ \approx\$5904 \end{gathered}[/tex]

**The resale value of the car after 3 years is $5904 (correct to the nearest dollar).**

I believe the answer is 5904

I have a calculus question about initial velocity, pic included.

### Answers

The constant acceleration of a ball shot up from the ground is a = -32 ft/sec^2.

The acceleration is defined as the instant rate of change of the velocity:

[tex]a=\frac{dv}{dt}[/tex]

Integrating this equation, we have:

[tex]v=\int a\cdot dt[/tex]

Since the acceleration is a constant function:

[tex]\begin{gathered} v=\int-32\cdot dt \\ \\ v=-32\int dt \\ \\ v=-32t+v_o \end{gathered}[/tex]

The initial velocity is 48 ft/s, thus

[tex]v=48-32t[/tex]

The ball will stop and return to the ground when the velocity is 0:

[tex]48-32t=0[/tex]

Solving for t:

[tex]t=\frac{48}{32}=1.5[/tex]

Now we find the displacement function by integrating the velocity:

[tex]d=\int(48-32t)dt[/tex]

Integrating:

[tex]\begin{gathered} d=48t-\frac{32t^2}{2}+d_o \\ \\ d=48t-16t^2+d_o \end{gathered}[/tex]

The ball was shot from the ground, so do = 0:

[tex]d=48t-16t^2[/tex]

When t = 0, the position is d = 0.

When t = 1.5 seconds, the position is:

[tex]\begin{gathered} d=48\cdot1.5-16(1.5)^2 \\ \\ d=72-36 \\ \\ d=36 \end{gathered}[/tex]

**The ball goes up to 36 feet**

(THIS IS ONE QUESTION)The scatter plot shows the number of years of experience, x, and the hourly pay rate, y, for each of 24 cashiers in Florida.Use the equation of the line of best fit, =y+0.91x7.99, to answer the questions below.Give exact answers, not rounded approximations. (a) What is the predicted hourly pay rate for a cashier with 9 years of experience?$(b) What is the predicted hourly pay rate for a cashier who doesn't have any experience?$(c) For an increase of one year of experience, what is the predicted increase in the hourly pay rate?$

### Answers

**Solution:**

Given the scatterplot below:

where the line of best fit is expressed as

[tex]y=0.91x+7.99[/tex]

**A) Predicted hourly rate for cashier with 9 years of experience:**

Thus, we have

[tex]x=9[/tex]

By substituting the value of 9 for x into the equation, **we have**

[tex]\begin{gathered} y=0.91\left(9\right)+7.99 \\ =\$16.18 \end{gathered}[/tex]

**B) Predicted hourly rate for cashier with no experience:**

This implies that

[tex]x=0[/tex]

By substitution,** we have**

[tex]\begin{gathered} y=0.91(0)+7.99 \\ \Rightarrow y=\$7.99 \end{gathered}[/tex]

**C) Predicted increase in the hourly rate for an increase of one year of experience: **

Recall that the equation of a line is expressed as

[tex]\begin{gathered} y=mx+c \\ where \\ m\Rightarrow slope \\ m=\frac{increase\text{ in y}}{increase\text{ in x}} \end{gathered}[/tex]

From the equation of the line of best fit, by comparison, **we have**

[tex]\begin{gathered} slope=0.91 \\ where \\ slope=\frac{incresre\text{ in hourly pay}}{increase\text{ in year of experince}} \\ \Rightarrow0.91=\frac{increase\text{ in hourly pay}}{1} \\ thus,\text{ we have} \\ predicted\text{ increase in hourly pay = \$0.91} \\ \end{gathered}[/tex]

Rewrite the following equation in slope intercept form18x - 13y = 11Write your answer using integers, proper fractions, and improper fractions.Can this be simplifiedIf so what is it?

### Answers

The slope intercept form is expressed as

y = mx + c

Where

m represents slope

c represents y intercept

The given equation is

18x - 13y = 11

We would re-arrange the equation so that it takes the slope intercept form. It becomes

18x - 13y = 11

13y = 18x - 11

Dividing both sides of the equation by 13, it becomes

y = 18x/13 - 11/13

**The equation in slope intercept form is**

**y = 18x/13 - 11/13**

Rani dilates figure ABCD to form figure A'B'C'D'. She uses a scale factor of and a center of dilation at the origin. Then she translates the image up 7 units to form figure A"B"C"D". What are the coordinates of the vertices of figure A'B'C'D"? Show your work.

### Answers

The **coordinates **of the vertices of figure A'B'C'D" will be A''(4,4),B''(13,4),C''(13,1) and D''(4,1).

What is geometric transformation?

It is defined as the change in **coordinates **and the shape of the geometrical body. It is also referred to as a two-dimensional **transformation**. In the geometric transformation, changes in the **geometry **can be possible by rotation, translation, reflection, and **glide **translation.

It is given that, Rani dilates figure ABCD to form figure A'B'C'D'. She uses a **scale factor **of and a center of dilation at the origin. Then she translates the image up to 7 units to form **figures **A"B" C" and D".

The **transformation **dilation is used to resize an item. Dilation is a technique for making items appear larger or smaller. The image created by this **transformation **is identical to the original shape.

Thus,,the **coordinates **of the vertices of figure A'B'C'D" will be A''(4,4),B''(13,4),C''(13,1) and D''(4,1).

Learn more about the **geometric transformation **here:

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Marty's friend Tom makes and hourly wage of $15.00 per hour. Using that there are 40 hours in a standard work week, there are 52 weeks in a year, Social Security Tax is $6.20 for every $100 earned, Medicare Tax is $1.45 for every $100 earned, and the following income tax designations, calculate the following (round your answers to the nearest penny if needed): A. Tom's annual income tax is $B. Tom's net annual income is $C.Tom's net monthly income is $

### Answers

**Given:-**

Marty's friend Tom makes and hourly wage of $15.00 per hour. Using that there are 40 hours in a standard work week, there are 52 weeks in a year, Social Security Tax is $6.20 for every $100 earned, Medicare Tax is $1.45 for every $100 earned.

**To find:-**

A. Tom's annual income tax.

B. Tom's net annual income.

C.Tom's net monthly income .

So toms wage per week is,

[tex]40\times15=600[/tex]

So wage per week is **$600.**

So total income tax is,

[tex]6(6.20+1.45)=6\times7.65=45.9[/tex]

So the annual income tax is,

[tex]52\times45.9=2366[/tex]

So the required income tax is **$2366.**

Tom's net annual income is,

[tex]52\times600=31200[/tex]

So toms net annual income is **$31200.**

Tom's net monthly income is**,**

[tex]600\times4=2400[/tex]

So net monthly income is **$2400.**

Your friend has a credit card with an APR of 49.9%. What would his finance charge be on a $500 balance for just 1month? (round to the hundredths place)

### Answers

**Finance charge** be on a $500 **balance** for just 1month is equal to $20.79.

APR stands for the annual percentage rate on a loan which is the **interest rate **on a one year loan. To calculate the monthly rate r, we know that:

49.9 / 100 / 12 * $500 = $20.79

The **finance charge **is $20.79.

The **amount of interest **due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate. The total interest on a loaned or borrowed sum is determined by the principal amount, the **interest rate**, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.

To learn more about **interest rate **visit:https://brainly.com/question/13324776

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It takes 3 hr and 10 min to ride the tram to the top of Pike's Peak in Colorado. The tram will travel a total distance of 14.32 km. What is the speed of the tram?

### Answers

Time: 3hr and 10 minutes

Distance: 14.32 km

Apply the next formula:

Speed: Distance/ time

First, convert the time into hours:

60 min = 1 hour

10 min = 10/60 = 0.167 hours

3+0.167 = **3.167 hours**

Back with the formula:

Speed: 14.32/3.167 **= 4.52 km/h**

what's equivalent to 45/46

### Answers

Simplify the fractions.

OPTION A

[tex]\begin{gathered} \frac{88}{92}=\frac{44}{46} \\ =\frac{22}{23} \end{gathered}[/tex]

Not equivalent of fraction 45/46.

OPTION B

[tex]\begin{gathered} \frac{135}{138}=\frac{45\cdot3}{46\cdot3} \\ =\frac{45}{46} \end{gathered}[/tex]

Fraction 135/138 is simplify to 45/46. So fraction 135/138 is equivalent to 45/45.

OPTION C

[tex]\begin{gathered} \frac{90}{93}=\frac{30\cdot3}{31\cdot3} \\ =\frac{30}{31} \end{gathered}[/tex]

Fraction 90/93 is not equivalent to 45/46.

OPTION D

[tex]\begin{gathered} \frac{170}{178}=\frac{85\cdot2}{89\cdot2} \\ =\frac{85}{89} \end{gathered}[/tex]

Fraction 170/178 is not equivalent to 45/46.

So answer is OPTION **B.**

**135/138**

A rancher is making a corral in the shape of a rectangle using sections of fence. The length of the corral is twice the width. Each section of fence is 10 feet in length. The corral has an area of between 5,000 and 45,000 square feet. The function f(x) = 2 describes the situation, where x is the width of the corral. What is the domain of the function? Show workA. 50 , for all values of x that are multiples of 10.B. 50 , for all values of x that are multiples of 50.C. 5,000 , for all values of x that are multiples of 50.D. 5,000 , for all values of x that are multiples of 10.

### Answers

The shape of the corral is rectangle

The length of the corral is twice the width

If x represents the width, and l represents the length

l = 2w

given f(x) =-7x+9 and h(x)=-5f(x) what are the slope an y intercept of the graph of function h?slope=y-intercept =

### Answers

[tex]\begin{gathered} f(x)=-7x+9 \\ h(x)=-5f(x) \end{gathered}[/tex]

First step let us multiply f(x) by -5

[tex]\begin{gathered} h(x)=-5\lbrack-7x+9\rbrack \\ h(x)=(-5)(-7x)+(-5)(9) \\ h(x)=35x+(-45) \\ h(x)=35x-45 \end{gathered}[/tex]

The general form of the linear equation is **f(x) = mx + b**, where

**m is the slope**

**b is the y-intercept**

Since h(x) = 35 x - 45, then

m = 35

b = -45

So:

**The slope = 35**

**y-intercept = -45**

Linekis mapped to linek'by a dilation. If lineskandk'share pointAin common, which statement must be true?A)Lineskandk'are perpendicular.B)PointAmust be the center of dilation.C)Lineskandk'intersect only at pointA.D)The center of dilation must lie on linek.

### Answers

Dilation could be an enlargement or a reduction. If line k is mapped to line k', it means that k' is a reduction or an enlargement of k. If point A is common to both lines, then it means that Lines k and k' intersect only at point A.

**Thus, the correct option is C**

This composite figure is made up of three simpler shapes. What is the area of the figure? 14 cm 5 cm 7 cm 7 cm 16 cm

### Answers

The figure consist of parallelogram, square and right angle triangle.

The dimension of parallelogram is.

Base B= 14

Height H = 5.

The dimension of square is,

side a = 7.

The dimensions of rectangle is,

Base b = 16

Height h = 7 cm

Determine the area of composite figure.

[tex]\begin{gathered} A=B\cdot H+a\cdot a+\frac{1}{2}\cdot b\cdot h \\ =14\cdot5+7\cdot7+\frac{1}{2}\cdot16\cdot7 \\ =70+49+56 \\ =175 \end{gathered}[/tex]

Thus area of composite figure is 175 square centimeter.

Find the perimeter of the given triangle.A ABC, if AABC – APQR, BC = 6, QR= 11, PQ = 9, and PR = 13P.A13B6CR11QA. 60.5B. 22C. 18D. 15.23

### Answers

[tex]\begin{gathered} \frac{AB}{BC}\text{ = }\frac{PQ}{RQ} \\ \frac{AB}{6}=\text{ }\frac{9}{11} \\ 11AB\text{ = 9}\times6 \\ AB\text{ = }\frac{54}{11}\text{ = 4.9} \\ \\ \text{lets find, AC} \\ \frac{AC}{CB}\text{ = }\frac{PR}{RQ} \\ \frac{AC}{6}\text{ =}\frac{13}{11} \\ 11AC\text{ = 13 }\times6 \\ AC\text{ = }\frac{78}{11}\text{ = 7} \\ \end{gathered}[/tex]

To now find the perimeter of ABC

AB + BC + AC

4.9 +6 +7 = 17.9 approximately 18

3,12,48,...t8find the 5th term

### Answers

Hello

This is a geometric progression and we have the first term and we have to find the common ratio.

first term = a

common ratio = r

[tex]\begin{gathered} a=3 \\ r=\frac{12}{3}=4 \end{gathered}[/tex]

The 5th term would be

[tex]\begin{gathered} T_5=ar^4 \\ T_5=3\times4^4 \\ T_5=3\times256 \\ T_5=768 \end{gathered}[/tex]

**The value of the 5th term of the sequence is 768**

9 and 10. find the slope of KM and ST. Determine if they are parallel, perpendicular,or neither .

### Answers

**Answer:**

9 is parallel and 10 is perpendicular

**Step-by-step explanation:**

You find the slope by the change in y over the change in x

Points are in the form(x,y) You take the y numbers on top of the fraction and subtract them and you take the x numbers on the bottom of the fraction and subtract those. Simplify and you have the slope.

(-4,10) (2, -8)

[tex]\frac{-8 - 10}{2 - - 4}[/tex] = [tex]\frac{-18}{2+4}[/tex] = [tex]\frac{-18}{6}[/tex] Divide the top and bottom by 6

[tex]\frac{-3}{1}[/tex] = -3

The slope is -3. Let's compare to the other 2 points.

(1,2) (4, -7)

[tex]\frac{-7 - 2}{4 - 1}[/tex] = [tex]\frac{-9}{3}[/tex] = -3

The slopes are the same. When the slopes are the same, the lines are parallel.

10)

(-3, -7) (3,-3)

[tex]\frac{-3 - -7}{3 - -3}[/tex] = [tex]\frac{-3 + 7}{3 + 3}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]

(0,4) (6,-5)

[tex]\frac{-5 -4}{6 - 0}[/tex] = [tex]\frac{-9}{6}[/tex] = [tex]\frac{-3}{2}[/tex]

The slope are opposite reciprocals of each other so they are perpendicular.