A kangaroo leaps a total distance of 3 feet with a maximum height of 1 foot. another kangaroo is originally 5 feet in front of the first kangaroo and jumps the same distance, but 6 inches higher. write the equation representing the path of each kangaroo.
a. kangaroo 1: y=-(x-3)^2+1 ; kangaroo 2: y=-(x-5)^2+1.5
b. kangaroo 1: y=-(x-1.5)^2+1 ; kangaroo 2: y=-(x-6.5)^2+1.5
c. kangaroo 1: y=-4/9(x-3)^2+1 ; kangaroo 2: y=-2/3(x-5)^2+1.5
d. kangaroo 1: y=-4/9(x-1.5)^2+1 ; kangaroo 2: y=-2/3(x-6.5)^2+1.5

The polynomial with roots 4, 2i, and −2i is f(x)= x^3-4x^2+4x-16, which can be found by using the factor theorem.

c. f(x)= x^3-4x^2+4x-16

The polynomial with the given roots is a cubic polynomial. To get the coefficients of the polynomial, we can use the factor theorem. The factor theorem states that if a polynomial has a factor (x - a), then a is a root of the polynomial.

Therefore, the polynomial with roots 4, 2i, and -2i is f(x) = (x - 4)(x - 2i)(x +2i)

Expanding this polynomial, we get f(x) = x^3-4x^2+4x-16

The polynomial with roots 4, 2i, and −2i is f(x)= x^3-4x^2+4x-16, which can be found by using the factor theorem.

Learn more about polynomial here

https://brainly.com/question/11536910

#SPJ4

The Sine Ratio is written as [tex]\frac{Perpendicular }{Hypoynuse}[/tex] , then the maximum possible value of a Sine Ratio is 1 .

What is Sine Ratio ?

In a Right Triangle , the Sine of angle is defined as the ratio of length of the opposite side divided by the length of the hypotenuse .

we know that the domain for the Sine function is ⇒ all real numbers ;

and the range of Sine function is ⇒  [-1,1] ;

so , from the range we can conclude that , the maximum value is 1 .

Therefore , the maximum value of Sine ratio is = 1 .

Learn more about Sine Ratio here

https://brainly.com/question/30132088

#SPJ4

Therefore , the solution to the given problem of number line comes out to be option 2 543 is correct.

An introduction to mathematics tool is the number line, which is a visual integer depiction of real numbers. It is a representation of an intensity line. Each actual figure is taken to symbolize a point on the real number, or each precise figure is taken to symbolize a position. On a number line, distances between increments are equal. A line's numbers can only be answered in the way that is specified by those numbers. The question that corresponds with the number will define how it is used. B: Speak your mind.

Here,

Given :

Number are as follows : 221 ,543,28492 and 92349

Thus,

To find that the number is divisible by 3 but not 9.

So , as we know that sum of individual number of that number is divisible by 3 .

Then thw hole number is divisible by 3 .

So , we see 543 is divisible by 3 but not 9 .

Therefore , the solution to the given problem of number line comes out to be option 2 543 is correct.

To know more about number line visit:

https://brainly.com/question/13425491

#SPJ4

a number is  divisible by 3 if the sum of its digits is divisible by 3.

a number is  divisible by 9 if the sum of its digits is divisible by 3.

the  number  divisible by 3 but not by 9 is 543,  

The equation that represent the relationship between pounds of garbage y and of days x is y = 4.5x

Direct variation describes a simple relationship between two variables . We say y varies directly with x , then y=kx. for some constant k , called the constant of variation or constant of proportionality .

From the graph when y = 4.5 , x = 1 and when y = 9 , x = 2. we can take any of these values to find K

y = kx

9 = 2k

therefore K = 9/2 = 4.5

representing K for 4.5 in y = kx

then, y = 4.5x

therefore the equation of the relationship between y and x is y = 4.5x

learn more about variation from

https://brainly.com/question/6499629

#SPJ1

Amy will earn $28.70 + $3.80 = $32.50.

Profit and loss:

A profit and loss (P&L) statement refers to a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a quarter or fiscal year. These records provide information about a company’s ability or inability to generate profit by increasing revenue, reducing costs, or both. P&L statements are often presented on a cash or accrual basis. Company managers and investors use P&L statements to analyze the financial health of a company.

Amy will earn $28.70 from selling 7 large necklaces (7 x $4.10 = $28.70) and $3.80 from selling 1 small necklace, so in total, she will earn $28.70 + $3.80 = $32.50.

To learn more about profit and loss, refer to the link:brainly.com/question/29494194

#SPJ4

Answer:

20° , 40° , 120°

Step-by-step explanation:

sum the parts of the ratio, 1 + 2 + 6 = 9 parts

divide the sum of the angles in a Δ , 180° by 9 to find the value of one part of the ratio.

180° ÷ 9 = 20° ← value of 1 part of the ratio, then

2 parts = 2 × 20° = 40°

6 parts = 6 × 20° = 120°

the 3 angles are 20° , 40° and 120°

The sine function that intersects its midline at (0,-6) and then has a minimum point at (2.5,-9) is given as follows:

y = 3sin(0.6πx) - 6.

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

For which the parameters are given as follows:

The midline is at y = -6, while the minimum point is at y = -9, hence the amplitude of the function is given as follows:

A = -6 - (-9)

A = 3.

A sinusoidal function with amplitude 3 should oscillate between -3 and 3, while it oscillates between -3 and -9, hence the vertical shift is given as follows:

C = -6.

The distance from the midline to the minimum value is of 3/4 of the period, hence the period is of:

3/4P = 2.5

P = 4 x 2.5/3

P = 10/3.

This means that the parameter b is obtained as follows:

2π/B = 10/3

10B = 6π

B = 0.6π

This means that the function is defined as follows:

y = 3sin(0.6πx) - 6.

The graph of the sinusoidal function is given by the image presented at the end of the answer, and the labeled points show that the desired features are present.

The complete problem is given as follows:

The graph of a sinusoidal function intersects its midline at (0,-6)(0,−6)left parenthesis, 0, comma, minus, 6, right parenthesis and then has a minimum point at (2.5,-9).

A similar problem, also featuring trigonometric functions, is presented at brainly.com/question/21558626

#SPJ1

The number of places you put the lens to form a well-focused image of the candle flame on the wall is either we have to move the screen towards the lens or the lens towards the screen.

Here we have given that the lens to form a well-focused image of the candle flame on the wall.

As we all know that if the candle is further from the wall than the focal length of the lens, then there are two places which will result in an image. Here we have know that one of them is just beyond the focal length from the wall.

Here we have given the other is that same distance from the candle.

Then the position near the wall will yield a small image.

Here the position near the candle will produce a large image.

To know more about image here.

https://brainly.com/question/14322187

#SPJ4

Answer:

If the truck's value dropped 15% each year, after one year the value of the truck is 22000*(1-0.15) = $18700

After the second year, the value of the truck would be 18700*(1-0.15) = $15995

After the third year, the value of the truck would be 15995*(1-0.15) = $13596.75

Rounding the answer to the nearest dollar, the value of the truck after 3 years is $13597

Step-by-step explanation:

now you should be able to dive these things yourself.

A no

(1/4)v = 4

4×(1/4)v = 4×4

v = 16

this is not v = 4

B no

n + 4 = 25

n + 4 - 4 = 25 - 4

n = 21

this is not n = 17

C yes

2z = 28

2z/2 = 28/2

z = 14

The measurement of side AC in the given right triangle is 10.12 units.

A triangle having at least one angle measuring 90° is called a right triangle.

Given that, a triangle ABC, right-angled at A,

AB = 15 and BC = 18.1, we need to find AC,

Please refer to the figure attached,

Using Pythagoras theorem,

BC² = AB² + AC²

AC² = BC² - AB²

AC² = (18.1)² - 15²

AC² = 327.61 - 225

AC² = 102.61

AC = 10.12

Hence, the value of AC = 10.12

Learn more about right triangles, click;

https://brainly.com/question/4364353

#SPJ1

The approximate measure of angle JGH is 70.5°.

According to this question, we have a right triangle in which lengths of its hypotenuse (GH), in centimeters, and one leg (JH) are known and we must determine the measure of an angle (∠JGH), in degrees. A representation of this triangle is included in the image attached below.

By trigonometry we have the following expression for the required angle:

cos∠GJH = HJ/GH               .......(1)

Given, HJ = 2, GH = 6

cos∠GJH = 2/6

     ∠GJH = [tex]cos^{-1}\frac{2}{6}[/tex]

                ≈ 70.529

The approximate measure of angle JGH is 70.5°.

To learn more about angle here:

https://brainly.com/question/28451077

#SPJ4

We have to pay $129,216.31; $64,800.

Option (c) is correct.

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. It is the interest on interest, and it is the mechanism that causes an investment to grow at an exponential rate.

To calculate the amount of money you will have in the investment plan after 18 years, we can use the formula for compound interest:

A = P(1 + r)^n

Where:

A is the final amount (the future value)

P is the principal, or the initial deposit, in this case $300

r is the annual interest rate, in this case 7% (expressed as 0.07)

n is the number of years, in this case 18

m is the number of times the interest is compounded per year. in this case 12 (monthly)

By using this formula, the final amount will be:

A = 300(1 + 0.07/12)^(12*18)

A = $129,218.51

To compare this amount to the total deposits made over the time period, we can calculate the total amount of money deposited by multiplying the deposit amount ($300) by the number of deposits made per month (12) by the number of years (18).

Total deposit = 3001218 = $64,800

Hence, we have to pay $129,216.31; $64,800.

Option (c) is correct.

To learn more about compound interest visit:

https://brainly.com/question/22621039

#SPJ4

The vertex form of the parabolae equations are, respectively:

Parabolae are described by quadratic equations, whose standard and factor form are shown below:

Standard form

y = a · x² + b · x + c

Factor form

y = a · (x - r₁) · (x - r₂)

Where:

This equation can be modified into vertex form:

y - k = C · (x - h)²

Where:

The complete procedure to find vertex form is described below:

Now we proceed to find the vertex form of each expression:

Case 1

y = x² - 6 · x - 27

y = (x² - 6 · x + 9) - 36

y + 36 = (x - 3)²

Case 2

y = x² - 2 · x + 7

y = (x² - 2 · x + 4) + 3

y = (x - 2)² + 3

y - 3 = (x - 2)²

Case 3

y = x² + 10 · x

y + 25 = x² + 10 · x + 25

y + 25 = (x + 5)²

Case 4

y = x² + 14 · x + 50

y = (x² + 14 · x + 49) + 1

y = (x + 7)² + 1

y - 1 = (x + 7)²

Case 5

y = x² - 3 · x

y + 9 / 4 = x² - 3 · x + 9 / 4

y + 9 / 4 = (x - 3 / 2)²

Case 6

y = x² - 5 · x + 8

y = (x² - 5 · x + 25 / 4) + 7 / 4

y - 7 / 4 = (x - 5 / 2)²

Case 7

y = 2 · x² + 8 · x

y = 2 · (x² + 4 · x)

y + 2 · 4 = 2 · (x² + 4 · x + 4)

y + 8 = 2 · (x + 2)²

Case 8

y = 3 · x² + 6 · x + 10

y = 3 · (x² + 2 · x + 10 / 3)

y = 3 · (x² + 2 · x + 1) + 7

y - 7 = 3 · (x + 1)²

Case 9

y = 5 · x² + 40 · x - 6

y = 5 · (x² + 8 · x - 6 / 5)

y + 5 · 16 = 5 · (x² + 8 · x + 16) - 6

y + 86 = 5 · (x + 4)²

Case 10

y = (x + 5) · (x - 9)

y = x² - 4 · x - 45

y + 4 = (x² - 4 · x + 4) - 45

y + 49 = (x - 2)²

Case 11

y = (x - 4) · (x + 10)

y = x² + 6 · x - 40

y + 9 = (x² + 6 · x + 9) - 40

y + 49 = (x + 3)²

Case 12

y = (x + 2) · (x + 10)

y = x² + 12 · x + 20

y + 16 = x² + 12 · x + 36

y + 16 = (x + 6)²

Case 13

y = (x - 2) · (x - 6)

y = x² - 8 · x + 12

y + 4 = x² - 8 · x + 16

y + 4 = (x + 4)²

Case 14

y = (x + 1) · (x + 4)

y = x² + 5 · x + 4

y + 9 / 4 = x² + 5 · x + 25 / 4

y + 9 / 4 = (x + 5 / 2)²

Case 15

y = (x + 4) · (x - 5)

y = x² - x - 20

y + 1 / 4 = (x² - x + 1 / 4) - 20

y + 81 / 4 = (x - 1 / 2)²  

Case 16

y = 2 · (x + 2) · (x + 4)

y = 2 · (x² + 6 · x + 8)

y + 2 · 1 = 2 · (x² + 6 · x + 9)

y + 2 = 2 · (x + 3)²

Case 17

y = x · (x + 6)

y = x² + 6 · x

y + 9 = x² + 6 · x + 9

y + 9 = (x + 3)²

Case 18

y = 3 · (x + 4) · (x - 8)

y = 3 · (x² - 4 · x - 32)

y + 3 · 4 = 3 · (x² - 4 · x + 4) - 3 · 32

y + 12 = 3 · (x - 2)² - 96

y + 108 = 3 · (x - 2)²

To learn more on parabolae: https://brainly.com/question/21685473

#SPJ1

By using the given relationship the values of k are 2.5 , 2.5,2.5,2.5 respectively.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given,

table shows the relation y = kx .

so the given x values = 2,3,5,8 .

and the y values = 5,7.5,12.5,20

From the relation y = kx .

By substituting the given values

we get,

y = kx

y=5 x = 2

5 = k * 2

k = 2.5

y=7.5 x = 3

7.5 = k*3

k = 7.5/3

k = 2.5

y = 12.5 x = 5

12.5 = 5*k

k= 12.5 / 5

k = 2.5

y=20 x = 8

20 = k*8

k = 20/8

k = 5/2

k = 2.5

Hence, By using the given relationship the values of k are 2.5 , 2.5,2.5,2.5 respectively.

To learn more about Algebraic expression from the given link.

https://brainly.com/question/953809

#SPJ1

If the business owner wanted to make the case that the workers are paid well, she would use the range of central tendency.

The range, D

You are undoubtedly most familiar with the mean, which is the arithmetic average and a measure of central tendency. It is extremely easy to calculate the mean. Simple addition and division by the dataset's observation count are all that are required to calculate the values. All data values are included in the mean calculation.

Finding a variable's maximum observed value (also known as the range) and deducting its least observed value will yield the range (the minimum).

To know more about  central tendency visit:

https://brainly.com/question/30218735

#SPJ4

The word "and" in probability implies that we use the Multiplication rule.

The correct option is Option D.

The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.

The relationship between two events is explained by the probability multiplication rule.

Set A∩B represents the events in which both events A and B have occurred for two events A and B related to a sample space S. Consequently, (A∩B) indicates that occurrences A and B happened at the same time. You can write the event A∩B as AB. Using the characteristics of conditional probability, the likelihood of event AB is calculated.

To learn more about Probability visit:

https://brainly.com/question/29564879

#SPJ4

Answer:

x (number of games) = 8

Step-by-step explanation:

We want these two to be equal, which means we want:

4.50x + 5 = 4.75x + 3

We will minus 4.50x and 3 from both sides, giving us:

2 = .25x

Then, multiply by 4 to get a whole number of x, which gives us:

x = 8

Now, we will check our answer. We have:

4.50 * 8 + 5 = 4.75 * 8 + 3

36 + 5 = 38 + 3

41 = 41

So this proves x = 8.

So, the amount of games where the price would be the same is 8, x = 8.

Hope this helped!

Answer:

Step-by-step explanation:

Answer: The answer is 0.25 inches every minute

Step-by-step explanation: The equation tells you that the pool started at 30 inches (0.25t+30). It says that the pool's depth rises 0.25 inches every minute. So the answer is that the pool started out as 30 inches (which is the y-intercept) and rose 0.25 inches every minute.

Hope this helped

A T-score of -3.6 indicates that the individual has a severe case of osteoporosis

A T-score is a standard score used to compare an individual's bone mineral density (BMD) to that of a healthy young adult population. A T-score of -3.6 on a BMD test indicates that the individual's BMD is significantly lower than that of a healthy young adult. Specifically, it means that the individual's BMD is 3.6 standard deviations below the average BMD of a healthy young adult.

A T-score of -2.5 or lower is considered to indicate osteoporosis, which is a condition characterized by low bone density and an increased risk of fractures. Therefore, a T-score of -3.6 indicates that the individual has a severe case of osteoporosis, and the doctor will likely recommend treatment such as medication and lifestyle changes to help increase bone density and reduce the risk of fractures.

Learn more about bone mineral density (BMD) here: brainly.com/question/29056984

#SPJ4

5-card hands have at least one club  2023203

5-card hands have at least two cards with the same rank 916,272

N[at least one club] = N[total ways] - N'[at least one club]

                               = N[total ways] - N[no clubs]

There are 39 cards without a club. So there are 39 choose 5 = 575757 ways to not get a club.

There are 2598960 possible hands, leaving us with 2598960-575757 ways.

Which is 2023203 hands.

How many 5 card hands will have (at least) two of the same number?

This is a standard deck. Take 2–10 to be what I mean by numbers.

N=∑k=24(91)(4k)⋅(125−k)(41)5−k+[(92)+(91)(41)](42)2⋅(111)(41)

+(91)(42)⋅(121)(43)+(91)(43)⋅(41)(42)

=(760,320+38,016+432)+114,048+2,592+864

=916,272

A standard deck of playing cards contains 13 unique ranks, each with 4 distinct suits. Since we are interested in only pairs from ranks 2 to 10, we shall define A be the collection of the 9 relevant ranks and B be the collection of the 4 ranks (ace, jack, queen, king) where pairs are not a consideration. Collection C is the union of A and B, which contains all 13 ranks.

When computing probabilities we need to select the ranks(s) from a collection and then choose a number of suits (cards). When ranks are chosen from either A or B they are also chosen from C. This is important since we might choose twice from the same collection. For example, we might choose a rank from A for a pair (9 choose 1) and later choose 3 ranks from C for singletons (12 choose 3).

To hopefully make understanding the logic easier, I have first chosen the ranks either from A, B, or C, and immediately following I have chosen the number of cards, which is always choosing from 4 suits. I have inserted a dot between different card selections.

We begin by computing the number of combinations with exactly 2, 3, and 4 of a kind from A. The singletons come from C.

N1=∑k=24(91)(4k)⋅(125−k)(41)5−k=760,320+38,016+432=798,768

We add the case of either two pairs from A or a pair from each of A and B. The singleton comes from C.

N2=[(92)+(91)(41)](42)2⋅(111)(41)=114,048

We add the case of a pair from A and 3 of a kind from C.

N3=(91)(42)⋅(121)(43)=2,592

Finally, we add the case of 3 of a kind from A and a pair from B. Note that the case of both 3 of a kind and a pair from A is the same as the case of both a pair and 3 of a kind from A, which has already been included.

N4=(91)(43)⋅(41)(42)=864

N=N1+N2+N3+N4=916,272

5-card hands have at least one club  2023203

5-card hands have at least two cards with the same rank 916,272

To know more about probability visit brainly.com/question/30034780

#SPJ4

The provided statement indicates that the regression line's equation is[tex]\hat{Y}[/tex] =  -0.06392X + 3.42231. Hence the formula for predicting the anticipated sepal size of a floral with panicle length 6.39 is [tex]\hat{Y}[/tex] = 3.01

More specifically, the nature and degree of the correlation between a variable y and a number of different independent variables are assessed using linear regression. It aids in the creation of models for making predictions, such as projecting the stock price of a corporation.

Let X represent the sepal's length, and Y represent its breadth. Next, we have the information below:

Cov (X, Y) = -0.0438254

[tex]$$\begin{aligned}& \bar{Y}=3.04966 \\& \sigma_Y=0.445429 \\& \bar{X}=5.829932 \\& \sigma_X=0.828054\end{aligned}$$[/tex]

The following provides the least squares estimates of the intercept and regression coefficient:

[tex]\hat{\beta_0}=\bar{Y}-\hat{\beta_1} \bar{X}[/tex]

[tex]$\hat{\beta_1}$[/tex] = Cov (X, Y)/[tex]$\sigma_X^2$[/tex]

[tex]\begin{aligned}& \hat{\beta}_1=\frac{-0.0438254}{0.828054^2} \\& \hat{\beta}_1=-0.06392\end{aligned}[/tex]

and,

[tex]$$\begin{aligned}& \hat{\beta_0}=3.04966-(-0.06392) *(5.829932) \\& \Rightarrow \hat{\beta}_0=3.42231\end{aligned}$$[/tex]

Thus, the regression line's equation is as follows:

[tex]\hat{Y}[/tex] =  -0.06392X + 3.42231

With a sepal length of 6.39, the following formula predicts the sepal breadth of a flower:

[tex]$$\begin{aligned}\hat{Y} & =-0.06392 * 6.39+3.42231 \\\Rightarrow \hat{Y} & =3.0138612 \simeq 3.01\end{aligned}$$[/tex]

To know more about Linear regression visit:

https://brainly.com/question/25987747

#SPJ4

The complete question is-

The famous iris dataset (the first sheet of the spreadsheet linked above) Was first published in 1936 by Ronald Fisher. The dataset contains 50 samples from 3 iris species. setosa, virgiria, and versicolor. Four features are measured, all in cm sepal length, sepal with, petal length, and petal width.

What is the equation tor the least,square regressian line where the independen; or predictor variabie is pelat Iength and the dependent of response variable is petal width for iris versicolar?

What is the predicted petal width for iris versicolor for a flower with a pelal length of 4.1?

Answer: It takes 3 years

Step-by-step explanation:

20 percent of 1000 is 200 so 1000-200=800.  Year 1

20 percent of 800 is 160 so 800-160=640.       Year 2

20 percent of 640 is 128 so 640-128=512.         Year 3

So in total in takes 3 years

Answer:

See photo

Step-by-step explanation:

Edmentum/Plato

[tex]\angle 3[/tex] and [tex]\angle 6[/tex]

Using the equation, the restaurant owner can determine how long it will take before the high-water mark is less than 30 cm from the base of the walkway. In this case, the answer is 40 years.

1. Subtract the desired end point from the current height of the walkway:

50 cm - 30 cm

= 20 cm

2. Divide the difference by the rate of submergence:

20 cm / 0.5 cm/yr

= 40 years

The restaurant owner can use the equation to calculate the number of years it will take for the high-water mark to be less than 30 cm from the base of the pier’s walkway. By subtracting the desired end point from the current height of the walkway, the owner can determine the difference in height. Then, by dividing this difference by the rate of submergence, the owner can calculate the number of years it will take before it is necessary to take action to protect the pier from flooding. In this case, the answer is 40 years.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

The proof of the vertical angle theorem as required is explained in the answer below:

What are vertical angles?

Vertical angles are two angles that have the same properties and measure of their angles. Majorly these angles are opposite to each other and formed by the same extended lines.

So that, the required proof of the vertical angle theorem is;

             STATEMENT                                            REASON

1. AC intersect BD at E                                       Given

2. m<AEB m<DEA = 180^o                                 Linear pair theorem

3. m<DEC + m<DEA = m<AEB + m<DEA           Substitution property

4. m<DEC = 180^o - m<BEC                                Subtraction property

5. m<DEC = m<AEB                                             Vertical angle theorem

Therefore it can be deduced in the diagram that;

m<DEC = m<AEB           (vertical angle theorem)

Learn more about the property of vertically opposite angles at https://brainly.com/question/68367

#SPJ1

The interval should be 12 hours and 25 minutes for the two high tides and two low tides.

What is interval ?

An interval refers to the amount of time it takes for a tide to go from high to low or low to high

The reason for two high tides and two low tides each day is due to the gravitational pull of the moon and the sun on Earth's oceans. These gravitational forces cause the water in the oceans to bulge, creating high tides. The gravitational pull of the moon is stronger than that of the sun, so the moon has a greater impact on tides.

The time it takes for the tide to go from high to low and back to high is called the tidal period, which is about 12 hours and 25 minutes. This is not exactly 24 hours because the Earth is also rotating on its axis, so the position of the Moon and the Sun relative to a specific location on the Earth's surface is constantly changing.

So, the interval should be 12 hours and 25 minutes for the two high tides and two low tides.

To learn more about interval visit : brainly.com/question/13708942

#SPJ4

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{3}{4}[/tex] x - 1 ← is in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

• Parallel lines have equal slopes , then

y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the parallel line

to find c substitute (8, 4 ) into the partial equation

4 = [tex]\frac{3}{4}[/tex] (8) + c = 6 + c ( subtract 6 from both sides )

- 2 = c

y = [tex]\frac{3}{4}[/tex] x - 2 ← equation of parallel line

---------------------------------------------------------------

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex] , then

y = - [tex]\frac{4}{3}[/tex] x + c ← is the partial equation of the perpendicular line

to find c substitute (8, 4 ) into the partial equation

4 = - [tex]\frac{4}{3}[/tex] (8) + c = - [tex]\frac{32}{3}[/tex] + c ( add [tex]\frac{32}{3}[/tex] to both sides )

4 + [tex]\frac{32}{3}[/tex] = c , then

c = [tex]\frac{44}{3}[/tex]

y = - [tex]\frac{4}{3}[/tex] x + [tex]\frac{44}{3}[/tex] ← equation of perpendicular line