8.) A line passes through the points (k, 4) and (3, -6). The line is perpendicular to
the graph of 5y + 4x = 8. What is the value of k?

Answers

Answer 1

Answer:

K = 43

Step-by-step explanation:

We'll begin by determining the gradient of the equation 5y + 4x = 8. This can be obtained as follow:

5y + 4x = 8

Rearrange

5y = 8 – 4x

5y = –4x + 8

Comparing 5y = –4x + 8 with y = mx + c, the gradient m is –4

Next, we shall determine the gradient of the line perpendicular to the line with equation 5y = 8 – 4x.

This can be obtained as follow:

For perpendicular lines, their gradient is given by:

m1 × m2 = – 1

With the above formula, we can obtain the gradient of the line as follow:

m1 × m2 = – 1

m1 = –4

–4 × m2 = – 1

Divide both side by –4

m2 = –1/–4

m2 = 1/4

Finally, we shall determine the value of k as follow:

Coordinate => (k, 4) and (3, –6)

x1 coordinate = k

y1 coordinate = 4

x2 coordinate = 3

y2 coordinate = –6

Gradient (m) = 1/4

m = (y2 – y1) / (x2 – x1)

1/4 = (–6 – 4) / (3 – K)

1/4 = –10 /(3 – K)

Cross multiply

3 – K = 4 × –10

3 – K = –40

Collect like terms

– K = – 40 –3

–k = –43

Divide both side by – 1

K = –43/–1

k = 43


Related Questions

which shape is a rectangle?
question 7 on -ready

Answers

Answer:

I’m not sure about I-ready, everyone has different ones but I’ll give you some options.

A rectangle is a quadrilateral

A rectangle is a parallelogram

Unless I-ready is asking bout which SHAPE can be a rectangle then it’s a lot of different options.
A square can be a rectangle

Or a parallelogram with the givens being able to fit in to all the things that defines as a rectangle.

These are the options I can think of but pretty sure theres more. But it’s I-ready so it’s not complicated.

PLEASE !!! HELP QUICKLY !!!


Some credit cards offer a low introductory APR for a set period of time. After the introductory period is over, the APR is increased to a new rate. According to the sample credit card disclosure agreement, after a period of ,_______ the APR will increase to ______.

Blank 1 options (one month, six months, one year)
Blank 2 options (8.99%, 10.99%, 12.99%, 14.99%, 28.99%)

Answers

Answer:

1 Year & 14.99%

Step-by-step explanation:

Identify the steps to find the value of the inverse ( Please show your work thank you) ↓

Identify the steps to find the value of the inverse ( Please show your work thank you)

Answers

The value of the inverse of the equation is this: x³ -3 = y

How to find the inverse of the equation

To find the inverse of the equation follow these steps:

1. Replace H(x) with y.

y = (x + 4)³ - 1

2. Interchange the values of X and Y.

X = (y + 4)³ - 1

3. Find the cube root of both sides

x³ = y + 4  - 1

4. Find the value of y

x³ - 4 + 1 = y

x³ -3 = y

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How to simplify 3/18 it’s a fraction and it’s really hard can someone go step by step how to do it I need it ASAP

Answers

Answer:1/6

Step-by-step explanation: divide both sides by 3 as 3 itself and 18 can be divided by 3

different equation dy÷dx+ytanx=secx​

Answers

Answer:

First, we rearrange the equation to isolate the y-term on one side:

dy/dx + ytanx = secx

Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1

Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1

Integrating both sides with respect to x, we get:  y |secx| = x + C

where C is the constant of integration. Solving for y, we have:

y = (x + C)/|secx|

Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined

Trent needs a total of $320 to buy a new bicycle. He has $35 saved. He earns $15 each week delivering newspapers. How many weeks will Trent have to deliver papers to have enough money to buy the bicycle?

Answers

Answer:

Trend wants to buy a new bicycle which costs 320$.

He has 35$ saved and earns 15$ each week.

After a number of weeks (a), the amount money he has: A = 35 + 15 x a

If Trend has enough money to buy that bicycle, we have the equation:

35 + 15 x a = 320

=> 15 x a = 320 - 35

=> 15 x a = 285

\(a = \frac{285}{15} = 19\)

=> After 19 weeks, Trent will have had enough money to buy that bicycle

Hope this helps!

:)

what is the mean of 61, 55, 66, 58, 50, 70​

Answers

Answer:

Mean: 60

Step-by-step explanation:

First of all, in order to find the mean, one must add all the numbers together (61,55,66,58,50,70), which would give a total of 360.

After that, divide that total by the quantity of numbers (in other words, the total number of numbers, which in this case is 6). So, you would have to divide 360 by 6 leading to an answer of 60(the mean, which in other words is like finding the average).

0.445 to a fraction in simplest form and a percent.

Answers

Answer:

0.445 as a fraction in simplest form: 89/200

0.445 as a percent: 44.5%

Step-by-step explanation:

Pls help me do you know the answer let me know

Pls help me do you know the answer let me know

Answers

Answer:

Are you telling us to answer it all?

Step-by-step explanation:

Answer:

I'm so sorry I have no idea seems so so complicated

Step-by-step explanation:

But I think you would need a specific equation for it and substitute numbers in it.

the product of a number and three, increased by 5, is 32. What is the number?

Answers

Answer:

3n+5=32

Step-by-step explanation:

this is an example of a 2-step equation.

First, subtract the 5,and cross that out on the left side

and do the same to the other side.

Then you have 3n=32 now, so all you have to do is divide by 3 and you have your answer.

n=9

Sal paid (x + 2y) cents for a quart of milk and (2x + y) cents each for three cartons of orange juice. Write and simplify an expression for the total cost of Sal's purchases.

Answers

The expression for the total cost of Sal's purchases is 7x + 5y cents.

We know that Sal paid (x + 2y) cents for a quart of milk and (2x + y) cents each for three cartons of orange juice.To find the total cost of Sal's purchases we need to add the cost of the milk and the cost of the three cartons of orange juice and simplify the expression.The cost of the milk is given as (x + 2y) cents. The cost of three cartons of orange juice is (2x + y) cents each.

Therefore, the cost of three cartons of orange juice is (3 × (2x + y)) cents. To find the total cost of Sal's purchases, we add the cost of the milk and the cost of the three cartons of orange juice.(x + 2y) + (3 × (2x + y)) cents = x + 2y + 6x + 3y cents= 7x + 5y cents.

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4n^2-22=27 please show work

Answers

Answer:

n = 7/2

Step-by-step explanation:

4n^2-22=27

4n^2 = 27 + 22

4n^2/4 = 49/4

sqrtn^2 = sqrt(49/4)

n = 7/2

The function g(x)= 12,500(0.91)x represents the value of a piece of farm equipment after x years

Answers

so you would multiply the number of years by 0.91 and then times 12,500

which of the following is a Quadrilateral which must contain diagonals that are always congruent and must always have 90° angles?

which of the following is a Quadrilateral which must contain diagonals that are always congruent and

Answers

Answer: B

Step-by-step explanation:

Two regular six-sided dice are tossed. Compute the probability that the sum of the pips on the upward faces of the two dice is the following. at most 6

Answers

Answer:

For 6 it is 5/36.

Step-by-step explanation:

Answer: 5/12

Step-by-step explanation:

It is actually 5/12

Sam is 6 ft man and the length of his shadow is 4 feet. Find the height of the building casting a shadow of 100 feet.

Answers

the height of the building is approximately 150 feet.by forming equation by given data in question we can get answer

what is  approximately  ?

Approximately means close to or nearly, but not exactly. It is used to indicate that a value or number is an estimation or approximation, rather than an exact value. It is often used when a precise value is not necessary or when the exact value is unknown or difficult to determine.

In the given question,

We can solve this problem by using the concept of similar triangles. Similar triangles are triangles that have the same shape but different sizes, and their corresponding angles are equal. The ratio of the lengths of the corresponding sides of similar triangles is constant.

In the diagram, the height of the building is represented by "h", and the length of its shadow is represented by "D". Let's assume that the distance between the building and Sam is represented by "d".

Since Sam is 6 feet tall and his shadow is 4 feet long, we can set up a proportion:

h / d = 6 / 4

We can simplify this by multiplying both sides by 4:

h = (6/4) * d

h = 1.5d

Now, let's consider the larger triangle formed by the building, its shadow, and the sun's rays. This triangle is similar to the smaller triangle formed by Sam, his shadow, and the sun's rays. Therefore, we can set up the following proportion:

h / D = Sam's height / Sam's shadow length

Substituting the values we know:

h / 100 = 6 / 4

Simplifying:

h = (6/4) * 100

h = 150

Therefore, the height of the building is approximately 150 feet.

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Simplify
56
to lowest terms.
64

Answers

Answer:

7/8 is the simplified fraction for 56/64 by using the GCD or HCF method. Thus, 7/8 is the simplified fraction for 56/64 by using the prime factorization method.

Step-by-step explanation:

This is homework assignment it’s statistics class thank you for your time

This is homework assignment its statistics class thank you for your time

Answers

The best fit line given is:

P= -0.79t+20.95

P is the profit or loss

t is the time in years after 1965.

So, 1980-1965 = 15 => t=15

P= -0.79*15 +20.95

P= -11.85 + 20.95

P= 9,1

$9,1 thousands of dollars

I need help with this math sheet

Answers

Something wrong with the image? I can't see sheet

15 people working 5 hourse per day can make 30 units of a product in 10 days. Assuming all other factors remaining constant and people of same efficiency are used to make the same products, in how many days can 10 people make 10 units of the product if each of them works 10 hours per day?

- 2.5 days
- 7.5 days
- 12 days
- 26 days

Answers

Answer:

2.5 days

Step-by-step explanation:

To solve this problem, we can use the concept of work rate. The work rate is defined as the amount of work done per unit of time.

Given:

15 people working 5 hours per day can make 30 units of the product in 10 days.

From this information, we can calculate the work rate of these 15 people:

Work rate = Total units of the product / (Number of people × Number of hours × Number of days)

Work rate = 30 units / (15 people × 5 hours × 10 days)

Work rate = 0.04 units per person per hour

Now, we need to find how many days it will take for 10 people, working 10 hours per day, to make 10 units of the product.

Using the work rate formula:

Number of days = Total units of the product / (Number of people × Number of hours × Work rate)

Number of days = 10 units / (10 people × 10 hours × 0.04 units per person per hour)

Number of days = 2.5 days

Therefore, 10 people, working 10 hours per day, can make 10 units of the product in 2.5 days.

The correct answer is:

2.5 days

Solve for the Value of R

Answers

Answer:

whats the question

Compare the investment below to an investment of the same principal at the same rate compounded annually.
principal: $5,000, annual interest: 9%, interest periods: 4, number of years: 18
After 18 years, the investment compounded periodically will be worth $? more than the investment compounded annually.
(Round to two decimal places as needed.)

Answers

After 18 years, the investment compounded periodically (quarterly) will be worth $1,230.23 more than the investment compounded annually.

What is compounded interest?

Compounded interest refers to the interest system that charges interest on both principal and accumulated interest.

The period of compounding in a year determines the worth of the future value.

The future value can be ascertained using an online finance calculator as follows:

Interest periods: = 4 times yearly (Quarterly)

Principal = $5,000

Annual interest rate = 9%

Number of years: 18

N (# of periods) = 72 quarters (18 years x 4)

I/Y (Interest per year) = 9%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $24,815.83

Total Interest = $19,815.83

Interest periods: = Annually

N (# of periods) = 18 years

I/Y (Interest per year) = 9%

PV (Present Value) = $5,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $23,585.60

Total Interest = $18,585.60

Difference in Future Values $1,230.23 ($24,815.83 - $23,585.60)

Thus, an investment compounded periodically earns more than an investment compounded annually.

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F(x) = 3x + 2
What is f(5)

Answers

Step-by-step explanation:

to find f(5)   in f(x) , just put in '5' where 'x' is in the equation

f(5) = 3 (5) + 2 = 17

Answer:

f(5) = 17

Step-by-step explanation:

Let's evaluate the function for f(5)

\(\rm{f(x)=3x+2}\)

Insert 5 everywhere x appears:

\(\rm{f(5)=3(5)+2}\)\(\rm{f(5)=15+2}\)\(\rm{f(5)=17}\)

Therefore f(5) = 17

Mia took a taxi from her house to the airport. The taxi company charged a pick-up fee of $1.30 plus $4.25 per mile. The total fare was $31.05, not including the tip. How many miles was the taxi ride?

Answers

The taxi ride was 7 miles

How to calculate the number of miles ?

Mia took a taxi from her house to the airport

The taxi charged a pick up fee of $1.30

They also charged $4.25 per mile

The total fare was $31.05

The number of miles can be calculated as follows

31.05 - 1.30 = 4.25x

29.75= 4.25x

Divide both sides by the coefficient of x which is 4.25

29.75/4.25= 4.25x/4.25

x= 7

Hence the taxi ride was 7 miles

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There are two similar triangles on the graph below use the graph to answer the questions you must answer each question and explain how you found it HELP PLEASE

There are two similar triangles on the graph below use the graph to answer the questions you must answer

Answers

Answer:

we can use similarity of triangles in this case there will be formation of 2 pairs of equal (eg:-angle formed by the y- axis on the parallel lines) angles between triangles formed as the y- axis lines are parallel. So,slope of the graph between points A and B is the same as the slope of the graph between points A and B.

Step-by-step explanation:

.
91,375 ÷ 10 power of 5
9.1375
913.75
91.375
0.91375

Answers

Answer:

I'm not sure the right equation to used for this problem. can someone help me please.

Please solve this
∫ (log(1 + x ^ 2))/((x + 1) ^ 2) dx

Answers

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Need help on finding g .

Need help on finding g .

Answers

The numeric values for this problem are given as follows:

g(-1) = -2.g(2) = 0.g(3) = 0.5.

How to obtain the numeric values of the function?

The function in this problem is a piecewise function, meaning that it has different definitions based on the input x of the function.

For x between -2 and 2, the function is defined as follows:

g(x) = -(x - 1)² + 2.

Hence the numeric value at x = -1 is given as follows:

g(-1) = -(-1 - 1)² + 2 = -4 + 2 = -2.

For x at x = 2 and greater, the function is given as follows:

g(x) = 0.5x - 1.

Hence the numeric values at x = 2 and x = 3 are given as follows:

g(2) = 0.5(2) - 1 = 0.g(3) = 0.5(3) - 1 = 0.5.

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I need to do this class soon, please help me

I need to do this class soon, please help me

Answers

Answer:

Step-by-step explanation:

18. x + 25 = 55

     x = 30

19. 2x - 5 = 95

     2x = 100

      x = 50

20. 3x - 22 = 2x + 26

     x - 22 = 26

     x = 48

21. 3x - 18 + 105 = 180

    3x + 87 = 180

    3x = 93

      x = 31

22. 19x + 17x = 180

      36x = 180

       x = 5

   27(5) = 135

23. 5x + 40 + 2x = 180

7x + 40 = 140

7x = 140

x = 20

5(20) = 100

2(20) = 40

5(20) + 40 = 100 + 40 = 140

Matt has two very active dogs named Theia and Odin who need to eat extra snacks to increase
their caloric intake. He uses math to figure out how much more to feed them. He tracks their
activity level to determine the increase.
The table below shows the number of treats per dog per week.
What is the average rate of change for the number of treats that Odin gets each week between
Week 1 and Week 5?
Week 2
Week 3
Week 5
Odin
Theia
Week 1
7
5
3
2.
00 00
Week 4
9
7
4
5
Week 6
5
6

Matt has two very active dogs named Theia and Odin who need to eat extra snacks to increasetheir caloric

Answers

Answer:

Step-by-step explanation:

That is cheating no help for you sorry

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