How do I write the equations of lines through the given point parallel to the given line and perpendicular to the given line?

Answers

Answer 1

Answer: first we find the slope of the original equation
4x - 2y = 3
-2y = -4x + 3
y = -4/-2x - 3/2
y = 2x - 3/2......slope here is 2

for a parallel line, we use the same slope
y = mx + b
slope(m) = 2
(2,1)...x = 2 and y = 1
now we sub and find b, the y int
1 = 2(2) + b
1 = 4 + b
1 - 4 = b
-3 = b
so ur parallel equation is : y = 2x - 3

for a perpendicular slope, we need the negative reciprocal. All that means is flip the slope and change the sign. So we have a slope of 2...the negative reciprocal we need is -1/2
y = mx + b
slope(m) = -1/2
(2,1)...x = 2 and y = 1
now we sub again
1 = -1/2(2) + b
1 = -1 + b
1 + 1 = b
2 = b
ur perpendicular line is : y = -1/2x + 2
=========================
x + 4 = 0
x = -4....this is a vertical line with an undefined slope....sorry but I am not sure about this one

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0.06 or 0.06666666666 As a fraction

Answers

0.06 = 6/100
When simplified, that's 3/50 .

0.06666666666 = 6,666,666,666/10,000,000,000
When simplified, that's 3,333,333,333/5,000,000,000 .

1. Elena bought 320 tropical fish for a museum display. She bought 7 times as many triggerfish as parrotfish. How many of each type of fish did she buy?Which is a system of equations to model the problem if x represents the number of parrotfish Elena bought and y represents the number of triggerfish she bought?

A. x + 7y = 320
y = 7x

B. x + y = 7
y = 320x

C. x + y = 320
y = 7x

D. x−y=320
y = 7x

2. Nancy bought 360 tropical fish for a museum display. She bought 8 times as many goldfish as angelfish.

How many of each type of fish did she buy?

A. 40 angelfish, 320 goldfish

B. 160 angelfish, 200 goldfish

C. 20 angelfish, 160 goldfish

D. 320 angelfish, 40 goldfish

3. Michael and Kathryn bowl together and their combined total score for one game was 425 points. Michael’s score was 70 less than twice Kathryn’s. What were their scores?

Which is a system of equations to model the problem if x represents Kathryn’s score and y represents Michael’s score?

A. x + y = 70
y = 2x – 425

B. x + y = 425
y = 2x – 70

C. x – y = 425
y = 2x – 70

D. x + y = 425
y = 2x + 70

4. Michael and Kathryn bowl together and their combined total score for one game was 425 points. Michael’s score was 70 less than twice Kathryn’s.

What were their scores?

A. Kathryn: 260, Michael: 165

B. Kathryn: 150, Michael: 275

C. Kathryn: 275, Michael: 150

D. Kathryn: 165, Michael: 260

5. A collection of nickels and dimes is worth $6.10. There are 67 coins in all.

How many nickels are there?

A. 12

B. 18

C. 49

D. 55

Answers

Answer:

Step-by-step explanation:

If im wrong, please correct me in the comments.

Answer:

5. D, Let d represent the number of dimes and n represent the number of nickel. We have been given that a collection of coins has 67 coins in all. This means that total number of nickels and dimes is 67. We can represent this information in an equation as:

Since we know that a dime is worth $0.10, so d dimes will be worth 0.10d.

A nickel is worth $0.05, so n nickels will be worth 0.05n. We are also told that the collection is worth $6.10. We can represent this information in an equation as:

We will use substitution method to solve system of linear equations. From equation (1) we will get, upon substituting in equation (2) we will get, Let us divide both sides of our equation by .

A diagram of a hockey rink is shown below. The diameter of the middle circle is 30 Feet. What is the area of the middle circle? Use 3.4 for

Answers

The formula of the area of the circle is
Area = pi * (d/2)^2

So using the formula,
Area = 3.14 * (30/2)^2
Area = 3.14 * 15^2
Area = 706.5 ft^2

So the area of the hockey rink is 706.5 ft^2

HELP
If m∠ABC = 72°, what is m∠DAB?

Answers

Value of ∠DAB is 108°

Intersection of Parallel lines:

Given that;

∠ABC = 72°

Find:

Value of ∠DAB

Computation:

We know that Line AD is parallel to line CB

So,

∠ABC + ∠DAB = 180°

72° + ∠DAB = 180°

∠DAB = 108°

Find out more information about 'Parallel line'

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Answer: m∠DAB=72

Step-by-step explanation:

Since we have given that

∠ABC = 72°

Since the lines AD and BC are parallel to each other,

As we know that when the two parallel lines cut by a transversal then the corresponding angles will be formed.

And the corresponding angles will be equal.

So, m∠ABC =m∠DAB=72°

Hence, m∠DAB=72°

A law firm charges $100 per hour for the first 3 hours plus a $300 organization fee for its services. show work.

Answers

I believe it would be 100 * 3 + 300 = 600. But there isn't too much information to understand what you're asking.
Hope I helped anyways! :)

Which is a recursive formula for the sequence 99.4, 0, –99.4, –198.8, where f(1) = 99.4?

Answers

f(x)= -99.4x + 198.8

f(1) = -99.4*1 + 198.8 = 99.4

f(2) = -99.4*2 + 198.8 = 0

f(3) = -99.4*3 + 198.8 = -99.4

f(4) = -99.4*4 + 198.8 = -198.8

Answer:

Which is a recursive formula for the sequence 99.4, 0, –99.4, –198.8, where f(1) = 99.4?

The answer will be : f(n + 1) = f(n) – 99.4, n ≥ 1