Determine the constant of variation for the direct variation given.R varies directly with S. When S is 16, R is 80.
1/5
5
16

Answers

Answer 1

Answer:

Answer:

The constant of variation is k=5

Step-by-step explanation:

Proportions

A direct proportion is a relation between variables where their ratio is a constant value. This means that if y and x are proportional, then:

$y=k\cdot x$

Where k is the constant of proportionality.

We know R varies directly with S. Their relationship is:

$R=k\cdot S$

We also have when S=16, R=80. Thus:

$80=k\cdot 16$

Solving for k:

$k=80/16=5$

The constant of variation is k=5

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Completing Proofs Involving Linear PairsGiven: m ZELG = 124°

Prove: x = 28

Statements

Reasons

1. m ZELG = 124

1. given

2. m ZELD = 2x

2. given

H

L

3. ZELG and ZELD are

a linear pair

3. definition of a linear pair

(2x)

G

4. m ZELD + m ZELG = 180

4.

Ε

• F.

5. 2x + 124 = 180

5. substitution

Complete the steps in the two-column proof.

6.

6. subtraction property

7. x = 28

7. division property

Intro

Done

vity

Answers

The corresponding angles of the lines solved and the value of x = 28°

What are angles in parallel lines?

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.

We can conclude three factors determining parallel lines ,

Alternate angles are equal

Corresponding angles are equal

Co-interior angles add up to 180°

Given data ,

Let the measure of ∠ELG = 124°

The measure of ∠ELD = 2x

∠ELG and ∠ELD are a linear pairs of angles

So , the measure of ∠ELG + ∠ELD = 180°

On simplifying , we get

2x + 124° = 180°

Subtracting 124° on both sides , we get

2x = 56°

Divide by 2 on both sides , we get

x = 28°

Therefore , the value of x is 28°

Hence , the angle is x = 28°

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Answer:

1. angle addition post

2. 2x=56

What is the slope of the line through (1, 9) and (–3, 16)?

Answers

For this case we have that by definition, the slope of a line is given by:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}$

Where:

$(x_ {1}, y_ {1})$ and $(x_ {2}, y_ {2})$ are two points through which the line passes.

We have as data that:

$(x_ {1}, y_ {1}) :( 1,9)\n(x_ {2}, y_ {2}): (- 3,16)$

Substituting we have:

$m = \frac {16-9} {- 3-1} = \frac {7} {- 4} = - \frac {7} {4}$

Thus, the slope of the line is $- \frac {7} {4}$

Answer:

$m = - \frac {7} {4}$

Answer:

-7/4.

Step-by-step explanation:

This is the difference in the y coordinates / corresponding difference in the x coordinates.

here it is (16 - 9) / (-3-1)

= 7 / -4

= -7/4.

How many seconds in 2.6 days

Answers

1 minute = 60 seconds
1 hour = 60 minutes = 3600 seconds
1 day = 24 hours = 1440 minutes = 86400 seconds
2.6 day = 2.6 * 86400 seconds = 224 640 seconds

What is the factored form of 5x+x^2=0

Answers

$5x+x^2=0\n \nx(5+x)=0\n \nx=0 \ \vee \ 5+x=0 \n\n x=0 \ \vee \ x=-5$

How do you find the ratio of a fraction

Answers

A ratio is the relationship between two numbers.

Probably the easiest way to write a ratio is in the form of a fraction.

A fraction IS a ratio.

It means (the top number) divided by (the bottom number), and
that's the ratio between them.

Write the equation of the hyperbola that has a center at (4, - 1), a focus at (11, - 1), and a vertex at (0, - 1).

Answers

Answer: 56

Step-by-step explanation:

Final answer:

Given the center, focus, and vertex of a hyperbola, the equation of the hyperbola can be determined using the standard formula for a hyperbola and calculations for the values of a and b. For the hyperbola with center (4, -1), focus (11, -1), and vertex (0, -1), the equation is (x - 4)²/16 - (y + 1)²/33 = 1.

Explanation:

The subject of the question is to write the equation of the hyperbola given the center, focus, and vertex. In general, the equation of a horizontal hyperbola is (x - h)²/a² - (y - k)²/b² = 1 where the (h, k) is the center, a is the distance from the center to a vertex, and b is the distance from the center to a co-vertex. In this case, the center is (4, -1), the focus is (11, -1), the and vertex is (0, -1).

To determine a, calculate the distance from the center to a vertex. With the center at (4, -1) and vertex at (0, -1), a = 4. To determine b, apply the hyperbola's relationship of c² = a² + b², where c is the distance from the center to a focus. Given that the distance to the focus (from (4, -1) to (11, -1)) is 7 (so, c = 7) and a = 4, solve for b to get b = sqrt(c² - a²) = sqrt(49-16)= sqrt(33). Therefore, the equation of the hyperbola is (x - 4)²/16 - (y + 1)²/33 = 1.

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