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2 years ago

Find an equation of the line described. Leave the solution in the form Ax + By = C.

Mathematics

1 answer:

Tatiana [17]2 years ago

3 0

Answer:

y = (-5/3)x + 4

Step-by-step explanation:

Line contains (-3, 9) and (3, -1)

slope A = Δy/Δx = (-1 - 9) / (3 - (-3)) = -10 / 6 = -5/3

y = (-5/3)x + B

find the intercept B by plugging in either known point set.

9 = (-5/3)(-3) + B

9 = 5 + B

B = 4

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What is the largest power of 2 that is a divisor of 13^4 - 11^4?

OverLord2011 [107]

Answer:

$2^5$

Step-by-step explanation:

Given:

$(13^4 - 11^4)(13^2+11^2)$

add all together with exponents

=48*290

= Then turn into a smaller exponent

= $2^4 * 3 * 2*145$

combine like terms

$2^4 *2$

= $2^5$

5 0

2 years ago

Read 2 more answers

In circle D, angle ADC measures (7x + 2)°. Arc AC

Akimi4 [234]

Answer:

The measure of angle ABC is 36° ⇒ 1st answer

Step-by-step explanation:

Let us revise some important facts in the circle

The measure of the center angle is equal to the measure of its subtended arc

The measure of the inscribed angle is equal to half the measure of the central angle subtended by the same arc

The vertex of a central angle is the center of the circle and its sides are radii in the circle

The vertex of an inscribed angle is a point on the circle, and its sides are chords in the circle

In circle D

∵ D is the center of the circle

∵ A and C lie on the circle

- DA and DC are radii

∴ ∠ADC is a central angle subtended by arc AC

∴ m∠ADC = m of arc AC

∵ m∠ADC = (7x + 2)°

∵ m of arc AC = (8x - 8)°

- Equate them to find x

∴ 8x - 8 = 7x + 2

- subtract 7x from both sides

∴ x - 8 = 2

- Add 8 to both sides

∴ x = 10

Substitute the value of x in the measure of ∠ADC

∵ m∠ADC = 7(10) + 2 = 70 + 2

∴ m∠ADC = 72°

∵ AB and BC are two chords in circle D

∴ ∠ABC is an inscribed angle subtended by arc AC

∵ ∠ADC is a central angle subtended by arc AC

- By using the 2nd fact above

∴ m∠ABC = m∠ADC

∴ m∠ABC = × 72

∴ m∠ABC = 36°

7 0

2 years ago

It is given that y varies inversely as x^2. If x is decreased by 50%, find the percentage change in y.

vova2212 [387]

Answer:

300%

Step-by-step explanation:

Given

$y\ \alpha\ \frac{1}{x^2}$

Required

Find the percentage change in y when x decreased by 50%

First, convert to equation

$y\ = \ \frac{k}{x^2}$

Where k is the constant of proportionality

When x decreased by 50%

$Y = \frac{k}{(x - 0.5x)^2}$

$Y = \frac{k}{(0.5x)^2}$

$Y = \frac{k}{0.25x^2}$

Expand

$Y = \frac{1}{0.25} * \frac{k}{x^2}$

Substitute $\frac{k}{x^2}$ for y

$Y = \frac{1}{0.25} * y$

$Y = 4 * y$

$Y = 4 y$

The percentage change is then calculated as:

$\%Change = \frac{Y - y}{y} * 100\%$

$\%Change = \frac{4y - y}{y} * 100\%$

$\%Change = \frac{3y}{y} * 100\%$

$\%Change = 3 * 100\%$

$\%Change = 300\%$

<em>The percentage in y is 300%</em>

7 0

2 years ago

PLEASE HELP!? Not that hard.

kobusy [5.1K]

Y = 4x - 1

// Plug this in for variable y in equation [1]

[1] 20x - 5•(4x-1) = 5
[1] 0 = 0 => Infinitely many solutions

8 0

2 years ago

Read 2 more answers

a recipe requires 1/4 pound of potatoes to make 3 servings of soup Don has one and a half pound of potatoes how many servings ca

tamaranim1 [39]

18 servings of soup he can make with the potatoes!

8 0

3 years ago