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4 years ago

7

Choose the point-slope form of the equation below that represents the line that passes through the point (6, -3) with a slope of

1/2.

1 answer:

Firlakuza [10]4 years ago

3 0

The point-slope form is
$y = mx + b$
m, the slope, is 1/2.
To find b, we plug in the point (6,-3) to the equation:
$y = \frac{1}{2} x + b \\ ( - 3) = \frac{1}{2} (6) + b \\ - 3 = 3 + b \\ - 6 = b$
First, we multiply 1/2 × 6 = 3. Then we subtract 3 from both sides. We find that b is -6.

Therefore, the point-slope equation is:
$y = \frac{1}{2} x - 6$
This is the second option.

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two angles form a linear pair. the measure of one angle is three times the measure of the other. find the measure of each angle.

Galina-37 [17]

Answer:

Step-by-step explanation:

Two angles form a linear pair.

The measure of one angle is 3.5 times the measure of the other angle.

Find the measure of each angle.

The measure of one angle is 180º/4.5 or 40º

The measure of the other angle is 140º

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3 years ago

Read 2 more answers

PLZ HELP!!! Plz answer ASAP And show work/ explain

GalinKa [24]

Answer:

5a

Step-by-step explanation:

Just use the reflexive property / reflexive angles, 5a = x and 4a equals the remaining side.

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3 years ago

Read 2 more answers

Mary and Gary had some stickers in the ratio 5:3. After Mary had given 1/3 of her stickers to Gary, the new ratio of the number

polet [3.4K]

The total number of stickers the 2 children had was 192 stickers.

Let x represent Mary initial stickers, y represent Gary initial stickers and z represent the total stickers.

x + y = z

x + y - z = 0 (1)

They shared in the ratio of 5:3, hence:

x = (5/8)z

8x - 5z = 0 (2)

Mary gives 1/3 of her stickers to Gary to have 32 more stickers than her.

(1/3)x = (1/3)(5/8)z = (5/24)z

y + (1/3)x = (2/3)x + 32

y - (1/3)x = 32 (3)

Solving equation 1, 2 and 3 gives:

x = 120, y = 72, z = 192

The total number of stickers the 2 children had was 192 stickers.

Find out more on equation at: brainly.com/question/13763238

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2 years ago

A ball is thrown from an initial height of 3 feet with an initial upward velocity of 21 ft/s. The ball height h (in feet) after

Alexxx [7]

Answer:

Step-by-step explanation:

The position equation is given as

$s(t)=-16t^2+21t+3$ and we are looking for the times when the position of the ball is 9 feet. That means that we simply plug in a 9 for s(t) and factor to solve for t:

$9=-16t^2+2t+3$ and

$0=-16t^2+21t-6$ and this is what we factor to find t:

t = .42 sec and then again on its way back down at t = .89 sec

5 0

3 years ago

Solve the equation uding the most direct method: 3x(x+6)=-10?

Tanzania [10]

To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.

<h3>Distribute</h3>

Use the distributive property to distribute 3x into the term (x + 6):

$3x(x+6)=-10$

$3x^2+18x=-10$

<h3>Rearrange</h3>

To create a quadratic equation, add 10 to both sides of the equation:

$3x^2+18x+10=-10+10$

$3x^2+18x+10=0$

<h3>Use the Quadratic Formula</h3>

The quadratic formula is defined as:

$\displaystyle x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.

Therefore:

a = 3
b = 18
c = 10

Set up the quadratic formula:

$\displaystyle x=\frac{-18 \pm \sqrt{(18)^2 - 4(3)(10)}}{2(3)}$

Simplify by using BPEMDAS, which is an acronym for the order of operations:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Use BPEMDAS:

$\displaystyle x=\frac{-18 \pm \sqrt{324 - 120}}{6}$

Simplify the radicand:

$\displaystyle x=\frac{-18 \pm \sqrt{204}}{6}$

Create a factor tree for 204:

204 - 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102 and 204.

The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:

$\sqrt{4\times51}$

Then, using the Product Property of Square Roots, break this into two radicands:

$\sqrt{4} \times \sqrt{51}$

Since 4 is a perfect square, it can be evaluated:

$2 \times \sqrt{51}$

To simplify further for easier reading, remove the multiplication symbol:

$2\sqrt{51}$

Then, substitute for the quadratic formula:

$\displaystyle x=\frac{-18 \pm 2\sqrt{51}}{6}$

This gives us a combined root, which we should separate to make things easier on ourselves.

<h3>Separate the Roots</h3>

Separate the roots at the plus-minus symbol:

$\displaystyle x=\frac{-18 + 2\sqrt{51}}{6}$

$\displaystyle x=\frac{-18 - 2\sqrt{51}}{6}$

Then, simplify the numerator of the roots by factoring 2 out:

$\displaystyle x=\frac{2(-9 + \sqrt{51})}{6}$

$\displaystyle x=\frac{2(-9 - \sqrt{51})}{6}$

Then, simplify the fraction by reducing 2/6 to 1/3:

$\boxed{\displaystyle x=\frac{-9 + \sqrt{51}}{3}}$

$\boxed{\displaystyle x=\frac{-9 - \sqrt{51}}{3}}$

The final answer to this problem is:

$\displaystyle x=\frac{-9 + \sqrt{51}}{3}$

$\displaystyle x=\frac{-9 - \sqrt{51}}{3}$

3 0

2 years ago