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3 years ago

Each equation represents a linear relationship. Examine each and determine the slope and y- intercept

Mathematics

1 answer:

marysya [2.9K]3 years ago

6 0

Answer:

Slope is -3/7. Y intercept is 250/7.

Step-by-step explanation:

Since they asking for the slope and y intercept, let put it in slope intercept form.

$y = mx + b$

where m is the slope and b is the y intercept.

The equation given is in standard form so we will convert it to slope intercept.

$3x + 7y = 250$

$7y = 250 - 3x$

$y = \frac{250}{7} - \frac{3}{7} x$

$y = - \frac{3}{7} x + \frac{250}{7}$

The slope is -3/7

The y intercept is 250/7

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3 years ago

Compute the mode, median, and mean for 23455

Katarina [22]

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3 years ago

Use vectors to find the interior angles of the triangle with the given vertices. (Enter your answers as a comma-separated list.

SOVA2 [1]

Answer:

23.92°, 78.503°, and 77.577°

Step-by-step explanation:

The coordinates of the vertices of the triangle are;

X(-3, -5), Y(2, 6), Z(6, 3)

The vectors are;

z = $\left \langle 2 - (-3), 6 - (-5) \right \rangle$ = $\left \langle 5, 11 \right \rangle$

y = $\left \langle 6 - (-3), 3 - (-5) \right \rangle$ = $\left \langle 9, 8 \right \rangle$

x = $\left \langle 2 - 6, 6 - 3 \right \rangle$ = $\left \langle -4, 3 \right \rangle$

$cos (\alpha ) = \dfrac{z \cdot y}{\left | z \right | \times \left | y \right |}$

Therefore, we get;

$cos (\alpha ) = \dfrac{5 \times 9 + 11 \times 8 }{\left | \sqrt{5^2 + 11^2} \right | \times \left | \sqrt{9^2 + 8^2} \right |} = \dfrac{133}{\sqrt{146} \times \sqrt{145} } \approx 0.91409$

α = arccos(0.91490) ≈ 23.92°

γ = The angle between -y and x

-y = $\left \langle -9, -8 \right \rangle$

We get;

$cos (\gamma) = \dfrac{-y \cdot x}{\left | -y \right | \times \left | x \right |}$

Therefore;

$cos (\gamma) = \dfrac{-9 \times -4 + -8 \times 3 }{\left | \sqrt{(-9)^2 + (-8)^2} \right | \times \left | \sqrt{(-4)^2 + 3^2} \right |} = \dfrac{12}{\sqrt{145} \times \sqrt{25} } \approx 0.199309$

γ = arccos(0.199309) ≈ 78.503°

γ ≈ 78.503°

By angle sum property, β = 180° - (α + β)

β ≈ 180° - (23.92° + 78.503°) = 77.577°

β ≈ 77.577°

The interior angles are;

23.92°, 78.503°, and 77.577°

4 0

3 years ago

Two chicken coops are to be built adjacent to one another from 168 ft of fencing. What dimensions should be used to maximize the

Cerrena [4.2K]

Answer:

21 ft by 28 ft

Step-by-step explanation:

To maximize the area, see the attached.

Perimeter will be 4l+3w which is equal to the fencing perimeter, given as 168

4l+3w=168

Making l the subject then

4l=168-3w

l=42-¾w

Area of individual land will be lw and substituting l with l=42-¾w

Then

A=lw=(42-¾w)w=42w-¾w²

A=42w-¾w²

Getting the first derivative of the above with respect to w rhen

42-w6/4=0

w6/4=42

w=42*4/6=28

Since

l=42-¾w=42-¾(28)=21

Therefore, maximum dimensions are 21 for l and 28 for w

4 0

3 years ago

An arc on a circle measures 125°. The measure of the central angle, in radians, is within which range? 0 to StartFraction pi Ove

tiny-mole [99]

Answer:

The answer is B or pi/2 to pi radians.

Step-by-step explanation:

4 0

3 years ago

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