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kondaur [170]
2 years ago
11

Write an equation that passes through the points (0,-5) and (8,-5)

Mathematics
1 answer:
bezimeni [28]2 years ago
6 0

Answer:

Equation of the line: y = -5.

Step-by-step explanation:

Let (x_0,\, y_0) and (x_1,\, y_1) denote the coordinates of these two points, respectively.

Calculate the slope m of this line:

\displaystyle m = \frac{y_1 - y_0}{x_1 - x_0} = \frac{(-5) - (-5)}{8 - 0} = 0.

Notice that the slope is zero because the two points have the same y-coordinates (y_0 = y_1 = -5) even though their x-coordinates are distinct (x_0 \ne x_1.)

Equation for this line in point-slope form:

y - y_0 = m\, (x - x_0).

y - (-5) = 0\, (x - 0).

Rewrite and simplify to obtain the equation of this line in slope-intercept form:

y = -5.

The x-term was eliminated because the slope was zero.

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Katie is twice as old as her sister Mara. The sum of their ages is 24. Find their ages.
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So k=katie's' age
m=mara's age

k is 2 times as old as m
k=2m

sum is 24
add means sum
k+m=24

so we have
k+m=24 and
k=2m
subsitute
2m+m=24
add
3m=24
divide both sides by 3
m=8
subsitute again
k=2m
k=2(8)
k=16

katie=16
mara=8
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3 years ago
12.7 = x – 3.8 help again
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Help with Algebra 2: 1. <img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B7%5D%7Bx%5E5%7D%20%7D%7B%5Csqrt%5B4%5D%7Bx%5E2%7D%
Mars2501 [29]

Answer:

See explanation

Step-by-step explanation:

1. Given the expression

\dfrac{\sqrt[7]{x^5} }{\sqrt[4]{x^2} }

Note that

\sqrt[7]{x^5}=x^{\frac{5}{7}} \\ \\\sqrt[4]{x^2}=x^{\frac{2}{4}}=x^{\frac{1}{2}}

When dividing \sqrt[7]{x^5} by \sqrt[4]{x^2}, we have to subtract powers (we cannot subtract 4 from 7, because then we get another expression), so

\dfrac{5}{7}-\dfrac{2}{4}=\dfrac{5}{7}-\dfrac{1}{2}=\dfrac{5\cdot 2-1\cdot 7}{14}=\dfrac{3}{14}

and the result is x^{\frac{3}{14}}=\sqrt[14]{x^3}

2. Given equation 3\sqrt[4]{(x-2)^3} -4=20

Add 4:

3\sqrt[4]{(x-2)^3} -4+4=20+4\\ \\3\sqrt[4]{(x-2)^3}=24

Divide by 3:

\sqrt[4]{(x-2)^3} =8

Rewrite the equation as:

(x-2)^{\frac{3}{4}}=8\\ \\(x-2)^{\frac{3}{4}}=2^3

Hence,

\left((x-2)^{\frac{3}{4}}\right)^{\frac{4}{3}}=(2^3)^{\frac{4}{3}}\\ \\x-2=2^{3\cdot \frac{4}{3}}\\ \\x-2=2^4\\ \\x-2=16\\ \\x-2+2=16+2\\ \\x=18

3 0
2 years ago
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