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Dovator [93]
2 years ago
12

Find an equation for the line that passes through the points (-6, 3) and (6, -6).

Mathematics
2 answers:
MrRissso [65]2 years ago
7 0
Slope=-9/12 = -3/4

y=mx+b y=-3/4x+b

3=-3/4(-6)+b

b=3+9/2=7.5

Equation is y=-0.75x+7.5
Georgia [21]2 years ago
6 0

Answer:

y = -\frac{3}{4}x-\frac{3}{2}

Step-by-step explanation:

First, calculate the slope of the line:

m = \frac{y_2-y_1}{x_2-x_1}\\m = \frac{(-6) - 3}{6 - (-6)}\\m = \frac{-9}{12}\\m = \frac{-3}{4}

Next, calculate the y-intercept:

<em>Choose any point on the line</em>.

(-6,3)

Solve for b.

y = mx + b\\b = y - (mx)\\b = 3 - (\frac{-3}{4} * -6)\\b = 3 - \frac{9}{2}\\b = \frac{-3}{2}

Finally, create the equation:

 y = -\frac{3}{4}x-\frac{3}{2}

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You can also multiply fractions to find the percent of a number but that is not necessary in this case.
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IceJOKER [234]

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Step-by-step explanation:

4 0
2 years ago
Anyone have the answer for this
sergiy2304 [10]

\huge\bold{Given:}

Length of the base = 16 km.

Length of the hypotenuse = 34 km. \huge\bold{To\:find:}

✎ The length of the missing leg ''a".

\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}

The length of the missing leg "a" is\boxed{30\:km}.

\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}

Using Pythagoras theorem, we have

({perpendicular})^{2}  +  ({base})^{2}  =  ({hypotenuse})^{2}  \\ ⇢ {a}^{2}  +  ({16 \: km})^{2}  =  ({34 \: km})^{2}  \\ ⇢ {a}^{2}   + 256 \:  {km}^{2}  = 1156 \:  {km}^{2}  \\ ⇢ {a}^{2}  = 1156 \:  {km}^{2}  - 256 \:  {km}^{2}  \\ ⇢ {a}^{2}  = 900 \:  {km}^{2}  \\ ⇢a \:  =  \sqrt{900  \: {km}^{2} }  \\ ⇢a =  \sqrt{30 \times 30 \:  {km}^{2} }  \\ ⇢a = 30 \: km

\sf\blue{Therefore,\:the\:length\:of\:the\:missing\:leg\:"a"\:is\:30\:km.}

\huge\bold{To\:verify :}

( {30 \: km})^{2}  +  ({16 \: km})^{2}  =(  {34 \: km})^{2}  \\ ⇝900 \:  {km}^{2}  + 256 \:  {km}^{2}  = 1156 \:  {km}^{2}  \\⇝1156 \:  {km}^{2}  = 1156 \:  {km}^{2}   \\ ⇝L.H.S.=R. H. S

Hence verified. ✔

\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘

7 0
2 years ago
Explain how to evaluate simplify and convert to radical form (x^3/8)^3/4
Vaselesa [24]

Answer:

(x^\frac{3}{8})^\frac{3}{4}  = \sqrt[32]{x^9}

Step-by-step explanation:

Given

(x^\frac{3}{8})^\frac{3}{4}

Required

Convert to radical form

(x^\frac{3}{8})^\frac{3}{4}

Evaluate the exponents

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

(x^\frac{3}{8})^\frac{3}{4} = x^\frac{9}{32}

Split the exponent

(x^\frac{3}{8})^\frac{3}{4} = (x^9)^\frac{1}{32}

Apply the following law of indices

(x^a)^\frac{1}{b} = \sqrt[b]{x^a}

So, we have:

(x^\frac{3}{8})^\frac{3}{4}  = \sqrt[32]{x^9}

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