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3 years ago

Simplify and expand (1/3)to 2nd power × 18 + (1/2)to 2nd power × 4

1 answer:

6 0

Step 1. Use Division Distributive Property $( \frac{x}{y} ) ^{a} = \frac{ x^{a} }{ y^{a} }$

Step 2. Simplify $3^{2}$ to $9$

$\frac{1}{9} *18+( \frac{1}{2} ) ^{2}*4 
$

Step 3. Use Division Distributive Property $( \frac{x}{y} ) ^{a} = \frac{ x^{a} }{ y^{a} }$

$\frac{1}{9} *18+ \frac{1}{ 2^{2} } *4$

Step 4. Simplify $2^{2}$ to $4$

$\frac{1}{9} *18+ \frac{1}{4} *4$

Step 5. Simplify $\frac{1}{9} *18$ to $\frac{18}{9}$

$\frac{18}{9} + \frac{1}{4} *4$

Step 6. Simplify $\frac{18}{9}$ to $2$

$2+ \frac{1}{4} *4$

Step 7. Simplify $\frac{1}{4} *4$ to $1$

$2+1$

Step 8. Simplify

$3$

Done! Your answer is 3

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Solve the inequality for x -5x - 49 > 113

Anika [276]

X < -40.5

To find this, here are the steps:

Combine like terms like so:

-4x - 49 > 113

Then, begin to isolate the variable x by adding 49 to both sides leaving you with:

-4x > 162

Then divide by negative four. Don’t forget, dividing by negatives switches the way the sign points so your final product will be:

x < -40.5

Hope this helps!

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3 years ago

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Answer: C) 4

Step-by-step explanation:

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2 years ago

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Answer:

C. 12x + 40

Step-by-step explanation:

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3 years ago

What is the equation of this line in standard form?

horsena [70]

Option B 6x-7y = -11 is correct

Step-by-step explanation:

We need to write the equation of the given line in standard form.

The points are (1/2,2) and (3,1)

The equation used is:

$y-y_{1}=m(x-x_{1})$

where m is the slope.

Finding slope :

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

x₁= 1/2, y₁=2, x₂=-3, y₂=-1

Putting values:

$m=\frac{-1-2}{-3-1/2} \\m=\frac{6}{7}$

Now taking point (1/2,2) and s;ope m = 6/7 finding equation:

$y-y_{1}=m(x-x_{1})$

$y-2=\frac{6}{7}(x-\frac{1}{2})\\ 7(y-2)=6(x-\frac{1}{2})\\7y-14=6x-3\\7y-6x=-3+14\\7y-6x= 11\\Multiply \,\,with\,\, -1\\-7y+6x=-11\\6x-7y=-11$

So, Option B 6x-7y=-11 is correct

Keywords: Standard form of equation

Learn more about Standard form of equation at:

#learnwithBrainly

5 0

3 years ago

Find the equation of the line that

Aleonysh [2.5K]

Answer:

y = 3x/2-14

Step-by-step explanation:

We are given that the line is perpendicular to y = -2/3 and contains (4,-8).

Perpendicular Def.

$\displaystyle \large{m_1m_2 = - 1}$

Both slopes multiply each others equal to -1.

Finding another slope that is perpendicular to -2/3, substitite m1 = -2/3 in.

$\displaystyle \large{ - \frac{2}{3} m_2 = - 1}$

Multiply both sides by 3.

$\displaystyle \large{ - \frac{2}{3} m_2( 3) = - 1(3)} \\ \displaystyle \large{ - 2 m_2= - 3} \\ \displaystyle \large{ m_2= \frac{3}{2} }$

Therefore, another slope that is perpendicular to -2/3 is 3/2.

Then rewrite in slope-intercept form.

Slope-Intercept

$\displaystyle \large{y = mx + b}$

where m = slope and b = y-intercept; substitute m = 3/2 in.

$\displaystyle \large{y = \frac{3}{2} x + b}$

Since the line contains (4,-8), substitute x = 4 and y = -8 in and solve for b.

$\displaystyle \large{ - 8 = \frac{3}{2} (4) + b} \\ \displaystyle \large{ - 8 = 3(2)+ b} \\ \displaystyle \large{ - 8 = 6 + b} \\ \displaystyle \large{ - 8 - 6 = b} \\ \displaystyle \large{ - 14 = b}$

Therefore, b is -14; rewrite again in slope-intercept form.

Thus:-

$\displaystyle \large{y = \frac{3}{2} x + b} \\ \displaystyle \large{y = \frac{3}{2} x - 14}$

4 0

2 years ago