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4 years ago

5 + 6x = 2x - 7 what is x

Mathematics

1 answer:

makvit [3.9K]4 years ago

5 0

Answer:

x =-3

Step-by-step explanation:

5 + 6x = 2x - 7

Subtract 2x from each side

5 + 6x- 2x = 2x-2x - 7

5+4x = -7

Subtract 5 from each side

5+4x -5 = -7-5

4x = -12

Divide each side by 4

4x/4 = -12/4

x =-3

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of the 400 vehicles that passed the intersection, 98 are buses, what percent of the vehicles that passed the intersection are bu

frutty [35]

It should be 24.5%. If you divide 98 by 400 it's .245. Then multiply it by 100, you get 24.5%.

5 0

3 years ago

What is the slope between the points (3,-4)&(7,6)?

olchik [2.2K]

Answer: The slope is $\frac{5}{2}$

Step-by-step explanation:

1. You need to apply the following formula for calculate the slope:

$m=\frac{y_{2}-y_1}{x_{2}-x_1}$

2. Given the points, (3,-4) and (7,6), you have:

$y_{2}=6\\y_1=-4\\x_{2}=7\\x_{1}=3$

3. Substitute these values into the formula for calculate the slope, as following:

$m=\frac{6-(-4)}{7-3}\\m=\frac{10}{4}$

4. Simplify the result. Therefore, you obtain that the slope is:

$m=\frac{5}{2}$

5 0

3 years ago

-3 1/3 divided by -1/2

Alexandra [31]

Answer:

8/3

Step-by-step explanation:

keep change flip

-3 1/3 (turn the divide into multiplication) and flip the fraction- 1/2 -2/1

-4/3 times -2/1

5 0

3 years ago

Which rectangle if reflected over the x-axis and then translated 8 units right will result in rectangle E?

Komok [63]

Answer:

Rectangle D is reflected over the x-axis and then translated 8 units right will result in rectangle E

Step-by-step explanation:

The coordinates of rectangle D are:

(-1, 1)

(-1, 4)

(-3, 1) and

(-3, 4)

The rule of reflection across x-axis is given by:

$(x, y) \rightarrow (x , -y)$

$(-1, 1) \rightarrow (-1 , -1)$

$(-1, 4) \rightarrow (-1 , -4)$

$(-3, 1) \rightarrow (-3 , -1)$

$(-3, 4) \rightarrow (-3 , -4)$

Next, translate this 8 unit right which is given by:

$(x, y) \rightarrow (x+8 , y)$

$(-1, -1) \rightarrow (-1+8 , -1) =(7, -1)$

$(-1, -4) \rightarrow (-1+8 , -4) =(7, -4)$

$(-3, -1) \rightarrow (-3+8 , -1) =(5, -1)$

$(-3, -4) \rightarrow (-3+8 , -4) =(5, -4)$

⇒(7, -1) , (5, -1) , (5, -4) and (7, -4) represents the coordinate of rectangle E.

Therefore, Rectangle D if reflected over the x-axis and then translated 8 units right will result in rectangle E

5 0

3 years ago

Read 2 more answers

Write the given expression as an algebraic expression in x. tan(2 cos^-1(x))

miv72 [106K]

$\bf tan\left[ 2cos^{-1}(x) \right]\implies tan\left[ 2cos^{-1}\left( \frac{x}{1} \right) \right]
\\\\\\
\textit{if we say }cos^{-1}\left( \frac{x}{1} \right)=\theta\textit{ that means }tan\left[ 2cos^{-1}\left( \frac{x}{1} \right) \right]\iff tan(2\theta)\\\\
-----------------------------\\\\
cos^{-1}\left( \frac{x}{1} \right)=\theta\implies cos(\theta)=\cfrac{x}{1}\cfrac{\leftarrow adjacent=a}{\leftarrow hypotenuse=c}\\\\
-----------------------------\\\\
$

$\bf \textit{again, using the pythagorean theorem to get the opposite side}
\\\\\\
c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\implies \pm\sqrt{1^2-x^2}=b
\\\\\\
\pm\sqrt{1-x^2}=b\\\\
-----------------------------\\\\
tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\implies tan(2\theta)=\cfrac{2\cdot \frac{\pm\sqrt{1-x^2}}{x}}{1-\left( \frac{\pm\sqrt{1-x^2}}{x} \right)^2}
\\\\\\$

$\bf tan(2\theta)=\cfrac{\frac{\pm2\sqrt{1-x^2}}{x}}{1-\frac{1-x}{x}}\implies 
tan(2\theta)=\cfrac{\frac{\pm2\sqrt{1-x^2}}{x}}{\frac{x-1+x}{x}}
\\\\\\
tan(2\theta)=\cfrac{\pm2\sqrt{1-x^2}}{x}\cdot \cfrac{x}{2x-1}
\implies 
tan(2\theta)=\cfrac{\pm 2\sqrt{1-x^2}}{2x-1}$

6 0

4 years ago