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2 years ago

Solve for x: 3x − 2 > 5x + 10. (5 points)

Mathematics

1 answer:

velikii [3]2 years ago

5 0

Answer:

Option 2.. x > -6

Step-by-step explanation:

3x -5x - 2 > 5x -5x + 10

-2x - 2 + 2 > 10 + 2

-2x/-2 > 12/-2

x > -6

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Find the difference of 16 5/8 and 12 9/12.

yawa3891 [41]

First find the least common denominator (8), and then subtract. After subtracting you should get 31/8, which as a decimal is 3.875 and as a mixed number is 3 7/8.

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2 years ago

A company that makes hair-care products had 5,000 people try a new shampoo. Of the 5,000 people, 10 had a mild allergic reacti

Margarita [4]

Answer:

0.002%

Step-by-step explanation:

10/5,000 = 0.002

Hope this helps!

4 0

2 years ago

Read 2 more answers

Find the equation of the line specified. The line passes through the points ( 5, 2) and ( 6, 4) a. y = 2x - 8 c. y = 2x + 12 b.

o-na [289]

( 5, 2) and ( 6, 4)
slope m = (4-2)/(6-5) = 2

y = mx + b
b = y - mx
b = 2 - 2(5)
b = 2 - 10
b = -8

so now you have slope m = 2 and y intercept b = -8

equation
y = 2x - 8

answer
a. y = 2x - 8

4 0

2 years ago

Read 2 more answers

Use Cramer Rule to solve the following system: 8x−5y=70 and 9x+7y=3

nlexa [21]

Answer:

$(x,y) = (5,-6)$

Step-by-step explanation:

$\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\$

$~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)$

$\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\$

$\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5$

$y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6$

$\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)$

7 0

1 year ago

The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rater.

Anni [7]

Interest rate = 7%

I= PRT where I is the interest earned, p is the principal, r is rate as a decimal, and t is time in years.

A - P will give us the interest earned.

12,150 - 9,000 = 3,150

3150 = (9000)(r)(5)
3150 = 45,000r
r = 0.07
r = 7%

4 0

2 years ago