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3 years ago

Solve the equation 3(-a-3)-2(3a+3)=-78

Mathematics

2 answers:

garri49 [273]3 years ago

4 0

Given equation is 3(-a-3)-2(3a+3)=-78

we can start by distributing numbers which are outside parenthesis

3(-a-3)-2(3a+3)=-78

-3a-9-6a-6=-78

combine like terms

-9a-15=-78

-9a=-78+15

-9a=-63

a=-63/-9

a=7

Hence final answer is a=7.

mote1985 [20]3 years ago

4 0

We are given this equation:

3(-a-3)-2(3a+3)=-78

We will use distributive property here :

a(b+c) =a*b +a*c

-3a-9 -6a-6=-78

combining like terms

-9a - 15 =-78

we add 15 to both sides

-9a -15 +15 = -78+15

-9a =-63

dividing both sides by -9

a=7

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Dawn took two pies to a school bake. She cut Pie A into 8 slices and Pie B into 6 slices. She sold two slices of Pie A and three

evablogger [386]

2 of the 8 slices of pie A were sold (2/8)
3 of the 6 slices of pie B were sold (3/6)

Both of these fractions can be simplified

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Now we can add the two

1/4 + 2/4 = 3/4

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3 years ago

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3 years ago

The function below has at least one rational zero.

Dmitry_Shevchenko [17]

Answer:

$x=-7,x=-1,x=-0.289898,x=0.689898$

or $x=-7,x=-1,x=\frac{1}{5}-\frac{\sqrt{6}}{5},x=\frac{1}{5}+\frac{\sqrt{6}}{5}$

Step-by-step explanation:

<u>Factor by grouping</u>

$g(x)=5x^4+38x^3+18x^2-22x-7\\\\g(x)=5x^4+33x^3-15x^2-7x+5x^3+33x^2-15x-7\\\\g(x)=x(5x^3+33x^2-15x-7)+1(5x^3+33x^2-15x-7)\\\\g(x)=(x+1)(5x^3+33x^2-15x-7)\\\\g(x)=(x+1)(5x^3+35x^2-2x^2-14x-x-7)\\\\g(x)=(x+1)(5x^2(x+7)-2x(x+7)-1(x+7))\\\\g(x)=(x+1)(x+7)(5x^2-2x-1)\\\\0=(x+1)(x+7)(5x^2-2x-1)\\$

We can easily see that the first two zeroes are $x=-1$ and $x=-7$ , however, the third zero will need the help of the quadratic formula:

$0=5x^2-2x-1\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(5)(-1)}}{2(5)}\\\\x=\frac{2\pm\sqrt{4+20}}{10}\\ \\x=\frac{2\pm\sqrt{24}}{10}\\ \\x=\frac{2\pm2\sqrt{6}}{10}\\ \\x=\frac{2}{10}\pm\frac{2\sqrt{6}}{10}\\ \\x=\frac{1}{5}\pm\frac{\sqrt{6}}{5}\\\\x_1\approx0.689898\\\\x_2\approx-0.289898$

Therefore, the zeroes of the function are $x=-7,x=-1,x=-0.289898,x=0.689898$

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Answer:

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