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oksian1 [2.3K]
3 years ago
5

Select the number of solutions the following equation has:

Mathematics
1 answer:
elena-s [515]3 years ago
6 0

Answer:

6x-5=(x-1)+12

6x-5=x-1+12

6x-x=11+5

5x=16

5/5x=16/5

x= 3.2

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Which line has a slope of -3/4 and y-intercept of 3/2
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Y=mx+b
m=slope
b=yintercept
slope=-3/4
yintercept=3/2

y=-3/4x+3/2

it could also be written
3x+4y=6
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James correctly answered 85% of the 60 problems on his math test. how many problems did James answer correctly?
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Solve for x: 4 over x plus 4 over quantity x squared minus 9 equals 3 over quantity x minus 3. (2 points) Select one: a. x = -4
Kay [80]

Answer:

<h2>c. x = -4 or x = 9</h2>

Step-by-step explanation:

\dfrac{4}{x}+\dfrac{4}{x^2-9}=\dfrac{3}{x-3}

Domain:

x\neq0\ \wedge\ x^2-9\neq0\ \wedge\ x-3\neq0\\\\x\neq0\ \wedge\ x\neq\pm3

solution:

\dfrac{4}{x}+\dfrac{4}{x^2-3^2}=\dfrac{3}{x-3}

use <em>(a - b)(a + b) = a² - b²</em>

\dfrac{4}{x}+\dfrac{4}{(x-3)(x+3)}=\dfrac{3}{x-3}

multiply both sides by (x - 3) ≠ 0

\dfrac{4(x-3)}{x}+\dfrac{4(x-3)}{(x-3)(x+3)}=\dfrac{3(x-3)}{x-3}

cancel (x - 3)

\dfrac{4(x-3)}{x}+\dfrac{4}{x+3}=3

subtract \frac{4(x-3)}{x} from both sides

\dfrac{4}{x+3}=3-\dfrac{4(x-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x}{x}-\dfrac{(4)(x)+(4)(-3)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-\bigg(4x-12\bigg)}{x}\\\\\dfrac{4}{x+3}=\dfrac{3x-4x-(-12)}{x}\\\\\dfrac{4}{x+3}=\dfrac{-x+12}{x}

cross multiply

(4)(x)=(x+3)(-x+12)

use FOIL

4x=(x)(-x)+(x)(12)+(3)(-x)+(3)(12)\\\\4x=-x^2+12x-3x+36

subtract 4x from both sides

0=-x^2+12x-3x+36-4x

combine like terms

0=-x^2+(12x-3x-4x)+36\\\\0=-x^2+5x+36

change the signs

x^2-5x-36=0\\\\x^2-9x+4x-36=0\\\\x(x-9)+4(x-9)=0\\\\(x-9)(x+4)=0

The product is 0 if one of the factors is 0. Therefore:

x-9=0\ \vee\ x+4=0

x-9=0            <em>add 9 to both sides</em>

x=9\in D

x+4=0          <em>subtract 4 from both sides</em>

x=-4\in D

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Which system of equations represents the matrix shown below?
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Answer:

I don't know how to do it...

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Can someone help me please ill give brainy
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Y = 6

Since there is no slope the equation would look like this y=0x+6

Well 0 times x is 0 so y=+6
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