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3 years ago

Simplify the rational expression. State any excluded values.

Mathematics

1 answer:

ANEK [815]3 years ago

7 0

So on the top, you split it up using the difference of squares rule.
You get (x - 6)(x + 6) on the top.

On the bottom, you can undistribute (pull out) -7x.
This gives you -7x(x-6) on the bottom.

Now you can cancel like terms in the numerator and denominator.
You can cancel the (x-6).
You can also move the negative sign from the 7x to the (x + 6)

This leaves you with -(x + 6) over 7x, or (6 - x) over 7x.

To find excluded values, all you need to know is that you can't divide by zero under any circumstances, and you can't have a zero on the top in a rational expression.
The only values for x that would make either of these statements true are if x = 0 (7 × 0 = 0 on the bottom), or if x = 6 (6 - 6 +0 on the top)

So the answer is (6 - x) over 7x, x ≠ 0, 6

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Solve the system of linear equations by ellmination. 5x + 9y = -11 3x + 9y = -3 A. (-4,-1) -B. (-1, –4) C. (-4,1) D. (1,-4)

valentina_108 [34]

Answer:

Step-by-step explanation:

5x + 9y = -11

3x + 9y = -3

5x + 9y = -11

-3x - 9y = 3

2x = -8

x = -4

-12 + 9y = -3

9y = 9

y = 1

(-4, 1)

Answer is C

5 0

2 years ago

Find x. A. 11√6/2 B. 22 C. 33 D. 11√3/2

Phoenix [80]

Answer:

Step-by-step explanation:

using the tangent ratio on the triangle on the right and the exact value

tan60° = $\sqrt{3}$ , then letting the altitude be h

tan60° = $\frac{opposite}{adjacent}$ = $\frac{11\sqrt{6} }{h}$ = $\sqrt{3}$ ( multiply both sides by h )

11 $\sqrt{6}$ = h × $\sqrt{3}$ ( divide both sides by $\sqrt{3}$ )

11 $\sqrt{2}$ = h

using the sine ratio in the triangle on the left and the exact value

sin45° = $\frac{\sqrt{2} }{2}$ , then

sin45° = $\frac{opposite}{hypotenuse}$ = $\frac{h}{x}$ = $\frac{11\sqrt{2} }{x}$ = $\frac{\sqrt{2} }{2}$ ( cross- multiply )

$\sqrt{2}$ × x = 22 $\sqrt{2}$ ( divide both sides by $\sqrt{2}$ )

x = 22

6 0

1 year ago

What would the circumference be of a circle if the radius is 3 units

MAVERICK [17]

If we have a circle with a radius of 3 we need to find the diameter of the circle. Remember radius is half of the diameter. So, the diameter is 6 units.

Use the circumference formula: C=3.14D

C=3.14(6)

C=18.84 units

7 0

3 years ago

Solve each equation. Record your work and check your solution. a. 5(x-2)+(-9)= -7(1-x)

Daniel [21]

The solution for equation is x = -6

Solution:

Given equation is:

$5(x-2) + (-9) = -7(1-x)$

We have to solve the equation

According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right

Therefore, solve for brackets in given equation

$5(x-2) + (-9) = -7(1-x)\\\\5x - 10 -9 = -7 + 7x$

Solve for terms in left hand side of equation

$5x - 19 = -7+7x$

Move the variables to one side and constants to other side

$7x -5x = -19+7\\\\2x = -12\\\\Divide\ both\ sides\ by\ 2\\\\x = -6$

Thus the solution for equation is x = -6

8 0

3 years ago

Find the sum. 7/30 + 9/20 PLS

e-lub [12.9K]

Answer:

41/60

Step-by-step explanation:

Convert the fractions into like denominators: 7/30 = 140/600, 9/20 = 270/600

Add: 140/600+270/600 = 410/600

Divide into a smaller fraction: 41/60

3 0

3 years ago