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3 years ago

G(x) = x2 + 8x +12 over x² – 2x-8

Mathematics

1 answer:

den301095 [7]3 years ago

6 0

Answer:

The domain of the function in interval notation is -∞ < x < -2, -2 < x < 4, x > 4

Step-by-step explanation:

The given function is presented as follows;

$G(x) = \dfrac{x^2 + 8 \cdot x + 12}{x^2 - 2 \cdot x - 8}$

The function given in rational format will not be defined when the value of the denominator = 0

Therefore, for the function to be undefined, we have;

x² - 2·x - 8 = 0

(x - 4)·(x + 2) = 0

Which gives;

x = 4, or x = -2

Therefore, the function is undefined for x = 4 and x = -2

The domain of the function in interval notation = -∞ < x < -2, -2 < x < 4, x > 4

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F (x)=2x-1<br>find (-1)

torisob [31]

-3

Explanation:

If f(x)=f(-1) then you just fill in -1 where x is.

2*-1-1
-2-1
-3

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3 years ago

Find the percent of increase or decrease from the first number to the second number. 140 to 84

tresset_1 [31]

We can automatically see that we are dealing with a percent decrease because we are going from a smaller to a bigger number. We need to first find what percent of 140the number 84 is. to do this we can set up the following equation:

140/84=100/x (this equation is basically saying if 140 is 100(%) what would 84 be?)

solving for x here gives us x = (84 X 100)/140 = 60, so 84 is 60 percent of 140 which means 140 decreased by 40 percent.

Let me know if I can clear anything else up.

8 0

3 years ago

Line M passes through point (3,1) and is perpendicular to the line of the equation y=3x+4. Which equation describes the graph of

zheka24 [161]

Answer:

y = -1/3x + 2

Step-by-step explanation:

The gradient of the given line is 3 because (y = mx +c where m is the gradient)

Therefore, to find the gradient of the perpendicular line (at 90 degrees), you need to find the negative reciprocal.

The negative reciprocal of 3 is -1/3 because imagine if 3 = 3/1, to get the reciprocal, you flip it, and to get the negative, you just flip the sign.

Now we know that Line M is y = -1/3x + c, we need to find the y-intercept.

To do this, just input the point (3,1) into y = -1/3x + c, to get c. This is because we know (3,1) is on the line from the question.

So it would be 1 = (-1/3 x 3) +c

Which would be 1 = -1 +c

And so c = 2

Put everything together and you get y = -1/3x + 2

8 0

3 years ago

Jasmine purchased 3 bags of hot cheetos and 2 packs of sour patch kids from the vending machine and spent 5.25. Michael also loa

Charra [1.4K]

Answer:

cost of a bag of hot Cheetos = 0.75 and cost of a pack of sour patch kids = 1.5

Step-by-step explanation:

Let the cost of a bag of hot cheetos be c

Let the cost of a pack of sour patch kids be k

Thus, for Jasmine, the equation will be;

3c + 2k = 5.25 - - - - (eq1)

For Michael, the equation will be;

7c + 3k = 9.75 - - - - - (eq2)

We will use method of elimination to solve this.

Multiply (eq 1) by 3 and (eq 2) by 2 to give;

9c + 6k = 15.75 - - (eq4)

14c + 6k = 19.5 - - -(eq5)

Subtract (eq4) from (eq 5) to get;

5c = 19.5 - 15.75

5c = 3.75

c = 3.75/5

c = 0.75

Put 0.75 for c in (eq 4) to get;

9(0.75) + 6k = 15.75

6.75 + 6k = 15.75

6k = 15.75 - 6.75

6k = 9

k = 9/6

k = 1.5

Thus; cost of a bag of hot Cheetos = 0.75 and cost of a pack of sour patch kids = 1.5

7 0

3 years ago

Which expression is equivalent to 2 (14x-37+28x+12.2-5y-17.5)?

ziro4ka [17]

Answer:

A. 84x - 16y - 10.6

Explanation:

$\sf \rightarrow 2(14x-3y+28x+12.2-5y-17.5)$

$\sf \rightarrow 2 (42x-8y-5.3)$

apply distributive method: a(b + c) = ab + ac

$\sf \rightarrow 2 (42x) -2(8y)-2(5.3)$

$\sf \rightarrow 84x -16y-10.6$

7 0

2 years ago