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3 years ago

Which graph represents the function of f(x) 9x^2 + 9x - 18 / 3x + 6

Mathematics

1 answer:

Irina-Kira [14]3 years ago

7 0

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$f(x)=\frac{9x^{2}+9x-18}{3x+6}$

Remember that in a quotient, the denominator cannot be equal to zero

The value of x cannot be equal to x=-2

Simplify the expression

Using a graphing tool

The roots of the quadratic equation in the numerator are

x=-2 and x=1

$9x^{2}+9x-18=9(x+2)(x-1)$

Simplify the denominator

$3x+6=3(x+2)$

substitute in the original expression

$f(x)=\frac{9(x+2)(x-1)}{3(x+2)}$

Simplify

$f(x)=3(x-1)$

$f(x)=3x-3$

Is the equation of a line

The y-intercept is the point (0,-3) (value of the function when x is equal to zero)

The x-intercept is the point (1,0) (value of x when the value of the function is equal to zero)

Graph the line, but remember that the value of x cannot be equal to -2

The graph in the attached figure

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Solving quadratic equations with complex solutions x2 + 4x + 8 = 0.

Daniel [21]

Answer:

$\large\boxed{x=-2\pm2i}$

Step-by-step explanation:

$x^2+4x+8=0\qquad\text{subtract 8 from both sides}\\\\x^2+4x+8-8=0-8\\\\x^2+2(x)(2)=-8\qquad\text{add}\ 2^2\ \text{to both sides}\\\\x^2+2(x)(2)+2^2=-8+2^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+2)^2=-8+4\\\\(x+2)^2=-4\iff x+2=\pm\sqrt{-4}\\\\x+2=\pm\sqrt{(4)(-1)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\x+2=\pm\sqrt4\cdot\sqrt{-1}\qquad\text{use}\ \sqrt{-1}=i\\\\x+2=\pm2\cdot i\qquad\text{subtract 2 from both sides}\\\\x=-2\pm2i$

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3 years ago

. John has two coupons to use at a clothing store. One is for $20 off and the other is for 20% off. John wants to purchase a shi

zlopas [31]

Complete question :

John has two coupons to use at a clothing store. One is for $20 off and the other is for 20% off. John wants to purchase a shirt with one of the coupons and wants to pay the least amount that he can. Choose the answer that BEST describes the situation. * 1 point A. The shirt will have the lowest price with the $20 off coupon. B. The shirt will have the lowest price with the 20% off coupon. C. The shirt will cost the same with either coupon. D. It depends on the cost of the shirt as to which coupon will help John pay the lowest price.

Answer: D. It depends on the cost of the shirt as to which coupon will help John pay the lowest price.

Step-by-step explanation:

Given two different coupon options :

First: 20% off

Second = $20 off

To our hase with one which enables one to pay the amount of money :

The price of the shirt will determine which of the coupons will give the least amount. For instance, a shirts which which cost below $100 will require the $20 off coupon in other to attain the least payment amount. However for shirts which cost above $100, the 20% coupon yield the least amount. Shirts which cost $100. Both coupons yields the same discount amount.

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3 years ago

I WILL GIVE BRAINLIEST!! I really need help with this question.

Annette [7]

Answer: x = 70, y = 110, z = 85

Step-by-step explanation:

If BE = CD, then using corresponding angles (are equal), x = 70

If x = 70, then 70+y = 180 (angles on a straight line)

y = 110

And z = 85 (corresponding angles again): angle ABE = angle ACD

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3 years ago