Kevin read the number''two hundred seven thousand,forty-eight'' in the book.What is this number in standard form?

What are the zeros of the quadratic function f(x) = 6x2 + 12x – 7?

Gnom [1K]

Answer:

A quadratic equation is of the form: $ax^2+bx+c= 0$ .....[1] where

a. b and c are coefficient and x is the variable.

The solutions of the equation are;

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Given the function: $f(x) = 6x^2+12x-7$

To find the zero of this function.

Set f(x) = 0

⇒ $6x^2+12x-7=0$

On comparing this with equation [1] we have;

a = 6, b = 12 and c = -7

then;

$x = \frac{-12\pm\sqrt{(12)^2-4(6)(-7)}}{2(6)}$

$x = \frac{-12\pm\sqrt{144+168}}{12}$

or

$x = \frac{-12\pm\sqrt{312}}{12}$

or

$x = \frac{-12\pm 2\sqrt{78}}{12}$

$x = \frac{-6\pm \sqrt{78}}{6}$

Therefore, the zeros of the quadratic function f(x) are;

$\frac{-6+\sqrt{78}}{6}$ and $\frac{-6-\sqrt{78}}{6}$

8 0

2 years ago

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The diagram represents the factorization of a2+8a+12. A 2-column table with 2 rows. First column is labeled a with entries a squ

Lapatulllka [165]

Answer:

(A)6

Step-by-step explanation:

Given the quadratic expression: $a^2+8a+12$

We factorize:

$a^2+8a+12=a^2+6a+2a+12\\=a(a+6)+2(a+6)\\=(a+2)(a+6)$

Therefore, the missing number that will complete the factorization is 6.

3 0

1 year ago

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A financial advisor tells you that you can make your child a millionaire if you just start saving early. You decide to put an eq

Blababa [14]

Answer:

$12159 per year.

Step-by-step explanation:

If I invest $x each year at the simple interest of 7.5%, then the first $x will grow for 35 years, the second $x will grow for 34 years and so on.

So, the total amount that will grow after 35 years by investing $x at the start of each year at the rate of 7.5% simple interest will be given by

$x( 1 + \frac{35 \times 7.5}{100}) + x( 1 + \frac{34 \times 7.5}{100}) + x( 1 + \frac{33 \times 7.5}{100}) + ......... + x( 1 + \frac{1 \times 7.5}{100})$

= $35x + \frac{x \times 7.5}{100} [35 + 34 + 33 + ......... + 1]$

= $35x + \frac{x \times 7.5}{100} [\frac{1}{2} (35) (35 + 1)]$

{Since sum of n natural numbers is given by $\frac{1}{2} (n)(n + 1)$ }

= 35x + 47.25x

= 82.25x

Now, given that the final amount will be i million dollars = $1000000

So, 82.25x = 1000000

⇒ x = $12,158. 05 ≈ $12159

Therefore. I have to invest $12159 per year. (Answer)

5 0

2 years ago

Julie tried to use the law of syllogism to draw a conclusion based on the statements below. Explain why she is not able to do so

ira [324]

Answer: The conditional statements are not in the correct form to make a conclusion using the law of syllogism. “If p, then q and if p, then r” cannot be used to draw a conclusion using the law of syllogism. The law of syllogism could be used if the hypothesis in the second statement was "if two pairs of congruent angles are formed."

Step-by-step explanation:

"If p, then q and if p, then r" cannot be used to draw a conclusion using the law of syllogism.

Neither of the conclusions of the conditional statements are the hypothesis of the other.

"If two pairs of congruent angles are formed" could be the hypothesis of the second statement.

** Both can be used to answer the question :)

4 0

2 years ago

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Brahmagupta solved a quadratic equation of the form ax2 + bx = c using the formula x =, which involved only one solution. Using

weeeeeb [17]

X2+7x-8=0
product=-8 times 1 = -8
sum= 7
{-1, 8}
x2-1x+8x-8=0
x(x-1)+8(x-1)=0
x+8=0 or X-1=0
x=-8

4 0

1 year ago

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