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3 years ago

Simplify 4(12 + 6) using distributive property

Mathematics

2 answers:

Doss [256]3 years ago

7 0

Answer:

Step-by-step explanation:

Tomtit [17]3 years ago

3 0

Answer:

Step-by-step explanation:

4(12+6)

4 times 12 is 48

4 times 6 is 24

48+24

add them both together

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Which equation has the steepest parabola?

ICE Princess25 [194]

Given:

The equations of parabolas in the options.

To find:

The steepest parabola.

Solution:

We know that, if a parabola is defined as

$(y-k)=n(x-h)^2$

Then, the greater absolute value of n, the steeper the parabola.

It can be written as

$\dfrac{1}{n}(y-k)=(x-h)^2$

$p(y-k)=(x-h)^2$

where $p=\dfrac{1}{n}$ , the smaller absolute value of p, the steeper the parabola.

Now, find the value of |p| for eac equation

For option A, $|-0.5|=0.5$

For option B, $|5|=5$

For option C, $|8|=8$

For option D, $|-10|=10$

Since, the equation is option A has smallest value of |p|, therefore, the equation $(x+2)^2=-0.5(y+3)$ represents the steepest parabola.

Hence, the correct option is A.

7 0

3 years ago

50 multiplied by 100

ra1l [238]

When multiplying by 100 just add 2 zero's behind your second number. ANSWER:5,000

3 0

3 years ago

What is the solution to this equation? 6(x-4)+7=-5

EleoNora [17]

Answer:

x = 2

Step-by-step explanation:

6(x-4) + 7 = -5

6(x-4) + 7 - 7 = -5 - 7

6(x-4) = -12

6(x-4)/6 = -12/6

x - 4 = -2

x - 4 + 4 = -2 + 4

x = 2

4 0

4 years ago

Use the Factor Theorem and synthetic division to show x + 5 is a factor of f(x) = 2x3 + 7x2 − 14x + 5

olga2289 [7]

Answer:

Factor theorem: $f(-5) = 0$ .

Synthetic division: $f(x) = (x + 5)\, (2\, x^2 -3\, x + 1)$ .

Step-by-step explanation:

<h3>Factor Theorem</h3>

By the factor theorem, a monomial of the form $(x - a)$ (where $a$ is a constant) is a factor of polynomial $f(x)$ if and only if $f(a) = 0$ .

In this question, the monomial is $(x + 5)$ , which is equivalently $(x - (-5))$ . $a = -5$ .

$\begin{aligned}& f(-5) \\ &= 2 \times (-5)^{3} + 7 \times (-5)^{2}- 14\times (-5) + 5\\ &= -250 + 175 + 70 + 5 \\ &= 0\end{aligned}$ .

Hence, by the factor theorem, $(x + 5)$ , which is equivalent to $(x - (-5))$ , is a factor of $f(x)$ .

<h3>Synthetic Division</h3>

$\begin{aligned}& f(x) \\ &= 2\, x^{3} + 7\, x^{2} - 14\, x + 5 \\ &= \underbrace{(x + 5) \, (2\, x^2)}_{2\, x^{3} + 10\, x^{2}} - 3\, x^{2} - 14\, x + 5 \\ &= \underbrace{(x + 5) \, (2\, x^2)}_{2\, x^{3} + 10\, x^{2}} + \underbrace{(x + 5)\, (-3\, x)}_{-3\, x^{2} - 15\, x} + (x + 5) \\ &= (x + 5)\, (2\, x^{2} - 3\, x + 1)\end{aligned}$ .