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3 years ago

15

Factor the polynomial completely. x2 + 3x + 4

1 answer:

shusha [124]3 years ago

8 0

Answer:

x = 4

x = -1

Step-by-step explanation:

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HELP ME ON THIS PLEASE!!!! SHOW WORK!!!!

Mumz [18]

Answer:

<h2>1. x = 4</h2><h2>2. x = 20</h2>

Step-by-step explanation:

1.

ΔABC and ΔAJK are similar (AA). Therefore the sides are in proportion:

$\dfrac{AC}{AJ}=\dfrac{AB}{AK}$

We have:

AC = 1 + 4 = 5

AJ = 1

AB = 1 + x

AK = 1

Substitute:

$\dfrac{5}{1}=\dfrac{1+x}{1}$

$5=1+x$ <em>subtract 1 from both sides</em>

$4=x\to x=4$

2.

ΔVUT and ΔVMN are similar (AA). Therefore the sides are in proportion:

$\dfrac{VU}{VM}=\dfrac{VT}{VN}$

We hve:

VU = x + 8

VM = x

VT = 49

VN = 49 - 14 = 35

Substitute:

$\dfrac{x+8}{x}=\dfrac{49}{35}$ <em>cross multiply</em>

$35(x+8)=49x$ <em>use the distributive property a(c + b) = ab + ac</em>

$35x+280=49x$ <em>subtract 35x from both sides</em>

$280=14x$ <em>divide both sides by 14</em>

$20=x\to x=20$

3 0

3 years ago

What is the best for the total weight of these cold meats 1 7/8 of bologna 1 1/2 pounds of ham and 7/8 of roast beef ?

In-s [12.5K]

We need to have common denominators, so I will multiply 1 1/2 by 4
15/8 + 12/8 + 7/8 = 34/8
4&1/4 pounds of meat

5 0

3 years ago

Which phrase best describes the graph of a proportional relationship?

Darya [45]

<span>A relationship that occurs when variable quantities are directly proportional to one another. A linear relationship can be represented on a graph as a straight line.
</span>

4 0

3 years ago

Read 2 more answers

Try this hard Math Problem if you dare!!

Dennis_Churaev [7]

Answer:

a. $(x - 3)^2 + 16$

b. $8(x -7)^2$

c. $(a^2 - 1)(7x - 6)$ or $(a+1)(a-1)(7x-6)$

d. $(x^2-4)(x^2+3)$ or $(x-2)(x+2)(x^2+3)$

e. $(a^n+b^n)(a^n-b^n)(a^{2n} +b^{2n})$

Step-by-step explanation:

$a.\ (x + 1)^2 - 8(x - 1) + 16$

Expand

$(x + 1)(x + 1) - 8(x - 1) + 16$

Open brackets

$x^2 + x + x + 1 - 8x + 8 + 16$

$x^2 + 2x + 1 - 8x + 24$

Collect Like Terms

$x^2 + 2x - 8x+ 1 + 24$

$x^2 - 6x+ 25$

Express 25 as 9 + 16

$x^2 - 6x+ 9 + 16$

Factorize:

$x^2 - 3x - 3x + 9 + 16$

$x(x -3)-3(x - 3) + 16$

$(x - 3)(x - 3) + 16$

$(x - 3)^2 + 16$

$b.\ 8(x - 3)^2 - 64(x-3) + 128$

Expand

$8(x - 3)(x - 3) - 64(x-3) + 128$

$8(x^2 - 6x+ 9) - 64(x-3) + 128$

Open Brackets

$8x^2 - 48x+ 72 - 64x+192 + 128$

Collect Like Terms

$8x^2 - 48x - 64x+192 + 128+ 72$

$8x^2 -112x+392$

Factorize

$8(x^2 -14x+49)$

Expand the expression in bracket

$8(x^2 -7x-7x+49)$

Factorize:

$8(x(x -7)-7(x-7))$

$8((x -7)(x-7))$

$8(x -7)^2$

$c.\ 7a^2x - 6a^2 - 7x + 6$

Factorize

$a^2(7x - 6) -1( 7x - 6)$

$(a^2 - 1)(7x - 6)$

The answer can be in this form of further expanded as follows:

$(a^2 - 1^2)(7x - 6)$

Apply difference of two squares

$(a+1)(a-1)(7x-6)$

$d.\ x^4 - x^2 - 12$

Express $x^4$ as $x^2$

$(x^2)^2 - x^2 - 12$

Expand

$(x^2)^2 +3x^2- 4x^2 - 12$

$x^2(x^2+3) -4(x^2+3)$

$(x^2-4)(x^2+3)$

The answer can be in this form of further expanded as follows:

$(x^2-2^2)(x^2+3)$

Apply difference of two squares

$(x-2)(x+2)(x^2+3)$

$e.\ a^{4n} -b^{4n}$

Represent as squares

$(a^{2n})^2 -(b^{2n})^2$

Apply difference of two squares

$(a^{2n} -b^{2n})(a^{2n} +b^{2n})$

Represent as squares

$((a^{n})^2 -(b^{n})^2)(a^{2n} +b^{2n})$

Apply difference of two squares

$(a^n+b^n)(a^n-b^n)(a^{2n} +b^{2n})$

6 0

3 years ago

Evaluating Expressions

d1i1m1o1n [39]

Answer: 13. -12 , 14. 40 , 15. 16 , 16. 4.5

Step-by-step explanation:

8 0

2 years ago