Last question! please help this is due today!!!

(x+2) is one of the factors of the polynomial x³+13x²+32x+20. Find its remaining factors.

Liula [17]

Answer:

x^2+11x+10

or

(x+1)(x+10) since you can factor x^2+11x+10

Step-by-step explanation:

Let's do synthetic division.

We are dividing by x+2, so -2 will be on the outside. Like this:

-2 | 1 13 32 20

| -2 -22 -20

|___________________________

1 11 10 0

The remainder is 0, so (x+2) is indeed a factor of x^3+13x^2+32x+20.

The other factor we found by doing this is (x^2+11x+10).

You can find more factors by factoring x^2+11x+10.

Two numbers that multiply to be 10 and add to be 11 is 10 and 1 so the factored form of x^2+11x+10 is (x+10)(x+1).

6 0

3 years ago

How many quarts of pure antifreeze must be added to 8 quarts of a 40% antifreeze solution to obtain a 60% antifreeze solution?

Vinvika [58]

Answer:

we have 8 quarts of 40% antifreeze,

according to the britain equivalent, 1 quart = 1.13L

so, we have 8 * 1.13L = 9.04 L

out of the 9.04 L, 40% is antifreeze

amount of antifreeze = 0.4 * 9.04 = 3.616 L

moles of antifreeze present = 3.616/22.4 = 0.16 moles

moles of antifreeze in 60% solution = 0.6 * v/22.4 = 0.027 * v

(where v is the volume of final solution)

molarity of initial solution = 0.16/9.04 = 0.018 M

molarity of final solution = 0.027*v/v = 0.027 M

m1*v1 = m2*v2

0.018 * 9.04 = 0.027 * v

v = 0.018 * 9.04/0.027

v = 6.026 L

amount if antifreeze in the final solution = 6.026 * 0.027 =

0.163 Moles of antifreeze

amount in L = 0.163 * 22.4 = 3.65 L

amount in quarts = 3.65/1.13 = 3.23 quarts

4 0

3 years ago

Healthy Gym

ehidna [41]

Answer:

$c=2d+5$

Step-by-step explanation:

Let

d ------> the number of days

c -----> the cost

we know that

The cost is equal to the number of days multiplied by $2 per day plus the initial fee of $5

The linear equation in slope-intercept form is

$c=md+b$

where

m is the slope

b is the c-intercept (value of c when the value of d is equal to zero)

in this problem we have

m=$2 per day

b=$5

substitute

$c=2d+5$

8 0

3 years ago

Read 2 more answers

Conti. 7-10 thanks a lot! unhelpful answers will be deleted.

Marysya12 [62]

Answers:

10. b. $\displaystyle 13$

9. b. $\displaystyle 20$

8. a. $\displaystyle 33$

7. a. $\displaystyle 25°$

Step-by-step explanations:

10. Both segments are considered congruent, so turn both expressions into an equation:

$\displaystyle 3x - 5 = x + 7 \hookrightarrow \frac{-12}{-2} = \frac{-2x}{-2} \\ \\ 6 = x$

Plug this back into the equation to get $\displaystyle 13$ on both sides.

9. All edges in a square obtain congruent right angles and edges, so set $\displaystyle 45$ equivalent to the given expression:

$\displaystyle 45 = 2x + 5 \hookrightarrow \frac{40}{2} = \frac{2x}{2} \\ \\ \boxed{20 = x}$

8. Both angles are considered supplementary, so turn both expressions into an equation and set it to one hundred eighty degrees:

$\displaystyle 180 = (4x - 15)° + (x + 30)° \hookrightarrow 180° = (15 + 5x)° \hookrightarrow \frac{165}{5} = \frac{5x}{5} \\ \\ \boxed{33 = x}$

7. In this rectangle, segment EO is a segment bisectour, making these angles Complementary Angles. Therefore, set an equation up to find its complement:

$\displaystyle 90° = 65° + m\angle{VOE} \\ \\ \boxed{25° = m\angle{VOE}}$

I am joyous to assist you at any time.

3 0

2 years ago

How many solutions does the equation have? 7x +3 - x=3(1 + 2x) (A) 0 (B) 1. (C) infinitely many

tekilochka [14]

Answer:

C) Infinitely many

Step-by-step explanation:

7x+3-x=3(1+2x)

6x+3=3+6x

Subtract 3 from both sides

6x = 6x

Infinitely many solutions

5 0

3 years ago