Someone please tell me how to solve this

Determine the equation whose roots are –1 –5 and –3

Alexus [3.1K]

Well you are given the roots.

if we have 3 it would.have to be x^3. So something like:

y = ax^3 + bx^2 + cx + d

this could.also be written:

y = (x + a) (x + b) (x + c)

when you are able to write it like this, we know that the opposite of a, b, and c are roots. this is because if we can make any of the insides of the 3 parenthesis equal 0 then y = 0 and that x.is a root. Well if we know the 3 roots that x will be then we just have to figure out the a, b, and c. So let's plug our roots in.

y = (-1 + a) (-5 + b) (-3 + c)

now we have to make each parenthesis equal 0 to find what a, b, and c should be. It is obvious a = 1 to make.that one zero and b = 5 and c = 3. So we know a, b, and c. now let's plug.those into our first equation.

y = (x + 1) (x + 5) (x + 3)

this is your equation. You can multiply out if necessary

5 0

3 years ago

a 10-foot ladder leans against a wall with its foot braced 3 feet from wall's base. how far up the wall does the ladder reach? r

andrezito [222]

Use pythagoras teorem

10^2 = 3^2 + x^2

x^2 = 100 - 9 = 91

x = 9.54 feet to nearest hundredth

8 0

3 years ago

Increasing numbers of businesses are offering child-care benefits for their workers. However, one union claims that fewer than 8

Y_Kistochka [10]

Answer: c. -2.15

Step-by-step explanation:

As per given we have:

Null hypothesis : $H_{a}: p\geq0.80$

Alternative hypothesis : $H_{a}: p$

let p be the proportion of firms in the manufacturing sector offer child-care benefits

A random sample of 390 manufacturing firms is selected and 295 of them offered child-care benefits.

sample size : n= 390

sample proportion : $\hat{p}=\dfrac{295}{390}=0.7564$

Test statistic for proportion :

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

Substitute the values , we get

$z=\dfrac{0.7564-0.80}{\sqrt{\dfrac{0.80(1-0.80)}{ 390}}}$

$z=\dfrac{-0.0436}{\sqrt{0.000410256410256}}$

$z=-2.15257752474\approx-2.15$

Hence, the value of test statistic = -2.15

Correct option is c. -2.15 .

4 0

3 years ago

Please give me the answers ASAP

dlinn [17]

Answer:

I think C i'm not sure yet just let someone else answer and yea. But have a nice day as well.

Step-by-step explanation:

7 0

2 years ago

How do you solve this step by step?

Sphinxa [80]

Answer:

x = 41

Step-by-step explanation:

To solve this problem, we want to find the value of 'x' by isolating it (separating 'x' from all other numbers).

First, simplify the expression by using the <u>distributive property</u>, where you multiply the number outside the brackets with each term inside the brackets.

Then isolate 'x' by doing reverse operations (on both sides) for every number that is on the same side as 'x'. Reverse operations are opposites (addition and subtraction, multiplication and division) and "cancel out" a number, which "moves" it to the other side.

7(x - 5) = 252 Use the distributive property

7x - 35 = 252 Result of 7 times x and 7 times -5

7x - 35 + 35 = 252 + 35 Add 35 to both sides

7x = 252 + 35 -35+35 on the left side cancelled out. Simplify right side

7x = 287 Continue to isolate 'x'

7x/7 = 287/7 Divide both sides by 7

x = 287/7 Left side cancelled out to be 'x'. Simplify the right side

x = 41 Answer

Check your answer:

Substitute 'x' for 41 in the original equation. Then, make sure that the equation is still balanced. Keep in mind BEDMAS order (brackets, exponents, division, multiplication, addition, subtraction).

7(x - 5) = 252

7(41 - 5) = 252 Simplify inside the brackets first

7(36) = 252 Multiply

252 = 252 Same answer

LS = RS

Since left side (LS) equals (=) right side (RS), the equation is still balanced and we got the correct value for 'x'.

6 0

3 years ago