MATHEMATICS MIDDLE SCHOOL

The remainder obtained when x^4 + 3x^2 - 2x + 2 is divided by (x + b) is the square of the
remainder obtained when x^2 – 3 is divided by (x + b). Find the values of b.​

Answers

Answer 1
Answer:

Use the polynomial remainder theorem: the remainder upon dividing a polynomial p(x) by x-c is p(c).

(-b)^4+3(-b)^2-2(-b)+2=b^4+3b^2+2b+2

((-b)^2-3)^2=b^4-6b^2+9

Now

b^4+3b^2+2b+2=b^4-6b^2+9\implies9b^2+2b-7=0

\implies(9b-7)(b+1)=0

\implies b=\frac79\text{ or }b=-1

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Kelly is having a party. She wants to make punch. The recipe for punch uses 3 pints of pineapple juice, 5 cups or orange juice, 1/4 gallon of lemonade, and 1 quart of apricot nectar. Kelly says her recipe will make 20 cups of punch. Is Kelly correct? Explain your answer.

An expression is shown below. What is the product of the two factors ?

Answers

Answer:  The required product is x^2.

Step-by-step explanation:  We are given to find the product of the following two factors.

P=(x^(4)/(3))(x^(2)/(3)).

We will be using the following property of exponents:

a^x* a^y=a^(x+y).

We have

P\n\n=(x^(4)/(3))(x^(2)/(3))\n\n=x^(4+2)/(3)\n\n=x^(6)/(3)\n\n=x^2.

Thus, the required product is x^2.
Simplify the expression....
you have...
( x^{ (4)/(3) } )( x^{ (2)/(3) } )
simplifying it...
x^(2)
The product of the two factors....
Thus, your answer. 

Candace used 5/8 of her savings to buy a $531.25 laptop.  How much did she have in savings before purchasing the laptop?

Answers

x-savings\n\n(5)/(8)x=531,25\ \ \ \ |\cdot(8)/(5)\nx=850\n\nCandance\ had\ \$ 850\ savings.

Final answer:

To find out how much Candace had in savings before purchasing the laptop, we will use the equation: Savings before purchase = Total savings + Amount spent on laptop. Candace had $849.20 in savings before purchasing the laptop.

Explanation:

To find out how much Candace had in savings before purchasing the laptop, we will use the equation:

Savings before purchase = Total savings + Amount spent on laptop

Since Candace used 5/8 of her savings to buy the laptop, the amount spent on the laptop is 5/8 of the total savings. We can set up the equation as:

  1. Total savings = Amount spent on laptop / 5/8
  2. Total savings = $531.25 / 5/8
  3. Total savings = $531.25 * 8/5
  4. Total savings = $849.20

Therefore, Candace had $849.20 in savings before purchasing the laptop.

Learn more about Savings calculations here:

brainly.com/question/33031196

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in the pet store, 1/6 of the puppies are black and 1/4 are white. what fraction of the puppies are black or white?​

Answers

Answer:

5/12

1/6+1/4=5/12

A punch  recipe calls for 3 pints of orange juice does the recipe How many ounces oof oranges juice does it requirew

Answers

16 fl oz = 1 pint
16 x 3
48
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Rick is deciding what to wear to school. He has two different shirts, two different pants and two different pairs of shoes to choose from. How many different outfit combinations does he have to choose from?

Answers

Answer:

a total of 8 outfits

Step-by-step explanation:

shoes: L1, L2

shirts: S1, S2

pants: P1, P2

1: S1, P1, L1

2: S1, P1, L2

3: S1, P2, L1

4: S1, P2, L2

5: S2, P1, L1

6: S2, P1, L2

7: S2, P2, L1

8: S2, P2, L2

I hope that makes sense, since I couldnt figure out how to show the diagram.

If rectangles must have right angles, explain how a rhombus could also be called a rectangle.

Answers

It can because u can flip or change it the other way
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