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damaskus [11]
3 years ago
8

if joelle multiplied 792 by a positive integer and came up with a perfect square, what is the smallest integer she could have mu

ltiplied by?
Mathematics
1 answer:
antoniya [11.8K]3 years ago
7 0
The positive integer is 22.
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Answer please I’m dying from math
charle [14.2K]

Answer:

\huge\boxed{\text{D)} \  15x^4 + 2x^3 - 8x^2 - 22x - 15}

Step-by-step explanation:

We can solve this multiplication of polynomials by understanding how to multiply these large terms.

To multiply two polynomials together, we must multiply each term by each term in the other polynomial. Each term should be multiplied by another one until it's multiplied by all of the terms in the other expression.

  • <em>We can do this by focusing on one term in the first polynomial and multiplying it by </em><em>all the terms</em><em> in the second polynomial. We'd then repeat this for the remaining terms in the second polynomial.</em>

Let's first start by multiplying the first term of the first polynomial, 3x^2, by all of the terms in the second polynomial. (5x^2+4x+5)

  • 3x^2 \cdot  5x^2 = 15x^4
  • 3x^2 \cdot 4x = 12x^3
  • 3x^2 \cdot 5 = 15x^2

Now, we can add up all these expressions to get the first part of our polynomial. Ordering by exponent, our expression is now

  • \displaystyle 15x^4 + 12x^3 + 15x^2

Now let's do the same with the second term (-2x) and the third term (-3).

  • -2x \cdot 5x^2 = -10x^3  
  • -2x \cdot 4x = -8x^2
  • -2x \cdot 5 = -10x
  • Adding on to our original expression: \displaystyle 15x^4 + 12x^3 - 10x^3 + 15x^2 - 8x^2 - 10x

  • -3 \cdot 5x^2 = -15x^2
  • -3 \cdot 4x = -12x
  • -3 \cdot 5 = -15
  • Adding on to our original expression: \displaystyle 15x^4 + 12x^3 - 10x^3 + 15x^2 - 8x^2 - 15x^2 - 10x - 12x - 15

Phew, that's one big polynomial! We can simplify it by combining like terms. We can combine terms that share the same exponent and combine them via their coefficients.

  • 12x^3 - 10x^3 = 2x^3
  • 15x^2 - 8x^2 - 15x^2 = -8x^2
  • -10x - 12x = -22x

This simplifies our expression down to 15x^4 + 2x^3 - 8x^2 - 22x - 15.

Hope this helped!

7 0
2 years ago
Read 2 more answers
Mrs. Walters drove 360 miles on 25 gallons of gas. Mr. Walter drove 480 miles on 32 gallons of gas. SHOW YOUR WORK.
Dovator [93]
Mrs. Walters : 360/25 = 14.4 miles per gallon
Mr. Walter : 480/32 = 15 miles per gallon

Mr. Walter is getting better mileage per gallon


6 0
3 years ago
Isla pick tomatoes from her vegetable patch and then sells them in boxes she changes 14p for each tomatoes and 25p for each boxe
amid [387]

9514 1404 393

Answer:

  • 18 tomatoes: £3.02
  • £4.39 ⇒ 26 tomatoes

Step-by-step explanation:

a) at 12 tomatoes per box, 18 tomatoes will require 2 boxes. Then Isla's price will be ...

  2(25p) +18(14p) = 50p +252p = £3.02

18 tomatoes in 2 boxes cost £3.02.

__

b) The 3 boxes cost 3(25p) = £0.75, so the tomatoes cost ...

  £4.39 -0.75 = £3.64

at 14p each, the number of tomatoes is £3.64/£0.14 = 26

There are 26 tomatoes in 3 boxes costing £4.39.

7 0
2 years ago
The sector of a circle with a 12-inch radius has a central angle measure of 60°. What is the exact area of the sector in terms o
goldfiish [28.3K]
75.3982237 inches squared is the answer, round it to whatever decimal place your asked to.
3 0
3 years ago
Please help me solving this. I don't understand it and need help!!!!
KATRIN_1 [288]
56.6 ft is the side and the angle is 32 hope this helps!

8 0
3 years ago
Read 2 more answers
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