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Vikki [24]
3 years ago
7

What are two different strategies for finding the product of 472 and 33.

Mathematics
1 answer:
Bad White [126]3 years ago
4 0
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Can someone please help me on 9 and 10 ty!!
vitfil [10]

Answer:

9. slope = 7-2/7-1

= 5/6

10. slope = 8- -2/5-4

= 10/1 = 10

5 0
3 years ago
Given that 2y^3+by-cy+d,where b,c and d are constants,leaves a remainder R when divided by (y+1) , (y-2) and (2y-1). Find the va
Eddi Din [679]

The polynomial remainder theorem says that a polynomial <em>p(x)</em> leaves a remainder of <em>p(k)</em> when it's divided by <em>x</em> - <em>k</em>.

We're given that dividing <em>p(y)</em> = 2<em>y</em>³ + <em>by</em>² - <em>cy</em> + <em>d</em> leaves the same remainder <em>R</em> after dividing it by <em>y</em> + 1, <em>y</em> - 2, and 2<em>y</em> - 1. So we have

<em>p</em>(-1) = 2(-1)³ + <em>b</em>(-1)² - <em>c</em>(-1) + <em>d</em> = <em>R</em>

==>  <em>R</em> = -2 + <em>b</em> + <em>c</em> + <em>d</em>

<em>p</em>(2) = 2(2)³ + <em>b</em>(2)² - <em>c</em>(2) + <em>d</em> = <em>R</em>

==>  <em>R</em> = 16 + 4<em>b</em> - 2<em>c</em> + <em>d</em>

<em>p</em>(1/2) = 2(1/2)³ + <em>b</em>(1/2)² - <em>c</em>(1/2) + <em>d</em> = <em>R</em>

==>  <em>R</em> = 1/4 + <em>b</em>/4 - <em>c</em>/2 + <em>d</em>

<em />

We're also given that <em>y</em> + 2 is a factor, which means dividing <em>p(y)</em> by it leaves no remainder, and so

<em>p</em>(-2) = 2(-2)³ + <em>b</em>(-2)² - <em>c</em>(-2) + <em>d</em> = 0

==>  0 = -16 + 4<em>b</em> + 2<em>c</em> + <em>d</em>

<em />

Solve the system of equations in boldface. You can eliminate <em>d</em> from the first 3 to first solve for <em>b</em> and <em>c</em>, then solve for <em>d</em> :

(-2 + <em>b</em> + <em>c</em> + <em>d</em>) - (16 + 4<em>b</em> - 2<em>c</em> + <em>d</em>) = <em>R</em> - <em>R</em>

-18 - 3<em>b</em> + 3<em>c</em> = 0

<em>b</em> - <em>c</em> = -6

(-2 + <em>b</em> + <em>c</em> + <em>d</em>) - (1/4 + <em>b</em>/4 - <em>c</em>/2 + <em>d</em>) = <em>R</em> - <em>R</em>

-9/4 + 3<em>b</em>/4 + 3<em>c</em>/2 = 0

<em>b</em> + 2<em>c</em> = 3

(<em>b</em> - <em>c</em>) - (<em>b</em> + 2<em>c</em>) = -6 - 3

-3<em>c</em> = -9

<em>c</em> = 3

<em>b</em> - 3 = -6

<em>b</em> = -3

-16 + 4(-3) + 2(3) + <em>d</em> = 0

<em>d</em> = 22

7 0
3 years ago
An investor puts $2,500 into a life insurance policy that pays 10% simple annual interest. If no additional investment is made i
Novosadov [1.4K]

Answer:

$3750

Step-by-step explanation:

Amount = principal + interest

Simple interest = Principal *Rate * time/100

Simple interest = 2500*10*5/100

Simple interest  = 25*50

Simple interest = $1250

Amount = $2500+$1250

Amount after 5 years is $3750

4 0
2 years ago
Lacey decides to take her five year old son to the history museum. The price for the child's ticket is 2.75 dollars less than th
Andrei [34K]
If the price for the adult ticket is $2.75 more than the child ticket, the adult ticket would be x + $2.75
3 0
3 years ago
What number is 2 * 10 ^100
Studentka2010 [4]

Answer:

2.00000000e+100

Step-by-step explanation:

2

2 \times {10}^{100}  = \\  2 \times 1.00000000e + 100=  \\  2.00000000e + 100

8 0
2 years ago
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