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ELEN [110]
3 years ago
14

The smallest integer that can be added to -2m3 − m + m2 + 1 to make it completely divisible by m + 1 is .

Mathematics
1 answer:
dangina [55]3 years ago
4 0

Recall the polynomial remainder theorem: if m-c is a factor of some polynomial p(m), then the remainder upon dividing p(m) by m-c is p(c).

Let c=-1 and p(m)=-2m^3+m^2-m+1. The remainder left from dividing p(m) by m+1 is

p(-1)=-2(-1)^3+(-1)^2-(-1)+1=5

If we subtract 5 from both sides, we'd get a "remainder" of 0, which suggests that we have to add -5 to p(m) to make m+1 a factor.

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. The larger number is 19 more than the smaller number. What are the numbers?
ASHA 777 [7]

Answer:

1

Step-by-step explanation:

4 0
3 years ago
The weekly incomes of a large group of executives are normally distributed with a mean of $2,000 and a standard deviation of $10
8_murik_8 [283]

Answer:

The z-score for an income of $2,100 is 1.

Step-by-step explanation:

If X \sim N (µ, σ²), then  Z=\frac{x-\mu}{\sigma}, is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z \sim N (0, 1).

The distribution of these z-variate is known as the standard normal distribution.

Given:

µ = $2,000

σ = $100

<em>x</em> = $2,100

Compute the <em>z</em>-score for the raw score <em>x</em> = 2100 as follows:

Z=\frac{x-\mu}{\sigma}=\frac{2100-2000}{100}=\frac{100}{100}=1

Thus, the z-score for an income of $2,100 is 1.

4 0
3 years ago
Math help @LIEMONDER
klio [65]
First picture)
I: 5x+2y=-4
II: -3x+2y=12

add I+(-1*II):
5x+2y-(-3x+2y)=-4-12
8x=-16
x=-2

insert x=-2 into I:
5*(-2)+2y=-4
-10+2y=-4
2y=6
y=3

(-2,3)

question 6)
I: totalcost=115=3*childs+5*adults
II: 33=adults+childs
33-adults=childs

insert childs into I:
115=3*(33-adults)+5*adults
115=99-3*adults+5*adults
16=2*adults
8=adults

insert adults into II:
33-8=childs
25=childs

so it's the last option

question 7)
a) y<6 and y>2 can also be written as 2<y<6, so solution 3 exist for example
b) y>6 and y>2 can also be written as 2<6<y, so solution 7 exist for example
c) y<6 and y<2 inverse of b: y<2<6, so for example 1
d) y>6 and y<2: y<2<6<y, this is impossible as y can be only either bigger or smaller than 2 or 6

so it's the last option

question 8)
I: x+y=12
II: x-y=6

subtract: I-II:
x+y-(x-y)=12-6
2y=6
y=3

insert y into I:
x+3=12
x=9

(9,3)

question 9)
I: x+y=6
II: x=y+5

if you take the x=y+5 definition of II and substitute it into I:
(y+5)+y=6

which is the second option :)
5 0
3 years ago
Multiply. (2.5 times 10^-8) (9 times 10^-10)
Lorico [155]

The complete answer is 2.25E-17

but I think it may be A

8 0
3 years ago
What is 38,800 rounded to the nearest hundred mark all that apply?
SashulF [63]
38,800 is the answer

4 0
3 years ago
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