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saw5 [17]
2 years ago
7

1. If your local library allows you to check out up to 10 books every month, what is the

Mathematics
1 answer:
ANEK [815]2 years ago
5 0

Answer:

290 books

Step-by-step explanation:

10 × 12= 120

120×2= 240

10×5=50

50+240= 290 books in 2 years and 5 months. hope this helps!

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What is the smallest prime number p such that
Ne4ueva [31]

The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.

<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>

The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.

i.e.

  • p^3 + 4p^2 + 4p

By factorization, we have:

  • = p(p+2)²

Now, to get exactly 30 divisor.

  • (p+2)² requires to give us 15 factors.

Therefore, we can have an equation p + 2 = p₁ × p₂²

where:

  • p₁ and  p₂ relate to different values of odd prime numbers.

So, for the least values of p + 2, Let us assume that:

  • p₁ = 5 and p₂ = 3

p + 2 = 5 × 3²

p + 2 = 5 × 9

p + 2 = 45

p = 45 - 2

p = 43

Therefore, we can conclude that the smallest prime number p such that

p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.

Learn more about prime numbers here:

brainly.com/question/145452

#SPJ1

8 0
2 years ago
Solve the system of equations. y = -5x + 24 y = 4x - 21 a. ( -5, -1) c. ( -1, 5) b. ( 5, -1) d. No solution
Svetlanka [38]

y = -5x + 24

y = 4x - 21

Since both of these equations are equal to Y, theyre equal to each other.

So we can make an equation with y = -5x + 24 in one side and y = 4x - 21 on the other.

-5x + 24 = 4x - 21

Now in order to get the value of x we need to isolate it in one side of the equation. We can do this by subtracting 24 from both sides of the equation:

-5x + 24 - 24 = 4x - 21 - 24

-5x = 4x - 45

Now we subtract 4x from both sides so the 4x shift to the other side

-5x - 4x = 4x - 4x - 45

-9x = -45

Finally divide both sides by -9 so x is by itself

(-9)÷(-9x) = -(45)÷(-9)

x = 5

Since we did all of this to BOTH sides of the equation, both sides are still equal to each other and the equation still is true.

Now apply x = 5 to either of the initial equations to find the value of Y

y = -5x + 24 or y = 4x - 21

(I'll do both but u only need one)

y = -5(5) + 24

y = -25 + 24

y = -1

y = 4(5) - 21

y = 20 - 21

y = -1

Either way, X is 5 and Y is -1

Answer (5, -1)

5 0
3 years ago
214 out of 450 students went to a concert, what percent did not go?
Vera_Pavlovna [14]

Answer:

.75% .0075 of the people that went to the concert said they would go if they could not see the band again. To find this you simply divide 9 by 1200, which equals .0075

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
a class voted for either rollerblading, swimming, or biking as their favorite summer activity. if rollerblading got 21% percent
Sauron [17]

Answer:  39% voted for biking

Step-by-step explanation:

Add the other two percentages and subtract from 100

40 + 21 = 61

100 - 61 = 39

8 0
3 years ago
Find F of G of X where f of x equals 9 over X and G of x equals x over x + 1​
Sergeu [11.5K]
Sorry I can’t answer this right now but I’ll will answer later
8 0
3 years ago
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