Select the two binomials that are factors of this trinomial.

Please help me complete this quiz lol

melomori [17]

I believe the first answer is correct

7 0

3 years ago

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:

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8 0

2 years ago

Hundred chart: I am thinking of a number that is greater than 70 but less than 100.

Katyanochek1 [597]

The numbers which is greater than 70 but less than 100, not divisible by 10, not divisible by 4, not an odd number are 74, 78, 82, 86, 94, 98

<h3>Even and odd numbers</h3>

A number greater than 70 but less than 100
Not divisible by 10
Not divisible by 4
Not odd number

A number greater than 70 but less than 100

71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 98

Not odd number

72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98

Not divisible by 10

72, 74, 76, 78, 82, 84, 86, 88, 92, 94, 96, 98

Not divisible by 4

74, 78, 82, 86, 94, 98

Therefore, the numbers which is greater than 70 but less than 100, not divisible by 10, not divisible by 4, not an odd number are 74, 78, 82, 86, 94, 98.

Learn more about even and odd numbers:

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7 0

2 years ago

Solve the system of linear equations below. 2x + 3y = 2 x + 6y = 4 x........A.X=0, y =2/3..B..x =2, y = -2/3...C..x=4/3, y=2/9..

Bogdan [553]

I will solve your system by substitution.2x+3y=2;x+6y=4xStep: Solve2x+3y=2for x:2x+3y+−3y=2+−3y(Add -3y to both sides)2x=−3y+22x2=−3y+22(Divide both sides by 2)x=−32y+1Step: Substitute−32y+1forxinx+6y=4x:x+6y=4x−32y+1+6y=4(−32y+1)92y+1=−6y+4(Simplify both sides of the equation)92y+1+6y=−6y+4+6y(Add 6y to both sides)212y+1=4212y+1+−1=4+−1(Add -1 to both sides)212y=3212y212=3212(Divide both sides by 21/2)y=27Step: Substitute27foryinx=−32y+1:x=−32y+1x=−32(27)+1x=47(Simplify both sides of the equation)Answer:x=4/7 and y=2/7
is what i got sorry if it don't help

3 0

4 years ago

Find the surface area of the tool box. Round your answer to the nearest tenth and explain your answer. Pls I NEED THE ANSWER NO

Andrej [43]

Answer:

807.8 in^2

Step-by-step explanation:

The total area of the box is the sum of the areas of all faces of the box. The top, bottom, front, and back faces are rectangles 18 in long. The end faces each consist of a rectangle and a triangle. We can compute the sum of these like this:

The areas of top, bottom, front, and back add up to be 18 inches wide by the length that is the perimeter of the end: 2·5in +2·8 in + 9.6 in = 35.8 in. That lateral area is ...

(18 in)(35.6 in) = 640.8 in^2

The area of the triangle on each end is equivalent to the area of a rectangle half as high, so we can compute the area of each end as ...

(9.6 in)(8.7 in) = 83.52 in^2

Then the total area is the lateral area plus the area of the two ends:

640.8 in^2 + 2·83.52 in^2 = 807.84 in^2 ≈ 807.8 in^2

7 0

3 years ago