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3 years ago

When factored, the trinomials x2 + 4x − 21 and x2 + 11x + 28 have one binomial factor in common. What is this factor?

Mathematics

1 answer:

Gelneren [198K]3 years ago

6 0

Answer:

x + 7

Step-by-step explanation:

x2 + 4x − 21

set equal to 0

x2 + 4x − 21 = 0

factor

(x - 3) (x + 7)

x2 + 11x + 28

set equal to 0

x2 + 11x + 28 = 0

factor

(x + 4) (x + 7)

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Use the identity (x+y)(x2−xy+y2)=x3+y3 to find the sum of two numbers if the product of the numbers is 10, the sum of the square

professor190 [17]

Answer:

The sum of two numbers is 7.

Step-by-step explanation:

Given : the product of the numbers is 10, the sum of the squares of the numbers is 29, and the sum of the cubes of the numbers is 133.

Using identity $(x+y)(x^2-xy+y^2)=x^3+y^3$ and given details, we have to find the sum of two numbers.

Since, given that the product of the numbers is 10 that is $xy=10$

Also, given the sum of the squares of the numbers is 29 that is $x^2+y^2=29$

and the sum of the cubes of the numbers is 133 that is $x^3+y^3=133$

Using, the given identity $(x+y)(x^2-xy+y^2)=x^3+y^3$ ,

Substitute, the given values, we have,

$(x+y)(29-10)=133$

Simplify , we get,

$(x+y)(19)=133$

Divide both side by 19, we have,

$(x+y)=7$

Thus, the sum of two numbers is 7.

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3 years ago

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A bank contains 35 coins, all nickels and quarters. The total value of coins is $8.15. How many of each coin does the bank conta

Lina20 [59]

n + q = 35

n = 35-q

0.05n + 0.25q = 8.15

0.05(35-q) +0.25q = 8.15

1.75 -0.05q + 0.25q =8.15

1.75 + 0.20q = 8.15

0.20q = 6.40

q = 6.40 / 0.20 = 32

32 quarters and 3 nickels

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3 years ago

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2 years ago

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Marrrta [24]

Answer:

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Step-by-step explanation:

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I need this question solved with derivatives please:

Shkiper50 [21]

Answer:

16,242. 7 cm^3.

Step-by-step explanation:

We need to cut off a square piece at the 4 corners of the cardboard.

Let the length of their edges be x cm.

The volume of the box will be:

V = height * width * length

V = x(100-2x)(40-2x)

V = x(4000 - 200x - 80x + 4x^2)

V = x(4x^2 - 280x + 4000)

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V" = 24x - 560, when x = 8.8 V" is negative so this is a Maximum for V.

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3 years ago