3 years ago

Factor as the product of two binomials. x^2 + 3x +2

Mathematics

1 answer:

Sergio039 [100]3 years ago

5 0

The answer would be (x+2) (x+1)

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Supply and demand coordinate to determine prices by working

Verdich [7]

The Answer is Together

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4 years ago

A rectangular box is to have a square base and a volume of 12 ft3. If the material for the base costs $0.17/ft2, the material fo

katen-ka-za [31]

Answer:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

Step-by-step explanation:

Let the dimensions of the box be x, y and z

The rectangular box has a square base.

Therefore, Volume of the box $V=x^2z$

Volume of the box $=12 ft^3\\$

$Therefore, x^2z=12\\z=\frac{12}{x^2}$

The material for the base costs $\$0.17/ft^2$ , the material for the sides costs $\$0.10/ft^2$ , and the material for the top costs $\$0.13/ft^2$ .

Area of the base $=x^2$

Cost of the Base $=\$0.17x^2$

Area of the sides $=4xz$

Cost of the sides= $=\$0.10(4xz)$

Area of the Top $=x^2$

Cost of the Base $=\$0.13x^2$

Total Cost, $C(x,z) =0.17x^2+0.13x^2+0.10(4xz)$

Substituting $z=\frac{12}{x^2}$

$C(x) =0.17x^2+0.13x^2+0.10(4x)(\frac{12}{x^2})\\C(x)=0.3x^2+\frac{4.8}{x} \\C(x)=\dfrac{0.3x^3+4.8}{x}$

To minimize C(x), we solve for the derivative and obtain its critical point

$C'(x)=\dfrac{0.6x^3-4.8}{x^2}\\Setting \:C'(x)=0\\0.6x^3-4.8=0\\0.6x^3=4.8\\x^3=4.8\div 0.6\\x^3=8\\x=\sqrt[3]{8}=2$

Recall: $z=\frac{12}{x^2}=\frac{12}{2^2}=3\\$

Therefore, the dimensions that minimizes the cost of the box are:

(a)Length =2 feet

(b)Width =2 feet

(c)Height=3 feet

7 0

3 years ago

Point (6, 0) lies on the<br><br> X-axis<br> Oy-axis<br> line y = x

tresset_1 [31]

Answer:

x - axis

Step-by-step explanation:

Since, y-coordinate of point (6, 0) is zero.

Hence, it lies on x - axis.

4 0

3 years ago

Read 2 more answers

what is the volume of a triangular prism that is 75 centimeters long and that has a base with an area of 30 square centimeters

pychu [463]

75 * 30= 2250 that's how u get the answer

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3 years ago

Determine two compatible numbers to use to estimate the quotient 5,071/62?

Charra [1.4K]

C. Both of those numbers are very close to the original numbers.

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3 years ago