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2 years ago

Need help Asap thank you in advance

Mathematics

1 answer:

julia-pushkina [17]2 years ago

3 0

Answer:

$12x^4-20x^2+32x=4x(3x^3-5x+8)$

Step-by-step explanation:

<u>Common Factors</u>

An algebraic expression that is formed by sums or subtractions of terms can be factored provided there are numeric or variable common factors in all the terms.

The following expression

$Z=12x^4-20x^2+32x$

Can be factored in the constants and in the variable x.

1. To find the common factor of the variable, we must locate if the variable is present in all terms. If so, we take the common factor as the variable with an exponent which is the lowest of all the exponents found throughout the different terms. In this case, the lowest exponent is x (exponent 1).

2. To find the common factors of the constants, we take all the coefficients:

12 - 20 - 32

and find the greatest common divisor of them, i.e. the greatest number all the given numbers can be divided by. This number is 4, since 12/4=3, 20/4=5 and 32/4=8

3. The factored expression is

$Z=12x^4-20x^2+32x=4x(3x^3-5x+8)$

$\boxed{12x^4-20x^2+32x=4x(3x^3-5x+8)}$

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Brass is made from a mixture of copper and other elements. a mixture that is 80% copper is combined with a mixture that is 60% c

algol [13]

The equation that can be used to find x, the amount of the 60% mixture used to create the 65% mixture is:

0.60*x + 0.80*(100 - x) = 0.65*(100).

<h3>Which equation we should use?</h3>

First, let's define two variables:

x = pounds of the 60% copper brass.
y = pounds of the 80% copper brass.

We know that we want to make 100 lb of 65% copper brass, then we must have that:

x + y = 100

And the percentage of copper before and after mixing must be the same, so we can write:

0.60*x + 0.80*y = 0.65*(x + y).

(where the percentages are written in decimal form).

Then we have a system of equations:

x + y = 100

0.60*x + 0.80*y = 0.65*(x + y).

To get a single equation, we can isolate the variable "y" on the first equation:

y = 100 - x

Now we replace that in the other equation:

0.60*x + 0.80*(100 - x) = 0.65*(100).

This is what we wanted to get, an equation that can be used to find x, the amount of the 60% mixture used to create the 65% mixture.

If you want to learn more about systems of equations:

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4 0

1 year ago

A triangle has an area of 24 square units. Its height is 6 units.

devlian [24]

Area of triangle=1/2 times base times height
given that area=24 and height=6
24=1/2 times base times 6
24=1/2 times 6 times base
24=3 times base
divide both sides by 3
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the base is 8 units long

4 0

2 years ago

Read 2 more answers

a portion of 7200 is invested at 5 1/2 percent interest, and the rest is invested at 5 percent interest. if the yearly income fr

lana [24]

Answer:

A 5.5% = 5400 B 5% = 1800

Step-by-step explanation:

A + B = 7200

A * 0.055 + B * 0.05 = $387

A = 7200 - B

(7200 - B)*0.055 + B*0.05 = 387

396 - 0.055B + 0.05B = 387

396 - 0.005B = 387

0.005B = 9

B = 1800

A = 7200 - B = 7200 - 1800

A = 5400

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2 years ago

Find the value of x.

Elena-2011 [213]

Answer:

x = 13

Step-by-step explanation:

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2 years ago

URGENT!!!!<br> Please add workings out

Artist 52 [7]

Answer: 26.457 cm

Explanation:

First, the height of an equilateral triangle of side length a is:

$h = \frac{\sqrt{3} }{2}*a$

In this case, the side-length of the triangles is a = 10cm, then the height will be:

$h = \frac{\sqrt{3} }{2}*10cm = 8.66cm$

Now we can think on a triangle rectangle such that:

Point A and point F are vertexes of the triangle.

The line we want to find, the line from A to F, is the hypotenuse.

One cathetus is a the height of the triangle, that comes down from point A, the length of this cathetus is 8.66cm

The other cathetus is equal to half the side length of the triangles (5cm) plus the segments BD and DF (of 10cm each)

Then the length of this cathetus is 10cm + 10cm + 5cm = 25cm

Now, we can remember the Pythagorean theorem.

If H is the hypotenuse, and A and B are the catheti, then we have:

A^2 + B^2 = H^2

In this case, we know the length of both cathetus, and want to know the length of the hypotenuse, then:

(25cm)^2 + (8.66cm)^2 = H^2

√( (25cm)^2 + (8.66cm)^2) = H = 26.457 cm

Then the line from A to F is 26.457 cm

6 0

2 years ago