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3 years ago

FACTOR OUT THE GCF: 6d^5-10d^2

Mathematics

1 answer:

Ainat [17]3 years ago

8 0

Answer:

GCF: 2d²

Step-by-step explanation:

Write out all the factors of 6:

-----------

6 1

3 2

Write all the factors of 10:

--------------

10 1

5 2

The GFC of both of those numbers is 2.

Since both numbers have a variable of d, and since they both have exponents, you can multiply both numbers by d², because there is at least one d² in each variable.

Your full answer would be: 2d²(3d³ - 5)

If you use foil, remember you don't multiply exponents, you add them.

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Nter the equation of the line in slope-intercept form.<br><br> Slope is 6, and (1, 3)

kupik [55]

Answer:

The equation in the slope-intercept form will be:

$y=6x-3$

Step-by-step explanation:

Given

slope = m = 6

point = (1, 3)

As we know that the equation of a line in point-slope form is

$y-y_1=m\left(x-x_1\right)$

substituting the values m = 6 and point = (1, 3)

$y-3=6\left(x-1\right)$

Writing the equation in slope-intercept form

$y=mx+b$

where m is the slope, and b is the y-intercept

so the equation of the line in slope-intercept form becomes

$y-3=6\left(x-1\right)$

add 3 to both sides

$y-3+3=6\left(x-1\right)+3$

$y=6x-3$

Therefore, the equation in the slope-intercept form will be:

$y=6x-3$

6 0

3 years ago

Conversion. Write a reduced fraction notation for 0.56.

____ [38]

Answer:

Reduced fraction: 14/25

Step-by-step explanation:

To write 0.56 in terms of fractions we need to multiply and divide the number by 100:

(0.56 * 100)/100 = 56/100. Then we simplify the fraction by dividing the numerator and denominator by the common factor 2 as many times as possible:

56/100 = 28/50 = 14/25

The fraction 14/25 cannot be more simplified

7 0

3 years ago

Read 2 more answers

How to Factor r^2-5r-14

12345 [234]

Answer:

(r-7)(r+2)

Step-by-step explanation:

First, let's look at the -14. Possible factors for that number are (-2, 7) (2, -7) (1, -14) and (-1, 14).

Now, let's look at the -5. How can we make -5 with the pairs that we just found?

The only possible way is 2 and -7 (added together equals -5)

6 0

3 years ago

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Find the length of the height of the right trapezoid shown below, if it has the greatest possible area and its perimeter is equa

Artyom0805 [142]

Answer:

The height of the right trapezoid is $\frac{6}{5+\sqrt{3}}\ units$

Step-by-step explanation:

Let

x ----> the height of the right trapezoid in units

we know that

The perimeter of the figure is equal to

$P=AB+BC+CD+DH+HA$

we have

$P=6\ units$

$AB=BC=CH=HA=x$ ---> because is a square

substitute

$6=x+x+CD+DH+x$

$6=3x+CD+DH$ -----> equation A

<em>In the right triangle CDH</em>

$sin(30\°)=\frac{CH}{CD}$

$sin(30\°)=\frac{1}{2}$

Remember that $CH=x$

$\frac{1}{2}=\frac{x}{CD}$

$CD=2x$

$tan(30\°)=\frac{CH}{DH}$

$tan(30\°)=\frac{\sqrt{3}}{3}$

$\frac{\sqrt{3}}{3}=\frac{x}{DH}$

$DH=x\sqrt{3}$

substitute the values in the equation A

$6=3x+CD+DH$ -----> equation A

$CD=2x$

$DH=x\sqrt{3}$

$6=3x+2x+x\sqrt{3}$

$6=5x+x\sqrt{3}$

$6=x[5+\sqrt{3}]$

$x=\frac{6}{5+\sqrt{3}}\ units$

5 0

2 years ago

What is the midpoint of side AB in the triangle below?

Ierofanga [76]

Step-by-step explanation:

half of 11 is 5.5 so counting that from either of the points leads to .5

Then continuing from there, half of 9 is 4.5 so moving the point up would get 2.5

3 0

3 years ago

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