What is the measure of y?

How do you factor 125-x^3?

xz_007 [3.2K]

Step-by-step explanation:

We have

$125 - x {}^{3}$

First, 125 is a perfect cube because

$5 \times 5 \times 5 = 125$

and

x^3 is a perfect cube because

$x \times x \times x = x {}^{3}$

so we can use the difference of cubes identity

$( {x}^{3} - {y}^{3} ) = (x - y)( {x}^{2} + xy + {y}^{2} )$

Let say we have two perfect cubes:

64 because 8×8×8=64

and 27 because 3×3×3=27 and let subtract

$64 - 27$

we know that

$64 - 27 = 37$

but using the difference of cubes identity we should get the same thing.

Remeber cube root of 64 is 4 and cube root of 27 is 3 so we have

$(4 - 3)( {4}^{2} + 4(3) + 3 {}^{2} )$

$1(16 + 12 + 9) = 1(37) = 37$

So the difference of cubes works for real numbers. This is a good way to help remeber the identity using real numbers.

Back on to the topic,

we know that 5 is cube root of 125 and x is the cube root of x^3 so we have

$(5 - x)( {5}^{2} + 5x + {x}^{2} ) =$

$(5 - x)(25 + 5x + {x}^{2} )$

3 0

2 years ago

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Yvonne is solving the quadratic equation 6x2 + 24x + 7 = 0 by completing the square. Her first four steps are shown in the table

vladimir1956 [14]

The step in which Yvonne first makes an error while solving the quadratic equation by completing the square in step 1.

<h3>What is a quadratic equation?</h3>

A quadratic equation is an equation in which the highest power of the variable is two.

Yvonne is solving the quadratic equation, which is,

6x² +24x +7 =0

He is solving the above equation by completing the square.

The first step to solving this quadratic equation by completing the square is, Take the constant value 7 at the opposite side of the equation as,

6x² +24x = -7

Here, the number seven was a positive number, which we have changed to negative because this number brings the other side of the equation.

In the image attached below, the first step of the Yvonne while solving the equation by completing the square is,

6x² +24x = 7

Here, Yvonne does not change the sign of the number 7 while taking it to another side of the equation.

Hence, the step in which Yvonne first makes an error while solving the quadratic equation by completing the square is step 1.

The table is attached with the answer below

Learn more about the quadratic equation here;

brainly.com/question/17177510

#SPJ1

8 0

2 years ago

find An Equation Of The Line Containg(3,-4) and Having slope -2.If This Line Contain The Points (a,8) and (5,b) find a and b

ss7ja [257]

Answer:

equation: y=-2x+2

a=-3

b=-8

Step-by-step explanation:

we need to find the equation of the line containing the point (3,-4) and has the slope (m) of -2

slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

we can plug what we know into the equation:

y=-2x+b

we need to find b though

since the point will pass through the point (3,-4) we can subsitute it into the equation to find b

-4=-2(3)+b

-4=-6+b

2=b

the y intercept is 2

so the equation is y=-2x+2

the line also contains the points (a,8) and (5,b)

first, let's find a

a is the x value of the point

we know the value of y (8)

substitute y as 8 and solve for x

8=-2x+2

subtract

6=-2x

-3=x=a

so a is -3

now find b

b is the y value of the point

we know the x value (5)

substitute x as 5 and solve for y

y=-2(5)+2

y=-10+2

y=-8=b

so b is -8

hope this helps!

4 0

3 years ago

Help please. I'll give the Brainliest.

sdas [7]

Answer:

Options 1,2,3 are correct statements

The first values in an ordered pair ( the coordinates) are the domain : ( -3,-2,-1,0,1)

The second values are the range : (-1,1,2,3,4,5)

One input should have only one output for a function.

But -1 input has 2 outputs: -1 and 3.

Thus, it is a relation and not a function.

Hope it helps :)

Mark it Brainliest pls:)

8 0

3 years ago

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A blue Jay wanted to store some acorns for the winter. If she hides 18 acorns per tree, she will be left with four acorns; if sh

Semenov [28]

Answer:

4 trees and 76 acorns.

Step-by-step explanation:

Let the amount of trees be x.

$18x+4=20x-4\\\\\implies2x=8\\\\\implies x=4$

There are 4 trees, and there are $18x+4$ acorns or 76 acorns.

Hope you have a nice day, and also you should mark brainliest :)

8 0

2 years ago

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