MATHEMATICS HIGH SCHOOL

Find the greatest common factor.
2y^3, 8y

Answers

Answer 1
Answer:

Answer:

STEP1:Equation at the end of step 1

2y3 - 8y

STEP2:

STEP3:Pulling out like terms

 3.1     Pull out like factors :

   2y3 - 8y  =   2y • (y2 - 4) 

Trying to factor as a Difference of Squares:

 3.2      Factoring:  y2 - 4 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

         A2 - AB + BA - B2 =

         A2 - AB + AB - B2 =

         A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 4 is the square of 2

Check :  y2  is the square of  y1 

Factorization is :       (y + 2)  •  (y - 2) 

Final result :

2y • (y + 2) • (y - 2)

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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room.

Mario paid $44.25 in taxi fare from the hotel to the airport. The cab charged $2.25 for the first mile plus $3.50 for each additional mile. How many miles was it from the hotel to the airport?

Answers

Answer:

12 miles

Step-by-step explanation:

2.25+3.50x=44.25

3.50x=42

x=12

Find the upper bonds for the following lengths : a) 40cm measured to the nearest cmB)82.8cm measured to the nearest tenth of a cm

Answers

Answer: a= 40.5 b= 82.85

Step-by-step explanation:

WILL FAN AND MEDAL!! Dilation problem!!!Polygon MNOPQ is dilated by a scale factor of 0.8 with the origin as the center of dilation, resulting in the image M′N′O′P′Q′. If M = (2, 4) and N = (3, 5), what is the slope of line M'N'?

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Answer:

Slope of line M'N' is 1.

Step-by-step explanation:

Given: M= (2,4) and N = (3, 5) ; K = 0.8

The rule of dilation with origin as the center:

(x ,y) \rightarrow (kx , ky) where k is the scale factor i.e k = 0.8

or   (x ,y) \rightarrow (0.8x , 0.8y)

Then:

Apply this on coordinates of MNOPQ to find M' and N'.

M(2 ,4) * (0.8\cdot 2 , 0.8\cdot 4) = M'(1.6 , 3.2)

N(3 ,5) * (0.8\cdot 3 , 0.8\cdot 5) = N'(2.4 , 4)

Slope of line for any two points (x_1 , y_1) and (x_2, y_2) is given by:

m = (y_2-y_1)/(x_2-x_1)

To find the slope of line M'N':

we have M' = (1.6 , 3.2) and N' = (2.4, 4)

then by slope formula;

Slope of line M'N' = (4-3.2)/(2.4-1.6)=(0.8)/(0.8) = 1

Therefore, slope of line M'N' is 1.
slope=((y2)−(y1))/((x2)−(x1))=(5-4)/(3-2)=1/1=1 The answer is one

Helpp ill mark u as brainlist ​

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Answer:

Inverse proportion

Step-by-step explanation:

Inverse proportion, as x increases, y decreases

You start at (10 ,6). you move down 2 units and up 4 units

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