MATHEMATICS MIDDLE SCHOOL

Find the constant variation for the direct variation given 10y=13x 

f(x)=4.5x

x + y = 0

Answers

Answer 1
Answer: 10y=13x\ \ \ /:10\n\ny=1.3x\n\nconstant=1.3\n==================\nf(x)=4.5x\n\nconstant=4.5\n==================\nx+y=0\ny=-x\n\nconstant=-1

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Determine the number of solutions that exist to the equation. 8(j-4)=2(4j-16)

Answers

8(j-4)=2(4j-16)
8j - 32 = 8j - 32

Since both sides are equal, there are is an infinite number of solutions. 

triangle MKL is an isosceles triangle with MK congruent to ML. If Mk=7x-15, KL=4x-5, and ML=10x-42, find x and the measure of each side

Answers

Answer:

For given isosceles triangle ΔMKL with MK≅ML, x=9; MK=48, KL=31, ML=48.

Explanation:

An isosceles triangle has two of its 3 sides congruent.

For given ΔMKL, MK is congruent to ML (MK ≅ ML); i.e. length of side MK is equal to length of the side ML.

Given:

MK=7x-15

KL=4x-5

ML=10x-42

Equating MK with ML, we get:

MK=ML

7x-15 = 10x-42

Taking all x terms to the right,

42-15 = 10x-7x

27 = 3x

x=9

To find measure of each side MK, ML and KL; substitute the value of x=9 in corresponding equations.

MK = 7x-15  

= (7×9) - 15

= 63-15  

= 48

KL = 4x-5

= (4×9)-5

= 36-5

= 31

ML = 10x-42

= (10×9)-42

= 90-42

= 48

Therefore, for given ΔMKL with MK≅ML, x=9; MK=48, KL=31, ML=48.

Explain why 2 x 3/8 is equivalent to 2 x 3 x 1/8 ?

Answers

If you put the 2 over 1 in 2 x 3/8 and multiply cross like normal fractions, you will get 6/8. This reduces to 3/4. Similarly, if you multiply 2 x 3, you get 6. Put the 6 over 1 and multiply by 1/8 to get 6/8 as an answer which reduces to 3/4 as well.
2x + 3 = 8

Transpose 3

2x + 3 - 3 = 8 - 3

2x = 5

Divide both sides of the equation by 2

2x / 2 = 5 / 2

x = 5 / 2

x = 2 1/2

Which is the greatest of these rational numbers?19/25, 0.33, 0.680, 5/20

A) 0.33
B) 0.680
C) 19/25
D) 5/20

Answers

Answer:

19/25

Step-by-step explanation:

Convert the two fractions into decimals by dividing the numerator by the denominator. 19/25 = 0.76 and 5/20 = 0.25

Now you have: 0.76, 0,680, 0.33 and 0.25.

0.76 is the greatest rational number because it is closest to 1.0, making 19/25 the correct answer.

If a cow has a mass of 9×10^2 kilograms, and a blue whale has a mass of 1.8×10^5 kilograms, which of these statements is true?The blue whale has about 200 times more mass.


The cow has about 200 times more mass.


The blue whale has about 500 times more mass.


There is no way to compare the masses.

Answers

Answer:

The 1st answer, The blue whale has about 200 times more mass. might be correct.

Step-by-step explanation:

9 x 10 ^2= 900 kilograms

1.8 × 10 ^5= 180000 kilograms

180000 kilograms / 900 kilograms= 200 times

31000 rounded to the nearest ten thousand

Answers

The 3 is in the ten thousands place so the number to the right of that tells you if you need to tound up or down. Anynumber 5 or higher then you round up. If lower than five you leave it alone.
So answer is slready rounded -
A number rounded to the nearest 10000, means that the last four digits of that number (on the left of the decimal point) are 0.  
However, if the fourth-last digit to the left of the decimal point is 5 or greater, the number to the left of that is rounded to 1 number higher.  For example, if you were rounding 145293 to the nearest 10000, it would be 150000. 

However, the fourth-last digit to the left of the decimal point in this case is 1.  
Therefore,  31000 rounded to the nearest 10000 is 30000. 
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