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2 years ago

What is the value of y in the system of equations 6x-y=2 and 4x-y=-8

Mathematics

1 answer:

uysha [10]2 years ago

8 0

Answer:

y=28

Step-by-step explanation:

6x-y=2

-y=2-6x

y=6x-2

4x-(6x-2)=-8

4x-6x+2=-8

-2x=-10

x=5

y=6*5-2=30-2=28

y=28

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leva [86]

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2 years ago

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ABCD is a square. M is the midpoint of BC and N is the midpoint of CD. A point is selected at random in the square. Calculate th

almond37 [142]

Answer:

1/8 or 0.125

Step-by-step explanation:

Let x be the length of the sides of the square ABCD.

Therefore, the length of CN and CM is x/2.

The area of the triangle MCN is:

$A_t = \frac{0.5x*0.5x}{2}=\frac{x^2}{8}$

The area of the square ABCD is:

$A_s =x*x =x^2$

Thus, the probability that a random point lies in the triangle MCN is:

$P=\frac{A_t}{A_s}=\frac{\frac{x^2}{8}}{x^2}=\frac{1}{8}=0.125$

The probability that the point will lie in the triangle MCN is 1/8 or 0.125.

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3 years ago

Martin uses his power saw every 15 seconds.How many times did he use it in one hour ?

Alina [70]

Answer:

60÷15 =4

Therefore Martin uses his power saw 4 times in one hour 

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3 years ago

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The Empire State Building is just over 1,450 feet tall. In anticipation of visiting this landmark on your vacation, you create a

Sergio [31]

Answer:

365 and 1/2 blocks will be used

The scale fact is 0.25

Step-by-step explanation:

So . .

We create a ratio 1:2

This represents 1 block is equivalent to 2 feet

Simply 1450 ÷ 2 = 725

So . . There are 725 feet and because One block is equal to 2 feet you divide 725 ÷ 2 = 362.5 blocks will be used

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362.5 ÷ 1450 = .25

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2 years ago

Y=4x-6 and passes through point 8,12

umka2103 [35]

Answer:

Slope of required line if both lines are parallel: y=4x-20

Slope of required line if both lines are perpendicular: y=-1/4x+14

Step-by-step explanation:

We need to find equation of line while we are given another line having equation y=4x-6 and passes through point (8,12)

Note: Since it is not given if the required line is parallel or perpendicular to the given line. I will solve for both cases.

If Both lines are parallel the equation of new line will be:

We need to find slope and y-intercept to write equation of new line.

When lines are parallel there slopes are same

So, slope of given line y=4x-6 is 4 (Compare with general equation y=mx+b, m is slope so m=4)

Slope of new line is: m=4

Now finding y-intercept

Using slope m=4 and point (8,12) we can find y-intercept

$y=mx+b\\12=4(8)+b\\12=32+b\\b=12-32\\b=-20$

y-intercept of new line is: b=-20

Equation of required line having slope m=4 and y-intercept b=-20 is

$y=mx+b\\y=4x-20$

If Both lines are perpendicular the equation of new line will be:

We need to find slope and y-intercept to write equation of new line.

When lines are perpendicular there slopes are opposite of each other

So, slope of given line y=4x-6 is 4 (Compare with general equation y=mx+b, m is slope so m=4)

Slope of new line is: m=-1/4

Now finding y-intercept

Using slope m=-1/4 and point (8,12) we can find y-intercept

$y=mx+b\\12=-\frac{1}{4} (8)+b\\12=-2+b\\b=12+2\\b=14$

y-intercept of new line is: b=14

Equation of required line having slope m=-1/4 and y-intercept b=14 is

$y=mx+b\\y=-\frac{1}{4} x+14$

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2 years ago