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3 years ago

Write an equivalent expression for each question

Mathematics

1 answer:

Mandarinka [93]3 years ago

4 0

Answer:

A. 16 - 4 x = 4(4 - x)

B. 4 x + 8 = 4( x + 2)

C. -8 b - 24 = -8(b + 3)

D. 54 + 9 x = 9 (x + 6)

Step-by-step explanation:

Here, the given expressions are:

A. 16 - 4 x

Now, 16 and 4 have 4 as their COMMON FACTOR.

⇒Taking out 4 as the factor, we get: 16 - 4 x = 4 ( 4 - x)

Hence, the equivalent expression of 16 - 4 x = 4 ( 4 - x)

B. 4x + 8

Now, 4 and 8 have 4 as their COMMON FACTOR.

⇒Taking out 4 as the factor, we get: 4 x + 8 = 4 ( x + 2)

Hence, the equivalent expression of 4 x + 8 = 4 ( x + 2)

C. -8b - 24

Now, -8 and -24 have (-8) as their COMMON FACTOR.

⇒Taking out (-8) as the factor, we get: -8b - 24 = (-8) ( b+ 3)

Hence, the equivalent expression of -8b - 24 = (-8) ( b+ 3)

D. 54 + 9x

Now, 54 and 9 have (9) as their COMMON FACTOR.

⇒Taking out (9) as the factor, we get: 54 + 9 x = 9( 6 + x)

Hence, the equivalent expression of 54 + 9 x = 9( 6 + x)

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Lines P and Q are parallel. What is the measure of angle 1

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Answer:

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Step-by-step explanation:

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8 0

3 years ago

If the slope of a line is 2 and it's y-intercept is 5, what is the equation of the line? A.x=2y+5 B. Y=5x+2 C. Y=2x+5 D. X=5y+2

frez [133]

The answer is y=2x+5

4 0

3 years ago

Please help, I didn't learn this in class!

NemiM [27]

Solve the following system using elimination:
{-2 x + 2 y + 3 z = 0 | (equation 1)
{-2 x - y + z = -3 | (equation 2)
{2 x + 3 y + 3 z = 5 | (equation 3)

Subtract equation 1 from equation 2:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
{0 x - 3 y - 2 z = -3 | (equation 2)
{2 x + 3 y + 3 z = 5 | (equation 3)

Multiply equation 2 by -1:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
{0 x+3 y + 2 z = 3 | (equation 2)
{2 x + 3 y + 3 z = 5 | (equation 3)

Add equation 1 to equation 3:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
{0 x+3 y + 2 z = 3 | (equation 2)
{0 x+5 y + 6 z = 5 | (equation 3)

Swap equation 2 with equation 3:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
{0 x+5 y + 6 z = 5 | (equation 2)
{0 x+3 y + 2 z = 3 | (equation 3)

Subtract 3/5 × (equation 2) from equation 3:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
{0 x+5 y + 6 z = 5 | (equation 2)
{0 x+0 y - (8 z)/5 = 0 | (equation 3)

Multiply equation 3 by 5/8:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
{0 x+5 y + 6 z = 5 | (equation 2)
{0 x+0 y - z = 0 | (equation 3)

Multiply equation 3 by -1:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
{0 x+5 y + 6 z = 5 | (equation 2)
{0 x+0 y+z = 0 | (equation 3)

Subtract 6 × (equation 3) from equation 2:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
{0 x+5 y+0 z = 5 | (equation 2)
{0 x+0 y+z = 0 | (equation 3)

Divide equation 2 by 5:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
{0 x+y+0 z = 1 | (equation 2)
{0 x+0 y+z = 0 | (equation 3)

Subtract 2 × (equation 2) from equation 1:
{-(2 x) + 0 y+3 z = -2 | (equation 1)
{0 x+y+0 z = 1 | (equation 2)
v0 x+0 y+z = 0 | (equation 3)

Subtract 3 × (equation 3) from equation 1:
{-(2 x)+0 y+0 z = -2 | (equation 1)
{0 x+y+0 z = 1 | (equation 2)
{0 x+0 y+z = 0 | (equation 3)

Divide equation 1 by -2:
{x+0 y+0 z = 1 | (equation 1)
{0 x+y+0 z = 1 | (equation 2)
{0 x+0 y+z = 0 | (equation 3)

Collect results:

Answer: {x = 1, y = 1, z = 0

7 0

3 years ago

Points A and B are on the different sides of a line 1, the distance between point A and the line lis 10 in, the distance between

givi [52]

Answer: Distance between O and the line 1 is 3 inches.

Explanation:

Since we have given that

Distance between point A and the line 1 = 10 inches

Distance between point B and the line 1 = 4 inches

Total length of segment AB is given by

$10+4=14\ inches$

Since O is midpoint of the line segment AB.

so, AO is given by

$\frac{14}{2}=7\ in.$

Now, Distance between O and the line 1 is given by

$10-7=3\ in.$

Hence, Distance between O and the line 1 is 3 inches.

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3 years ago

The sum of a two digit number and the number obtained by interchanging the digits is 132. If the two digits differ by 2, find th

damaskus [11]

Answer:

A two-digit number can be written as:

a*10 + b*1

Where a and b are single-digit numbers, and a ≠ 0.

We know that:

"The sum of a two-digit number and the number obtained by interchanging the digits is 132."

then:

a*10 + b*1 + (b*10 + a*1) = 132

And we also know that the digits differ by 2.

then:

a = b + 2

a = b - 2

So let's solve this:

We start with the equation:

a*10 + b*1 + (b*10 + a*1) = 132

(a*10 + a) + (b*10 + b) = 132

a*11 + b*11 = 132

(a + b)*11 = 132

(a + b) = 132/11 = 12

Then:

a + b = 12

And remember that:

a = b + 2

a = b - 2

Then if we select the first one, we get:

a + b = 12

(b + 2) + b = 12

2*b + 2 = 12

2*b = 12 -2 = 10

b = 10/2 = 5

b = 5

then a = b + 2= 5 + 2 = 7

The number is 75.

And if we selected:

a = b - 2, we would get the number 57.

Both are valid solutions because we are changing the order of the digits, so is the same:

75 + 57

than

57 + 75.

6 0

3 years ago