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kobusy [5.1K]
2 years ago
12

Simplify the Expression

Mathematics
1 answer:
nlexa [21]2 years ago
6 0

Answer:

125a^{3}b^{2}

Step-by-step explanation:

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Write an equation in slope - intercept form for the line that satisfies each set of conditions
ivanzaharov [21]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(1)

Rearrange 3x + 2y = 1 into this form by subtracting 3x from both sides

2y = - 3x + 1 ( divide all terms by 2 )

y = - \frac{3}{2} x + \frac{1}{2} ← in slope- intercept form

with slope m = - \frac{3}{2}

Parallel lines have equal slopes, thus

y = - \frac{3}{2} x + c ← is the partial equation

To find c substitute (- 6, 15) into the partial equation

15 = 9 + c ⇒ c = 15 - 9 = 6

y = - \frac{3}{2} x + 6 ← equation of line

(2)

Rearrange x + 2y = 8 into slope- intercept form by subtracting x from both sides

2y = - x + 8 ( divide all terms by 2 )

y = - \frac{1}{2} x + 4 ← in slope- intercept form

with slope m = - \frac{1}{2}

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{-\frac{1}{2} } = 2, thus

y = 2x + c ← is the partial equation

To find c substitute (5, - 2) into the partial equation

- 2 = 10 + c ⇒ c = - 2 - 10 = - 12

y = 2x - 12 ← equation of line

3 0
3 years ago
Read 2 more answers
The expressions below represent either exponential growth or exponential decay. Check all the expressions that represent exponen
asambeis [7]

Answer:

Answers B, E and F (1, 5 and 6).

Step-by-step explanation:

In an exponential equation, (y=ab^x), the "b" value must be a decimal less than 1 (but greater than 0) for it to be considered an exponential decay function. Only equations B, E and F have a "b" value that fits this criteria.

6 0
3 years ago
If 2x + 6y = 16, which of the following expressions represents x in terms of y?
Andrej [43]

Answer:

x=-3y+8

Step-by-step explanation:

2x+6y=16

2x=16-6y

2x=-6y+16

x=-6/2y+16/2

x=-3y+8

7 0
3 years ago
The cost to manufacture t shirts can be represented by the function c(x)=10.5x complete the following statement about the functi
Advocard [28]

For this case we have:

Cost of manufactures of T-shirts C(x)=10.5x

where x represents the number of T-shirts

Part A:

Substituting x = 8 in the total cost equation you have to:

C (8) = (10.5) (8)\\\\C (8) = 84\\

Thus, the cost of 8 shirts will be C (8) = 84\\

Part B:

If x = 12 then

C (12) = (10.5) (12)\\\\C (12) = 126\\

Thus, the cost of 12 shirts will be C (12) = 126\\

Answer:

C (8) = 84\\\\C (12) = 126\\\\


8 0
3 years ago
Read 2 more answers
I need help now please
LekaFEV [45]

Answer:

12

Step-by-step explanation:

A = ½(b1 + b2)h

A = (3 + 5)(3)/2

A = 12

8 0
3 years ago
Read 2 more answers
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