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Nady [450]
3 years ago
12

Find the range of ƒ(x) = 3g – 5 for the domain {–1.5, 2, 4}

Mathematics
1 answer:
timofeeve [1]3 years ago
6 0
-1.5 ------ f(x) = 3(-1.5) - 5
= -4.5 -5
= 9.5

2 -------- f(x) = 3(2) - 5
= 6 -5
= 1

4 -------- f(x) = 3(4) - 5
= 12 - 5
= 7
(9.5, 1 , 7)
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Find the value of B - A if the graph of Ax + By = 3 passes through the point (-7, 2), and is parallel to the graph x + 3y = -5.
Elena-2011 [213]

Answer:

B - A = -6

Step-by-step explanation:

Given

Point: (-7,2)

x + 3y = -5

Required

Find B- - A in Ax + By = 3

To start with; we need to calculate the slope of x + 3y = -5

x + 3y = -5

Subtract x from both sides

x - x + 3y = -5 - x

3y = -5 - x

Divide both sides by 3

\frac{3y}{3} = -\frac{5}{3} - \frac{x}{3}

y = -\frac{5}{3} - \frac{x}{3}

The slope of the line is the coefficient of x

Slope = - \frac{1}{3}

The question says line Ax + By = 3 is parallel to line x + 3y = -5; This means that they have the same slope of - \frac{1}{3}

Having calculated the slope, next is to calculate the equation of the line using the following formula;

m = \frac{y - y_1}{x - x_1}

Where m is the slope; m = - \frac{1}{3}; (x_1, y_1) = (-7,2)

Substitute these values in the formula above; the formula becomes

-\frac{1}{3} = \frac{y - 2}{x - -7}

-\frac{1}{3} = \frac{y - 2}{x +7}

Cross Multiply

-1(x+7) = 3(y-2)

Open brackets

-x - 7 = 3y - 6

Add x to both sides

x - x - 7 = 3y - 6 + x

-7 = 3y - 6 +x

Add 6 to both sides

-7 + 6 = 3y -6 + 6 + x

-1 = 3y + x

Multipby both sides by -3

-3(-1) = -3(3y + x)

3 = -9y - 3x

-9y - 3x = 3

-3x - 9y = 3

Comparing the above to Ax + By = 3

Ax = -3x\\A = -3

By = -9y\\B = -9

B - A = -9 - (-3)

B - A = -9 + 3

B - A = -6

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