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2 years ago

H. Goes through (-3, -2) and parallel to y = 5 x +5

Mathematics

1 answer:

olchik [2.2K]2 years ago

7 0

Answer: y = 5x + 13

Step-by-step explanation:

Parallel means it has the same slope.

Given line y = 5x + 5 --> the slope is 5, so parallel slope is 5

Use the Point-Slope formula: y - y₁ = m(x - x₁) such that

m = 5
(x₁, y₁) = (-3, -2)

y + 2 = 5(x + 3) input m and (x₁, y₁) into the Point-Slope formula

y + 2 = 5x + 15 distributed

y = 5x + 13 subtracted 2 from both sides

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3 years ago

If f(x) = 6x − 5 and f(5a) = 73, then what is the value of a?

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Answer:

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2 years ago

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2 years ago

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In the figure, triangle CAE is an enlargement of triangle CBD with scale factor of 4/3. The area of the smaller triangle is 9cm2

balandron [24]

Answer:

16 cm^2

Step-by-step explanation:

Given

$\triangle CAE$ -- Bigger Triangle

$\triangle CBD$ -- Smaller Triangle

$k = \frac{4}{3}$ --- Scale factor

Area of CBD = 9

Required

Determine the area of CAE

The area of triangle CBD is:

$A_1 = \frac{1}{2}bh$

$\frac{1}{2}bh = 9$

The area of CAE is:

$A_2 = \frac{1}{2}BH$

Where:

$B = \frac{4}{3}b$ and

$H = \frac{4}{3}h$

The above values is the dimension of the larger triangle (after dilation).

So, we have:

$A_2 = \frac{1}{2}*\frac{4}{3}b * \frac{4}{3} * h$

$A_2 = \frac{1}{2}*\frac{4}{3} * \frac{4}{3} *b* h$

$A_2 = \frac{1}{2}*\frac{16}{9} *b* h$

Re-order

$A_2 = \frac{16}{9}*\frac{1}{2}* b* h$

$A_2 = \frac{16}{9}*\frac{1}{2}bh$

Recall that:

$\frac{1}{2}bh = 9$

$A_2 = \frac{16}{9}*9$

$A_2 = 16$

Hence, the area is 16 cm^2

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2 years ago