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3 years ago

Please please help me out

Mathematics

1 answer:

masya89 [10]3 years ago

8 0

Answer: y = 3x + 1

Step-by-step explanation:

The equation is in Slope-Intercept format: y = mx + b where

m is the slope (difference in y's over difference in x's)
b is the y-intercept (value of y when x = 0)

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\\text{Let }(x_1,y_1)=(0,1)\quad \text{and}\quad \text{let }(x_2, y_2)=(1,4)\quad then\\\\m=\dfrac{4-1}{1-0}=\dfrac{3}{1}=3$

b = 1 refer to the table that shows y = 1 when x = 0

Now input m = 3 and b = 1 into the Slope-Intercept formula:

y = 3x + 1

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Amanda needs to make a garden plot which has an area less than 18 sq. feet. The length should be 3 feet longer than the width. W

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Answer:

Any width less than 3 feet

Step-by-step explanation:

Inequalities

The garden plot will have an area of less than 18 square feet. If L is the length of the garden plot and W is the width, the area is calculated by:

A = L.W

The first condition can be written as follows:

LW < 18

The length should be 3 feet longer than the width, thus:

L = W + 3

Substituting in the inequality:

(W + 3)W < 18

Operating and rearranging:

$W^2 + 3W - 18 < 0$

Factoring:

(W-3)(W+6)<0

Since W must be positive, the only restriction comes from:

W - 3 < 0

Or, equivalently:

W < 3

Since:

L = W + 3

W = L - 3

This means:

L - 3 < 3

L < 6

The width should be less than 3 feet and therefore the length will be less than 6 feet.

If the measures are whole numbers, the possible dimensions of the garden plot are:

W = 1 ft, L = 4 ft

W = 2 ft, L = 5 ft

Another solution would be (for non-integer numbers):

W = 2.5 ft, L = 5.5 ft

There are infinitely many possible combinations for W and L as real numbers.

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