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4 years ago

6

A rectangular plot of land is represented on a coordinate plane where each unit is one foot. The vertices are at (50,20), (50,90

), (100,20) and (100,90). What is the perimeter of the rectangular plot?
A. 120 feet
B. 240 feet
C. 530 feet
D. 3500 feet

2 answers:

Zina [86]4 years ago

4 0

The answer is b I believe

Phoenix [80]4 years ago

3 0

Answer:

The correct answer is b. 240 feet!

Have the best day!

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3 years ago

Evaluate for f(-2).<br> f(x) = 8x-10

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3 years ago

Jim has a rectangular poster with dimensions of 5 feet 7 inches by 4 feet 4 inches. He needs a piece of glass that is one inch t

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3 years ago

What is the base of lnx^4?

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3 years ago

Determine the coordinates of the point on the straight line y=3x+1 that is equidistant from the origin and (−3, 4).

oee [108]

Answer:

$x = \frac{17}{18}$

$y = \frac{23}{6}$

Step-by-step explanation:

Given

$y = 3x + 1$

$Points = (0,0)\ to\ (-3,4)$

Required

Determine (x,y) equidistant from the equation and the given point

This question will be answered using distance formula;

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

Considering The first Point $(0,0)\ to\ (x,y)$

$(x_1 ,y_1) = (0,0)$

$(x_2,y_2) = (x,y)$

The distance is:

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$d = \sqrt{0 - x)^2 + (0 - y)^2}$

$d = \sqrt{(- x)^2 + (- y)^2}$

$d = \sqrt{x^2 + y^2}$

Considering the second point: $(x,y)\ to\ (-3,4)$

$(x_1,y_1) = (x,y)$

$(x_2,y_2) = (-3,4)$

The distance is:

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}$

$d = \sqrt{(x - (-3))^2 + (y - 4)^2}$

$d = \sqrt{(x + 3)^2 + (y- 4)^2}$

$d = \sqrt{x^2 + 6x + 9 + y^2- 8y + 16}$

$d = \sqrt{x^2 + 6x + y^2- 8y + 16 + 9}$

$d = \sqrt{x^2 + 6x + y^2- 8y + 25}$

Equate both values of d

$\sqrt{x^2 + 6x + y^2- 8y + 25} = \sqrt{x^2 + y^2}$

Square both sides

$x^2 + 6x + y^2- 8y + 25 = x^2 + y^2$

Collect Like Terms

$6x - 8y + 25 = x^2 -x^2+ y^2 -y^2$

$6x - 8y + 25 =0$

Recall that $y = 3x + 1$

$6x - 8(3x + 1) + 25 = 0$

$6x - 24x - 8 + 25 = 0$

$-18x+ 17 = 0$

$-18x=- 17$

Solve for x

$x = \frac{-17}{-18}$

$x = \frac{17}{18}$

Substitute $\frac{17}{18}$ for x in $y = 3x + 1$

$y = 3 * \frac{17}{18} + 1$

$y = \frac{17}{6} + 1$

$y = \frac{17 + 6}{6}$

$y = \frac{23}{6}$

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3 years ago