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slamgirl [31]
1 year ago
5

The endpoints of one diagonal of a rhombus are (-7, -2) and (-1, -4). If the coordinates of the 3rd vertex are (-6, -9), what ar

e the coordinates of the 4th vertex? (-8, 13) (-2, 3) (-6, 13) (7, -8)
Mathematics
1 answer:
podryga [215]1 year ago
8 0

The coordinates of the 4th vertex of the rhombus are (-2,3)

<h3>How to determine the coordinates of the 4th vertex?</h3>

The diagonals are given as:

(-7, -2) and (-1, -4)

The 3rd vertex is given as: (-6,-9)

Calculate the distance between the vertices of the diagonals and the 3rd vertex using:

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

So, we have:

d_1 = \sqrt{(-7 + 6)^2 + (-2 + 9)^2} =\sqrt{50

d_2 = \sqrt{(-1 + 6)^2 + (-4 + 9)^2} =\sqrt{50

Let the 4th vertex be (x,y)

So, we have:

d_3 = \sqrt{(-7 - x)^2 + (-2 - y)^2} =\sqrt{50

d_4 = \sqrt{(-1 - x)^2 + (-4 - y)^2} =\sqrt{50

Equate d3 and d4

\sqrt{(-1 - x)^2 + (-4 - y)^2} = \sqrt{(-7 - x)^2 + (-2 - y)^2}

Take the square of both sides

(-1 - x)^2 + (-4 - y)^2 = (-7 - x)^2 + (-2 - y)^2

Expand

1 + 2x + x^2 + 16 + 8y + y^2 = 49 + 14x + x^2 + 4 + 4y + y^2

Evaluate the like terms

1 + 2x  + 16 + 8y  = 49 + 14x + 4 + 4y

Collect like terms

14x - 2x + 4y - 8y = 1 + 16 - 49 - 4

12x - 4y = -36

Divide through by 4

3x - y = -9

Next, we test the options in the above equation

Point (-8,13) means x = -8 and y = 13

So, we have:

3x - y = -9

3(-8) - 13 = -9

-37 = -9 --- this is false

Point (-2, 3) means x = -2 and y = 3

So, we have:

3x - y = -9

3(-2) - 3 = -9

-9 = -9 --- this is true.

Hence, the coordinates of the 4th vertex are (-2,3)

Read more about rhombus at:

brainly.com/question/20627264

#SPJ1

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Answer:

The expression to compute the amount in the investment account after 14 years is: <em>FV</em> = [5000 ×(1.10)¹⁴] + [3000 ×(1.10)⁸].

Step-by-step explanation:

The formula to compute the future value is:

FV=PV[1+\frac{r}{100}]^{n}

PV = Present value

r = interest rate

n = number of periods.

It is provided that $5,000 were deposited now and $3,000 deposited after 6 years at 10% compound interest. The amount of time the money is invested for is 14 years.

The expression to compute the amount in the investment account after 14 years is,

FV=5000[1+\frac{10}{100}]^{14}+3000[1+\frac{10}{100}]^{14-6}\\FV=5000[1+0.10]^{14}+3000[1+0.10]^{8}

The future value is:

FV=5000[1+0.10]^{14}+3000[1+0.10]^{8}\\=18987.50+6430.77\\=25418.27

Thus, the expression to compute the amount in the investment account after 14 years is: <em>FV</em> = [5000 ×(1.10)¹⁴] + [3000 ×(1.10)⁸].

4 0
3 years ago
the average starting salary for this year's graduates at a large university (lu) is $55,000 with a standard deviation of $6,000.
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0.84% of the graduates will receive the tax break

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean  and standard deviation , the z-score of a measure X is given by:

Z = x - μ / σ

Z-scores are used to measure how far a measure is from the mean. We find the p-value associated with this Z-score by looking at the z-score table after finding the Z-score. The p-value represents the probability that the measure is smaller than X, which is the percentile of X. The probability of the measure being greater than X is calculated by subtracting 1 from the pvalue.

μ = $55,000 σ = $6,000

This is the pvalue of Z when X = $39,600. So

z = 39600 - 55000 / 6000

z = -2.5

z = -2.5 has a o value of 0.0084

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7 0
1 year ago
A boundary stripe 6 in. wide is painted around a rectangle whose dimensions are 120 ft by 230 ft. Use differentials to approxima
Nimfa-mama [501]

Answer:

350 square feet

Step-by-step explanation:

We are given that

Width of strip=6 in

Dimension of rectangle=20 ft\times 230 ft

We know that

Area  of rectangle ,A=xy

Differentiate

dA=\frac{\partial A}{\partial x}x+\frac{\partial A}{\partial y}y

We have \frac{\partial A}{\partial x}=y=230 ft

\frac{\partial A}{\partial y}=x=120

dx=\frac{12}{12}=1 ft

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Because 6 in added in both side of breadth

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Because 6 in added on both sides of length of rectangle

Substitute the values

dA=230\times 1+120\times 1=350 ft^2

Hence, the number of square feet of paint in the strip=350 square feet

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3 years ago
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Answer:

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Step-by-step explanation:

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3 years ago
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