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2 years ago

The area in square feet of a rectangular field is x^2-80x+1500. the width, in feet, is x-30. what is the length in feet.

Mathematics

1 answer:

Mariulka [41]2 years ago

8 0

Answer:

Step-by-step explanation:

Area = x² - 80x + 1500

= x² -30x - 50x + 1500

= x(x - 30) - 50(x - 30)

= (x -30) (x - 50)

Length =(x -50) ft

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SU and VT are chords that intersect at point R.

vovikov84 [41]

Answer:

<h2>The length of the line segment VT is 13 units.</h2>

Step-by-step explanation:

We know that SU and VT are chords. If the intersect at point R, we can define the following proportion

$\frac{RS}{RT} =\frac{RV}{RU}$

Where

$RS=SR=x+6\\RT=x+4\\VR=RV=x+1\\RU=x$

Replacing all these expressions, we have

$\frac{x+6}{x+4} =\frac{x+1}{x}$

Solving for $x$ , we have

$x(x+6)=(x+4)(x+1)\\x^{2} +6x=x^{2} +x+4x+4\\6x-5x=4\\x=4$

Now, notice that chord VT is form by the sum of RT and RV, so

$VT=VR+RT\\VT=x+1+x+4\\VT=2x+5$

Replacing the value of the variable

$VT=2(4)+5\\VT=8+5\\VT=13$

Therefore, the length of the line segment VT is 13 units.

5 0

3 years ago

Read 2 more answers

Maya spent 40% of her savings to pay for a bicycle that cost $60 how much was in her savings

Ahat [919]

Answer:

$150

Step-by-step explanation:

First use a proportion to find the answer:

40/100=60/x

Now we solve for x

60*100=6,000

6,000 divided by 40= 150

x=150

Therefore the answer is $150

3 0

3 years ago

In the figure, angle D measures 45° and angle E measures 87°. What is the measurement of angle H? 42°

Vinvika [58]

The complete question is shown in the attached image

Answer:
measure angle H = 42°

Explanation:
There is a theorem that states that:
"In a triangle, the measure of the exterior angle is equal to the sum of the measures of the two non-adjacent angles to the exterior angle"

In the given, we have:
angle E is an exterior angle to triangle DFH
The two non-adjacent angles to angle E are angles D and H

Based on the above rule:
measure angle E = measure angle D + measure angle H

We are given that:
angle E = 87°
angle D = 45°

Substitute with the givens in the above rule and solve for the measure of angle H as follows:
angle E = angle D + angle H
87° = 45° + measure angle H
measure angle H = 87° - 45°
measure angle H = 42°

Hope this helps :)