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3 years ago

Which value of x makes the equation 0.5(x + 16) = 3 + 0.25(x – 4) true?

Mathematics

1 answer:

Fynjy0 [20]3 years ago

5 0

Answer:it is confusing

Step-by-step explanation:

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A rectangular prism has a length of 12 feet, a width of 4 feet, and a height of 8 feet. What is the volume of the prism?

hjlf

Answer:

Hello! answer: 384

Finding volume for rectangular prisms is very simple! You just do length × width × height.

So our length is 12 our height is 8 and width is 4 so 12 × 4 × 8 = 384 So 384 is the volume hope that helps!!

8 0

2 years ago

The image below shows two dilated figures with lines UV and WX drawn. If the larger figure was dilated using a scale factor of 4

NARA [144]

The lines have a parallel relationship!

I hope this helped! Mark me Brainliest! :) -Raven❤️

3 0

2 years ago

Your task is to build a road joining a ranch to a highway that enables drivers to reach the city in the shortest time. The perpe

lubasha [3.4K]

Answer:

(a)In the attachment

(b)The road of length 35.79 km should be built such that it joins the highway at 19.52km from the perpendicular point P.

Step-by-step explanation:

(a)In the attachment

(b)The distance that enables the driver to reach the city in the shortest time is denoted by the Straight Line RM (from the Ranch to Point M)

First, let us determine length of line RM.

Using Pythagoras theorem

$|RM|^{2}=30^2+x^2\\|RM|=\sqrt{30^2+x^2}$

The Speed limit on the Road is 60 km/h and 110 km/h on the highway.

Time Taken = Distance/Time

Time taken on the road $=\frac{\sqrt{30^2+x^2}}{60}$

Time taken on the highway $=\frac{50-x}{110}$

Total time taken to travel, T $=\frac{\sqrt{30^2+x^2}}{60}+\frac{50-x}{110}$

Minimum time taken occurs when the derivative of T equals 0.

$T^{'}=\frac{x}{60\sqrt{30^2+x^2}}-\frac{1}{110}\\\frac{x}{60\sqrt{30^2+x^2}}-\frac{1}{110}=0\\\frac{x}{60\sqrt{30^2+x^2}}=\frac{1}{110}\\110x=60\sqrt{30^2+x^2}\\$

Square both sides

$12100x^2=3600(30^2+x^2)\\12100x^2=3240000+3600x^2\\12100x^2-3600x^2=3240000\\8500x^2=3240000\\x^2=\frac{3240000}{8500} =381.18\\x=\sqrt{381.18} =19.52$

The road should be built such that it joins the highway at 19.52km from the point P.

In fact,

$|RM|=\sqrt{30^2+19.52^2}=35.79km$

4 0

3 years ago

Dwayne is 4 years older than Sarah. In 7 years the sum of their ages will be 48 . How old is Dwayne now?

zalisa [80]

Answer: 37

Step-by-step explanation: If you start your math by taking 48 and subtracting 7 you will get 41, this question says it the sum of both ages will be 48 in 7 years so subtract those to get 48. After, you can subtract 4 from 41 since that is just the sum of both ages, you take 41 and minus 4, your answer is 37 (sorry if its wrong but I think its most likely going to be correct)

5 0

1 year ago

9{[(9 X 9 - 10) = 2] – 5}

Lina20 [59]

Answer:

Step-by-step explanation:

9{[(9×9-10)-2]-5}

=9{[(81-10)-2]-5}

=9{[71-2]-5}

=9{69-5}

=9(64)

=576

4 0

2 years ago