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3 years ago

Proportions in Triangles

Mathematics

1 answer:

Finger [1]3 years ago

5 0

Answer:

First we need to calculate the height of the triangle ( because from that, we can also calculate both x and y)

We know that: h² = b'c'

And in our case:

b' = 9

c' = 3

=> h² = b'c' = 9 · 3

=> h = √(9 · 3) = √27

Now using pythagorean theorem:

(√27)² + 3² = x²

=> x² = 27 + 9

=> x = √(27 + 9) = √36 = 6

So x = 6 and the answer is C.

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Tamara and Jason work at a widget factory. Tamara arrived at work before Jason and began making widgets. Tamara had already made

Mrac [35]

Answer:

See explanation!

Step-by-step explanation:

The remaining question reads:

Part A: Write a system of equations to represent the situation. Let x = hours and y = widgets.

Part B: How much time does it take for Tamara and Jason to produce the same number of widgets?

Part C: How many widgets will Tamara and Jason have produced?

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To solve this problem we can construct an linear algebraic expression for each person, principally denoted as:

$y=ax+c$

where

$y$ :is our dependent variable (which is a function of $x$ )

$x$ :is our independent variable

$a$ :is the slope

$c$ :is the y-intercept constant value (if any present)

Part A: Write a system of equations to represent the situation. Let x = hours and y = widgets.

Tamara

Has already made 20 widgets and produces at a rate of 8 widgets per hour thus here $c=20$ and $a=8$ , so Tamara's equation reads:

$y_{T}=8x+20$

Jason

Has not produced any widgets yet and produces at a rate of 12 widgets per hour thus here $c=0$ and $a=12$ , so Jason's equation reads:

$y_{J}=12x$

So the system of equations will be

$y_{T}=8x+20\\y_{J}=12x$

Part B: How much time does it take for Tamara and Jason to produce the same number of widgets?

Since we want to find the amount of time (i.e. the value of $x$ ) it takes for both of them to produce the same number of widgets we can just equate the two equations ans solve for $x$ as follow:

$y_{T}=y_{J}\\8x+20=12x\\8x-12x=-20\\-4x=-20\\x=\frac{-20}{-4}\\ x=5$

So it takes them 5 hours to produce the same amount of widgets.

Part C: How many widgets will Tamara and Jason have produced?

Now we can simply plug in the value of $x=5$ in any of the two equations (i.e. either for Tamara or Jason) to find the number of widgets produced.

$y_{T}=8(5)+20=40+20=60$

So in a time-space of 5 hours Each will have produced 60 widgets and in total will be 60+60 = 120 widgets.

6 0

3 years ago

The volume of a cube is 64 cubic feet. What are the lengths of the side of the cube?

Elis [28]

so if the cube is 64 cubic feet, you would have to set up an equation. For ex 3 square root of 64 then it will get u the answer

7 0

2 years ago

Can someone pls answer:(

Yuliya22 [10]

Answer:

1. m=2x b=1 2. m=5/8x b= -1 3. m=7/8x b= -3/4 4. m=3/4x b=4

Step-by-step explanation:

7 0

3 years ago

The price of a stock decrease by 19 and thin increase by 0

ZanzabumX [31]

So your answer would be x-19+0. Let x represent the original price of the stock.

7 0

4 years ago

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dexar [7]

Answer:

1. 4 and 4sqrt2

2. 6sqrt2 and 6sqrt2

3. 5 and 5sqrt2

4. 5sqrt2 and 5sqrt2

5. 6 and 6

6. 8 and 8sqrt2

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Step-by-step explanation:

3 0

3 years ago