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MariettaO [177]
2 years ago
9

Triangles 1 and 2 are similar. What ratio relates a side length of triangle 1 to the corresponding side length of triangle 2?

Mathematics
1 answer:
andreyandreev [35.5K]2 years ago
6 0
Which means that they are putting them side by side
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The sum of $3,000 is deposited into an account paying 10% annually. If $1,206 is withdrawn at the end of years 1 and 2, how much
Yakvenalex [24]
What we have so far: 
INITIAL CASH AMOUNT IN THE BANK: USD3,000
ANNUAL INCREASE OF THE CASH AMOUNT IN THE BANK: 10%
YEARS THE CASH STAYED IN THE BANK: 2 years.
AMOUNT WITHDRAWN AT THE END OF YEAR 1: USD1,206
AMOUNT WITHDRAWN AT THE END OF YEAR 2: USD1,206

First, we need to solve for YEAR 1:
FOR YEAR 1: 
Initial Deposit * Annual Increase Rate = Annual Increase
3,000 * 0.10 = Year 1's Annual Increase
Year 1's  Annual Increase = USD300
∴The YEAR 1'S ANNUAL INCREASE IS USD300.
∴The NEW AMOUNT is now USD3,300.

BUT NOT SO FAST! After the year, you took out USD1,206.
New Amount - USD1,206 = Year 1 Amount
3,300 - 1,206 = Year 1 Amount
Year 1 Amount = USD2094
∴The YEAR 1 AMOUNT which will carry over to YEAR 2 is USD2094.

Now, let us solve for the REMAINING BALANCE.
FOR YEAR 2's Annual Increase: 
YEAR 1 AMOUNT * Annual Increase = Year 2's Annual Increase
2094*0.10 = Year 2's Annual Increase
Year 2's Annual Increase = USD209.4
∴The YEAR 1'S ANNUAL INCREASE IS USD209.4.
∴The NEW AMOUNT is now USD2,303.4.

But you took out USD1,206
USD2,303.4 - USD1,206 = Remaining Balance
Remaining Balance = USD1097.4

∴The Answer is: USD1097.4

7 0
3 years ago
If 4f(x)+f(5-x)=x2<br><br> What is f(x)?
aksik [14]
We are given that 4f(x)+f(5-x)=x^2.

Substitute x with 5-x, then the above equation becomes:

4f(5-x)+f(5-(5-x))=(5-x)^2, that is

4f(5-x)+f(x)=(5-x)^2


So, we have the following system of equations:

i) 4f(x)+f(5-x)=x^2
ii) 4f(5-x)+f(x)=(5-x)^2

multiply the first equation by -4, so that we eliminate f(5-x)'s

i) -16f(x)-4f(5-x)=-4x^2
ii) 4f(5-x)+f(x)=(5-x)^2

adding the 2 equations side by side we have:

-15f(x)=-4x^2+(5-x)^2

expanding the binomial, and collecting same terms we have:

-15f(x)=-4x^2+(25-10x+x^2)

-15f(x)=-3x^2-10x+25

dividing by -5:

3f(x)=\frac{3}{5}x^2+2x-5

dividing by 3:

\displaystyle{f(x)= \frac{1}{5}x^2+ \frac{2}{3}x-\frac{5}{3}


Answer: \displaystyle{f(x)= \frac{1}{5}x^2+ \frac{2}{3}x-\frac{5}{3}

6 0
3 years ago
Expand and combine like terms.<br><br> (2x4 + 32°) (224 – 3.2%)
Charra [1.4K]

Answer:

This can be wrong but somehow I got 2015.712

Step-by-step explanation:

Maybe wait for another answer tho, I can be wrong.

4 0
2 years ago
What is the result of 4÷ 8/12 ? <br>A. 1/6<br>B. 3/8<br>C. 3<br>D. 6<br>help me please ! thank you
IRINA_888 [86]

Answer:

D 6

Step-by-step explanation:

4/1 / 8/12

4/1 * 12/8

48 / 8 = 6


3 0
2 years ago
Math question pls help
Ivanshal [37]

Answer:

190

Step-by-step explanation:

Find 19 on the x axis.

Go straight up until you hit the line representing the line made from a scatterplot.

Go horizontally to your left.

You should come to 190 and that's your answer.

6 0
3 years ago
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