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chubhunter [2.5K]
2 years ago
15

For questions 15-17 use this triangle.

Mathematics
1 answer:
SIZIF [17.4K]2 years ago
8 0

Answer:

Part A)  The length of the hypotenuse of triangle ABC is

 

Part B) The length of the shorter leg of triangle ABC is

Part C) The length of the longer leg of triangle ABC is

Step-by-step explanation:

see the attached figure  to better understand the problem

Step 1

Find the length of the longer leg of triangle ABC  (side BC)

we know that  

In the right triangle DBC  

substitute the values and solve for BC

Step 2

Find the length of the shorter leg of triangle ABC  (side AC)

we know that  

In the right triangle ACD

substitute the values and solve for AC

Step 3

Find the length of the hypotenuse of triangle ABC (side AB)

Applying the Pythagoras theorem

we have

substitutes

 

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Alina [70]

Answer:

what is the substitution method???

Step-by-step explanation:

7 0
2 years ago
You saved $20,000.00 and want to diversify your monies. You invest 45% in a Treasury bond for 3 years at 4.35% APR compounded an
Maru [420]

Compound Interest

A total of $20,000 is invested in different assets.

45% is invested in a Treasury bond for 3 years at 4.35 APR compounded annually.

For this investment, the principal is P = 0.45*$20,000 = $9,000.

The compounding period is yearly, thus the interest rate is:

i = 4.35 / 100 = 0.0435

The duration (in periods) is n = 3

Calculate the final value with the formula:

M=P_{}(1+i)^n

Substituting:

\begin{gathered} M=\$9,000_{}(1+0.0435)^3 \\ M=\$9,000\cdot1.136259062875 \\ M=\$10,226.33 \end{gathered}

The second investment is a CD at 3.75% APR for 3 years compounded annually. The parameters for the calculations are as follows:

P = 15% of $20,000 = $3,000

i = 3.75 / 100 = 0.0375

n = 3

Calculating:

\begin{gathered} M=\$3,000_{}(1+0.0375)^3 \\ M=\$3,000\cdot1.116771484375 \\ M=\$3,350.31 \end{gathered}

The third investment is in a stock plan. The initial value of the investment is

P = 20% of $20,000 = $4,000

By the end of the first year, the stock plan increased by 8%, thus its value is:

M1 = $4000 * 1.2 = $4,800

By the end of the second year, the stock plan decreased by 4$, thus the value is:

M2 = $4,800 * 0.96 = $4,608

Finally, the stock plan increases by 6%, resulting in a final balance of:

M3 = $4,608 * 1.06 = $4,884.48

Finally, the last investment is in a savings account at 2.90% APR compounded annually for 3 years (not mentioned, but assumed).

P = $20,000 - $9,000- $3,000 - $4,000 = $4,000

i = 2.90 / 100 = 0.029

n = 3

Calculating:

\begin{gathered} M=\$4,000_{}(1+0.029)^3 \\ M=\$4,000\cdot1.089547389 \\ M=\$4,358.19 \end{gathered}

To summarize, the final balances for each type of investment at the end of the third year are:

Investment 1; $10,226.33

Investment 2: $3,350.31

Investment 3: $4,884.48

Investment 4: $4,358.19

Total balance: $22,819.32

3 0
1 year ago
What is 3 divided by 2/3 x 3? <br><br> please show work!
IgorC [24]

<u>Answer:</u>

<em>The correct answer is 1 1/2</em>

<u>Step-by-step explanation:</u>

<em>First, We need to find out the sum of 2/3  x 3, change 3 into a fraction if you want</em>

<em>3x2=6 and 1x3 is 3, So 2/3 x 3 is 6/3 or 2</em>

<em>Next, divide 3 by 2, change to fractions if needed</em>

<em>Remember keep, change and flip, flip 2/3 to 1/2</em>

<em>Then, you multiply 3/1 and 1/2 3x1=3 1x2=2</em>

<em>Finally divide 3 by 2. 3  ÷ 2 is 1 1/2</em>

<em>I hope this helped!</em>

<em />

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3 years ago
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SVETLANKA909090 [29]

Answer:

x = -4

Step-by-step explanation:

You kind of didn't capture the directions in your image, but it looks like maybe they want you to write the equation of the line.

So this is what you need to know: the equation of a vertical (up and down) line is

x = anumber

For future reference on the next question, the equation of a horizontal (flat, left and right) line is

y = anumber

For this question, though, it's vertical.

so x = -4

You can check by picking as many points as you like and find that they ALL have -4 as the x value. Also, you will find the slope formula gives you an answer that is undefined. That's why you can't write an equation using y=mx+b. Hope this helps! I can edit if the question is something wildly different for real.

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1 year ago
Using Trig to find angles !! help please
notsponge [240]

Answer:

56.1°

Step-by-step explanation:

\tan \:x \degree =  \frac{64}{43}  \\  \tan \:x \degree =  1.48837209 \\ x \degree =  { \tan}^{ - 1} (1.48837209) \\ x \degree = 56.103833383 \degree \\ x  =56.1 \degree

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3 years ago
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