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Dimas [21]
3 years ago
5

In right △ABC , the right angle is at C, m∠A=30 degrees , and AC=7√5 units.

Mathematics
1 answer:
Archy [21]3 years ago
4 0

Answer:

P=(7\sqrt{15}+7\sqrt{5})\ units

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the length side AB (hypotenuse)

we know that

cos(30^o)=\frac{AC}{AB}

substitute

cos(30^o)=\frac{7\sqrt{5}}{AB}

Remember that

cos(30^o)=\frac{\sqrt{3}}{2}

so

\frac{\sqrt{3}}{2}=\frac{7\sqrt{5}}{AB}

AB=\frac{14\sqrt{5}}{\sqrt{3}}

AB=\frac{14\sqrt{15}}{3}\ units

step 2

Find the length side BC

sin(30^o)=\frac{BC}{AB}

sin(30^o)=\frac{1}{2}

\frac{1}{2}=\frac{BC}{AB}

BC=\frac{AB}{2}

substitute the value of AB

BC=\frac{\frac{14\sqrt{15}}{3}}{2}

BC=\frac{7\sqrt{15}}{3}\ units

step 3

Find the perimeter

P=AB+BC+AC

substitute

P=\frac{14\sqrt{15}}{3}+\frac{7\sqrt{15}}{3}+7\sqrt{5}

P=\frac{21\sqrt{15}}{3}+7\sqrt{5}

P=(7\sqrt{15}+7\sqrt{5})\ units

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Answer:

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7 0
2 years ago
The sum of five consecutive positive integers is 2020. Find the largest of these numbers.
lawyer [7]

Answer:

406

Step-by-step explanation:

Five consecutive positive integers = x, (x+1), (x+2), (x+3), (x+4)

x + (x+1) + (x+2) + (x+3) + (x+4) = 2020

5x + 10 = 2020

5x = 2020-10

5x = 2010

x = 2010÷5

x = 402

The largest of the number is = x+4

x+4 = 402 + 4 = 406

8 0
2 years ago
∠E∠E and ∠F∠F are vertical angles with m∠E=9x+12m∠E=9x+12 and m∠F=3x+24m∠F=3x+24 .
Mama L [17]

Since ∠E and ∠F are vertical angles, they are congruent, meaning that m∠E = m∠F

Plugging in the equations that were originally given, we can form the equation 9x + 12 = 3x + 24

Subtract both sides of the equation by 3x

6x + 12 = 24

Subtract 12 from both sides

6x = 12

Divide both sides by 6

x = 2

This should be your answer. Have an awesome day! :)

3 0
3 years ago
How many terms are in the expression<br><br> a3 + 3a2b - 4b - 11b + 7<br><br> 5<br> 6<br> 4<br> 7
Contact [7]

Answer:

there are 5 terms!

Step-by-step explanation:

trust me

6 0
2 years ago
Gracie bought a cd for $810 that earns a 2.9 APR and is compounded quarterly. The CD matures in 5 years. How much will this CD b
enyata [817]

Answer:

The amount that this CD will be worth at maturity would be $935.90. The right answer is B.

Step-by-step explanation:

In order to calculate How much will this CD be worth at maturity we would have to use and calculate the formula of future value as follows:

Future Value=Present value×(1+i/n)∧nt

Future Value=$810×(1+2.9%/4)∧(4×5)

Future Value=$935.90

The amount that this CD will be worth at maturity would be $935.90

8 0
3 years ago
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