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Lemur [1.5K]
2 years ago
10

Matthew invests $500 into an account with a 2.5% interest that is compounded quarterly. How much money will he have in this acco

unt if he keeps it for 10 years? Round your answer to the nearest cent. D
Mathematics
2 answers:
Levart [38]2 years ago
8 0

Answer:

$642

Step-by-step explanation:

Use the compound interest formula and substitute the correct values: A=500(1+0.025/4)^{4(10)}.

Simplify by using order of operations: A=500(1.00625)^{40}=500(1.283026821) ≈ 642.

Karo-lina-s [1.5K]2 years ago
3 0

Answer:

$641.4

Step-by-step explanation:

500(1 + 0.025/4)⁴⁰

= 641.5134103

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marta [7]

A is 1/2 the size of B.

You would divide B by 2 to get 12/2

The answer is C.

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2 years ago
Determine the roots of the following function of the quadratic formula:<br> x^2-5x-4=0
noname [10]

Answer:

4,1

Step-by-step explanation:

(x-4)(x-1)

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3 years ago
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I need help with questions #7 and #8 plz
katen-ka-za [31]

Answer:

7. A = 40.8 deg; B = 60.6 deg; C = 78.6 deg

8. A = 20.7 deg; B = 127.2 deg; C = 32.1 deg

Step-by-step explanation:

Law of Cosines

c^2 = a^2 + b^2 - 2ab \cos C

You know the lengths of the sides, so you know a, b, and c. You can use the law of cosines to find C, the measure of angle C.

Then you can use the law of cosines again for each of the other angles. An easier way to solve for angles A and B is, after solving for C with the law of cosines, solve for either A or B with the law of sines and solve for the last angle by the fact that the sum of the measures of the angles of a triangle is 180 deg.

7.

We use the law of cosines to find C.

18^2 = 12^2 + 16^2 - 2(12)(16) \cos C

324 = 144 + 256 - 384 \cos C

-384 \cos C = -76

\cos C = 0.2

C = \cos^{-1} 0.2

C = 78.6^\circ

Now we use the law of sines to find angle A.

Law of Sines

\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}

We know c and C. We can solve for a.

\dfrac{a}{\sin A} = \dfrac{c}{\sin C}

\dfrac{12}{\sin A} = \dfrac{18}{\sin 78.6^\circ}

Cross multiply.

18 \sin A = 12 \sin 78.6^\circ

\sin A = \dfrac{12 \sin 78.6^\circ}{18}

\sin A = 0.6535

A = \sin^{-1} 0.6535

A = 40.8^\circ

To find B, we use

m<A + m<B + m<C = 180

40.8 + m<B + 78.6 = 180

m<B = 60.6 deg

8.

I'll use the law of cosines 3 times here to solve for all the angles.

Law of Cosines

a^2 = b^2 + c^2 - 2bc \cos A

b^2 = a^2 + c^2 - 2ac \cos B

c^2 = a^2 + b^2 - 2ab \cos C

Find angle A:

a^2 = b^2 + c^2 - 2bc \cos A

8^2 = 18^2 + 12^2 - 2(18)(12) \cos A

64 = 468 - 432 \cos A

\cos A = 0.9352

A = 20.7^\circ

Find angle B:

b^2 = a^2 + c^2 - 2ac \cos B

18^2 = 8^2 + 12^2 - 2(8)(12) \cos B

324 = 208 - 192 \cos A

\cos B = -0.6042

B = 127.2^\circ

Find angle C:

c^2 = a^2 + b^2 - 2ab \cos C

12^2 = 8^2 + 18^2 - 2(8)(18) \cos B

144 = 388 - 288 \cos A

\cos C = 0.8472

C = 32.1^\circ

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The solution to this question is 39.0625.

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The calculation that will need to be done is the following :

6.25ft X 6.25ft which will equal 39.0625.

6.25 has three significant digits so rounding 39.0625 off to three significant digits is 39.1 square feet

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