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3 years ago

If m∠ABD = 70° and m∠CBD = 30°, then m∠ABC = ?

Mathematics

1 answer:

Rufina [12.5K]3 years ago

4 0

If it’s on a straight line then the answer should be 80

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Kristen invests $ 5745 in a bank. The bank 6.5% interest compounded monthly. How long must she leave the money in the bank for i

podryga [215]

Answer:

1. 10.7 years

2. 17.0 years

3. 2nd option

Step-by-step explanation:

Use formula for compounded interest

$A=P\cdot \left(1+\dfrac{r}{n}\right)^{nt},$

where

A is final value, P is initial value, r is interest rate (as decimal), n is number of periods and t is number of years.

In your case,

1. P=$5745, A=2P=$11490, n=12 (compounded monthly), r=0.065 (6.5%) and t is unknown. Then

$11490=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12t},\\ \\2=(1.0054)^{12t},\\ \\12t=\log_{1.0054}2,\\ \\t=\dfrac{1}{12}\log_ {1.0054}2\approx 10.7\ years.$

2. P=$5745, A=3P=$17235, n=12 (compounded monthly), r=0.065 (6.5%) and t is unknown. Then

$17235=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12t},$

$3=(1.0054)^{12t},$

$12t=\log_{1.0054}3,$

$t=\dfrac{1}{12}\log_{1.0054}3\approx 17.0\ years.$

3. 1 choice: P=$5745, n=12 (compounded monthly), r=0.065 (6.5%), t=5 years and A is unknown. Then

$A=5745\cdot \left(1+\dfrac{0.065}{12}\right)^{12\cdot 5},\\ \\A=5745\cdot (1.0054)^{60}\approx \$7936.39.$

2 choice: P=$5745, n=4 (compounded monthly), r=0.0675 (6.75%), t=5 years and A is unknown. Then

$A=5745\cdot \left(1+\dfrac{0.0675}{4}\right)^{4\cdot 5},\\ \\A=5745\cdot (1.0169)^{20}\approx \$8032.58.$

The best will be 2nd option, because $8032.58>$7936.39

5 0

2 years ago

Read 2 more answers

What is the area of and the perimeter of this triangle?

Veseljchak [2.6K]

Answer:

A = 40 square yards; P = 33 yards.

Step-by-step explanation:

Perimeter of the triangle

= ( 8 + 15 + 10)

= 36 yards.

Area of the right angled triangle

= 1 /2 * 10 * 8

= 40 square yards.

Hope it will help :)

7 0

2 years ago

Select the correct answer.

taurus [48]

Answer:
A. -4

Explanation:
-4 - 6 = -10
5 (-4+2) = -10

8 0

3 years ago

True or False: The value of r represents the reference angle when plotting a point in polar coordinates.

Anarel [89]

The answer to the statement above would be false. The value of r does not represent the reference angle when plotting a point in polar coordinates. Instead, it represents the polar distance instead of the angle. The reference angle is represented by t.

8 0

3 years ago

Read 2 more answers

The volume of a rectangular prism can be represented by the expression 216x^3y^2. If the length is 8 y and the width is 9 x , wh

Nastasia [14]

Answer:

h= 216x^3y^2÷(8yx9X) = 3x^2y

3 0

3 years ago