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3 years ago

14

Write an equation and then use it to solve: Sasha gives half of her books to the local library and keeps the other half. Her bes

t friend gives her 3 more books. She now has 57 books. How many books did she have to begin with?

1 answer:

boyakko [2]3 years ago

8 0

Answer:

120 books

Step-by-step explanation:

57 + 3 = 60

60 x 2 = 120

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Determine the range of the following graph

Ierofanga [76]

Given:

The graph of a function is given.

To find:

The range of the graph.

Solution:

We know that, the domain is the set of input values and range is the set of output values.

In a graph, domain is represented by the x-axis and range is represented by the y-axis.

From the given graph it is clear that there is an open circle at (-8,-8) and a closed circle at (3,4). It means the function is not defined at (-8,-8) but defined for (3,4).

The graph of the function is defined over the interval $-8$ . So, the domain is (-8,3].

The values of the function lie in the interval $-8$ . So, the range is (-8,4].

Therefore, the range of the function are all real values over the interval (-8,4].

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3 years ago

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

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

<u>2 choice:</u> 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

3 years ago

Read 2 more answers

Find the measure of <C in the following figure:

Yuki888 [10]

Answer:

angle C =160 degree

Step-by-step explanation:

since the given triangle is an isosceles triangle their base angles must be equal. So,

x - 10 =x/2

2(x - 10) =x

2x - 20 = x

2x - x = 20

x = 20

for angle B

x - 10

20 - 10

10 degree

for angle A

x/2

20/2

10

For angle c

angle A + angle B + angle C =180 degree (sum of interior angle of a triangle)

10 + 10 + angle C =180

20 + angle C =180

angle C =180 - 20

angle C =160 degree

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3 years ago

(-3x^2+4x-2)/(-3x+19)

prohojiy [21]

\left[x _{1}\right] = \left[ \frac{2}{3}+\left( \frac{-1}{3}\,i \right) \,\sqrt{2}\right][x1]=[32+(3−1i)√2] totally answer

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3 years ago

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You invest $1,100 in an account that has an annual interest rate of 2.1%, compounded continuously. How much money will be in the

uranmaximum [27]

$1100 x 1.021^7 = $1272 (whole number.)

the $1100 is the original amount of money put in the bank with the 1.021 being the interest rate. this was put to the power of 7 to represent the years the money will be in the account.

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3 years ago