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3 years ago

14

A teacher instructs the class to construct the midpoint of a segment. Jeff pulls out his ruler and measure the segment to the ne

arest millimeter and then divides the length by two to find the exact middle of the segment. has he done this correctly?

1 answer:

Sliva [168]3 years ago

8 0

<h2><u><em>Yes, He Has That Correctly</em></u></h2>

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3 years ago

25,000(4+3x) =125,000

Amanda [17]

To solve this equation, first we have to use the distributive property to eliminate the parentheses on the left side of the equation.

If done correctly, your simplified equation should be

100,000 + 75,000x = 125,000

Next, we would subtract 100,000 from both sides, resulting in the equation

75,000x = 25,000

Finally, we would divide both sides of the equation by 75,000, resulting in your final answer of

x= 25,000/75,000

However, many mathematics teachers ask for fractional answers to be simplified. To simplify fractions, we first find the GCF of both numbers, and then divide both the numerator and the denominator by the GCF.

The GCF of 25,000 and 75,000 is 25,000.

So, in simplest form, your final answer is

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3 years ago

George is considering two different investment options. The first offers 7.4% per year simple interest on the initial deposit. T

pentagon [3]

Answer:

Part A) $\$12,220.00$

Part B) $\$12,134.08$

Part C) The simple interest investment is better than the compounded interest investment at the end of three years.

Part D) see the explanation

Step-by-step explanation:

Part A) Determine the value of the simple-interest investment at the end of three years

we know that

The simple interest formula is equal to

$A=P(1+rt)$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest

t is Number of Time Periods

in this problem we have

$t=3\ years\\ P=\$10,000\\r=7.4\%=7.4/100=0.074$

substitute in the formula above

$A=10,000(1+0.074*3)$

$A=10,000(1.222)$

$A=\$12,220.00$

Part B) Determine the value of the compound-interest investment at the end of three years

we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$t=3\ years\\ P=\$10,000\\r=6.5\%=6.5/100=0.065\\n=4$

substitute in the formula above

$A=10,000(1+\frac{0.065}{4})^{4*3}$

$A=10,000(1.01625)^{12}$

$A=\$12,134.08$

Part C) Which investment is better over the first three years?

Compare the two investment

$\$12,134.08 < \$12,220.00$

The compounded interest investment is less than the simple interest investment

therefore

The simple interest investment is better than the compounded interest investment at the end of three years

Part D) How would you advise George to invest his money if he is unsure how long he’ll keep the money in the account?

we have

$A=10,000(1+0.074t)$ ----> simple interest formula as a function of the time t

$A=10,000(1.01625)^{4t}$ ----> compound interest formula as function of the time t

Look to the attached graph below

The red line represents the simple interest investment

The blue curve represents the compounded interest investment

After 0 years and before 4.179 years the red line is over the blue curve, that means the simple interest is better because it gives more money than the compounded interest

After that the blue curve is over the red line that means the compounded quarterly is better because it gives more money than the simple interest

therefore

I advise George to invest his money in the compounded interest investment if he will keep the money for a long time

4 0

3 years ago