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ArbitrLikvidat [17]

2 years ago

12

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equ

ation 2000=16000(1-r)^2 represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number.
1 year
2 year
5 year
8 year

1 answer:

irga5000 [103]2 years ago

7 0

I hope the equation will be 2000=16000(1-r)^t because t is missing in the equation which we need to find.

Given rate: r= 35%= 0.35.

So, first step is to plug in 0.35 for r in the given formula to get the value of t.

Hence, the equation will be:

2000=16000(1-0.35)^t

2000=16000(0.65)^t (By subtraction)

2000/16000= 16000(0.65)^t /16000 (Dividing each sides by 16000)

0.125 = 0.65^t (By simplifying).

log 0.125 = log 0.65^t (Taking log each sides to isolate t).

log 0.125 = t log 0.65 (By applying the log property).

$\frac{log 0.125}{log 0.65} =t$ (Dividing each sides by log 0.65)

-0.903/-0.187 =t

t= 4.83

t= 5 ( Rounded to nearest integers)

So, Devon's car is 5 years old.

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Given that the map reported that the scale is 1 inch to 20 miles.

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1 year ago

I would like to purchase 20 products at a cost of $65 per product. What would be my total with 3.5 sales tax

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Answer:

Answer:

The total is: $ 1345.5

Step-by-step explanation:

It is given that:

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This means that the cost of 20 products will be:

Also, there is a sales tax of 3.5%

This means that a person has to pay a extra 3.5% on the total cost of the items he purchased.

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1 year ago

Polygons ABCD and EFGH are similar. Find the length of EH?

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Most likely, polygon <span>ABCD</span> has sides of known lengths.
It is also likely that one of the sides of polygon <span>EFGH</span> (not <span>EH</span>) is also known. For instance, its side <span>EF</span>.

If the above is true, we can find the scaling factor as a ratio between lengths of corresponding sides:
<span>r=<span><span>EF</span><span>AB</span></span></span>

Since this ratio is constant for any two corresponding lengths,
<span>r=<span><span>EH</span><span>AD</span></span></span>

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<span>EH=AD⋅<span><span>EF</span><span>AB</span></span></span>

Hope That Helped : ) (Took a minute)

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2 years ago

Figure ABCD is transformed to obtain figure A'B'C'D': A coordinate grid is shown from negative 6 to 6 on both axes at increments

nika2105 [10]

Given:

Vertices of ABCD are A(-4,4), (-2,2), C(-2,-1) and D(-4,1).

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To find:

The sequence of transformations that changes figure ABCD to figure A'B'C'D'.

Solution:

Part A:

The figure ABCD reflected across the x-axis, then

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Using this rule, we get

$A(-4,4)\to A_1(-4,-4)$

Similarly, the other points are $B_1(-2,-2),C_1(-2,1),D_1(-4,-1)$ .

Then figure translated 7 units right to get A'B'C'D'.

$(x,y)\to (x+7,y)$

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Similarly, the other points are $B'(5,-2), C'(5,1),D'(3,-1)$ .

Therefore, the figure ABCD reflected across the x-axis and then translated 7 units right to get A'B'C'D'.

Part B:

Reflection and translation are rigid transformation, it means shape and size of figures remains same after reflection and translation.

Therefore, the two figures congruent.

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