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3 years ago

Triangle DEF is on a coordinate plane with its

Mathematics

1 answer:

antoniya [11.8K]3 years ago

7 0

Answer:

$21\ \text{square units}$

Step-by-step explanation:

The points are $D(-3,5), E(-3,-2)$ and $F(3,0)$ .

Area of a triangle is given by

$A=\dfrac{D_x(E_y-F_y)+E_x(F_y-D_y)+F_x(D_y-E_y)}{2}$

$\Rightarrow A=\dfrac{-3(-2-0)+-3(0-5)+3(5-(-2))}{2}$

$\Rightarrow A=21\ \text{square units}$

The area of the given triangle is $21\ \text{square units}$ .

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Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10

zvonat [6]

The approximate difference in the ages of the two cars, which depreciate to 60% of their respective original values, is 1.7 years.

<h3>What is depreciation?</h3>

Depreciation is to decrease in the value of a product in a period of time. This can be given as,

$FV=P\left(1-\dfrac{r}{100}\right)^n$

Here, (P) is the price of the product, (r) is the rate of annual depreciation and (n) is the number of years.

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%.

Suppose the original price of the first car is x dollars. Thus, the depreciation price of the car is 0.6x. Let the number of year is $n_1$ . Thus, by the above formula for the first car,

$0.6x=x\left(1-\dfrac{10}{100}\right)^{n_1}\\0.6=(1-0.1)^{n_1}\\0.6=(0.9)^{n_1}$

Take log both the sides as,

$\log 0.6=\log (0.9)^{n_1}\\\log 0.6={n_1}\log (0.9)\\n_1=\dfrac{\log 0.6}{\log 0.9}\\n_1\approx4.85$

Now, the second car depreciates at an annual rate of 15%. Suppose the original price of the second car is y dollars.

Thus, the depreciation price of the car is 0.6y. Let the number of year is $n_2$ . Thus, by the above formula for the second car,

$0.6y=y\left(1-\dfrac{15}{100}\right)^{n_2}\\0.6=(1-0.15)^{n_2}\\0.6=(0.85)^{n_2}$

Take log both the sides as,

$\log 0.6=\log (0.85)^{n_2}\\\log 0.6={n_2}\log (0.85)\\n_2=\dfrac{\log 0.6}{\log 0.85}\\n_2\approx3.14$

The difference in the ages of the two cars is,

$d=4.85-3.14\\d=1.71\rm years$

Thus, the approximate difference in the ages of the two cars, which depreciate to 60% of their respective original values, is 1.7 years.

Learn more about the depreciation here;

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2 years ago

PLEASE ANSWER THEMM!!!!

natita [175]

Answer:

a.) b⁷÷b⁴

= b⁷

b⁴

= b^7-4

= b³

b.) x × x⁵

x² × x

= x^1+5

x^2+1

= x⁶

x³

= x^6-3

= x³

5 0

2 years ago

where would an imaginary line need to be drawn to reflect across an axis of symmetry so that a regular pentagon can carry onto i

irina [24]

Answer:

An imaginary line would need to be drawn at any angle to the center of the side opposite the angle to reflect across an axis of symmetry so that a regular pentagon can carry onto itself. Hope this answer helps.

5 0

3 years ago

Solve for the unknown angle

Naya [18.7K]

Answer:

(?)=70

Step-by-step explanation:

8 0

2 years ago

1. Which number makes this equation true? v 2 + 10v + 16 = (v + 8)(v + ?) (1 point) 2 4 6 8 2. What is the factored form of x 2

rusak2 [61]

1. The answer is two because if you factor what you can from the equation and then simplify, you are left with 2v+16=(v+8)(?), and by looking at it, the correct answer is two, or A. Review your work, make sure to check your answers before submitting
2. Since two simple factors of 8 are 4 and 2, and they add up to 6, the correct answer is (x+4)(x+2), or B
3. Again, two simple factors of 12 are -4 and -3, so the correct answer is (x-3)(x-4), or D
4. Basically, just factor the quadratic trinomial g^2-2g-24, which turns out to (G+4)(g-6), which is B

5 0

3 years ago

Read 2 more answers