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3 years ago

Help with full calculations, please

Mathematics

1 answer:

beks73 [17]3 years ago

5 0

Answer:

Step-by-step explanation:

8) B(x) = $5^{x +1}$

$5^{x + 1} = 3125 \\\\5^{x +1} = 5^{5}\\\\$

Compare the exponents,

x + 1 = 5

x = 5 - 1

x = 4

$10)2^{x-4}=512\\\\2^{x -4} = 2^{9}\\\\$

Compare exponents,

x - 4 = 9

x = 4 + 9

x = 13

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Helen borrowed money from her aunt to pay for college expenses. The graph below shows the amount left

enot [183]

Answer:

$y = -100x + 13000$

Step-by-step explanation:

See attachment for graph

First, we need to take any corresponding values of x and y

$(x_1,y_1) = (0,13000)$

$(x_2,y_2) = (130,0)$

Next, we calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{0 - 13000}{130 - 0}$

$m = \frac{- 13000}{130}$

$m = -100$

Next, we calculate the line equation using:

$y - y_1=m(x-x_1)$

$y - 13000 = -100(x - 0)$

$y - 13000 = -100x$

Make y the subject

$y = -100x + 13000$

Hence, the line equation is:

$y = -100x + 13000$

4 0

3 years ago

Find the area of each sector. Show your work.

hodyreva [135]

Area of the shaded sector = (120/360) * pi * 10^2

= 104.72 square units

Area of the other sector = 2 * 104.72 = 209.44 sq units

6 0

3 years ago

PLEASE HELP ITS URGENT

malfutka [58]

Answer:

So the annual percent of decay is: 7.77%

Step-by-step explanation:

If the value of a car was $18000 in 2006, and in 2016 it was worth $4000 it means, it lose 77.77% of its value in 10 years.

To calculate the percentage of decay we use the rule of three:

If the price of the car in 2006 ($18000) represents 100%, then, how much does $4000 represents?

4000*100/18000 = %22.22

Now, we know that $4000 represents 22.22% the original value, so it lose 100% - 22.22% = 77.77% of its value.

So the annual percent of decay is: 77.77% / 10 = 7.77%

7 0

4 years ago

640, 160, 40, 10, ...

WARRIOR [948]

Answer:

Option 3 and 5 are correct

Step-by-step explanation:

We have given a geometric series 640,160,40,10....

Common ratio of geometric series is $r=\frac{a_2}{a_1}$

$r=\frac{160}{640}=\frac{1}{4}$

Here our common ratio is less than zero

It will show the graph of exponential decay

Hence, option 5 is correct.

The general term of geometric series is $a_n=a\cdotr^(n-1)$

Domain will be all natural numbers since, geometric series take only natural numbers.

Here, values of "n" is domain

Hence, option 3 is correct.

Range can be any positive real numbers not only natural number

Range is the value of $a_n$

Hence, option 4 is discarded.

Graph can not be linear of a geometric series being exponential

Hence, option 2 is discarded.

Option 1 is discarded because it is exponential decay function so it can not be exponential growth.

Therefore, Option 3 and 5 are correct.

4 0

3 years ago

Read 2 more answers

What is the component form of the vector whose tail is the point (-3,2) and whose head is the point (1, -6)?

Bess [88]

Answer:

(4, -8)

Step-by-step explanation:

The components of a vector are found by subtracting the tail from the head.

Head - Tail = (1, -6) -(-3, 2) = (1 -(-3), -6 -2) = (4, -8)

⇒ The component form is (4, -8), or maybe 4i -8j.

_____

Additional comment

There are many ways that the components of vectors can be described. The particular format you are expected to use will likely be found in your curriculum materials.

4 0

2 years ago