One-third of a number t is equal to 7.
Write the word sentence as an equation then solve

Answer:

It would take 5 years for the car to have a value of less than $25,000

Step-by-step explanation:

Exponential Decaying Model

The exponential function is often used to model natural decaying processes, where the change is proportional to the actual quantity.

We have the initial value of a car is $40,000. Each year it depreciates by 10%.

Thus the first year its value is 90% of the initial value:

V1 = 90 * $40,000 / 100 = $36,000

By the second year its value is 90% of $36,000:

V2 = 90 * $36,000 / 100 = $32,400

Note the value for a year n is the original value multiplied by 90% (or 0.9) to the power of n:

[tex]Vn = $40,000 \cdot 0.9^n[/tex]

To find the number of years needed to have a value of less than $25,000, we solve the equation:

[tex]40,000 \cdot 0.9^n = 25,000[/tex]

Dividing by 40,000:

[tex]0.9^n = 25,000/40,000 = 0.625[/tex]

Taking logarithms:

[tex]n\log 0.9=\log 0.625[/tex]

[tex]n=\log 0.625 / \log 0.9[/tex]

n =4.5

We'll round up to n = 5

It would take 5 years for the car to have a value of less than $25,000

Answer:

y=mx + b

Step-by-step explanation:

y= y intercept coordinate

m=slope=x coordinate

b = y intercept

Answer:

382

Step-by-step explanation:

Answer:

BANANA

Step-by-step

Answer:

2/21

Step-by-step explanation:

Answer:

Step-by-step explanation:

The given equation is:

f(x) = 3 - 48x + 4x²      [5,7]

where; f(x) is continous and derivable in [5,7]

f'(x) = -48x + 8x

f(5) = 3 - 48(5) + 4(5)² = -137

f(7) = 3 - 48(7) + 4(7)² = -137

Thus, it satisfies the hypotheses of Rolle's Theorem

f'(x) = f'(c) = 0

-48 + 8c = 0

c =48/8

c = 6

Answer: 0.96875

Step-by-step explanation:

Probability of obtaining at least one tail on a toss of coin 5 times ;

P(success) in a coin toss = 1/2 = 0.5

Using the binomial distribution formula :

P(x) = nCx * p^x * (1 - p)^(n-x)

P(at least one tail) = 1 - p(0 tails)

P( 0 tails) = 5C0 * 0.5^0 * 0.5^(5-0)

= 1 * 1 * 0.03125

= 0.03125

P(at leat 1 tail) = 1 - 0.03125

P(atleast 1 tail) = 0.96875

Answer:

w = 9

x = 12

y = 5

z = 3

Step-by-step explanation:

The corresponding sides of similar polygons are proportional.

Therefore:

[tex] \frac{w}{3} = \frac{x}{4} = \frac{15}{y} = \frac{9}{z} = \frac{6}{2} [/tex]

Solve for each variable as follows:

✔️[tex] \frac{w}{3} = \frac{6}{2} [/tex]

Multiply both sides by 3

[tex] w = \frac{6}{2} \times 3 [/tex]

[tex] w = 3 \times 3 [/tex]

[tex] w = 9 [/tex]

✔️[tex] \frac{x}{4} = \frac{6}{2} [/tex]

Multiply both sides by 4

[tex] x = \frac{6}{2} \times 4 [/tex]

[tex] x = 3 \times 4 [/tex]

[tex] x = 12 [/tex]

✔️[tex] \frac{15}{y} = \frac{6}{2} [/tex]

Cross multiply

[tex] y \times 6 = 2 \times 15 [/tex]

[tex] 6y = 30 [/tex]

Divide both sides by 6

[tex] y = 5 [/tex]

✔️[tex] \frac{9}{z} = \frac{6}{2} [/tex]

Cross multiply

[tex] z \times 6 = 2 \times 9 [/tex]

[tex] 6z = 18 [/tex]

Divide both sides by 6

[tex] z = 3 [/tex]

Answer: 21, 21

Step-by-step explanation: 21 × 3 = 63, so 21 + 21 + 21 is 63.

Answer:21,21

Step-by-step explanation:

21 × 3 = 63, so 21 + 21 + 21 is 63.

Answer:

Step-by-step explanation:

m∠1 = x

m∠2 = 3x

m∠3 = ( [tex]\frac{1}{3}[/tex] )(3x) = x

x + 3x +x = 180°

x = 36°

m∠1 = 36°

m∠2 = 108°

m∠3 = 36°

Answer:

7) y = -2

8) x = 4

Step-by-step explanation:

Any straight horizontal/vertical line you find will be x= or y=. The vertical lines are always x= because they only touch the x axis. It's the opposite for horizontal lines. For example, on number 7, the line touches -2 on the y axis. That's why it's "y=-2". Same goes for 8. the line only touches 4.

I hope this helped and wasn't confusing!

Answer:

16

Step-by-step explanation:

I am doing Prepworks Basic triangles as well :D

Answer:

1/x^3 and 1/a^2

Step-by-step explanation:

Answer:

The parabola is translated down 2 units.

Step-by-step explanation:

You have the parabola f(x) = 2x² – 5x + 3

To change this parabola to f(x) = 2x² - 5x + 1, you must have performed the following calculation:

f(x) = 2x² – 5x + 3 -2= 2x² - 5x + 1  Expresion A

The algebraic expression of the parabola that results from translating the parabola f (x) = ax² horizontally and vertically is g (x) = a(x - p)² + q, translating in the same way as the function.

In the expression A it can be observed then that q = -2 and is less than 0. So the displacement is down 2 units.

This can also be seen graphically, in the attached image, where the red parabola corresponds to the function f(x) = 2x² – 5x + 3 and the blue one to the parabola f(x) = 2x² – 5x + 1.

In conclusion, the parabola is translated down 2 units.

First, you will want to get the denominators of both fractions to be the same, the easiest way to do this is by multiplying the denominators, so 5 x 7 = 35

next you need to do the same for the numerators, so 2 x 7 = 14 and 2 x 5 = 10

now you have the equation 14/35 + 10/35

next, you add the numerators. so, 14 + 10 = 24

therefor, 2/5 + 2/7 =24/35

so your answer is 24/35

Answer:

c

Step-by-step explanation:

the guy is a champ

Answer:

12-pack

Step-by-step explanation:

We find the unit cost of each one by dividing its price by the number of juice containers.

4.49/8 = 0.56125

6.59/12 = 0.5491666...

The 12-pack has a lower unit cost, so the 12-pack is a better buy.

Answer:

The answer is C

Step-by-step explanation:

Answer: The answer should be 9 2/7 I suppose.

Similarity cannot be determined because angle measurements are not given.​ Option D is correct.

Given that,
A figure is shown we have to determine whether the given triangles are similar or not.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
The ratio of the sides is not equivalent,
70/13 ≠ 42 / 25 ≠ 94 / 30
and also the angles are not given,

Thus, similarity cannot be determined because angle measurements are not given.​ Option D is correct.

Learn more about similar triangles here:

brainly.com/question/25882965

#SPJ6

Answer:

d=35

Step-by-step explanation:

Answer:

$1.40

Step-by-step explanation:

I used a unit rate to understand it.

$70/50

70÷ 50= 1.4

50÷50=1

1.4/1 = 1.4 OR $1.40, adding a zero doesn't change it amount, it just places a filler, so the final answer is, one dollar and forty cents.

Answer:

The equation of your line is y=1x+2

Step-by-step explanation:

first you take y2-y1/x2-x1

y2=-1     y1=5

x2= -3   x1= 3

that gives you your slope so (-1-5)/ (-3-3) = 1

y=mx+b

mx is your slope

y=1x+b

to solve for b you input your slope and one of your points (I used (3,5)

5=1(3) +b

solve for b and you get 2

then put your mx and b into the equation of a line

y=1x+2

and thats your answer

You can also check your work by using a graphing calculator and checking that the line goes through those two points.

Answer:

the first one is 101 degrees

the second one is 106 degrees

the third one is 106 degrees

Step-by-step explanation:

Answer:

1. x = 101, x is an opposite interior angle

2. x = 106, x is an opposite interior angle

3. x = 106, x is a same-side interior angle

Answer:

none of these

Step-by-step explanation:

Answer:

125%

Step-by-step explanation:

first set up a proportion where 80 is over 64 and x is over 100 . 80/64=x/100

then cross multiply and divide to get 125%

Answer:

144

Step-by-step explanation:

You will multiply 4 tablespoons by the number of cups, that is how you get your answer.  ; )

Answer:

we need to know how much she earns per hour

Step-by-step explanation:

just do whatever you did now