Solve the equation.

8 (4 - x) = 7x + 2​

Answer:

theyre both the same rate.

Step-by-step explanation:

12months at 1% turns into 12% a year

Answer:

38

Step-by-step explanation:

Step-by-step explanation:

Set up an equation. 80 percent equals 0.8

0.8x=48

since 80 percent of x, the amount of questions on the exam equals to 48 questions correct.

Divide both sides by 0.8 to get 60

Answer:

$22554.45

Step-by-step explanation:

Since we are given a function to use to find the cost of the car, we first need to find the difference in the years 2017 and 2010

2017 - 2010 = 7

So our value for t will be 7.

We can use the formula because it still falls under the expected increase within the 10 year range.

So now let's substitute t in the function.

[tex]f(7) = 15000*(1.06)^{7}[/tex]

[tex]f(7) = 22554.45[/tex]

So it will cost the company $22554.45 to build the car in 2017.

The cost to build the car in 2017 is $22,554.45.

1. Identify the given function:

[tex]\[ f(t) = 15000 \times (1.06)^t \][/tex]

2. Substitute [tex]\( t = 7 \)[/tex] into the function:

[tex]\[ f(7) = 15000 \times (1.06)^7 \][/tex]

3. Calculate [tex]\( (1.06)^7 \):[/tex]

[tex]\[ (1.06)^7 \approx 1.50363 \][/tex]

4. Multiply by the initial cost:

[tex]\[ f(7) = 15000 \times 1.50363 \approx 22554.45 \][/tex]

Answer:

The slope is 3/2

Step-by-step explanation:

Slope is calculated by rise over run so there are three points for you. You start from a point that hits the line then you go up 3 units and across 2 units and you hit the next point. That means the slope is 3/2

Hope this helps and I tried my best on explaining it's hard without being able to show it to you!

Answer:

The slope of given line = 2/3

Step-by-step explanation:

Let (x₁, y₁) and (x₂, y₂) be the two points on a line, the slope of the line is given by,

Slope = (y₂ - y₁)/(x₂ - x₁)

Form the figure we get some coordinates points

(2, 3),  (4,6) , (6, 9)

To find the slope of  line

Consider two points

(x₁, y₁)  = (2, 3) and  (x₂, y₂) = (4, 6)

Slope = (y₂ - y₁)/(x₂ - x₁) = (4 - 2)/(6 - 3) = 2/3

Therefore the slope of given line = 2/3

Answer:

It really depends on what type of equation you are solving.

However, if you're working with an equation that contains variables, it's advised that you should get rid of the variables first before the whole numbers/integers.

Step-by-step explanation:

x2=400

x=√400

=20

20^2=400

The solutions to the equation x² = 400 are x = 20 and x = -20, obtained by taking the positive and negative square roots.

The given equation is x² = 400. This is a simple quadratic equation, and we can solve it by taking the square root of both sides. Any positive number n has two square roots: positive root √n and negative root -√n. So this results in two equations: x = √400 and x = -√400.

Solving these, we find that x = 20 and x = -20. So, the solutions to the equation x² = 400 are x = 20 and x = -20.

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Answer:

The correct function for this table is A Linear

Enjoy Brainly,

Homepage10

Step-by-step explanation:

Answer:   c) 28

Step-by-step explanation:

x² - 7x + 10   ; x = -2

replace x with -2:

(-2)² - 7(-2) + 10

= 4 -  -14 + 10

= 4 + 14 + 10

=    18    + 10

=        28

Answer:

The answer is 2760000

Step-by-step explanation:

Answer:2760000

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello :)

Sorry I cant draw a graph on here but I can explain this to you. So if you have a calculator on you (a scientific one) you can use the table mode by pressing mode and then table. If you do not have a calculator then the axis on the graph you have needs to be substituted where x is.

If the axis is from -3 to 3 you need to enter every single value from -3 to 3 and substitute where x is

EG - (-3)^2-6(-3)+5 that is 32

Keep following for the rest of the values (it depends on your scale)

In this case we have

32,21,12,5,0,-3,-4 these each correspond and these are values on the y axis.

These each correspond to -3,-2,-1,0,1,2,3 in this exact order.

Plot the Graph with the values from this so on the x axis you will have -3 and on the y axis you will have 32 and so on.

This allows you to plot your graph

Answer:

Step-by-step explanation:

We can factor the equation to find the zeros

y = x^2 − 6x + 5

0 =   x^2 − 6x + 5

0 = (x-5) (x-1)

Using the zero product property

x-5 = 0      x-1 =0

x=5   x=1

The zeros are at (1,0) and (5,0)

The vertex is 1/2 way between the zeros

1+5 = 6  6/2 =3

The x coordinate of the vertex is 3

Substituting into the equation

y = 3^2 -6(3) +5

y = 9-18+5

y= -4

The vertex is at (3,-4)

We know it is symmetric around x=3

The y intercept is (0,5)

Answers are on attached sheet! :)

➷ It would be 5

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

[(2 + √3)/4] = 0.9330127

Step-by-step explanation:

We know that

cos (pi/12) ^ 2 =

cos (pi/12)* cos (pi/12)  =

[(√6 + √2)/4]*[(√6 + √2)/4] =

(0.9659)*(0.9659) = 0.9330127

[(2 + √3)/4] = 0.9330127

set f(x) equal to y

y = 19/ x^3

swap x and y

x = 19/y^3

make y the subject

xy^3 = 19

y^3 = 19/x

[tex]y = \sqrt[3]{ \frac{19}{x} } [/tex]

then just replace y with f^-1(x)

[tex]f(x) = \sqrt[3]{ \frac{19}{x} } [/tex]

hope this helped! have a good day ~ •lipika•

The inverse of the function F(x) is:

          [tex]\sqrt[3]{\dfrac{19}{x}}[/tex]

We are given a rational function F(x) as:

[tex]F(x)=\dfrac{19}{x^3}[/tex]

The steps to find the inverse function of a given function f(x) are as follows:

1.   Put f(x)=y

2.  Interchange the value of x and y

3.  Solve for y.

Hence, we find the inverse of F(x) as follows:

[tex]F(x)=y[/tex]

i.e.

[tex]\dfrac{19}{x^3}=y[/tex]

Now we interchange x and y

i.e.

[tex]\dfrac{19}{y^3}=x[/tex]

Now we solve for y as follows:

[tex]y^3=\dfrac{19}{x}\\\\i.e.\\\\y=\sqrt[3]{\dfrac{19}{x}}[/tex]

      Hence, the inverse function is:

                 [tex]\sqrt[3]{\dfrac{19}{x}}[/tex]

Answer:

1/25

Step-by-step explanation:

Total number of DVD's in the box = 20

Number of defective DVD's = 4

The probability of picking up a defective DVD = [tex]\frac{4}{20}=\frac{1}{5}[/tex]

This DVD is being replaced back. So this does not change the total number of DVD's in the box and the number of defective DVD's in the box.

So again the probability of picking up the second defective DVD = [tex]\frac{4}{20}=\frac{1}{5}[/tex]

The probability that both DVD's are defective will be the product of probabilities of individual events i.e.

[tex]\frac{1}{5} \times \frac{1}{5}  = \frac{1}{25}[/tex]

Thus, the probability that both DVDs are defective is 1/25

The probability of selecting two defective DVDs from a box containing 20 DVDs with 4 defective ones, with replacement, is 1/25.

To find the probability that both DVDs are defective, we need to consider the probability of selecting a defective DVD on each trial.

Since the DVDs are selected with replacement, the probability remains constant.

There are 20 DVDs in total, with 4 of them being defective.

So the probability of selecting a defective DVD on the first trial is 4/20 = 1/5.

Similarly, the probability of selecting a defective DVD on the second trial is also 1/5.

To find the probability that both DVDs are defective, we multiply these probabilities together:

Probability = (1/5) * (1/5) = 1/25

Answer:

13 miles

Step-by-step explanation:

divide 391 minutes by 17, to find out how many minutes for 1 mile.

its 23 min= 1 mile.

do 23 multiplied by 13 to get your desired amount of time, which is 299 min.

It will travel 12.65 miles

see the image

The length is 12 feet

The width of the garden is 5 feet

After that the total edging is telling us the area

We know that

So

60 = length x 5

Length = 60 / 5

Length = 12 feet

Answer:

If not, stop and use Steps for Solving an Exponential Equation with Different Bases. Step 2: Rewrite the problem using the same base. Step 3: Use the properties of exponents to simplify the problem. Step 4: Once the bases are the same, drop the bases and set the exponents equal to each other.

4+1/5 could be modeled using the diagram

Answer:

This ordered pair is NOT a solution of the equation.

Step-by-step explanation:

First, it is important to note that ordered pairs consist of (x, y) so in this case

x = 15 and y = -3.  And that any variable directly next to a number calls for multiplication.  So, plugging in the variables the equation would look like

"-3 = 5 x 15"  

To see if 5 x 15 = -3 we will multiply them.  5 x 15 actually equals 75 not -3.  So we know this ordered pair is NOT the solution for the problem.  

Answer: D

Step-by-step explanation: Based on the chart, we can tell that both the median (The line inside the box) and the interquartile range (the box itself) is bigger on Friday than it is on Saturday.

Answer:

Surface Area = 471.2 cm^2

Surface Area = 60.75 m^2

Step-by-step explanation:

The surface area formula for a cylinder is π x diameter x (diameter / 2 + height), where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is π x radius x 2 x (radius + height). ( π =3.14 )

FORMULA:

π x 5 x 2 x 15

WORK:

π x 5 = 15.7

15.7 x 2 = 31.4

31.4 x 15 = 471

The surface area formula for a triangular prism is 2 * (height x base / 2) + length x width1 + length x width2 + length x base.

FORMULA:

2 x (2.5 x 1.5/2) + (6 x 4) + (6 x 4) + (6 x 1.5)

WORK:

(2.5 x 1.5) = 3.75/2 = 1.875

1.875 x 2 = 3.75

(6 x 4) = 24

(6 x 4) = 24

(6 x 1.5) = 9

3.75 + 24 + 24 + 9 = 60.75

I've already done the first one for you, but here's the second one: (its in the attached sheet)

Answer:

[tex]\$7,770.81[/tex]  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]V=P(1-r)^{x}[/tex]  

where  

V is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

[tex]P=\$8,599\\r=2.5\%=0.025\\x=4\ years[/tex]

substitute

[tex]V=\$8,599(1-0.025)^{4}=\$7,770.81[/tex]  

Final answer:

After 4 years, Mariah's car will depreciate to approximately $7,761.66, following a 2.5% annual depreciation rate.

Explanation:

To calculate the depreciated value of a car, we can use the formula for exponential decay, which is:

V = P[tex](1 - r)^t[/tex]

where V is the final value of the car after time t, P is the initial purchase price of the car, r is the rate of depreciation per year, and t is the number of years.

For Mariah's car, the initial purchase price (P) is $8,599, the rate of depreciation (r) is 2.5%, or 0.025 when expressed as a decimal, and the time period in question (t) is 4 years.

Now we can perform the calculation:

V = $8,599[tex](1 - 0.025)^4[/tex]
V = $8,599[tex](0.975)^4[/tex]
V = $8,599(0.9025)
V ≈ $7,761.66

So, after 4 years, the value of the car will approximately be $7,761.66, when rounded to the nearest hundredth.

Answer with explanation:

[tex]Q={\text{Median}}=90\\\\Q_{1}=78\\\\Q_{3}=102[/tex]

There are 100 students in the group.

If we divide 100 students into groups

→First quartile =25.5

means, first quartile of students has median value ≤ 78.

→Median =50.5

Most of the students sends ,90 messages a day.

→Third Quartile=75.5

Students lying above the third Quartile ,sends ≥102 messages per day.

First Quartile means, approximately 0- 25 students in the group , sends 78 messages.

[tex]Q_{1}\leq 78[/tex]

Third Quartile means, 75-100 , students in the group, sends 102 messages .

[tex]Q_{3}\geq 102[/tex]

Approximately 25 students in the sample send

1. more than 102 text messages.

2.less than 78 text messages.

it is 4 1/2 inches long

The right end of the board lines up with the mark halfway between 4 and 5, which means the mark is at 4.5 inches.

Since the board ends at the mark, the length of the board is 4.5 inches.

The length of the board in the image is 4.5 inches.

We can determine this by looking at the scale on the ruler in the image. The scale is marked in inches, and the right end of the board lines up with the mark halfway between 4 and 5.

This means that the mark is at 4.5 inches, and since the board ends at the mark, the length of the board is 4.5 inches.

Another way to think about this is to imagine that you are measuring the board with a ruler.

If you place the ruler at the left end of the board and line up the zero mark with the left end of the board, then the right end of the board will be at the 4.5-inch mark on the ruler.

Here is a more creative way to answer your question:

The board in the image is 4.5 inches long, or as long as a half-dollar coin laid on its side.

Imagine that you have a half-dollar coin. If you place the coin on its side next to the board, you will see that the coin is exactly the same length as the board. This is a fun and easy way to remember the length of the board without having to use a ruler.  

For similar question on board lines.

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Answer:

[tex]+6x^2[/tex] and [tex]-10y^2[/tex]

Step-by-step explanation:

Let's go one term at a time from the right side and match it with the left side.

Clearly Option B is right.

Answer:

The correct answer option is [tex]+6x^2[/tex] and [tex]-10y^2[/tex].

Step-by-step explanation:

We are given the following incomplete expression:

[tex] 3 x^2 + 5 y^2 [/tex] __ [tex] + 3 [/tex] __ [tex] + 4 y^2 + 6 [/tex]

and then there is its simplified expression as shown below:

[tex] 9 x^2 - y^2 + 9 [/tex]

We are to determine whether which terms could be in the boxes to make the expressions equivalent.

[tex]+6x^2[/tex] and [tex]-10y^2[/tex] are the two terms which justify the given expression:

[tex] 3 x^2 + 5 y^2 +6x^2 + 3 -10y^2 + 4 y^2 + 6 = 9 x^2 - y^2 + 9[/tex]

B is correct. 7*-1= -7. -2*1=-2 -7+2= -5

Answer:

The correct answer is D because both ordered pair when substituted to the equation, both sides of the equation didn't equal to each other.

Explanation:

All you do is substitute. (x,y)

A:

Substitute

7(1) - 2(5) = -5

Multiply the number inside the parentheses by the number outside.

7 - 10 = -5

Subtract the numbers.

-3 = -5

This is not the solution to the equation because the numbers on both sides don't equal to each other.

B:

Substitute

7(-1) - 2(1) = -5

Multiply the number inside the parentheses by the number outside.

-7 - 2 = -5

Subtract the numbers.

-9 = -5

This also not the solution to the equation because the numbers on both sides don't equal to each other.

C:

They both are not the solution to the equation because the numbers on both sides don't equal.

Answer:

1/12

Step-by-step explanation:

Answer:

x = -1/2

Step-by-step explanation:

4(x + 3) = 9x + 16 + 3x

Distribute the 4

4x +12 = 9x+16+3x

Combine like terms

4x+12 = 12x+16

Subtract 4x

4x-4x+12 = 12x-4x+16

12 = 8x+16

Subtract 16

12-16 = 8x+16-16

-4 =8x

Divide by 8

-4/8 =8x/8

-1/2 =x

Answer:

D is your answer

Step-by-step explanation:

What you do to figure this out is you take the 3^15 and make it to where there is 15 3's.

3, 3, 3, 3, 3, 3, 3, 3, 3 ,3, 3, 3 ,3, 3, 3.

You will then put them in groups of 2 to get them out of the Square root.

3,3    3,3    3,3    3,3    3,3    3,3    3,3    3.

There are 7 groups where the 3 can come out of the Square root.

So your answer is 3^7sqrt3. D is your answer.

Answer:

d. 3⁷√3

Step-by-step explanation:

√(3¹⁵) can be written as √(3¹⁴ₓ 3)

=√(3¹⁴)ₓ√3

To find the the square root of the number in index form, we divide the index by 2.

√(3¹⁴)=3⁷

let √3 remain in surd form, then we shall have the solution as 3⁷×√3

=3⁷√3