A car wash had to make their soap last 8 days .If they only have one-seventh of a gallon of soap ，how many should they use each day so it lasts 8 days ？

Answer: Second Option

[tex]f (x)=\frac{2}{x}[/tex] and [tex]g(x)=\frac{2}{x}[/tex]

Step-by-step explanation:

If we have a function f(x) and its inverse function [tex]f ^ {- 1} (x) = g (x)[/tex]

Then by definition:

[tex](fog) (x) = (gof) (x) = x[/tex]

Notice that the inverse of the function [tex]f (x)=\frac{2}{x}[/tex] is [tex]f ^ {- 1}(x)=\frac{2}{x}[/tex]

then:

If [tex]f (x)=\frac{2}{x}[/tex] and [tex]g(x)=\frac{2}{x}[/tex]

Then:

[tex](fog) (x) =\frac{2}{\frac{2}{x}}[/tex]

[tex](fog) (x) =\frac{2x}{2}[/tex]

[tex](fog) (x) =x[/tex]

The answer is the second option

Answer:

D

Step-by-step explanation:

This is exponential growth, and to my understanding, the format goes:

initial amount (percent growth/ decay)^time

percent growth = (decimal percent + 1)

percent decay = (1 - decimal percent)

Your equation:

1500(1.02)^t

Using the above format, 1500 appears to be the initial amount, which increases by 2% per annum.

i think

Answer:

C

Step-by-step explanation:

your answer will be option number

(3) {(1,1),(2,9),(4,8)}

I hopes its help's u

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@Abhi.❤❤

Answer:

what graph? there is no graph?

Answer:

Residual in this case is -4.215

Step-by-step explanation:

A residual can be defined by

Residual = Actual value - Predicted value

We are given:

Predicted value of y = 34.215

Actual value of y = 30

Putting values in the formula:

Residual = Actual value - Predicted value

Residual = 30 - 34.215

Residual = -4.215

So, residual in this case is -4.215

Answer:

domain of (f O g)(x) is {x|x≠0}

Step-by-step explanation:

Given:

f(x) = x + 7

g(x) = 1/x -13

Putting g(x) in f(x) i.e f(g(x))

(fog)(x)= 1/x -13 +7

          = 1/x-6

Domain of 1/x-6 is {x|x≠0} !

For this case we have the following functions:

[tex]f (x) = x + 7\\g (x) = \frac {1} {x} -13[/tex]

We must find [tex](f_ {0} g) (x).[/tex] By definition we have to:

[tex](f_ {0} g) (x) = f (g (x))[/tex]

So:

[tex](f_ {0} g) (x) = \frac {1} {x} -13 + 7 = \frac {1} {x} -6[/tex]

By definition, the domain of a function is given by all the values for which the function is defined.

The function [tex](f_ {0} g) (x) = \frac {1} {x} -6[/tex] is no longer defined when x = 0.

Thus, the domain is given by all real numbers except zero.

Answer:

x nonzero

Answer:

-1680

Step-by-step explanation:

Above would be positive.

Below would be negative.

You have 1680 below, so the answer as a signed number for the elevation would be -1680.

The signed number - 1680 feet addresses the excavator's exhuming point 1680 feet underneath ocean level (negative worth demonstrates beneath ocean level).

The signed number addressing the height of the point 1680 feet beneath ocean level is - 1680 feet. The negative sign demonstrates that the worth is beneath the reference point, which for this situation is ocean level.

With regard to heights, we utilize positive numbers to address positions over the reference point (ocean level) and negative numbers to address positions beneath it.

The miner dug downward in this scenario, lowering the elevation above sea level. Since it is below the reference point, the elevation is negative.

The greatness of - 1680 feet shows the separation from ocean level to the place of removal, and the negative sign demonstrates the bearing beneath ocean level.

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Your answer is a right triangle, reason is because they usually use it for right triangles, not obtuse nor acute. Tangent ratio is used to find the length for the right triangle sides and it also gives the degree for each right triangle angle (right triangle has three angles, where there are 2 angles and 1 right angle.)

Hope this helped!

Nate

Answer:

The tangent ratio is used for right  triangles.

Step-by-step explanation:

We have been given an incomplete statement. We are supposed to fill in the given blank for statement using correct option.

Statement:

The tangent ratio is used for _  triangles.

We know that tangent is a trigonometric ratio, which represent relation between opposite side of right triangle to its adjacent side.

Therefore, the correct term for our given statement is 'right' and option C is the correct choice.

Answer with explanation:

Both the normal distribution curves have sample mean equal to 16.

Normal distribution curve 1 is more wider than Curve 2, resulting in greater standard deviation.

So, Curve 1 has the  greatest standard deviation.

The first normal distribution curve has the greatest standard deviation.

Standard deviation describes how far from the mean the given data set spread out.

Thus, we can conclude that the first normal distribution curve has the greatest standard deviation.

Learn more about normal distribution curve here: https://brainly.com/question/14644201

Answer:

t=-8

Step-by-step explanation:

-2 (t- 1) = 18

Divide each side by -2

-2 (t- 1)/-2 = 18/-2

t-1 = -9

Add 1 to each side

t-1+1 = -9+1

t = -8

Answer:

t = -8

Step-by-step explanation:

Isolate the variable, t. Note the equal sign, what you do to one side, you do to the other.

First, Divide -2 from both sides:

(-2(t - 1))/-2 = (18)/-2

t - 1 = 18/-2

t - 1 = -9

Isolate the variable t. Add 1 to both sides:

t - 1 (+1) = -9 (+1)

t = -9 + 1

t = -8

t = -8 is your answer.

~

Answers:

22

9

20

17

20

35

26

32

23

9

Answer:

4√3

Step-by-step explanation:

The question is to simplify √6 × √8

Applying surds

√6 can be written as √2 ×√3

and

√8 can be written as √2 × √4

but √4=2

so;

√8 is 2√2

Write the whole question as

√2×√3×2√2

This can be written as

2√2×√2×√3

But you know √2×√2 = √4 =2

So, write as

2×2×√3 = 4√3

4√3 is the simplified form

Simplified form of expression √6 × √8 is,

⇒ 4√3

We have to given that,

An expression to simplify,

⇒ √6 × √8

Simplify as,

⇒ √6 × √8

Since, √6 = √2 × √3

√8 = √2 × √2 × √2

Hence, We can write as,

⇒ √6 × √8

⇒ √2 × √3 × √2 × √2 × √2

⇒ 4√3

Therefore, Simplified form of expression √6 × √8 is,

⇒ 4√3

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Answer:

The correct option is A

Step-by-step explanation:

The given expression is:

√10/4√8

We have to eliminate the √ from the denominator

4√8 = (2^3)^1/4

Multiply the whole expression by (2)^1/4

=(2)^1/4 * √10/ 2^(1/4)*(2^3)^(1/4)

= 2^(1/4) · 10^(2/4)  / 2^1/4+3/4

=2^(1/4) · 10^(2/4) / 2^1+3/4

=2^(1/4) · 10^(2/4) / 2^4/4

=2^(1/4) · 10^(2/4) /2

=2^(1/4) · 100^(1/4) /2

=200^1/4 /2

= 4√200 /2

Thus the correct option is A....

Answer:

correct answer is a

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

20=2(x-4)

therefore, x=14

Answer:

2(x -4) = 20

2x - 8 = 20

2x = 28

x = 14

Answer:

[tex]\large\boxed{\sqrt{-36}+\sqrt{-100}+7=7+16i}[/tex]

Step-by-step explanation:

[tex]\sqrt{-1}=i\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\=====================\\\\\sqrt{-36}=\sqrt{(36)(-1)}=\sqrt{36}\cdot\sqrT{-1}=6i\\\sqrt{-100}=\sqrt{(100)(-1)}=\sqrt{100}\cdot\sqrt{-1}=10i\\\\\sqrt{-36}+\sqrt{-100}+7=6i+10i+7=7+16i[/tex]

Answer:

The answer is [tex]16i+7[/tex]

Step-by-step explanation:

In order to determine the answer, we have to know about imaginary numbers.

The imaginary numbers are different to real numbers because they use a new unit called "imaginary unit":

[tex]i=\sqrt{-1}[/tex]

i: imaginary unit

This new unit is applied like a factor when we have even roots with negative numbers inside.

In this case:

[tex]\sqrt{-36}=\sqrt{-1}*\sqrt{36}=6i\\\sqrt{-100}=\sqrt{-1}*\sqrt{100}=10i\\   \\\sqrt{-36}+\sqrt{-100}+7\\ 6i+10i+7\\16i+7[/tex]

Finally, the answer is [tex]16i+7[/tex]

Answer:

Option B - [tex]20\leq x\leq 24.60[/tex]  

Step-by-step explanation:

Given : Tyrese works each day and earns more money per hour the longer he works. Write a function to represent a starting pay of $20 with an increase each hour by 3%.

To find : Determine the range of the amount Tyrese makes each hour if he can only work a total of 8 hours.

Solution :

A starting pay is $20.

let x be the number of hours.

There is pay of $20 with an increase each hour by 3%.

i.e. Increment is [tex]\frac{3}{100}\times 20\times x=\frac{3}{5}x[/tex]

Total earnings a function can represent is

[tex]y=20+\frac{3}{5}x[/tex]

We have given, he can only work a total of 8 hours.

So, The maximum amount she make in 8 hours is

[tex]y=20+\frac{3}{5}\times 8=20+4.8[/tex]

[tex]y=24.8[/tex]

Initial amount is $20.

Therefore, The range of the amount Tyrese makes each hour if he can only work a total of 8 hours is [tex]20\leq x\leq 24.80[/tex]

So, Approximately the required result is option B.

Answer:

1 and 4

5 and 8  are alternate exterior angles

2 and 3

6 and 7 are alternate interior angles

Step-by-step explanation:

The alternate exterior angles are the angles on the outside that are opposite each other

1 and 4 are alternate exterior angles

5 and 8 are alternate exterior angles

The alternate interior angles are the angles on the inside that are opposite each other

2 and 3 are alternate interior angles

6 and 7 are alternate interior angles

Answer:

1 and 4 , 5 and 8

Step-by-step explanation:

Answer:

It is terminating decimal expansion.

Step-by-step explanation:

17/3125 is a terminating decimal expansion.

REASON:

If the factors of the denominator are in the form of 2^n 5^m then the rational number is a terminating decimal expansion otherwise it is recurring. Here n and m are non negative integers.

Proof:

Lets have a look on the solution of the given term.

17/1325

We will break the denominator in the factors:

If we multiply 5 five times than it will give us 1325.

17/1325 = 17/5^5 * 2^0 = 17/2^0 * 5^5

We know that any number with exponent zero = 1

∴ 2^0 = 1

So it satisfies our explanation that the factors of the denominator are in the form of 2^n * 5^m and n and m are non negative integers.

Thus this term has a terminating decimal expansion....

Answer:

Two of the most important characteristics of seawater are temperature and salinity – together they control its density, which is the major factor governing the vertical movement of ocean waters. The temperature of seawater is fixed at the sea surface by heat exchange with the atmosphere.

Step-by-step explanation:

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[tex]((5 \times 1) - (4 \times - 1) = \\ 5 - ( - 4) = \\ 5 + 4 = \\ 9[/tex]

Answer:

D is the correct answer.

Step-by-step explanation:

Step 1: Write the data

Total number of songs = 100

Total ratio = 1

Total percentage = 100%

Ratio of jazz songs = 1/4

Percentage of jazz songs = 1/4 x 100 = 25%

Ratio of pop songs = 1 - 1/4 = 3/4

Percentage of pop songs = 3/4 x 100 = 75%

Step 2: Match the statement.

The correct statement is D; 25% are Julian's songs are jazz because 1/4 = 25/100 and 75% are pop because 3/4 = 75/100.

!!

Answerits not

Step-by-step explanation:

Answer:

Step 1: 5

Step 2: -1/5

Step 3: 2/3

Step 4: 2/3

Only one pair of opposite sides is parallel

Step-by-step explanation:

Answer:

x = -6 or x = 2

Step-by-step explanation:

The given equation is:

[tex]x^{2}+4x-4=8\\\\ x^2+4x-4-8=0\\\\ x^2+4x-12=0\\\\[/tex]

This is quadratic equation, so we can use the quadratic formula to find the roots of the equation i.e. the value of x that satisfy the given equation.

According to the quadratic formula, the two roots will be:

[tex]x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}[/tex]

Here,

a = coefficient of x² = 1

b = coefficient of x = 4

c = constant term = -12

Using these values, we get:

[tex]x=\frac{-4 \pm \sqrt{(4)^2-4(1)(-12)}}{2(1)}\\\\ x=\frac{-4 \pm \sqrt{64}}{2}\\\\ x=\frac{-4 \pm 8}{2}\\\\ x = \frac{-4-8}{2} , x = \frac{-4+8}{2}\\\\ x=-6, x = 2[/tex]

Thus, the two values of x that satisfy the given equation are: -6 and 2. So 1st option gives the correct answer.

Answer:

[tex]\large\boxed{y=-\dfrac{31}{5}x-8}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept - (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

====================================

We have the points (0, -8) → b = -8, and (-5, 23).

Substitute:

[tex]m=\dfrac{23-(-8)}{-5-0}=\dfrac{31}{-5}=-\dfrac{31}{5}[/tex]

Put the value of the slope and of the y-intercept to the equation of a line:

[tex]y=-\dfrac{31}{5}x-8[/tex]

Answer:

We have the following equation: y = 36 - x. And we need to find which of the following points belong to the graph:

If any of the points belong to the equation, then the equality will be met.

Then:

7 = 36 - (-13)

7 = 36 + 13

7 = 49 ❌

1 = 36 - (-35)

1 = 71❌

5 = 36 - 11

5 = 25 ❌

3 = 36 - 27

3 = 9 ❌

None of the points belong to the graph. Therefore, all points are NOT on the grah of p(x) = 36 - x.

Answer:

ANSWER IS (-35,1)

Step-by-step explanation:

I got it because I am looking at the answer right now

Answer:

27+4x+8y

or

4x+8y+27 ( I can reorder this a few different ways. I don't know what your choices are)

Step-by-step explanation:

11+4(x+2y+4)

We can apply distributive property to the 4(x+2y+4), this will give us 4x+8y+16.

Bring down the 11+ and we have 11+4x+8y+16.

The only like terms we have is 11 and 16.  So reorder using commutative property and get 11+16+4x+8y.

I'm going to simplify the 11+16 part which gives us 27.

In the end we have 27+4x+8y.

Let me line up so it is all nice and neat:

11+4(x+2y+4)

11+4x+8y+16

11+16+4x+8y

27+4x+8y

Answer:

a. 8g 1dg 3cg 3mg

b. 11dag 8g

c. 24kg 9hg

d. 7kg 1hg

Step-by-step explanation:

Answer:

a. 8g 1dg 3cg 3mg  

b. 11dag 8g  

c. 24kg 9hg  

d. 7kg 1hg

Step-by-step explanation:

got it from the other person

Answer:

Part a) The values of the function f(x) are {-1,5,11}

Part b) The value of g(5) is -4

Part c) The values of the function f(n) are {8,9,4}

Step-by-step explanation:

Part a) we have

f(x)=3x+5

Evaluate for  {-2,0,2}

1) For x=-2

substitute the value of x in the function

f(-2)=3(-2)+5=-1

2) For x=0

substitute the value of x in the function

f(0)=3(0)+5=5

3) For x=2

substitute the value of x in the function

f(2)=3(2)+5=11

Part b) we have

g(x)=x-9

Evaluate for x=5

substitute the value of x in the function

g(5)=5-9=-4

Part c) we have

f(n)=(3-n)+4

Evaluate for  {-1,-2,3}

1) For n=-1

substitute the value of n in the function

f(-1)=(3-(-1))+4=8

2) For n=-2

substitute the value of n in the function

f(-2)=(3-(-2))+4=9

3) For n=3

substitute the value of n in the function

f(3)=(3-(3))+4=4

Answer:

[tex]\large\boxed{y=\sqrt[3]{x+3}+3}[/tex]

Step-by-step explanation:

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units to the left

f(x - n) - shift the graph n units to the right

===========================================

The original graph ( y = ∛x) shifted 3 units to the left and 3 units up.

Therefore, the new equation is:

y = ∛(x + 3) + 3

Answer:

6m wide

14m long

Step-by-step explanation:

Let the length be represented by L.

Let the width be represented by W.

We are given we want the length to be 8 m longer than it's width.

So we want L=8+W.

The area of the rectangle is 84 m squared, this means that LW=84.

So I'm going to substitute L=8+W into LW=84.

LW=84

(8+W)W=84             (L=8W)

So we are going to solve (8+W)W=84 for W.

(8+W)W=84

Distribute:

8W+W^2=84

Rearrange left hand side using commutative property:

W^2+8W=84

Subtract 84 on both sides:

W^2+8W-84=0

Now to factor a quadratic with leading coefficient 1 (assuming it isn't prime) is to find two numbers that multiply to be c=-84 and add up to be b=8.

I'm going to play with factor pairs that multiply to be -84

c=-84=4(-21)=12(-7)=6(-14)

So the number we are looking for is -6 and 14 since -6(14)=-84 and -6+14=8.

The factored form of our equation is:

(W+14)(W-6)=0

This means we need to solve both W+14=0 and W-6=0.

W+14=0

W=-14  (I subtracted 14 on both sides)

W-6=0

W=6 (I added 6 on both sides)

The solution W=-14 makes no sense.

W=6 is the solution for the width.  That is the width is 6 m long.

Now the length is 8 more than the width so the length is 14 m long.

Answer:

6m wide  and  14m long

Step-by-step explanation:

If a rectangular flower bed is to be 8 m longer than it is wide and the flower bed will have an area of 84 m squared, its dimensions will be 6m wide  by  14m long.

L = length

W = Width

Answer:

[tex]\frac{1}{2}[/tex] x²

Step-by-step explanation:

let the length of the side be l

Then using Pythagoras' identity on the right triangle formed by the diagonal ( hypotenuse ) and the 2 sides

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

l² + l² = x²

2l² = x² ( divide both sides by 2 )

l² = [tex]\frac{1}{2}[/tex] x² ( since A of square = l² )