At a bookstore, the cost for a novel and a magazine is $8.27. The cost for 3 novels and 5 magazines is $20.22. Which pair of equations can be used to determine n, the cost of a novel, and m, the cost of a magazine? n + 5m = 8.27 3n + m = 20.22 n + 5m = 8.27, , 3n + m = 20.22, n + m = 8.27 3n + 5m = 20.22 n + m = 8.27, , 3n + 5m = 20.22, n + m = 20.22 3n + 5m = 8.27 n + m = 20.22, , 3n + 5m = 8.27, 3n + m = 8.27 n + 5m = 20.22

Answer:

[tex]f^{-1}(x)=\sqrt{x+1}-3[/tex]

Step-by-step explanation:

We have the function:

[tex]f(x)=y=x^2+6x+8[/tex] with the domain restriction [tex]\{x\geq -3\}[/tex].

And we want to find the inverse of our function.

To find the inverse of our function, we take the following steps:

Therefore, our inverse will be:

[tex]x=y^2+6y+8[/tex]

First, let's subtract 8 from both sides. So:

[tex]x-8=y^2+6y[/tex]

To solve for y, we can complete the square. To complete the square, we:

Our b term is 6. [tex]6/2=3[/tex], and [tex]3^2=9[/tex]. So, we will add 9 to both sides. This yields:

[tex](x-8)+9=(y^2+6y+9)[/tex]

Simplify the left. Complete the square on the right. So:

[tex]x+1=(y+3)^2[/tex]

Take the square root of both sides and solve for y:

[tex]y+3=\sqrt{x+1}\Rightarrow y=\sqrt{x+1}-3[/tex]

Subtract 3 from both sides. So, our inverse is:

[tex]f^{-1}(x)=\sqrt{x+1}-3[/tex]

Part 2)

See below for graph.

Here is also a good time to reinforce the idea of inverses. Notice that the domain of our original function f(x) is [tex]x\geq-3[/tex]. So, this means that the range of f(x) is (looking at the graph) is [tex]y\geq-1[/tex].

When we find the inverse, we will flip the domain and range. Therefore, the domain of our inverse function will be the range of our original function, and the range of our inverse function will be the domain of our original function.

From the graph, we can see that f⁻¹(x) has a domain of [tex]x\geq-1[/tex] and a range of [tex]y\geq -3[/tex]. Therefore, their domain and range are indeed opposites.

And we're done!

Answer:

546 pages

Step-by-step explanation:

the mean is the average .So just multiply the number of pages by chapters.

1×42 for 1 chapter = 42 pages a chapter

thterefore 13×42 for 13 chapters = 546 pages

The total area of the Happyland or the total number of acre which is in Happyland is 35 acre.

The population per acre is the total number of people lives in the area or place.

To find the population per acre, divide the total number of population  lives in an area with total number of acre of that area.

The population of Happyland is 15.8 Happys per acre. Exactly 553 Happys live in Happyland.

Suppose there is total x acres in Happyland. Therefore, the population per acre can be given as,

[tex]15.8=\dfrac{553}{x}\\[/tex]

Solve it for x as,

[tex]x=\dfrac{553}{15.8}\\x=35\rm acre[/tex]

Hence, the total area of the Happyland or the total number of acre which is in Happyland is 35 acre.

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Answer:

21 units

Step-by-step explanation:

7x3 is 21

The value of a = 24 and b = 32. Let the original numbers be 3x and 4x since they are in the ratio 3 : 4.

Step 1: Form the new ratios after the given decreases.

The first number decreased by 4 becomes 3x - 4, and the second number decreased by 2 becomes 4x - 2. The new ratio is 2 : 3.

Step 2: Set up the equation based on the new ratios.

We have the following equation based on the new ratios:

(3x - 4) / (4x - 2) = 2 / 3

Step 3: Solve the equation for x.

To solve the equation, we can cross-multiply:

3(3x - 4) = 2(4x - 2)

Expand and simplify:

9x - 12 = 8x - 4

Now, isolate the variable on one side:

9x - 8x = 12 - 4

x = 8

Step 4: Find the values of a and b.

Now that we have the value of x, we can find the values of a and b:

a = 3x = 3 * 8 = 24

b = 4x = 4 * 8 = 32

So, a = 24 and b = 32.

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The percentage of the car's original value will be 33%

We have given that the car was worth $24,000, being this the original value, after three years the car will be worth $16,000.

Therefore to find the percentage of the car’s original value will Ralph need to pay as part of his lease, We have to find  the difference between the original value and the new value.

So the difference between the original value and new value is,

24,000-16,000= $8000.

A percentage is a number or ratio expressed as a fraction of 100.

And the percentage can be calculated dividing the difference by the original value of the car.

[tex]\frac{8000}{24000}\times 100=33.3\%[/tex]

Therefore the percentage of the car's original value will be 33%

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Answer:

We are given a defined function: f(x) = 2x + 1. This function is the same as saying y = 2x + 1 (y and f(x) are used interchangeably and are the same value - just a different way of representing it). Because we want to find f(1), math states that if you replace one variable with a value, you must replace all of the same variables with that value. Because of this, if we change f(x) to f(3x), we are declaring that the variable x has a value of 3x. Or, if we were to change f(g) to f(3g + 4), we would then be replacing the g's in the function with 3g + 4.

Using these examples, we can the find the value of f(1). We would simply replace the x-values in the function with the value of 1 and then take any operations necessary - be sure to use PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

[tex]f(x) = 2x + 1\\\\f(1) = 2(1) + 1\\\\f(1) = 2 + 1\\\\f(1) = 3[/tex]

Therefore, the first step to solve the problem would be to replace the x-values in the equation with the value of 1. From there, you would simplify your equation and find what the value of the function is if evaluated at f(1).

Hope this helps! :)

Answer:

9043.2 inches³

Step-by-step explanation:

the volume of a sphere is (4÷3)πr³

the radius is 6÷2=3

so each ball needs (4÷3)(3.14)(3)³=113.04 inches³ of lead

113.04×80=9043.2

Answer:

96

Step-by-step explanation:

Total goals scored by peter in second season = 15

In first season he was said to have scored 6 fewer goals. 15-6 = 9

The team as a whole scored 4times as much as peter did.

Let's call the total number of goals peter scored , T

So t = 15 + 9 = 24

4 times as much as peter = 4 x T

= 4x24

= 96 goals in both seasons were scored by the team.

Answer:

Step-by-step explanation:

Given that the total number of days she run is

monday, tuesday, thursday, saturday= 4

and the number of miles is

2.5,4.6,6.75,4.8

the total number of miles is

2.5+4.6+6.75+4.8=18.35 miles

the average is given as = total miles/number of days

average= 18.35/4

average= 4.587

to the nearesth hundreth

average= 4.59miles

Answer:

[tex]\sf\boxed{ \sf \dfrac{1}{2} \ is \ the\ slope }[/tex]

If lines are parallel or tangent, the slope remains same.

[tex]\sf \large\boxed{\sf m_1 \rightarrow m_2}[/tex]

If lines are perpendicular or normal, the slope becomes negatively inverse

[tex]\sf \large\boxed{\sf m_1 \rightarrow -(\frac{1}{m_2} )}[/tex]

With this Here the line a is perpendicular to line b,

therefore using formula: [tex]\sf \large {-(\dfrac{1}{-2} )} \rightarrow \dfrac{1}{2}[/tex]

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Answer:

x = 7, x = -7

Step-by-step explanation:

Hi there!

We are given the following equation:

x²-49=0

And we want to solve it for x

x²-49 is actually written in the difference of squares formula, which is a²-b²=(a+b)(a-b)

In this case, x² and 49 represent a² and b², so we'll need to find a and b

For x², we need to find which number or variable multiplies itself to equal x²; in this case, it will be x (x*x=x²)

For 49, we need to find which number multiplies itself to equal 49; in this case, it will be 7 (7 * 7 = 49)

Thus, a in this case is x, and b is 7

Now substitute these values into the formula.

(a+b)(a-b)= (x+7)(x-7)

Now set (x+7)(x-7) (which is x²-49, just expanded out) equal to 0

(x+7)(x-7)=0

Now using zero product property, split and solve:

x+7=0

subtract 7 from both sides

x=-7

x-7=0

Add 7 to both sides

x=7

Therefore, the answer is x = 7, x = -7 (there are 2 answers here that work!)

Hope this helps!

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to 2.5\%\to \frac{2.5}{100}\dotfill &0.025\\ t=years\dotfill &6 \end{cases} \\\\\\ I = (600)(0.025)(6)\implies I=90[/tex]

Answer:

k=60

Step-by-step explanation:

k+2k=180

3k=180

k=60

Answer:

k = 60

Step-by-step explanation:

Because supplementary angles are either 2 angles where the sum equals 180, if we take 60 for [tex]\angle {1}[/tex], and then add it to [tex]\angle {2}[/tex], we get 2(60) = 120 for [tex]\angle 2[/tex] and 60 for [tex]\angle 1[/tex], meaning that if we add the values of both angles together, it will be 120 + 60 = 180.

Step-by-step explanation: If you're asked to solve a quadratic equation by the method of your choice, you should always check to see if the quadratic factors before you try any other method.

In this case, we have a trinomial that

factors as the product of two binomials.

In the first position for each binomial, we will use

our factors of 6x² which are either 6x · x or 3x · 2x.

It's a good idea to try less extreme extreme factors.

That means choose factors a little closer together.

So 3x and 2x would be first on our list.

We do the same for the factors of -35.

Since our constant term is negative, it will factor

as the product of a positive times a negative.

So the factors of -35 are +7 · -5, -5 · +7, -7 · +5, +5 · -7.

Remember to reverse the order of the

factors is your lead coefficient is not 1.

The factors that work in this case are -5 and +7.

So we have (3x - 5)(2x + 7).

To check, take the product of the outer terms and inner terms.

So we have -21x + 10x which is our middle term.

Now set it equal to 0.

So we have (3x - 5)(2x + 7) = 0.

Now use the zero product property.

So either 3x - 5 = 0 or 2x + 7 = 0.

Solving each equation from here, we have x = 5/3 or x = -7/2.

Answer:

not me

Step-by-step explanation:

why?

Answer:

D

Step-by-step explanation:

because 4 quarters is 100 and 3 quarters is 75 so 4 and 3 quarters is 7 quarters and that would give you 175 so if you add both 200 and 175 that gives you 375

Answer:

they do know true the callender

Answer:

what thing i help you

Step-by-step explanation:

what question

Answer:

There 68 bicycles , 33 tricycles and 17 Tandem bicycles

Step-by-step explanation:

Let B be the no. bicycles , TB be the no. of tandem bicycles and C be the no. of tricycles

No. of seats in 1 bicycle = 1

No. of seats in B bicycle = B

No. of seats in 1 Tandem bicycle = 2

No. of seats in TB Tandem bicycle = 2TB

No. of seats in 1 Tricycle = 1

No. of seats in C Tricycle = C

We are given that There are a total of 135 seats

So, B+2TB+C=135 ----1

Similarly

There are total 118 front handlers

So,1B + 1TB + 1C = 118 ----2

There are total 269 wheels

So,2B + 2TB + 3TR = 269

Substract 1 from 2

B+2TB+C-B-TB-C=135-118

TB=17

Adding 1 and 2 and substracting from 3

[2 - (1+1)]B + [2- (2+1)]TB +  [3- (1+1)]C = 269-253

- 1x17 +C= 16

C= 16 + 17 = 33

Replacing in eq. 32

1B + 17 + 33 = 118

B = 118 - 17 - 33 =  68

Hence There 68 bicycles , 33 tricycles and 17 Tandem bicycles

Answer:

4 students

Step-by-step explanation:

4 students are in the middle of the diagram, which means that they like all three colors evenly

Answer:

x = 11

Step-by-step explanation:

4 - 1 / x - 7 (simplify)

3 / x - 7 = 3/4 (multiply by x - 7)

3 = 3/4 (x - 7)

3 = 3/4x - 5.25 (add 5.25 to both sides)

8.25 = 3/4x (divide both sides by 8.25)

x = 11

sub into the formula to check:

4-1 / 11 - 7

3 / 4

Answer:

75-53=22

Step-by-step explanation: D is close to  A so u have to minus 75-53 to get the number of degrees for d

Answer: 400%?

Step-by-step explanation: 2 is 1/4 of 8 which means to get from 2 you need to multiply it by 4, 1=1.00 which is 100% so it is 400%

Answer:

0.25 or 25%

Step-by-step explanation:

p x 8 = 2

= 2/8

Then turn this into a percent which is 25% hope this helped

Answer:

this would be 12/6+(-1/6)

Step-by-step explanation:

if you want to solve it would be 11/6, or "1 5/6ths"

we need to first find the common denominator, which is 6, but since we multiplied the bottom by 2, we multiply the top by 2. next we just subtract the values, and i put the 1 because there is only one "6" that goes in to the bottom ,and 5 is left over.

please mark as brainlest.

Answer:

Step-by-step explanation:

The sample space is just A, B, C, D, E, F.

The probability of choosing B, C, E can be found as follows:

There are 3 desired possibilities: picking B, picking C, or picking E.

There are 6 total possibilities (from the sample space)

So the probability is 3/6 = 1/2.

The faction expression with which it produces an equivalent fraction with a rational denominator is [tex]\dfrac{\sqrt{17}+\sqrt{2}}{5}[/tex].

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

We have the expression given below.

[tex]\dfrac{3}{\sqrt{17} - \sqrt2}[/tex]

Multiple and divide the expression by [tex]\sqrt{17} + \sqrt{2}[/tex]. Then we have

[tex]\dfrac{3}{\sqrt{17} - \sqrt2} \times \dfrac{\sqrt{17} + \sqrt2}{\sqrt{17} + \sqrt2}\\\\\\\dfrac{3(\sqrt{17} + \sqrt{2})}{(\sqrt{17})^2 - (\sqrt{2})^2}\\\\\\\dfrac{3(\sqrt{17} + \sqrt{2})}{17 - 2}\\\\\\\dfrac{3(\sqrt{17} + \sqrt{2})}{15}\\\\\\\dfrac{\sqrt{17} + \sqrt{2}}{5}[/tex]

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Answer:

b

Step-by-step explanation:

Using linear function concepts, it is found that:

A linear function is modeled by:

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

In which:

For Company A, the equation is:

y = 1.35y + 100.

The slope is of m = 1.35, hence the unit rate is of $1.35.

For Company B, as already stated in the problem, the unit rate is of $2.05.

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Answer:

option 'C' is the correct one or parent function of linear.

Answer: Choice D)

6 unit cubes and 18 smaller cubes of volume 1/27 cubic inches

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

Explanation:

Block A = unit cube that has side length of 1 inch

Block B = cube that has side length 1/3 inch

Block B has a volume of (1/3)*(1/3)*(1/3) = 1/27 cubic inches

If we have 180 of block B, then

180*(1/27) = 180/27 = 6.6667 approximately

The first 6 before the decimal point tells us we have 6 block A's. This is the same as saying that we have 6 cubic inches so far.

The 0.6667 at the end means we have 0.6667*27 = 18.0009 = 18 block B's

So we have 6 unit cubes (block A) and 18 smaller cubes (block B) that have a volume of 1/27 cubic inches

--------------

Another way to look at it

180/27 = (162+18)/27

180/27 = 162/27+18/27

180/27 = 6+18/27

180/27 = 6 remainder 18

The last line can also be found through using long division.

The 6 refers to 6 unit cubes and the remainder 18 is the left over 18 smaller blocks.