When filling your gas tank, if you pay c dollars for g gallons of gas, you have the following table.


Choose all of the following statements that are true.


a.
The domain is {4, 8, 11, 15}.


b.
An 11 gallon tank would cost $44.00 to fill completely.


c.
A 9.1 gallon fill-up would cost $35.49.


d.
A 12 gallon tank would cost $47.40 to fill completely.

Answer:

4/15

Step-by-step explanation:

in fractions, the number that goes on top is the dividend (the first number in the division problem) which is 4 in this case and the number that goes on the bottom of the fraction is the divisor, which is 15 in this case. therefore, the answer is 4/15.

Option: B

The area of a circle is pi times the radius squared (A = π r²).

Answer:

Is the question even complete ?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the total distance be x.

We have:

Set this as equation and solve for x:

Total distance from the park to the station is approximately 311 m.

Let that be d

Answer:

27

Step-by-step explanation:

3.75/2.5x18=27

The simplification form of the provided expression is 6/5x¹⁰ option first is correct.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

[tex]\rm = \sqrt{\dfrac{72x^{16}}{50x^{36}}}[/tex]

[tex]\rm = \sqrt{\dfrac{72}{50}} \sqrt{\dfrac{x^{36}}{x^{16}}}[/tex]

[tex]\rm = \sqrt{\dfrac{36\times2}{25\times2}} \sqrt{\dfrac{x^{36}}{x^{16}}}[/tex]

[tex]\rm ={\dfrac{6x^{8}}{5x^{18}}}[/tex]

[tex]\rm ={\dfrac{6}{5x^{10}}}[/tex]

Thus, the simplification form of the provided expression is 6/5x¹⁰ option first is correct.

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Answer:

6x3

Step-by-step explanation:

Edge 2023

Answer:

E; 10% off %20 sweater with $6 shipping

Step-by-step explanation:

Similar to what I said last time,

this time is with percentages,

How to calculate percent off?

Divide the number by 100 (move the decimal place two places to the left).

Multiply this new number by the percentage you want to take off.

Subtract the number from step 2 from the original number. This is your percent off number.
________________________________________________________
A. 35% off a $35 sweater with 4 dollar shipping is basically
  0.35 x 35 = 12.25 and 35-12.25 = $22.75 + the $4 shipping fee (if no tax)
    which the total would be $26.75

B. 20% off $35 is
   0.2x35=7 and 35-7 = 28 so your total is $28

C. 30% off $30 with $6 for shipping is

   0.3x30=9 and 30-9 is $21 plus the shipping fee
   $27

D.  $20 sweater with $5 shipping is $25 no discount involved :D

E. 10% off %20 sweater with $6 shipping is

    0.1x20 is 2 which 20 - 2 = 18 and plus shipping fee 18+6 is $24
________________________________________________________
Hope this helped again.

Answer:

The minimum cost of the X-ray machines is 12,197dollars.

Step-by-step explanation:

First, we check whether it’s a Quadratic Equation or not

The general form of the Quadratic equation [tex]f(x) =[/tex] [tex]ax^{2} + bx + c[/tex]

Let’s compare it with the given equation, we get

a = 1

b = -520

c = 79,79

Hence, it’s a quadratic equation.

Now, we will use the VERTEX FORMULA as we are asked to find the ‘minimum’ unit cost.

X = [tex]\frac{-b}\[2a[/tex]  =  [tex]\frac{-(-520)}\[2(1)[/tex] = [tex]260[/tex]

So , number of X-ray machines are = 260 (value of x)

To find the minimum unit cost, plug the value of x into the given equation, and we get

[tex]f(260) = (260)^{2} -520(260) + 79,797[/tex]

[tex]=12,197[/tex]

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Lashawn's scrambled eggs have a stronger salsa taste than Gilberta's scrambled eggs. Then the correct option is A.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Lashawn makes scrambled eggs with 3 spoonfuls of salsa for every 2 eggs.

Gilberta adds 7 spoonfuls of salsa for every 5 eggs.

Then the scrambled eggs have a stronger salsa taste will be

Lashawn's eggs = 3/2 = 1.5

Gilberta's eggs = 7/5 = 1.4

Lashawn's scrambled eggs have a stronger salsa taste than Gilberta's scrambled eggs.

Then the correct option is A.

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Answer:

>

Step-by-step explanation:

Given:      [tex]\frac{1}{2} ? \frac{1}{3}[/tex]

Want:       Which fraction is larger?

To identify the size of a fraction, converting it into a fraction is easier

[tex]\frac{1}{2}[/tex] = 0.5

[tex]\frac{1}{3}[/tex] = 0.33

where 0.5 is greater than 0.33

Choices:

< is less than symbol

> is greater than symbol

= is equal to

[tex]\frac{1}{2} > \frac{1}{3}[/tex]

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Visual Representation:

Answer:

f(x) = (x + 1)^2 + 2

Step-by-step explanation:

A parabola function has different forms:

standard form: f(x) = ax + bx + c^2

vertex form:  f(x) = a (x − h)^2 + k

Our equation that includes a horizontal translation is h

- negative h shifts right

- positive h shifts left

this graph shows a shift to the left by 1 so h = 1

Our equation that includes a vertical translation is k

- negative k shifts down

- positive k shifts up

this graph shows a shift to the up by 2 so k = 2

- a represents a compression / stretch which seems not to be in this graph

combine, f(x) = (x + 1)^2 + 2

Answer:yw

Step-by-step explanation:

Part A

The notation [tex]\lim_{x \to 2^{+}}f(x)[/tex] means that we're approaching x = 2 from the right hand side (aka positive side). This is known as a right hand limit.

So we could start at say x = 2.5 and get closer to 2 by getting to x = 2.4 then to x = 2.3 then 2.2, 2.1, 2.01, 2.001, etc

We don't actually arrive at x = 2 itself. We simply move closer and closer.

Since we're on the positive or right hand side of 2, this means we go with the rule involving x > 2

Therefore f(x) = (x/2) + 1

Plug in x = 2 to find that...

f(x) = (x/2) + 1

f(2) = (2/2) + 1

f(2) = 2

This shows [tex]\lim_{x \to 2^{+}}f(x) = 2[/tex]

Then for the left hand limit [tex]\lim_{x \to 2^{-}}f(x)[/tex], we'll involve x < 2 and we go for the first piece. So,

f(x) = 3-x

f(2) = 3-2

f(2) = 1

Therefore, [tex]\lim_{x \to 2^{-}}f(x) = 1[/tex]

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

Part B

Because [tex]\lim_{x \to 2^{+}}f(x) \ne \lim_{x \to 2^{-}}f(x)[/tex] this means that the limit [tex]\lim_{x \to 2}f(x)[/tex] does not exist.

If you are a visual learner, check out the graph below of the piecewise function. Notice the gap or disconnect at x = 2. This can be thought of as two roads that are disconnected. There's no way for a car to go from one road to the other. Because of this disconnect, the limit doesn't exist at x = 2.

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

Part C

You'll follow the same type of steps shown in part A.

However, keep in mind that x = 4 is above x = 2, so we'll deal with x > 2 only.

So you'd only involve the second piece f(x) = (x/2) + 1

You should find that f(4) = 3, and that both left and right hand limits equal this value. The left and right hand limits approach the same y value. The limit does exist here. There are no gaps to worry about when x = 4.

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

Part D

As mentioned earlier, since [tex]\lim_{x \to 4^{+}}f(x) = \lim_{x \to 4^{-}}f(x) = 3[/tex], this means the limit [tex]\lim_{x \to 4}f(x)[/tex] does exist and it's equal to 3.

As x gets closer and closer to 4, the y values are approaching 3. This applies to both directions.

Answer:

Look at the pic for answer.

Step-by-step explanation:

the price of the watch plus tax = 100% + 7% = 107%

Divide the total cost by 107%:

234.33 / 1.07 = 219.00

The original price was $219.00

Answer:

r = 1

Step-by-step explanation:

we know that :

[tex]Slope=\frac{y_{B}-y_{A}}{x_{B}-x_A}[/tex]

Then

[tex]\frac{5}{4} =\frac{16-r}{-3-(-15)}[/tex]

Then

[tex]\frac{5}{4} =\frac{16-r}{12}[/tex]

Then

5×12 = 4×(16-r)

Then

60 = 64 - 4r

Then

4r = 64 - 60

Then

4r = 4

Then

r = 1

Answer:

Step-by-step explanation:

You are given a system of equations and asked to solve it by the method of addition. That method requires you add a multiple of one equation to the other so that one of the variables is eliminated. In some cases, this is easier if multiples of both equations are added together. The resulting single-variable equation is then solved in the usual way.

__

The given system of equations is ...

We notice the first equation has the variables on opposite sides of the equal sign, and both their coefficients are 1. The second equation has the variables on the same side of the equal sign, and their coefficients are 0.08 and 0.02.

To eliminate a variable by the "addition method," we need to have the variable on the same side of the equal sign with opposite coefficients. Or, we need to have the variable on opposite sides of the equal sign with the same coefficient.

Both of the x-variables are on the left side, so we need opposite coefficients. We can get that by multiplying the first equation by -0.08, or by multiplying the second equation by -12.5. We judge the first of these choices to be easier.

The y-variables are on opposite sides of the equal sign, so we need equal coefficients. We can get that by multiplying the first equation by 0.02, or the second equation by 50.

We choose to multiply the first equation by 0.02, so we can eliminate the y-variable. Here is the result of doing that, then adding the results

  (0.02)(x) +(0.08x +0.02y) = (0.02)(y +1300) +(350)

  0.10x +0.02y = 0.02y +376 . . . . . eliminate parentheses

  0.10x = 376 . . . . . . . . . subtract 0.02y from both sides. y is eliminated

  x = 3760 . . . . . . . . . divide by 0.10

  y = x -1300 = 2460

__

The amount invested at 8% was $3760; the amount invested at 2% was $2460.

_____

Additional comment

We chose to eliminate y for a couple of reasons. x is the amount at the higher rate. We have found that solving for the higher-rate amount usually works best for preventing errors. The other reason is that multiplying by 0.02 results in smaller numbers, which we consider easier to deal with.

Had we multiplied by -0.08 to eliminate x, we would have ...

  -0.08(x) +(0.08x +0.02y) = -0.08(y +1300) +(350)

  0.02y = -0.08y +246

We judge -0.08(1300) +350 harder to calculate mentally, than 0.02(1300) +350.

  0.10y = 246

  y = 2460; x = 2460+1300 = 3760

The answer will be Rs. 4330.

Step-by-step explanation:

Because if you subtract 340 from 4670, you will get the answer which is 4330.

See the attached truth tables.

• A ∧ B is true only when both A and B are true

• A ⇒ B is true only when both A and B are true, or A is false. This logically equivalent to ¬A ∨ B

• ¬A is true only when A is false

• A ⇔ B is true only when both A ⇒ B and B ⇒ A are true. Equivalently, (¬A ∨ B) ∧ (¬B ∨ A)

Step-by-step explanation:

the answer is (c)

because 0 is 3 in number,

1 is 4 in number,

2 is 3in number

3 is 2 in number,

4 is 2 in number,

no 5,6,7

8 is 1 in number

and no 9

The dot plot ( C )is solved and each dot represents one student's response

A dot plot, also known as a dot chart or dot graph, is a type of data visualization that displays the frequency of values in a dataset. It is a simple graphing technique that uses dots to represent data points on a horizontal or vertical axis.

Each data point in the dataset is represented by a dot placed above the corresponding value on the axis. If there are multiple data points with the same value, the dots are stacked vertically above that value. The resulting plot shows the distribution of data points along the axis, with the height of the stack of dots representing the frequency of each value.

Given data ,

Let the data of the number of pets owned by student be represented as A

Now , the value of A = { 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8 }

The frequency of 0 = 3

The frequency of 1 = 4

The frequency of 2 = 3

The frequency of 3 = 2

The frequency of 4 = 2

The frequency of 8 = 1

In this dot plot, each dot represents one student's response. The number on the left indicates how many pets the students reported owning, and the dots are arranged vertically above that number.

For example, three students reported owning 2 pets, so there are three dots arranged above the number 2. This type of plot is useful for displaying the frequency of different values in a dataset.

Hence , the dot plot is solved

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Taking into account the definition of a system of linear equations, the number of adult tickets sold is 615 and the number of children's tickets sold is 195.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that

Galen sold tickets of his church’s carnival for a total of $2,820. Children’s tickets cost $3 each and adult tickets cost $5 each. The number of children’s tickets sold was 30 more than 3 times the number of adult tickets sold.

So, the system of equations to be solved is

[tex]\left \{ {{3x+5y=2820} \atop {x=3y+30}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first you get:

3×(3y+30)+5y=2820

Solving:

3×3y+3×30+5y=2820

9y+90+5y=2820

9y+5y=2820 - 90

14y= 2730

y= 2730÷ 14

y= 195

Remembering that x=3y +30, then:

x= 3×195 + 30

Solving

x=585 +30

x=615

Finally, the number of adult tickets sold is 615 and the number of children's tickets sold is 195.

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Answer:

$6074.36

Step-by-step explanation:

The formula for continuous compounding is

F = Pe^(rt)

F = $4500 × e^(0.1 × 3)

F = $6074.36

Answer: $6074.36

The exponential equation with a base of e is:

[tex]f(x) = 6*e^{2.639*x}[/tex]

We start with:

[tex]f(x) = 6*(14)^x[/tex]

We want to rewrite this to:

[tex]f(x) = 6*(e^n)^x[/tex]

So we only need to find the value of n such that:

[tex]e^n = 14[/tex]

If we apply the natural logarithm to both sides:

[tex]ln(e^n) = ln(14)\\n = ln(14) = 2.639[/tex]

Then the exponential equation with base of e is:

[tex]f(x) = 6*e^{2.639*x}[/tex]

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Answer:

right angle

acute

acute

obtuse

obtuse

Step-by-step explanation:

Since angle <ABC is a straight line, the angle is 180 degrees. This means all the angles in between should also add up to 180 degrees. Using this knowledge you can solve for the value of angle <FBE which is going to be equal to 180 - (40 + 25 + 50) = 65.

< DBF = <DBE + <EBF

< DBF = 25 + 65 = 90 (right angle)

<EBD = 25 (given) (acute)

<DBC = 50 (given) (acute)

<ABE = <ABF + <FBE

<ABE = 40 + 65

<ABE = 105 (obtuse)

<CBF = <CBD + <DBE + <EBF

<CBF = 50 + 25 + 65

<CBF = 140 (obtuse)

Answer:

Power of a quotient

Answer:

57905.8

Step-by-step explanation:

Plug in:

V = 4/3 * 24³π

= 4/3 * 13824π

= 18432π

= 57905.83579cm³

Rounded to nearest tenth:

57905.8

Answer: 18,432

Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO

The roots of the polynomial are done by using a calculator will be -2.3671, 2.1835 + 1.2527i, and 2.1835 – 1.2527i.

The polynomial is given below.

[tex]\rm f(x) = a_0x^n + a_1 x^{n - 1}+ ....+ a_{n-2}x^2 + a_{n-1}x + a_nx^0[/tex]

The roots of the polynomial are equal to n or less than n.

And if one imaginary root is a + bi, then the other imaginary root will be a – bi.

The roots of the polynomial are done by using a calculator.

x = -2.3671, 2.1835 + 1.2527i, 2.1835 – 1.2527i

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Answer:

a whole number is a number with no decmils other than .0000 and is not a fraction where the top and bottom are equal

whole: a,c,e&f

not:b&d