Miles paid $5824, including 4% sales tax, for an out-of-state purchase of a car. In order to calculate the amount of sales tax he owes in his state, he must first determine the price of the car without sales tax. How much did the car cost before sales tax? This one is a little bit tricky. The amount you need to find the sales tax of is not know. Let the original price be x. Then, 4% of that price is 0.04x. Adding the original price and the sales tax, we get the amount paid. Therefore, the equation is
X + 0.04x = 5824

Answer:

$96.25

Step-by-step explanation:

Find the unit rate of pay:

$52.50

------------- = $8.75/hr

 6 hours

Now multiply this rate by 11 hours:

($8.75/hr)(11 hrs) = $96.25

Answer: $ 96. 25

Step-by-step explanation:

It is said that two variables x and z vary directly if they meet the following relationship:

[tex]z = kx[/tex]

Where k is the constant of variation.

In this case z represents the gains and x represents the hours of work.

Now we must find the value of the constant k.

We know that for 6 hours of work the earnings are $ 52.50

So

[tex]x = 6[/tex]

[tex]z = \$\ 52.50[/tex]

[tex]52.50 = 6k[/tex]

[tex]k= \frac{52.50}{6}[/tex]

[tex]k= 8.75[/tex]

Then the equation is:

[tex]z = 8.75x[/tex]

Finally when x = 11, then:

[tex]z = 8.75*11\\\\z =\$\ 96.25[/tex]

Answer:

A clockwise rotation 90° about the origin followed by a translation

2 units to the right and 6 units down produces Δ X'Y'Z' from Δ XYZ

Step-by-step explanation:

* Lets revise the rotation and translation

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 180° anti-clock wise

∴ Its image is (-x , -y)

- If point (x , y) rotated about the origin by angle 270° anti-clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 90° clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180° clock wise

∴ Its image is (-x , -y)

- If point (x , y) rotated about the origin by angle 270° clock wise

∴ Its image is (-y , x)

- If the point (x , y) translated horizontally to the right by h units

∴ Its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

∴ Its image is (x - h , y)

- If the point (x , y) translated vertically up by k units

∴ Its image is (x , y + k)

- If the point (x , y) translated vertically down by k units

∴ Its image is = (x , y - k)

* Now lets solve the problem

- Δ XYZ has vertices X = (-5 , 3) , Y = (-2 , 3) , Z = (-2 , 1)

∵ Δ XYZ rotate 90° clockwise about the origin the image will be (y , -x)

∴ The image of X is (3 , 5)

∴ The image of Y is (3 , 2)

∴ The image of Z is (1 , 2)

- From the graph

∵ X' = (5 , -1)

∵ Y' = (5 , -4)

∵ Z' = (3 , -4)

- Every x-coordinate add by 2

∴ There is a translation 2 units to the right

- Every y-coordinate subtracted by 6

∴ There is a translation 6 units down

- From all above

* A clockwise rotation 90° about the origin followed by a translation

 2 units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ

Answer:

A clockwise rotation 90° about the origin followed by a translation

2 units to the right and 6 units down produces Δ X'Y'Z' from Δ XYZ

Step-by-step explanation:

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[-8-(-3)]^2+[1-(-4)]^2}\implies d=\sqrt{(-8+3)^2+(1+4)^2} \\\\\\ d=\sqrt{25+25}\implies d=\sqrt{50}\implies d\approx 7.071[/tex]

Answer:

C. -26

Step-by-step explanation:

First, subtract by 4 both sides of equation.

4+m/8-4=3/4-4

Then, simplify.

4+m/8-4=m/8

3/4-4=-13/4

m/8=-13/4

Multiply by 8 both sides of equation.

8m/8=8(-13/4)

Simplify to find the answer.

8(-13/4)

-8*13/4

13*8/4=-104/4

104/4=-26

X=-26 is the correct answer.

C. -26 is the correct answer.

For this case we must solve the following equation:

[tex]4+ \frac {m} {8} = \frac {3} {4}[/tex]

We subtract 4 on both sides of the equation:

[tex]\frac {m} {8} = \frac {3} {4} -4\\\frac {m} {8} = \frac {3-16} {4}\\\frac {m} {8} = \frac {-13} {4}[/tex]

We multiply by 8 on both sides of the equation:

[tex]m = \frac {-13 * 8} {4}[/tex]

[tex]m = -26[/tex]

Answer:

Option C

Answer:

4370*10^2

437*10^3

43.7*10^4

Step-by-step explanation:

The given number is

437000

Scientific notation can be used to write the number in different ways. We can use the powers of 10 to write the given number.

First way:

The first way is:

4370*10^2

Separating the hundred from the given number

The second way:

437*10^3

Separating the 1000 from the number in the form of power of 10

The third way:

43.7*10^4

Hence scientific notation can be used for writing the number in different ways..

The correct function that can be used to model the monthly profit for x trinkets produced is f(x) = (x + 50)(x + 250).

The correct function that can be used to model the monthly profit for x trinkets produced is f(x) = (x + 50)(x + 250).

To model the monthly profit, we need to consider the profit made for each trinket produced. The function f(x) = (x + 50)(x + 250) represents the profit made for x trinkets produced, where x is the number of trinkets produced. This function is a quadratic function with two factors that represent the difference between the production cost and the selling price of the trinkets.

For example, if we produce 100 trinkets, we can substitute x = 100 into the function to find the monthly profit. f(100) = (100 + 50)(100 + 250) = 150 * 350 = 52,500. So, the monthly profit for producing 100 trinkets would be $52,500.

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The quadratic function f(x) = –4(x – 50)(x – 250) accurately models the monthly profit for x trinkets produced, displaying a concave-downward parabola as expected in this context.

To determine the appropriate quadratic function to model the monthly profit for x trinkets produced, let's analyze the given options.

A quadratic function is generally represented as f(x) = ax^2 + bx + c. The given options are all factored forms of quadratic expressions. The correct form should represent a concave-downward parabola since the profit typically decreases as production increases.

Comparing the given options:

f(x) = –4(x – 50)(x – 250): This expression has a negative leading coefficient, indicating a concave-downward parabola.

f(x) = (x – 50)(x – 250): This expression also has a positive leading coefficient, which would create a concave-upward parabola. It does not match the expected behavior for profit in this context.

f(x) = 28(x + 50)(x + 250): This expression has a positive leading coefficient, indicating a concave-upward parabola. It does not align with the expected downward trend of profit.

f(x) = (x + 50)(x + 250): This expression has a positive leading coefficient, suggesting a concave-upward parabola. Similar to option 3, it does not represent the expected profit behavior.

Therefore, the correct quadratic function to model the monthly profit for x trinkets produced is f(x) = –4(x – 50)(x – 250).

The question probable may be:

All-Star Trinkets estimates its monthly profits using a quadratic function. The table shows the total profit as a function of the number of trinkets produced.

Which function can be used to model the monthly profit for x trinkets produced?

f(x) = –4(x – 50)(x – 250)

f(x) = (x – 50)(x – 250)

f(x) = 28(x + 50)(x + 250)

f(x) = (x + 50)(x + 250)

The number of revolutions the wheel makes when the bicycle travels 200 ft will be 26.

Distance is a numerical representation of the distance between two objects or locations.

The circumference of the bicycle wheel is;

C= π × diameter

C=π × 29 in

C= 91.11 in

Distance traveled by bicycle wheel in 1 revolution is 91.11 in

Unit conversion;

1 feet = 12 inches

1 inch=1/12 feet

91.11 in=7.592 ft

In one revolution, a bicycle wheel travels 7.592 feet. For a distance of 200 feet, the number of revolutions done by a bicycle wheel is:

[tex]\rm n= \frac{200}{7.5 } \\\\ n= 26.34 \\\\ n= 26 \ rev[/tex]

Hence, the number of revolutions the wheel makes when the bicycle travels 200 ft will be 26.

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Answer:

No

Step-by-step explanation:

A function has only one y value for each x value.  Here, we have two points that have the same x value but different y values: (-8, -6) and (-8, 1).  So this is not a function.

Answer:

[tex]\large\boxed{\dfrac{V_{cone}}{V_{prism}}=\dfrac{1}{3}}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a cone:}\ V_{cone}=\dfrac{1}{3}B_cH_c\\\\B_c-base\ area\ of\ a\ cone\\H_c-height\ of\ a\ cone\\\\\text{The formula of a volume of a prism:}\ V_{prism}=B_pH_p\\\\B_p-base\ area\ of\ a\ prism\\H_p-height\ of\ a\ prism\\\\\text{The cone and the prism have the same base area and height.}\\\text{Therefore}\\\\V_{cone}=\dfrac{1}{3}BH\ \text{and}\ V_{prism}=BH\\\\\text{The ratio of the volume of the cone to the volume of the prism:}[/tex]

[tex]\dfrac{V_{cone}}{V_{prism}}=\dfrac{\frac{1}{3}BH}{BH}=\dfrac{1}{3}[/tex]

The solution is, 1:3 the ratio of the volume of the come to the volume of the prism.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

The cone in the diagram has the same height and base area as the prism.

now, we know that,

The formula of volume of a cone:

if 'B' is the base of the cone,

and 'h' is the height of the cone,  

its volume is V = (1/3) (Bh) cubic units.

The formula of volume of a prism:

if 'B' is the base of the prism,

and 'h' is the height of the prism,  

its volume is V = (Bh) cubic units.

The cone in the diagram has the same height and base area as the prism.

so, the ratio of the volume of the come to the volume of the prism:

The formula of volume of a cone: The formula of volume of a prism

= 1/3 *BH : BH

=1/3

=1:3

Hence, The solution is, 1:3 the ratio of the volume of the come to the volume of the prism.

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Answer:

100000

Step-by-step explanation:

Since we have the natural base of the log, the base is 10.

Now think of it this way, since we are solving for the value that is being "logged" we can say 10 to the power of 5 equals what?

And since 10^5 is 100000, x is 100000.

The value of x is 100000.

A logarithm helps us know by what power a number must be raised to get the desired number.

A natural log is a log with base 10.

For example,

We want to know by what power must 10 be raised so we get 1000 as an output,

therefore, we can write it as,

[tex]\bold{log_{10} 1000 = 3}[/tex]

[tex]\bold{10^3 = 1000}[/tex]

where, 10 is the base meaning number to which power is to be raised,

1000 is the desired number,

And 3 is the answer.

Now, looking at our question,

[tex]\bold{log\ x= 5}[/tex]

can be written as

[tex]\bold{log_{10} x= 5}[/tex]

[tex]\bold{10^5 = x}[/tex]

[tex]\bold{10^5 = 100000}[/tex]

Therefore, 10 is been raised to the power of 5 giving the desired result which is 100,000.

Hence, the value of x is 100000.

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Answer:

[tex]\large\boxed{1.\ the\ slope\ is\ \dfrac{1}{4}}\\\boxed{2.\ y=3x-5}\\\boxed{3.\ (3, 6)}[/tex]

Step-by-step explanation:

[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_2}\\\\l\ \parallel\ k\iff m_1=m_2\\\\m-slope\\b-y-intercept\to(0,\ b)\\\\1.\\\\y=-4x+1\to m_1=-4\\\\m_2=-\dfrac{1}{-4}=\dfrac{1}{4}[/tex]

[tex]2.\\y=3x+2\to m_1=3\\\\m_2=3,\ b=-5\\\\y=3x-5[/tex]

[tex]\text{Calculate}\ a\ \text{and}\ b:\\\\a=\dfrac{6-(-9)}{5}=\dfrac{15}{5}=3\\\\b=\dfrac{8-(-2)}{5}=\dfrac{10}{5}=2\\\\\text{Calculate the coordinates of a point:}\\\\x=-9+4a\to x=-9+4(3)=-9+12=3\\\\y=-2+4b\to y=-2+4(2)=-2+8=6[/tex]

Answer:

f(9) =21

Step-by-step explanation:

I will assume you want to find f(9) when x=9

Let x=9

f(9) = 2(9) +3

    = 18+3

     =21

f(9) =21

Answer: C is the answer.

Step-by-step explanation:

It is 5/8 because, there is 3 out of 8 chances of the event happening. The rest of the chances, that is 5 out of eight chances, that are not going to happen.

Answer:

they can both take 7 lessons each

Answer:

Each one can take 7 lessons.

Step-by-step explanation:

Dylan and Dusty plan to take weekly surfing lessons together.

They want to spend $100 each on new surfboards = $100 × 2

                                                                                     = $200

They want to spent total amount for lessons and surfboards is at most $480.

After spending on two new surfboards the money left with

= 480 - 200

= $280

The charges for 2-hours classes for surfing lessons = $20 per person

The charges for 1 hour classes for them = $20.00

With $280  they will be able to take maximum number of lessons

= [tex]\frac{280}{20}[/tex]

= 14 lessons

Each one can take 14/2 = 7  lessons.

Answer:

Approximately 10.39 ft.

Step-by-step explanation:

First, draw a short diagram to understand the sides of the right triangle.

The 12 foot ladder leaning against the building would be the hypotenuse and because the bottom of the ladder is 6 feet from the house, that would be the bottom leg. We are trying to figure out the leg to the left (the top of the ladder from the ground.

To solve this, we must use the converse of the Pythagorean Theorem. To do this, we can set up the following equation.

12^2 - 6^2

144 - 36 = 108

Then we must find the square root of 108, which is approximately 10.39 feet.

Answer:

LN=64 units

Step-by-step explanation:

step 1

Find the value of x

we know that

LN=LM+MN -----> equation A

see the attached figure to better understand the problem

we have

LN=12x+16

LM=10x+8

MN=5x-4

substitute the values in the equation A

12x+16=(10x+8)+(5x-4)

Solve for x

12x+16=15x+4

15x-12x=16-4

3x=12

x=4

step 2

Find the value of LN

LN=12x+16

LN=12(4)+16=64 units

Answer:

B

Step-by-step explanation:

Given

x² - 2x + 26 = 0 ← in standard form : ax² + bx + c = 0 : a ≠ 0

with a = 1, b = - 2, c = 26

Use the quadratic formula to solve for x

x = ( - (- 2) ± [tex]\sqrt{(-2)^2-(4(1)(26)}[/tex] ) / 2

  = ( 2 ± [tex]\sqrt{4-104}[/tex] ) / 2

  = ( 2 ± [tex]\sqrt{-100}[/tex] ) / 2

  = ( 2 ± 10i ) / 2

  = 1 ± 5i

Solutions are x = 1 + 5i or x = 1 - 5i → B

The equation x² - 2x + 26 = 0 has no real solutions. Thus, none of the given options are correct.

To solve the equation x² - 2x + 26 = 0, we can use the quadratic formula.

For an equation of the form ax² + bx + c = 0, the quadratic formula is given by:

x = (-b ± √(b² - 4ac)) / (2a)

By substituting the values a = 1, b = -2, and c = 26 into the formula, we get:

x = (-(-2) ± √((-2)² - 4(1)(26))) / (2(1))

Simplifying further:

x = (2 ± √(-92)) / 2

Since taking the square root of a negative number results in a complex solution, we can conclude that there are no real solutions to the equation x² - 2x + 26 = 0.

Answer:

2 + r = 7

Step-by-step explanation:

To write an equation for the image, simply look on both sides and add everything together. On the left side we have seven 1's, which adds up to 7. On the right side, we have 2 1's, which add up to 2, and a variable r. Now, we do not know the value of the variable r, so we simply leave it be. Therefore, the right side is equal to 2 + r. Since the image represents a balanced equation, the left side must equal the right side.

Left side = 7

Right side = 2 + r

Left side = Right side

7 = 2 + r

2 + r = 7

Answer:

794.42 in²  (since I used the pi = 3.14159 , the result is slightly different,

Step-by-step explanation:

Formula: Given radius and slant height calculate the height, volume, lateral surface area and total surface area.  

Given r, s find h, V, L, A

h = √(s² - r²)

r = 11 in

h = 4.796 in

s = 12 in

V = 607.7 in³

L = 414.7 in²

B = 380.1 in²

A = 794.8 in

Agenda: r = radius

h = height

s = slant height

V = volume

L = lateral surface area

B = base surface area  

A = total surface area

π = pi = 3.14159

√ = square root

Answer:  the correct option is

(A) 794.42 in.²

Step-by-step explanation:  We are given to find the surface area of the cone shown in the figure.

We know that

the SURFACE AREA of a cone with height h units and radius r units is given by

[tex]S=\pi r(r+\sqrt{h^2+r^2}).[/tex]

For the given cone, we have

r = 11 in. and

[tex]h=\sqrt{12^2-11^2}=\sqrt{144-121}=\sqrt{23}=4.8.[/tex]

Therefore, the surface area of the given cone is

[tex]S\\\\=\pi r(r+\sqrt{h^2+r^2})\\\\=3.14\times11(11+\sqrt{4.8^2+11^2})\\\\=34.54(11+12)\\\\=34.54\times23\\\\=794.42.[/tex]

Thus, the required surface area of the given cone is 794.42 in.²

Option (A) is CORRECT.

Answer:

[tex]\cos x=15\div 17[/tex]

Step-by-step explanation:

Recall the mnemonics SOH-CAH-TOA.

The CAH means the cosine ratio is the ratio of the adjacent side to the hypotenuse.

From the given triangle;

[tex]\cos x=\frac{Adjacent}{Hypotenuse}[/tex]

The side adjacent to the [tex]x\degree[/tex] is 15cm and the hypotenuse is 17cm.

We substitute the values to get;

[tex]\cos x=\frac{15}{17}[/tex] or [tex]\cos x=15\div 17[/tex].

Answer:

a. 21/4, 11/2, 49/10, 5/1

b. James 5.5, Olivia 5 1/4, Feng 5, Carmela 4.9

Step-by-step explanation:

Answer with Step-by-step explanation:

Olivia:   [tex]5\dfrac{1}{4}[/tex]

             = [tex]\frac{21}{4}[/tex]    (21/4=5.25)

James: 5.5

           = [tex]\dfrac{55}{10}[/tex]

           = [tex]\dfrac{11}{2}[/tex]

Carmela: 4.9

             =  [tex]\dfrac{49}{10}[/tex]

Feng: 5

         =   [tex]\dfrac{5}{1}[/tex]

b. Heights from greatest to least is:

James 5.5

Olivia 5.25

Feng 5

Carmela 4.9

Statistical questions are questions that are answered by collecting variable data, which can be given as an average/range/percentage. This question has a single answer, and therefore it is not a statistical question. A statistical question would be, for example, What is the average amount of time students in this class spend playing musical instruments?

Answer:

D

Step-by-step explanation:

you cannot take the root of a negative number so that eliminates B and C. you can take the root of 0 to be 0 so D is valid.

The correct inequality will be x≥0

Inequality a statement of an order relationship which are greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

So, here the values of x will be all the numbers greater or equal to 0

So the correct inequality will be x≥0

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Answer:

4

Step-by-step explanation:

We are given that a PE class has 12 boys and 8 girls. The teacher needs to divide in maximum number of teams so that each team has an equal number of boys and girls.

For this, we will factors of 12 and 8 and their greatest common factor.

12 = 4 × 3 = 2 × 2 × 3

8 = 4 × 2 = 2 × 2 × 2

The greatest common factor is 4, therefore the maximum number of teams with equal number of boys and girls is 4.

Answer:

[tex]12[/tex]

Step-by-step explanation:

[tex]3 \times (5 + 4) \times 2 - 42 \\ \\ 1. \: 3 \times 9 \times 2 - 42 \\ 2. \: 54 - 42 \\ 12[/tex]

Answer: 10

Step-by-step explanation:

We know that a regular decagon has 10 sides.

The sum of all exterior angles of any regular polygon is [tex]360^{\circ}[/tex].

Given: Each exterior angle of a regular decagon has a measure of [tex](3x+6)[/tex].

Then the sum of all the exterior angle will be :-

[tex]10\times(3x+6)=360\\\\\Rightarrow\ 30x+60=360\\\\\Rightarrow 30x=300\\\\\Rightarrow x=\dfrac{300}{30}=10[/tex]

Hence, the value of x = 10

Answer:

That can be factored:

(x +6) * (x -2)

Therefore, x = -6 and x =2

Step-by-step explanation:

For this case we have the following quadratic equation:

[tex]x ^ 2 + 4x-12 = 0[/tex]

We can factor the equation, for it, we must find two numbers that when multiplied give as result -12 and when summed give as result +4. These numbers are: +6 and -2.

Then, the factorization is given by:

[tex](x + 6) (x-2) = 0[/tex]

Thus, the solutions are:

[tex]x_ {1} = - 6\\x_ {2} = 2[/tex]

Answer:

[tex]x_ {1} = - 6\\x_ {2} = 2[/tex]

Answer:

X=- 12

Step-by-step explanation:

Answer:

x = -12

Step-by-step explanation:

—10x + 1 + 7х = 37

Combine like terms

-3x +1 = 37

Subtract 1 from each side

-3x+1-1 = 37-1

-3x = 36

Divide each side by -3

-3x/-3 = 36/-3

x = -12

Answer:

50 is the answer

Step-by-step explanation: