Divide the fractions. ½÷⅞​

Part (a)

The cost is the initial cost plus the cost per slushie multiplied by the number of slushies sold.

\(C(x)=500+1.25x\)

Part (b)

The revenue is the number of slushies sold multiplied by the amount charged per slushie.

\(R(x)=3.50x\)

Answer:

The difference between the games won and lost = 21 - 6 =15

Step-by-step explanation:

According to the question In a football season a team gets 3 points for a win, 1 point for a draw and 0 points for a loss.

A particular season a team played 34 games and lost 6 games . Finding the difference between game won and game lost simply means we have to know the number of game lost and game won.

The team played a total of 34 games.

Total games played = 34

Out of the 34 games played they lost 6 games. That means the remaining games is either win or draw. Therefore,

34 - 6 = 28 games was won or draw

Let

the number of games won = x

the number of game drew = y

3x + y = 70.............(i)

x  + y = 28................(ii)

x = 28 - y

insert the value of x in equation(i)

3(28 - y) + y = 70

84 - 3y + y = 70

84 - 70 = 3y -y

14 = 2y

divide both sides by 2

y = 14/2

y = 7

insert the value of y in equation(ii)

x + y = 28

x = 28 - 7

x = 21

The team won 21 games , drew 7 games and lost 6 games.

The difference between the games won and lost = 21 - 6 =15

Answer:

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    63-(9*j)=0

Step by step solution :

STEP

1

:

Pulling out like terms

1.1     Pull out like factors :

  63 - 9j  =   -9 • (j - 7)

Equation at the end of step

1

:

STEP

2

:

Equations which are never true:

2.1      Solve :    -9   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

2.2      Solve  :    j-7 = 0

Add  7  to both sides of the equation :

                     j = 7

solved

j = 7

The volume of the glasses is as follows;

The volume of cylinder glass 1 = πr²h

The volume of cylinder glass 1 = 3.14 × 3² × 6

The volume of cylinder glass 1 = 3.14 × 9 × 6

The volume of cylinder glass 1 = 169.56 cm³ = 170 cm³

The volume of the glass 2 = 2 / 3 π r³ + πr²h

The volume of the glass 2 = 2 / 3 × 3.14 × 3³ + 3.14 × 3² × 3

The volume of the glass 2 = 56.52 + 84.78

The volume of the glass 2 = 141.3 cm³ = 141 cm³

The volume of conical glass 3 = 1 / 3 πr²h

The volume of conical glass 3 = 1 / 3 × 3.14 × 3² × (√7² - 3² = √40)

The volume of conical glass 3 = 9.42 × √40

The volume of conical glass 3 = 59.5773111176

The volume of conical glass 3 = 60 cm³

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Answer:

4, 2, 9, 3, 6

Step-by-step explanation:

756/4= 189

756/2= 378

756/9= 84

756/25= 30.24

756/5= 151.2

756/8= 94.5

756/10= 75.6

756/3= 252

756/6= 126

The dimensions of the box is 6 ft by 6 ft by 8 ft. The width (and length) of the box is 6 ft.

Let x = width (and length) of the box

If the height is 2 ft greater than both the length and the width, then

x + 2 = height of the box

If the surface area is 228 ft², then

SA = (l x w) + 2(l x h) + 2(w x h)

228 ft² = x(x) + 2(x)(x + 2) + 2(x)(x + 2)

Simplify the equation.

228 = x² + 2x² + 4x + 2x² + 4x

228 = 5x² + 8x

5x² + 8x = 228

Get the positive root(s) of the equation.

(5x + 38)(x - 6) = 0

x = 6

width (and length) of the box = 6 ft

height of the box = x + 2 = 8 ft

Check the volume of the box.

V = l x w x h

288 = 6 x 6 x 8

288 = 288

Hence, the dimensions of the box is 6 ft by 6 ft by 8 ft.

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Answer:

A

Step-by-step explanation:

Answer:

the answer is C

Step-by-step explanation:

Answer:

m∠ABC = 53°

Step-by-step explanation:

m∠ABC + m∠CBD = m∠ABD

m∠ABC + 37° = 90°

m∠ABC = 53°

Answer:

53º

Step-by-step explanation:

abc = 90 - 37

abc = 53º

Answer:

x = 30

Step-by-step explanation:

1/2(x+6) = 18

Expand brackets or use distributive law.

1/2(x) + 1/2(6) = 18

1/2x + 6/2 = 18

1/2x + 3 = 18

Subtract 3 on both sides.

1/2x + 3 - 3 = 18 - 3

1/2x = 15

Multiply both sides by 2.

(2)1/2x = (2)15

x = 30

Answer:

30

Step-by-step explanation:

Answer: What is the question

Step-by-step explanation:

Answer:

√52

Step-by-step explanation:

6^2 = 36

4^2 = 16

   a.       b

√36 + √16 = c

c = √52

Step-by-step explanation:

2

\(2 \sqrt{13 } \)

Answer:Ok i will help you out

-11/4n - 1/8

Step-by-step explanation:

Cause yes and most likely is it

Source: Trust me + I did the math(dunno correct) just try tho

9514 1404 393

Answer:

  A, C, F, G, I

Step-by-step explanation:

A relation is "odd" if it is symmetrical about the origin. That is, f(-x) = -f(x). Here are the symmetries of the graphs shown:

  A: origin

  B: y-axis

  C: origin, and x- and y-axes

  D: x-axis

  E: no symmetry

  F: origin

  G: origin, and x- and y-axes

  H: x-axis

  I: origin, and x- and y-axes

Answer:

They throw out the records they no longer need or seen unnecessary because they no longer see the importance of having it.

Step-by-step explanation:

Answer:

a = 12

Step-by-step explanation:

Formula:

a² + b² = c²

Given:

b = 9

c = 15

Finding a:

a² + b² = c²

a² = c² - b²

a² = 15² - 9²

a² = 225 - 81

a² = 144

\(\sqrt{a^2} =\sqrt{144}\)

a = 12

Answer:

12

Step-by-step explanation:

To solve this, use the pythagreons theorm:

a^2+b^2=c^2

A and B are the side lengths, while is the hypotenuse, which in this case is 15 meters.

So lets plug in our values and solve for the missing length:

9^2+b^2=15^2

Square all the values except for the unknown:

81+b^2=225

Subtract from both sides to get b alone:

b^2=144

Take the square root of both sides so b^2 becomes b:

b=12

So your answer is 12!

Hope this helps!

Answer:

The unit vector in component form is \(\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)\) or \(\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j\).

Step-by-step explanation:

Let be \(\vec u = (2,-3)\), its unit vector is determined by following expression:

\(\hat {u} = \frac{\vec u}{\|\vec u \|}\)

Where \(\|\vec u \|\) is the norm of \(\vec u\), which is found by Pythagorean Theorem:

\(\|\vec u\|=\sqrt{2^{2}+(-3)^{2}}\)

\(\|\vec u\| = \sqrt{13}\)

Then, the unit vector is:

\(\hat{u} = \frac{1}{\sqrt{13}} \cdot (2,-3)\)

\(\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)\)

The unit vector in component form is \(\hat{u} = \left(\frac{2}{\sqrt{13} },-\frac{3}{\sqrt{13}} \right)\) or \(\hat{u} = \frac{2}{\sqrt{13}}\,i-\frac{3}{13}\,j\).

Answer: (4x - √3)(4x + √3).

Step-by-step explanation: Use factoring. The equation (when factored out) is: ax^2 + bx + c. Hence, the equation you wrote rewritten is: 16x^2 + 0x - 3. (√3)(√3) = 3 and (4x)(4x) = 16x^2. It is divisible.

So, the quadratic function f(x) = 16x^2 - 3 can be expressed as a product of linear factors as (4x - √3)(4x + √3).

Answer:

(8,1)

Step-by-step explanation:

(8,1) you have to add do to the same to B

Pont B is located at coordinates at the line AB (8, 1)

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, The midpoint of AB is M(6,-3). If the coordinates of A are (4, - 7)

From the general formula of midpoints of a line

coordinates of midpoint = ((x₂ + x₁)/2, (y₂ + y₁)/2)

where,

(x₁, y₁) are the coordinates of A

(x₂, y₂) are the coordinates of B

And in our case Coordinates of the midpoint are (6, -3)

Thus,

6 = (4 + x₂)/2

x₂ = 8

-3 = (-7 + y₂)/2

y₂ = 1

therefore, the coordinates of Pont B at line AB are (8, 1)

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Answer:

5 kilograms

Step-by-step explanation:

1000 grams is equal to 1 Kilogram, so 5000 Grams is equal to 5 Kilograms

Answer:

The correct function is

\(f(b) = {b}^{2} - 4\)

Answer:

The last one - 256 people

Answer:

4005

Step-by-step explanation:

3,998 - (-7) = ?

Two negative signs will make a positive sign.

3,998 - (-7) = 3998 + 7 = 4005

So, the answer is 4005

Answer:

\(\Delta s_{T} = 4712.4\,m\)

Step-by-step explanation:

(This exercise is written in Spanish and for this reason the response will be presented in such language).

La distancia recorrida por la mulita tras una vuelta es:

\(\Delta s = 2\pi\cdot (5\,m)\)

\(\Delta s \approx 31.416\,m\)

Ahora, la distancia recorrida total es directamente proporcional a la cantidad de vueltas invertidas. Este indicador se determina por regla de tres simple:

\(\Delta s_{T} = \frac{150}{1}\times (31.416\,m)\)

\(\Delta s_{T} = 4712.4\,m\)

The unit rate of change (slope) from 1996 to 2016 is -.025

What is Ratio?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all. Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, m = y/x, where m is the slope, can be used to express the change in the y coordinate with regard to the change in the x coordinate.

Take notice that tan = y/x.

The given problem is about the decrease of two variables, which represent years and represent video rental.

The ratio here refers to the slope of the linear decreasing behavior, where pairs are (1996,9) and (2016, 4).

The formula for the slope is

\(&m=\frac{y_2-y_1}{x_2-x_1}\)

So, In the given question, we have:

10 video rental locations in 1996;

So,  Assuming a constant decrease in the number of stores:

The slope or the unit rate of change from 1996 to 2016 is:

\(\begin{aligned}&m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-9}{2016-1996}=\frac{-5}{20}=-\frac{1}{4} \\&m=-0.25\end{aligned}\)

So, The Value of the Slope is -0.25

This means that the linear relation decreases, with a constant ratio of 0.25, that is, video rental decreases one per 4-years periods.

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Answer:

B

Good luck in Geometry my guy!

The given quadrilaterals, 1 and 2,  are parallelograms because the pair of opposite sides are parallel and the other pairs are congruent.

3. According to Theorem 7.9, quadrilateral ABCD is a parallelogram.

4. According to Theorem 7.12, quadrilateral PQRS is a parallelogram.

3. Quadrilateral ABCD with vertices A(0,0), B(7,1), C(5,6), D(-2,5), and Theorem 7.9:

Theorem 7.9 states that if the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Using the distance formula, we can calculate the lengths of the sides of quadrilateral ABCD:

AB = √((7 - 0)² + (1 - 0)²) = √50

BC = √((5 - 7)² + (6 - 1)²) = √29

CD = √((-2 - 5)² + (5 - 6)²) =√50

DA = √((0 - (-2))² + (0 - 5)²) = √29

We can see that AB = CD and BC = DA, indicating that the opposite sides are congruent.

Quadrilateral PQRS with vertices P(-2,0), Q(3,1), R(4,4), S(-1,3), and Theorem 7.12:

Theorem 7.12 states that if both pairs of opposite sides of a quadrilateral are parallel and congruent, then the quadrilateral is a parallelogram.

Using the slope formula, we can calculate the slopes of the sides of quadrilateral PQRS:

Slope of PQ = (1 - 0) / (3 - (-2)) = 1/5

Slope of RS = (4 - 3) / (4 - (-1)) = 1/5

Slope of QR = (4 - 1) / (4 - 3) = 3

Slope of SP = (3 - 0) / (-1 - (-2)) = 3

The lengths of opposite sides can be calculated using the distance formula:

PQ = √((3 - (-2))² + (1 - 0)²) = √(25 + 1) = √26

RS = √((4 - 4)² + (4 - 1)²) = √(9) = 3

QR = √((4 - 3)² + (4 - 1)²) = √(1 + 9) = √10

SP = √((-1 - (-2))² + (3 - 0)²) = √(1 + 9) = √10

We can see that PQ = RS and QR = SP, indicate that the opposite sides are parallel and congruent.

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Group B has lower range.

Group A shows variability.

Mean is the best to make concussion about age of Salsa students.

Upon visual examination, it appears that Group A is likely to have a lower average age of music students compared to Group B.

This inference is supported by the observation that the majority of data points in Group B are concentrated around younger ages.

In contrast, Group A exhibits a more dispersed distribution of data points across a wider range of ages, including higher.

So, Group B has lower range.

and, Group A shows variability.

Lastly, Mean is the best to make concussion about age of Salsa students.

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