The manufacturer's suggested retail price (MSRP) for a particular car is $24,705, and it is expected to be worth $13,905 in 4 years. (a) Find a linear depreciation function for this car. (b) Estimate the value of the car 7 years from now. At what rate is the car depreciating? (a) What is the linear depreciation function for this car?

Given:

The histogram shows the time students ran the mile in gym class.

Explanation:

a) To find: The interval contains the fewest data values.

The interval which contains the fewest data values is 9-10, Because, it has the data value 2.

Answer: The interval 9-10

b) To find: The number of students in the class.

The number of students in the interval 9-10 is 2.

The number of students in the interval 11-12 is 12.

The number of students in the interval 13-14 is 11.

The number of students in the interval 15-16 is 9.

So, the total number of students is 34.

c) To find: The percent of students who ran the mile in 12 minutes or less.

The number of students who ran the mile in 12 minutes or less is,

Then the percent of students who ran the mile in 12 minutes or less is,

Answer: The percentage is 41%.

Answer =  A.  Aella

Step-by-step explanation: Add 60, 25, and 95 degrees because that will equal 180 which is what the triangle equals.

Answer:

  a) x = 1 ± (3/7)√7

  b) (-∞, -5) ∪ [-2, 5) ∪ [6, ∞)

Step-by-step explanation:

You want solutions to the relations ...

We like to solve these in the form f(x) = 0. It helps avoid extraneous solutions.

  \(7+\dfrac{1}{x} -\dfrac{1}{x-2}=0\\\\\\\dfrac{7x+1}{x}-\dfrac{1}{x-2}=0\\\\\\\dfrac{(7x+1)(x-2)-x}{x(x-2)}=0\\\\\\ \dfrac{7x^2-14x-2}{x(x-2)}=0\)

The roots of the numerator quadratic are found by ...

  x² -2x -2/7 = 0 . . . . . divide by 7

  x² -2x +1 -9/7 = 0 . . . . add and subtract 1

  (x -1)² = 9/7 . . . . . . . . . . write as a square, add 9/7

  x -1 = ±√(9·7/49) = ±(3/7)√7 . . . . take the square root

  x = 1 ± (3/7)√7

Rational inequalities are best solved by identifying the roots of numerator and denominator. These tell you where the function changes sign. The end behavior of the rational function tells you what the signs are changing from.

  \(\dfrac{x^2-4x-12}{x^2-25}\ge 0\\\\\\\dfrac{(x+2)(x-6)}{(x+5)(x-5)}\ge0\)

This has a horizontal asymptote at y=1 for |x|→∞. It has vertical asymptotes at x=±5.

The sign changes occur at x ∈ {-5, -2, 5, 6}. The rational expression is positive (approaching +1) for x < -5 and for x > 6. It is negative in the adjacent intervals, so positive again for -2 < x < 5.

The inequality is satisfied for ...

Answer:

Step 1: Calculate the mean of the data—this is xˉx, with, \bar, on top in the formula.

Step 2: Subtract the mean from each data point. ...

Step 3: Square each deviation to make it positive.

Step 4: Add the squared deviations together.

Step-by-step explanation:

can i get brainlyest

The profit for 24 sales is $64.

The profit for 24 sales, we first need to calculate the revenue and then determine the profit based on the given information.

The revenue function is given as f(x) = 5x, where x represents the number of hamburgers sold.

To find the revenue for 24 sales, we substitute x = 24 into the revenue function:

Revenue = f(24)

= 5 × 24

= 120 dollars

Now, let's calculate the profit.

The profit is $20 less than 70% of the revenue.

We can express this mathematically as:

Profit = 0.7 × Revenue - $20

Substituting the value of Revenue we calculated earlier:

Profit = 0.7 × 120 - $20

= 84 - $20

= $64

We must first compute the revenue for 24 sales before calculating the profit based on the available data.

The revenue function is denoted by the formula f(x) = 5x, where x is the quantity of hamburgers sold.

We add x = 24 to the revenue function to get the revenue for 24 sales:

f(24) = 5 x 24 = 120 dollars is the revenue.

Let's now determine the profit.

The profit is $20 below the revenue's 70%.

This may be written mathematically as:

Revenue - $20 x Profit = 0.7

Substituting the earlier determined figure of Revenue:

Earnings = 0.7 x 120 - $20 = 84 - $20 = $64

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Answer:

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

Real distance is 4.4 miles and on the map it is 8 inches.

The scale is:

or

Answer:

x = 3

Step-by-step explanation:

Let's solve your equation step-by-step.

7x−3=18

Step 1: Add 3 to both sides.

7x−3+3=18+3

7x=21

Step 2: Divide both sides by 7.

7x/7 = 21/7

x=3

Answer:

240

Step-by-step explanation:

If you are referring to:

2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 + 28 + 30, then your answer would be 240

Hope this helps :)

Answer:

x = 4

Step-by-step explanation:

Add 1 to 7 to get 8. Divide 8 by 2 to get 4. The answer is then x = 4

Answer:

50.1

The area of the composite figure is 50.1

Trust me

Answer:

Slope = -3

Step-by-step explanation:

Right off the bat, some nice points I see are (0, 3) and (1, 0) because you can tell their exact coordinates. It doesn't matter which point you call what, but I would call (0, 3) point₁ and (1, 0) point₂. To calculate the slope, subtract the y-coordinate of point₁ minus the y-coordinate of point₂. Let's call this difference Δy (which means "change in y"). Next, we'll do the same thing, but for the x-coordinates. Now we'll call this difference Δx (which means "change in x"). Now, you want to divide Δy / Δx. And there's your slope!

Here's how I did it:

(0, 3) and (1, 0)

y-coordinate of point₁ - y-coordinate of point₂ = (3) - (0) = 3. We called this Δy.

Next:

x-coordinate of point₁ - x-coordinate of point₂ = (0) - (1) = -1. We called this Δx.

So now we have 3 = Δy and -1 = Δx.

If we divided Δy / Δx, we get 3 / -1, or -3.

NOTE: Remember to stay consistent with the order you subtract. If you're going to find Δy from point₁ - point₂, then you need to find Δx from point₁ - point₂.

You can't subtract point₁ - point₂ = Δy and then decide to change the order to point₂ - point₁ to find Δx.

Now as to what to draw, first draw a vertical line from either point. Draw the vertical line until you reach the y-coordinate of the other point. Now, draw a horizontal line that will now connect the vertical line to the second point.

The graph of the solution to the given inequality on the number line plotted is attached.

Inequalities are the mathematical expressions in which both sides are not equal.

In inequality, unlike in equations, we compare two values.

The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is q < 69.5​.

The result can be shown in multiple forms.

Inequality Form:q<69.5

Interval Notation:(−∞,69.5)

Therefore, the graph the solution to the given inequality on the number line plotted below.

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The name of this circle is Circle R.

The name of the radius is RB.

The name of the diameter is RI or RD.

In Mathematics, a circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

In Mathematics, a line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points. Additionally, a line segment typically has a fixed length.

In this context, we have the following names;

Circle R.

Radius = RB.

Diameter = RD or RI.

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A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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Answer:

  5

Step-by-step explanation:

The 5 terms in the expression are ...

  6y

  3

  y

  4y

  5

__

If like terms were combined, the expression could be reduced to one with 2 terms:

  11y +8

Answer:

5 terms

Step-by-step explanation:

In an expression, a term can be a number, a variable, or a number and variable multiplied together. Terms are separated by addition or subtraction.

In the expression:

6y+3+y+4y+5

There are 5 terms. The 5 terms are:

1. 6y

2. 3

3. y

4. 4y

5. 5

We can simplify this expression by combining like terms. We can add the constants (just numbers) and the terms with variables being multiplied by numbers.

6y+3+y+4y+5

(6y+y+4y)+(3+5)

11y+(3+5)

11y+8

The value of x in this problem, considering the intersecting chords, is given as follows:

x = 10.

A chord of a circle is a straight line segment that connects two points on the circle, that is, it is a line segment whose endpoints are on the circumference of a circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Hence the value of x is obtained as follows:

12x = 15 x 8

12x = 120

x = 10.

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The 15 terms are: 2, -12, 7, -2, 20, -30, 42, -56, 72, -90, 110, -132, 156, -182, 210.

Arithmetic Progression (AP) is a numerical series in which the differences between any two successive integers is a fixed value. Arithmetic Sequence is another name for it. We will come across various key terminologies in AP, which are designated as: The first term (a), Common distinction (d), nth Term (an),The total of the first n terms (Sn).

A progression is a sort of sequence in which a formula for the nth term may be found. The Arithmetic Progression is the most often used sequence in mathematics, using simple formulae. There are three types of progressions in mathematics. They are as follows: Arithmetic Progression (AP), Geometric Progression (GP), and Harmonic Progression (HP).

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9514 1404 393

Answer:

  (a) has complex solutions

Step-by-step explanation:

The values of a, b, c in the formula correspond to the coefficients of x^2, x, and the constant, respectively. Substitute these into the discriminant formula and do the arithmetic.

  #1: a = 1, b = 2, c = 5.

     d = b^2 -4ac = 2^2 -4(1)(5) = 4 -20 = -16 ⇒ complex solutions

__

I find repetitive calculation is nicely done by a spreadsheet. The other discriminants are shown in the attachment.

Answer:

the x coordinate is 1 and the y coordinite is 5

Answer:

<

Step-by-step explanation:

1) Substitute 5 into the question

2) Work out the sides

3) Put it into an inequality

5 < 7

Hope this helps, have a great day!

Step-by-step explanation:

100 ÷ 10⁷ = 10² ÷ 10⁷ = \(10^{-5}\) = 1/100.000

This problem is about combined operations. We have a square power, a subtraction and whole products.

To solve this we can use PEMDAS which is an strategy to remember the order of operations, that is, Parentheses, Exponents, Multiplication-Division, Addition-Subtraction, that's the right order to solve.-

According to PEMDAS, we solve the power first:

Then, we solve multiplications:

Finally, we subtract:

Just remember, PEMDAS dictates the right order to use operations.

Answer:

Step-by-step explanation:

You want the coordinates of the vertices of QRST after it has been translated right 2 units, then reflected across the y-axis. The original coordinates are Q(1, 5), R(3, -1), S(0, 0), T(-2, 3).

The problem statement is written as a composition of the transformations Ry and T(2,0). A composition of functions is generally executed right to left, meaning the translation will be done first, then the reflection.

The numbers in the translation vector are added to the coordinates:

  (x, y) ⇒ (x+2, y+0)

Reflection over the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y)

Then the composition of transformations is ...

  (x, y) ⇒ (-(x+2), y)

  Q(1, 5) ⇒ Q'(-3, 5)

  R(3, -1) ⇒ R'(-5, -1)

  S(0, 0) ⇒ S'(-2, 0)

  T(-2, 3) ⇒ T'(0, 3)

Check the picture below, so Francesca's throw looks more or less like that, and it hits the ground when h(t) = 0

\(\stackrel{h}{0}=1+14t-5t^2\implies 5t^2-14t-1=0 \\\\\\ ~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{5}t^2\stackrel{\stackrel{b}{\downarrow }}{-14}t\stackrel{\stackrel{c}{\downarrow }}{-1}=0 \qquad \qquad t= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}\)

\(t= \cfrac{ - (-14) \pm \sqrt { (-14)^2 -4(5)(-1)}}{2(5)} \implies t = \cfrac{ 14 \pm \sqrt { 196 +20}}{ 10 } \\\\\\ t= \cfrac{ 14 \pm \sqrt { 216 }}{ 10 }\implies t=\cfrac{ 14 \pm 6\sqrt { 6 }}{ 10 }\implies t=\cfrac{ 7 \pm 3\sqrt { 6 }}{ 5 }\implies t\approx \begin{cases} ~~ 2.870~\checkmark\\ -0.070 \end{cases}\)

so there are two valid values, however we can't use the negative one, since the phenomena is for seconds and we can't have negative seconds in this case.

Answer:

17/51 simplified in lowest terms is 1/3

Step-by-step explanation:

Answer:

Exact from: 1/3

Decimal form: 0.3

So I Reduce the expression, if possible, by cancelling the common factors and simplify 17/51

Answer:

I think you should change it to 4x + 3y

Step-by-step explanation:

hope this helps

The expression factoring out the greatest common factor is  (3pf - 21p²)(f + 2).

We have the expression as

3pf² - 21p²f + 6pf - 42p²

Now, factorising the expression as

= 3pf² + 6pf - 21p²f - 42p²

= 3pf(f +2) - 21p²(f + 2)

= (3pf - 21p²)(f +2)

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