Paulina bought a used car as she was entering college and planned to trade it in when she graduated four years later. She had learned in her high school financial algebra class that the average used car depreciated at an annual rate of 15%. If she had paid $13,900 for her car, how much can she expect to get when it is time for her to trade it in for a new car?

Answer:

If the 'm' u r trying to say is slope of line on the graph then it will be parallel to x axis

Answer:

c. The period is 2π

Step-by-step explanation:

The period of a function is the smallest value of $p$ for which\( f(x+p) = f(x)\) for all x.

For the function f(x) = 2cos(x^2), we can see that f(x+2π) = f(x) for all x.

This is because the cosine function has a period of 2π. Therefore, the period of f(x) = 2cos(x^2) is \(\boxed{2\pi}\)

Answer:

Step-by-step explanation:

→ (7*4-4³)/6

→ (28-64)/6

→ -36/6

→ -6

The length of side f is 12.0 inches

From the question, we have the following parameters that can be used in our computation:

In ΔDEF, e = 9.2 cm, m m∠F=72° and m m∠D=61°

The sum of angles in a triangle is 180 degrees

Using the above as a guide, we have the following:

E = 180 - 72 - 61

E = 47

Using the law of sines, we have

f/sin(F) = e/sin(E)

substitute the known values in the above equation, so, we have the following representation

f/sin(72) = 9.2/sin(47)

So, we have

f = sin(72) * 9.2/sin(47)

Evaluate

f = 12.0

Hence, the length is 12.0 inches

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The function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

How to find  x-intercepts?

To find the x-intercepts, we set y = 0 and solve for x:

(x⁴/4) - x² + 1 = 0

This is a fourth-degree polynomial equation, which is difficult to solve analytically. However, we can use a graphing calculator or software to find the approximate x-intercepts, which are approximately -1.278 and 1.278.

To find the y-intercept, we set x = 0:

y = (0/4) - 0² + 1 = 1

So the y-intercept is (0, 1).

To find the vertical asymptotes, we set the denominator of any fraction in the function equal to zero. There are no denominators in this function, so there are no vertical asymptotes.

To find the horizontal asymptote, we look at the end behavior of the function as x approaches positive or negative infinity. The term x^4 grows faster than x^2, so as x approaches positive or negative infinity, the function grows without bound. Therefore, there is no horizontal asymptote.

To find the critical points, we take the derivative of the function and set it equal to zero:

y' = x³- 2x

x(x² - 2) = 0

x = 0 or x = sqrt(2) or x = -sqrt(2)

These are the critical points.

To determine the intervals where the function is increasing and decreasing, we can use a sign chart or the first derivative test. The first derivative test states that if the derivative of a function is positive on an interval, then the function is increasing on that interval. If the derivative is negative on an interval, then the function is decreasing on that interval. If the derivative is zero at a point, then that point is a critical point, and the function may have a relative maximum or minimum there.

Using the critical points, we can divide the real number line into four intervals: (-infinity, -sqrt(2)), (-sqrt(2), 0), (0, sqrt(2)), and (sqrt(2), infinity).

We can evaluate the sign of the derivative on each interval to determine whether the function is increasing or decreasing:

Interval (-infinity, -sqrt(2)):

Choose a test point in this interval, say x = -3. Substituting into y', we get y'(-3) = (-3)³ - 2(-3) = -15, which is negative. Therefore, the function is decreasing on this interval.

Interval (-sqrt(2), 0):

Choose a test point in this interval, say x = -1. Substituting into y', we get y'(-1) = (-1)³ - 2(-1) = 3, which is positive. Therefore, the function is increasing on this interval.

Interval (0, sqrt(2)):

Choose a test point in this interval, say x = 1. Substituting into y', we get y'(1) = (1)³ - 2(1) = -1, which is negative. Therefore, the function is decreasing on this interval.

Interval (sqrt(2), infinity):

Choose a test point in this interval, say x = 3. Substituting into y', we get y'(3) = (3)³ - 2(3) = 25, which is positive. Therefore, the function is increasing on this interval.

Therefore, the function is decreasing on the intervals (-infinity, -sqrt(2)) and (0, sqrt(2)), and increasing on the intervals (-sqrt(2), 0) and (sqrt(2), infinity).

To find the inflection points, we take the second derivative of the function and set it equal to zero:

y'' = 3x² - 2

3x² - 2 = 0

x² = 2/3

x = sqrt(2/3) or x = -sqrt(2/3)

These are the inflection points.

To determine the intervals where the function is concave up and concave down, we can use a sign chart or the second derivative test.

Using the inflection points, we can divide the real number line into three intervals: (-infinity, -sqrt(2/3)), (-sqrt(2/3), sqrt(2/3)), and (sqrt(2/3), infinity).

We can evaluate the sign of the second derivative on each interval to determine whether the function is concave up or concave down:

Interval (-infinity, -sqrt(2/3)):

Choose a test point in this interval, say x = -1. Substituting into y'', we get y''(-1) = 3(-1)² - 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Interval (-sqrt(2/3), sqrt(2/3)):

Choose a test point in this interval, say x = 0. Substituting into y'', we get y''(0) = 3(0)² - 2 = -2, which is negative. Therefore, the function is concave down on this interval.

Interval (sqrt(2/3), infinity):

Choose a test point in this interval, say x = 1. Substituting into y'', we get y''(1) = 3(1)²- 2 = 1, which is positive. Therefore, the function is concave up on this interval.

Therefore, the function is concave up on the interval (-infinity, -sqrt(2/3)) and (sqrt(2/3), infinity), and concave down on the interval (-sqrt(2/3), sqrt(2/3)).

To find the relative extrema, we can evaluate the function at the critical points and the endpoints of the intervals:

y(-sqrt(2)) ≈ 2.828, y(0) = 1, y(sqrt(2)) ≈ 2.828, y(-1.278) ≈ -0.509, y(1.278) ≈ 2.509

Therefore, the function has a relative minimum at (-1.278, -0.509) and a relative maximum at (1.278, 2.509).

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Based on the information we can infer that the equation shown in the image is 1.23 - 0.35 = 0.88 (option B).

To identify the correct equation we must look at the graph and identify the information it provides. In this case we have two squares divided into 100 squares each. Additionally, the square on the left has 88 squares painted in red and 12 squares with an X inside. In the case of the square on the right, it has 23 squares colored in red with an X inside.

In total we have 123 squares painted in red, which in decimal number is equivalent to 1.23. On the other hand, the number of squares painted red and with an X inside is 35, this value would be 0.35.

On the other hand, the squares painted only in red are 88, so the equivalent in decimal numbers would be 0.88. Therefore, the correct way to express this relationship through an equation would be:

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Based on the given information, we have a square pyramid with points M and N being the midpoints of the edges of one face. and forms a parallelogram. Option D

Since the base of the pyramid is a square, the cross section will consist of a square shape. Additionally, since the slice is made through the midpoints of the edges of the face, the resulting cross section will have parallel sides.

Considering these characteristics, we can conclude that the shape of the resulting cross section is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel. In this case, the opposite sides of the square cross section will be parallel, as the slice passes through the midpoints of the edges.

Therefore, the correct answer is D. parallelogram.

It's important to note that a triangular prism is not the correct answer because a triangular prism is a three-dimensional figure with two triangular bases and three rectangular faces. The cross section resulting from the given slice will not have the characteristics of a triangular prism. Option D.

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Answer:

780

Step-by-step explanation:

In this example we will call Original Price = y

72%=0.72

218.40=0.72*y

1-0.72=0.28

218.4÷0.28=780

Answer:

the answer is 105

Step-by-step explanation:

because 5×3=15 so 15×7 =105

The function notation of 9x + 3y = 12 is given as follows:

f(x) = 4 - 3x.

The function in the context of this problem is given as follows:

9x + 3y = 12.

The format for the function notation is given as follows:

Hence we must isolate the variable y, as follows:

3y = 12 - 9x

y = 4 - 3x (each term of the expression is divided by 3).

f(x) = 4 - 3x.

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Based on the information, the cost of adult's ticket is $24 while the student's tickets cost $18.

The equation to solve the question will be:

4a + 2s = 132 ..... i

2a + 6s = 156 ...... ii

Multiply equation i by 2

Multiply equation ii by 4

8a + 4s = 264

8a + 24s = 624

Subtract the equations

20s = 360

s = 360/20 = 18

From equation i

4a + 2s = 132

4a + 2(18) = 132

4a + 36 = 132

4a = 132 - 36

4a = 96

a = 96/4

a = 24

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The blanks that are missing in the sequence are -3 and 11

from the question, we have the following parameters that can be used in our computation:

The blanks in the sequence

When listed out, we have

_, _, 25, 39

Assuming that the sequence, is an arithmetic sequence, then we have

Common difference = 39 - 25

Common difference = 14

This means that

Previous term = 25 - 14 = 11

Firs term = 11 - 14 = -3

So, the missing terms are -3 and 11

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Step-by-step explanation:

To solve the equation for s we've got to leave s alone

\(n = \frac{s + 360}{180} \\ 180n = s + 360 \\ 180n - 360 = s\)

64,781

/\

|

60,000

---

hope it helps

Answer:

60,000

Step-by-step explanation:

Hope This Helps ; )

Plz Mark Brainliest

The required equation is g(x) = 10(3)x which is the correct answer would be an option (A).

The graph of g(x) is obtained by stretching the graph of f(x) vertically by a factor of 2.

Since the vertical stretch of a graph multiplies the y-coordinates of each point on the graph by a constant factor, the equation of g(x) must be obtained by multiplying the y-coordinate of each point on the graph of f(x) by 2.

In the given equation f(x) = 5(3)x, the y-coordinate of each point on the graph of f(x) is 5(3)x.

Thus, to stretch the graph of f(x) vertically by a factor of 2, we need to multiply this y-coordinate by 2 to get the y-coordinate of the corresponding point on the graph of g(x). This gives us the following equation for g(x):

⇒ g(x) = 2 × 5(3)x = 10(3)x

Therefore, the required equation is g(x) = 10(3)x.

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Answer:

a = -10

Step-by-step explanation:

Simplifying

7 + 4(2a + 15) = -13

Reorder the terms:

7 + 4(15 + 2a) = -13

7 + (15 * 4 + 2a * 4) = -13

7 + (60 + 8a) = -13

Combine like terms: 7 + 60 = 67

67 + 8a = -13

Solving

67 + 8a = -13

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-67' to each side of the equation.

67 + -67 + 8a = -13 + -67

Combine like terms: 67 + -67 = 0

0 + 8a = -13 + -67

8a = -13 + -67

Combine like terms: -13 + -67 = -80

8a = -80

Divide each side by '8'.

a = -10

Simplifying

a = -10

The value of k is 0.32 .

What is an exponential function?

The exponential function is one of the most important functions in mathematics (though it would have to admit that the linear function ranks even higher in importance). To form an exponential function, we let the independent variable be the exponent.

An exponential function is a function that usually takes the form f(x) = bˣ.

The exponential curve depends on the exponential function and it depends on the value of the x.

where;

b = base

ˣ = power

The general exponential function that models  the data given is:

\(y = ce^{kt}\)

According to the (5,5c)

\(ce^{5k} = 5c\\\\e^{5k} = 5\\\\5k = ln5\\\\k = \frac{ln5}{5} \\\\k = 0.32\)

Hence , the value of k is 0.32 .

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Graph B represents the system of linear inequalities the best.

Hence the correct option is (B).

Let Tami needs to work x hours per week as server and y hours per week as tutors.

So it is given that she can work at most 20 hours a week.

So, the suitable inequality to describe the situation:

x + y \(\le\) 20 ............. (i)

Now the corresponding equation of this above inequality is,

x + y = 20

x/20 + y/20 = 1

comparing to inception form of straight line we can say that the equation says about a line which cuts axes at (20, 0) and (0, 20) respectively.

since (0, 0) gives 0 + 0 = 0 \(\le\) 20 is true.

So the solution area towards origin.

It is also given that she makes $6 per hour as server and makes $12 per hour as tutor and she needs to earn at least $150.

The best suited inequality for this condition,

6x + 12y \(\ge\) 150 .................(ii)

The corresponding equation of the above inequality:

6x + 12y = 150

6x/150 + 12y/150 = 1

x/25 + y/(12.5) = 1

So it is the line cuts the axes at (25, 0) and (0, 12.5) respectively.

since (0, 0) gives 6*0 + 12*0 = 0 \(\ge\) 150 is not true so the solution area for this inequality towards opposite of origin along the straight line.  

So Graph B represents the system of linear inequalities the best.

Hence the correct option is (B).

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Answer:

200

Step-by-step explanation:

15% × ? = 30

? =

30 ÷ 15% =

30 ÷ (15 ÷ 100) =

(100 × 30) ÷ 15 =

3,000 ÷ 15 =

200

If there is a pair of parallel sides in the following shape. the area of the shape is:  21 unit².

Using this formula to determine or find  the area of the shape

Area  = (1/2)× (Area+ breadth )height

Where:

Area= 9

Breadth= 5

Height = 3

Now Let plug in the formula so as to find the area

Area of the shape = (1/2)× (9 + 5) ×3

Area of the shape = (1/2)× (14)×3

Area of the shape = (1/2)× 42

Area of the shape= 21 unit²

Therefore If there is a pair of parallel sides in the following shape. the area of the shape is:  21 unit².

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The correct order from least to greatest is log₂ 26, log₂ 33, log 26, eln 4, the correct option is D.

We are given that;

The logs log, 26, log, 33 and log3 26

Now,

We can simplify these expressions using the following identities:

eln x = x

log a a = 1

log a (b × c) = log a b + log a c

log a (b / c) = log a b - log a c

Using these identities and the properties of logarithms listed above, we can compare the given expressions as follows:

A. eln 4 = 4; log 26 < log 33; so we have:

4 < log 26 < log 33

B. eln 4 = 4; so we have:

log 33 < 4 < log 26 < log 26

C. eln 4 = 4; so we have

log₂ 26 < log 26 < log 33 < 4

D. eln 4 = 4; so we have:

log₂ 26 < log₂ 33 < log 26 < 4

Therefore, by logarithm the answer will be log₂ 26, log₂ 33, log 26, eln 4.

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Answer:

25/15 - 12/15

Step-by-step explanation:

turn the mixed number to an improper fraction, then multiply the denominator and numerator by 5 to reach 15 and then 5 x 3 and 4 x 3 to get 12/15. I hope this helps

The solution of the system is then given by:

x = t[1 -1 1 0.5 0.5 0.33] + s[0 -2 1 1 -2 1]

This is the general solution of the system in the form of a sum of scalar multiples of fixed column vectors.

The system of linear equations can be written in matrix form as:

[1 0 1 2 1 3 | 1]

[2 1 2 4 0 10| 5]

[3 1 3 6 6 15| 8]

where the augmented matrix is [A | B].

To solve the system using the method of specifying appropriate free variables, we first convert the coefficient matrix into reduced row echelon form using Gaussian elimination.

In reduced row echelon form, the first non-zero element of each row (known as the leading entry) is 1, and the leading entries of lower rows are to the right of the leading entries of higher rows.

Applying Gaussian elimination to the coefficient matrix, we get:

[1 0 1 2 1 3 | 1]

[0 1 0 2 -2 7| 0]

[0 0 0 0 0 0| 0]

We can see that there are two non-zero rows, indicating that the system has two independent equations.

We can choose two of the variables to be free variables, and express the other variables in terms of the free ones.

Let's choose x1 and x3 as the free variables.

We can find x2 as follows:

x2 = -x1 - 2x3 + 7

And we can find x4, x5 and x6 as follows:

x4 = (1 - x1 - x3)/2

x5 = 1 - x1 - 2x3 + 2x4

x6 = (1 - x1 - x3 - 2x4)/3

So the general solution of the system can be expressed as a sum of scalar multiples of fixed column vectors:

x1 = t

x2 = -t - 2s + 7

x3 = s

x4 = (1 - t - s)/2

x5 = 1 - t - 2s + (1 - t - s)/2

x6 = (1 - t - s)/3

where t and s are scalars.

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Answer:

7x10^2

Step-by-step explanation:

So scientific notation involves two numbers: one is ten and the other ranges from 0 to 10. In this case your value would be 7 and to notate it so it is equal to 700 you would put 10 to the second power... hope this helps :)))

Answer:

(scientific notation)

= 7e2

(scientific e notation)

= 700 × 10⁰

(engineering notation)

(one)

= 700

(real number)

Answer: 2.75(3) + 4x = 11.25

Step-by-step explanation:

It says each bag costs $2.75 and there are 3 bags so multiply those 2 and then subtract them from the total cost (11). What you get after you subtract is the total costs of the salsa so divide that by 4 to get the cost of each, in this case it doesn't ask so we leave it as 4x.

Answer:

Step-by-step explanation:

115 woman

Answer:

y intercept is 3, slope is 2

The inequalities that could show the weight of each horse are:

h ≤ 1248

t ≤ 352

To determine the inequalities that could show the weight of each horse, we can use the fact that the total weight of the horses and tack must be less than or equal to the capacity of the horse trailer. We can set up the following inequalities:

5h + 5t ≤ 8000

where h represents the average weight of each horse.

However, we don't know the value of t, so we need to express it in terms of h. We are given that the combined weight of the horses is 6,240 pounds, so we can write:

5h ≤ 6240

Solving for h, we get:

h ≤ 1248

This means that the weight of each horse must be less than or equal to 1,248 pounds.

Now we can substitute this upper bound for h into the first inequality to get:

5(1248) + 5t ≤ 8000

6240 + 5t ≤ 8000

5t ≤ 1760

t ≤ 352

This means that the average weight of tack per horse must be less than or equal to 352 pounds.

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