A vehicle purchased for $27500 depreciates at a constant rate of 13 % each year. Its value after t years can be modeled by the equation A P(0.87)^t where P is the original value of the vehicle. Determine the number of years that it takes for the vehicle to depreciate to $12000 Round to the nearest tenth.

The size of angle x is equal to 100°.

Based on the identical isosceles triangles ΔABD and ΔACD, we can logically deduce the following:

m∠DAB = 25°

AD = BD = CD

In triangle ΔABD, we have:

AD = BD (Given)

m∠DBA = ∠DAB (Angle opposite to equal sides are congruent)

m∠DBA = 25°.

Next, we would determine the measure of m∠ADB;

m∠DBA + m∠DAB + m∠ADB = 180° (Sum of angle in a triangle)

25° + 25° + m∠ADB = 180°

m∠ADB = 180° - 50°

m∠ADB = 130°.

Since ΔABD and ΔACD are two identical isosceles triangles, we have:

m∠DCA = m∠DBA

m∠DCA = 25°

Similarly, we have:

m∠DAC = m∠DAB = 25°

m∠ADC = m∠ADB = 130°

Generally speaking, we know that a complete revolution (circle) is equal to 360°:

m∠ADC + m∠ADB + m∠CDB = 360°

130° + 130° + x = 360°

x = 360° - 260°

x = 100°.

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If we can observe this behavior in the data or the context of the problem, we can infer that a is diagonal.

If the matrix a is diagonal, it means that its eigenvectors are orthogonal to each other. Geometrically, this means that the linear transformation t corresponding to a scales the input vector along the direction of the eigenvectors without rotating it.

More specifically, let λ1 and λ2 be the eigenvalues of a, and let v1 and v2 be the corresponding eigenvectors. If a is diagonal, then we have:

a * v1 = λ1 * v1

a * v2 = λ2 * v2

This means that the linear transformation t scales the input vector v1 by a factor of λ1 along the direction of v1, and scales the input vector v2 by a factor of λ2 along the direction of v2. Since v1 and v2 are orthogonal, this scaling does not rotate the input vector.

Geometrically, this means that the linear transformation t corresponding to a stretches or shrinks the input vector along the direction of the eigenvectors without rotating it. If we can observe this behavior in the data or the context of the problem, we can infer that a is diagonal.

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Answer:

B

Step-by-step explanation:

Answer:

46 cents per minute.

Explanation:

The long-distance call costs $7.36 for 16 minutes.

The goal is to determine the unit rate in cents per minute.

In order to do this, first convert the amount, $7.36 to cents.

Next, to find the unit rate, divide the number of cents by the number of minutes.

The unit rate is 46 cents per minute.

Answer:

The length of line AD is 24 units.

Step-by-step explanation:

Got it right on edge2020. :)

Answer:

24

Step-by-step explanation:

got it right on edge

Answer: 192

Step-by-step explanation:

Use algebra

x + 3x + x + 3x = 64 (perimeter)

Combine Like Terms

8x = 64

x = 8

8 + 24 + 8 + 24 = 64

24/8 = 3

Answer:

  D.  -3 must be a root

Step-by-step explanation:

You want to know what it means that dividing 2x² +9x +9 by x+3 leaves a remainder of zero.

The remainder theorem tells you that dividing f(x) = (2x² +9x +9) by (x +3) has a remainder equal to f(-3). When that remainder is zero, it tells you that ...

  f(-3) = 0   ⇒   -3 is a root of the polynomial (2x² +9x +9), choice D.

__

Additional comment

It also tells you that 2x+3 = 0 will give you the other root: x = -3/2.

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To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.

To find a quadratic equation with the y-intercept and vertex, we can follow these steps:

For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:

3 = a(0)^2 + b(0) + c

1 = a(-2)^2 + b(-2) + c

Simplifying these equations, we get:

c = 3

4a - 2b + c = 1

By substituting c = 3 into the second equation, we can solve for a and b:

4a - 2b + 3 = 1

4a - 2b = -2

2a - b = -1

By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:

y = x^2 + x + 3

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To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.

Example:

Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).

To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.

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The answer is 23/40

To simplify this expression, we need to find a common denominator for each pair of fractions that are being added or subtracted.

 
The common denominator for 1/4 and 1/5 is 20, so we can rewrite 1/4 as 5/20 and 1/5 as 4/20. Then, we can subtract these fractions to get 1/20.

 
The common denominator for -3/4 and 1/8 is 8, so we can rewrite -3/4 as -6/8. Then, we can add these fractions to get -5/8.

 
Now, we can combine the two simplified fractions by finding a common denominator of 40. We can do this by multiplying 20 and 8, which gives us 160.

Then, we can rewrite 1/20 as 2/40 and -5/8 as -25/40. Adding these fractions together gives us:

2/40 - 25/40 = -23/40.

The absolute value of any number is always positive so it becomes 23/40.

The simplified version of (1/4 - 1/5) + (-3/4 + 1/8) is 23/40.

Answer:

Tampa Bay had 7 points in first quarter and Kansas City had 3.

Step-by-step explanation:

Rounded: KC - 0; TB - 10

Added: 10

Multiplied: 21

Hope it helps!

Answer:

To calculate the surface area and volume of a cylinder, we can use the following formulas:

a) Surface Area of a Cylinder:

The surface area of a cylinder consists of two circles (top and bottom) and the curved surface area.

The formula for the surface area of a cylinder is:

SA = 2πr² + 2πrh

Where:

SA = Surface Area

r = Radius of the base (half the diameter)

h = Height of the cylinder

Given that the diameter is 16 yards, the radius is half of that, so r = 8 yards. The height is 20 yards.

Substituting the values into the formula, we get:

SA = 2π(8)² + 2π(8)(20)

= 2π(64) + 2π(160)

= 128π + 320π

= 448π

So, the surface area of the cylinder is 448π square yards.

b) Volume of a Cylinder:

The formula for the volume of a cylinder is:

V = πr²h

Using the same values for the radius (r = 8 yards) and height (h = 20 yards), we can calculate the volume:

V = π(8)²(20)

= 64π(20)

= 1280π

The volume of the cylinder is 1280π cubic yards.

The given statement is True because If the sample mean is close to the population parameter, it suggests representative sampling regarding the variable of interest, although other factors should be considered too.

When the sample mean closely approximates the population parameter, it indicates that the sample is capturing the central tendency of the population. The mean is a measure of central tendency that reflects the average value of the variable of interest in the population.

If the sample mean is similar to the population mean, it suggests that the sample is a good representation of the population in terms of that particular variable.

However, it is important to note that representativeness is a relative concept. A sample may be considered representative in one sense but not necessarily in all aspects. Other factors, such as the sampling method, sample size, and sampling bias, also influence the representativeness of a sample.

In summary, when the obtained mean of the observations in a research study is close to the population parameter, it provides evidence that the sample is representative of the target population to some degree, indicating that the sample captures the central tendency of the population for the variable under investigation.

However, representativeness should be assessed in consideration of other factors as well.

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The graph of the function is a straight line, there are no local maximum or minimum values either.

As per data f(x) = 5 - x

Sketching the graph of the function f(x):

Here, the graph of the function f(x) is a straight line, and its slope is -1. Let's plot some points:

When x = 0, y = 5

When x = 1, y = 4

When x = -1, y = 6

When x = 2, y = 3

When x = -2, y = 7

We can plot more points as well using the slope to find more points.

Finding the absolute maximum and minimum values of f(x): The graph of f(x) is a straight line that extends infinitely in both directions, meaning there is no absolute maximum or minimum value. Finding the local maximum and minimum values of f(x):

Since the graph of the function is a straight line, there are no local maximum or minimum values either. Therefore, the answer is: DNE, DNE, DNE, DNE.

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Step-by-step explanation:

That's it bro hope it helps you

The solution to the inequality x^4 - x^3 - 16x^2 - 20x ≤ 0 is {-2 U [0,5] }

To solve the inequality x^4 - x^3 - 16x^2 - 20x ≤ 0 algebraically, we can follow these steps:

1. Factor the expression,

x^4 - x^3 - 16x^2 - 20x ≤ 0

x(x+2)^2(x-5)≤ 0

2. Identify the critical points by setting the expression equal to zero and solving for x. To find the critical points, we need to solve the equation x(x+2)^2(x-5)=0.

The critical points are -2,  0,  5.

3. Use the critical points to create test intervals.

x=-2 or 0≤ x≤ 5

The solution to the inequality x^4 - x^3 - 16x^2 - 20x ≤ 0 is {-2 U [0,5] }

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Answer: Read the step by step explanation for the answer

Step-by-step explanation:

We can use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the given point (4, 3) and the origin (0, 0):

r = √(4² + 3²) = 5

Then we can use the coordinates of the point (4, 3) to determine the values of the trigonometric functions:

sin(θ) = opposite/hypotenuse = 3/5

cos(θ) = adjacent/hypotenuse = 4/5

tan(θ) = opposite/adjacent = 3/4

csc(θ) = hypotenuse/opposite = 5/3

sec(θ) = hypotenuse/adjacent = 5/4

cot(θ) = adjacent/opposite = 4/3

Therefore, the values of the six trigonometric functions of θ are:

sin(θ) = 3/5

cos(θ) = 4/5

tan(θ) = 3/4

csc(θ) = 5/3

sec(θ) = 5/4

cot(θ) = 4/3

The trigonometric ratios for each triangles are:

Please note that all angles B are the right angle, then:

cos B = 1; sin B = 0; tan B = -

The trigonometric ratio of sin, cos, tan, can be formulated as:

(please refer to the attached triangle below for reference)

cos A = side adjacent to A / Hypotenuse

Cos A = b/c

Sin A = side opposite to A / Hypotenuse

Sin A = a/b

Tan A = Side opposite to A / Side adjacent to A

Tan A = a/b

From these formulas, we can find that:

Triangle 1

Cos A = 40/50 = 4/5

Sin A = 30/50 = 3/5

Tan A = 30/40 = 3/4

Cos C = 30/50 = 3/5

Sin C = 40/50 = 4/5

Tan C = 40/30 = 4/3

Triangle 2

Cos A = 27/45 = 3/5

Sin A = 36/45 = 4/5

Tan A = 36/27 = 4/3

Cos C = 36/45 = 4/5

Sin C = 27/45 = 3/5

Tan C= 27/36 = 3/4

Triangle 3

Cos A = 15/17

Sin A = 8/15

Tan A = 8/15

Cos C = 8/17

Sin C = 15/17

Tan C = 15/8

Please note that all angle B on the three triangles are all a right angle, then:

Cos B = 1

Sin B = 0

Tan B = -

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The speed of the boat in still water and the speed of the current is 18 and 5 miles/hour respectively.

Define speed, distance and time.

A key idea in mathematics is time speed and distance. Questions like circular motion, boats and streams, mobility in a straight line, clocks, races, etc. frequently involve the concepts of time and distance.

Formula of speed distance and time is Distance/Time = Speed

Speed describes the distance traveled divided by the time required to cover the distance and indicates how quickly or slowly an object goes.

Given data -

Time to travel 299 miles downstream = 13 hours

Time to travel 299 miles upstream = 23 hours

Let the speed of the boat in still water = x miles/hour

Let the speed of the current = y miles/hour

Then, speed of the boat downstream = (x + y) miles/hour

And speed of the boat upstream = (x - y) miles/hour

According to the concept of speed, distance and time

As time to travel 299 miles downstream = 13 hours,

299 / (x + y) = 13

x + y = 23          --------- equation 1

Similarly, as time to travel 299 miles upstream = 23 hours

299 / (x - y) = 23

x - y = 13            ------------equation 2

By adding equation 1 and 2, we will get

2x = 36

x = 18

Substitute the value of x in equation 2, we will get

y = 5

The speed of the boat in still water = 18 miles/hour

The speed of the current = 5 miles/hour

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Answer:

2

Step-by-step explanation:

The coordinate vector of x = [-3, 5, -1] with respect to the ordered basis e = {[1, 7, 8], [0, 1, -5], [0, 0, 1]} is [x]e = [5, -6, -1].

To find the coordinate vector of x with respect to the basis e, we need to express x as a linear combination of the basis vectors and determine the coefficients.

x = [-3, 5, -1]

e = {[1, 7, 8], [0, 1, -5], [0, 0, 1]}

We need to find the coefficients c1, c2, c3 such that:

x = c1 * [1, 7, 8] + c2 * [0, 1, -5] + c3 * [0, 0, 1]

This can be written as a system of equations:

-3 = c1 * 1 + c2 * 0 + c3 * 0

5 = c1 * 7 + c2 * 1 + c3 * 0

-1 = c1 * 8 + c2 * (-5) + c3 * 1

Simplifying the equations, we have:

c1 = -3

7c1 + c2 = 5

8c1 - 5c2 + c3 = -1

Substituting the value of c1 in the second equation:

7(-3) + c2 = 5

-21 + c2 = 5

c2 = 26

Substituting the values of c1 and c2 in the third equation:

8(-3) - 5(26) + c3 = -1

-24 - 130 + c3 = -1

c3 = 105

Therefore, the coefficients are:

c1 = -3

c2 = 26

c3 = 105

The coordinate vector of x with respect to the basis e is:

[x]e = [c1, c2, c3] = [-3, 26, 105]

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The missing Value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

The missing value that, when multiplied by 5/3^4, gives the result of 5^4, we can set up the equation:

(5/3^4) * x = 5^4

To solve for x, we can simplify both sides of the equation. First, let's simplify the right side:

5^4 = 5 * 5 * 5 * 5 = 625

Now, let's simplify the left side:

5/3^4 = 5/(3 * 3 * 3 * 3) = 5/81

Now we have:

(5/81) * x = 625

To solve for x, we can multiply both sides of the equation by the reciprocal of 5/81, which is 81/5:

(81/5) * (5/81) * x = (81/5) * 625

On the left side, the fraction (81/5) * (5/81) simplifies to 1, leaving us with:

1 * x = (81/5) * 625

Simplifying the right side:

(81/5) * 625 = 13125

Therefore, the missing value, x, that when multiplied by 5/3^4 gives the result of 5^4 is 13125.

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Answer:

= 12x4=48

48-9=39

so 39 is your answer

Answer:

The first one is correct.

Step-by-step explanation:

Answer:

thats right!

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

√6 + √5= 4.69

Step-by-step explanation:

First,  simplify the radicals-

in this situation, we have nothing to simplify.

√6 = aprx 2.45

√5 = aprx 2.23

√6 + √5= 4.685

= aprx 4.69

Answer: Z

Step-by-step explanation: it is trust me but what’s the question

The exponential form of the given complex number is\[z=4e^{-j2.94}\]

Given,  \[z=-4-1 j\]

To convert a complex number from rectangular form to polar or exponential form,

we use the following formulas:\[r=\sqrt{x^2+y^2}\]and \[\theta =\arctan \frac{y}{x}\]

where \(x\) is the real part of the complex number and \(y\) is the imaginary part of the complex number.

Thus, we have:\[z=-4-1j\]\[=4\angle-168.69^{\circ}\]%

Hence, the answer is 4e^(-j2.94).

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Answer:

192 in 2. multiply all of the numbers together

Step-by-step explanation:

6x4x8=192