In a volatile housing market, the overall value of a home can be modeled by V(x)=325x2-4600x+145000, where V represents the value of the home and x
represents each year after 2020. Find the vertex and interpret what the vertex of this function means in terms of the value of the home. Show the work you completed
to determine the vertex

Answer:

well 2 times three is 5 so then you would end up with

18 divided by 5

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

5-2

then 18 divided by 5 is 3.6 so then you have

3.6

---------

5-2

and five minus 2 is three

3.6

-----

3

and 3.6 divided by three is 1.2

YOUR ANSWER IS 1.2 ;)

Step-by-step explanation:

Answer: Answers and work are all in the picture that I attached. Hope this helps

Answer:

7π/6, 11π/6

Step-by-step explanation:

2cscx + 17 = 15 + cscx

1. Subtract cscx and 17 from both sides ⇒ cscx = -2

2. cscx = 1/sinx ⇒ 1/sinx = -2

3. Multiply by sinx and divide by -2 ⇒ sinx = -1/2

When is sinx equal to -1/2? ⇒ 7π/6, 11π/6

The solution of the equation 2cosec x+17 = 15+cosec x is 7π/6 and 11π/6.

Given:

Find:

Solution:

2Cosec x + 17 = 15 + Cosec x

⇒ 2Cosec x - Cosec x = 15 - 17

⇒ Cosec x = -2

Now, 1/sinx = -2

   ⇒  sinx = -1/2

we know, sin 30° = 1/2

Since, sinx is negative,

x will be in 3rd and 4th quadrant.

value in 3rd quadrant = 180° + 30° = 210°

value in 4th quadrant = 360° - 30° = 330°

So, x = 210° = 210 * π/180 = 7π/6

Also, x = 330° = 330 * π/180 = 11π/6

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The expression that is always equivalent to sin x when 0° < x < 90° is (1) cos (90° - x). Option 1

To understand why, let's analyze the trigonometric functions involved. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Since we are considering angles between 0° and 90°, we can guarantee that the side opposite the angle will always be the shortest side of the triangle, and the hypotenuse will be the longest side.

Now let's examine the expression cos (90° - x). The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. In a right triangle, when we subtract an angle x from 90°, we are left with the complementary angle to x. This means that the remaining angle in the triangle is 90° - x.

Since the side adjacent to the angle 90° - x is the same as the side opposite the angle x, and the hypotenuse is the same, the ratio of the adjacent side to the hypotenuse remains the same. Therefore, cos (90° - x) is equivalent to sin x for angles between 0° and 90°.

On the other hand, options (2) cos (45° - x) and (3) cos (2x) do not always yield the same value as sin x for all angles between 0° and 90°. The expression cos x (option 4) is equivalent to sin (90° - x), not sin x.

Option 1 is correct.

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Answer:

hnahnahnahnahhnahnahnahnahhnahnahnahnahhnahnahnahnah

A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;

g(x) = kf(x)

g(x) = 1/2f(x)

\(g(x) = \frac{1}{2} e^x -4\)

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Answer:

$0.40

I had the same question and it was $0.40

Answer:

$0.55

Got it on the test, hope this helps :)

The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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Answer:

y-4=5 (x-2)

Step-by-step explanation:

it's point-slope form.

y-y1 = m or slope (x-x1).

y1 being the y coordinate and x1 being the x coordinate.

if you need slope-intercept it is y=5x-6

Answer:

x ≥ -1

Step-by-step explanation:

Divide everything by 7 to isolate x and you have your answer!

Answer:

x ≥ –1

Step-by-step explanation:

7x ≥ –7

Divide by 7

7x /7≥ –7/7

x ≥ –1

There is a decrease in the percentage which is 40%.

Given that, 10 hours to 6 hours.

We need to find the per cent of change increase or decrease.

To calculate the change per cent follow the steps given below:

Step 1: Calculate the change (subtract the old value from the new value)

Step 2: Divide that change by the old value (you will get a decimal number)

Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)

Now, 10-6=4

=4/10=0.4

=0.4×100=40%

Hence, there is a decrease in the percentage which is 40%.

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The graph of the system of inequalities:

y  ≤ (1/4)*x - 2

y  ≥ −(5/4)x +2

Is in the image at the end.

Here we have the system of inequalities:

y  ≤ (1/4)*x - 2

y  ≥ −(5/4)x +2

To graph this, we just need to graph both of the linear equations, and we need to shade the region below the first line (the one with positive slope) and the region above the second line, the one with negative slope.

Then the graph of the system of inequalities is the graph you can see in the image at the end of the answer.

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Answer:

Two Equal Angles = 45°

Third Angle = 90°

Step-by-step explanation:

Given information

Two equal angles of an isosceles triangle are half the third angle

Set variables

Let x be the angle of the equal angles of the isosceles triangle

Let 2x be the angle of the third angle

Set equations

x + x + 2x = 180 (Triangle angle sum theorem)

Combine like terms

2x + 2x = 180

4x = 180

Divide 4 on both sides

4x / 4 = 180 / 4

\(\Large\boxed{x=45^\circ}\)

Substitute the x value into the expression to find the third angle

Third angle = 2x

                   = 2 (45)

                   = \(\Large\boxed{90^\circ}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer: B

Step-by-step explanation:

multiply the 1/2 of a mile by 3 (to complete the full hour)

Option A) and C) are the correct option which is the remote interior angles of ∠1 are ∠4 and ∠6.

Remote interior angles are the angles that are inside the given triangle and opposite from the exterior angle.

According to the given question we have been given that the ∠1 is an exterior angle and an exterior angle has two remote interior angles.

Thus from the figure we can see that opposite of ∠1 is the vertex with angle ∠4 and ∠6.

Hence the remote interior angles of ∠1 are ∠4 and ∠6. That is option A) and C) is the correct option.

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a) The definition of the composite function is: \((f \circ g)(x) = \frac{6}{12 + 2x}\)

b) The domain of the composite function is: (-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

The composite function of f(x) and g(x) is given by the function rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the composite function is obtained as follows:

\((f \circ g)(x) = f(\left\frac{6}{x}\right)\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{6}{x} + 2}\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{12 + 2x}{x}}\)

\((f \circ g)(x) = \frac{6}{12 + 2x}\)

The domain is all real values except x = 0, x = -2 and x = -6, as f(x) is not defined at x = -2 and g(x) is not defined at x = 0 and the composite function is not defined at x = -6, hence the interval notation is:

(-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

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Answer:

17.5

Step-by-step explanation:

i just used a calculator my man

Answer:

Fraction 24 2/100 which equals 24 1/50 OR in decimal form 24.020

Step-by-step explanation:

Hope this helps! :)

a. The center of the circle is (-2, -1).

b. The radius of the circle is √136.

c. The equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.

a. To find the center of the circle, we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

In this case, the endpoints of the diameter are P(-7, -4) and Q(3, 2).Applying the midpoint formula:

Midpoint = ((-7 + 3)/2, (-4 + 2)/2)

= (-4/2, -2/2)

= (-2, -1)

Therefore, the center of the circle is at the coordinates (-2, -1).

b. To find the radius of the circle, we can use the distance formula, which calculates the distance between two points (x1, y1) and (x2, y2). The radius of the circle is half the length of the diameter, which is the distance between points P and Q.

Distance = √\([(x2 - x1)^2 + (y2 - y1)^2]\)

Using the distance formula:

Distance = √[(3 - (-7))^2 + (2 - (-4))^2]

= √\([(3 + 7)^2 + (2 + 4)^2]\)

= √\([10^2 + 6^2\)]

= √[100 + 36]

= √136

Therefore, the radius of the circle is √136.

c. The equation for a circle with center (h, k) and radius r is given by:

\((x - h)^2 + (y - k)^2 = r^2\)

In this case, the center of the circle is (-2, -1), and the radius is √136. Substituting these values into the equation:

\((x - (-2))^2 + (y - (-1))^2\) = (√\(136)^2\)

\((x + 2)^2 + (y + 1)^2 = 136\)

Therefore, the equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.

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The graph of the function y = 5|x - 4| is added as an attachment

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

y = 5|x - 4|

The above function is an absolute value function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

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The probability that two cards will be drawn at random, without replacement, is 13/18.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our answer-

P(at least 1 green) = 1 - P(no green)

P(no green) = draw yellow on both draws

= P(draw yellow on 1st draw) * P( draw yellow on 2nd draw, given draw yellow on 1st draw)

= 5/9 * 4/8 = 20/72 = 5/18

P(at least 1 green) = 1 - 5/18

= 13/18

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Answer:

B

Step-by-step explanation:

Answer:

C) -2/9

Step-by-step explanation:

\(\displaystyle -\frac{1}{6}\biggr[3-15\biggr(\frac{1}{3}\biggr)^2\biggr]\\\\=-\frac{1}{6}\biggr[3-15\biggr(\frac{1}{9}\biggr)\biggr]\\\\=-\frac{1}{6}\biggr[3-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{27}{9}-\frac{15}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{12}{9}\biggr]\\\\=-\frac{1}{6}\biggr[\frac{4}{3}\biggr]\\\\=-\frac{4}{18}\\\\=-\frac{2}{9}\)

Answer:

Hence, Option (C) - 2/9 is the Answer:

Step-by-step explanation:

-1/6 [3 -15(1/3)^2]

-1/6(3 -15)(1/9))

-1/6(3 - 5/3)

-1/6 (4/3)

Hence, Option (C) - 2/9 is the Answer:

I hope it helps!

Let's say instead of x2-x1, we say, "The difference between x2 and x1", let's call this value A. We'll do the same for the y variables and call that difference B, for simplicity.

For (2,3) and (4,9), we're really dealing with those differences, so A should equal 2, and B should equal 6. So far so good. But this is pretty much the "rise and run" of a triangle. 2 to the right, then 6 up. But if you walk 2 miles east, then 6 north, while you, personally, have travelled 8 miles, the distance between your starting point and where you are is NOT the way you walked.

So in the case of the triangle, using 2 as the run and 6 as the rise, to get the straight line between the starting point and the ending point, we have to do Pythagorean's Theorem, or A2 + B2 = C2 to get that last direct line between the two points. Cancelling the root and exponents removes the process to get that exact distance squared. We then take the square root of that to get the exact distance.

Answer:

the correct answer is 193

Step-by-step explanation:

25×1-0=25

25×2-1=49

49×2-1=97

97×2-1=193

Answer:

  d.  m = 9/4

Step-by-step explanation:

You want the solution to ...

  1/√8 = 4^(m -3)

It will be convenient to rewrite this equation in terms of powers of 2.

  \(\dfrac{1}{\sqrt{8}}=4^{(m-3)}\qquad\text{given}\\\\\dfrac{1}{2^{\frac{3}{2}}}=(2^2)^{(m-3)}\qquad\text{using powers of 2}\\\\-\dfrac{3}{2}=2(m-3)\qquad\text{equate the exponents of 2}\\\\-\dfrac{3}{4}=m-3\qquad\text{divide by 2}\\\\\boxed{m=\dfrac{9}{4}}\qquad\text{add 3}\)

Answer:

The square root of 50 is approximately 7.07.

Answer:

7.07106781187...

Step-by-step explanation:

its an irrational number

Answer:

6

Step-by-step explanation:

75% of 8 = 6

Hope this helps! Please give brainiest if correct.