Find the value of X that makes S|| T
(4x+16)
(7x-20)

The correct option is D, the simplification of the expression is:

\(16x^4y^4\)

The first thing we need to do is simplify both numerator and denominator.

Remember that when we have the exponent of an exponent, wejust need to take the product between the exponents, then we can rewrite the numerator as follows:

\((2x^2y^2)^4 = 2^4*x^{2*4}*y^{2*4} = 16x^8y^8\)

And the denominator can be written as:

\(y*x^4*y^3 = x^4*y^{1+3} = x^4*y^4\)

Now we can take the quotient, remember that for the quotient of powers with the same base, we just need to subtract the exponents, so we have:

\(\frac{16x^8y^8}{x^4y^4} = 16*x^{8-4}*y^{8 -4} = 16x^4y^4\)

So the correct option is D.

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Answer:

for vertex at (h,k)

the equation is

y=a(x-h)^2+k

for vertex at (0,-1)

equation is

y=a(x-0)^2+(-1) or

y=ax^2-1

find what a is

(2,2)

x=2

y=2

2=a(2^2)-1

2=a(4)-1

add 1

3=a(4)

divide both sides by 4

3/4=a

the equation is

y=3/4x^2-1

Step-by-step explanation:

I really hope it helps!

The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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Answer:

x=1 y=-2

Step-by-step explanation:

hope this helps

This is quite simple. Toby ran 5 units, and it says Kate ran 4 times Toby ran meaning the person ran \(4 * 5\) so 20 units. Then it says Jim ran 3 times the units Kate ran. Meaning it would be \(3 * 20\) which is 60 units. Hence Jim ran 60 units or 60 miles. :D

Answer:

The z-score for this data point is -1.5

Step-by-step explanation:

Mean = M = 150

Standard Deviation = S = 20

Value = x = 120

We find the z value,

\(z = (x-M)/S\\z = (120 - 150)/20\\z = (-30)/20\\z=-3/2\\z=-1.5\)

Hence the z value is z = -1.5

Answer:

$2789

Step-by-step explanation:

A = P(1+r)^n

n = "every 3 years" = 12 years ÷ 3 years = 4

A = $1000(1+0.27)^4 = 2789

The angle between the two vectors (4,1) and (-8,3) will be 145.4°.

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

It is possible to calculate the angle () between two vectors using the formula

\(\rm \theta = cos ^{-1} \frac{ (a.b)}{|a||b|}\)

Calculate dot product:

=a · b

= ax · bx + ay · by

= 4 · (-8) + 1 · 3

= - 32 + 3

= -29

=|a|

= √ax² + ay²

= √4² + 1²

= √16 + 1

= √17

=|b|

=√ bx² + by²

= √(-8)² + 3²

= √64 + 9

= √73

\(\rm \alpha = cos ^{-1} \frac{ (a.b)}{|a||b|}\)

α = 145.40771131249005°

Thus, the angle between the two vectors (4,1) and (-8,3) will be 145.4°.

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The volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes is V = π∫ln 8eˣdx,

The volume of a solid generated by revolving a region about a line is calculated by using the method of slices.

In this case, we have a region in the first quadrant bounded by the coordinate axes, the curve y = eˣ and the line x = ln 8, which is being revolved about the line x = ln 8.

To find the volume of this solid, we need to take slices perpendicular to the line of rotation and calculate the area of each slice.

The volume can then be calculated by multiplying the area of each slice by its corresponding distance from the line of rotation and summing up the results.

The volume of this solid is calculated by the equation

=> V = π∫ln 8eˣdx,

where V is the volume of the solid, x is the distance from the line of rotation, and π is the constant pi

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Answer:

The range is {18, 22, 26}

Step-by-step explanation:

Answer:

x = 49

Step-by-step explanation:

3x - 33 = 2x + 16

subtract 2x from both sides: x - 33 = 16

add 33 to both sides: x = 49

Answer:

Hey! No fret so the answer is $8.40

Step-by-step explanation:

Hoped I helped! I'm Eve btw. Have an amazing day and consider marking this brainliest if you do thank you so much!

The amount paid as a car loan is $19,500 at 6% compounded annually of the principal amount of $15,000.

The Amount is calculated by \(A=P(1+\frac{r}{n} )^{nt}\)

where A is the Amount

P is the Principal

r is the Interest rate (in decimals)

n is the frequency at which the interest is compounded per year

t is the Time duration

According to the question,

Principal = $15,000

interest rate = 6% compound annually

Since interest is compounded annually, n =1

Time duration = 6 years

Therefore,

\(A= 15,000*(1+\frac{0.06}{1})^{1*5}\\ = 15,000*(1+0.06)^{5}\\= 15,000*(1.06)^{5}\\= 15,000*1.3\\= 19,500\)

Hence, the amount paid is $19,500.

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The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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Answer:

3.3

Step-by-step explanation:

The slope of the line perpendicular to the segment AB is 1/4

The slopes of perpendicular lines are negative reciprocals of each other.

Given the endpoints A(-8.1, 4.9) and B(-7.6, 2.9), the slope of this line is as follows:

(2.9 - 4.9)/[-7.6 - (-8.1)]

= (2.9 - 4.9)/(-7.6 + 8.1)

= -2/0.5

= -4

The negative reciprocal of -4 is 1/4

Therefore, the slope of the line perpendicular to the segment AB is 1/4

Adam's 3.5-oz container of mealworms for $8.75 is the better deal compared to Marco's 3.75-oz container for $9.75.

To determine which container of mealworms is the better deal, we compare the price per ounce of the two containers. Adam buys a 3.5-oz container for $8.75, while Marco buys a 3.75-oz container for $9.75.

The better deal can be determined by calculating the price per ounce for each container.

To compare the price per ounce, we divide the total cost of the container by its weight.

For Adam's container, the price per ounce would be $8.75 divided by 3.5 ounces, which equals $2.50 per ounce.

For Marco's container, the price per ounce would be $9.75 divided by 3.75 ounces, which equals $2.60 per ounce.

Comparing the price per ounce, we can see that Adam's container is the better deal as it costs $2.50 per ounce, while Marco's container costs $2.60 per ounce.

Adam's container offers a slightly lower price per ounce, making it the more cost-effective option.

Therefore, in terms of price per ounce, Adam's 3.5-oz container of mealworms for $8.75 is the better deal compared to Marco's 3.75-oz container for $9.75.

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Answer: no it does matter because it just the same numbers repeating

Step-by-step explanation:

Given data: Principal amount (P) = $3,500Number of years (t) = 70 - 26 = 44 years. Rate of Interest (R) = 7%Total amount that client will have after 44 years can be calculated as follows: Total Amount (A) = P[(1 + R/100)^t - 1]/(R/100)Putting the values:

Therefore, Total Amount (A) = $3,500[(1 + 7/100)^44 - 1]/(7/100)Total Amount (A) = $680,471.44Therefore, client will have $680,471.44 at the age of 70 years.

If the client saves $3,500 per year and invests in securities that provide an average annual return of 7 percent, she will have $680,471.44 by the time she reaches the age of 70. Since the first payment will be made one year from now, the amount of money that will accumulate will be for 44 years (70-26). The formula for calculating the total amount that the client will have after 44 years can be derived as follows:

Total Amount (A) = P[(1 + R/100)^t - 1]/(R/100)Where P is the principal amount, R is the rate of interest, and t is the number of years. The value of P is given as $3,500, and the rate of interest is 7 percent. Putting these values in the above equation, we get:

Total Amount (A) = $3,500[(1 + 7/100)^44 - 1]/(7/100)The total amount that the client will have after 44 years is $680,471.44. Therefore, it is advisable for the client to save $3,500 per year and invest it in securities that provide an average annual return of 7 percent. This investment plan will help the client to accumulate a substantial amount of money for her retirement.

Thus, the client can have $680,471.44 by the time she reaches the age of 70 if she saves $3,500 per year and invests it in securities that provide an average annual return of 7 percent. This investment plan will help the client to accumulate a substantial amount of money for her retirement.

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This formula calculates the lower limit for the mean at the 90% confidence level. It subtracts the product of the score (B7) and the standard error of the mean from the sample mean.

To find the score from the appropriate probability table to construct a 90% confidence interval, you can use the T.INV.2T function in Excel.

Assuming you want to calculate the confidence interval for the shipment time data provided, follow these steps:

1. In cell B7, enter the formula:

  ```

  =T.INV.2T(1-0.1, COUNT(A2:A89)-1)

  ```

  This formula calculates the score corresponding to a 90% confidence level using the T.INV.2T function. The first argument is `1-0.1` because we subtract the confidence level from 1 to get the significance level (0.1). The second argument is `COUNT(A2:A89)-1` to calculate the degrees of freedom, which is the count of data points minus 1.

2. In cell B9, enter the formula:

  ```

  =AVERAGE(A2:A89) + (B7 * (STDEV(A2:A89)/SQRT(COUNT(A2:A89))))

  ```

  This formula calculates the upper limit for the mean at the 90% confidence level. It adds the product of the score (B7) and the standard error of the mean to the sample mean. The standard error is calculated by dividing the standard deviation by the square root of the sample size.

3. In cell B10, enter the formula:

  ```

  =AVERAGE(A2:A89) - (B7 * (STDEV(A2:A89)/SQRT(COUNT(A2:A89))))

  ```

  This formula calculates the lower limit for the mean at the 90% confidence level. It subtracts the product of the score (B7) and the standard error of the mean from the sample mean.

Based on the values in cell B9 and B10, you can be 90% confident that the true mean shipment time falls within the calculated confidence interval.

Note: Make sure to adjust the cell references in the formulas based on the actual location of your data in the spreadsheet.

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Answer:

x=-2,y=-3

Step-by-step explanation:

x=7+3x

-3x+8y=-18

-21-y=-18

x=7+3x

y=-3

x=7+3x

x=-2

y=-3

Answer:

x = -2

y = -3

Step-by-step explanation:

There are three methods for solving system of equations: elimination, substitution, and graphing. In this case elimination would be the best method since you have -3x for both equations. When solving by elimination, your goal is to eliminate one of the variables, in this case we will eliminate x. Subtract the bottom equation from the top (it is important to remember here that the negative will distribute to the entire equation).

-3х + 9y = -21

- (- 3х +8y = -18)

_____________

y = -3

Now plug this y-value in to either equation and solve for x

-3х + 9y = -21

-3х + 9(-3) = -21

-3x - 27 = -21

-3x = 6

x = -2

Check your answer by plugging both values in to the second equation

- 3х +8y = -18

- 3(-2) +8(-3) = -18

6 - 24 = -18

-18 = -18

Answer:

It's proportional because it has a constant rate of change

Step-by-step explanation:

To determine the maximal velocity from an acceleration vs. time graph, you need to follow these steps:

Identify the time interval during which the acceleration remains constant or nearly constant. This interval can be identified as a straight line on the graph.

Calculate the acceleration value during this interval by finding the slope of the line. The slope is the change in acceleration divided by the change in time.

Use the acceleration value and the time interval to calculate the change in velocity during this interval using the formula:

Δv = aΔt

Where Δv is the change in velocity, a is the acceleration, and Δt is the time interval.

Add the change in velocity to the initial velocity at the start of the time interval to obtain the maximal velocity. If the initial velocity was zero, then the maximal velocity will be equal to the change in velocity.

vmax = vi + Δv

Where vmax is the maximal velocity and vi is the initial velocity.

Note that this method assumes that the acceleration is constant or nearly constant during the time interval of interest. If the acceleration changes significantly during this time interval, you will need to break it down into smaller intervals and repeat the above steps for each interval to determine the maximal velocity.

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Answer:

Insurance my friend..

Step-by-step explanation:

Can I pls have brainiest?

Answer:

15°

Step-by-step explanation:

Answer:

y = -17/2

Step-by-step explanation:

Substitute with the givens.

30= 8(8) + 4y.

Multiply parentheses.

30 = 64 + 4y

Subtract.

30-64= -34

-34 = 4y.

Divide each side by 4.

y = - 8.5, or -17/2

hope that is right!

The balance Laura’ account is $380,367. 00. The 39 months have passed since Laura retired.

Let's assume that x is the number of months that have passed since Laura retired. The amount Laura withdrew each month is $2,446, so the total amount withdrawn after x months is $2,446 * x.

The balance of Laura's account after x months can be calculated as follows:

initial balance - total amount withdrawn

= $458,639 - $2,446 * x

We know that the balance of Laura's account after x months is $380,367, so we can substitute that value into the equation:

$458,639 - $2,446 * x = $380,367

Solving for x, we get:

x = ($458,639 - $380,367) / $2,446

= 39 months

Account balance refers to the total amount of money that is available in a particular account, such as a savings account, checking account, or credit card account. The account balance represents the total funds that an individual or entity has at their disposal for making transactions, such as paying bills, making purchases, or withdrawing money. The account balance is usually updated regularly, usually daily, to reflect any transactions that have taken place, including deposits, withdrawals, or fees.

In the case of credit card accounts, the account balance also includes any interest and fees charged on the outstanding balance. It is important to regularly check the account balance to ensure that there are sufficient funds to cover transactions and to avoid overdraft fees. Maintaining a positive account balance is also essential to establishing and maintaining good credit standing.

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Coordinates of point B are (5x₂+6x₁)/11 and (5y₂+6y₁)/11

What is the section formula in coordinate geometry?

When the line segment is divided internally in the ratio m:n, we use this formula.  That is when point C lies somewhere between points A and B. p= (mx₂+nx₁)/(m+n) & q= (my₂+ny₁)/(m+n)

Given here,  point B on AC such that the ratio of AB to AC is 5:6

Let the point B(p,q) internally divide the line joining points A(x₁, y₁) and C(x₂, y₂) in the ratio m : n , then,

p= (mx₂+nx₁)/(m+n)

q= (my₂+ny₁)/(m+n)

Here. m=5 and n=6

p=(5x₂+6x₁)/11 , q=(5y₂+6y₁)/11

Hence, the Coordinates of point B are (5x₂+6x₁)/11 and (5y₂+6y₁)/11

I hope this helps <3