Find the length of the missing side

Using the concept of vector sum, the coordinate of the fourth vertex is (6, -4)

The fourth vertex of a parallelogram can be found by taking the vector sum of the vector connecting the first and second vertex with the vector connecting the third and second vertex.

So, using the given coordinates, we can find the vector connecting the first and second vertex as (2 - (-3), -8 - (-2)) = (5, -6)

And, the vector connecting the third and second vertex as (6 - 2, -4 - (-8)) = (4, 4)

So, the vector sum of these two vectors is (5 + 4, -6 + 4) = (9, -2).

To find the fourth vertex, we add this vector to the first vertex's coordinates: (-3, -2) + (9, -2) = (6, -4)

So, the fourth vertex of the parallelogram is (6, -4)

Learn more on vertex of parallelogram here;

https://brainly.com/question/3050890

#SPJ1

why are there two of these?
Answer:

53.9

Step-by-step explanation:

89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9

Answer:

(z+w)y = X

Step-by-step explanation:

first add Z to both sides

w+z = x/y

then multiply both sides by Y

(w+z)y=x

Answer:

The max is 85F

The min is 75F

Step-by-step explanation:

For the max 80+5=85F

For the min 80-5=75F

Answer:

104

Step-by-step explanation:

Hey There!

So essentially what this problem is asking us to do is solve for the missing angle in a triangle

Remember all of the angles in a triangle will add up to 180

so to find the missing angle we subtract the given angles (38 and 38) from 180

180-38-38=104

so we can conclude that angle A equals 104

Hope this helps!

Answer:

104 degrees

Step-by-step explanation:

Hope this helps!

Have a great day!

Answer:

Step-by-step explanation:

We can use the formula for the future value of an annuity to determine how much Marcia needs to invest today to meet her retirement goal of $90,000. The formula for the future value of an annuity is:

FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)

where:

FV = future value of the annuity

PMT = payment (or deposit) made at the end of each compounding period

r = annual interest rate

n = number of compounding periods per year

t = number of years

In this case, we want to solve for the PMT (the amount Marcia needs to invest today). We know that:

Marcia wants to retire in 15 years (when she is 65), so t = 15

The interest rate is 10% per year, compounded semiannually, so r = 0.10/2 = 0.05 and n = 2

Marcia wants to have $90,000 in her retirement account

Substituting these values into the formula, we get:

$90,000 = PMT x [(1 + 0.05/2)^(2*15) - 1] / (0.05/2)

Simplifying the formula, we get:

PMT = $90,000 / [(1.025)^30 - 1] / 0.025

PMT = $90,000 / 19.7588

PMT = $4,553.39 (rounded to the nearest cent)

Therefore, Marcia needs to invest $4,553.39 today in order to meet her retirement goal of $90,000, assuming an interest rate of 10% per year, compounded semiannually.

Answer:

Step-by-step explanation:

Let x be the side length of the square window. Then the area of the square window is x^2, and the area of the rectangular window is 16 * 4 = 64.

We can write the equation:

x^2 = 64

To solve for x, we can take the square root of both sides:

x = √64

x = 8

Therefore, the side length of the square window is 8 inches.

Rounded to the nearest dollar, the average daily balance of the credit card for the August 1 through August 31 billing period is $74.

To find the average daily balance of the credit card for the August 1 through August 31 billing period, we need to calculate the sum of the daily balances and divide it by the number of days in the billing period.

Let's calculate the daily balances for each day:

Day 1: Closing Balance = $850

Day 8: Closing Balance = $300

Day 16: Closing Balance = $500

Day 24: Closing Balance = $650

To calculate the daily balances, we need to consider the activities that occurred on each day.

On Day 1, there was no activity recorded, so the closing balance remains at $850.

On Day 8, a payment of $550 was made. Therefore, the closing balance is $850 - $550 = $300.

On Day 16, a purchase of $200 was made. Therefore, the closing balance is $300 + $200 = $500.

On Day 24, a purchase of $150 was made and an adjustment of $4 was applied. Therefore, the closing balance is $500 + $150 - $4 = $650.

Now, let's calculate the average daily balance:

Sum of daily balances = $850 + $300 + $500 + $650 = $2300

Number of days in the billing period = 31

Average daily balance = Sum of daily balances / Number of days = $2300 / 31 ≈ $74.19

For more such questions on balance

https://brainly.com/question/11070711

#SPJ8

The inequality that represents c, the number of candles she needs to sell to pay for a visit to Knotts costing $100 when each candle is sold for $5, is expressed as: c ≥ 20.

The inequality c * 5 ≥ 100 is derived from the fact that each candle is sold for $5, so the total amount of money she earns from selling c candles is given by 5c. This amount must be greater than or equal to the cost of the visit, which is $100.

By multiplying both sides of the inequality by 1/5, we get c ≥ 20, which means that she needs to sell at least 20 candles to be able to pay for the visit to Knotts. If she sells fewer than 20 candles, she won't have enough money to cover the cost of the visit.

Therefore, the answer is: c ≥ 20.

Learn more about inequality on:

https://brainly.com/question/30239213

#SPJ1

Answer:

I think its the first one? 12 <x<15

Step-by-step explanation:

The index value of 99.2 in 1980 mean Gas in 1980 cost 0.992 times as much as gas in 1990, because the ratio of the gas price index in 1980 to the gas price index in 1990 is 0.992, the correct option is D.

Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We are given that;

Years, prices, prices as a percentage of 1990 price, price index 1990=100

Now,

The given table shows the average gasoline prices per gallon for various years, as well as the price index for each year, with 1990 being the reference year with a price index of 100. The price index measures the change in the price of gasoline relative to the price in 1990. Therefore, the price index value of 99.2 for 1980 means that the average gasoline price in 1980 was 0.992 times the price of gasoline in 1990.

It is important to note that the gas price index does not directly measure the cost per gallon of gas. Rather, it is a measure of the change in gasoline prices over time, with a reference year (in this case, 1990) used as a baseline.

Therefore, by ratio the answer will be  Gas in 1980 cost 0.992 times as much as gas in 1990, because the ratio of the gas price index in 1980 to the gas price index in 1990 is 0.992.

Learn more about the ratio here:

brainly.com/question/13419413

#SPJ1

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

Read more about sequence at

https://brainly.com/question/30499691

#SPJ1

Answer:

x=5

Step-by-step explanation:

5x-3=4x+2

x-3=2

x=5

Answer:

x=5

Step-by-step explanation:

mark me brainliest!

It will take 15 days for the hair to grow from 12mm to 16.5mm

By "average rate" in this context, we mean the typical or usual amount of hair growth per unit of time, which is often measured in millimeters per day. This rate can vary slightly depending on factors such as age, gender, genetics, diet, and overall health.

Let's first find out how much the hair needs to grow by subtracting its initial length (12mm) from its target length (16.5mm):

16.5mm - 12mm = 4.5mm

Now we can divide this growth by the average rate of hair growth to find the number of days it will take to grow this much:

4.5mm ÷ 0.3mm/day = 15 days

Therefore, it will take 15 days for the hair to grow from 12mm to 16.5mm.

To know more about average rate:

https://brainly.com/question/17219001

#SPJ1

Check the picture below, tis corrected.

btw the picture is rather long, so the thumbnail here may not show all its size, so you may have to open the image in a new tab or window.

The ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) do not correspond to the intervals where the graph of f(x) is decreasing. The pairs (1, -2) and (-3, -18) are the correct ones.

To determine where the graph of f(x) is decreasing, we need to examine the intervals where the function's derivative is negative. The derivative of f(x) is given by f'(x) = -3x^2 - 8x + 3.

Now, let's evaluate f'(x) for each of the given x-values:

f'(-1) = -3(-1)^2 - 8(-1) + 3 = -3 + 8 + 3 = 8

f'(2) = -3(2)^2 - 8(2) + 3 = -12 - 16 + 3 = -25

f'(0) = -3(0)^2 - 8(0) + 3 = 3

f'(1) = -3(1)^2 - 8(1) + 3 = -3 - 8 + 3 = -8

f'(-3) = -3(-3)^2 - 8(-3) + 3 = -27 + 24 + 3 = 0

f'(-4) = -3(-4)^2 - 8(-4) + 3 = -48 + 32 + 3 = -13

From the values above, we can determine the intervals where f(x) is decreasing:

f(x) is decreasing for x in the interval (-∞, -3).

f(x) is decreasing for x in the interval (1, 2).

Now let's check the ordered pairs in the table:

(-1, -6): Not in a decreasing interval.

(2, -18): Not in a decreasing interval.

(0, 0): Not in a decreasing interval.

(1, -2): In a decreasing interval.

(-3, -18): In a decreasing interval.

(-4, -12): Not in a decreasing interval.

Therefore, the ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) are not located in the intervals where the graph of f(x) is decreasing. The correct answer is: (1, -2), (-3, -18).

For more question on  intervals visit:

https://brainly.com/question/30460486

#SPJ8

Note the complete and the correct question is

Q- Consider the function below, which has a relative minimum located at (-3, -18) and a relative maximum located at 1/3, 14/27).

\(f(x) = -x^3 - 4x^2 + 3x\).

Select all ordered pairs in the table which are located where the graph of f(x) is decreasing: Ordered pairs: (-1, -6), (2, -18), (0, 0),(1 , -2), (-3 , -18), (-4. , -12)

Using the probability table, it is found that:

a) There is a 0.25 = 25% probability that this couple spends 45 dollars or more.

b) The expected amount the couple actually has to pay is $36.85.

From the table, the probabilities of each total cost are:

\(P(X = 30) = P(X = 15|Y = 15) = 0.2\)

\(P(X = 35) = P(X = 15|Y = 20) + P(X = 20|Y = 15) = 0.15 + 0.15 = 0.3\)

\(P(X = 40) = P(X = 15|Y = 25) + P(X = 20|Y = 20) + P(X = 25|Y = 15) = 0.05 + 0.15 + 0.05 = 0.25\)

\(P(X = 45) = P(X = 20|Y = 25) + P(X = 25|Y = 20) = 0.1 + 0.1 = 0.2\)

\(P(X = 50) = P(X = 25|Y = 25) = 0.05\)

Item a:

This probability is:

\(P(X \geq 45) = P(X = 45) + P(X = 50) = 0.2 + 0.05 = 0.25\)

There is a 0.25 = 25% probability that this couple spends 45 dollars or more.

Item b:

The expected value is the sum of each outcome multiplied by it's respective probability.

Hence:

\(E(X) = 0.2(30) + 0.3(35) + 0.25(40) + 0.9[0.2(45) + 0.05(50)] = 36.85\)

The expected amount the couple actually has to pay is $36.85.

A similar problem is given at https://brainly.com/question/24855677

Answer:

xx=5 and yy=6

Step-by-step explanation:

Hope it helps you

Answer:

- 1

Step-by-step explanation:

All you need to do is find the slope. How you do that is y2-y1/x2-x1

Yours would look like this:

\(\frac{1-7}{5-(-1)}=\frac{-6}{6}\)

Then you simplify to get -1

Answer:

8 times a number plus 7

Step-by-step explanation:

Let the number be f.

Simply, 8 f+7 is the expression.

Thank you!

Answer: the volume would be 384 but if you want it separately it would 8*4= 32

8*12=96

4*12=48

but the total cost would be 176 after you add up the equations

and the surface area would be 352

hope this helped :D

Answer: It is 384 is for volume and  352 for surface area

Step-by-step explanation: 384 square inches for volume because you multiply all the numbers together.  V = LWH (volume=lengh+with+hight)

352 for surface area.

V = (8) x (4) x (12)

V = 384 inches squared

SA = 2(LH)+2(LW)+2(WH)

SA = 2(8x12) + 2(8x4) + 2(4x12)

SA = 192 + 64 + 96

SA = 348 inches squared

I hope this helps! =3

The mean for the data items in the given frequency distribution is 4.152

To find the mean of the data items in the frequency distribution, we need to use the formula:

Mean = (Sum of (xi * fi)) / (Sum of fi)

where xi is the midpoint of the class interval and fi is the corresponding frequency.

So, we have

Mean = (3 + 12 + 15 + 20 + 20 + 30 + 21 + 16)/(3 + 6 + 5 + 5 + 4 + 5 + 3 + 2)

Evaluate

Mean = 4.152

Hence, the mean is 4.152

Read more about mean at

https://brainly.com/question/548811

#SPJ1

Based on the triangle similarity theorem:

A. ΔPQR ~ ΔPAB

B. AB corresponds to  QR

C. ∠A corresponds to ∠Q.

According to the triangle similarity theorem, when a segment that is parallel to one side of a triangle intersects the other two sides, the new triangle formed is therefore similar to the original triangle. This also implies that the two sides would be divided by the line segment proportionally.

Part A:

Based on the diagram given, we have:

AB is parallel to QR, therefore, the new triangle formed, triangle PAB is similar to the original triangle PQR, based on the triangle similarity theorem.

Part B:

Line segment AB corresponds to line segment QR because they lie in the same position facing angle P.

Part C:

Angle A lies in similar position with angle Q, so, angle A corresponds tp angle Q.

Learn more about the triangle similarity theorem on:

https://brainly.com/question/21247688

#SPJ1

Based on the triangle similarity theorem:

A. ΔPQR ~ ΔPAB

B. AB corresponds to  QR

C. ∠A corresponds to ∠Q.

Triangle similarity theorem, when a segment that is parallel to one side of a triangle intersects the other two sides, the new triangle formed is therefore similar to the original triangle. This also implies that the two sides would be divided by the line segment proportionally.

Part A:

AB is parallel to QR, therefore, the new triangle formed, ΔPAB is similar to the original ΔPQR, based on the triangle similarity theorem.

Part B:

Line segment AB corresponds to line segment QR because they lie in the same position facing angle P.

Part C:

Angle A lies in similar position with angle Q, so, angle A corresponds to angle Q.

Learn more about triangle similarity theorem from:

brainly.com/question/21247688

#SPJ1

Answer:

100

Step-by-step explanation:

60*2=120

10 seats taken up on 2 buses=20

120-20=100

Answer:

the last one (100) 60+60 equals120 10+ 10 equals 20 120-20 equals 100

Answer:

59,582π/375 (approximately 499.153) square centimeters

Step-by-step explanation:

Volume:

\( \frac{1}{3} \pi {(6.2)}^{2} (12.4)\)

\( \frac{1}{3} {( \frac{31}{5}) }^{2} ( \frac{62}{5} )\pi\)

\( \frac{59582\pi}{375} \)

Answer:

  y = {-1/2x +7 for x < 6; 1/2x +1 for x ≥ 6}

Step-by-step explanation:

You want y = 1/2|x -6| +4 written as a piecewise function.

The absolute value function changes its definition when its argument is negative:

  y = |x|   ⇒   y = -x for x < 0, and y = x for x ≥ 0

This means our piecewise function will have one definition for (x-6) < 0 and another for (x -6) ≥ 0.

The argument is negated in this domain, so we have ...

  y = -1/2(x -6) +4

  y = -1/2x +3 +4

  y = -1/2x +7

The absolute value function is an identity function in this domain:

  y = 1/2(x -6) +4

  y = 1/2x -3 +4

  y = 1/2x +1

Combining these descriptions into one, we have ...

  \(\boxed{y=\begin{cases}-\dfrac{1}{2}x+7&\text{for }x < 6\\\\\dfrac{1}{2}x+1&\text{for }x\ge6\end{cases}}\)

<95141404393>

Answer:

(1/5, 9/5)

Step-by-step explanation:

Given the set of inequities

x+y>2..... 1

4x-y≥-1 .... 2

We are to get the solution point (x,y)

Solving simultaneously

From 1:

x>2-y

Substitute into 2

4(2-y)-y≥-1

4(2)-4y-y≥-1

8-5y≥-1

-5u ≥-1-8

-5y ≥-9

y≤9/5

Since x>2-y

x>2 - 9/5

x>1/5

Hence the required point is (x,y) = (1/5, 9/5)

Answer:

C. (0,3)

Step-by-step explanation:

hope this helps :)