In trapezoid LOVE, the length of the midsegment is 2x inches. If one
parallel side is x inches, what is the length of the other parallel side?

Answer:

a. 1ab (4 -28+7)

b 2(a² - 183²)

c. cde(12-9-8+6)

d ab(a+b +2 -2-2 -3)

e 5(1- 9a²)

f py- 2p - qz -qy

pqy (1 - 2 -z -1)

Answer:

Given PR is perpendicular to QS, and PQ and PS are congruent. Angle PRQ and angle PRS are right angles by the definition of perpendicular segments. Therefore triangle PRQ and triangle PRS are right triangles. Segment PR is congruent to segment PR by the reflexive property of congruence. By the HL Theorem, triangles PRQ and PRS are congruent.

SOLUTION :

a² = hypo² - base²

a² = 13² - 12²

a² = 169 - 144 = 25

a = √25

a = 5 units.

________________________________

HOPE IT HELPS

c. They have the same vertical shift.

A vertical shift is just an alternate within the y-price of each characteristic. it's miles literally picking up the entire characteristic or graph and moving the whole element up or down. If it's far moved up, we add to the y-cost, if it's far moved down, we subtract from the y-cost.

Vertical shift and lateral shift are phenomena because of the refraction of mild rays once they journey from one medium into every other. while light rays travel across two parallel surfaces, the emergent rays from the second one floor are parallel to the incident rays on the primary floor.

The segment Shift is how far the function is shifted horizontally from the standard position. The Vertical Shift is how long way the function is shifted vertically from the same old function.

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The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).

First, we find the vector between the two points by vector sum:

[tex]\vec r = (-8, -9, - 11) - (- 3, 0, -7)[/tex]

[tex]\vec r = (- 5, - 9, - 4)[/tex]

The distance between the two points is found by the following Pythagorean expression:

[tex]d = \sqrt{(-5)^{2}+(-9)^{2}+(-4)^{2}}[/tex]

d ≈ 11.1

And the midpoint is found by linear algebra:

[tex]\vec m = 0.5\cdot (-3, 0, -7) + 0.5 \cdot (-8, -9, - 11)[/tex]

[tex]\vec m = (- 1.5, 0, - 3.5) + (- 4, - 4.5, -5.5)[/tex]

[tex]\vec m = (- 5.5, - 4.5, - 9)[/tex]

The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).

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Answer:

Option (4)

Step-by-step explanation:

See attached image.

a) The approximate area below the curve using five rectangles is 1280 square units.

b) The approximate area below the curve using ten rectangles is 1320 square units.

c) The approximate area below the curve using infinite number of rectangles is 1333.333 square units.

In this problem we must estimate the value of the area below the curve by finite number of rectangles using Riemann sums, whose expression is:

A ≈ [(b - a) / n] · ∑ f[a + i · (b - a) / n], for i = {0, 1, 2, 3, ..., n - 1}     (1)

Where:

The approximate area below the curve using five rectangles is: f(x) = 20 · x - x², a = 0, b = 20, n = 5

A ≈ [(20 - 0) / 5] · ∑ f[0 + i · (20 - 0) / 5]

A ≈ 4 · ∑ f(4 · i)

A ≈ 4 · [f(0) + f(4) + f(8) + f(12) + f(16)]

f(0) = 20 · 0 - 0² = 0

f(4) = 20 · 4 - 4² = 64

f(8) = 20 · 8 - 8² = 96

f(12) = 20 · 12 - 12² = 96

f(16) = 20 · 16 - 16² = 64

A ≈ 4 · (0 + 64 + 96 + 96 + 64)

A ≈ 1280

And using ten rectangles:

A ≈ [(20 - 0) / 10] · ∑ f[0 + i · (20 - 0) / 10]

A ≈ 2 · ∑ f(2 · i)

A ≈ 2 · [f(0) + f(2) + f(4) + f(6) + f(8) + f(10) + f(12) + f(14) + f(16) + f(18)]

f(0) = 20 · 0 - 0² = 0

f(2) = 20 · 2 - 2² = 36

f(4) = 20 · 4 - 4² = 64

f(6) = 20 · 6 - 6² = 84

f(8) = 20 · 8 - 8² = 96

f(10) = 20 · 10 - 10² = 100

f(12) = 20 · 12 - 12² = 96

f(14) = 20 · 14 - 14² = 84

f(16) = 20 · 16 - 16² = 64

f(18) = 20 · 18 - 18² = 36

A ≈ 2 · (0 + 36 + 64 + 84 + 96 + 100 + 96 + 84 + 64 + 36)

A ≈ 1320

And using infinite rectangles:

A ≈ [(b - a) / n] · ∑ f[a + i · (b - a) / n]

A ≈ (20 / n) · ∑ [20 · (20 / n) · i - (20 / n)² · i²]

A ≈ (20 / n) · ∑ [400 · i / n - 400 · i² / n²]

A ≈ ∑ (8000 · i / n² - 8000 · i² / n³)

A ≈ (8000 / n²) · ∑ i - (8000 / n³) · ∑ i²

A ≈ (8000 / n²) · [n · (n + 1) / 2] - (8000 / n³) · [n · (n + 1) · (2 · n + 1) / 6]

A ≈ (8000 / n²) · [(n² + n) / 2] - (8000 / n³) · [(n² + n) · (2 · n + 1) / 6]

A ≈ 4000 · (n² + 2) / n² - (8000 / n³) · [(2 · n³ + 3 · n² + n) / 6]

A ≈ 4000 · (1 + 2 / n²) - (4000 / 3) · [2 + 3 · (1 / n) + (1 / n²)]

As n → + ∞, then:

A ≈ 4000 - 8000 / 3

A ≈ 1333.333

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Answer: 422.5

Step-by-step explanation: To find how many mangoes were sold at 15.50 pesos, find 3/5 of the total number of mangoes. 3/5 of 25 is 15 because 3 (numerator) times 25 (mangoes) divided by 5 (denominator) is 15. 15 times 15.50 (price) is 232.5 pesos. Next we take the remaining mangoes (10) and multiply it by the price (19) to get 190 pesos. Add the sales and you get 422.5 pesos.

Answer:

422.50 pesos total

Step-by-step explanation:

3/5 ths of 25 = 15

(1/5th of 25 is 5, so we can multiply that number by 3 (3)(5) to get what 3/5ths of 25 are)

So, 15 mangoes were sold at 15.50 pesos

15 × 15.50 = 232.50

(why is this multiplication?  

remember that repeated addition is multiplication. We are adding the cost of each mango (15.50) 15 times, which we could write as 15.50 + 15.50... 15 times, or we could simply multiply the two values :)   )  

Because this vendor has sold 15 of his mangoes, he has 10 left (25 - 15 = 10), so we multiply

10 × 19.00 to find the combined cost:

10 × 19.00 = 190.00

Now, we want to find the total sale (how much money he made in total, from all 25 mangoes)

So, let's add our two values together:

  232.50

+ 190.00

 422. 50

So, the vendor made 422.50 pesos total from his mangoes

hope this helps! have a lovely day :)

The Future value is:

a) $10,210.25

b) $11,220.41

c) $12,308.99

d) $18,938.90

e) $44,835.28

What is future value?

The future value (FV) of any asset can be understood as an increase in its value at a fixed rate over a period of time. For a given principal sum P, rate of interest r, and time period t, the future value of an asset can be calculated as:

FV=P*(1+r) ^t

We can find future value as shown below:

P=$8,000

t=5 year

a) r=6%=0.06

FV=8000*(1+0.05) ^5

=8000*(1.0) ^5

=$10,210.25

b) r=7%=0.07

FV=8000*(1+0.07) ^5

=8000*(1.07) ^5

=$11,220.41

c) r=9%=0.09

FV=8000*(1+0.09) ^5

=$12,308.99

d) r=9% compounded semiannually

= 0.09

t=2*5=10

FV=8000*(1+0.09) ^10

=8000*(1.09) ^10

=$18,938.90

e) r=9 percent compounded quarterly

=0.09

t=5*4=20

FV=8000*(1+0.09) ^20

=8000*(1.09) ^20

=$44,835.28

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The equation that describes the new function is y' = x^2 + 5

The function is given as:

y = x^2

Shifting the function up by 5 units, the rule is

(x, y) = (x, y + 5)

So, we have:

y' = x^2 + 5

Hence, the equation that describes the new function is y' = x^2 + 5

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One linear equation y=x ......(i)

And quadratic equation y=x^2 .....(ii)

(1)Solving them

y=x=x^2

x-x^2=0

x(x-1)=0

If x=0 then y=0

if x=1 then y=1

(x,y)=(0,0),(1,1)

(2) graphically [refer in attachemet]

What is linear equation ?

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Using proportions, the expected number of adults in Palm City whose main source of news is the internet or newspaper is of 19,413.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From the table, the proportion of adults in Palm City whose main source of news is the internet or newspaper is found as follows:

p = (62 + 88)/(62 + 88 + 128 +24 + 38) = 0.4412.

Hence, out of 44,000 adults, the expected number is found as follows:

0.4412 x 44000 = 19,413.

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If the value of μ is 65, σ is 5 and z is 1.14 then the value of possible voter age would be 70.6 years.

Given that value of μ is 65, σ is 5 and z is 1.14.

We have to calculate the possible voter age that can satisfy the given values of σ,μ and z.

We know that in z test,

z=X-μ/σ

in which μ is population mean,σ is population standard deviation.

We have to just put the values in the above formula to get the value of X which is our possible voter age.

Putting the values we get,

1.14=x-65/5

5.7=X-65

X=65+5.7

X=67.7

Hence the possible voter age is 67.7 which would satisfy the value of μ=65,σ=5 and z=1.14.

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The upper quartile for NFC is 3 points higher than that of AFC.

A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%

On the box, the third line on the box represents the upper quartile. 75% of the scores represents the upper quartile.

Upper quartile for AFC : 26

Upper quartile for NFC : 23

Difference = 26 - 23 = 3

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Answer:

26 rows

Step-by-step explanation:

this is like a rectangle length×width situation.

seats per row = s

number of rows = r

s × r = 884

s = r + 8

so, we can use e.g. the second equation in the first :

(r + 8) × r = 884

r² + 8r = 884

r² + 8r - 884 = 0

the general solution to such a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = r

a = 1

b = 8

c = -884

r = (-8 ± sqrt(8² - 4×1×-884))/(2×1) =

= (-8 ± sqrt(64 + 3536))/2 = (-8 ± sqrt(3600))/2 =

= (-8 ± 60)/2 = -4 ± 30

r1 = -4 + 30 = 26

r2 = -4 - 30 = -34

a negative number did not make any sense for the number of rows, so r = 26 is our answer.

Answer:

A=3Bz/2

B=2A/3z

Step-by-step explanation:

if you need more explanation you can ask me :)

The arithmetic average return is probably too high for longer periods and the geometric average is probably too low for shorter periods.

When we look at historical returns, the difference between the geometric and arithmetic average returns isn't too hard to understand.

To put it slightly differently, the geometric average tells you what you actually earned per year on average, compounded annually. The arithmetic average tells you what you earned in a typical year. You should use whichever one answers the question you want answered. A somewhat trickier question concerns forecasting the future, and there's a lot of confusion about this point among analysts and financial planners.

Now, If we have estimates of both the arithmetic and geometric average returns, then the arithmetic average is probably too high for longer periods and the geometric average is probably too low for shorter periods.

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Answer:

Answer C: m = 26, f = 22

there is a typo in answer D.

Step-by-step explanation:

There are 48 vehicles, so m + f = 48.

They have 140 wheels, so 2m+4f = 140.

You can rewrite the first as m = 48-f and then plug it into the second:

2(48-f) + 4f = 140 =>

96 - 2f + 4f = 140 =>

2f = 140 - 96 =>

2f = 44

f = 22

m = 48 - 22 = 26

Answer:

D

Step-by-step explanation:

Let m = motorcycles and c = cars

m + c = 48                 2m + 4c = 140

m + c  = 48  Multiple this equation through by -2

-2m -2c = -96  Add this to the second equation above

2m +4c = 140

        2c = 44  Divide both sides by 2

          c  = 22.  There are 22 cars.  Plug this back into the top equation to find the number of motorcycles.

m + c = 48

m + 22 = 48 Subtract 22 from both sides

m = 26

Answer:

x = 24

Step-by-step explanation:

Since this is a right angle, we can use the Pythagorean Theorem to find x. In the formula, a^2 + b^2 = c^2, variables a and b represent the lengths of the legs, and variable c represents the length of the hypotenuse.

a^2 + b^2 = c^2

18^2 + x^2 = 30^2

324 + x^2 = 900

x^2 = 576

x = 24

The probability is 1/5.

There are 3 red marbles and 3 white marbles, for a total of 6.

The probability that the first marble is red is:

P(red) = 3/6

The probability that the second marble is also red is:

P(red') = 2/5 (because now there are 2 red marbles and a total of 5).

The joint probability is:

P = (3/6)*(2/5) = 1/5

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The missing height is 65.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

Missing height = (mean x total number of students) - sum of existing heights

Sum of existing heights = (54 + 55 + 56 + 61 + 63 + 64 + 70 ) = 423

Missing height = (8 x 61) - 423 = 64

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An exponential expression is one in which a number has been raised to a certain power.

An exponential expression is one in which a number has been raised to a certain power.

Now;

1) 3^2 . (3^3)^2 . 3^-8 = 3^2 + 6 - 8= 3^0 = 1

2) (3^2) (2.3)^-3/2^-2 = 3^2 . 2^-3 . 3^-3/2^-3 = 1/3

3) (2^-1) . (3 . 2)^4/(3 . 2)^3 = 2^-1. 3^4 . 2^4/ 3^3. 2^3 = 3

4) 2^5 . 3^5 . 6^-5 = 32 * 243/7776 = 1

5) (2^3) . (2 . 3)^-1/2^2 = 2^3 . 2^-1 . 3^-1/2^2 = 1/3

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The ratio guest to appetizers at the party was 4 guest per appetizer.

An equation is an expression that shows the relationship between two or more variables and numbers.

Ratio of guest to appetizers = 8 guest / 2 appetizers = 4 guest per appetizer.

The ratio guest to appetizers at the party was 4 guest per appetizer.

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They need to sell 5 pieces to cover their expenditures (have a profit of zero).

We know that the costs are:

And the revenue is:

So, the profit (the difference between the revenue and the cost) for selling x pieces is:

p(x) = $8*x - $2*x - $30

p(x) = $6*x - $30

We want to find the value of x such that p(x) = 0, then:

0 =  $6*x - $30

x = $30/$6 = 5

They need to sell 5 pieces to cover their expenditures (have a profit of zero).

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The steps in evaluating each of the following expressions is shown below.

An expression can be defined as a mathematical equation which shows the relationship existing between two or more numerical quantities or variables.

15 - 35/7 - 2 + 3 - 4

15 - (35/7) - 2 + 3 - 4 (bracket and division)

15 - 5 - 2 + 3 - 4 (regroup)

15 + 3 - 5 - 2 - 4 (subtract and add)

18 - 11 = 7.

10 + 2(9 - 5) - 16/18

10 + (2 × 4) - 8/9 (bracket and division)

10 + 8 - 8/9 (add)

18 - 8/9 (subtract)

162/9 - 8/9 = 17 1/9 or 154/9.

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Complete Question:

Show your steps in evaluating each of the following expressions. The steps count 4 points each, the answer is 1 point.

A. 15 - 35/7 - 2 + 3 - 4

B. 10 + 2(9 - 5) - 16/18

The predicted value of y when x =7 is -8.5

Start by drawing the line of best fit through the points

See attachment for the graph.

From the attached graph, we have the following value

y = -8.5 when x = 7

Hence, the predicted value of y when x =7 is -8.5

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Answer:

Step-by-step explanation:

the smallest value is 96.25 or rounded to the nearest whole number it is 96

what i did was put in my calculator 1540 divided by 4^2 because it is squared and has 4 sides

The distance of the cruise liner from me 20 seconds later will be; 2600ft.

a) Since, the speed of the liner is 30ft/sec, it follows that after 20secs, the liner would cover; (30×20)ft = 600ft more; and consequently, the distance is now; √(2000²+600²) = ft.

b) For the boat to be 2500 ft away given the speed 30ft per sec; Time taken = 2500/30 = 83.3seconds. Hence, the boat will be more than 2500 feets away after 2 minutes.

c) If the boat's distance is 2000ft from me; it follows that the distance covered is 10 seconds is; √(2000²-1500²) = 1322.9ft

Hence, the speed to attain this distance is; 1322.9/10 = 132.29ft/sec.

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Answer:

Given,

Distance traveled = 20 km

Speed = 60 km/h

So, timetaken=DistanceSpeed=2060=13h

For the next journey

Distance traveled = 20 km

Speed = 80 km/h

So, timetaken=DistanceSpeed=2080=14h

Now,

Total distance traveled = 20 + 20 = 40 km

Total time taken = 13+14=712

We know,

Averagespeed=TotaldistancetraveledTotaltimetaken=40712=68.5 km/h

Hence the average speed of the train is 68.5 km/h