In APQR, p = 43.1 m, q = 83.2 m, and ZR = 26. Solve the triangle. Include a neatly labeled diagram.

Answer:

24.99

Step-by-step explanation:

25.9-6.91=24.99

These are the specified parameters:

The water rate is $1.33 per 751 gallons.

a. Determine the water bill

The water bill = 40,000 gallons × \(\displaystyle \frac{\$1.33}{751\ gallons}\)

                       = \(\displaystyle\frac{\$53,200}{751}\)

                       = $70,84

b. Determine many gallons of water can a customer use

Many gallons = $130 : \(\displaystyle \frac{\$1.33}{751\ gallons}\)

                       = $130 × \(\displaystyle \frac{751\ gallons}{\$1.33}\)

                       = \(\displaystyle \frac{97,630}{1.33}\) gallons

                       = 73,406 gallons

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Answer:

3(x-10)=15

Step-by-step explanation:

assuming 152 is a typo

240 mL of 15% alcohol solution contains 0.15 • 240 = 36 mL of alcohol.

If we add \(x\) mL of pure alcohol to it, we increase the total volume to \(240 + x\) mL, and it will contain \(36 + x\) mL of alcohol.

Solve for \(x\) such that the concentration of alcohol (the ratio of the volume of alcohol to total volume of solution) is 80%.

\(\dfrac{36 + x}{240 + x} = 0.80\)

\(36 + x = 0.80 (240 + x)\)

\(36 + x = 192 + 0.80x\)

\(0.2x = 156\)

\(x = 780\)

You need to add 780 mL of pure alcohol to get the desired concentration.

Answer:

answer to the question is $600

When more than 25 shirts are ordered, the price is $15 per shirt, plus $15 shipping and handling.  If $720 was spent on shirts,  the student council ordered 47 shirts.

Let x be the number of shirts ordered. We can set up an equation based on the given information:

If x ≤ 25, then the cost of the shirts is 20x + 20.

If x > 25, then the cost of the shirts is 15x + 15.

We know that the total cost of the shirts is $720. So, we can write:

20x + 20 if x ≤ 25

15x + 15 if x > 25

Setting these equal to each other, we get:

20x + 20 = 15x + 15

5x = 5

x = 1

This doesn't make sense, because the number of shirts ordered must be greater than 1. Therefore, we know that the student council ordered more than 25 shirts.

Using the equation 15x + 15 = 720, we can solve for x:

15x + 15 = 720

15x = 705

x = 47

To check, we can calculate the cost of the shirts:

If 47 shirts are ordered, then the cost is 15(47) + 15 = $720.

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Therefore, The Coordinates of the THIRD VERTEX is:  ( 5, -3 )

        Calculate the midpoint of the given vertices:

        MidPoint = ( -5 + 5/2,  3 + 3/2 )

        MidPoint = ( 0, 3 )

        Distance = √( -5 -5 )^2 + ( 3 - 3 )^2

        Distance = √( -10 )^2  +  (0)^2

        Distance = √100

        Distance =  10

        Side Length =  10/√3

        Side Length = 10/1.7

        Side Length = 5.88

        Height = √3/2  *  Side Length

        Height  = 1.7/2  *  5.88

        Height  =  5

Since the origin lies inside the triangle, The Third Vertex will have a Positive  X-Coordinate and a Negative Y-Coordinate.

       ( x, y )

        x  =  -5 + x/2

        y   =  3 + y/2

       x  =  5

       y  = -3

        Hence, The Coordinate  of the Third Vertex is:  ( 5, -3 )

I hope this helps!

Answer:

Step-by-step explanation:

Okay, Here we go!

To figure this out, lets write the problem down.

f(x)=1/6 (2x-8) ; f(-11)

We substitute -11 for x

f(-11)= 1/6 (2(-11)-8)

Now we solve

2 x -11 =-22

1/6 (-22-8)

-22-8 = -30

-30/6= -5

f(-11) = -5

hope this helps!^^

Answer:

-5

Step-by-step explanation:

just put -11 in place of x

Answer:

3 quarts

Step-by-step explanation:

12÷4=3

Hello !

Answer:

\(\large \boxed{\sf(a^2 - 3)^4 =a^8-12a^6+54a^4-108a^2+81}\)

Step-by-step explanation:

Let's use the binomial theorem to expand \(\sf (a^2 - 3)^4\) :

\(\sf \forall n \in \mathbb N, (x+y)^n=\sum\limits_{k=0}^{n}\binom{n}{k}x^ky^{n-k}\)

\(\sf Where\ \binom{n}{k}=\dfrac{n!}{k!(n - k)!}\)

We have :

Now we substitute these values into the formula :

\(\sf (a^2 - 3)^4=\sum\limits^4_{k=0}\binom{4}{k}(a^2)^k(-3)^{4-k}\)

\(\sf =\binom{4}{0}(a^2)^0(-3)^{4}+\binom{4}{1}(a^2)^1(-3)^{3}+\binom{4}{2}(a^2)^2(-3)^{2}+\binom{4}{3}(a^2)^3(-3)^{1}+\binom{4}{4}(a^2)^4(-3)^{0}\)

\(\sf =\binom{4}{0}81-\binom{4}{1}27a^2+\binom{4}{2}9a^4-\binom{4}{3}3a^6+\binom{4}{4}a^8\)

Let's calculate the binomial coefficients :

Now we can replace the binomial coefficients with their value:

\(\sf (a^2 - 3)^4 =1\times81-4\times27a^2+6\times 9a^4-4\times3a^6+1\times a^8\)

\(\sf(a^2 - 3)^4 =81-108a^2+54a^4-12a^6+a^8\)

\(\boxed{\sf(a^2 - 3)^4 =a^8-12a^6+54a^4-108a^2+81}\)

Have a nice day ;)

A rational number between -5.25 and -5.26 is -5.251.

What is rational number?

In mathematics, any number that can be written as p/q where q≠0 is considered a rational number. Also, every fraction that has an integer denominator and numerator and a denominator that is not zero falls into the category of rational numbers.

To find a rational number between -5.25 and -5.26, use the fact that the difference between these two numbers is 0.01, or 1/100.

Then choose any rational number between -5.25 and -5.26 by choosing a fraction whose decimal representation has two digits after the decimal point.

For example, choose the fraction -5.251, which is equal to -5251/1000.

This fraction is between -5.25 and -5.26, and it is a rational number because it can be expressed as the ratio of two integers.

Therefore, the rational number is -5.251.

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Answer:C

Step-by-step explanation: 2x=8 so x=4

If the force and acceleration are in the same direction, the mass of the object would be 0.83 kg.

The mass of the object cannot be determined with the given information. Acceleration is related to force and mass through Newton's Second Law: F = ma. However, in this case, we are given the acceleration and force, but not the mass. To find the mass, we would need either the acceleration and the force, or the force and the mass.

However, if we assume that the force and acceleration are both in the same direction, we can use the formula F = ma to find the mass. Rearranging the formula, we get m = F/a.

Substituting the given values, we get:

m = 10 N / 12 m/s²

m = 0.83 kg

So, if the force and acceleration are in the same direction, the mass of the object would be 0.83 kg.

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Complete Question:

A moving train accelerates at a rate of 12 meters per second. What would your mass be if the applied force were 10N?

Note:

Ortho centre :a point of intersection of altitudes of a triangle meets the opposite angle.

Given:

For Orthocentre:.

A(1, 2), B(2, 6), C(3,-4). are vertices of a triangle:

Slope of AB[m1]=\( \frac{6-2}{2-1} \)=4

Since it is perpendicular to CX.

slope of CX=m2

we have for slope of perpendicular

m1m2=-1

m2=-¼

It passes through the point C(3,-4)

equation of line CX becomes;

(y-y1)=m(x-x1)

y+4=-¼(x-3)

4y+16=-x+3

x+4y+16-3=0

x+4y+13=0........[1]

again:

Slope of AC[m1]=\( \frac{-4-2}{3-1} \)=-3

Since it is perpendicular to BY

slope of BY=m2

we have for slope of perpendicular

m1m2=-1

m2=⅓

It passes through the point B(2,6)

equation of line BY becomes;

(y-y1)=m(x-x1)

y-6=⅓(x-2)

3y-18=x-2

x-3y+18-2=0

x-3y+16=0.........[2]

Subtracting equation 1&2.

x+4y+13=0

x-3y+16=0

-__________

7y-3=0

y=\( \frac{3}{7} \)

again

Substituting value of y in equation 1.

x+4*\( \frac{3}{7} \)+13=0

x=-13-\( \frac{12}{7} \)

x=\( \frac{-103}{7} \)=-14\( \frac{5}{7} \)

So

orthocenter is (-14\( \frac{5}{7} \),\( \frac{3}{7}\))

Circumcentre: a point of intersection of perpendicular bisector of the triangle.

Now

X,Y and Z are the midpoint of AB,AC and BC respectively.

X(a,b)=(\( \frac{2+1}{2} \),\( \frac{2+6}{2} \))=

(\( \frac{3}{2} \),4)

Slope of AB=4

Slope of OX=-¼

Equation of line OX passes through (\( \frac{3}{2} \),4)is

y-4=-¼(x-\( \frac{3}{2} \))

4y-16=-x+\( \frac{3}{2} \)

8y-16*2=-2x+3

2x+8y=3+32

2x+8y=35

x+4y=\( \frac{35}{2} \)........[1]

again

Y(c,d)=(\( \frac{3+1}{2} \),\( \frac{-4+2}{2} \)=(2,-1)

Slope of AC:-3

Slope of OY=⅓

Equation of line OY passes through (2,-1) is

y+1=⅓(x-2)

3y+3=x-2

x-3y=3+2

x-3y=5......[2]

Multiplying equation 2 by 3 and

Subtracting equation 1&2.

x+4y=35/2

x-3y=5

-_______

7y=\( \frac{25}{2} \)

y=\( \frac{25}{14} \)

Substituting value of y in equation 2.

x-3*\( \frac{25}{14} \)=5

x=5+\( \frac{75}{14} \)

x=\( \frac{145}{14} \)

x=10\( \frac{5}{14} \)

circumcenter of a triangle: (10\( \frac{5}{14} \),1\( \frac{11}{14} \))

Answer:

1: 11

2: 1

3: -9

4: -49

Answer:

See screenshot below

Step-by-step explanation:

I hope this helps!

Answer:

When she came to work the next day, she was delighted because four hundred sixteen hundred, nine hundred forty-three containers had been delivered. How many things (Problem 3) would fill them all?

https://www.louisianabelieves.com/docs/default-source/assessment/grade-7-answer-key.pdf

Step-by-step explanation:

The mean is 0.8 and the standard deviation is 0.8579.

The experimental probability consists of many trials. When the difference between the theoretical probability of an event and its relative frequency get closer to each other, we tend to know the average outcome. This mean is known as the expected value of the experiment denoted by .

In a normal distribution, the mean is zero and the standard deviation is 1.

In a binomial experiment, the number of successes is a random variable. If a random variable has a binomial distribution, its standard deviation is given by: = √npq, where mean: = np, n = number of trials, p = probability of success and 1-p =q is the probability of failure.

In a Poisson distribution, the standard deviation is given by = √λt, where λ is the average number of successes in an interval of time t.

Sample space = n = 10

Probability of winning = p = 0.08

Probability of losing = q = 1 - p = 1 - 0.08 = 0.92

Mean, μ = np = 10×0.08 = 0.8

Standard deviation, σ =  \(\sqrt{npq}\)

∴ σ = \(\sqrt{10 * 0.08* 0.92} = \sqrt{0.736} = 0.8579\)

Thus, the mean is 0.8 and the standard deviation is 0.8579.

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Answer:

Therefore, the book value of the equipment at the end of year four (including year four) is $2,880.

Step-by-step explanation:

To calculate the book value of the equipment at the end of year four using the MACRS method with GDS recovery period of five years, we can use the following steps in Excel:

1. Open a new Excel spreadsheet and create the following headers in row 1: Year, Cost, Depreciation Rate, Annual Depreciation, Cumulative Depreciation, and Book Value.

2. Fill in the Year column with the years 1 through 6 (since the truck has a life of six years).

3. Enter the cost of the truck, $12,000, in cell B2.

4. Use the following formula in cell C2 to calculate the depreciation rate for each year:

=MACRS.VDB(B2, 5, 5, 1, C1)

This formula uses the MACRS.VDB function to calculate the depreciation rate for each year based on the cost of the truck (B2), the GDS recovery period of five years, the useful life of six years, the salvage value of $2,000, and the year (C1).

5. Copy the formula in cell C2 and paste it into cells C3 through C7 to calculate the depreciation rate for each year.

6. Use the following formula in cell D2 to calculate the annual depreciation for each year:

=B2*C2

This formula multiplies the cost of the truck (B2) by the depreciation rate for each year (C2) to get the annual depreciation.

7. Copy the formula in cell D2 and paste it into cells D3 through D7 to calculate the annual depreciation for each year.

8. Use the following formula in cell E2 to calculate the cumulative depreciation for each year:

=SUM(D$2:D2)

This formula adds up the annual depreciation for each year from D2 to the current row to get the cumulative depreciation.

9. Copy the formula in cell E2 and paste it into cells E3 through E7 to calculate the cumulative depreciation for each year.

10. Use the following formula in cell F2 to calculate the book value of the equipment for each year:

=B2-E2

This formula subtracts the cumulative depreciation for each year (E2) from the cost of the truck (B2) to get the book value.

11. Copy the formula in cell F2 and paste it into cells F3 through F7 to calculate the book value for each year.

12. The book value of the equipment at the end of year four (including year four) is the value in cell F5, which should be $2,880.

-15/2+√31.(3/2)i is the width of the garden.

The area of Rectangle is length times of width.

Given,

As an architect, your job is to fulfill the requirements of the client.

You are demanded by your client to have a plan or sketch in planting a garden and surrounding it with decorative stones.

Let width be x

The desired length of the lot is 15 meters longer than its width.

Length =x+15

The area of the rectangular plot should not be more than 126 m²

Area=Length×width

126=x(x+15)

126=x²+15x

x²+15x-126=0

Apply it in Quadratic formula.

x=-b±√b²-4ac/2a

a=1, b=15 and c=-126.

x=-15±√15²-4(1)(-126)/2(1)

x=-15/2+√31.(3/2)i.

Hence, the width of the garden is -15/2+√31.(3/2)i.

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Answer:

the product X Y is constant so the relationship is not an inverse variation.

Step-by-step explanation:

The building is 19.078 feet tall.

Given:

A 20-foot ladder is leaning against a building in order to reach the roof. the foot of the ladder is 6 feet from the building.

Let x be the building height.

here it forms a right angled triangle,

ladder length (hypotenuse) = 20 feet.

base length = 6 feet

According to pythagorean theorem,

\(hypotenuse^{2} = side^{2} +side^{2}\)

\(20^{2} =6^{2} +x^{2}\)

400 = 36 + \(x^{2}\)

\(x^{2}\) = 400 - 36

\(x^{2}\) = 364

x = \(\sqrt{364}\)

x = 19.078 feet.

Therefore the height of the building is 19.078 feet.

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The correct answer is A. 600 nautical miles is not the distance you will cover when traveling south along the 180° longitude from 5°N to 5°S. The correct distance is 0 nautical miles since the points are on the same line of longitude.

The distance traveled along a line of longitude can be calculated using the formula:

Distance = (Latitude 1 - Latitude 2) * (111.32 km per degree of latitude) / (1.852 km per nautical mile)

Given:

Latitude 1 = 5°N

Latitude 2 = 5°S

Substituting the values into the formula:

Distance = (5°N - 5°S) * (111.32 km/°) / (1.852 km/nm)

Converting the difference in latitude from degrees to minutes (1° = 60 minutes):

Distance = (0 minutes) * (111.32 km/°) / (1.852 km/nm)

Simplifying the equation:

Distance = 0 * 60 * (111.32 km/°) / (1.852 km/nm)

Distance = 0 nm

Therefore, traveling south along the 180° longitude from 5°N to 5°S, you will cover approximately 0 nautical miles.

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Answer:

The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.

Answer: On interval f(x) is increasing =  \(( -\infty, -2)\)

On interval f(x) is decreasing = \(( -\infty, -2)\)

Step-by-step explanation:

The given function: \(f(x)=-(x+2)^2+4\)

The graph of the function is attached below

In graph , function is increasing till point (-2,4) or x=-2 and then it is decreasing.

So f(x) is increasing in \(( -\infty, -2)\) and decreasing in \((-2, \infty)\)

So, On interval f(x) is increasing =  \(( -\infty, -2)\)

On interval f(x) is decreasing = \(( -\infty, -2)\)

the dot means multiplication so just multiply a and b which are -4 and -8. -4 x -8 = 32! 32 is the answer. hope this helped.

The triangle with a base of 88 centimeters and a height of 52.8 centimeters is an enlargement of the original triangle by a scale factor of 2.2.

To determine which triangle is an enlargement of the original by a scale factor of 2.2, we can compare the dimensions of the original triangle with the dimensions of each option. The original triangle has dimensions of 24 cm by 40 cm.

Calculating the dimensions of the first option, which has a base of 18.18 centimeters and a height of 10.9 centimeters, we find that the scale factor is approximately 0.4545 (18.18/40) for the base and 0.2725 (10.9/40) for the height. These values do not match a scale factor of 2.2.

Calculating the dimensions of the second option, which has a base of 42.2 centimeters and a height of 26.2 centimeters, we find that the scale factor is approximately 1.055 (42.2/40) for the base and 0.655 (26.2/40) for the height. These values do not match a scale factor of 2.2 either.

Calculating the dimensions of the third option, which has a base of 88 centimeters and a height of 52.8 centimeters, we find that the scale factor is approximately 2.2 (88/40) for the base and 1.32 (52.8/40) for the height. These values match a scale factor of 2.2, indicating that this triangle is the enlargement of the original.

Therefore, the triangle with a base of 88 centimeters and a height of 52.8 centimeters is an enlargement of the original triangle by a scale factor of 2.2.

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The total number of hands that contain exactly two 3s and two 6s is: 6 * 6 * 44 = 1584.

To find the number of hands that contain exactly two 3s and two 6s when 5 cards are randomly chosen from a standard deck of playing cards, we can use combinatorics.

First, we need to choose the two 3s from the four 3s in the deck. This can be done in (4 choose 2) = 6 ways.

Next, we need to choose the two 6s from the four 6s in the deck. This can also be done in (4 choose 2) = 6 ways.

After selecting the 3s and 6s, we have one remaining card to choose from the remaining 44 cards in the deck.

Thus, the total number of hands that contain exactly two 3s and two 6s is: 6 * 6 * 44 = 1584.

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Answer:

7:6

14:12

28:24

Answer:

The method of substitution involves three steps:

Solve one equation for one of the variables.

Substitute (plug-in) this expression into the other equation and solve.

Resubstitute the value into the original equation to find the corresponding variable.

Step-by-step explanation: