Town Hall is located 4.3 miles directly east of the middle school. The fire station is located 1.7 miles directly north of Town Hall.
What is the length of a straight line between the school and the fire station? Round to the nearest tenth.

Mollie and Ted can use the Side-Side-Side (SSS) postulate to justify why their triangles must be congruent.

According to the given information, the two triangles share three corresponding sides of equal length: ML = TD, OL = ED, and L = D.

The SSS postulate states that if three corresponding sides of two triangles are congruent, then the triangles are congruent. Therefore, because Mollie's triangle and Ted's triangle share three corresponding sides of equal length, they are congruent by the SSS postulate.

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The cost of one apple is $2.15.

To find the cost of one apple, we can set up a system of equations with the given information. Let's use A for the cost of one apple and B for the cost of one banana:

1) 4A + 9B = $12.70
2) 8A + B = $17.70

Now, we can solve this system of equations. We can multiply equation 1 by 2 to match the number of apples in equation 2:

1) 8A + 18B = $25.40

Now subtract equation 2 from the modified equation 1:

(8A + 18B) - (8A + B) = $25.40 - $17.70
17B = $7.70

Now, divide by 17 to find the cost of one banana:
B = $7.70 / 17 = $0.45

Now that we know the cost of one banana, we can substitute B in equation 2 to find the cost of one apple:

8A + ($0.45) = $17.70
8A = $17.25
A = $17.25 / 8 = $2.15

So, the cost of one apple is $2.15.

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Using Pythagorean theorem the distance between the school and the fire station is approximately 4.7 miles, while the distance between the school and the hospital is approximately 7.8 miles.

To solve this problem, we can use the Pythagorean theorem to find the distances and then add them up to get the total distance between the school and the fire station, and then between the school and the hospital.

Part A:

Let's call the middle school point A, Town Hall point B, and the fire station point C. We can draw a right triangle with AB as the base, BC as the height, and AC as the hypotenuse. Using the Pythagorean theorem, we have:

AC^2 = AB^2 + BC^2

AC^2 = 4.3^2 + 1.7^2

AC^2 = 18.98 + 2.89

AC^2 = 21.87

AC ≈ 4.7 miles (rounded to the nearest tenth)

Therefore, the length of the straight line between the school and the fire station is approximately 4.7 miles.

Part B:

Let's call the hospital point D. We can draw another right triangle with CD as the base, BC as the height, and BD as the hypotenuse. Using the Pythagorean theorem, we have:

BD^2 = BC^2 + CD^2

BD^2 = 1.7^2 + 3.1^2

BD^2 = 2.89 + 9.61

BD^2 = 12.5

BD ≈ 3.5 miles (rounded to the nearest tenth)

Now, we can add the distance between A and B (4.3 miles) to the distance between B and D (3.5 miles) to get the total distance between A and D:

AD ≈ 7.8 miles (rounded to the nearest tenth)

Therefore, the length of the straight line between the school and the hospital is approximately 7.8 miles.

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The most common distance in miles would be = 1,200 miles.

To determine the distance that is most travelled the following is considered;

The total number of road trips = 7

On day 3 the distance travelled = 600 and 1,200 miles

On day 4 the distance travelled = 1,000,1,100 and 1,200 miles

On day 5 the distance travelled = 800 miles.

On day 6 the distance travelled = 1,300 miles

Therefore the most travelled distance = 1,200 miles.

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The average speed that your brother was traveling is approximately 45.63 miles per hour

The average speed is the total distance traveled divided by the total time taken. So we have:

Average speed = total distance ÷ total time

We are given the total distance as 115 miles and the total time as 2.52 hours. Therefore, the average speed is:

Average speed = 115 miles ÷ 2.52 hours

Average speed = 45.63 miles per hour

So, the average speed that your brother was traveling is approximately 45.63 miles per hour.

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The area of a rectangle can be found by multiplying its length and width.

To find the area of rectangles with different perimeters, we need to use the formula:

Area = length x width

Possible dimensions:

Length = 5 cm, Width = 3 cm

Length = 4 cm, Width = 4 cm

Area of the first rectangle = 5 cm x 3 cm = 15 cm²

Area of the second rectangle = 4 cm x 4 cm = 16 cm²

Possible dimensions:

Length = 6 cm, Width = 4 cm

Length = 5 cm, Width = 5 cm

Area of the first rectangle = 6 cm x 4 cm = 24 cm²

Area of the second rectangle = 5 cm x 5 cm = 25 cm²

Possible dimensions:

Length = 4 cm, Width = 3 cm

Area of the rectangle = 4 cm x 3 cm = 12 cm²

Therefore, the areas of the possible rectangles with perimeters 16cm, 20cm, and 14cm are:

For perimeter 16cm: 15 cm² and 16 cm²

For perimeter 20cm: 24 cm² and 25 cm²

For perimeter 14cm: 12 cm²

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The length of NM and OL in the parallelogram LMNO are both 36 units.

Since LMNO is a parallelogram, we know that opposite sides are equal in length. Therefore, we can set NM and OL equal to each other:

NM = OL

We also know that NM = x + 27 and OL = 3x + 9, so we can substitute these expressions into the equation:

x + 27 = 3x + 9

Solving for x:

2x = 18

x = 9

Now that we know x, we can substitute it back into the expressions for NM and OL:

NM = x + 27 = 9 + 27 = 36

OL = 3x + 9 = 3(9) + 9 = 36

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Verónica jogged 7/4 or 1 and 3/4 more miles in the first week than in the second week.

Verónica jogged 10 3/16 miles in the first week and 8 7/16 miles in the second week. To find how many more miles she jogged in the first week, we need to subtract the distance she jogged in the second week from the distance she jogged in the first week:

10 3/16 miles - 8 7/16 miles

We need to first convert both mixed numbers to improper fractions:

10 3/16 = (10 x 16 + 3) / 16 = 163 / 16

8 7/16 = (8 x 16 + 7) / 16 = 135 / 16

Now we can subtract the two fractions:

163 / 16 - 135 / 16 = (163 - 135) / 16 = 28 / 16

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor (GCF), which is 4:

28 / 16 = (4 x 7) / (4 x 4) = 7 / 4

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Answer:

B) <FBG

Step-by-step explanation:

An adjacent angle is an angle that is right next to the given angle.

In this case, the given angle is <EBF.

We can see that the only 2 options here for an adjacent set of angles is either <FBG or <EBD.

Looking at the options, we can only see that <FBG is an option, making B the correct option.

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The number of times that the little monsters will do an overhead press and a squat at the same instant  during the drill is: 3 times

We are told that, Rote tells the little monsters to carry out an overhead press every 12 seconds and then also a squat every 30 seconds.

Thus, prime factorization of 12: 2² x 3.

Thus, prime factorization of 30: 2 x 3 x 5.

For us to get the least common multiple, we will have to find the highest power of each of the prime factors that show up in either factorization. Therefore, we can say that the smallest common multiple of 12 and 30 are: 2² x 3 x 5 = 60

This tells us that the little monsters will carry out an overhead press and then a squat at the same instant for every 60 seconds.

For us to find how many times this will occur during the 200-second drill, we will then divide 200 by 60:

200 ÷ 60 = 3 remainder 20

This tells us that there will exist 3 complete cycles of both of the exercises during the 200-second drill, with an additional 20 seconds left over.

Therefore, we can say that the little monsters will do an overhead press and a squat at the same instant 3 times during the drill.

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The solution is, Options 1, 3, and, 5 are true.

The statements given are,

1.)   The product of reciprocals is 1.

Let the fraction be a/b , and reciprocal be b/a ,

The product of the two will be 1.

Hence, the statement is true.

2.)   To divide fractions, multiply the divisor by the reciprocal of the dividend.

Let the fraction be a/b , now,

a/b*1/a = a^2/b,

Hence, the statement is false.

3.)    The reciprocal of a whole number is 1 over the number.

Let the number be  3, now,

The reciprocal of number 3 is 1/3 .

Hence, the statement is true.

4.)   Reciprocals are used to multiply fractions.

The statement is false, Reciprocals are not used to multiply fractions.

5.)    To find the reciprocal of a fraction, switch the numerator and denominator.

Let the fraction be a/b , then the reciprocal will be b/a .

Hence, the statement is true.

Therefore, Options 1, 3, and, 5 are true.

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complete question:

Select all that apply. Determine which of the following statements are true of reciprocals. Select all that apply. The product of reciprocals is 1 To divide fractions, multiply the divisor by the reciprocal of the dividend The reciprocal of a whole number is 1 over the number Reciprocals are used to multiply fractions To find the reciprocal of a fraction, switch the numerator and denominator

Josue and Pho brought 3 1/5 liters of lemonade altogether

Josue and Pho brought 1 3/5 liters of lemonade each, so the total amount of lemonade they brought is:

1 3/5 + 1 3/5 = 3 1/5

To add the two mixed numbers, we first need to find a common denominator. In this case, the common denominator is 5. Then we convert both mixed numbers into fractions with a denominator of 5:

1 3/5 = (5 × 1 + 3) / 5 = 8/5

1 3/5 = (5 × 1 + 3) / 5 = 8/5

Now we can add the fractions:

8/5 + 8/5 = (8 + 8) / 5 = 16/5

Finally, we can convert the fraction back to a mixed number:

16/5 = 3 1/5

Therefore, Josue and Pho brought 3 1/5 liters of lemonade altogether.

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Therefore , the solution of the given problem of unitary method comes out to be  the carpenter divided the wood into 60 pieces.

The well-known minimalist approach, current variables, and any crucial elements from the initial Diocesan tailored query can all be used to accomplish the work. In response, you can be granted another chance to utilise the item. If not, important impacts on our understanding of algorithms will vanish.

Here,

Divide the overall length of the wood by the length of each piece to get how many pieces the carpenter cut.

Each piece measures 0.25 feet, or 1/4 of a foot.

By dividing the overall length of the wood by the length of each component, we can determine the number of pieces:

=> Quantity = Length overall / Length of each element

=> Piece count is 15 feet divided by 0.25 feet. or 15/0.25

=> There are 60 parts total.

So, the carpenter divided the wood into 60 pieces.

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The given equation 4x - y = 18 and -4x + y = -18 has b. infinitely many solutions.

To determine how many solutions there are for the system of equations 4x - y = 18 and -4x + y = -18, follow these steps:

Step 1: Notice that the second equation is just the negative of the first equation:
4x - y = 18
(-1)(4x - y) = (-1)(18)
-4x + y = -18

Step 2: Since the second equation is just the negative of the first, the two equations are dependent and represent the same line.

Step 3: When two equations represent the same line, there are infinitely many points where they intersect, as they overlap completely.

So, the answer is: b. infinitely many solutions.

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There are 17,576,000 different license plates possible, considering 26 letters (A-Z) and 10 numbers (0-9).

There are 26 options for each of the three letters and 10 options for each of the three numbers. Therefore, using the multiplication principle, the total number of possible license plates is 26 x 26 x 26 x 10 x 10 x 10 = 17,576,000.

Alternatively, we can use the permutation formula to calculate the number of arrangements: P(26,3) x P(10,3) = 15,600 x 720 = 11,251,200.

However, since order does not matter in a license plate, we need to divide by the number of permutations of three letters and three numbers, which is 3! x 3! = 36, resulting in 11,251,200 / 36 = 17,576,000 possible license plates.

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The best inequality that represents the relationship between the amount of hydrochloric acid (x) and the amount of distilled water (y) in the given graph is 3y - 2x > 0, option D is correct.

The graph shows a straight line with a negative slope passing through the origin. As the amount of hydrochloric acid, x, increases, the amount of distilled water, y, decreases

To see why, let's use a point on the line, such as (2, 3), and plug it into the inequality. We get:

3(3) - 2(2) > 0

9 - 4 > 0

This is true, so the point (2, 3) is a solution to the inequality. Any point on the line will also satisfy this inequality since it represents all possible combinations of x and y that Corrine can use in her experiment.

Alternatively, we can rewrite the inequality in slope-intercept form:

y < (2/3)x

This means that the y-values on the line are less than the corresponding values of (2/3)x. So as x increases, y must decrease to stay below the line. This confirms that 3y - 2x > 0 is the correct inequality.

Hence, option D is correct.

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The correct question is:

For a science experiment, Corrine is adding hydrochloric acid to distilled water. The relationship between the amount of hydrochloric acid, x, and the amount of distilled water, y, is graphed below. Which inequality best represents this graph?

A. 2y - 3x < 0

B. 3y - 2x < 0

C. 2y - 3x > 0

D. 3y - 2x > 0

Answer:

Step-by-step explanation:

Let's call the two numbers x and y. We know that:

x + y = 30 (since the sum of the two numbers is 30)

We want to find the values of x and y that maximize their product, which is given by:

P = xy

To solve for x and y, we can use the fact that the sum of the two numbers is 30, so we can rewrite one of the numbers in terms of the other:

y = 30 - x

Substituting this into the equation for the product, we get:

P = x(30 - x)

Expanding this expression, we get:

P = 30x - x^2

To find the maximum value of P, we can take the derivative of this expression with respect to x and set it equal to zero:

dP/dx = 30 - 2x = 0

Solving for x, we get:

x = 15

So one of the numbers is x = 15, and the other is y = 30 - x = 15.

To confirm that this gives the maximum product, we can take the second derivative of P with respect to x:

d2P/dx2 = -2

Since the second derivative is negative, this means that the function P = 30x - x^2 has a maximum at x = 15.

Therefore, the two numbers are 15 and 15, and their product is maximized at P = 15 * 15 = 225.

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The product of the given expression is 2,916,000,000x³√(9,900x²).

The given expression contains several terms with roots and variables. To simplify and find the product, we'll first multiply the terms with similar roots and variables. The expression is:

√(3x)√5 √(15x)√2 √(30) 3x√5 3√(165x) √10 √6 3x√5 √6 √(10x) √5 √(3x) √10 √6 3x√5 √10 √6 √(3x) √5 √(3x) √10 √6

We can group terms with the same roots and variables together:

(√(3x))⁴ (3x)³ (√5)⁴ (√10)³ (√6)³ √15x √2 √30 √165x

Now, we can simplify each group:

81x³ * 625 * 1000 * 216 * √(2 * 15x * 30 * 165x)

Combine the constants and variables under the root:

81x³ * 625 * 1000 * 216 * √(9,900x²)

Calculate the product of the constants:

13,500,000 * 216 = 2,916,000,000

So, the final simplified expression is:

2,916,000,000x³√(9,900x²)

In summary, the product of the given expression is 2,916,000,000x³√(9,900x²).

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Doug is filing singly, and his net taxable income is $80,575. The tax amount for this income range is $16,539. Every week, $304 is withheld from his earnings for income tax. Doug can expect he will owe an additional $731. So option d is the correct answer.

Since the result is a positive number, Doug will owe an additional $731 when his taxes are due. Therefore, the correct answer is d. Doug will owe an additional $731.

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The volume of the prism in 120 cubic centimeter.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is a scalar quantity that characterizes the "size" or "capacity" of an object in three dimensions.

A prism is a three-dimensional geometric shape that has two parallel and congruent bases connected by lateral faces that are typically rectangular or parallelogram-shaped. Prisms are classified based on the shape of their base, such as rectangular prisms, triangular prisms, pentagonal prisms, hexagonal prisms, and so on. The lateral faces of a prism are perpendicular to the bases, and the bases are usually parallel to each other.

According to the given information:

Given the measures of prism is length = 8cm, breadth = 6 cm, height = 5 cm

The formula for volume of prism = 1/2 l*b*h

                                                      = 1/2 8*6*5

                                                      = 120 cubic centimeter

Hence the volume of prism is 120 cubic centimeter.

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Molly gave away 90 trading cards, which is option (c).

Let's start by figuring out how many trading cards Marcus gave away. We know that Molly gave away n trading cards, so she has 250 - n cards left. Marcus gave away three times as many cards as Molly did, so he gave away 3n cards. That means he has 430 - 3n cards left.

We also know that Molly and Marcus have the same number of trading cards left, so:

250 - n = 430 - 3n

Simplifying and solving for n, we get:

2n = 180

n = 90

Therefore, Molly gave away 90 trading cards, which is option (c).

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The single simplified fraction is (m + n)(p + m) / 2m.

To simplify the expression

[tex](3m^2 - 3n^2) / (m^2 + mp)÷ (6m - 6n) / (p + m)[/tex]

we need to invert the second fraction and multiply by the first.

[tex](3m^2 - 3n^2) / (m^2 + mp) \times (p + m) / (6m - 6n)[/tex]

We can then factor out a 3 from the numerator and the denominator, and cancel out the (m - n) terms. 3(m + n)(m - n) / 3m(m - n) x (p + m) / 6(m - n)

Simplifying further, we can cancel out the 3's and the (m - n) terms. (m + n) / m x (p + m) / 2

The simplified expression is (m + n)(p + m) / 2m.

To simplify the given expression, we invert the second fraction and multiply it by the first. Then we factor out common terms and cancel out like terms. We simplify the expression to obtain the single fraction (m + n)(p + m) / 2m.

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The base is decreasing at 1.917 cm/min when altitude is 12cm and  area=84cm².

Let A be the area of the triangle, h be the height of the triangle, and b be the base of the triangle.

Then the formula for the area of a triangle is:

A = (1/2)bh

We are given that dh/dt = 2.5 cm/min (the height is increasing at a rate of 2.5cm/min), and dA/dt = 3 cm²/min (the area is increasing at a rate of 3cm²/min).

We want to find db/dt, the rate of change of the base of the triangle when h = 12 cm and A = 84 cm².

To solve this problem, we need to use the chain rule of differentiation.

We start by differentiating both sides of the formula for the area of a triangle with respect to time t:

dA/dt = (1/2) d/dt (bh)

Next, we can use the product rule of differentiation to find d/dt (bh):

d/dt (bh) = b dh/dt + h db/dt

Substituting this into the previous equation gives:

dA/dt = (1/2) [ b dh/dt + h db/dt ]

Now we can substitute the given values of dh/dt and dA/dt, as well as h = 12 cm and A = 84 cm².

To find db/dt:

3 cm²/min = (1/2) [ b (2.5 cm/min) + 12 cm db/dt ]

Simplifying this expression gives:

6 cm²/min = 2.5 b cm²/min + 12 cm db/dt

Substituting A = 84 cm² and h = 12 cm into the formula for the area of a triangle gives:

84 cm² = (1/2) b (12 cm)

Simplifying this expression gives:

b = 14 cm

Now we can substitute b = 14 cm into the previous equation to find db/dt:

6 cm²/min = 2.5 (14 cm) cm²/min + 12 cm db/dt

Simplifying this expression gives:

db/dt = (6 cm²/min - 35 cm²/min) / (12 cm)

db/dt = -1.917 cm/min (rounded to three decimal places)

Therefore, the base of the triangle is decreasing at a rate of 1.917 cm/min when the height is 12 cm and the area is 84 cm².

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Answer:

Step-by-step explanation:

you take 24 multiplied by 18 then by 8 and that'll equal

24 x 18 x 8 = 3456

Answer:

r = 14.60

Step-by-step explanation:

r²= 9²+(23/2)²

= 9²+11.5²

= 81+132.25

r² = 213.25

r = √213.25

= 14.60 to 2d.p

Answer:

Step-by-step explanation:

The arc length formula is

[tex]L=\frac{\theta}{360}*2\pi r[/tex]

Theta is the angle that intersects arc HJ. That measure is 180-122 which is 58 degrees. We put that into the formula along with the radius measure of 10 to get:

[tex]L=\frac{58}{360}*2\pi (10)[/tex] which gives us, rounded to the nearest hundredth,

L = 10.12 units

We solve this problem using the angle of elevation, we can apply the tangent function from trigonometry. The approximate distance between the fishing vessel and the base of the lighthouse is 235.2 meters, which corresponds to option C. 235. 2 meters

Find the approximate distance between the fishing vessel and the base of the 50-meter-tall lighthouse when the angle of elevation is 12 degrees.
Set up the equation using tangent function.
tan(angle of elevation) = (height of lighthouse) / (distance between vessel and lighthouse base)
Plug in the values.
tan(12°) = 50 / distance
Solve for the distance.
distance = 50 / tan(12°)
Calculate the distance using a calculator.
distance ≈ 235.2 meters
So, the approximate distance between the fishing vessel and the base of the lighthouse is 235.2 meters, which corresponds to option C. 235. 2 meters

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The net worth of the Worthington family is $28,900, which is greater than the requirement of $100,000 for the loan. Therefore, they meet the net worth requirement for the loan.

To calculate the net worth of the Worthington family, we need to add up all their assets and subtract their liabilities (debts). Let's start by listing them:

Assets:

- Savings account: $18,800

- Vehicles: $64,600

- Antique necklace: $6,200

- College fund: $24,700

Total assets: $114,300

Liabilities:

- Mr. Worthington's student loans: $85,400

Total liabilities: $85,400

To calculate the net worth, we subtract the liabilities from the assets:

Net worth = Total assets - Total liabilities

Net worth = $114,300 - $85,400

Net worth = $28,900

The net worth of the Worthington family is $28,900, which is greater than the requirement of $100,000 for the loan. Therefore, they meet the net worth requirement for the loan.

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Answer: V = 2527.2 in^3

Step-by-step explanation:

V = Bh

that is, Volume = base area x height

the base area is the hexagon, and the height is given as 12.

Think of dividing the hexagon into 6 equal triangles, with height 7.8

so the area of all 6 triangles, (effectively the area of the hexagon), will be:

6(0.5 x 9 x 7.8) = 210.6 in^2

multiply this by the height to get the volume:

210.6 x 12 = 2527.2 in^3

thats it!

V = 2527.2 in^3

To find the temperature at 6pm, we need to start with the temperature at 9am and then add or subtract the changes in temperature that occurred during the day.

We know that the temperature at 9am was -1.9°F. Between 9am and noon, the temperature rose 11.3°F, so at noon the temperature was:

-1.9 + 11.3 = 9.4°F

Between noon and 3pm, the temperature dropped 7.9°F, so at 3pm the temperature was:

9.4 - 7.9 = 1.5°F

Between 3pm and 6pm, the temperature dropped 12.7°F, so at 6pm the temperature was:

1.5 - 12.7 = -11.2°F

Therefore, the temperature at 6pm was -11.2°F.