Stephanie wanted to solve the equation 16=3x+1. Which inverse operations should she use to find the solution?

The quadrilateral PQRS is a parallelogram since opposite sides PQ and SR have the same lengths and slopes.

To determine the correctness of the statements and calculate the lengths and slopes of the given quadrilateral PQRS, let's perform a coordinate proof.

Length and slope of PQ:

The coordinates of points P and Q are P(0, 2) and Q(3, -4), respectively.

Length of PQ: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(3 - 0)² + (-4 - 2)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of PQ: (y₂ - y₁) / (x₂ - x₁)

= (-4 - 2) / (3 - 0)

= -6 / 3

= -2

Therefore, the length of PQ is approximately 3√5, and its slope is -2.

Length and slope of SR:

The coordinates of points S and R are S(-2, 1) and R(1, -5), respectively.

Length of SR: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(1 - (-2))² + (-5 - 1)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of SR: (y₂ - y₁) / (x₂ - x₁)

= (-5 - 1) / (1 - (-2))

= -6 / 3

= -2

Therefore, the length of SR is approximately 3√5, and its slope is -2.

Length and slope of SP:

The coordinates of points S and P are S(-2, 1) and P(0, 2), respectively.

Length of SP: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(0 - (-2))² + (2 - 1)²]

= √[4 + 1]

= √5

Slope of SP: (y₂ - y₁) / (x₂ - x₁)

= (2 - 1) / (0 - (-2))

= 1 / 2

Therefore, the length of SP is √5, and its slope is 1/2.

Length and slope of HQ:

The coordinates of points H and Q are H(0, 2) and Q(3, -4), respectively.

Length of HQ: √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(3 - 0)² + (-4 - 2)²]

= √[9 + 36]

= √45

= 3√5 (approx.)

Slope of HQ: (y₂ - y₁) / (x₂ - x₁)

= (-4 - 2) / (3 - 0)

= -6 / 3

= -2

Therefore, the length of HQ is approximately 3√5, and its slope is -2.

Based on the calculations, we can conclude that both statements are correct:

The quadrilateral PQRS is a parallelogram since opposite sides PQ and SR have the same lengths and slopes.

The quadrilateral PQRS is not a rectangle since the lengths of the adjacent sides PQ and SP are not equal.

Summary:

Length of PQ is approximately 3√5, and its slope is -2.

Length of SR is approximately 3√5, and its slope is -2.

Length of SP is √5, and its slope is 1/2.

Length of HQ is approximately 3√5, and its slope is -2.

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Answer:

5

She must therefore earn 5 points on the last test to achieve a mean score of 4.

Step-by-step explanation:

The sum of the data divided by the total number of data represents the mean, which is the average of a set of data.

The solution of this equation is z = 3.

We are given that;

1-3+4z = 1

Now,

To solve for z, we need to isolate it on one side of the equation. We can do this by following these steps:

Subtract −31​

from both sides to eliminate it from the left side.

Multiply both sides by z to eliminate the fraction on the left side.

Divide both sides by 4 to isolate z on the left side.

Let’s see how this works:

−31​+z4​=1

−31​+z4​=1

z4​=1+31​

z4​=34​

4=4/3 ​z

z=3*4​/4​

z=4/4×3​

z=3

Therefore, by the equation answer will be z = 3.

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It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

We have,

To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.

The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.

Let's calculate the number of half-lives required to reach 150mg:

Initial amount of aspirin = 625mg

Final amount of aspirin = 150mg

625mg / 150mg = 4.17

This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.

Since each half-life is 6 hours, we can calculate the total time it will take:

Total time = Number of half-lives * Half-life duration

Total time = 4.17 x 6 hours

Total time ≈ 25 hours and 1 minute

Therefore,

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

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Answer:

42

Step-by-step explanation:

Rectangle: A = 6 x 5 = 30

Triangle: A = 1/2(6 x 4) = 12

Area of figure: 30 + 12 = 42

Answer: 4 small bags, 3 large bags (equations below in explanation)

Step-by-step explanation:

x=number of small bags

y=number of large bags

x+y=7

4x+10y=52

Subtract them after multiplying the first equation by 4.

4x+4y=28

4x+10y=52

-6x=-24

x=4

x+y=7

4+y=7

y=3

The percentage discount between $38 and $95 is 150%.

We shall follow these steps to estimate the percentage discount between $38 and $95:

First, find the difference between the original price and the discounted price.

Next, divide the result by the original price.

Finally, multiply the result by 100 to present it as a percentage.

Given:

Original price = $95

Discounted price = $38

Difference = $95 - $38 = $57.

Next, Difference / Original price  * 100:

($57 / $38) * 100 ≈ 150%

Therefore, the percentage discount between $38 and $95 is 150%.

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These are the coordinates of the vertices of the transformed triangle.

Vertex A: (-15, 8)

Vertex B: (-4, 5)

Vertex C: (-9, 6)

To plot ΔABC and perform the given transformations, let's follow the steps:

Plot ΔABC:

Point A(10,4)

Point B(-1,1)

Point C(4,2)

Reflect ΔABC by multiplying the x-coordinates by -1:

Reflecting A: (-10,4)

Reflecting B: (1,1)

Reflecting C: (-4,2)

Translate the reflected triangle using the function (x,y) → (x-5, y+4):

Translating (-10,4): (-10-5, 4+4) = (-15, 8)

Translating (1,1): (1-5, 1+4) = (-4, 5)

Translating (-4,2): (-4-5, 2+4) = (-9, 6)

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If the height (h) of the prism is less than or equal to 0.978 cm, then Andrea has enough modeling clay for both prisms. If the height exceeds 0.978 cm, she will be short of modeling clay.

Let's calculate the volumes of both prisms:

Volume of the first prism: V1 = (8.4 cm²) × h

Volume of the second prism: V2 = (16 × 8.4 cm²)×(4h)

= 537.6 cm³ h

We know that Andrea has 533.8 cm³ of modeling clay.

To determine if she has enough clay for both prisms, we need to compare the total volume of the prisms to the amount of clay she has:

Total Volume = V1 + V2 = (8.4 cm²) × h + (537.6 cm³ × h)

Total Volume = (546 cm²) × h

Now we can set up the equation:

Total Volume ≤ Amount of Clay

(546 cm²) × h ≤ 533.8 cm³

Solving for h:

h ≤ 533.8 cm³ / (546 cm²)

h ≤ 0.978 cm

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By connecting these points with a straight line, we can graph the line y = 3x - 8.

The line should have a positive slope, rising from left to right.

To graph the line y = 3x - 8, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this equation, m represents the slope of the line, and b represents the y-intercept.

Comparing the given equation with the slope-intercept form, we can see that the slope, m, is 3, and the y-intercept, b, is -8.

To plot the graph, we'll start by plotting the y-intercept, which is the point (0, -8)T.

his point represents where the line intersects the y-axis.

Next, we can use the slope to find additional points on the line. The slope of 3 means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3.

Starting from the y-intercept (0, -8), we can move 1 unit to the right and 3 units up to reach the next point (1, -5).

We can continue this pattern to plot more points.

Using this information, we can plot multiple points and then connect them to form the line:

Point 1: (0, -8)

Point 2: (1, -5)

Point 3: (2, -2)

Point 4: (-1, -11)

Point 5: (-2, -14)

By connecting these points with a straight line, we can graph the line y = 3x - 8.

The line should have a positive slope, rising from left to right.

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Answer:

60 degrees

Step-by-step explanation:

To convert radians to degrees, multiply by 180/pi

pi/3 * 180/pi = 180/3 = 60 degrees

Step-by-step explanation:

3 radians =

171.887 degrees

 AreaData Transfer RateDigital StorageEnergyFrequencyFuel EconomyLengthMassPlane AnglePressureSpeedTemperatureTimeVolume 

  ArcsecondDegreeGradianMilliradianMinute of arcRadian 

  ArcsecondDegreeGradianMilliradianMinute of arcRadian 

Formula

3rad × 180/π = 171.887°

Dependent variable: Total cost of riding the trolley

Independent variable: Number of times Henry rides the trolley.

In this scenario, the dependent variable is the total cost of riding the trolley, and the independent variable is the number of times Henry rides the trolley.

The dependent variable, the total cost of riding the trolley, depends on the independent variable, which is the number of times Henry rides the trolley. As Henry rides the trolley multiple times, the total cost will vary based on the number of rides.

The independent variable, the number of times he rides, determines the value of the dependent variable, the total cost.

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The quantity of goods and services that sellers are willing and able to sell is known as the quantity supplied.

Quantity supplied is defined as the amount of goods and services that a supplier is able to produce and sell at a given market price.

The quantity supplied differs from the actual amount of supply as price changes influence how much supply producers actually put on the market.

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Step-by-step explanation:

We can begin by using the fact that the selling price was 117.81, including a sales tax of 5%. Let x be the original price of the lawnmower.

After the discount of 32%, the selling price is:

0.68x + 0.05(0.68x) = 117.81

Simplifying and solving for x, we get:

0.68x + 0.034x = 117.81

0.714x = 117.81

x = 165

Therefore, the original price of the lawnmower was $165.

The index forms are of different bases and thus cannot be multiplied and their exponents added.

To determine Deigo's mistake, we need to know index forms and their rules.

Index forms are defined as mathematical forms that are used in representing numbers or variables that are too large or too small in more convenient forms.

They are also called scientific notation or standard forms.

The rules of index forms are;

From the information given, we have;

6⁴ × 8³ = 48⁴⁷

They are not of like bases and thus cannot be multiplied

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Answer:

189

Step-by-step explanation:

To multiply 31.5 percent by 600, you need to convert the percentage to a decimal by dividing it by 100 and then multiply it by 600.

31.5 percent = 31.5/100 = 0.315

Multiplying 0.315 by 600 gives us:

0.315 * 600 = 189

Therefore, 31.5 percent of 600 is equal to 189.

Both planes will reach the city at the same time again at 11 PM.

Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.

The periods for this problem are given as follows:

As 5 and 3 are prime numbers, the least common factor is given as follows:

5 x 3 = 15.

15 hours after 8 AM is of 11 PM.

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Answer:

Approx 8.47 [tex]m^2[/tex]

Step-by-step explanation:

First, find the area of the entire figure. Which can be found by multiplying the two sides of the square by each other=  [tex]6*6=36m^2[/tex]

Now, ignore the square and just focus on the pentagon and finding the area of that. The formula for the area of a pentagon is [tex]A=1/2Apothem*Perimeter[/tex]

In order to find the apothem, you can make a mini triangle and use trig (Tangent) to find the height (apothem) of the triangle. Then, you take the side length of the base of the pentagon which is 4 and then you multiply it by the number of sides (5) to get 20. Then, by plugging it into our formula, you use the apothem*10 (divided by 2) and you get the area, and then you just subtract that from 36.

Answer:

42

Step-by-step explanation:

Rectangle: A = 6 x 5 = 30

Triangle: A = 1/2(6 x 4) = 12

Area of figure: 30 + 12 = 42

Answer:

area of rectangle+area of triangle= area of figure

6×5 + 1/2×4×6=30+24= 42

or

given figure is a trapezium

so we know are of trapezium= 1/2×sum of parallel sides×height

= 1/2×( 5+9)×6

=42

The given box plot represented by the data sets in option A and B.

From the given box plot, we have

Minimum value = 3

Maximum value = 18

First quartile (Q1) = 7

Third quartile (Q3) = 13

Median = 10

Option A:

3, 4, 8, 9, 9, 12, 12, 13, 13, 16, 18

Median = 12

First quartile (Q1) = 8

Third quartile (Q3) = 13

Option B:

3, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 7

Third quartile (Q3) = 13

Option C:

3, 4, 8, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 8

Third quartile (Q3) = 13

Option D:

2, 4, 7, 9, 9, 10, 12, 13, 13, 16, 18

Median = 10

First quartile (Q1) = 7

Third quartile (Q3) = 13

Therefore, the correct options are B and D.

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Answer:

Step-by-step explanation:

48 out 52 cards are not a 2:

        [tex]P(not 2)=\frac{48}{52} =\frac{12}{13}[/tex]

An equation for the total cars and trucks for dealership A is: x + y = 164.

An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.

The number of cars that dealership A sold is: 98 cars.

The number of trucks that dealership B sold is: 66 trucks.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:

Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;

x + y = 164.

Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;

2x + 0.5y = 229.

By solving the systems of linear equations simultaneously, we have:

2x + 0.5(164 - x) = 229

1.5x + 82 = 229

x = 98 cars.

For the y-value, we have;

2(98) + 0.5y = 229

0.5y = 229 - 196

y = 33/0.5

y = 66 trucks.

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Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Given statement solution is :- On average, she spent approximately $115 per visit.

To calculate the total amount spent on the visits, we need to add up the co-payments and the cost of the shots.

Co-payments:

The co-pay for each visit is $25, and you visited the doctor 3 times a week for 8 weeks within 2 months. So the total co-payment is:

3 visits/week * $25/visit * 8 weeks = $600.

Shots:

You received the shot 2 times out of each visit, and you visited the doctor 3 times a week for 8 weeks within 2 months. So the total cost of the shots is:

2 shots/visit * $135/shot * 8 weeks = $2,160.

Total amount spent:

Co-payments + Shots = $600 + $2,160 = $2,760.

Therefore, the total amount spent for the visits and shots over 2 months is $2,760.

Trivia Answer:

To find out the average amount spent per visit, we can divide the total amount spent by the total number of visits. In this case, the total amount spent is $2,760, and the total number of visits is 3 visits/week * 8 weeks = 24 visits.

Average spent per visit = Total amount spent / Total number of visits

Average spent per visit = $2,760 / 24 visits

Average spent per visit ≈ $115.

Therefore, on average, you spent approximately $115 per visit.

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The simplified form of the rational expression [tex](7x)/(14x^6)[/tex] is [tex]1/(2x^6).[/tex]

To simplify the rational expression [tex](7x)/(14x^6)[/tex], we can begin by simplifying the numerator and denominator separately.

In the numerator, 7x, we can see that both 7 and x have a common factor of 7. So, we can rewrite the numerator as 7 × x = 7x.

In the denominator, [tex]14x^6[/tex], we can see that both 14 and x^6 have a common factor of [tex]2x^6[/tex].

So, we can rewrite the denominator as

[tex]14 \times x^6 = 2 \times 7 \times x^6 = 2 \times 7x^6.[/tex]

Now, we can simplify the rational expression by canceling out the common factors in the numerator and denominator:

[tex](7x)/(14x^6) = (7x)/(2 \times 7x^6) \\= (7x)/(2 \times 7 \times x^6) \\= (cross(7x))/(2 \times cross(7) \times x^6) \\= 1/(2x^6)[/tex]

Therefore, the simplified form of the rational expression[tex](7x)/(14x^6)[/tex] is [tex]1/(2x^6).[/tex]

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Given statement solution is :- The quartile value above which 75% of the data lies is 31.625.

To find the value above which 75% of the data lies, you can determine the third quartile (Q3) of the data set. In this case, the upper quartile (Q3) is given as 30.5.

Since the data is represented on a number line with tick marks every one-half unit, we can divide the range between Q3 and the maximum value (32) into four equal parts. Each part represents 25% of the data.

To find the value that corresponds to 75% of the data lying above, we need to determine the value that is three-fourths of the way between Q3 and the maximum value.

First, calculate the range between Q3 and the maximum value: 32 - 30.5 = 1.5.

Next, divide the range by four to find the size of one-fourth of the range: 1.5 / 4 = 0.375.

Now, multiply the size of one-fourth of the range by three to find the size of three-fourths of the range: 0.375 * 3 = 1.125.

Finally, add the size of three-fourths of the range to Q3 to find the value above which 75% of the data lies: 30.5 + 1.125 = 31.625.

Therefore, the quartile value above which 75% of the data lies is 31.625.

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Apologies, but your questions seem to have errors and incomplete information.

For the first question about Jessica and Melissa sharing 12 pieces of dried pears, it is unclear how much Jessica ate as the fraction is missing. Similarly, information about how many pears Melissa ate is also missing. To answer the question accurately, I need the missing information.

For the second question about the children playing in the park, you mentioned that one-third of the children returned home, but you didn't provide the total number of children initially in the park. Without that information, I cannot determine how many children stayed in the park.

Please provide complete and accurate information for a precise answer.

Answer:160 students

Step-by-step explanation:

did I do it

(your answer needs to be more than 20 characters long)

The algebraic expression for the sentence in this problem is given as follows:

n - (x + 8).

The sentence in this problem is given as follows:

"A number n minus the sum of the number and eight".

The sum of an unknown number x and eight is given as follows:

x + 8.

The subtraction of the number n by the expression is given as follows:

n - (x + 8).

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