What is the measure of ∠SPQ in this rhombus?
m∠SPR = (2x+13)°
m∠QPR = (3x−12)°

The US Constitution requires that there be a census every ten years in order to apportion the seats in the House of Representatives among the states. Census information is also used by federal, state, and local governments to assess needs and allocate funding, by academics to study the changing population, by individuals to trace their genealogy, and for many other purposes.

Assuming there are 4 walls

6/4 = 1.5 rolls per wall

Answer:

A

Step-by-step explanation:

Acceleration determines whether an object speeds up or slows down, which can be positive or negative based on the direction of motion and the chosen coordinate system. Negative acceleration occurs when an object slows down while moving in the positive direction or speeds up while moving in the negative direction. Positive acceleration occurs when an object speeds up in the positive direction or slows down in the negative direction.

Acceleration is the rate of change in velocity, and it can be characterized as positive or negative depending on its direction relative to a chosen coordinate system. Understanding acceleration involves recognizing how it affects an object's speed in relation to its direction of motion. Let's clarify which statements describe acceleration correctly.

It is important to distinguish between speeding up, slowing down, and the sign of acceleration. For example, if we assume rightward motion is positive:

Summarizing these principles:

This understanding can help distinguish between deceleration, which always indicates slowing down, and negative acceleration, which may increase speed if the velocity is also negative.

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The equation that describes Emily's robot's movement is y = -mx + c where 'm' is the number of steps per second the robot climbs down, and 'c' is the initial number of steps. The equation would be negative because the number of steps decreases over time.

In the given context, Emily's robot is being tested for its ability to climb down steps. As it performs this task, the number of steps it needs to climb down decreases over time. This relationship could be described by a linear equation. If every second the robot climbs down a fixed number of steps, this would translate to a constant rate of change or slope in the graph. Therefore, the equation would be of the form y = mx + c, where 'm' is the slope (representing the number of steps per second the robot climbs down) and 'c' is the y-intercept (representing the initial number of steps).

For instance, if the robot climbs down 1 step per second, and we started with 10 steps, the equation would be y = -x + 10 (negative because the number of steps is decreasing).

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To calculate the number of days between two dates, subtract the start date from the end date and add 1.

To find the number of days between two dates, you can use the formula:

Number of days = (End date) - (Start date) + 1

For example, if the start date is July 10, 2022, and the end date is July 15, 2022, the number of days between them would be:

Number of days = (15) - (10) + 1 = 6

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The number will be greater than 54 such that a negative one-sixth of a number is less than -9.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

A mathematical phrase in which the sides are not equal is referred to as being unequal.

Inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

Let's suppose that number is x

Then,

negative one-sixth of x

-(1/6)x is less than -9

-(1/6)x < -9

-x < -54

Multiplying by - will change the sign of inequality

So,

x > 54

Hence "The number will be greater than 54 such that a negative one-sixth of a number is less than -9".

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Answer:

1.25x>35

Step-by-step explanation:

If x is the number of times you must ride the subway and the monthly pass is $35, we must determine the expression where the cost per ride is greater than $35. Therefore:

1.25x>35

We can solve x to determine the number of rides you must ride for the monthly pass to be a better deal.

x>35/1.25

x>28

The student must take more than 28 rides for the mothly pass to be a better deal.

Answer:

A. p=6.25h

because

6.25 (2) = p 12.50

6.25 (4) = p 25.00

6.25 (6) = p 37.50

6.25 (8) = p 50.00

The measure of an interior angle of the regular polygon is 156 degrees and the polygon has 15 sides.

In a regular polygon, the measure of an exterior angle is equal to 360 degrees divided by the number of sides of the polygon. In this case, the measure of the exterior angle is given as 24 degrees. So we can set up the equation:

24 = 360 / n

Where n is the number of sides. Cross multiplying, we get:

n = 360 / 24 = 15

So the polygon has 15 sides. To find the measure of an interior angle, we can use the formula:

Interior Angle = 180 - Exterior Angle

Interior Angle = 180 - 24 = 156 degrees

To determine the number of one-dollar decreases that would yield a revenue of $55,000, set up the equation (1,700 + 200y) * (25 - x) = 55,000 and solve for x.

To determine the number of one-dollar decreases, x, that would yield a revenue of $55,000, we can set up an equation based on the given information.

Let y be the number of one-dollar decreases and (1,700 + 200y) be the number of tickets sold. The revenue can be calculated by multiplying the number of tickets sold by the price of each ticket. So in this case, the equation can be written as:

(1,700 + 200y) * (25 - x) = 55,000

Now we can solve this equation to find the value of x.

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The answer (APEX) is: "7 units."

The average rate of change of the function will be -93.75.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

Given that the interval from x = 0 to x = 2 and the function is [tex]f(x)=250(0.5)^x[/tex].

Calculate the value of the function at x = 0 and x = 2

[tex]f(x)=250(0.5)^x[/tex].

[tex]f(0)=250(0.5)^0=250\\f(0)=250(0.5)^2=62.5[/tex].

The average rate of change will be calculated as,

Rate of change = ( 62.5 - 250 ) ( 2 - 0)

Rate of change = -93.75

Therefore, the average rate of change of the function will be -93.75.

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slope =

7- - 2 =9

8-0 = 8

slope = -9/8

y intercept = 7

equation: y=-9/8x+7

The domain of the given function f(x)= -6x+11 for the given range is

{2,4,6,8}

Given :

The function f(x)= -6x+11  

range given by {-37,-25,-13,-1)

Range is the f(x) values . Domain are the x values .

To find out domain , we substitute the values of f(x) that is range and solve for x

First we substitute -37 for f(x) in the given function and solve for x

[tex]f(x)= -6x+11 \\x=-37\\-37=-6x+11\\-37-11=-6x\\-48=-6x\\x=8[/tex]

Now substitute -25 for f(x)

[tex]x=-25\\-25=-6x+11\\-25-11=-6x\\-36=-6x\\x=6\\\\\\x=-13\\-13=-6x+11\\-13-11=-6x\\-24=-6x\\x=4\\\\\\x=-1\\-1=-6x+11\\-1-11=-6x\\-12=-6x\\x=2[/tex]

x values are the domain

Domain is {2,4,6,8}

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Final answer:

The area of triangle ΔABC with m∠A = 120°, side b = 13 cm, and side c = 15 cm, when calculated using the formula for area ½ bc sin A, is approximately 84.2 cm² when rounded to the nearest tenth.

Explanation:

To find the area of triangle ΔABC with m∠A = 120°, side b = 13 cm, and side c = 15 cm, we will use the formula for the area of a triangle when two sides and the included angle are known:

Area = ½ bc sin A

First, we need to find the sine of angle A, which is sin(120°). Using a calculator, we find that sin(120°) ≈ 0.866. Now, we can plug in the values into the area formula:

Area = ½ × 13 cm × 15 cm × sin(120°)

Area = ½ × 13 cm × 15 cm × 0.866

Area ≈ ½ × 13 cm × 15 cm × 0.866 ≈ 84.225 cm²

Rounding to the nearest tenth, the area is approximately 84.2 cm².

Final answer:

To measure 1 liter, one could fill a 500 mL cup twice, or fill a 300 mL cup once, a 500 mL cup once, and a 100 mL cup twice, summing to a total of 1,000 mL which equals 1 liter.

Explanation:

To measure exactly 1 liter using cups of 100 mL, 300 mL, and 500 mL, we can use two different methods. It's important to note that 1 liter (L) equals 1,000 milliliters (mL). Here are the steps for each method:

Method 1:

Fill the 500 mL cup twice and pour the contents into another container. (500 mL + 500 mL = 1,000 mL)

This gives you exactly 1 liter, since 1,000 milliliters is equivalent to 1 liter.

Method 2:

First, fill the 300 mL cup and pour it into an empty container.

Then, fill the 500 mL cup and add it to the same container. (300 mL + 500 mL = 800 mL)

Lastly, fill the 200 mL remaining by using the 100 mL cup twice. (100 mL + 100 mL = 200 mL)

Combining all the measurements gives you 1,000 mL, which is exactly 1 liter. (800 mL + 200 mL = 1,000 mL)

Answer:

49.075 minutes

Step-by-step explanation:

Your welcome :]

Okay, well we start out with the equation P=66, where P is perimeter. You should create equations using variables to explain each piece of information you are given. Follow the equations below and see if you can understand how to do another one like this. In this problem, l is length and w is width.

P = 66                               The perimeter is equal to 66

l = 3 + w                           The length of one side is 3 more than the width

2l + 2w = 66                      A rectangle's perimeter is calculated by adding the lengths and widths

2(3 + w) + 2w = 66           Use what you know about length from step 2 to replace the variable in step 3

6 + 2w + 2w = 66              Multiply

6 + 4w = 66                       Add like terms

4w = 60                            Subtract

w = 15                             Divide

l = 3 + w                         Remember step 2?

l = 3 + 15                       Replace the variable using your value for w

l = 18                             Add

And you're done! Always check your work. It helps to create a picture of a rectangle while you're doing these problems as well. As you get used to these problems more and more, you can show more or less work than I've shown, but try to stay true to what the teacher asks of you. Good luck!