define a variable and write an inequality to model each situation. The school auditorium can seat at most 1200 people.

Given the information, we can determine that the cost of the toothbrush is $1.15. To arrive at this, we created an equation based on the given information and solved for the unknown, which in this case is the cost of the toothbrush.

If Brooke buys a toothbrush and toothpaste for $2.95, and the toothbrush costs $.65 less than the toothpaste, we have to use the information to solve for the cost of the toothbrush.

Let's define the cost of the toothpaste as x. Therefore, the cost of the toothbrush would be x - $0.65 (since the toothbrush costs $0.65 less than the toothpaste).

The combined cost of the toothbrush and toothpaste is $2.95, so we can set up the equation: x + (x - $0.65) = $2.95

If we simplify and solve this equation, we get x = $1.80. That's the cost of the toothpaste. The cost of the toothbrush would therefore be $1.80 - $0.65 = $1.15.

So, the toothbrush costs $1.15.

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Answer:

Death Valley's elevation is -282 feet and Mount McKinley Alaska elevation is 20,320 feet

Step-by-step explanation:

Consider the provided information.

Integers are the number that do not contain any decimal or fraction. They contains positive counting number, negative counting numbers and zero.

For example:{...-3,-2,-1,0,1,2,3...}

It is given that Death Valley, California has the lowest elevation in the United States. It's elevation is 282 feet below sea level.

Mount McKinley Alaska has the highest elevation in the United States. It's elevation is 20,320 feet above sea level.

We need to use integers to describe these two locations in the United States.

Both the statements are related with sea level.

Let say the sea level is at the zero, if a point is below sea level then we will indicate it by placing a negative sign in the front of the number and if it is above the sea level then we will indicate it by placing a positive sign or no sign in the front of the number.

Now consider the provided information.

Death Valley's elevation is 282 feet below sea level.

Which can be written as: -282 Feet (In integer)

Mount McKinley Alaska elevation is 20,320 feet above sea level.

Which can be written as: 20,320 Feet (In integer)

With the given ratio of $9 for 6 sheets of sheetrock, the builder would spend $18 if he bought 12 sheets of sheetrock.

This is a question about simple ratios in mathematics. In the given situation, the ratio of the price is $9 for 6 sheets of sheetrock. To calculate the cost of 12 sheets, we simply need to multiply the price for 6 sheets by 2.

Alternatively, you could set up a proportion to solve this problem: 9 dollars / 6 sheets = x dollars / 12 sheets. After solving for x, we get x = 18 dollars.

So, if the builder bought 12 sheets of sheetrock, he would have spent $18.

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If the instantaneous velocity of an object is zero, then its acceleration must be zero.

If the instantaneous velocity of an object is zero, then its acceleration must be zero. When the velocity is zero, it means the object is not changing its position and therefore not accelerating. So, if the instantaneous velocity is zero, the acceleration is also zero.

Final answer:

An object with an instantaneous velocity of zero could still have positive or negative acceleration, or no acceleration at all. Additional information about the forces acting on the object or its further motion is needed to determine the acceleration.

Explanation:

If the instantaneous velocity of an object is zero, this does not necessarily mean that its acceleration must also be zero. Instantaneous velocity being zero simply indicates that at that particular instant, the object is not moving. However, the object could be accelerating (either positively or negatively), which means it could start moving immediately after. For example, a ball thrown vertically upwards has an instantaneous velocity of zero at the peak of its trajectory, but the acceleration due to gravity is still acting on it, giving it a negative acceleration. Acceleration can also be positive if the object starts to move from a state of rest due to a force. Therefore, with only the information that instantaneous velocity is zero, we cannot determine the acceleration without additional context about the forces acting on the object or its subsequent motion.

The correct answer to the question is: not enough information.

Answer:

[tex]-46[/tex] meters per year.

Step-by-step explanation:

We have been given that a glacier advanced down a mountain from an elevation of 2010 m to 1780 m in 5 years.

[tex]\text{Rate of change}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\text{Rate of change}=\frac{1780-2010}{5-0}[/tex]

[tex]\text{Rate of change}=\frac{-230}{5}[/tex]

[tex]\text{Rate of change}=-46[/tex]

Since the glacier is melting down, therefore, the glacier's rate of change would be [tex]-46[/tex] meters per year.

Answer:24

Step-by-step explanation:

To find the distance from Pittsburgh as a function of time, the formula is d = 80 miles + (65 miles/hour × t). The distance increases by 65 miles for each hour of travel.

To find a formula for distance (d) from Pittsburgh as a function of travel time (t), we use the concept that velocity equals distance divided by time (v=d/t). Since you start 80 miles east of Pittsburgh and drive east at a constant speed of 65 miles per hour, your distance from Pittsburgh increases linearly with time. The formula will be:

d = start_distance + (velocity
× time)

d = 80 miles + (65 miles/hour × t)

So, for example, if you drive for 2 hours (t=2), the distance (d) from Pittsburgh will be:

d = 80 miles + (65 miles/hour × 2 hours) = 80 miles + 130 miles = 210 miles

After 9 months, the amount she has paid for the car is 2375.

Given,

Felicity put down 800 on a used car.

She took out a loan to pay off the balance of the cost of the car.

Monthly payment = 175.

We need to find the amount paid for the car after 9 months.

It is a sum of money that a buyer pays in the early stages of purchasing a good.

We have,

Down payment = 800

Monthly pay = 175

So we can write it as,

1 month = 175

Multiply 9 on both sides.

We get,

9 x 1 month = 9 x 175

9 months = 1575

The total amount she has paid after 9 months is :

= Down payment + 9 months payment

= 800 + 1575

= 2375.

Thus after 9 months, the amount she has paid for the car is 2375.

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Answer:

Harry's weight fluctuated significantly within minutes, indicating a potential issue with the scale's accuracy or calibration. He should address the problem to ensure reliable weight measurements.

Explanation:

It seems like there might be a problem with the scale's accuracy or consistency. Harry's weight fluctuated significantly within just a few minutes, which is highly unlikely under normal circumstances. Such drastic changes in weight in such a short amount of time are not physically possible, indicating a potential issue with the scale's functionality or calibration. It's possible that the scale is malfunctioning, providing inaccurate readings, or there may be external factors affecting the measurements, such as an unstable surface or improper usage of the scale. It's important for Harry to address this issue with the scale and possibly seek assistance from a professional to ensure accurate and reliable weight measurements.

The statement that If a figure has four congruent angles, then it is a square is a false conditional statement which is the correct option (A).

A conditional statement is defined as the two fundamental components that make up a conditional statement are Hypothesis (if) and Conclusion (then).

Let us consider the example to understand the parts of a conditional statement.

Conditional Statement: If today is Friday, then yesterday was Thursday.

Hypothesis: "If today is Friday."

In the given problem,

Conditional Statement:  If a figure has four congruent angles, then it is a square

Hypothesis: "If a figure has four congruent angles"

One example of a counterexample is a rectangle, which although not a square, has four congruent angles.

Hence, the statement that If a figure has four congruent angles, then it is a square is a false conditional statement which is the correct option (A).

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Answer:

The correct option is C.

Step-by-step explanation:

From the given figure it is clear that the vertices of the parallelogram are (0,0), (0,-6), (4,-8) and (4,-2).

If a figure rotated 180° about (a,b), then

[tex](x,y)\rightarrow (2a-x,2b-y)[/tex]

If the figure rotated 180° about (2,-4), then

[tex](x,y)\rightarrow (2(2)-x,2(-4)-y)[/tex]

[tex](x,y)\rightarrow (4-x,-8-y)[/tex]

So, the vertices of image after rotated 180° about (2,-4) are

[tex](0,0)\rightarrow (4,-8)[/tex]

[tex](0,-6)\rightarrow (4,-2)[/tex]

[tex](4,-8)\rightarrow (0,0)[/tex]

[tex](4,-2)\rightarrow (0,-6)[/tex]

The vertices of image are same as vertices of preimage. So, 180° rotation about (2,-4) maps the figure onto itself.

Therefore the correct option is C.

Answer:

The Answer Is True

Step-by-step explanation: