The function f(t) = t2 + 6t − 20 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work.
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know?
Part C: Determine the axis of symmetry for f(t)

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:

[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

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.

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.

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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Givens

x = - 1/3

y = 3x - 2

Problem solve for y

y = 3(-1/3) - 2

but 3 * (1/3) = 1

and 3 * (- 1/3) = - 1

So y = -1 - 2

y = - 3

Think of this as a money question. If you are one dollar in the whole and you spend 2 more, you are not 3 in the whole which is minus 3.

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.

multiply both sides by 2 to get

2A = (a+b)*h

divide both sides by h

 to get 2A/h = a+b

 subtract b from both sides to get a = 2A/h -b

3rd choice is correct

Option C - a = [tex]$\frac{2A-bh}{h}[/tex] is the correct alternative.

We have the formula for a trapezoid that relates the area - A, the two bases - a and b and the height - h as follows -

[tex]$A=\frac{(a+b)}{2} h[/tex]

We have to solve for ' a '.

On solving -

x( 1 + 2 + 3 + .... + n) = π

[tex]\frac{xn(n+1)}{2} =\pi[/tex]

[tex]x =\frac{2\pi }{n(n+1)}[/tex]

According to the question, we have -

[tex]$A=\frac{(a+b)}{2} h[/tex]

2A = (a + b)h

2A = ah + bh

2A - bh = ah

a = [tex]$\frac{2A-bh}{h}[/tex]

Hence, Option C is the correct alternative.

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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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