Mathematics College

a car's velocity is modeled by
\( v(t) = 0.5t {}^{2} - 10.5t + 45 \: for\leqslant t \leqslant 10.5\)
Where velocity is in feet per second and time is in seconds. When does the car come to a complete stop?​

A Car's Velocity Is Modeled By [tex] V(t) = 0.5t {}^{2} - 10.5t + 45 \: For\leqslant T \leqslant 10.5[/tex]Where

Answers

Answer 1

In accordance with the function velocity, the car will have a complete stop after 6 seconds.

When does the car stop?

Herein we have a function of the velocity of a car (v), in feet per second, in terms of time (t), in seconds. The car stops for t > 0 and v = 0, then we have the following expression:

0.5 · t² - 10.5 · t + 45 = 0

t² - 21 · t + 90 = 0

By the quadratic formula we get the following two roots: t₁ = 15, t₂ = 6. The stopping time is the least root of the quadratic equation, that is, the car will have a complete stop after 6 seconds.

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Related Questions

I NEED HELP ASAP PLEASE HELP

I NEED HELP ASAP PLEASE HELP

Answers

Answer:

C

Step-by-step explanation:

Solve for X in the questions​

Solve for X in the questions

Answers

Step-by-step explanation:

x = 360°- (90°+36°+36°)

= 360 - (162°)

= 198°

>> Answer

___________

\( \: \)

Step by step :

PQR = 360°

QR = 90°

PQ = 36°

RX = 36°

Soo :

x = 360° - (90° + 36° × 2)

x = 360° - (90° + 72°)

x = 360° - (162)

x = 198°✔

PLEASE HELP! i have by the end of the day to turn this in. PLEASE DONT GUESS :)

PLEASE HELP! i have by the end of the day to turn this in. PLEASE DONT GUESS :)

Answers

Answer:

x = 101°

Step-by-step explanation:

180-147 = 32

180-47-33 = 101

also this is not college math what

STANKY PLSS HELP ME ❤️

STANKY PLSS HELP ME

Answers

Answer:

PQS is a triangle

Step-by-step explanation:

Area of triangle= L×B

So,

20×7

140cm²

Answer :70

Step-by-step explanation:

Area formula: a times b/ 2

PQS: 7 times 20/ 2= 70

Your answer is 70

I hope this helps and may God bless you.  have a nice day, bye!

Find the numbers with the following property three times the sum of four and a number is less than seven times the same number

Answers

Let's represent the number with the variable "x". According to the given property, we can write the following equation:

3(x + 4) < 7x

Now, let's solve this inequality to find the range of numbers that satisfy the property.

3x + 12 < 7x

Subtract 3x from both sides:

12 < 4x

Divide both sides by 4 (since the coefficient of x is 4):

3 < x

So, the range of numbers that satisfy the given property is x > 3.

Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:

Let's call the number we're looking for "x".

According to the problem, we know that:

3(4 + x) < 7x

Simplifying:

12 + 3x < 7x

Subtracting 3x from both sides:

12 < 4x

Dividing both sides by 4:

3 < x

So the number we're looking for must be greater than 3.

Charles can type 675 words in 9 minutes. How many words can he type per minute?
Group of answer choices

6075 words per minute

75 words per minute

86 words per minute

75 minutes per word

Answers

Answer:

675 devided bye 9 = 75

Step-by-step explanation:

Answer: 75 words per minute

Step-by-step explanation:

We can set this problem up similar to a ratio
675:9
Knowing that this is for 9 minutes, dividing by 9 will give you the amount per one minute
675/9   9/9
75:1 or 75 words per minute

The machinery in a cereal plant fills 350 g boxes of cereal. The specifications for the machinery permit for a certain amount of fill tolerance. It is found that the weights of filled cereal boxes are normally distributed with a mean of 350 g and a standard deviation of 4 g. What is the probability that a box of cereal is under filled by 5 g or more?

Answers

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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I give brainliest!!!!

I give brainliest!!!!

Answers

Answer:

(3，2) i hope this answer will help you

I believe your answer is (2,3)

I hope this is correct and helps!

# 3 symbols of inequalities and the coordinate system...hello I'm a 7th grader can u please help me with my math summer package and explain it in a way that a 7th grader can understand it

# 3 symbols of inequalities and the coordinate system...hello I'm a 7th grader can u please help me with

Answers

Given: A grocery store is located at the origin (0,0). Madison lives 3 blocks west of the grocery store, and Gavin lives 5 blocks west of the grocery store.

Required: To determine the coordinates of Madison's house and Gavin's house and the distance between the grocery store and madison's and Gavin's house. Also, write inequalities for the distance.

Explanation: Let the graph represents the directions as follows-

Then, the direction west lies on the negative x-axis. So, according to the question, Madison lives 3 blocks west of the grocery store, and Gavin lives 5 blocks west of the grocery store. This can be represented as follows-

Here, M represents Madison's house, and G represents Gavin's house. Now the distance from the grocery store to Madison's house is 3 blocks and to Gavin's house is 5 blocks.

Gavin lives at a greater distance from the store. Let d(M) represent the distance of Madison's house from the store and d(G) represent the distance of Gavin's house from the store. Then-

\(\begin{gathered} 0Final Answer: Coordinates of Madison's house=(0,-3).

Coordinate of Gavin's house=(0,-5)

Distance from the grocery store to Madison's house=3 unit blocks.

Distance from the grocery store to Gavin's house=5 unit blocks.

Inequalities are-

\(\begin{gathered} 0\lt d(M))\leqslant3 \\ 0\lt d(G))\leqslant5 \end{gathered}\)

# 3 symbols of inequalities and the coordinate system...hello I'm a 7th grader can u please help me with
# 3 symbols of inequalities and the coordinate system...hello I'm a 7th grader can u please help me with

Solve for x: −8 < x − 1 < 5

−7 < x < 6

7 < x < 6

−7 > x > 6

7 > x > 6

Answers

Answer:

- 7 < x < 6

Step-by-step explanation:

- 8 < x - 1 < 5 ( add 1 to each interval )

- 7 < x < 6

Write a trinomial with 3x as the GCF of its terms.​

Answers

Answer:

3x (x² + x + 1)

You could write any trinomial like this

what is the constant of proportionality of between 45.57 and 3​

Answers

Answer:

The COP is between 45.57 and 3 is 15.19 (I think)

Step-by-step explanation:

It is pretty simple, you just divide 45.57 and 3 to get an answer for just a single digit, in this case, it would be 1-15.19 just like 3-45.57.

the assumption is that "3" is the value of the independent variable whilst 45.57 is the result, thus if that's the case, then we can say that

\(\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of proportionality}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we know that} \begin{cases} x=3\\ y=45.57 \end{cases}\implies 45.57=k(3)\implies \cfrac{45.57}{3}=k\implies 15.19=k\)

What are the coordinates of point A?

What are the coordinates of point A?

Answers

Answer:

Step-by-step explanation:

I believe its

(-2,-6)

An economy package of cups has 210 green cups. If the green cups are 10% of the total package, how many cups are in the package?

Answers

2,100 would be the answer. Please mark brainliest!

Kristy downloads two songs to her MP3
player. The songs are 3 minutes and 4- minutes
long. About how many minutes of memory will these
two songs use altogether?

Answers

Answer:

About 7 minutes

Step-by-step explanation:

3 minutes + 4 minutes= 7 minutes memory used for two songs

Does 8÷10+7÷100 equal to 0.87

Answers

Answer:

Yes

Step-by-step explanation:

8÷10+7÷100=

8/10 + 7/100=

80/100 + 7/100=     ==> make the denominators equal to each other

(80+7)/100=

87/100=0.87 √

Answer:

yes it does

Step-by-step explanation:

8÷10=0.8

7÷100=0.07

0.8+0.07=0.87

or the easy way ig

8÷10+7÷100=0.87

Time sensitive! Please get back to me within the next 30 minutes :)

At a bakery, a latte costs three times as much as a bagel. I bought a latte and a bagel, and the
total cost was $5.00. How much does a latte cost, and how much does a bagel cost?

Answers

Answer:

bagel $1.25

latte: $3.75

Step-by-step explanation:

Let the price of a bagel = b.

A latte costs 3 times as much as a bagel, so the price of a latte is 3b.

b + 3b = 5

4b = 5

b = 1.25

3b = 3.75

Answer:

bagel $1.25

latte: $3.75

Answer: A bagel cost 1.25$ and a latte cost 3.75$

Step-by-step explanation:

Let a latte be y

Let a bagel be x

3x = y   Total cost = 5$

A bagel is x, plus the 3x

4x = 5

x = 1.25

Sub back into 3x = y

3*1.25 = 3.75

If two cubes have edges of 2 ft and 4 ft, what is the ratio of their surface areas?​

Answers

Answer:

1/4

Step-by-step explanation:


Help me please please

Help me please please

Answers

Answer:

It is right

Step-by-step explanation:

Because the hypotenuse must be greater than all the legs, we have that \(17\) is the hypotenuse. So, we want to determine if \(8^2+15^2=17^2\).

\(8^2=8*8=64\\15^2=15*15=225\\17^2=17*17=289\\225+64=289\\\)

This means the triangle is indeed right!

Ron wants to save $5,000 in 5 years. Can he do this by having $100 deposited into a payroll savings plan each month? Explain. use a calculator if you like.

Answers

Answer:

Yes.

Step-by-step explanation:

Yes because 100 times the 12 months in a year equals $1,200 and $1,200 times 5 is $6,000 and $6,000 is greater than $5,000, so yes.

Arthur hs 20/8 cups of dish wahing detergent, he uses 1/4 cup for each load, how many loads can he do​

Answers

Answer:

10

Step-by-step explanation:

Speeding tickets provide a significant source of revenue for many American cities. For one city in South Florida, the average annual speeding ticket revenue per police officer is $300,000. The standard deviation for these annual speeding ticket revenues is $58,000. If these amounts have a normal distribution, find the cutoff amount of annual speeding ticket revenue that separates the highest five percent of revenue generating officers from the other ninety-five percent.

Answers

Explanation

To find the cutoff amount of annual speeding ticket revenue that separates the highest five percent of revenue-generating officers from the other ninety-five percent.

We will need to find

\(P\left(x>z\right)=0.05\)

Therefore; using a z score calculator, this gives;

\(z=1.645\)

We can then find the cutoff amount z using the formula below;

\(\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \end{gathered}\)

Since

\(\begin{gathered} \mu=$ 300,000. $ \\ \sigma=58,000 \end{gathered}\)

Therefore, we will have

\(\begin{gathered} 1.645=\frac{x-300000}{58000} \\ \mathrm{Switch\:sides} \\ \frac{x-300000}{58000}=1.645 \\ crossmutiply \\ x-300000=58000\times1.645 \\ x=300000+95410 \\ x=395410 \end{gathered}\)

Answer: 395410

F(x)=0.5^x what is the domain and range

Answers

Answer:

XER (X are all real numbers)

Step-by-step explanation:

as;dbdjkdbusaj hfsvd

¿De qué número 64 es el 80%?

Answers

80 is the number 80*.8=64

What type of triangle is this?
Options:
- SSS
- SAS
- ASA
- AAS
- HL
- Not Possible

What type of triangle is this?Options: - SSS - SAS - ASA - AAS - HL - Not Possible

Answers

Answer:

HL

Step-by-step explanation:

In both triangle, hypotenuse and one leg is congruent. So, HL congruent

every 3 out of 12 vehicles on a highway is a truck. How many trucks are expected to be on the highway with 3600 vehicles

Answers

Answer:

900 trucks on a highway with 3600 vehicles

Step-by-step explanation:

3 out of 12 is also 1/4  (one quarter)

so 3600 ÷ 4 = 900 trucks on a highway with 3600 vehicles

hope this helps :))

Ms. Jones washed
2
7
of her laundry. Her son washed
1
3
of it. Who washed most of the laundry? How much of the laundry still needs to be washed?

Answers

Her son washed the most laundry. 2/7 is a smaller fraction then 1/3.



I can’t help with the next one because I don’t know how much laundry it was in total.

Sphenathi and other matriculants plan to pass Bloemfontein at 07.25 to travel the above stated distance to Uptington. Determine (to the nearest km/h) the average speed at which they must travel to be in Uptington by 09:45.​

Answers

Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

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how many faces pyramid had​

Answers

Answer:

5......

Step-by-step explanation:

Can I have brainliest?

Answer:

5 faces

Step-by-step explanation:

It has six vertices and nine edges. A rectangular pyramid has 5 faces. Its base is a rectangle or a square and the other 4 faces are triangles. It has 8 edges and 5 vertices

hope this helps

The index number representing the price level changes from 109 to 118 in one year. The inflation rate during the year is _____ percent. Round your answer to two digits to the right of the decimal

Answers

The price levels given are:

\(Initial=109\)\(final=118\)

The inflation rate can be calculated using the relationship

\(\begin{gathered} \frac{\text{price level change}}{initial\text{ }price}\times100\text{ \%} \\ \\ =\frac{\text{final price-initial price}}{i\text{nitial price}}\times100\text{ \%} \end{gathered}\)

Substituting the values into the formula we will have

\(\frac{118-109}{109}\times100\text{ \%}\)

Simplifying further, we will have

\(8.26\text{ \%}\)

Thus, we have the inflation rate to be:

8.26 percent

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