Mathematics High School

A car's velocity is modeled by v(t) = 0.5t^2 -14t+ 80 for 0 less than or equal to t less than or equal 14, where the velocity is in feet per second and time is in seconds. Where does the car come to a complete stop?

A Car's Velocity Is Modeled By V(t) = 0.5t^2 -14t+ 80 For 0 Less Than Or Equal To T Less Than Or Equal

Answers

Answer 1

The car stops after moving for 20 seconds

How to determine when the car comes to a stop?

From the question, the function is given as

v(t) = 0.5t^2 - 14t + 80

When the car comes to a stop, the vehicle is 0

This is represented as

v(t) = 0

So, we have

0.5t^2 - 14t + 80 = 0

Expand the equation

0.5t^2 - 10t - 4t + 80 = 0

Factorize the equation

0.5t(t - 20) - 4(t - 20) = 0

So, we have

(0.5t - 4)(t - 20) = 0

Solve for t

t = 8 and t  = 20

20 is greater than 8

Hence, the car comes to a stop at 20 seconds

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Related Questions

What is x in this equation 6(x+7)=-12

Answers

Answer:

x = -9

6x + 42 = -12

6x = -54

x = -9

I would really appreciate your help ​

Answers

Answer:

The answer is 35

Step-by-step explanation:

Pls mark this answer as brainliest

James and Simon have a reading assignment to complete. James has read rrr pages, and Simon has read 757575 pages. Together they have read a total of 200200200 pages.

Answers

Just do the number of total pages subtract the number of pages Simon read to find the number of pages James read

Write the recurring decimal 0.45....... as a fraction.

Answers

Given the following question:

We are given the repeating decimal of 0.45

We will use the formula:

[tex]\begin{gathered} \frac{(d\times10^r)-n}{10^r-1} \\ \frac{0.45\times10^2)-0}{10^2-1} \\ \text{ Simplify} \\ \frac{0.45\times2\cdot10^2}{10^2-1}=\frac{45}{99} \\ \text{ Simplify once more} \\ \frac{45}{99}\div9=\frac{5}{11} \\ =\frac{5}{11} \end{gathered}[/tex]

x + m = p - n + yx Solve for x

Answers

Answer:

[tex]x=\frac{-m-n+p}{-y+1}[/tex]

Step-by-step explanation:

What is the value of this expression.

Answers

here's your answer hope it helps

Suppose that R(x) is a polynomial of degree 13 whose coefficients are real numbers. also, suppose that R(x) has the following zeros. answer the following.edit: if possible please double check the answers just to be safe.

Answers

(a) Complex zeros of a polynomial come in pairs.

If a + bi is a zero of a polynomial then its conjugate a - bi is also a zero of the polynomial.

The given complex zeros of R(x) are 1 + 3i and -2i.

1 - 3i is the conjugate of 1 + 3i.

Hence, another zero of R(x) is 1 - 3i

b)

Since the polynomial R(x) is of order 13 then R(x) must have 13 zeros.

The given complex zeros of R(x) are 1 + 3i and -2i. We also know that the conjugates of 1 + 3i and -2i are zeros of R(x). Hence, R(x) has at least 4 complex roots

Hence, the maximum number of real zeros of R(x) is (13 -4).

The maximum number of real zeros of R(x) is 9

c) Let the maximum number of nonreal zeros (complex roots) be n

Complex roots come in pairs. Therefore, n must be even.

Hence, n ≤ 13 - 1 = 12

n ≤ 10

We have been given a real zero of R(x), 3 ( With the multiplicity of 4).

12 - 4 = 8

Therefore,

n ≤ 8.

Hence the maximum number of nonreal zeros of R(x) is 8

1. Alex and chris share sweets
In ratio Alex : Chris= 7:3
Work out the number of
Sweets chris recieves.

Answers

Using ratios, we can conclude that Chris gets 12 sweets.

What are ratios?In mathematics, a ratio shows how many times one number is represented by another. If there are eight oranges and six lemons in a bowl of fruit, the proportion of oranges to lemons would be eight to six. 8:14 for oranges and 6:8 for lemons, respectively, are the ratios of oranges to the total amount of fruit.

So, a number of sweets Chris receive:

Alex : Chris = 7:3Let, Chris sweets be 'x' and Alex sweets be 'x + 20'

Now, 7:3 = x+20:x, solve as follows:

7:3 = x+20:x7/3 = x+20/x7x = 2x + 607x - 2x = 605x = 60x = 60/5x = 12


Therefore, using ratios, we can conclude that Chris gets 12 sweets.

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The correct question is given below:
Alex and Chris share sweets in the ratio Alex: Chris = 7 : 3. Alex receives 20 more sweets than Chris. Work out the number of sweets Chris receives.

(01.06 MC)
Ray IL bisects angle HIJ. If mzHIL = (6x - 7)° and mzJIL = (5x + 4)°, what is mzJIL?
118°
59°
44°
11°

Answers

Option C, 59° is correct answer, The angle JIL is equal to 59 degree.

What is angle?

Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned. Angles are also produced when two planes intersect. These are what are known as dihedral angles. Another characteristic of intersecting curves is the angle generated by the rays that are perpendicular to the two crossing curves at the point of junction.

Given information in the question,

∠HIL = (6x-7)°

∠JIL = (5x+4)°

The ray IL bisects the ∠HIJ

Since, IL bisects angle HIJ then, angle HIL = angle JIL

So,

6x - 7 =  5x + 4

x = 11

Putting the value of x in given value of JIL to get the angle JIL

∠JIL = (6x-7)°

∠JIL = (6(11)-7)°

∠JIL = 59°

Therefore angle JIL is equal to 59 degrees.

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(MULTIPLE CHOICE) Write an expression that would represent the perimeter of a rectangle with a width of 10n and a length of 4.

A) 10n + 4 + 10n + 4
B) 10n + 4
C) 4(20n) (this is multiplication)
D) 10 + 4 + 20n + 4

Answers

It would be A because you would add two 10n and two 4’s

If f(x) is an exponential functionwhere f(-2) = 1 and f(7) = = 63,then find the value of f(1) , to thenearest hundredth.

Answers

An exponential function has the form

[tex]y=ab^x[/tex]

Therefore, to find an exponential function that satisfies our condition, we need to find a and b.

From f(-2) = 1, we have

[tex]1=ab^{-2}\: ^{}\: \: \: \: \; ^{}\: \: \: \: \; (1)[/tex]

and from f(7) = 63, we have

[tex]63=ab^7\: \: \: \: \; ^{}\: \: \: \: \; (2)[/tex]

Solving for a in equation (1) gives

[tex]a=b^2[/tex]

substituting this value of a into equation (2) gives

[tex]63=b^2\cdot b^7[/tex][tex]63=b^8[/tex][tex]\begin{gathered} \therefore b=\sqrt[8]{63} \\ b=1.6785 \end{gathered}[/tex]

With the value of b in hand, we now find the value of a:

[tex]\begin{gathered} a=b^2 \\ \therefore a=2.8173 \end{gathered}[/tex]

Hence, the exponential function is

[tex]f(x)=(2.8173)(1.6785)^x[/tex]

Evaluating the above function at x = 1 gives

[tex]\begin{gathered} f(1)=(2.8173)(1.6785)^1 \\ \boxed{\therefore f(1)=4.73.} \end{gathered}[/tex]

which is our answer!

when a grizzly bear hibernates, its heart rate drops to 101010 beats per minute, which is 20\ , percent of its normal value. what is a grizzly bear's normal heart rate when not hibernating? beats per minute

Answers

A grizzly bear's normal heart rate when not hibernating is 50 beats per minute.

What is a heart rate?

The number of heartbeats that occur in a specific amount of time, usually one minute. The wrist, side of the neck, back of the knees, top of the foot, groin, and other areas of the body where an artery is close to the skin can all detect the heartbeat.

Here,

We let his normal heart rate = h

and given in the question,

20% of h = 10

20/100 * h = 10

h = 10*5

= 50 beats/min

Hence, a grizzly bear's normal heart rate when not hibernating is 50 beats per minute.

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Donna bought 5 bags of dog treats for $12.50. What is the cost per bag of dog treats?

I really need help on this please guys

Answers

Answer:

2.5

Step-by-step explanation:

$12.50 ÷ 5 bags = $2.5 per bag

Answer:

2.50

Expination:

devide 12.50 by the total amount of dog food purchased (5 bags)

12.50/5 = 2.50

the price per bag is $2.50

The corner grocery store sells bananas for $2.91 per pound. Select the store that sells bananas at a lower unit price. Mark all that apply.Store A: $8.16 for 4 poundsStore B: $6.51 for 3 poundsStore C: $2.66 for 2 poundsStore D: $11.40 for 4 pounds

Answers

Let's find the unit price of each store

Store A : $8.16 /4 = $2.04 per pound

store B: $6.51 / 3 = $2.17 per pound

store c: $2.66 / 2 = $1.33 per pound

store D : $11.40 / 4 = $ 2.85 per pound

Therefore, store A, store B, store C and store D sells at a lower unit price than Corner grocery store.

Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.

Which choice represents the sample space, S, for this event?

S = {PQR}
S = {PQR, PRQ, QPR, QRP, RPQ, RQP}
S = {PQ, PR, QR}
S = {PQ, QP, PR, RP, QR, RQ}

Answers

The resulting sample space of the given situation is S = {PQ, QP, PR, RP, QR, RQ}

Sample space:

Sample space refers the collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.

Given,

Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.

Here we need to find the sample space for the event.

Let us consider,

P represents Patty

Q represents Quinlan

R  represents Rashad

And through the question we have know that, the teacher drawn two card at a time,

So we have consider that the teacher is going to draw out of the hat one first, without replacement, and then draw another one.  

The first chosen one will be the president, and that could be P, Q or R, Now, the chosen second one is the Vice president, and already one has already being drawn, that could only be two fellows.

Therefore, the total of likely outcomes is PQ,QP, PR, RP, QR, RQ, one paired up with either of the two remaining in the hat.

So, the resulting sample space is

S = {PQ, QP, PR, RP, QR, RQ}

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Amy found that she could use the function P(t)=3t^2+5t+8 to model the population of a collection of fruit flies over time, where t is the time in days and P(t) is the number of flies. According to her model, how many flies will there be after 16 days?

A: 8
B: 768
C: 856
D: 2204​

Answers

The total number of files after 16 days using the function P(t) = 3t² + 5t + 8 is 856.

A relationship between a group of inputs having different outputs is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output.

The function P(t) represents the population of a collection of fruit flies at a particular time in days.

P(t) is the number of flies and t is the time in days.

Now, consider the function:

P(t) = 3t² + 5t + 8

Therefore, the number of flies after 16 days will be:

When t = 16,

P(t) = 3t² + 5t + 8

P(16) = 3(16)² + 5(16) + 8

P(16) = 3 × 16 × 16 + 5 × 16 + 8

P(16) = 768 + 80 + 8

P(16) = 856

Hence, the number of flies after 16 days will be 856 flies using the function P(t).

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What’s the answer plss I really need help

Answers

Answer:

The answer is d) 22.4

Step-by-step explanation:

I attached a file below if you want to see the process!

Select the correct answer.An engineering firm designs a custom hexagonal screw for a computer board. A sketch of the top of the screw is below. To the nearest tenth,what is the area of the screw head?ymm8.€4-2-x mmO-2--4--4OA15.6 mm2.OB. 93.5 mm2OC 62.4 mm2OD.1871 mm²402

Answers

We will have the following:

We can see that the shape of the head can be subdivided in smaller shapes, that is:

Now, we calculate the 5 areas, that is:

[tex]\begin{gathered} A_1=\frac{(6)(3)}{2}\Rightarrow A_1=9 \\ \\ A_2=\frac{(6)(3)}{2}\Rightarrow A_2=9 \\ \\ A_3=(6)(12)\Rightarrow A_3=72 \\ \\ A_4=\frac{(6)(3)}{2}\Rightarrow A_4=9 \\ \\ A_5=\frac{(6)(3)}{2}\Rightarrow A_5=9 \end{gathered}[/tex]

Now, the total area is:

[tex]\begin{gathered} A_T=A_1+A_2+A_3+A_4+A_5\Rightarrow A_T=9+9+72+9+9 \\ \\ \Rightarrow A_T=108 \end{gathered}[/tex]

So, the total area is 108 mm^2-

Which of the following variable expressions represents the phrase "five more than the quotient of a number x and eight"?

Answers

The variable expression is;

[tex]5\text{ + }\frac{x}{8}[/tex]

Here, we want to select an option that represents the phrase

The quotient of a number x and 8 means that we divide x by 8

That means we have a fraction, with x as the numerator and 8 as the denominator

We have this as;

[tex]\frac{x}{8}[/tex]

5 more than this quotient means that we are to add 5 to the result

We have this as;

[tex]5\text{ + }\frac{x}{8}[/tex]

Find the probability of at least 6 failuresin 7 trials of a binomial experiment inwhich the probability of success in anyone trial is 9%.p=[?1%Round to the nearest tenth of a percent.

Answers

[tex]\begin{gathered} The\text{ binomial probability distribution is given in the following form:} \\ P\text{ = nCx \lparen p}^x)(q^{n-x}) \\ Finding\text{ the probability of at least 6 failures means the probability of 6 or 7 failures.} \\ This\text{ corresponds to 1 or 0 successes.} \\ P(1)\text{ = 7C1 \lparen9\%}^1)(91\%^6) \\ \text{ =0.3278} \\ P(0)\text{ = 0.5168} \\ Probability\text{ of at most one success \lparen at least 6 failures\rparen} \\ =\text{ 0.844 = 84.5\%} \end{gathered}[/tex]

Two similar pyramids have slant height of 4 and 6.1. Find the scale factor.2. If the volume of the smaller pyramid is 48 meters cubed, what is the volume of the larger pyramid?

Answers

1) Considering that the slant height of those pyramids is 4 and 6, we can find the scale factor by dividing their slant heights:

[tex]\frac{6}{4}=\frac{3}{2}\text{ or 1.5}[/tex]

So we can state that the bigger pyramid is larger than the 1st pyramid by a scale factor of 1.5.

2) For the Volume of the Pyramid, we can write out the formula below:

[tex]V=\frac{1}{3}\cdot Ab\cdot h[/tex]

Since the scale factor is 1.5 Then we can state that

[tex]\begin{gathered} V=\frac{48}{\frac{3}{2}} \\ V=32 \end{gathered}[/tex]

the Volume of the smaller one is by similarity 1.5 or 3/2 times smaller than the larger one.

3) Hence, the answers are:

1.k=1.5

2. 32 m³

12 nights camp accommodation costs #6720. What will be the cost of a)7 nights number b)4 nights

Answers

EXPLANATION :

The cost of a 12 nights camp accommodation is 6720.

We need to divide the cost by 12 to get the cost per day.

[tex]6720\div12=560[/tex]

Now, we are asked to find the cost of 7 nights and 4 nights.

We just need to multiply the daily rate by the number of nights.

a. 7 nights :

7 x 560 = 3920

b. 4 nights :

4 x 560 = 2240

ANSWER :

a. 3920

b. 2240

The vertices of △ABC are A(2, −3), B(−3, −5), and C(4, 1). If (x,y)--> (x-2, y+3), give the vertices of △A′B′C′.

Answers

Answer:

A' = (0, 0)

B' = (-5, -2)

C' = (2, 4)

Step-by-step explanation:

Vertices of triangle ABC:

A = (2, -3)B = (-3, -5)C = (4, 1)

Given mapping rule:

(x, y) → (x - 2, y + 3)

This notation tells you that the x-coordinate is translated 2 units to the left, and the y-coordinate is translated 3 units up.

Substitute the coordinates of each point into the mapping rule to find the vertices of triangle A'B'C':

⇒ A' = (2 - 2, -3 + 3) = (0, 0)

⇒ B' = (-3 - 2, -5 + 3) = (-5, -2)

⇒ C' = (4 - 2, 1 + 3) = (2, 4)

Dwayne is making a poster about friendship in his art class. He divides his poster into 12 equal parts. Dwayne writes the names of his friends all over each part. Dwayne uses 7 parts for his neighborhood friends and 5 parts for his friends from school. What fraction of the poster does Dwayne use for his friends from school?

Answers

The fraction of the poster does Dwayne use for his friends from school is 5/12.

What is the fraction of the poster that Dwayne uses for his friends from school?

A fraction is a non-integer that has a numerator and a denominator. The numerator is the number that is above the line and the denominator is the number below the line. An example of a fraction is 5/12.

In this question, the numerator is the number of parts he gives his friends from school. The denominator is the total number of parts he divides the poster.

Fraction = parts he gave his friend from school / total number of parts

5 / 12.

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1/3 divided by 2 (1/2)^3
please help me

Answers

Answer:

1/24

Step-by-step explanation:

.........................

Answer:

I'll assume that "2 (1/2)^3" means 2*(1/2)^3.

Step-by-step explanation:

(1/3)/(2*(1/2)^3)

(1/3)/(1)^3

= (1/3)

===========================

If "2(1/2)^3" means (2+1/2)^2:

((5/2)^2 = (25/4)

--

(1/3)/(25/4)

(1/3)*(4/25) = 4/75 or 0.05333

Given the linear function in slope-intercept, what is the slope
and y-intercept of this line?
f(x) = x +9
Select TWO answers.

Answers

Answer:

Slope is 1 and y-intercept is 9

Step-by-step explanation:

y=mx+b

The slope is the coefficient of x in this case it would be 1

The y-intercept is whatever b is and it is +9 so it is 9

Graph line with slope 1/2 passing through the point (-1,3)

Answers

Answer:

Step-by-step explanation:

First, graph your first point at (-1,3) Then, take your slope which is 1/2 and use rise over run. So from your point of (-1,3) go up 1 in your y coordinate, and 2 in your x coordinate. So your next point should be at (1,4)

5. Let the graph of g be a translation 2 units up and 2 units right, followed by a reflection in the x-axis of the graph off(x) = -(x+3)^2 - 2. Write a rule for g.

Answers

Answer:

[tex]g(x)=-f(x-2)+2[/tex]

Explanation:

Given the function f(x)

A translation of 2 units up = f(x)+2

Next, a translation of 2 units right = f(x-2)+2

When we reflect the result above in the x-axis, we have:

[tex]g(x)=-f(x-2)+2[/tex]

A rule for g is therefore:

[tex]g(x)=-f(x-2)+2[/tex]

32+40+…+120=? Someone help PLEASE

Answers

The answers u are looking for us 190

Answer:

912

Step-by-step explanation:

the assumption is that this is an arithmetic progression

the nth term of an arithmetic progression is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

use this to find which term 120 is in the sequence

with a₁ = 32 and d = a₂ - a₁ = 40 - 32 = 8 , then

32 + 8(n - 1) = 120 ( subtract 32 from both sides )

8(n - 1) = 88 ( divide both sides by 8 )

n - 1 = 11 ( add 1 to both sides )

n = 12

given the first and last terms in the sequence then sum is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( first + last)

S₁₂ = [tex]\frac{12}{2}[/tex] (32 + 120) = 6 × 152 = 912

If n in an odd integer that is less than -3.25, what is the greatest possible value of n?

Answers

The greatest possible value of n is -5

How to determine the possible value of n?

From the question, the given parameters are:

n = Odd integerN is less than -3.25

The second highlight above can be represented as

n < -3.25

Since n is an integer, then the possible values of n are

n = -4, -5, -6, -7, -8....

Remove the even integers from the above list of numbers because n is an odd integer

So, we have

n = -5, -7, -9....

The greatest value above is n

This means that n can have the highest value of -5

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Graph for a 3rd degree polynomial function whose graph crosses the horizontal axis more than one You're driving home from the grocery store at 18 m/s with a 7. 0 kg bag of groceries on the front seat when the light ahead turns red. What is the shortest distance in which you can stop, after the brakes are applied, without the groceries sliding off the seat? the static and kinetic coefficients of friction are, respectively, 0. 65 and 0. 45. Assume that the surface of the seat is horizontal A Census Burcau report on the income of Americans says that with 95% confidence themedian income of all U.S. households is $49,841 to $50,625. The point estimate and margin oferror for this interval are: *Point estimate = $49,841; Margin of error = $784Point estimate = $50,233; Margin of error = $784oPoint estimate = $50,233; Margin of error = $392Point estimate = $50,625; Margin of error = $392 N8) solve the system using substitution method and then graph the equations.2x - 4y = -23x + 2y = 3- any place where, or any mechanism by which, buyers and sellers interact to trade goods, services, or resources is a(n) . (enter one word in the blank) 6. Express the given function h as a composition of two functions f and gsuch that H(x) = (fog)(x).a) H(x) = |3x +2|b) H(x) = 5x +4 if you halved a recipe that calls for 5 c. chicken broth how much broth would you use question In photograph The sharing of physical hardware by many organizations in the cloud, termed pooling, is accomplished with __________. Two methods to solve (X+3)^2=6 A cylinder sits on top of the rectangular prism. What is the combined volume? (use the Pi, round to the nearest tenth of an inch) ______ in3 help meeeeeeeeee pleaseee !!!!! Tyee has $720 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $401.83. He buys 4 bicycle reflectors for $12.85 each and a pair of bike gloves for $23.83. He plans to spend some or all of the money he has left to buy new biking outfits for $40.49 each. Use the drop-down menu below to write an inequality representing oo, the number of outfits he can buy while staying within his budget. There are no solutions to the system of inequalities shown below. y< 4X-6 y > 4x + 2 A.true B. false Match the description to the rules of England in the 17th century Simplify (5x + 7) - (x + 2) The cost of mailing a package is proportional to the weight of the package. The proportional relationship can be represented with the equation c = 0.4w, where c represents the total cost and w represents weight in ounces. A graph for the equation is shown.graph with x axis labeled weight in ounces and y axis labeled cost in dollars, with a line from 0 comma 0 going through 2 comma 0.8Which of the following statements is true about the graph shown? The graph is incorrect and the line should go through the point (0.4, 1). The equation c = 0.4w is correctly represented by the graph. The x-axis and y-axis are labeled incorrectly. The graph does not show a proportional relationship. 10. A city has a population of 125,500 in the year 1989. In the year 2007, its population is 109, 185. A. Find the continuous growth/decay rate for this city. Be sure to show all your work.B. If the growth/decay rate continues, find the population of the city in the year 2021.C. In what year will the population of the city reach 97,890? Be sure to show all your work. a is less than or equal to 10 How did scientific discoveries in the late 1800s impact the way people saw themselves and their world?