You take measurements of the distance traveled by an object that is increasing its speed at a constant rate. The distance traveled d as a function of time t can be modeled by a quadratic function. What is the quadratic function that models distances of 21 ft at 1 s, 59 ft at 2 s, and 141 ft at 4 s?

Answers

Answer 1

Answer:

Follows are the solution to this question:

Step-by-step explanation:

Given:

[tex]s_1 = 21 \ \ t_1 = 1\\\\s_2 = 59 \ \ t_2 = 2\\\\s_3 = 141 \ \ t_3 = 4[/tex]

All points are on the graph including its quadratic function, in order to install their coordinates to values of x and y with the following values:

[tex]y= ax^2 + bx + c\\\\21=a+b+c[/tex]      Inserting the coordinates of the first point

[tex]y= ax^2 + bx + c\\\\59 =4a+2b+c[/tex]              Inserting the coordinates of the second point

[tex]y= ax^2 + bx + c\\\\141=16a+4b+c[/tex]       Inserting the coordinates of the third point


Related Questions

6 =a/4 + 2 * pls help me, thank you

Answers

Answer:

16

Step-by-step explanation:

16/4+2( 16 divided by 4 then add 2)

What is the surface area of the pyramid formed from the net shown here? The triangles are equilateral, and each triangle has a height of 5.2 centimeters. Write your answer rounded to one decimal point and with the correct unit. 6.3 Incorrect. The surface area of an equilateral triangular pyramid is given by the formula surface area = 2bh. The surface area of this equilateral triangular pyramid is 2bh = 2 × 6 cm × 5.2 cm = 62.4 square centimeters. Enter the correct answer. the net of an equilateral triangular pyramid

Answers

Answer:

the surface area of the pyramid is 62.4 square centimeters

Step-by-step explanation:

The computation of the surface area of the pyramid is shown below:

As we know that

The surface area = 2bh

= 2 × 6 cm × 5.2 cm

= 62.4 square centimeters

Hence, the surface area of the pyramid is 62.4 square centimeters

Beth used 1 1/4 tubes of glue on her science project. Each Tube holds 1/3 ounce of paint. Write an equation to represent the situation. How many ounces of glue did Beth use?

Answers

Answer:

5/12 ounces

Step-by-step explanation:

If each tube holds 1/3 oz of paint, the you multiply 1/3 by the number of tubes that she used. 1/3oz/tube(1.25 tubes)= 5/12 ounces

Write an equation in slope-intercept form: (7,7) and (-3,7) are on the line

Answers

Answer:

The only equation that would work is y=7

Step-by-step explanation:

I’m pretty sure one that would work is y=7

Help with the question below

Answers

Answer:

51

Step-by-step explanation:

24 ^2+45^2=x^2

=51

HELP 40 POINTS!!!! ILL GIVE BRAINLIEST TOO

Answers

Answer:

40 students

10 teachers

Step-by-step explanation:

32 + 8 = 40

5 + 5 = 10

Hope this helps!! ♥︎

A farmer sells 7.6 kilograms of apples and pears at the farmer's market. 3 5 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?

Answers

Answer:

4.1 kilograms

Step-by-step explanation:

A farmer sells 7.6 kilograms of apples and pears at the farmer's market. 3.5 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?

= 7.6 kilograms - 3.5 kilograms

= 4.1 kilograms

Steve uses 14 blue beads and 6 green beads to make a bracelet.
Which ratio compares the number of blue beads to the total number of beads in one bracelet?

Answers

Answer:

blue:total

14:20

Answer:

14:20

Step-by-step explanation:

because 14 + 6= 20 so blue beads are 14 and the other is alltogether 20 so it is 14:20 or 14 to 20

Find the slope of the line shown below.

Answers

Answer:

slope is -2

Step-by-step explanation:

trust me :)

Answer: The slope would be -2

A group of friends had dinner at a restaurant. The total bill for the dinner was $41 and they left a 15% tip. What was the total amount that they paid?

Answers

Answer:

$47.15

Step-by-step explanation:

41x15%=6.15

6.15+41=47.15

Answer: $47.15

Step-by-step explanation:

[tex]41 (1+.15)\\41 (1.15)\\= 47.15[/tex]

or you could do it in pieces

[tex]41(.15)= 6.15\\41+6.15= 47.15[/tex]

If x - 8 = -10, then find the value of 4x - 12

Answers

Answer:

60 is your answer.

Step-by-step explanation:

x - 8 = 10

add 8 to both sides,

x = 18

substitute 18 for x in the second equation:

4(18) - 12 = 72 - 12 = 60

Please lmk if you have questions.

Plane tickets to Chicago usually cost $120. On a travel deal website, you scored a coupon for 35% off. Your budget for the trip allows you to spend a hundred dollars on a ticket; can you go?

Answers

Answer: yes it’s 78$

Step-by-step explanation: The difference is 42.00

standard deviation of the data. 160,220,220,249,190​

Answers

Answer:

Population: 30.32. Sample: 33.99

If the graph of the function moves to the right two units what is the new vertex of the function

Answers

Answer:

Let's talk through this a one step at a time.

*Since f(x) is concave-up with its vertex on the x-axis, we know f(x) ≥ 0.

*We also know that when we shift a function's domain by a positive number, we shift the function left and when we shift a function's domain by a negative number, we shift the function right. So f(x-5) is f(x) shifted to the right by 5.

*At this point, f(x-5) has its vertex at (5,0).

*When we negate f(x-5), the parabola becomes concave down yet the vertex remains at (5,0). Now we're at -f(x-5). At this point we have -f(x-5)≤0 with a range (-∞,0]

*If we add 2 to create g(x)=2-f(x-5), then we have a concave down parabola with its vertex shifted up by 2, at (5,2). So, g(x) is concave down with its vertex at (5,2). Hence

Someone help me with this

Answers

Answer:

And it was not the first time that a lot of the people to a new report by a single limited few single few group an

Step-by-step explanation:

I have been using the address of the most important thing to remember is that you have the right to be able to use the same time as I thing

URGENT, PLEASE ANSWERR If someone who is 5 feet tall uses a potato gun to shoot a potato in the air at 100 feet per second, we can use the function ℎ()=−162+100+5 to calculate how far the potato will be from the ground at any given second (t). What does the h(0) represent in the context of the problem?

Answers

Given:

Consider the function is:

[tex]h(t)=-16t^2+100t+5[/tex]

This function is used to calculate how far the potato will be from the ground at any given second (t).

To find:

The value of h(0) and its meaning in the context of the problem.

Solution:

We have,

[tex]h(t)=-16t^2+100t+5[/tex]

At t=0,

[tex]h(0)=-16(0)^2+100(0)+5[/tex]

[tex]h(0)=0+0+5[/tex]

[tex]h(0)=5[/tex]

Therefore, the value of h(0) is 5. It means the potato is 5 feet from the ground at the time of shooting.

Lily and Wilder live 810 miles apart. If they leave at the same time and drive towards each other with Lily driving at 55 mph and Wilder driving at 80 mph, after how many hours will they meet?

Answers

Given:

Distance between Lily and Wilder = 810 miles

They drive towards each other with Lily driving at 55 mph and Wilder driving at 80 mph.

To find:

After how many hours will they meet?

Solution:

Lily driving at 55 mph and Wilder driving at 80 mph towards each other. So, the relative speed is:

Relative speed [tex]=(55+80)\text{ mph}[/tex]

                         [tex]=135 \text{ mph}[/tex]

We know that,

[tex]Time=\dfrac{Distance}{Speed}[/tex]

[tex]Time=\dfrac{810}{135}[/tex]

[tex]Time=6[/tex]

Therefore, Lily and Wilder will meet after 6 hours.

WILL MARK BRAINLIEST

Answers

A ..................

HELP ME !!
The linear equation c = 6.5n + 1500 models cost c, in dollars, to produce n toys at a toy factory. What is the y-intercept, and what does it mean in this context?

A)The y-intercept is 6.5 and represents the number of toys produced increases by about 6.5 for each $1 increase in cost.
B)
The y-intercept is 1500 and represents the costs $1500 to run the factory if no toys are produced.
C)The y-intercept is 1500 and represents The factory can produce 1500 toys at no cost.
D)The y-intercept is 6.5 and represents the cost increases by $6.50 for each toy produced.

Answers

Answer:

B

Step-by-step explanation:

This is because 6.5n is the slope and the +1500 is the y-intercept. Remember its y=mx+b.

Answer:

B

Step-by-step explanation:

Hope this helps have a great day :)

please I need someone to help my assignment​

Answers

Answer: x = 10

Step-by-step explanation:

The Pythagorean's theorem says that for a triangle rectangle with catheti A and B, and with hypotenuse H, we have:

A^2 + B^2 = H^2

In this case, we have:

A = (x - 4)

B = (x - 2)

H = x

Then we have the equation:

(x - 4)^2 + (x - 2)^2 = x^2

Now we need to solve this for x, first let's simplify it.

(x^2 - 2*x*4 + 16) + (x^2 - 2*2*x + 4) = x^2

2*x^2 - 12*x + 20 = x^2

2*x^2 - 12*x + 20 - x^2 = 0

x^2 - 12*x + 20 = 0

The solutions of this equation are given by the Bhaskara's equation, such that for an equation like:

a*x^2 + b*x + c = 0

The solutions are:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4*a*c} }{2*a}[/tex]

Then the solutions for our equation are:

[tex]x = \frac{-(-12) \pm \sqrt{(-12)^2 - 4*1*20} }{2*1} = \frac{12 \pm 8 }{2}[/tex]

Then the two possible solutions are:

x = (12 - 8)/2 = 4/2 = 2

Notice that if x = 2, then the length of the catheti will be:

A = 2 - 4 = -2

B = 2 - 2 = 0

This has no sense, so we can discard this solution.

The other solution for x is:

x = (12 + 8)/2 = 10

x = 10

Then:

H = 10

A = 10 - 4 = 6

B = 10 - 2 = 8

This solution makes sense, then x = 10.

Please help i will give brainleist and 25 points please dont play please

Complementary Angles are two angles that add up to 90 degrees. If ∠1=30 then ∠2=60 because 90-30=60.

Find the missing angle that makes them complementary. ∠3=50 so ∠4=

∠5=25 so ∠6=

∠7=80 so ∠8=

Answers

Step-by-step explanation:

1)90-50= 40°

2)90-25= 65°

3)90-80=10°

Write the equation of a line parallel to f(x)=1/2x+1 and passing through the point (-5, -2).

Answers

Answer:

y = 1/2x + 1/2

Step-by-step explanation:

y = 1/2x + b  [Parallel lines have the same slope but different y-intercepts]

-2 = (1/2)(-5) + b  [Plug in the coordinates (-5,-2) to find the y-intercept b]

b = 1/2  [Solve for b]

y = 1/2x + 1/2

Answer:

y= 1/2x + 0.5

Step-by-step explanation:

plug in the x and y values to get the y-intercept the slope stays the same. hope this helps! :P

can you explain for me question number 4,5,6,7,8 thanks i will give you a brainliest

Answers

Answer:

17/24 pizza

7/8 of questions

7/10 of   the newspapers

dylan 1 1/4 miles sonia 1 1/10 miles

answer b

Step-by-step explanation:

Given: cos θ = 5/13 where 0 ≤ θ < 90
Find tan 2θ

Answers

Answer:

Given: cos θ = 5/13 where 0 ≤ θ < 90

Find tan 2θ

Step-by-step explanation:

pls hurry will give brainlyest or whatever !!!

Which coordinate rule matches this description? Dilation of original by 5.

(5x, y)

(x+5, y+5)

(5x, 5y)

(x, 5y)

Answers

Answer:

D  (x,5y)

Step-by-step explanation:

PLS help. 30 points and brainliest

In triangle ABC, a = 3, b = 5, and c = 7. Find the measure of B.

158°
142°
38°
22°

Answers

Answer:

C

Step-by-step explanation:

Since we are given three sides and we want to find an angle, we can use the law of cosines.

The law of cosines is given by:

[tex]b^2=a^2+c^2-2ac\cos(B)[/tex]

In this case, a = 3, b = 5, and c = 7. Therefore:

[tex](5)^2=(3)^2+(7)^2-2(3)(7)\cos(B)[/tex]

Evaluate:

[tex]25=58-42\cos(B)[/tex]

Therefore:

[tex]-42\cos(B)=-33[/tex]

Dividing both sides:

[tex]\displaystyle \cos(B)=\frac{33}{42}[/tex]

And by taking the inverse cosine of both sides:

[tex]\displaystyle \angle B=\cos^{-1}\Big(\frac{33}{42}\Big)=38.2132...\approx 38^\circ[/tex]

Our answer is C.

Answer:

38°

Step-by-step explanation:

Any help?? I’ve tried this for a hour and couldn’t figure anything out

Answers

Answer:

3. PR=51

4. FE=28

Step-by-step explanation:

3. since the two triangles are similar, set up a proportion:

x+8/3x-9=24/28

*cross multiply*:

28(x+8)=24(3x-9)

28x+224=72x-216

44x=440

x=20

to find PR:

PR=3x-9

PR=3(20)-9

PR=51

4. same here:

39/4x+2=42/5x-2

39(5x-2)=42(4x+2)

195x-78=168x+84

27x=162

x=6

to find FE:

FE=5x-2

FE=5(6)-2

FE=28

Find the 12 term of the geometric sequence 2,10,50,

Answers

Answer: 19,531,250

.......

answer for this question is = 97,656,250

Four people share 2/7 pound of peanuts equally. What fraction of a pound of peanuts does each person receive? Enter your answer in simplest form.

Answers

Slime was a toy product manufactured by Mattel, sold in a plastic trash can and introduced in February 1976. It consisted of a non-toxic viscous, squishy and oozy green or other color material made primarily from guar gum.

I really need help Please thank you​

Answers

Answer:

D

Step-by-step explanation:

the median is 85, the mean is 85, the mode is 80.

it can't be A, B, or C. so it must be D.

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