100 POINTS !! The trajectory of a potato launched from a potato cannon on the ground at an angle of 45 degrees with an initial speed of 70 meters per second can be modeled by the parabola f(x) = x − 0.002x2, where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the potato travels before hitting the ground. A.height: 125 m; distance: 500 m B.height: 250 m; distance: 22 m C. height: 500 m; distance: 125 m D. height: 22 m; distance: 250 m

Answer:

C. Point is a defined term

Step-by-step explanation:

kleann

Answer:

C)  y = -2x - 5

Step-by-step explanation:

[tex]\sf let \ (x_1,y_1)=(-3,1)\\\\let \ (x_2,y_2)=(0,-5)[/tex]

[tex]\sf slope=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-5-1}{0-(-3)}=-2[/tex]

Point-slope formula: [tex]\sf y-y_1=m(x-x_1)[/tex]

[tex]\sf \implies y-1=-2(x-(-3))[/tex]

[tex]\sf \implies y=-2x-5[/tex]

Slope:-

Equation in point slope form

Answer:

4.57894737

Step-by-step explanation:

261 divided by 57 = 4.57894737

or 4.6 to 1 decimal place

If you need further explanation, let me know!

-profparis

Answer: 4.57894736842

Answer:

90 students

Step-by-step explanation:

So, if you have 100 students to start and it decreases by 10% then take the 100 and multiply it by .10. You should get 10. Then, subtract 10 from 100 and you end up with 90.

Answer:

hello

2010 = 100 students

2011 = 100 x 0.9 = 90

2012 =  90 x 1.1 =  99  

Step-by-step explanation:

Answer:

s^2 = 324 would mean side length s = 18

Step-by-step explanation:

The square root of 324 would be 18.

A square with side length s has an area of 324 square centimeters. So, the side of the square is 18cm

The area of a square can be calculated as the square of the sides of a given figure.

The area of a square = [tex]side^2[/tex]

A square with side length s has an area of 324 square centimeters.

The area of a square = [tex]side^2[/tex]

then s = √324

           =18

Thus, the side of the square is 18cm

Learn more about the area;

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The probability that Harold selected a pink square tile, and either a red or a blue round tile is 1/9.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

P(E) = Number of favorable outcomes / total number of outcomes

Considering the selections are independent, their combined probability is the product of the probabilities of the individual events.

 P(pink square) = (pink squares) / (squares) = 16/60 = 4/15

 P(red or blue round) = (red or blue rounds) / ( rounds) = 15/36

Then, the Total probability

 P(E) = (4/15)(15/36)

 P(E) = 4/36

 P(E) = 1/9

So, the probability that Harold selected a pink square tile, and either a red or a blue round tile is 1/9.

Learn more about probability here;

https://brainly.com/question/3591413

Answer:

Harold randomly selected one square tile and one round tile from the sets shown below. What is the probability that Harold selected a pink square tile, and either a red or a blue round tile?

Square tiles: 20 green, 16 pink, 9 red, 10 yellow, 5 blue.Round tiles: 5 black, 4 pink, 9 red, 6 blue, 3 yellow, 8 green, 1 white.

a.

3/5

b.

14/60

d.

4/45

Step-by-step explanation:

Edge 2022

Answer:

the answer is 5x divide by 12

The scale factor of the dilation of line segment ba for which the center of dilation is C, is 5.

Dilation of a figure, means the transformation of the figure. The factor by which the given figure dilated, called the scale factor of dilation.

Point c is the center of dilation. Line segment BA is dilated to create line segment b prime, a prime.  The image of the given problem is attached below. The length of CA is 4.

[tex]CA=4[/tex]

The length of a prime is 16.

[tex]AA'=16[/tex]

The new dimension will be,

[tex]CA'=CA+AA'\\CA'=4+16\\CA'=20[/tex]

Now, the scale factor is the ratio of the new dimension to the original dimension. Thus, the scale factor of the dilation is,

[tex]r=\dfrac{20}{4}\\r=5[/tex]

This will be the same for the line segment BA. Thus, the scale factor of the dilation of line segment ba for which the center of dilation is C, is 5.

Learn more about the dilation of the figure here;

https://brainly.com/question/3457976

Answer:

the answer is 5

Step-by-step explanation:

D

Answer:

make the n in side and join together

Answer:

y = -1/2x + 1

Step-by-step explanation:

We find slope using rise-over-run and by counting I got 1/2 but the slope is also negative. The y-intercept is 1 because the points are counting by 1/2 and the line goes through where half of 2 is on the y-axis. Hope this helps!

Answer:

Option C :- 7.5x + 8.1

Step-by-step explanation:

Let's simplify step-by-step.

4.5x+3.1−(−3x−5)

Distribute the Negative Sign:

=4.5x+3.1+−1(−3x−5)

=4.5x+3.1+−1(−3x)+(−1)(−5)

=4.5x+3.1+3x+5

Combine Like Terms:

=4.5x+3.1+3x+5

=(4.5x+3x)+(3.1+5)

=7.5x+8.1

Answer:

=7.5x+8.1

Answer:

x = -8

y = -3

Step-by-step explanation:

So first you're going to want to get x or y by itself using elimination or substitution. I used elimination to get x by itself.

You can multiply the second equation (2x + 2y = -22) by -2 so you can eliminate the y's. When you multiply it, you get -4x - 4y = 44

Then, you can add -3x + 4y = 12 and -4x - 4y = 44. The y's cancel out to leave -7x = 56. Divide both sides by -7 to get x = -8.

Now, you can plug in -8 for x in either one of the equations. I plugged it into the second equation to make it 2(-8) + 2y = -22.

2 · -8 = -16.

-16 + 2y = -22. Add 16 to both sides to get 2y = -6. Divide both sides by to get y = -3.

Hope this helps! :)

Answer:

height and the base your take height you square it then you square the base then you -

Answer:

B. y = 5x-1

Step-by-step explanation:

B. y = 5x-1 is not an exponential function.

Answer:

The base is equal to 30

And the Hight is equal to 15

Step-by-step explanation:

30 * 15 ÷2 = 225

Using the proportional relationship, it is found that the radius of the pipe that would allow the sink to drain completely in 14 seconds is of 1.25 cm.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

[tex]y = kx[/tex]

In which k is the constant of proportionality.

If they are inverse proportional, the relationship is:

[tex]y = \frac{k}{x}[/tex]

In this problem, the amount of time is inversely proportional to the square of the radius of the pipe, hence:

[tex]t = \frac{k}{r^2}[/tex]

A pipe of radius 1 cm can empty a sink in 22 seconds, hence k = 22.

The radius for 14 seconds is:

[tex]t = \frac{k}{r^2}[/tex]

[tex]14 = \frac{22}{r^2}[/tex]

[tex]r^2 = \frac{22}{14}[/tex]

[tex]r = \sqrt{\frac{22}{14}}[/tex]

[tex]r = 1.25[/tex]

The radius of the pipe that would allow the sink to drain completely in 14 seconds is of 1.25 cm.

More can be learned about proportional relationships at https://brainly.com/question/25890103

Answer:

66

Step-by-step explanation:

Lacrosse: 33

Tennis: 33

0.25 x 132 = 33

Basket ball:?

33 + 33 + b = 132

66 + b = 132

132 - 66 = 66

b = 66

Have a great day!

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Answer:

D.  66

Step-by-step explanation:

Total number of students = 132

If 25% of 132 students play tennis:

⇒ 0.25 × 132 = 33

So 33 students play tennis

Number of students who play basketball is: total number of students minus students play tennis minus students play lacrosse:

= basketball = 132 - 33 - 33 = 66

Answer:

3217.00

Step-by-step explanation:

V=πr^2h=π·8^2·16≈3216.99088

Answer:

804.2 or 803.8

Step-by-step explanation:

volume = π · r2 · h

π · [tex]4^{2}[/tex] · 16 = 804.2

3.14 · [tex]4^{2}[/tex] · 16 = 803.8

Answer:

10

Step-by-step explanation:

If you cut each sandwich in half and count how many halves there are, you are essentially multiplying it by 2. 5 times 2 is 10. Therefore, your answer is 10. Hope this helps:)

Answer:

10.66

Step-by-step explanation:

16/3 = 5.3

5.3 x 2 = 10.66

Have an amazing day!

Please rate and mark brainliest!

Answer:

140

Step-by-step explanation:

5t + 10 = 4t + 22

t + 10 = 22

t = 12

5(12) + 10 = 70

4(12)+ 22 = 70

70 + 70 = 140

CP + PK = CK

Edit:

I'm not sure if the solution is correct , but there is at least something.

Now

CK

For the first question it's 52.99 cm^3 because the formula for volume of a cylinder is V=πr^2h.

The second question is 722.57 or 722 cm^2 because the formula for surface area is A=2πrh+2πr^2.

hope it helps!

Answer:

For question 3: 52.9875 cm^3 or 52.99 cm^3.

For question 4: 1,413 cm^3.

Step-by-step explanation: To find the volume of a cylinder, you need the area of the base times the height.  We don't have the area of the base, but we can find out by using the formula 3.14 x r^2 where r is the radius, which is 1.5 for question 3 and 5 for question 4.  It should look like this:

For question 3: 3.14 x 1.5^2 = 7.065.

For question 4: 3.14 x 5^2 = 78.5.

When you find the area of the base, you multiply it by the height, which is 7.5 for question 3 and 18 for question 4.  It should look like this:

For question 3: 7.065 x 7.5 = 52.9875 or 52.99.

For question 4: 78.5 x 18 = 1,413.

Therefore, 52.9875 cm^3 or 52.99 cm^3 is your answer for question 3 and 1,413 cm^3 is your answer for question 4.

Let me know if this is right! :)

Answer:

a. 32%

B.8B.88

Step-by-step explanation:

100 -68=32%

32/100=x/275

100x=8800

x=88

Answer:

0.1 or 10%

Step-by-step explanation:

Cost: 500

Sell: 550

550-500 = 50

50/500 = 0.1 OR 10%

Therefore, the percentage profit for each sale is 10% of the original wholesale price.

Answer:

10%

Step-by-step explanation:

profit=buyingpirce _selling price

550_500=50

%profit=profit\buyingprice×100

50\500×100=10%

Answer: Not safe

Step-by-step explanation:

Let the angle of elevation of the ramp be θ, then:

[tex]\begin{aligned}&\sin \theta=\frac{1.5}{10}=0.15 \\&\theta=\sin ^{-1}(0.15) \approx 8.63^{\circ}\end{aligned}[/tex]

But the maximum angle for the ramp cannot exceed 7.1°. The calculated angle of elevation will make it difficult, if not impossible, for motorized wheelchairs to get up the ramp.

Therefore, the ramp at the local library is not safe for motorized wheelchairs

The 100th term of the sequence is -273

Arithmetic sequence is one derived from addition/subtraction of a constant term to find the next term. the constant term is usually called the common difference

first term a = 222

common difference, d = -5

nth term of an Arithmetic sequence. Tn = a + ( n - 1 ) d

T100 = a + ( 100 - 1 ) d

T100 = 222 + 99 * -5

T100 = -273

Read more on Arithmetic sequence here:

https://brainly.com/question/7882626

Answer:

[tex]\sf x < \dfrac{16}{7} ,x > \dfrac{16}{7}[/tex]

Step-by-step explanation:

Given function:

[tex]\sf f[g(x)]=\dfrac{-6+23}{7x-16}[/tex]

The domain will be values of x that do NOT make the denominator zero:

[tex]\sf \implies 7x-16=0[/tex]

[tex]\sf \implies 7x=16[/tex]

[tex]\sf \implies x=\dfrac{16}{7}[/tex]

Therefore, the domain is [tex]\sf x\neq \dfrac{16}{7}[/tex] so

[tex]\sf x < \dfrac{16}{7} ,x > \dfrac{16}{7}[/tex]