Can someone help me with these three

By solving a system of equations, we determined the quadratic function h(x) = 33.5x^2 + 14x + 53.5 and found that the height of the ball after 3 seconds is 229.5 feet.

Certainly! Let's go through the step-by-step calculation to find the quadratic function representing the height of the ball and then determine the height after 3 seconds.

Given information:

h(1) = 91 feet

h(2) = 164 feet

We need to find the coefficients a, b, and c in the quadratic function h(x) = ax^2 + bx + c.

Step 1: Setting up Equations

We have two equations based on the given information:

a + b + c = 91 (since h(1) = a(1)^2 + b(1) + c = a + b + c = 91)

4a + 2b + c = 164 (since h(2) = a(2)^2 + b(2) + c = 4a + 2b + c = 164)

Step 2: Solving the System of Equations

We can solve the system of equations to find the values of a, b, and c.

Subtracting the first equation from the second gives: 3a + b = 73.

Let's multiply the first equation by 3 and subtract it from the second:

3(3a + b) - (a + b + c) = 3(73) - 91

Simplifying, we get 6a - c = 110.

Step 3: Substituting into the First Equation

Substitute 6a - c = 110 into the first equation:

6a - c + c = 110 + 91

Solving, 6a = 201, which implies a = 33.5.

Step 4: Finding b and c

Substitute a back into the first equation to find b + c = 91 - 33.5, and then b and c are determined as b = 14 and c = 53.5.

Step 5: Quadratic Function

Now, we have the quadratic function h(x) = 33.5x^2 + 14x + 53.5.

Step 6: Finding h(3)

Finally, substitute x = 3 into the quadratic function:

h(3) = 33.5(3)^2 + 14(3) + 53.5

Solving this yields h(3) = 229.5 feet.

Final Answer:

The height of the ball after 3 seconds is 229.5 feet.

Step-by-step explanation:

Formula:

d×3.14=C

or

r×3.14×2=C

d=diameter

r=radius

Answer:

The length of the largest table that can be brought in the house on a diagonal is [tex]9.5\ ft[/tex]

Step-by-step explanation:

we know that

Applying the Pythagoras Theorem

Find the length of the diagonal of the frame

[tex]d^{2} =3^{2} +8^{2} \\\\ d^{2}=90\\\\ d=\sqrt{90}\ ft\\\\ d=9.5\ ft[/tex]

Answer:

Step-by-step explanation:

Alright, lets get started.

The height of the door is 8 feet.

The width of the door is 3 feet.

The largest size of the table that can be brought in this house from this given door is diagonally from this door.

So, lets find the diagonal of this door.

If we apply Pythagorean theorem ,

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

[tex]c^2=3^2+8^2[/tex]

[tex]c^2=9+64=73[/tex]

taking square root on both sides

[tex]c=\sqrt{73}=8.5[/tex]

So, the maximum length of the table would be 8.5 feet.  :  Answer

Hope it will help :)

ANSWER

Katnis is right

EXPLANATION

We use the Remainder Theorem to check if she is right.

According to the Remainder Theorem, if the polynomial function,

[tex]p(x) = {x}^{3} + 2 {x}^{2} - 3x - 4[/tex]

is divided by x+1, then the remainder is given by

[tex]p( - 1)[/tex]

We substitute x=-1 into the function to obtain,

[tex]p( - 1) = {( - 1)}^{3} + 2 { ( - 1)}^{2} - 3( - 1) - 4[/tex]

We simplify to get:

[tex]p( - 1) = - 1+ 2 (1) + 3 - 4[/tex]

[tex]p( - 1) = 4- 4[/tex]

[tex]p( - 1) = 0[/tex]

Katnis is right because the remainder is zero

[tex]63:21=3:1[/tex]

Hope this helps.

r3t40

you answer is b) -x^2-4x+7

Answer:

B

Step-by-step explanation:

4x² - 7x + 9 - (5x² - 3x + 2) ← distribute by - 1

= 4x² - 7x + 9 - 5x² + 3x - 2 ← collect like terms

= (4x² - 5x² ) + (- 7x + 3x ) + (9 - 2)

= - x² - 4x + 7 → B

For this case we must divide the following expression:

[tex]\frac {\frac {14x ^ 2} {15}} {7x}[/tex]

And in this way we get the amount of money that each person will receive.

Then applying double C we have:

[tex]\frac {14x ^ 2} {15 * 7x} =\\\frac {14x ^ 2} {105x} =\\0.133x[/tex]

Thus, each person has 0.133x of money!

Answer:

0.133x

Answer:

Volume of prism is 60 cm^3.

Step-by-step explanation:

The volume of prism can be found using formula:

V= B*h

Where B= base area and h= height.

In the question, we are given Base area B= 10cm^2 and height h= 6cm.

Putting values in the formula:

V= B8h

V= 10* 6

V = 60 cm^3

So, volume of prism is 60 cm^3.

Answer: The area is  [tex]320m^2[/tex]

Step-by-step explanation:

The formula for calculate the area of a rectangle is:

[tex]A=lw[/tex]

Where "l" is lenght and "w" is the width.

We know the width and the perimeter, then we can solve for the lenght from the following formula, which is used to calculate the perimeter of a rectangle:

[tex]P=2l+2w[/tex]

Then:

[tex]72m=2l+2(16m)\\72m-32m=2l\\\l=\frac{40}{2}\\\\l=20m[/tex]

Substituting values into the formula [tex]A=lw[/tex], we get that the area of the rectangle is:

[tex]A=(16m)(20m)[/tex]

[tex]A=320m^2[/tex]

Answer:

The area of rectangle = 320 m²

Step-by-step explanation:

Points to remember

Area of rectangle = lb

l - length and b - width

It is given that, perimeter of rectangle is 72 m. And width of rectangle = 16 m

To find the value of length

Perimeter = 2(l + b)

72 = 2(l + 16)

36 = l + 16

l = 36 - 16 = 20

To find the area of rectangle

Area = lb

 = 20 * 16

 = 320 m²

Therefore area of rectangle = 320 m²

Answer:

It's the second one:

yes; 4+5=6

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the center (0, -1) and the radius r = 5   (look at the picture).

Substitute:

[tex](x-0)^2+(y-(-1))^2=5^2\\\\x^2+(y+1)^2=25[/tex]

use (a + b)² = a² + 2ab + b²

[tex]x^2+y^2+2y+1=25[/tex]             subtract 25 from both sides

[tex]x^2+y^2+2y-24=0[/tex]

ANSWER

The correct answer is A

EXPLANATION

If the two functions are inverses , then

[tex]f(g(x)) = g(f(x)) = x[/tex]

Given

[tex]f(x) = 5x - 11[/tex]

and

[tex]g(x) = \frac{1}{5}x + 11[/tex]

[tex]f(g(x)) = f( \frac{1}{5} x + 11)[/tex]

This implies that,

[tex]f(g(x)) = 5(\frac{1}{5} x + 11) - 11[/tex]

Expand to get;

[tex]f(g(x)) =x + 55 - 11[/tex]

[tex]f(g(x)) =x +44[/tex]

Since

[tex]f(g(x)) \ne \: x[/tex]

The two functions are not inverses

The correct answer is A

Answer:

Correct choice is A.

Step-by-step explanation:

Given functions are [tex]f\left(x\right)=5x-11[/tex] and [tex]g\left(x\right)=\frac{1}{5}x+11[/tex].

Then [tex]f\left(g\left(x\right)\right)=f\left(\frac{1}{5}x+11\right)=5\left(\frac{1}{5}x+11\right)-11=x+55-11=x+44[/tex]

By definition of inverse we says that if f(x) and g(x) are inverse of each other then f(g(x)) must be equal to x.

But in above calculation we can see that f(g(x)) is not equal to x.

Hence correct choice is A.

Answer: OC

Step-by-step explanation: exact answer is 64.6

To estimate how many shoppers received free earbuds, 19% of 340 is calculated. The closest equivalent fraction to 19% is 20%, which means dividing 340 by 5, resulting in 68 shoppers receiving free earbuds, making option C correct.

The question revolves around the application of percentage calculations to a real-world scenario, where 340 shoppers at an electronics store are given various specials. To estimate how many shoppers received a free set of earbuds, we must calculate 19% of 340 shoppers.

Using equivalent fraction to estimate, 19% is close to 20%, and 20% of 340 can be found by dividing 340 by 5 (because 20% is the same as 1/5th).:

Therefore, about 68 shoppers received a free set of earbuds. This makes option C the correct choice. To note, we have not used the given table and information in the question as they do not relate to the calculation required for the current problem.

Answer:

8/15 chance

Step-by-step explanation:

To calculate the probability of forming an all-female group of three students from a class of 15 students, we find the total combinations of choosing three females and divide by the combinations of choosing any three students, resulting in a probability of 56/455.

The question involves calculating the probability that a group of three randomly selected students will consist of all females from a class of 15 students (8 females and 7 males). This is a problem of combinatorics and probability. We use combinations to determine the number of ways to choose three female students out of eight and divide that by the number of ways to choose any three students out of the fifteen.

First, we find the number of ways to choose three females: C(8,3) = 8! / (3! * (8-3)!) = 56. Then, we find the total number of ways to choose any three students: C(15,3) = 15! / (3! * (12!)) = 455. Therefore, the probability of choosing all females is 56/455.

Answer:

A

Step-by-step explanation:

Solving for x:

-3x + 8 ≥ 14

-3x ≥ 6

x ≤ -2

Notice the sign gets reversed when you divide or multiply by a negative number.

The only option less than -2 is -3, A.

Here's a tip: on multiple choice questions, sometimes it's faster to try each answer instead of solving the equation.  This can save time on tests like the SAT or ACT.

Let's try it:

-3(-3) + 8 = 9 + 8 = 17

-3(-1) + 8 = 3 + 8 = 11

-3(0) + 8 = 0 + 8 = 8

-3(3) + 8 = -9 + 8 = -1

So you can see the answer is A.

Consider a striking deviation as an outlier (Something that stands out in a pattern, EX: 2, 3, 4, 4, 4, 5, 5, 10 where the outlier would be 10.) Because there are no outliers (Or, Striking deviations), we can conclude that the answer would be D: No striking deviation.

Answer: A.4 units

Step-by-step explanation:

We know that if a figure is dilated by a scale factor of k , then the measure of the corresponding image (l') of a line segment having measure 'l' is given by :-

[tex]l'=kl[/tex]

Given : Square RSTU dilates by a factor of 1\2 with respect to the origin to create square R'S'T'U'.

The measure of line segment R'S' = 2 units

The scale factor : [tex]k=\dfrac{1}{2}[/tex]

Using the above equation , we have

[tex]R'S'=\dfrac{1}{2}RS\\\\\Rightarrow\ RS= 2\times R'S'\\\\\Rightarrow\ RS= 2\times2=4[/tex]

Hence, RS = 4 units.

Answer:

x<3/-2

Step-by-step explanation:

4x>6x+3

4x-6x>3

-2x>3

x<3/-2

Also help me with my question just click on my name and see my questions

Answer:

The probability is 0.953

Step-by-step explanation:

We know that the mean [tex]\mu[/tex] is:

[tex]\mu=10:30\ p.m[/tex]

The standard deviation [tex]\sigma[/tex] is:

[tex]\sigma=0:15\ minutes[/tex]

The Z-score is:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

We seek to find

[tex]P(10:00\ p.m.<x<11:00\ p.m.)[/tex]

The Z-score is:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]Z=\frac{10:00-10:30}{0:15}[/tex]

[tex]Z=\frac{-0:30}{0:15}[/tex]

[tex]Z=-2[/tex]

The score of Z =-2 means that 10:00 p.m. is -2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35%

and

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]Z=\frac{11:00-10:30}{0:15}[/tex]

[tex]Z=\frac{0:30}{0:15}[/tex]

[tex]Z=2[/tex]

The score of Z =2 means that 11:00 p.m. is 2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35%

[tex]P(10:00\ p.m.<x<11:00\ p.m.)=100\%-2.35\%-2.35\%[/tex]

[tex]P(10:00\ p.m.<x<11:00\ p.m.)=95.3\%[/tex]

[tex]P(10:00\ p.m.<x<11:00\ p.m.)=0.953[/tex]

the probability is 0.4772, or 47.72%.

To find the probability that Flight 202's arrival time is between 10:00 p.m. and 11:00 p.m., we need to standardize the times and use the properties of the normal distribution. The mean arrival time is 10:30 p.m., and the standard deviation is 15 minutes.

First, convert the times to minutes past 10:00 p.m.: 10:30 p.m. is 30 minutes past, and 11:00 p.m. is 60 minutes past. Now, standardize these times using the formula for z-scores:

Using the z-table or a standard normal distribution calculator, we find the area under the curve to the left of z = 0 is 0.5, and to the left of z = 2 is approximately 0.9772. Therefore, the probability that the arrival time is between 10:00 PM and 11:00 PM is the difference of these probabilities:

P(10:00 PM < X < 11:00 PM) = P(Z < 2) - P(Z < 0) = 0.9772 - 0.5 = 0.4772

So, the probability is 0.4772, or 47.72%.

Final Velocity = Initial Velocity + (Acceleration * time)

Final Velocity = ?

Initial Velocity = 3

Acceleration = 1.5

Time = 7

Plug in and solve

3+(1.5*7)

3+10.5

Velocity = 13.5m/s

Answer:

D:The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

hope this helps you

(ps.please make me  brainlyest)

Step-by-step explanation:

i just took the test on E2020 & got 100%

d) The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Number of tree purchased                            Total Cost ($)

                1                                                                 60

                2                                                                120

                3                                                                180

                4                                                                240

                5                                                                290

For the linear function rate of change is constant.

Now, between 2 and 3 trees rate of change is given by

[tex]=\frac{180-120}{3-2} \\\\=60\\[/tex]

Now, between 3 and 5 trees rate of change is given by

[tex]=\frac{200- 180}{5-3} \\\\=55[/tex]

This is clearly that the rate of change isn't constant. Therefore, the function is non-linear.

so,

d) The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Learn more about linear function here

brainly.com/question/11897796

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Answer:

The answer is B,

26-12.81=13.19

13.19-10=3.19

3.19/0.42 is a little greater than 7

Answer:

x>8

Step-by-step explanation:

The number has to be bigger than 8 in order to be at least fifteen, so x is greater than 8

ANSWER

72km/h

EXPLANATION

The average speed of the car can be calculated using the formula:

Average Speed=total distance/ total time taken.

The car covers a distance of 108km in 1½ hours.

We substitute the values into the formula to obtain,

[tex]Average \: \: Speed= \frac{108}{1.5} [/tex]

[tex]Average \: \: Speed=72 {kmh}^{ - 1} [/tex]

Therefore the average speed of the journey is 72km/h

The slope is 7/4 and the intercept is -10

The area of the two smaller squares are shown as 25 and 144, add them together to get 25 + 144 = 169.

The area of the larger square is shown as 169, which is the same as the sum of the two smaller ones.

The answer is Yes.

yes the sum of the smaller squares is equal to the largest one. 25 + 144 = 169

The area of the largest squares is 169, so the area of the smaller squares is equal to the largest square.

the answer is even is the right answer

ANSWER

even

EXPLANATION

The given function is

[tex]f(x) = |x| + {x}^{2} + 0.001[/tex]

If f(x) is even then f(-x) =f(x).

[tex]f( - x) = | - x| + {( - x)}^{2} + 0.001[/tex]

[tex]f( - x) = | x| + {x}^{2} + 0.001[/tex]

We can see that:

[tex]f( - x) = f(x)[/tex]

Hence the given function is even.

Answer:

13

Step-by-step explanation:

(x + 3)^3/2 = 64

√(x + 3)^3 = 64

(x + 3)^3 = 64^2

(x + 3)^3 = (4^3)^2

(x + 3)^3 = (4^2)^3

Same exponent

So

x + 3 = 4^2

x + 3 = 16

x = 13

For this case we have by definition, that the volume of a cone is given by "

[tex]V = \frac {1} {3} \pi * r ^ 2 * h[/tex]

Where:

h: It's the height

r: It is the cone radius

They tell us as data that the volume is 8 [tex]\pi[/tex]and the height is 6 cm, we must find an expression that allows to clear the radius, then:[tex]8 \pi = \frac {1} {3} \pi * r ^ 2 * 6[/tex]

Answer:

Option D

The answer is B. I think. Hope that helps!