X² - 24x + c
Find the answer for C.

The ball will come to ground after 6 seconds.

We have a function of time given by -

f(x) = [tex]-16t^{2} +96t[/tex]

that gives the height of the ball in feet at ' t ' second.

We have to find out after how much time the ball will hit the ground.

The type of motion discussed in the above question is a two - dimensional projectile motion.

We have - h(t) = f(x) = [tex]-16t^{2} +96t[/tex]

Now, in order to find out the time at which the ball will hit the ground again, we will equate h(t) = f(x) = 0

[tex]-16t^{2} +96t=0\\-16t(t - 6)=0\\-16t =0\;\;\;\;\;\;t -6 = 0[/tex]

Now, time can never be 0.

Hence -

t - 6 = 0

t = 6 seconds.

Hence, the ball will come to ground after 6 seconds.

To solve more questions on projectile motion, visit the link below -

https://brainly.com/question/12496840

#SPJ2

Answer:

105

Step-by-step explanation:

The sum of the angles of a triangle add to 180 degrees

<1 + <2 + <3 = 180

40 + 35 + <3 = 180

Combine like terms

75+ <3 = 180

Subtract 75 from each side

75-75 + <3 = 180-75

<3 = 105

Answer:

105 degrees

Step-by-step explanation:

In a triangle, the three interior angles always add to 180°

40 + 35 = 75

180-75 = 105 degrees

Final answer:

The equation representing the sumo wrestler's weight gain over time is y = 6x + 90, where y is the weight after x months, starting at 90 kilograms and increasing by 6 kilograms each month.

Explanation:

The student has provided the initial and final weights of the sumo wrestler, as well as the duration in months over which the weight gain occurred. We can use this information to calculate the rate of weight gain per month and create an equation to represent this relationship. The sumo wrestler started at 90 kilograms and reached 138 kilograms after 8 months. The equation will be in the form of y = mx + b, where m is the slope (rate of weight gain) and b is the y-intercept (initial weight).

To calculate the slope, m, we use the formula:

m = (Final weight - Initial weight) / (Final time - Initial time)

In this case, m = (138 kg - 90 kg) / (8 months - 0 months) = 48 kg / 8 months = 6 kg/month.

The y-intercept, b, is the initial weight of the sumo wrestler, which is 90 kilograms.

Therefore, the complete equation is y = 6x + 90, where y represents the sumo wrestler's weight after x months.

Answer:

15^2

18^2

Step-by-step explanation:

Answer:

549

Step-by-step explanation:

considering 'n²' to express first square on board.

Remember 'n' is an integer

Now expressing second square with (n+3)²  on the board.

(Therefore, The other two perfect squares in between are (n+1)² and (n+2)².

If asking for the difference that is 99:

(n+3)² - n² = 99

Solving for n:

n² + 6n + 9 - n² = 99

6n + 9 = 99

6n = 90

n = 90/6

n = 15

So the perfect squares on the board are:

n²  => 15² = 225

(n+3)²=> 18² = 324

The difference between the above is 99

and  exactly two other perfect squares (16² = 256 and 17² = 289) are in between.

Thus, the sum of the two perfect squares on the blackboard is,

225 + 324 = 549

Answer:

The number tickets sold was 120 student tickets, 95 children tickets and 285 adult tickets.

Step-by-step explanation:

Given:

A local theater sell all 500 tickets for a total of $8,070.

The price of tickets were $15 for students, $12 for children, and $18 for adults.

The adult tickets sold were three times as many as children’s tickets.

Now, to find the number of student tickets, children tickets and adult tickets  sold.

Let the number of students ticket be [tex]x.[/tex]

Let the number of children ticket be  [tex]y.[/tex]

So, the number of adults ticket be [tex]3y.[/tex]

Now, the total number of tickets sold:

[tex]x+y+3y=500\\\\x+4y=500\\\\x=500-4y\ \ \ ...(1)[/tex]

Now, the total cost of tickets:

[tex]x(15)+y(12)+3y(18)=8070\\\\15x+12y+54y=8070\\\\15x+66y=8070\\\\Substituting\ the\ value\ of\ x\ from\ equation\ (1):\\\\15(500-4y)+66y=8070\\\\7500-60y+66y=8070\\\\7500+6y=8070\\\\Subtracting\ both\ sides\ by\ 7500\ we\ get:\\\\6y=570\\\\Dividing\ both\ sides\ by\ 6\ we\ get:\\\\y=95.[/tex]

Thus, the number of children ticket is 95.

According the adult tickets sold were three times as many as children’s tickets.

Therefore, the number of adult tickets = 95 × 3 = 285.

Now, substituting the value of [tex]x[/tex] in equation (1) to get the number of student tickets:

[tex]x=500-4y\\\\x=500-4(95)\\\\x=500-380\\\\x=120.[/tex]

Hence, the number of student tickets is 120.

Therefore, the number tickets sold was 120 student tickets, 95 children tickets and 285 adult tickets.

The problem can be solved by creating a system of equations representing each type of ticket sales and their respective prices. Three equations are formed from the information provided and are then solved to find the numbers of each type of ticket sold.

This problem can be solved using a system of equations, representing each type of ticket sales and their prices. Let's define the variables. Let's let x represent the number of student tickets, y represent the number of children's tickets, and z represent the number of adult tickets.

We know that the total number of tickets sold is 500, so we can form the equation:
x + y + z = 500.
Moreover, we know that the total amount of money made from the tickets is $8070, so we can form the equation:
15x + 12y + 18z = 8070.
Lastly, we know that the theater sold three times as many adult tickets as children's tickets, forming the equation:
z = 3y.

Using these three equations, we can substitute and simplify to find the values of x, y, and z, representing the numbers of student, children, and adult tickets sold respectively.

https://brainly.com/question/35467992

#SPJ3

Answer:

0.043

Step-by-step explanation:

We are given that

Initially when t=0

Then, A=22 million

The population of a country after t years is given by

[tex]A=22e^{kt}[/tex]

When t=8 then A=31 million

Substitute the values

[tex]31=22e^{8k}[/tex]

[tex]\frac{31}{22}=e^{8k}[/tex]

[tex]1.409=e^{8k}[/tex]

[tex]8k=ln(1.409)=0.343[/tex]

[tex]k=\frac{0.343}{8}=0.043[/tex]

Answer: Tank B can hold 27.4 gallons

Step-by-step explanation:

Volume of a cylinder = πr^2h

Given that Cylindrical tank A has 9/10 of the radius and 9/10 of the height of cylindrical tank B

Let the radius of A = r

Radius of B = R

Height of A = h

Height of B = H

r = 0.9R and h = 0.9H

Volume of A = πr^2h

= π(0.9R)^2(0.9H)

= 2.29R^2H

Given that tank A can hold 20 gallons, approximately

20 = 2.29R^2H

R^2H = 20/2.29 = 8.73 ..... (1)

Volume of B = πR^2H

Substitutes R^2H in equation (1) into Volume of B

Volume of B = 3.143 × 8.73

Volume of B = 27.4 gallons

Answer: Tank B can hold 27.43 gallons

Step-by-step explanation: Please see the attachments below

Answer:

d dfghjkl

Step-by-step explanation:

i just knowvghnm,.

Answer:

x =17

Step-by-step explanation:

Given shape is of a irregular hexagon.

Sum of all angles of an irregular hexagon

[tex]=(6 - 2) \times 180 \degree = 4 \times 180 \degree = 720 \degree \\ \\ \therefore \: (6x - 2)\degree + (7x + 19)\degree + 116 \degree \\ \: \: \: + (5x + 36)\degree + (8x - 1)\degree + 110 \degree \\ \: \: \: = 720 \degree \\ \\ \therefore \:(26x + 52)\degree + 226\degree = 720 \degree \\ \\ \therefore \:26x\degree + 278\degree = 720 \degree \\ \\ \therefore \:26x\degree = 720 \degree - 278\degree \\ \\ \therefore \:26x\degree = 442 \degree \\ \\ \therefore \:x = \frac{442\degree}{26\degree} \\ \\ \huge \red{ \boxed{\therefore \:x = 17}}[/tex]

Answer:

The distance the tip of the second hand travels in 10 minutes is 502 cm.

Step-by-step explanation:

Given : The second hand on a clock is 8 cm long.

To find : What is the distance the tip of the second hand travels in 10 minutes?

Solution :

The circumference of clock is [tex]C=2\pi r[/tex]

The radius is r=8 cm

[tex]C=2\times 8\times \pi[/tex]

[tex]C=16\pi[/tex]

i.e. in 1 minute it cover  [tex]16\pi[/tex]

In 10 minutes it cover  [tex]16\pi\times 10[/tex]

In 10 minutes it cover  [tex]160\times 3.14[/tex]

In 10 minutes it cover  [tex]502.4[/tex]

Therefore, the distance the tip of the second hand travels in 10 minutes is 502 cm.

the cow will walk 2 miles

Step-by-step explanation:

half a mile - 0.5 miles

1/4 of an hour = 0.5 miles

2/4 of an hour = 1 Miles

3/4 of an hour = 1.5 miles

4/4 of an hour (one hour) = 2 miles

0.5 × 4 = 2

Independent variable is the variable that you change.

Dependent variable is the variable you measure that results from or depends on the independent variable.

Since you want "r" to be the independent variable, you isolate/get the variable "q" by itself in the equation: [this is because "r" would be the variable that changes, and "q" would be the variable you find/measure that depends on "r"]

10q - 5r = 30             Add 5r on both sides

10q = 5r + 20          Divide 10 on both sides to get "q" by itself

[tex]q=\frac{5r+30}{10}[/tex]

[tex]q=\frac{5r}{10} +3[/tex]

[tex]q=\frac{1}{2} r+3[/tex]

The value of r is the independent variable is [tex]\rm \dfrac{10q-30}{5}[/tex].

Given that,

Equation; [tex]\rm 10q-5r = 30[/tex]

We have to determine,

The value of r is the independent variable.

According to the question,

A variable whose values do not change is known as independent changes. They have their own value, which is not changed with the equation.

To determine the value of r is the independent variable following all the steps given below.

Therefore,

The value of r is the independent variable is,

[tex]\rm 10q-5r = 30\\\\10q=30+5r\\\\q = \dfrac{30+5r}{10}\\\\q = \dfrac{5}{5} \times \dfrac{6+r}{2}\\\\ q = \dfrac{1}{2}r + \dfrac{6}{2}\\\\ q = \dfrac{1}{2}r + 3\\\\[/tex]

Hence, The value of r is the independent variable is [tex]\rm \dfrac{1}{2}r + 3[/tex].

For more details refer to the link given below.

https://brainly.com/question/18826122

Answer:

1.23 x 10^-7

Step-by-step explanation:

you went back 7 so its negative

Answer:

123 x 10^(-9)

Step-by-step explanation:

just put it in scientific notations and you will get 123 x 10^(-9)

Answer:

350 ft long facing the barn and 175 ft wide

Step-by-step explanation:

Let a and b be the length and width of his rectangular fence. Since he has 700 feet of fencing and one side does not need fencing. We have the following constraint equation:

a + 2b = 700

a = 700 - 2b

We want to maximize the following area formula

A = ab

We can substitute a = 700 - 2b

[tex]A = (700 - 2b)b = 700b - 2b^2[/tex]

To find the maximum value of this, simply take the 1st derivative, and set it to 0

A' = 700 - 4b = 0

b = 700 / 4 = 175 ft

a = 700 - 2b = 700 - 350 = 350 ft

The area of the circle with a radius of 3 is approximately 28.26 square units using the approximation [tex]\( \pi \approx 3.14 \).[/tex]

The area [tex]\(A\)[/tex] of a circle with radius [tex]\(r\)[/tex] is given by the formula:

[tex]\[ A = \pi r^2 \][/tex]

Given that the radius [tex]\(r\)[/tex] is 3, we can substitute this value into the formula:

[tex]\[ A = \pi \times (3)^2 \][/tex]

[tex]\[ A = \pi \times 9 \][/tex]

Using the approximation [tex]\( \pi \approx 3.14 \),[/tex] we can calculate:

[tex]\[ A \approx 3.14 \times 9 \][/tex]

[tex]\[ A \approx 28.26 \][/tex]

Therefore, the area of the circle with a radius of 3 is approximately [tex]\(28.26\).[/tex]

Answer:

h(-5) = -13

Step-by-step explanation:

h(x) = 3x + 2

Let x = -5

h(-5) = 3(-5) +2

        = -15 +2

        = -13

Answer:

H(-5)= -13

Step-by-step explanation:

1) Plug in -5 for the variable X

2) Then Solve

h(-5)= 3(-5) + 2

h(-5)= -15 + 2

H(-5)= -13

Hope this Help!

Given:

The base of the given triangle has two part:

Left( left side of the hypotenuse) = 25

Right ( right side of the hypotenuse) = x

The altitude (h) = 60

To find the value of x.

Formula:

By Altitude rule we know that, the altitude of a triangle is mean proportional between the right and left part of the hypotenuse,

[tex]\frac{left}{altitude} =\frac{altitude}{right}[/tex]

Now,

Putting,

left = 25, altitude = 60 and right = x we get,

[tex]\frac{25}{60} =\frac{60}{x}[/tex]

or, [tex](25)(x )=(60)(60)[/tex] [ by cross multiplication]

or, [tex]x = \frac{3600}{25}[/tex]

or, [tex]x = 144[/tex]

Hence,

The value of x is 144.

Answer:

x = 144

Step-by-step explanation:

Height Theorem

60² = 25·x

3600 = 25x

x = 3600 : 25

x = 144

Answer: x(2x+4) = (x+2)^2

The equation that results from applying the tangent segment theorem to the given figure is; x(2x + 4) = (x + 2)²

According to the secant and tangent segment theorem, the square of the tangent line is equal to the product of the secant segments. This is;

Tangent² = whole secant segment × External secant segment

DE² = AD × BD

We are given that;

DE = x

AD = 2x + 4

BD = x + 2

Thus, we have;

x(2x + 4) = (x + 2)²

Read more about segment theorem at; https://brainly.com/question/9330100

Answer:

42,008

Step-by-step explanation:

The ending balance after 2 years will be equal to $42008.

The amount of interest calculated on the principal amount over a whole year of the loan amount is called simple interest.

In finance and economics, interest is the payment of an amount over repayment of the original sum by a borrower or deposit-taking financial institution to a lender or depositor at a specific rate by a borrower or depositor. It differs from a fee that the borrower may pay to the lender or a third party.

Given that the amount is $35600 at 9% interest for 2 years. The total balance after 2 years will be,

SI = ( P x R x T ) /100

SI = ( 35600 x 9 x 2 ) / 100

SI = 6408

Ending amount = 6408 + 35600

Ending amount = $42008

Therefore, the ending balance after 2 years will be equal to $42008.

To know more about simple interests follow

https://brainly.com/question/2294792

#SPJ6

Answer: Adult 84

Children 34

Junior 2

Step-by-step explanation:

Adults tickets = $5

Children tickets = $.10

Junior tickets = $2

Total ticket sold = 120 at $119

Total tickets price

= Adults + junior + children

= 5 + 2 + 0.10 = 7.1

No of tickets sold for adults

= 5 / 7.1 × 119

= 84

No of tickets sold for children

= 2/7.1 × 119

= 34

No of tickets sold for junior

= 0.10/7.1 × 119

= 2

Total ticket sold

= 84 + 34 + 2

= 120

Final answer:

During the sale, 22 adult tickets, 67 junior tickets, and 31 children's tickets were sold.

Explanation:

Let's assume that the number of adult tickets sold is x, the number of junior tickets sold is y, and the number of children's tickets sold is z.

According to the information given, the cost of an adult ticket is $5, the cost of a junior ticket is $2, and the cost of a children's ticket is $0.10 (10 cents).

The total number of tickets sold is 120, so we can write the equation:

x + y + z = 120

Additionally, the total amount collected from the ticket sales is $119, so we can write the equation:

5x + 2y + 0.10z = 119

We now have a system of equations that we can solve to find the values of x, y, and z.

By using substitution or elimination methods, we can find that x = 22, y = 67, and z = 31.

Therefore, during the sale, 22 adult tickets, 67 junior tickets, and 31 children's tickets were sold.

Answer:

29

Step-by-step explanation:

In this question we are trying to calculate the cost of exact amount of fabric used given the cost per area of the fabric.

To answer this question mathematically, we need to know the area of the bulletin board. To do this , we employ a mathematical approach. We know that the bulletin board is circular in shape from the question and thus we calculate the area of this shape.

Mathematically, the area of the circular bulletin board is pi * r^2 where r refers to the radius. From the question, we can identify that this radius is 2.5 feet. let’s insert this into the equation we have.

mathematically A = 2.5^2 * pi = 19.63 sq. feet

The cost of the fabric per square feet is 1.48.

now the cost for this area that we have will be 1.48 * 19.63 = 29.0524

This is nearest to 29

Answer:

$28.3

Step-by-step explanation:

x=rate for 1km

y=initial fee

Mike: $35 for 15km -> 35 = 15x + y

Thomas: $24.50 for 10km -> 24.50 = 10x + y

Using those two equations we see the following:

Mike paid $10.5 more for 5 more km. The initial fee remains unchanged, so we can calculate the rate for 1km, which is 10.5/5=2.1.

35 = 15x + y

24.50 = 10x + y

10.5 = 5x

2.1=x

Using that value with one of the original equations we can calculate the initial fee.

35 = 15x + y

35 = 15*2.1 + y

35 = 31.5 + y

3.5 = y

Mike paid 15*2.1=31.5 ($2.1 for every km) plus the initial fee, his total was $35.

We subtract the 31.5 from the 35(total) and get the initial fee, which is $3.5.

Let's see what Lex will pay:

Km travelled times 2.1 (the rate for 1km) plus 3.5 (the initial fee).

12*2.1 + 3.5 = 28.3

Lex will pay $28.3 for the same taxi company to travel 12 km.

Final answer:

Using a system of equations derived from his friends' taxi fares, it's determined that Lex will pay $28.70 for a 12 km taxi ride to work.

Explanation:

Lex wants to find out how much it will cost him to take a taxi for a distance of 12 km using the information from his friends' taxi rides from the same company. Thomas traveled 10 km and paid $24.50, and Mike traveled 15 km and paid $35. We can solve this problem by setting up a system of linear equations and solving for the unknowns, which are the initial fee and the rate per kilometer.

Step 1: Set up the equations

Let x represent the initial fee and y represent the rate per km. We get two equations from the information given:

10y + x = 24.50 (Thomas's trip)

15y + x = 35 (Mike's trip)

Step 2: Solve the system of equations

Subtract the first equation from the second to eliminate x and solve for y:

5y = 10.50

y = 2.10

Substitute y = 2.10 back into one of the equations to solve for x:

10(2.10) + x = 24.50

x = 3.50

Step 3: Calculate Lex's cost

Now that we have x = 3.50 and y = 2.10, we can calculate the cost for Lex:

12(2.10) + 3.50 = $28.70

Therefore, Lex will pay $28.70 for his taxi ride to work.

The surface area of the cylinder with a height of 5 inches and a radius of 3 inches is calculated using the formula A = 2πrh + 2πr² and comes out to approximately 150.796 in² when rounded to the nearest thousandth.

To calculate the surface area of a cylinder, we use the formula A = 2πrh + 2πr², where 'r' is the radius and 'h' is the height of the cylinder. Given the height 'h' is 5 inches and the radius 'r' is 3 inches, we substitute these values into the formula.

Calculating the lateral surface area (the area of the side):
A_lateral = 2πrh = 2π(3 in)(5 in) = 30π in².

Calculating the area of the two bases:
A_bases = 2πr² = 2π(3 in)² = 18π in².

Now, add the lateral area and the area of the bases to find the total surface area:
A_total = A_lateral + A_bases = 30π in² + 18π in² = 48π in².

Using π ≈ 3.14159, the total surface area is: A_total ≈ 48(3.14159) = 150.796 in². Rounded to the nearest thousandth, the surface area of the cylinder is 150.796 in².

Answer:

Because theres nothing to solve for x is all real numbers

Step-by-step explanation:

There is no way to solve it as theres nothing to solve for. You just plug in the x's with any number you want and it still will be there

Answer:

An "association" exists between two categorical variables if the row (or column) conditional relative frequencies are different for the rows (or columns) of the table. ... If the conditional relative frequencies are nearly equal for all categories, there may be no association between the variables.

Step-by-step explanation:

Answer:

x < -2; x > 5          

Step-by-step explanation:

5x + 7 < - 3                  3x - 4 > 11

     -7     -7                         +4   +4

    5x < - 10                        3x > 15

    / 5     /5                          /3     /3

      x < -2                             x > 5            

To solve two inequalities: 5x + 7 < -3 and 3x - 4 > 11. The solutions are x < -2 and x > 5, respectively.

1. 5x + 7 < -3

2. 3x - 4 > 11

Let's solve each inequality one by one.

For the first inequality, 5x + 7 < -3, subtract 7 from both sides to get 5x < -10, then divide both sides by 5 to find that x < -2.

For the second inequality, 3x - 4 > 11, add 4 to both sides to obtain 3x > 15, then divide by 3 yielding x > 5.

The solution to the system of inequalities is that x can be any number less than -2 or any number greater than 5.

Answer:

6xy - 8x + 5y - 4z

Step-by-step explanation:

6xy - 20y + 7z - 8x + 25y - 11z

Group the ones with the variable first to make an equation:

6xy - 8x - 20y + 25y + 7z - 11z

Solve the equation

6xy - 8x +5y - 4z

Distance = SQRT((X2 -x1)^2 + (y2-y1)^2)

Distance = sqrt((2 - (-2)^2) + (-2 - 1)^2))

Distance = sqrt(4^2 + -3^2)

Distance = sqrt(16 + 9)

Distance = sqrt(25)

Distance = 5

Answer is D. (5)

Answer:

D) 5

Step-by-step explanation:

sqrt[(-2 - 2)² + (1 - -2)²]

sqrt(25)

5

The first thing to do is identify the unnecessary information (that they met 2 years ago).  

From there, let's go back three years ago.  We'll call Daniel's age x, and Ben's age will be 3x.  Ben's age is also equal to x + 20.

3x = x+ 20

2x = 20

x = 10

Daniel was 10 three years ago, and Ben was 30.  Now, Ben is 33.