A bottle rocket is launched straight up. Its height in feet (y) above theground x seconds after launch is modeled by the quadratic function: y =-16x2 + 132x + 6.How many seconds did it take the rocket to reach its maximum height?

we have the expression

Solve for y

That means

Isolate the variable y

so

step 1

Multiply by 4 both sides to remove the fractions

step 2

subtract y both sides

step 3

Adds 48 both sides

step 4

Divide by 8 both sides

therefore

The slower worker takes 20 hours and faster worker takes 5 hours to complete the job .

In the question,

it is given that ,

two secretaries stuff the envelopes for a political fund-raising letter in 4 hours .

let the time taken by fast worker to complete the job be x hours .

the slower worker takes 15 hours longer to do the job than faster worker

So , the time taken by slow workers to complete the job will be (x+15) hours .

the amount of work done by faster worker in 1 day = 1/x

the amount of work done by slower worker in 1 day = 1/(x+15)

total work done by both in 1 day = 1/x + 1/(x+15)

their combined 1 day work will be equal to 1/4 .

The equation representing is

1/x + 1/(x+15) = 1/4

(x+15+x)/(x²+15x) = 1/4

(2x+15)/(x²+15x) = 1/4

4(2x+15) = x²+15x

8x + 60 = x²+15x

x² + 15x - 8x - 60 = 0

x² + 15x - 8x - 60 = 0

x² + 7x - 60 = 0

x² + 12x - 5x - 60 = 0

x(x+12) -5(x+12) = 0

(x-5)(x+12)=0

we get x -5 = 0   or    x+12=0

x = 5 or   x = -12 .

the time cannot be in negative ,

So , fast worker to complete the job in  = 5 hours

slow worker to complete the job in = 20 hours

Therefore , The slower worker takes 20 hours and faster worker takes 5 hours to complete the job .

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The correct option will be C that is x+y=15 and 7x+12y=145 as the system of equation defines, "A group of equations involving one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions to systems of equations".

A group of equations involving one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions to systems of equations. In order for one term to have equal and opposite coefficients in the two equations, multiply one or both equations by an integer. The equations are combined to form a single equation with a single variable. Do the variable's solution. Reintroduce the variable into the equation and then find the value of the other variable. Systems of linear equations in two variables can be solved in one of three ways: by graphing; by the substitution method; or by the elimination method.

Here,

Let x be the plate of 7 inch and y be the plate of 12 inch.

x+y=15

The total of diameter for both the plate is 145 inches.

7x+12y=145

The right option is C, which has the values x+y=15 and 7x+12y=145. according to the equations' definition, "A system of equations is a collection of equations involving one or more variables. Systems of equations have solutions that are either the variable mappings that satisfy each component equation or the locations where all of these equations intersect ".

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Answer:

C. is your answer nwow.

Step-by-step explanation:

Answer:

B (2, 3)

The two lines intersect near that point.

Mean for the girls is 137.6% of the mean for the boys.

What is Mean?

Suppose, there is a data and the average of the data has to be calculated. Mean is used to find the average of the data.

Mean is calculated by dividing the sum of all observations by the number of observations.

Here,

Let the midpoint be denoted by x and number of boys be denoted by f

[tex]\Sigma fx = 10 \times 18 + 30\times 9 + 50\times 7 + 70 \times 6\\[/tex]

       [tex]= 1220[/tex]

[tex]\Sigma f = 40[/tex]

Mean for boys = [tex]\frac{1220}{40}[/tex]

                        = 30.5

Let mean for the girls be x % of the mean of boys

By the problem,

[tex]\frac{x}{100}\times 30.5 = 48.8\\x = \frac{48.8 \times 100}{35.5}\\[/tex]

x =137.46%

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Student will kill the app and refuse to turn back to ongoing session

Session is in session history

Even though it's not finished yet

Student sees updates to Answer

But to see updates to Question he needs to kill the app

The slope of the given line is [tex]-\frac{3}{5}[/tex]

What is slope of a line?

Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis

If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by

m = [tex]tan\theta[/tex]

If the line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]

slope = [tex]\frac{y_2-y_1}{x_2 - x_1}[/tex]

The given line passes through ( -1, -5) and  (4, -8)

Slope of the line  =

                               [tex]\frac{-8-(-5)}{4-(-1)}\\-\frac{3}{5}\\\\[/tex]

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First let's make the picture of the movement of the little sister:

The green line represents the first trip and the red line represents the trip back.

Since she traveled 1000m and then came back 300m, we have that:

therefore, the little sister displaced 700 meters and she traveled 1300m

The largest possible square is of side 600m.

Given,  a developer wants to subdivide a rectangular lot into square pieces. The lot is 600m by 2400m.

We have to find the largest possible square.

Now, to find the largest possible square we have to find the HCF of 600 and 2400.

As, the HCF of 600 and 2400 is

HCF(600 , 2400) = 600

So, the largest possible square can be of the side 600m

Hence, The largest possible square is of side 600m

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Let us start by looking at the difference between statistical and non statistical question.

For a statistical question. a single answer is usually impossible while a statistical question has a single answer.

If someone asks how old are you, the answer is simple and it is expected to be a single answer.

If the question is how old are the boys in your neighborhood, a single answer is not possible. The ages are different since some are older than the others. In this case, there is spread in the data. We would be considering looking for the average age of a given number of boys. We may also consider the spread of the ages and other parameters like range, median etc

Solution:

As you can see in the diagram, there are two triangles. We will separate the two triangles into the smaller and the bigger one.

For the smaller triangle:

Now we will use the Pythagorean Theorem. The theorem states that the square of the longest side is equal to the sum of the squares of the two other sides.

To solve for the value of b, we will have:

For the bigger triangle:

We will also use the pythagorean theorem to find the value of c and by using the value of b we got from the smaller triangle.

ANSWER:

b = 4 cm

c = 7.2 cm

Answer:

A

Step-by-step explanation:

you can answer quadratic equations with a degree above 2

Given:

When the price of admission was $19, the attendance was about 1550 customers per week

And, when the price of admission was dropped to $16,

attendance increased to about 2350 per week

Let the attendance = A

And the price = p

The linear equation will be A = mp + b

Where (m) is the slope and (b) is the y-intercept

So,

When p = 19, A = 1550

When p = 16, A = 2350

So,

So,

we will find the value of (b) as follows:

So, the answer will be the linear equation is:

Answer:

B. 4.

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

With an equation such as

200÷12 = 16.666, or 16+(2/3)

You are able to determine how many miles each gallon contributed to. With that, you can take

16 × 3 = 48

3 x 2
1  x 3
(done for the fraction)

6/2 is the outputted fraction, which translates into 2.

48 + 2 = 50

Living species teeth is shorter than extinct species & large species teeth length is more concentrated.

Slope of the distribution:

For extinct species, the symmetric distribution

For living species, left -shaved distribution.

Measures of center:

For extinct species: mean = 3.02 cm

For large species: mean = 2.32 cm

Therefore living species teeth length is shorter than extinct species.

Measures of variability:

For extinct species: b = 6.015cm

For large species: b = 0.13 cm

Therefore large species teeth length is more concentrated.

Hence the answer is, living species teeth is shorter than extinct species & large species teeth length is more concentrated.

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Answer: −33.5 or - 67x over 2 -4

i might be wrong

Step-by-step explanation:

Answer:

-8 + 1 = -8

+8 +8

1 = 0

no solution

SOLUTION:

(a) We want to find the ratio of the volumes of the cubes,

5 x 5 x 5 = 125

3 x 3 x 3 = 27

125 : 27

(b) Since the two cones are similar, the ratio of the heights will be the same as the ratio of the radii, which means that the ratio of the volume will be;

Answer:

a

Step-by-step explanation:

Point 1 = (x1,y1)=(8,-1)

Point 2= (x2,y2)= (-8,5)

We have to apply the slope formula:

Replace with the coordinates given:

Answer:

-6x - 39

Step-by-step explanation:

-3(x + 7) -3x -18  Fist distribute the -3

-3(x) + -3(7) -3x -18  Simplify  (a negative times a positive is a negative)

-3x -21 -3x -18  Now combine like terms

-6x -39

Answer: y=x+2

Step-by-step explanation:

y-6=1(x-4)

y-6=x-4

y=x-4+6

y=x+2

The equation is given as

The value of x is 3/16.

Answer: 84 points

Step-by-step explanation:

There are two ways I see that you can solve this.
In the first method, we can find the points per coin. To do this, we divide 63/3 and we get 21.

63/3=21

Now we know that in 1 coin, there is 21 points.

1 coin=21 points
Next, since we have to find the total amount of points in 4 coins. We multiply 21 by 4.

21*4=84 points

We do this because in 1 coin there is 21 points, and there is not 21 points in 4 coins. So when we multiply 21 and 4, we get 84 points, and 84 points is our answer.

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Another way you could do this would be to use cross multiplication. In cross multiplication, we would set up our work like this:

63/3=x/4           or in ratio way           3 : 63 = 4 : x

When you look at the ratio formation, you can easily tell that it says 3 to 63 is the same as 4 is to x. This can be written in the fraction formation, making it able for us to cross multiply. When we write it the fraction way, we write

63                               x

____            =           ____      

  3                                 4


With this, we do what the name says, we cross the numbers over and multiply, so we do 63*4=3*x
This way can be harder we have bigger numbers, but we can always simplify before multiplying, like in this case-
We can divide the 3 from both sides

63 * 4

_____       =      x

  3

From this we can simplify the 63 and 3, and so we would cancel out the 3 and would be left with 21*4=x
And this is the same equation we ended up with before.
So when we solve, we get 84=x and so the amount of points Josiah will have is 84 points.

Given:

The local rate for electrical service is 6 cents per kilowatt-hour.

We need to know how much money would be saved in a year by using a dishwasher 4times per week rather than 6 times per week ​

From the table:

The cost of using a dishwasher 4 times per week = $29

The cost of using a dishwasher 6 times per week = $44

So, the saving will be = 44 - 29 = 15

So, the answer will be $15

The difference is calculated as:

15°F - ( - 15°F) = 15°F + 15 °F = 30°F

Because 15°f is the highest temperature and -15°F is the lowest temperature

Answer = 30 °F

338 students went on the field trip.

Given:

Four-ninth of the total participants rode a large bus, and the rest rode a smaller bus.

156 people rode the larger bus.

Let x be the total participants.

4/9 x = 156

multiply by 9 on both sides

4*9/9 x = 156*9

4x = 156*9

4x = 1404

divide by 4 on both sides

4x/4 = 1404/4

x = 1404/4

x = 351.

number of students = total participants - adult chaperones.

= 351 -13

= 338 students

Therefore 338 students went on the field trip.

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