MATHEMATICS
HIGH SCHOOL

Answer: A money market account.

MIDDLE SCHOOL

Keith is the leading goal scorer for a team in an ice hockey league. Last season, he scored 42 goals in 82 games. Assuming he scores goals at a constant rate, what is the slope of the line that represents this relationship if the number of games is along the x-axis and the number of goals is along the y-axis? A. 21/41

B. 22/41

C. 42/23

D. 41/21

Answer: Option 'a' is correct.

Step-by-step explanation:

Since we have given that

Number of goals = 42

Number of games = 82

Let x - axis denotes the number of games.

Let y - axis denotes the number of goals.

We need to find the slope of line that represents this relationship:

So, Slope of line is given by

Hence, Option 'a' is correct.

C because rise over run. Rise being the X-axis and Run being then Y-axis.

HIGH SCHOOL

How many different ways can six people be arranged in a line?

There are six people which means that each person can be arranged in 6 various arrangements

6×6=36

Answer: There can be 36 different ways for 6 people to be arranged

6×6=36

Answer: There can be 36 different ways for 6 people to be arranged

HIGH SCHOOL

What is the 10th term of the sequence 81 27 9

If you keep dividing by 3 the 10th term would end up to be 0.0014 in the sequence

In this sequence a=81

d=27-81=-54

So 10th term is a+9d=81+(9)(-54)=81-486=-405

d=27-81=-54

So 10th term is a+9d=81+(9)(-54)=81-486=-405

HIGH SCHOOL

Use the graph below to answer the question that follows: trig graph with points at 0, 0 and pi over 2, 3 and pi, 0 and 3 pi over 2, negative 3 and 2 pi, 0 and 5 pi over 2, 3 and 3 pi, 0

What trigonometric function represents the graph?

f(x) = −3 sin(x − pi over 2)

f(x) = −3 cos(x − pi over 2)

f(x) = 3 cos(x − pi over 2)

f(x) = 3 sin(x − pi over 2)

Note that the graph contains the point

The 3 comes from the multiplication of the y-value in the parent function by.

Not considering the multiplication by 3 we would have . Also remember that the available functions are

sin(x-π/2) and cos(x-π/2).

We can check that at π/2, sin(x-π/2) is sin(π/2-π/2)=sin(0)=0,

and, π/2, cos(x-π/2) is cos(π/2-π/2)=cos(0)=1.

Thus, our function is f(x)=3cos(x-π/2).

Check for π rad: f(π)=3cos(π-π/2)=3cos(π/2)=3*0=0.

and so on...

Answer: f(x) = 3 cos(x − pi over 2)

The 3 comes from the multiplication of the y-value in the parent function by.

Not considering the multiplication by 3 we would have . Also remember that the available functions are

sin(x-π/2) and cos(x-π/2).

We can check that at π/2, sin(x-π/2) is sin(π/2-π/2)=sin(0)=0,

and, π/2, cos(x-π/2) is cos(π/2-π/2)=cos(0)=1.

Thus, our function is f(x)=3cos(x-π/2).

Check for π rad: f(π)=3cos(π-π/2)=3cos(π/2)=3*0=0.

and so on...

Answer: f(x) = 3 cos(x − pi over 2)

COLLEGE

Express the limit as a definite integral on the given interval. lim nââ n xi ln(1 + xi2) Î´x, [0, 3] i = 1

I'm guessing the sum is

Comparing to the definition of the definite integral, this limit quite clearly corresponds to the definite integral

Comparing to the definition of the definite integral, this limit quite clearly corresponds to the definite integral

HIGH SCHOOL

An object is launched at 19.6 m/s from a height of 58.8 m. The equation for the height (h) in terms of time (t) is given by h(t) = -4.9t2 +19.6t + 58.8. What is the object's maximum height?

H(t) = Ho +Vot - gt^2/2

Vo = 19.6 m/s

Ho = 58.8 m

g = 9.8 m/s^2

H(t) = 58.8 + 19.6t -9.8t^2/2 = 58.8 + 19.6t - 4.9t^2

Maximun height is at the vertex of the parabole

To find the vertex, first find the roots.

58.8 + 19.6t - 4.9t^2 = 0

Divide by 4.9

12 + 4t - t^2 = 0

Change sign and reorder

t^2 - 4t -12 = 0

Factor

(t - 6)(t + 2) =0 ==> t = 6 and t = -2.

The vertex is in the mid point between both roots

Find H(t) for: t = [6 - 2]/2 =4/2 = 2

Find H(t) for t = 2

H(6) = 58.8 + 19.6(2) - 4.9(2)^2 = 78.4

Answer: the maximum height is 78.4 m

Vo = 19.6 m/s

Ho = 58.8 m

g = 9.8 m/s^2

H(t) = 58.8 + 19.6t -9.8t^2/2 = 58.8 + 19.6t - 4.9t^2

Maximun height is at the vertex of the parabole

To find the vertex, first find the roots.

58.8 + 19.6t - 4.9t^2 = 0

Divide by 4.9

12 + 4t - t^2 = 0

Change sign and reorder

t^2 - 4t -12 = 0

Factor

(t - 6)(t + 2) =0 ==> t = 6 and t = -2.

The vertex is in the mid point between both roots

Find H(t) for: t = [6 - 2]/2 =4/2 = 2

Find H(t) for t = 2

H(6) = 58.8 + 19.6(2) - 4.9(2)^2 = 78.4

Answer: the maximum height is 78.4 m

MIDDLE SCHOOL

-7 (2r -1) + 3(8 -r )

You need to apply the -7 to both 2r and -1. You need to do the same with the 3, applying it to 8 and -r.

-14r + 7 + 24 -3r

Now you would want to combine like terms.

-17r + 31

First do the distributive property and then combine like terms. You should get -17r+31

MIDDLE SCHOOL

A point P has coordinates (-8, 2). What are its new coordinates after reflecting point P across the x-axis?

Its new coordinates are (-8,-2).

reflections across the x-axis are (x, -y)

reflections across the x-axis are (x, -y)

COLLEGE

the dimensions of a porch are 16 feet long by 12 feet wide use the scale 1 inch=4 feet what is the width and length in inches

Hi there!

Since the scale is 1 in = 4 ft, we divide both the length and width by 4 to get the new length and width with the scale factor applied.

16 / 4 = 4

12 / 4 = 3

So, the

length = 4

width = 3

Hope this helps!

Since the scale is 1 in = 4 ft, we divide both the length and width by 4 to get the new length and width with the scale factor applied.

16 / 4 = 4

12 / 4 = 3

So, the

length = 4

width = 3

Hope this helps!