A small town has two local high schools. High School A currently has 850 students
and is projected to grow by 35 students each year. High School B currently has 700
students and is projected to grow by 60 students each year. Let A represent the
number of students in High School A int years, and let B represent the number of
students in High School B after t years. Write an equation for each situation, in terms
of t, and determine after how many years, t, the number of students in both high
schools would be the same.

Answers

Answer 1

Answer:

For High School A, let [tex]S_A(t)[/tex] denote the number of students after [tex]t[/tex] years. Define [tex]S_B(t)[/tex] analogously.

Then [tex]S_A(t) = 850 + 35t[/tex] and [tex]S_B(t) = 700 + 60t[/tex].

After 6 years the number of students in both high schools would be the same.

Step-by-step explanation:

For High School A, let [tex]S_A(t)[/tex] denote the number of students after [tex]t[/tex] years. Define [tex]S_B(t)[/tex] analogously.

Since we start out at 850 students at High School A and it is growing by 35 students every year, we must have that [tex]S_A(t) = 850 + 35t[/tex].

Since we start out at 700 students at High School B and it is growing by 60 students every year, we must have that [tex]S_B(t) = 700 + 60t[/tex].

Setting the two equations equal to each other, we see that [tex]850+35t=700+60t\\850-700=60t-35t\\25t=150\\t=6[/tex]

So after 6 years the number of students in both high schools would be the same.


Related Questions

i need help with my math problems

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Answer:

Step-by-step explanation:

X       Y                    X           Y    

0       3                     0           5

1        7                     1              8

2        11                    2           11

3        15                   3          14

4         19                   4            17  

What is the total number of common tangents that can be drawn to the circles?
A. 3
B. 2
C. 1
D. 0

Answers

A) 3. In this case, you can draw one down the middle, one on top, and one on the bottom.

The total number of common tangents that can be drawn to the circles is 3 Hence, the correct option is (A).

What is tangent?

The tangent is a line that goes by touching the circle.

If we meet that point to the circle then it gives us 90 degrees.

Given that the circle are intersecting so a common tangent will be

The First will be at the intersection point of that circle.

The second will be the upper portion of the circle.

The third will be the lower portion of the circle.

For more information about the common tangents.

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find the missing side of the triangle please

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the side length of c is 17 cm

what's a function????

Answers

Answer: Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences.

Step-by-step explanation:

Answer:

A relation of two or more numbers

One input one output

there can be more then one input for the same output

just not more then one output for one input

I need help please, I am weird. I know​

Answers

Answer: -10x+9

Step-by-step explanation:

1. Remove parantheses:

-2x+10-8x-1

2. Simpify: -2x-8x+10-1 => -10x+9

Have a nice day! :D

First remove parentheses , so you would have -2x+10 -8x-1 , combine like terms , -10x +10-1 , then subtract the numbers . Your solution is -10x+9 .

I HATE MATH SM ITS NOT FUNNY, HELP ME (please)

Answers

Answer:

11) 2

12) 1

13) 6

14) 6

15) m<1=58°

m<2=122°

m<3=58°

m<5=122°

m<6=58°

m<7=122°

m<8=58°

Step-by-step explanation:

11) 2

12) 1

13) 6

14) 6

15) m<1=58°

m<2=122°

m<3=58°

m<5=122°

m<6=58°

m<7=122°

m<8=58°

-3(x-2) i am having trouble with this lol

Answers

Answer: -3x + 6

Step-by-step explanation:

Multiply using the disturbutive property.

Answer:

-3x + 6

Step-by-step explanation:

-3x - 3x (-2)

multiply it

-3x+6

Write 20% as a fraction​

Answers

Answer:

1/5

Step-by-step explanation:

Find the slope between the points (2,9) and (3,1) *
Please I need help immediately

Answers

Answer:

1

Step-by-step explanation:

Distance between x's (Δx)

0

This field is calculated automatically, you cannot change it's value manually.

Distance between y's (Δy)

1

d = √(Δy2 + Δx2) = √(12 + 02) = √1 = 1

Find the area of the composite figure?


Answers

Answer:

128

Step-by-step explanation:

Let's start by figuring out the last side of the triangle

we can use the pathagoryous theroem and get

11.9²+x²=16.9²

Solve this and get x=12

Let's now compute the area of the triangle

b*h*.5

12*11.9*.5=71.4

So 71.4 is the area of the triangle

we now need to find the area of the semi circle.

to do this we are going to find the area and then divide it by 2

We know that the length is equal to 12 which means that the radius is 6

so we have

π6²/2

which is 56.55

We add the 71.4+56.55= 127.94 which rounds to 128

Answer:

212.758

Step-by-step explanation:

Find the semi-circle first, the diameter is 16.9 ft.

To find area:

Formula:

pi x radius x radius x 1/2

16.9 ÷ 2 = 8.45 (radius)

22/7 x 8.45 x 8.45 = 224.407 (Circle)

224.407 ÷ 2 = 112.203 (Semi circle)

Find the triangle:

1/2 x base x height or length x base x height

But for now, we will use the first one.

1/2 x 16.9 x 11.9 = 100.555

Now add them up.

100.555 + 112.203 = 212.758

(I don't know what units you to put for your answer since I don't learn American mathematics, so it's up to you)

The equation of line r is y = –3/2 x + 5. Line s is parallel to line r. What is the slope of line s?

Answers

Answer:

-3/2

Step-by-step explanation:

Parallel lines have same slopes.

What is the greatest common factor of the number pair 20 and 30

Answers

Answer:

10

Step-by-step explanation:

do prime factorizations of each number and multiply the common factors

20 = 2 · 2 · 5

30 = 2 · 3 · 5

common factors are 2 and 5

multiply them to get 10

Which sum describes the total number of apples in this
array?
3 + 3 + 3
3 + 3 + 3 + 3
3 + 4
4 + 4 + 4 + 4

Answers

Answer:

3+3+3+3

Step-by-step explanation:

what is 45 less than six times x​

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Answer:

6x - 45

Step-by-step explanation:

Can someone help me please

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Answer:55

Step-by-step explanation:

Do number 3 am giving brainliest look below

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Answer:

18 cm^2

Step-by-step explanation:

what is x=y+2 this geometry. thank you

Answers

Answer:

Square

Step-by-step explanation:

Its easy, duh

Heather drove at a constant rate. She traveled 162 miles in 3 hours. How far did Heather travel in 1 hour?

Answers

Answer:

54 miles

Step-by-step explanation:

I think it's right I did 162÷3=54 I hope it helps :D

There is a bag filled with 4 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 red?

Answers

Answer:

im not sure but this is just a guess (please keep it in mind)

Step-by-step explanation:

4+5= 9 marbles all together

9-1= 8

1 in 8? or 1 in 9

this is becuase we dont know if the one that was taken out randomly first wasnt a red or not but then i could be wrong and the fact if it was red or blue in the first place might not even matter. it really depends.

A store sells 5 T-shirts for $49.05. What is the unit cost per T-shirt?

Answers

9.81 hope this helps!!

(−3p2+5p−2)+(−p2−8p−15)=

Answers

Answer:

Step-by-step explanation:

When you distribute a positive sign to a parentheses, you essentially change nothing. So, you can drop all of the parentheses for this entire equation. Now combine like terms.

[tex]-4p^2-3p-17[/tex]

or

[tex]-1(4p^2+3p+17)[/tex]

Expand & simplify 4 ( g + 2 ) − 2 ( g − 6 )

Answers

Answer:

2g+20

Step-by-step explanation:

multiply the 4 by whats in the parenthasis. and multiply the negative 2 by whats in the parenthasis. combine the like terms.

Graph y=1.4xy=1.4xy, equals, 1, point, 4, x. plz help its not too late plz

Answers

Replace x with any number and solve for Y.

Do this at least twice to get 2 points.

Place these points on the graph and draw a line through them.

See attached graph.

Let x = 2

y = 1.4(2)

y = 2.8

First point = (2,2.8)

Let x = 5

y = 1.4(5)

y = 7

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The y-intercept is zero, that means the line is passing through origin.

What is the equation of line?

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

The equation is given below.

y = 1.4x

In the above equation, y-intercept is not there, which means the line is passing through origin.

More about the equation of line link is given below.

https://brainly.com/question/21511618

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The midpoint of \overline{\text{AB}} AB is M(5, 1)M(5,1). If the coordinates of AA are (3, 6)(3,6), what are the coordinates of BB?

Answers

Answer:

(7, -4)

Step-by-step explanation:

The formula for calculating midpoint is expressed as;

M(X, Y) = (x2+x1)/2, (y1+y2)/2

X = x1+x2/2

Y = y1+y2/2

Given

X = 5, Y = 1, x1 = 3, y1 = 6

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X = x1+x2/2

5 = 3+x2/2

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x2 = 10-3

x2 = 7

Get y2;

Y = y1+y2/2

1 = 6+y2/2

2 = 6+y2

y2 = 2-6

y2 = -4

Hence the coordinate of B is at (7, -4)

please help me will give you brainliest!!

Answers

Yes
No
No
Yes
I believe

Answer:

yes, no, no, yes

Step-by-step explanation:

Plug in each point into both equations to see which ones fit.

For the first point, (4,1) it works for both equations.

1=-2( 4 ) + 9, 1= -8 + 9, 1=1

4( 4 )+2( 1 )=18, 16 + 2 = 18, 18 = 18

Do it for the rest of the points and plug them in and you get,

no for (5,-3) because -1 does not equal to -3

no for (6,0) because -3 does not equal to 0

(-5,19) is yes because 19=19 and 18=18

Please mark me brainliest

A teacher interested in determining the effect of a new computer program on
learning to read conducted a study. One hundred students were randomly assigned
to one of two groups. The first group used the computer program while the second
group did not. Both groups were tested to determine how much their reading levels
improved. The results for the two groups were compared. What kind of study is this?
(2 points)
1) This is an experiment because a treatment was applied to a group.
2)
This is an experiment because students were able to choose which group to
join.
3) This is a survey because students were randomly assigned to groups.
4) This is a survey because a treatment was applied to both groups,

Answers

Answer:

an experiment because a treatment was applied to a group

Step-by-step explanation:

jayfeather friend me

Answer:

This is an experiment because a treatment was applied to a group.

Step-by-step explanation:

This is because it cannot be a survey since the children are taking a test, which has a hypothesis. Hope you get this right. I took the test and got right.

PLEASE MARK ME AS BRAINLIEST

ANSWER THIS AND ILL MAKE YOU BRAINLY!!

Answers

Answer:

C. undefined

Step-by-step explanation:

Have a nice day

Leslie's lunch bill is $13.95. She wants to leave a tip that is 15% of the bill. How much tip should she leave?

Answers

Answer:

She would leave a tip of 2.0925 ($2.09)

Step-by-step explanation:

I don't remember how to solve this problem I missed yesterday when we learned it. 4(x-2+y)

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Answer:

4x - 8 + 4y

Step-by-step explanation:

4(x - 2 + y)

4x - 8 + 4y

You multiply each term in the parenthesis by the number in front of it.

2/3 times what equals 3

Answers

Answer:

Should be 5 or 6

Step-by-step explanation:

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