1 pts
Question 20
The population of a town is increasing at 6.2% per year. The city
council believes they will have to add another elementary school
when the population reaches 100,000. If there are currently
76,000 people living in the town, how long until a new
elementary school is needed. Round to the nearest tenth.

Given:

The given function is:

[tex]y=-32x^2+90x+3[/tex]

To find:

The range of the given function.

Solution:

We have,

[tex]y=-32x^2+90x+3[/tex]

It is a quadratic function because the highest power of the variable x is 2.

Here, the leading coefficient is -32 which is negative. So, the graph of the given function is a downward parabola.

If a quadratic function is [tex]f(x)=ax^2+bx+c[/tex], then the vertex of the quadratic function is:

[tex]Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)[/tex]

In the given function, [tex]a=-32,b=90,c=3[/tex].

[tex]\dfrac{-b}{2a}=\dfrac{-90}{2(-32)}[/tex]

[tex]\dfrac{-b}{2a}=\dfrac{-90}{-64}[/tex]

[tex]\dfrac{-b}{2a}=\dfrac{45}{32}[/tex]

The value of the given function at [tex]x=\dfrac{45}{32}[/tex] is:

[tex]y=-32(\dfrac{45}{32})^2+90(\dfrac{45}{32})+3[/tex]

[tex]y=\dfrac{2121}{32}[/tex]

The vertex of the given downward parabola is [tex]\left(\dfrac{45}{32},\dfrac{2121}{32}\right)[/tex]. It means the maximum value of the function is [tex]y=\dfrac{2121}{32}[/tex]. So,

[tex]Range=\left\{y|y\leq \dfrac{2121}{32}\right\}[/tex]

[tex]Range=\left(-\infty, \dfrac{2121}{32}\right ][/tex]

Therefore, the range of the given function is [tex]\left (-\infty, \dfrac{2121}{32}\right ][/tex].

Answer:

-2

Step-by-step explanation:

since the base are the same you add the exponent.

4x+2 + 2x-1= -3x-17

4x+2x +3x =-17-2+1

9x =-18

x=-2

Answer:

-2

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

it would be 5. x is 5 so if it is wrong sorry its best e a while since i done that kind of math

Answer:

Simplified : -4y^(2)-y-11

Step-by-step explanation:

My bad if its wrong hope this helps tho

Answer:Cube  

Step-by-step explanation:

possibly a cube

Answer:

mike did i think im super sooooo sorry if im wrong

Step-by-step explanation:

Step-by-step explanation:

L+W+L+W=26 so 2L=26–2W and you can find length from the perimeter as L=13−W

LW=42 so L=42/W is the other way to find the length, from the area. Both ways require you to know W, but if you have both pieces of information the two answers for length must be the same 42/W=13−W, and you solve this:

42=13W−W2

W2–13W+42=0

(W−6)(W−7)=0

Either W−6=0 or  W−7=0

Answer:

[tex]x + 4[/tex]

Step-by-step explanation:

The question have missing details.

Because, the question says she collected some cans "after picnic"; This means that she has some cans "before picnic"

So, we assume that she has x bags of can before the picnic.

[tex]After\ Picnic = 4[/tex]

So, the total number of bags collected is:

[tex]Total = Before + After\ Picnic[/tex]

[tex]Total = x + 4[/tex]

If x is 5, then she took 9 bags of can to the recycling center

If x is 2, then she took 6 bags of can to the recycling center

If x is 0, then she took 4 bags of can to the recycling center

Answer:

V= +5 and -5

Step-by-step explanation:

just square root both sides

Answer:

4.

Step-by-step explanation:

28 = 2*2*7

48 = 2*2*2*2*3

72= 2*2*2*3*3

So the HCF = 2*2 = 4.

Answer:

hcf stand's for

highest common factor

and must be prime numbers

so the answers 3

Answer:

(2a,2b)

(-4a,b)

Step-by-step explanation:

for the first one

the x value of coordinate L is going to be twice the value of the x coordinate of k (a)

That being said the x value of L = 2a

The y value of L is going to be half the value of the y value of coordinate A ( 4b )

4b/2=2b so the y value of coordinate L is 2b

now we put the values as an ordered pair

The answer would be (2a,2b)

Answer:

1/20

Step-by-step explanation:

Simple probability is found by counting all the results which fit requirements and dividing by all possible results.

To find probability of two results in a row, multiply chance of first result by chance of second result.

Since you are replacing the marble before the second draw, we don’t have to figure out the various changes in odds for the different possible first draws. It’s just that simple.

There are 5 black marbles

There are 4 red marbles

There are always 20 marbles in all

5/20*4/20=1/4*1/5=1/20

By coincidence, the same as the chance of drawing the white marble in one draw.

Answer:

Combined together:

So

15≤x<10

Interval notation

Another way

10 is not included so open bracket

Answer:

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the volume of a Rectangular prism you have to do W*H*L

L=1/5

W=4/5

H=3/5

So just multiply them all and you get .0096 cm^3

Answer:

m=1 or m=-3

Step-by-step explanation:

when m=1,

(1+1)sq+1=5

4+1=5

5=5

True statement

when m=-3,

(-3+1)sq+1=5

(2)sq+1=5

4+1=5

5=5

True statement

Answer:

75:45

Step-by-step explanation:

3*15=45

5*15=45

Answer:

373248 cm³ of wax

Step-by-step explanation:

If the crayon is 90 millimeters long, how many cubic centimeters of wax is used to make a box of 8 crayons?

1 crayon = 90mm

8 crayons = x

Cross Multiply

x = 8 × 90mm

x = 720mm

Converting to cubic mm

= (720mm)³ = 373248000mm³

Converting to cubic centimeter

1 mm³ = 0.001 cm³

373248000 mm³ = x

Cross Multiply

373248000 × 0.001 cm³

= 373248 cm³ of wax

Answer:

oh i will what is that code of yours

Step-by-step explanation:

quv-xypc-xhm ←what is this

​

Answer:

Step-by-step explanation:

Using exponential function concepts, it is found that:

The model is: .

The car will be worth $13,625 in 7 years.

Answer:92.4

Step-by-step explanation:

4x+7x=132

10x=132

x=132/10

x=13.2

4x=4×13.2

=52.8

5x=7×13.2

=92.4

Answer:

3 is the answer bc it make more sense

Answer:

A=90

B=18

C=111

D=39

E=35

Step-by-step explanation:

Answer:

X = 45

Step-by-step explanation:

a^2 + b^2 = c^2

60^2 + a^2 = 75^2

3,600 + a^2 = 5,625

- 3,600            - 3,600

____________________

    a^2= 2025

square root them

a^2 = a

2025 = 45

so x =45

Answer:

Step-by-step explanation:

Answer:

y = 2x + 24

Step-by-step explanation:

Slope-intercept form equation => y = mx + b

m = slope = change in y / change in x

b = y-intercept

✔️using two pairs of values form the table, (-6, 12) and (-5, 14):

Slope (m) = (14 - 12)/(-5 -(-6))

m = 2/1

m = 2

✔️To find b, substitute (x, y) = (-6, 12) and m = 2 into y = mx + b.

12 = 2(-6) + b

12 = -12 + b

12 + 12 = b

24 = b

b = 24

✔️To write the equation, substitute m = 2 and b = 24 into y = mx + b:

y = 2x + 24

Answer: 100

Step-by-step explanation:

The formula for the area of a trapezoid is (B1+B2)/2*h

so substitute:

(8+12)/2*10

20/2*10

10*10

100

Answer:

100 sq inches

Step-by-step explanation:

Simply use the formula for finding the area:

[tex]\frac{1}{2} * (sum of parallel sides) * height\\= \frac{1}{2} * (8 + 12) * 10\\= \frac{1}{2} * 20 * 10\\= 100 sq. inches[/tex]

Answer:

is 3 units away from c

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

[tex]11^2=121\\12^2=144\\121<131<144[/tex]

Hence, [tex]\sqrt{131}[/tex] is in between 11 and 12