The graph represents a function related to a train's movement over time.
12
11
10
9
8
6
5
4
2
0 1 2 3 4
7 8 9 10 11 12
Time
Which function could this graph represent?
A.
the speed of a train as it decreases its rate of acceleration
B.
the speed of a train as it slows down when approaching a station
C.
the distance of a train from a station it has departed as it accelerates
D.
the distance of a train from a station it approaches at a constant speed

Given:

An exponential function [tex]f(x)=ab^x[/tex] passes through the points (0, 12000) and (2, 3000).

To find:

The values of a and b.

Solution:

We have,

[tex]f(x)=ab^x[/tex]      ...(i)

It passes through the point (0,12000). Putting x=0 and f(x)=12000 in (i), we get

[tex]12000=ab^0[/tex]

[tex]12000=a(1)[/tex]

[tex]12000=a[/tex]

Given function passes through the point (2,3000). Putting x=2, a=12000 and f(x)=3000 in (i), we get

[tex]3000=12000b^2[/tex]

[tex]\dfrac{3000}{12000}=b^2[/tex]

[tex]\dfrac{1}{4}=b^2[/tex]

Taking square root on both sides.

[tex]\pm \dfrac{1}{2}=b[/tex]

For an exponential function b cannot be negative. So, [tex]b=\dfrac{1}{2}[/tex].

Therefore, the value of a is 12000 and the value of b is [tex]\dfrac{1}{2}[/tex].

9514 1404 393

Answer:

  $1320

Step-by-step explanation:

The amount of commission is the product of the commission rate on sales and the amount of sales:

  Job A commission = 0.12 × $11,000 = $1320

_____

It may help you to realize that the percent symbol (%) is fully equivalent to /100. That is 12% = 12/100 = 0.12.

Answer:

g

Step-by-step explanation:

Answer:

(0,-1)

Step-by-step explanation:

(0,-1) will work because when you plug them is it is equivalent to 4

Answer:

D

Step-by-step explanation:

3x + 2(x + 1) = 12 ← distribute and simplify left side

3x + 2x + 2 = 12

5x + 2 = 12 ( subtract 2 from both sides )

5x = 10 ( divide both sides by 5 )

x = 2 → D

d .2

d will be the answer

by simplify

Answer:

x = 5 and y = 7

Step-by-step explanation:

Given that,

PT = x+2, TR=y, QT=2x, TS=y+3

We need to find the value of x and y.

The diagonal of a parallelogram bisect each other. It means,

PT = TR and QT = TS

ATQ,

y = x+2 ...(1)

and

y+3 = 2x ....(2)

Subtracting equation (1) and (2).

y-(y+3) = x+2-2x

y-y-3 = 2-x

-3 = 2-x

x = 2+3

x = 5

Put the value of x in equation (1).

y = 5 + 2

y = 7

Hence, the values of x and y are x = 5 and y = 7.

Answer:

^ they are correct

Step-by-step explanation:

Answer:

x = -8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

i had that on my test before

Answer:

2.29

Step-by-step explanation:

8.5-6.21

4 10

8.50

-6.21

2.29

Answer:

f(g(x)) = 3x + 25

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 3x - 5

g(x) = x + 10

Step 2: Find f(g(x))

Answer:

6.5, 6.49

Step-by-step explanation:

The numbers that are less than 6.58 is 6.58, 5.98, 6.538 and 6.49.

A group of numbers between integers on a number line are known as decimals. They are merely an additional mathematical representation of fractions.

Decimals allow us to express measurable quantities like length, weight, distance, money, etc. with greater accuracy. Integers, also known as whole numbers, are represented to the left of the decimal point, while decimal fractions are represented to the right of the decimal point. The next place, which is (1/10)th or tenth place value, is (1/10) times smaller if we move immediately from the first place.

Given number: 6.58

Now, we have to find the number less than 6.58

6.58 < 6.583

6.58 > 6.5

6.58 = 6.58

6.58 >5.98

6.58 > 6.538

6.58 > 6.49.

Hence, the numbers that are less than 6.58 is 6.58, 5.98, 6.538 and 6.49.

Learn more about decimal here:

https://brainly.com/question/548650

#SPJ2

9514 1404 393

Answer:

  A(-8, 6), D(-1, -16), E(17, -3)

Step-by-step explanation:

Any point with an x-value that matches any of {-8, -1, 5, 15, 17} will prove Mariela's claim incorrect. (A function cannot use an x-value more than once.)

Those points are ...

  (-8, 6), (-1, -16), (17, -3)

Answer:

[tex]9xy[/tex]

Step-by-step explanation:

I suppose you're asking for the GCF of [tex]45x^2y[/tex] and [tex]54xy^2[/tex].

[tex]45x^2y = 3^2 \times 5 \times x^2 \times y\\54xy^2 = 2 \times 3^3 \times x \times y^2[/tex]

The GCF is [tex]3^2 \times x \times y = 9xy[/tex].

Answer:

24%

Step-by-step explanation:

4 + 9 + 1 + 3 + 6 + 2 = 25

6/25 = .24 = 24%

Answer:

$37

Step-by-step explanation:

Delivery fee- $10

each sandwich- $4.50

Sandwiches ordered- 6

4.50(6)+10=37

Answer:

a. Green

b. Blue

c. Red

d. Purple

(Just for clarification, m is the slope and b is the y-intercept.)

Answer:

The answer is $9.60!

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope: −4

y-intercept: (0,4)

Answer:

D.) d

Step-by-step explanation:

Graph the line using the slope and y-intercept, or two points.

Slope: -4

y-intercept: (0,4)

x: 0 & 1

y: 4 & 0

Hence the answer is coordinate grid D.

Answer:

The cost of lesson for 9 hours on weekdays and 3 hours on weekends

Step-by-step explanation:

Given

[tex]Weekdays = \$m /hour[/tex]

[tex]Weekends = \$1.2m/hour[/tex]

Required

What does 9m + 3(1.2m) represent

The expression can be split to:

9m and 3(1.2m)

For 9m:

From the question, we understand that:

[tex]m = 1\ hour[/tex]

Multiply both sides by 9

[tex]9 * m = 1\ hour * 9[/tex]

[tex]9 m = 9\ hours[/tex]

This means that:

9m = the cost of lessons for 9 hours on weekdays

For 3(1.2m):

From the question, we understand that:

[tex]1.2m = 1 \ hour[/tex]

Multiply both sides by 3

[tex]3 * 1.2m = 1 \ hour * 3[/tex]

[tex]3(1.2m) = 3 \ hours[/tex]

This means that:

3(1.2m) = the cost of lessons for 3 hours on weekends

Hence, the expression represents:

The cost of lesson for 9 hours on weekdays and 3 hours on weekends

Answer: 18.84

1.  Multiply the radius by two (diameter)

2. Multiply the diameter by pi

3. Round

Answer:

the circles circumference is 18.84 cm

Answer: B

x looks like .9 so if -.9 + 3 = -2.1 then you can see that's the answer on the number line, hope it helps, I'm 80% sure it's right

Answer:

512??

Step-by-step explanation:

um i just multipled 8x8x8 but its probably wrong- sorry

Answer:

-1

Step-by-step explanation:

Okay, i might be wrong..? I tried and this is what I got.

Answer:

x = 2 for a, c, and f

Step-by-step explanation:

a)

6(2x - 1) = 4 + 7x

12x - 6 = 4 + 7x

5x = 10

x = 2

b)

10 - 3x = -2(x + 4)

10 - 3x = -2x - 8

18 = x

c)

-3(7 - 2x) = -1 - 4x

-21 + 6x = -1 - 4x

10x = 20

x = 2

d)

7x + 12 = 2(4x - 5)

7x + 12 = 8x - 10

22 = x

e)

-5(x + 1) = -4 - 7x

-5x - 5 = -4 - 7x

2x = 1

x = 1/2

f)

8x + 11 = 9(5 - x)

8x + 11 = 45 - 9x

17x = 45 - 11

17x = 34

x = 2

Answer:

A,C,F

Step-by-step explanation:

Answer:62.5

Hello

Step-by-step explanation:

1. 7.50 divided by 6 = 1.25 for 1 length of rope (Feet)

2.50x1.25=62.5

Hope this helped

Or I might be wrong Im not sure yet.

Answer:

y=1/13x - 4/13

Step-by-step explanation:

Just follow the slope intercept form formula-

Formula: y= mx+b

Key:

y = y-coordinate

m = slope

x = x-coordinate

b = y-intercept

Feel free to ask if you have any questions, hope this helps!(:

Answer:

− 414.302

(The answer is simplified, you did not specify the way to solve it.)

Answer:

785 cm³

Step-by-step explanation:

3.14x5x5x10=785

sasssssssssssssssssssssssssssssssssssss

Answer:

10x

Step-by-step explanation: