Jacob won 62 super bouncy balls playing
horseshoes at the county fair. At school he
gave two to every student in his math class. He only has 2 remaining. How
many students are in his class?

Given:

The graph of an exponential function.

To find:

The function in the form of [tex]f(x)=ab^x[/tex].

Solution:

The general form of an exponential function is

[tex]f(x)=ab^x[/tex]                ...(i)

From the given graph it is clear that the function passes through the points (0,4) and (1,7). It means these points will satisfy the function.

For x=0 and f(x)=4,

[tex]4=ab^0[/tex]

[tex]4=a(1)[/tex]

[tex]4=a[/tex]

For x=1 and f(x)=7,

[tex]7=ab^1[/tex]

Putting a=4, we get

[tex]7=4(b)[/tex]

[tex]\dfrac{7}{4}=b[/tex]

Substitute a=4 and [tex]b=\dfrac{7}{4}[/tex] in (i).

[tex]f(x)=4\left(\dfrac{7}{4}\right)^x[/tex]

Therefore, the required exponential function is [tex]f(x)=4\left(\dfrac{7}{4}\right)^x[/tex].

Answer:

25 bottles

Step-by-step explanation:

2 litres=2000 milliliters

2000/80=25 (or) 80x25=2000

The amount of containers it will take to fill the 2-liter bottle is 25 containers.

Given the following data:

To determine the amount of containers it will take to fill the 2-liter bottle:

In this exercise, you're required to determine the amount of 80-milliliter containers that would be required to fill the 2-liter bottle.

First of all, we would convert the volume in liters to milliliter.

Conversion:

1 Liter = 1000 millimeters

2 Liter = 2000 millimeters

Now, we can find the amount of containers by using the formula:

[tex]Number\;of\;containers = \frac{Volume \;of\;bottle}{Volume \;of\;containers}[/tex]

Substituting the parameters into the formula, we have;

[tex]Number\;of\;containers = \frac{2000}{80}[/tex]

Number of containers = 25 containers

Find more information: https://brainly.com/question/4728821

Answer:

2 days

Step-by-step explanation:

Step one:

let the number of days be x

and the total height be y

​Plant A is 6 cm tall and growing at a rate of 4 cm per day.

the total height is

y=6+4x------------1

Plant B is 10 cm tall and growing at a rate of 2 cm per day.​

y=10+2x-----------2

Required

time taken for both plants to have the same height

Step two:

equate the two equations to find when the plants will have the same height

6+4x=10+2x

collect like terms

4x-2x=10-6

2x= 4

divide both sides by 2

x= 4/2

x= 2 days

Answer:

35

Step-by-step explanation:

(7x7=49) (7x2=14)

then you do

49-14= 35

Answer:21m, 5n, 2=1

28m, 4n, 2=2

Step-by-step explanation:

Answer:

(a) [tex]x^4 * (-y)^4 = (xy)^4[/tex]

Step-by-step explanation:

Given

[tex]x^4 * (-y)^4[/tex]

Required

Select and equivalent expression

[tex]A.\ (xy)^4[/tex]     [tex]B.\ (-xy)^4[/tex]   [tex]C.\ -(xy)^4[/tex]    [tex]D.\ (x-y)^4[/tex]

[tex]x^4 * (-y)^4[/tex]

Apply law of indices:

[tex]x^4 * (-y)^4 =x^4 * (-y) * (-y) * (-y) * (-y)[/tex]

This gives:

[tex]x^4 * (-y)^4 = x^4 * (y) * (y) * (y) * (y)[/tex]

[tex]x^4 * (-y)^4 =x^4 * y^4[/tex]

x and y have the same exponent; So, they can be expressed as:

[tex]x^4 * (-y)^4 = (x*y)^4[/tex]

[tex]x^4 * (-y)^4 = (xy)^4[/tex]

Answer:

1,000 of 1,400 is 71.43%

Answer:

1/3

Step-by-step explanation:

4/3=1 1/3

1  2/3 - 1 1/3= 1/3

Hope this helps!

Answer:

x=0.88

y= -3.7

Step-by-step explanation:

-3.7=6x-9

5.3=6x

0.88=x

Answer:

B

Step-by-step explanation:

5:7

5×2 = 10

7×2 = 14

10:14 = 5:7

Answer:

2^3x7

your welcome

Answer:

23× 7

Step-by-step explanation:

have a wonderful day!!! :) :)

Answer:

It C

Step-by-step explanation:

6y-2y is 4y and 4y+ 8y is 12y

Answer:

12y

Step-by-step explanation:

you do 6y-2y=4y

then 4y+8y=12y

so it's 12y

hope that helps :)

Answer:

step below

Step-by-step explanation:

x + 4y = 30

x – 2y=0

x= 2y

2y + 4y = 30

6y = 30

y = 5

x = 10

Answer:

I'm not entirely sure if this is correct.

Step-by-step explanation:

[tex] \frac{2}{3} = \frac{30}{x} \\ 2x = 3(30) \\ \frac{2x}{2} = \frac{90}{2} \\ x = 45[/tex]

Answer:

1/-14 or 1 over - 14

Step-by-step explanation:

The equation you need is: y2-y1  over x2-x1

So if you plug it in it becomes 2-1 over -17 -(-3) so 2 - 1 is 1 that's the easy part, 17 - (-3) is the hard part because you can't minus a negative. So it becomes -17+3 which is still -14 because you take the sign of the bigger number. Sorry if it's hard to understand :(

Answer:

h(-6) = 3

Step-by-step explanation:

h(x) = -x - 3

h(-6) = -(-6) - 3

h(-6) = 6 - 3

h(-6) = 3

Answer:

b = 3√37

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Trigonometry

[Right Triangles Only] Pythagorean Theorem: a² + b² = c²

Step-by-step explanation:

Step 1: Define

a = b

b = 14

c = 23

Step 2: Find b

Answer:

b=3root37

Step-by-step explanation:

Answer:

y=-6

Step-by-step explanation:

the line needs to be vertical to be parallel to y=2, and pass through (-1,-6)

Answer:

[tex]12:20[/tex]

Step-by-step explanation:

Answer:

n=16

Step-by-step explanation:

6n=9246n=924 nn

Write the problem as a mathematical expression.

6n=9246n=924 nn

Cancel the common factor of 99 and 2424.

Factor 33 out of 99.

6n=3(3)246n=3(3)24

Cancel the common

Factor 33 out of 2424.

6n=3⋅33⋅86n=3⋅33⋅8

Cancel the common factor.

6n=3⋅33⋅86n=3⋅33⋅8

Rewrite the expression.

6n=386n=38

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

6⋅8=n⋅36⋅8=n⋅3

Solve the equation for nn.

Rewrite the equation as n⋅3=6⋅8n⋅3=6⋅8.

n⋅3=6⋅8n⋅3=6⋅8

Multiply 66 by 88.

n⋅3=48n⋅3=48

Divide each term by 33 and simplify.

Divide each term in n⋅3=48n⋅3=48 by 33.

n⋅33=483n⋅33=483

Cancel the common factor of 33.

Cancel the common factor.

n⋅33=48

Percent means per 100, so 45% would be 45 out of 100, which written as a fraction would be 45/100

The answer would be C.

Answer:

the answer could be 100 metre

Answer:

yes

Step-by-step explanation:

so i was doing some serching online and i typed what does a function mean and this wat came up an activity or purpose natural to or intended for a person or thing. so as i was thinking this answer fits the description on what i was given from the internet

Answer: p = 1

Step-by-step explanation:

2/5 + p = 4/5 + 3/5p

-2/5        -2/5

      p = 2/5 + 3/5p

-3/5p            -3/5p

2/5p = 2/5

Divide both sides by 2/5

p = 1

Answer:

(x-3)² + (y+5)² = 16

Step-by-step explanation:

Radius will be half of diameter means that radius = r = 8/2 = 4.

With Center (h,k) the equation of circle is

(x-h)² + (y-k)² = r²

so by putting values answer will be

(x-3)² + (y+5)² = 4²

(x-3)² + (y+5)² = 16

Simplify the expression.

18x + 7y/6

Answer:

x = 7

Step-by-step explanation:

[tex]\frac{10}{8} = \frac{3x-6}{12}[/tex] --> Triangle Similarity Theorem

120 = 8(3x - 6) --> Cross Multiplying

120 = 24x - 48 --> Distributing the 8

24x - 48 + 48 = 120 + 48 --> Adding 48 on both sides

24x = 168 --> Simplifying

24x/24 = 168/24 --> Divide 24 on both sides

x = 7 --> Simplifying

Hope this helped! <3

Answer:

Step-by-step explanation: