which number belongs to the solution set of the equation below? 9x=114
A.14
B.16
C.12
D.18

The equation of the exponential graph is y = 100(0.5)^x

On the graph, we have the following points

(x,y) = (0,100) and (1,50)

An exponential equation is represented as:

y = ab^x

Where a = y, when x = 0.

This means that

a = 100

So, we have:

y = 100b^x

At the point (1,50), we have:

50 = 100b^1

Evaluate

50 = 100b

Divide both sides by 100

b = 0.5

Substitute b = 0.5 in y = 100b^x

y = 100(0.5)^x

Hence, the equation of the exponential graph is y = 100(0.5)^x

Read more about exponential equations at:

https://brainly.com/question/11832081

#SPJ2

The solution of expression for the value of n is, n = - 3.

Used the concept of expression that states,

Mathematical expression is defined as the collection of numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that,

The expression is,

[tex]4n + 2 = 6 (\dfrac{1}{3} n - \dfrac{2}{3} )[/tex]

Now simplify the expression by combining like terms and apply the distributive property as,

[tex]4n + 2 = 6 (\dfrac{1}{3} n - \dfrac{2}{3} )[/tex]

Apply distributive property,

[tex]4n + 2 = (\dfrac{6}{3} n - \dfrac{12}{3} )[/tex]

[tex]4n + 2 = 2n - 4[/tex]

Combine like terms,

[tex]4n - 2n = - 4 - 2\\[/tex]

[tex]2n = - 6\\[/tex]

[tex]n = - 3[/tex]

Therefore, the value of n is - 3.

To learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ5

Answer with Step-by-step explanation:

We spent $37.50 for two sweaters.

Each sweater costs the same amount.

Cost of each sweater=$37.50/2

                                  =$18.75

The amount of money you spend varies directly with the number of sweaters you buy.

We have to find the constant of variation.

Here, cost of each sweater is the constant of variation.

Hence, constant of variation is:

$18.75

Final answer:

To find the length of MN, we can set up an equation using the fact that LN + LM = MN and substitute the given values. Solving for x, the length of MN is found to be 4.9 units.

Explanation:

To find the length of MN, we can use the fact that LN = 5.7 and LM = 1.3. We are also given that MN = x + 2.1. Since LN and LM are known, we can set up an equation using the fact that LN + LM = MN.

LN + LM = MN

5.7 + 1.3 = MN

Then, we can substitute the given value of MN = x + 2.1 into the equation and solve for x.

5.7 + 1.3 = x + 2.1

7 = x + 2.1

x = 7 - 2.1

x = 4.9

Therefore, the length of MN is 4.9 units.

Answer:

Step-by-step explanation:

The associative property of multiplication states that the product is the same regardless of their grouping. In this case, after simplifying the expression given, we can see that indeed the products are the same hence that fact that they have different grouping

Answer: [tex]51.4^{\circ}[/tex]

Step-by-step explanation:

We know that the sum of all the exterior angles of a regular polygon with n sides is [tex]360^{\circ}[/tex].

The measure of an exterior angle of a regular n-sided polygon is given by :-

[tex]\dfrac{360^{\circ}}{n}[/tex]

Now, the measure of an exterior angle of a regular 7-sided polygon is given  by :-

[tex]\dfrac{360^{\circ}}{7}=51.4285714286^{\circ}\approx51.4^{\circ}[/tex]

Hence, the  measure of an exterior angle of a regular 7-sided polygon =[tex]51.4^{\circ}[/tex]

Answer:

(-10,0),(-4,0) for Plato/Edmentum Users

Step-by-step explanation:

Have a great day

Answer:

B

Step-by-step explanation:

3x+5x= 8x

5x^3 - 2x^3= 3x^3

-2x^2= -2x^2

13+11=24

Answer:

Step-by-step explanation:

Notice to facts:

The expression has a common factor 6n. Then,

6n⁴-24n³+18n = 6n(n³-4n²+3).

In order to factor the term n³-4n²+3 we use Ruffini-Horner rule, which gives us that

n³-4n²+3 = (n-1)(n²-3n-3).

Then,

6n⁴-24n³+18n = 6n(n³-4n²+3) = 6n(n-1)(n²-3n-3).

If you don't know the formula for the general solution of second degree equation, you are done. Otherwise, it is only to use it in the quadratic factor.

Answer:

The factored form of the expression [tex]\( -4d^3 + 28d^2 - 4d \)[/tex] is [tex]\( -4d(d - 1)(d - 1)(6d - 1) \).[/tex]

Explanation:

To factor the expression [tex]\( -4d^3 + 28d^2 - 4d \)[/tex], we can first look for the greatest common factor (GCF) among the terms. In this case, the GCF is [tex]\( -4d \).[/tex]

So, we can factor out [tex]\( -4d \)[/tex] from each term:

[tex]\[ -4d(d^2 - 7d + 1) \][/tex]

Now, let's focus on factoring the quadratic expression inside the parentheses, [tex]\( d^2 - 7d + 1 \)[/tex]. To factor this quadratic expression, we need to find two numbers that multiply to give the constant term (1) and add to give the coefficient of the linear term (-7d). Since the constant term is 1, the only possible combination is 1 and 1.

So, we can rewrite the expression as:

[tex]\[ -4d(d^2 - 7d + 1) = -4d(d^2 - d - 6d + 1) \][/tex]

Now, we can group the terms and factor by grouping:

[tex]\[ -4d((d^2 - d) + (-6d + 1)) \][/tex]

[tex]\[ -4d(d(d - 1) - 1(6d - 1)) \][/tex]

Now, we can factor further:

[tex]\[ -4d(d - 1)(d - 1)(6d - 1) \][/tex]

Answer:

Step-by-step explanation:

Alright , lets get started.

The first mile charge = [tex]$2.5[/tex]

Total miles taxi covered = [tex]20[/tex]

Subtracting first mile frm the total ride = [tex](20-1)[/tex]

Means the fare will apply on this mile.

So, cost of total ride = [tex]2.5 + 0.4 (20-1)[/tex]

cost of total ride = [tex]2.5+0.4*19[/tex]

cost of total ride = [tex]2.5+7.6[/tex]

cost of total ride = [tex]10.1[/tex]

The answer is $ 10.1 .   :    Answer

Hope it will help :)

Answer:

10.10 (B)

Step-by-step explanation:

edgeeeEeEeEeEe

Answer:

[tex]m+1[/tex]

Step-by-step explanation:

The question is

Simplify the expression

we have

[tex]\frac{1}{3}(9-6m)+\frac{1}{4}(12m-8)[/tex]

using the distributive property

[tex]\frac{1}{3}(9)-\frac{1}{3}(6m)+\frac{1}{4}(12m)-\frac{1}{4}(8)[/tex]

[tex]3-2m+3m-2[/tex]

Combine like terms

[tex]m+1[/tex]

It will take 3 days for 1 man to dig half of that complete hole.

Direct proportion if increase in one quantity also results in increase in another quantity for example price and weight of something.

Inverse proportion is when increase in one quantity results in decrease in another quantity for example time is inversely proportional to (speed when distance is constant.

According to the given question

6 men are working together then it takes them 6 days to dig 6 holes.

∴ Number of men days = 6 days × 6 men = 36 men days

So, in 36 men days 6 holes are dug. Now the men days and the number of holes being dug are in direct proportion with one another.

Hence number of men-days required to dig one hole

= 36/6 men days

= 6 men days

∴ No. of men days required to dig half a hole

= 6/2

= 3 men days

So, It takes 1 man 3 days to dig half a hole.

Learn more about Time and work here :

https://brainly.com/question/3854047

#SPJ2

area of square = 14^2 = 196 square cm

 area of circle = 3.14 *7^2 = 153.86 square cm

196 - 153.86 = 42.14 square cm is shaded

The solution of expression is,

⇒ d = 5/16

We have to given that,

An expression is,

⇒ 3.2 - 4d = 2.3d + 3

Now, We can simplify the expression for solution as,

⇒ 3.2 - 4d = 2.3d + 3

Add 4d both side,

⇒ 3.2 - 4d + 4d = 2.3d + 3 + 4d

⇒ 3.2 = 6.3d + 3

Subtract 3 both side,

⇒ 3.2 - 3 = 6.3d

⇒ 0.2 = 6.3d

⇒ 6.3d = 0.2

Divide 6.3 both side,

⇒ d = 0.2/6.4

⇒ d = 20/64

⇒ d = 5/16

Thus, The solution of the expression is, d = 5/16

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ6