If 8(x) is the inverse of f(x) and f(x) = 4x + 12, what is g(x)?

Answer:

Option C [tex]1,102\ in^{2}[/tex]

Step-by-step explanation:

we know that

The lateral surface area of a cylinder is equal to

[tex]LA=2\pi rh[/tex]

we have

[tex]r=13.6\ in[/tex]

[tex]h=12.9\ in[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]LA=2(3.14)(13.6)(12.9)[/tex]

[tex]LA=1,101.76\ in^{2}[/tex]

Round to the nearest square inch

[tex]LA=1,102\ in^{2}[/tex]

Answer:

Unknown number, x=-4

Step-by-step explanation:

Forming the equation from the information provided above.  

9=2x+17

If we solve for the unknown number, we first collect like terms together.

2x=9-17

2x=-8

Divide both sides of the equal sign by 2 the coefficient of x

x=-4

Answer:

x = -4

Explanation:

We are given the following statement which we are to translate into a mathematical equation and then solve it:

'nine is seventeen more than two times a number'

Assuming [tex] x [/tex] to be the unknown number, this can be written as:

[tex] 9 = 2 x + 1 7 [/tex]

Solving for x:

[tex] 2 x = 9 - 1 7 [/tex]

[tex] 2 x = - 8 [/tex]

[tex]x=\frac{-8}{2}[/tex]

[tex]x=-4[/tex]

Therefore, the unknown number is -4.

Answer:

The mean of the combined group of 30 students is equal to 56.67

Step-by-step explanation:

Let

x ----> The sum of the notes of the 20 papers

y ----> The sum of the notes of the 10 papers

we know that

60=x/20 -----> x=60*20=1,200

50=y/10 -----> y=50*10=500

The mean of the combined group of 30 students is equal to

(x+y)/30

substitute

(1,200+500)/30=56.67

-2xy+3x-2xy+3x ( original equation)

-2xy-2xy+3x+3x ( just rearranging)

-4xy+6x

Answer :-4xy+6x- D.

Answer:

The correct answer is option D.  -4xy + 6x

Step-by-step explanation:

It is given an expression, −2xy + 3x − 2xy + 3x  

To simplify the given expression

Let the expression be −2xy + 3x − 2xy + 3x

−2xy + 3x − 2xy + 3x   = -2xy - 2xy + 3x + 3x     [write similar terms together]

 = -4xy + 6x

Therefore the correct answer is option D.

-4xy + 6x

Answer:

Answer:

The solutions for the equation are:

x = 2  

x = − 4

Step-by-step explanation:

Answer:

x = - 4, x = 2

Step-by-step explanation:

Given

x² + 2x - 8 = 0

Consider the factors of the constant term ( - 8) which sum to give the coefficient of the x- term ( + 2)

The factors are + 4 and - 2, since

4 × - 2 = - 8 and 4 - 2 = + 2, hence

(x + 4)x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x - 2 = 0 ⇒ x = 2

Answer:

Shortest side=5, Largest side=13, Other side=12

Step-by-step explanation:

Let's define the shortest side of the triangle as x, since the other two sides are defined in terms of this one.

The longest side is 2 less than 3 times the shortest side, then it is 3 * x - 2.

The other side is 2 more than twice the shortest side, then it is 2 * x + 2.

By the problem directions, we know that the perimeter or sum of sides is 30.

x + 3x - 2 +  2*x + 2 = 30

Adding all the terms "with x" together and all terms "without x" together, we get...

6*x = 30

Solving for x (dividing both sides by 6), we get...

x = 30/6 = 5

Finally,

Shortest side: 5

Largest side: 3 * 5 - 2 = 13

Other side: 2 * 5 + 2 = 12

The length of each side of the triangle are 5 in, 12 in and 13 in respectively

Given:

Perimeter of the triangle = 30 in

let

shortest side = x

other side = 2x + 2

Longest side = 3x - 2

Perimeter of the triangle = shortest side + other side + Longest side

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

30 = x + 2x + 2 + 3x - 2

30 = 6x

divide both sides by 6

x = 30 / 6

x = 5

Therefore,

shortest side = x

= 5 in

other side = 2x + 2

= 2(5) + 2

= 10 + 2

= 12 in

Longest side = 3x - 2

= 3(5) - 2

= 15 - 2

= 13 in

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Answer:

Part 1) The measure of angle x is 24°

Part 2) The measure of angle y is 66°

Step-by-step explanation:

step 1

Find the measure of angle m∠IKL

we know that

m∠JKI+m∠IKL=180° ----> supplementary angles (form a linear pair)

we have

m∠JKI=48°

substitute

48°+m∠IKL=180°

m∠IKL=180°-48°=132°

step 2

Find the measure of angle x

we know that

The triangle IKL is an isosceles triangle

so

m∠KIL=m∠KLI=x

Remember that

The sum of the interior angles of a triangle must be equal to 180 degrees

m∠IKL+2x=180°

132°+2x=180°

2x=180°-132°

x=24°

step 3

In the right triangle JIL

Angles x and y are complementary

so

x+y=90°

24°+y=90°

y=90°-24°

y=66°

Answer:

b = 101.52

Step-by-step explanation:

b^2 = a^2 + c^2 - 2ac CosB

b^2 = 105^2 + 9^2 - 2(105)(9) Cos 65°

b^2 = 11 106 - 798.75

b^2 = 10 307.25

b = 101.52

Answer:101.52

Step-by-step explanation:

Given

a=105

c=9

[tex]B=65^{\circ}[/tex]

using cosine rule

[tex]2acCosB=a^2+c^2-b^2 [/tex]

[tex]2(105)(9)Cos65=105^2+9^2-b^2[/tex]

[tex] b^2=11025+81-798.7485[/tex]

b=101.524

Answer:

54°

Step-by-step explanation:

Corn made up 15 % of the vegetables, so

Corn makes up 15 % of the degrees in the circle.

There are 360 degrees in a circle, so

15/100 × 360° = 54 °

The measure of the central angle for corn is 54°.

Answer:

(f*g)(0)=-2

f(g(0))=5  I think you meant this one based on your answer. Please read lower half of explanation for this answer.  Please ask me any question on this that you have.

Step-by-step explanation:

(f*g)(0) means f(0)*g(0).

f(0) means to replace x with 0 in x^2+1 (since g(x)=x^2+1).

g(0) means to replace x with 0 in x-1 (since g(x)=x-2).

f(0)=0^2+1=0+1=1

g(0)=0-2=-2

So (f*g)(0)=f(0)g(0)=(1)(-2)=-2.

But I guess you didn't mean this because you said the answer is 5...

Oh maybe you mean

[tex](f \circ g)(0)[/tex]?

[tex](f \circ g)(0)[/tex] means [tex]f(g(0))[/tex].

So f(g(0))...we start with the inside first... that is g(0)?

g(0)=-2 (we found this above)

f(g(0))

f(-2)           ->I replaced g(0) with -2

Now f(-2) means to replace x with (-2) in x^2+1 (since f(x)=x^2+1)

So let's do that:

(-2)^2+1

4+1

5

Step-by-step explanation:

The elevator is descending, so its velocity is -5 m/min.  After 1 hour (or 60 minutes), the position is:

x = (-5 m/min) (60 min)

x = -300 m

It's position after one hour is -300 meters.

Answer: D. Y=3/2x

Step-by-step explanation: When going from left to right, the line is going up. This means that the slope is positive. We can eliminate answers C and E because they are negative numbers. The slope is rise over run. From the bottom point, the line goes up 3 and to the right 2. Therefore, the answer is D. Y=3/2x.

Answer:

The pen costs $5.05, and the pencil costs $0.05

Step-by-step explanation:

First, we define 2 variables for the two prices.

Let x = price of the pen.

Let y = price of the pencil.

Now we use the given information to write two equations.

"A pen and a pencil together cost $5.10. "

x + y = 5.1

"The pen cost $5 more than the pencil. "

y = x + 5

The system of equations is:

x + y = 5.1

y = x + 5

Since the second equation is already solved for y, we will use the substitution method to solve the system of equations.

Substitute y of the first equation by x + 5.

x + x + 5 = 5.1

2x + 5 = 5.1

2x = 0.1

x = 0.05   (price of the pencil)

Now substitute 0.05 for x in the second equation.

y = 0.05 + 5

y = 5.05     (price of the pen)

The pen costs $5.05, and the pencil costs $0.05

Final answer:

The pencil costs $0.05 and the pen costs $5.05, with the pen being $5 more expensive than the pencil and the total cost for both being $5.10.

Explanation:

To solve this problem, we need to create equations based on the information given. Let's assign x as the cost of the pencil and x + $5.00 as the cost of the pen, since the pen costs $5 more than the pencil.

According to the problem, the total cost of both items is $5.10, so we can write the equation as follows:

Combining the like terms, we get:

Subtracting $5.00 from both sides, we find:

Dividing both sides by 2 to solve for x:

Thus, the pencil costs $0.05, and the pen, which costs $5 more, is $5.05.

Answer:

6

Step-by-step explanation:

m = 3

n = 1

Equation

m(m - n)     Substitute the givens

Solution

3(3 -1 )        Evaluate what is inside the brackets.

3(2)      multiply

6

Answer:

m=3 and n-1 ,find m2- mn

Step-by-step explanation:

Answer:

there are 3.3399 moles in 318 grams! ✔️

Step-by-step explanation:

So we know that 100 grams MgCl2 to mol = 1.0503 mol.

Therefore, to find the number of moles in 318g of the compound, we use the rule of three:

if 1.0503 mol -------------> 100 grams

       X            <------------- 318 grams

The solution is: X = (318*1.0503)/100 = 3.3399 mol.

Summarizing, there are 3.3399 moles in 318 grams! ✔️

B. 25 Km. The measure of BC is 25 km.

The easiest way to solve this problem is using the cosine theorem c = √a²+b²-2ab*cos A.

BC = √AC²+AB²-2(AC)(AB)*cos A

BC = √(21km)²+(14km)²-2(21km)(14km)*cos 89°

BC = √441km²+196km²-588km²*(0.017)

BC =√637km²-10.26km²

BC = √636.74km²

BC = 25.03km ≅ 25

Check the picture below.

Step-by-step explanation:

Given : The sales of a certain product after an initial release can be found by the equation [tex]s=12\sqrt{4t}+ 10[/tex], where s represents the total sales (in thousands) and t represents the time in weeks after release.

To find : Make a table of values, graph the function and use the graph to estimate the sales 12 weeks after release ?

Solution :

The equation [tex]s=12\sqrt{4t}+ 10[/tex]

where, s represents the total sales (in thousands) and t represents the time in weeks after release.

We put t=1,2,3,.....,12 and create a table

 t            [tex]s=12\sqrt{4t}+ 10[/tex]

 1                    34

 2                   43.94  

 3                   51.56

 4                   58

 5                   63.66

 6                   68.78

 7                   73.49  

 8                   77.88

 9                   82

 10                  85.89

 11                   89.59

 12                  93.13

Answer:

1705/64

Step-by-step explanation:

A geometric series contains terms that are in the form [tex]a_1\cdot(r)^{n-1}[/tex] where [tex]a_1[/tex] is the first term and [tex]r[/tex] is common ratio.

A common ratio is the number that is used to find the next term by multiplying previous term by [tex]r[/tex].

Now we can use a formula and we would be using [tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex] where n is the number of terms you are adding and [tex]a_1[/tex] is the first term and r is the common ratio.

Before we do that, I'm going to do this without that formula. Sum means we are just going to add these terms after finding them.

The first term is 20.

The second term is (1/4)(20)=5.

Third term is (1/4)(5)=5/4.

Fourth term is (1/4)(5/4)=5/16.

The fifth term is (1/4)(5/16)=5/64.

Now we add them (20)+(5)+(5/4)+(5/16)+(5/64)

Putting this into the calculator gives me: 1705/64.

Now let's do the formula way as well.

Again we have:

r=1/4

[tex]a_1=20[/tex]

n=5 since we adding the first 5 terms:

[tex]S_5=\frac{20(1-(\frac{1}{4})^5}{1-\frac{1}{4}}[/tex]

[tex]S_5=\frac{20(1-\frac{1}{1024}){\frac{3}{4}}[/tex]

[tex]S_5=\frac{20-\frac{20}{1024}}{\frac{3}{4}}[/tex]

Dividing by 3/4 is the same as multiply by 4/3.

[tex]S_5=(20-\frac{20}{1024})\frac{4}{3}[/tex]

[tex]S_5=20 \cdot \frac{4}{3}-\frac{20}{1024}\cdot\frac{4}{3}[/tex]

[tex]S_5=\frac{80}{3}-\frac{5}{256} \cdot \frac{4}{3}[/tex]

[tex]S_5=\frac{80}{3}-\frac{20}{256 \cdot 3}[/tex]

[tex]S_5=\frac{80}{3}-\frac{5}{64 \cdot 3}[/tex]

[tex]S_5=\frac{80}{3}-\frac{5}{192}[/tex]

Multiplying first fraction by 64/64:

[tex]S_5=\frac{80(64)}{3(64)}-\frac{5}{192}[/tex]

[tex]S_5=\frac{5120}{192}-\frac{5}{192}[/tex]

{tex]S_5=\frac{5115}{192}[/tex]

Dividing to and bottom by 3:

[tex]S_5=\frac{1705}{64}[/tex].

Step-by-step explanation:

To find the equation of the line, start by finding the slope. You can do this by using the slope formula below.

m(slope) = (y2 - y1)/(x2 - x1)

m = (2 - -1)/(-5 - 10)

m = 3/-15

m = -1/5

Now that we have the slope, we can use it along with either point in point-slope form to get the equation.

y - y1 = m(x - x1)

y - 2 = -1/5(x + 5)

y - 2 = -1/5x - 1

y = -1/5x + 1

Answer: In slope intercept formula it is y=-1/5x+3

Step-by-step explanation:

Answer:

A. is less than the radius.

Step-by-step explanation:

If a point is inside a circle, the distance from the center of the circle to that point is option (A) is less than the radius is the correct answer.

A circle is a collection of all points in a plane which are at a constant distance from a fixed point. A circle is a round-shaped figure that has no corners or edges.

For the given situation,

The distance from the center of the circle to any point on it's circumference is called radius.

So, when we consider the distance from the center of the circle, then the term should be related to radius.

Hence we can conclude that if a point is inside a circle, the distance from the center of the circle to that point is option (A) is less than the radius is the correct answer.

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Question 1:

In this question, it's asking you if the decreasing rate is linear or exponential.

The decreasing rate would be linear, due to the fact that it is decreasing at a constant rate of 11%. The decreasing rate doesn't change, which makes this linear.

Question 2:

In this question, it's asking you what would the component's cost be in 3 years if it started off at $120.

To find this, we're going to need multiply the price by -.11, and then subtract to get the price. We would repeat this until we reach 3 years.

Work:

[tex]120*-0.11=-13.2\\\\120-13.2=106.8\ \text{(Year 1)}\\\\106.8*-0.11= -11.748\\\\106.8-11.748=95.05\ \text{(Year 2)}\\\\95.05*-0.11=-10.4555\\\\95.05-10.4555=84.59\ \text{(Year 3)}\\\\\text{In year 3, the cost of the component would be \$84.59}[/tex]

Question 3:

In this question, it asks if the decline in price is linear or exponential.

The decline in price would be exponential, due to the fact that the decrease in price is not always the same, since it changes every year. The price doesn't decrease at the same price each year. As you see from question 2, the change in price is not the same each year.

The price decrease of the computer component is exponential. By using the exponential decay formula, the cost of the component that is $120 today will be approximately $84.96 in three years.

The decline in the price of a computer component that decreases at a rate of 11% per year is an exponential decline. This is because the price reduction each year is based on the current price of the component, not a fixed amount. To calculate the cost three years from now, we can use the formula for exponential decay:

New Value = Original Value × (1 - Rate of Decrease)^Number of Periods

If today's price is $120, the cost after three years would be:

New Price = $120 × (1 - 0.11)^3

New Price = $120 × (0.89)^3

New Price = $120 × 0.708

New Price = $84.96 (rounded to two decimal places)

Therefore, if the component costs $120 today, it will cost approximately $84.96 in three years.

Answer:

A. 7 in.

Step-by-step explanation:

We have been given that the perimeter of a rectangle is 16 inches. The equation that represents the perimeter of the rectangle is , where l represents the length of the rectangle and w represents the width of the rectangle.

We know that perimeter of rectangle is 2 times the sum of width and length of rectangle.

[tex]\text{Perimeter}=2(l+w)[/tex]

[tex]\text{16 in}=2(l+w)[/tex]

[tex]\frac{\text{16 in}}{2}=\frac{2(l+w)}{2}[/tex]

[tex]\text{8 in}=l+w[/tex]

To be a rectangle length cannot be 8 as length and width of the rectangle is 8 inches.

Therefore, 7 inches the possible value for the length of the rectangle.

Answer:

A

Step-by-step explanation:

Answer:

D.) 27 * ( 1/3) ^ (x-1)

Step-by-step explanation:

This is because the first value, 27, indicates the rest state, or the y intercept.  The second value, 1/3, is derived from the pattern of the values decreasing by the previous value being divided by 3, or technically multiplied by (1/3).  The (x-1) is derived from the original formula for the geometric series.

f(x) = x * r ^ (n-1)

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For any questions or more information, please comment below and I'll respond as soon as possible.

The explicit formula for the geometric sequence is:[tex]a_n = 27 \cdot \left(\frac{1}{3}\right)^{(n-1)}[/tex]

To find the explicit formula for the geometric sequence 27, 9, 3, 1, ..., we first need to identify key components of a geometric sequence.

First Term (a): The first term of this sequence, denoted as [tex]a[/tex], is 27.

Common Ratio (r): The common ratio [tex]r[/tex] is found by dividing the second term by the first term:
[tex]r = \frac{9}{27} = \frac{1}{3}[/tex]
We can check this by calculating further:
[tex]\frac{3}{9} = \frac{1}{3} \quad \text{and} \quad \frac{1}{3} = \frac{1}{3}[/tex]
Thus, the common ratio is consistent at [tex]r = \frac{1}{3}[/tex].

Explicit Formula: The explicit formula for a geometric sequence is given by:
[tex]a_n = a \cdot r^{(n-1)}[/tex]
where [tex]a_n[/tex] is the [tex]n[/tex]-th term, [tex]a[/tex] is the first term, and [tex]r[/tex] is the common ratio.

Substituting in our values:
[tex]a_n = 27 \cdot \left(\frac{1}{3}\right)^{(n-1)}[/tex]

Answer:

10

Step-by-step explanation:

Each term is the sum of the two after it:

a_n = a_n+1 + a_n+2

The next term is:

a₄ = a₅ + a₆

31 = 21 + a₆

a₆ = 10

Answer:

1/4

Step-by-step explanation:

Let the fraction be x/y

(x + 1)/y = 1/2

x/(y - 1) = 1/3          Cross multiply both equations.

====================

2*(x + 1) = y           Remove the brackets

2x + 2 = y

################

3x = y - 1               Add 1 to both sides.

3x + 1=y - 1+ 1

3x + 1 = y

#################

Equate both ys

3x + 1 = 2x + 2        Subtract 1 from both sides.

3x + 1-1 = 2x + 2 -1

3x = 2x + 1              Subtract 2x from both sides.

3x-2x = 2x-2x +1    Simplify

x = 1

==================

y = 3x + 1

y = 3(1) + 1

y = 3 + 1

y = 4

The original fraction was 1/4

:

starting value

-- :

the y-intercept is the starting value of the coin after no time has passed. :)

Answer:

D. In step 1, 12! divided by 10! is not equivalent to 6! divided by 5!.

F. There are sixty-six ways to choose ten items from twelve.  

Step-by-step explanation:

The expressions that determine Lorelei's solution include in step 1, 12! divided by 10! is not equivalent to 6! divided by 5! as well option F.

From the information given, Lorelei evaluates the expression to determine how many different groups of ten she can make out of twelve items.

In this case, the expressions that determine Lorelei's solution include in step 1, 12! divided by 10! is not equivalent to 6! divided by 5! and that there are sixty-six ways to choose ten items from twelve.

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I believe the answer is B. I apologize if this is incorrect

Answer:

B) 168.8

Step-by-step explanation:

Amongst all the options given, B is the correct answer.

!!

The type of tessellation used to cover a surface completely using one type of regular polygon is regular tessellation.

Tessellation is defined as the process of covering of a surface or a plane using the geometric shapes.

One geometric shape will not overlap with the other and there will not be any gaps in between.

Regular tessellation is the tiling which uses one type of regular polygon to form a pattern.

In semi-regular tessellation, two or more regular polygons are used such that each vertex is the same.

Here, it is only used one type of regular polygon. No other polygons are used.

So it can't be semi-regular tessellation.+

So it is regular tessellation.

Hence the tessellation is regular tessellation.

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