if 1 added to the numerator of fraction it becomes 1/2 and if one subtracted from the denominator it becomes 1/3 then the fraction is....?​

Answer:

log₁₀ (10¹²)

Step-by-step explanation:

First you should find the solution to the given equation

x-4=2³

x-4=8

x=8+4=12

Now observe the behavior of logarithmic equations with the base 10

log₁₀ 100=2

log₁₀ 10000=4

log₁₀ 1000000=6

To get the answer to

log₁₀ y=12

Then y=10¹².........................how?

check for the first case

log₁₀ 100=2 this can be written as

10²=100

This means to get y in log₁₀y=12  you should rise the base to power 12

y=10¹²

This is to say that

log₁₀ (10¹²) = 12

as you already know to get the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".

[tex]\bf y=x^2+16\implies \stackrel{\textit{quick switcheroo}}{\underline{x}=\underline{y}^2+16}\implies x-16=y^2\implies \sqrt{x-16}=\stackrel{f^{-1}(x)}{y}[/tex]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here slope m = [tex]\frac{1}{2}[/tex], hence

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute (- 2, - 4) into the partial equation

- 4 = - 1 + c ⇒ c = - 4 + 1 = - 3

y = [tex]\frac{1}{2}[/tex] x - 3 ← equation of line

Answer:

1500(1.02)^x  +   600x is how much he has in savings at the end of x years where it be in the bank or elsewhere

Step-by-step explanation:

x is in years

Let's just think about the investment of 1500 in an account earning 2% per year.

Before the years even start, you are at 1500 ( present value).

The next year (year 1), it would be 1500*.02+1500=(1500)(1.02).

The next year (year 2), it would be 1500(1.02)(.02)+1500(1.02)=1500(1.02)(1.02).

We keep multiplying factors of (1.02) each time.

So for year x, you would have saved 1500(1.02)^x.

Now we are saving 50 cash per month. Per year this would be 12(50) since there are 12 months in a year.  12(50)=600.  

So the first year you would have 600.

The second year you would have 600(2) or 1200.

The third year you would have 600(3) or 1800.

Let's put this together:

1500(1.02)^x  +   600x

Answer:

Step-by-step explanation:

Carrying out the indicated multiplication, we get

3y - 6 + 6x + 6 - 2 = 0.

Combining like terms, we get 3y = -6x + 2.

Solving for y:  y = -2x + 2/3.

The slope is -2 and the y-inercept is 2/3.

The slope will be -2 and y-intercept will be 8/3.

Slope and y-intercept are key elements of a linear equation. The slope, denoted by b, describes the steepness of a line, while the y-intercept, denoted by a, is where the line crosses the y-axis.

The equation 3(y - 2) + 6(x + 1) - 2 = 0 can be rewritten as 3y + 6x - 12 + 6 - 2 = 0, which simplifies to 3y + 6x - 8 = 0.

To find the slope-intercept form, we can rearrange the equation to y = -2x + 8/3, where the slope is -2 and the y-intercept is 8/3.

Answer:

7

Step-by-step explanation:

Those are alternate interior angles. Alternate interior angles are the ones that happen at different intersections along the transversal but on opposite sides while inside the lines the transversal goes through. If these lines are parallel, then the alternate interior angles are congruent. Same thing the other way around. Alternate interior angles being congruent implies those lines are parallel.

So we are looking to solve:

3x-2=2x+5

Subtract 2d on both sides:

x-2=5

Add 2 on both sides:

x=7

The phrase "A || B" in a mathematical context usually indicates that line A is parallel to line B. To find the value of x that makes A parallel to B, we must generally consider the properties of parallel lines, specifically in relation to their slopes.
If A and B are lines in a coordinate plane, they will be parallel if and only if their slopes are equal and they are not the same line (in which case they would be coincident). If you are given the equations of the lines in the form y = mx + b, where m represents the slope and b represents the y-intercept, then A and B are parallel if the m values of both equations are the same.
Here's how you would generally find x when A and B are lines defined by equations:
1. Start with the equations of lines A and B. Both will typically be in a format that allows you to solve for their slopes.
   - Line A's equation might look like y = mx + c, where m is the slope of line A.
   - Line B's equation might look like y = nx + d, where n is the slope of line B.
2. Set their slopes equal to each other, as parallel lines have the same slope. This would give you the equation:
   m = n
3. If either slope contains a variable x that you need to solve for, create an equation for x by equating the two slopes:
   mx = nx
4. Solve for x. If the slopes contain x, they might be presented in a linear equation with x, or they could involve more complex expressions.
This is a high-level overview since the specifics would depend greatly on the actual equations of lines A and B. Without the explicit equations for lines A and B, I cannot give a numerical answer. If the question provided equations for lines A and B, please provide them, and I will assist you in finding the value of x that makes A parallel to B.

Answer:

The tea's actual cost is $116.25

Step-by-step explanation:

* Lets revise how to find the z-score

- The rule the z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- The average cost of a glass of iced tea is $1.25

- The standard deviation of it is 7 cents

- A new restaurant charges a price for iced tea that has a

 z-value of -1.25

* Lets change the average cost to cent

∵ $1 = 100 cents

∴ The average cost of a glass of iced tea = 1.25 × 100 = 125 cents

∵ z = (x - μ)/σ

∵ z = -1.25

∵ μ = 125

∵ σ = 7

∴ -1.25 = (x - 125)/7 ⇒ multiply both sides by 7

∴ -8.75 = x - 125 ⇒ add 125 to both sides

∴ 116.25 = x

* The tea's actual cost is $116.25

Answer: It is actually 1.16$ (The guy below accidentally added an extra 1)

Step-by-step explanation:

Answer:

3.162 units

Step-by-step explanation:

First identify the points that undergo transformation

You have;

A = (0,0)   and B =(1,3)

The transformation is T: (x,y)= (x+2, y+1), this means to get the image you add the x coordinate of the object to 2, and the y coordinate to 1.

Finding coordinates of the image points A' and B'

A'= (0+2,0+1) = (2,1)

B'=(1+2, 3+1)=(3,4)

Finding the distance A'B'

The formula for distance d is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

where

x₁=2

x₂=3

y₁=1

y₂=4

d=distance between two points

Applying the formula

[tex]d=\sqrt{(3-2)^2+(4-1)^2} \\\\\\d=\sqrt{1^2+3^2} \\\\\\d=\sqrt{1+9} \\\\\\d=\sqrt{10} \\\\\\d=3.162[/tex]

The distance A'B' is √10 =3.162 units

Answer:

what bout the AA distance???

Step-by-step explanation:

Answer:

[tex]\large\boxed{\dfrac{5x\sqrt{x}}{8y^4}}[/tex]

Step-by-step explanation:

[tex]\sqrt{\dfrac{25x^9y^3}{64x^6y^{11}}}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b},\ \sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}};\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=\dfrac{\sqrt{25}}{\sqrt{64}}\cdot \sqrt{x^{9-6}y^{3-11}}=\dfrac{5}{8}\sqrt{x^3y^{-8}}=\dfrac{5}{8}\sqrt{x^3}\cdot\sqrt{y^{-8}}\\\\\text{use}\ a^na^m=a^{n+m},\ (a^n)^m=a^{nm}\\\\=\dfrac{5}{8}\sqrt{x^{2+1}}\cdot\sqrt{y^{(-4)(2)}}=\dfrac{5}{8}\sqrt{x^2x}\cdot\sqrt{(y^{-4})^2}[/tex]

[tex]=\dfrac{5}{8}\sqrt{x^2}\cdot\sqrt{x}\cdot\sqrt{(y^{-4})^2}\qquad\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=\dfrac{5}{8}x\sqrt{x}\cdot y^{-4}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{5x\sqrt{x}}{8y^4}[/tex]

Answer:

D is the correct answer on edge2021!!!

Answer:

$280.51

Step-by-step explanation:

The formula we want to use:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where:

P is the principal

r is the the rate

n is the number of compounding per year

t is total number of years

A is the ending amount

We are given P=200, r=.07, n=1 (compounded once a year), t=5.

So plugging this in:

[tex]A=200(1+\frac{.07}{1})^{1 \cdot 5}[/tex]

Simplify a little:

[tex]A=200(1+.07)^{5}[/tex]

Just a little more:

[tex]A=200(1.07)^{5}[/tex]

Now I'm going to put the rest of this in the calculator:

200*(1.07)^5 is what I'm putting in my calculator.

This is approximately 280.5103461.

To the nearest cent this is 280.51

Answer:

10

---------

9 t^2

Step-by-step explanation:

10t             20t-40

----------- * ------------

6t-12         30 t^3

Factor

10t             20(t-2)

----------- * ------------

6(t-2)         30 t^3

We can cancel 10t

1            20(t-2)

----------- * ------------

6(t-2)         3 t^2

We can cancel t-2

1            20

----------- * ------------

6               3 t^2

We can cancel a 2 from the 20 and from the 6

1               10

----------- * ------------

3               3 t^2

     10

-----------

9 t^2

Answer:

this should be right if not comment and I'll relook it.

FOIL Method.

You will get the same answer x^2+ 7x- 18

Answer:

X²+7x-18

Step-by-step explanation:

=X(x+9)-2(x+9)

=X²+9x-2x-18

=x²+7x-18

Answer:

D. (x, y, z) = (1, 1, 2). That is:

[tex]\left\{\begin{aligned}&x = 1\\ & y = 1 \\&z = 2\end{aligned}\right.[/tex].

Step-by-step explanation:

Step One: Make sure that the first coefficient of the first row is 1. In this case, the coefficient of [tex]x[/tex] in the first row is already 1.

Step Two: Using row 1, eliminate the first unknown of row 1 [tex]x[/tex] in the rest of the rows. For example, to eliminate [tex]x[/tex] from row 2, multiply row 1 by the opposite of the coefficient of [tex]x[/tex] in row 2 and add that multiple to row 2. The coefficient of [tex]x[/tex] in row 2 is [tex]3[/tex]. Thus, multiply row 1 by [tex]-3[/tex] to get its multiple:

[tex]-3x - 3y + 3z = 0[/tex].

Add this multiple to row 2 to eliminate [tex]x[/tex] in that row:

[tex]\begin{array}{lrrrcr}&-3x &-3y&+3z& =&0 \\ + & 3x& -y& +z& =& 4\\\cline{1-6}\\[-1.0em]\implies&&-4y &+ 4z&=&4\end{array}[/tex].

Similarly, for the third row, multiply row 1 by [tex]-5[/tex] to get:

[tex]-5x - 5y + 5z = 0[/tex].

Do not replace the initial row 1 with this multiple.

Add that multiple to row 3 to get:

[tex]\begin{array}{lrrrcr}&-5x &-5y&+5z& =&0 \\ + & 5x& & +z& =& 7\\\cline{1-6}\\[-1.0em]\implies&&-5y &+6z&=&7\end{array}[/tex].

After applying step one and two to all three rows, the system now resembles the following:

[tex]\left\{\begin{array}{rrrcr}x& + y & -z& = &0\\&-4y &+4z&=&4\\ &-5y &+6z&=&7\end{array}\right.[/tex].

Ignore the first row and apply step one and two to the second and third row of this new system.

[tex]\left\{\begin{array}{rrcr}-4y &+4z&=&4\\ -5y &+6z&=&7\end{array}\right.[/tex].

Step One: Make sure that the first coefficient of the first row is 1.

Multiply the first row by the opposite reciprocal of its first coefficient.

[tex]\displaystyle (-\frac{1}{4})\cdot (-4y) + (-\frac{1}{4})\cdot 4z = (-\frac{1}{4})\times 4[/tex].

Row 1 is now [tex]y - z = -1[/tex].

Step Two: Using row 1, eliminate the first unknown of row 1 [tex]y[/tex] in the rest of the rows.

The coefficient of [tex]y[/tex] in row 2 is currently [tex]-5[/tex]. Multiply row 1 by  [tex]5[/tex] to get:

[tex]5y - 5z = -5[/tex].

Do not replace the initial row 1 with this multiple.

Add this multiple to row 2:

[tex]\begin{array}{lrrcr}&-5y&+6z& =&7 \\ + & 5y& -5z& =& -5\\\cline{1-5}\\[-1.0em]\implies&&z &= &2\end{array}[/tex].

The system is now:

[tex]\left\{\begin{array}{rrcr}y & - z&=&-1\\& z &=&2\end{array}\right.[/tex].

Include the row that was previously ignored:

[tex]\left\{\begin{array}{rrrcr}x& + y & -z& = &0\\&y &-z&=&-1 \\ & &z&=&2\end{array}\right.[/tex].

This system is now in a staircase form called Row-Echelon Form. The length of the rows decreases from the top to the bottom. The first coefficient in each row is all [tex]1[/tex]. Find the value of each unknown by solving the row on the bottom and substituting back into previous rows.

From the third row: [tex]z = 2[/tex].

Substitute back into row 2:

[tex]y -2 = -1[/tex].

[tex]y = 1[/tex].

Substitute [tex]y = 1[/tex] and [tex]z = 2[/tex] to row 1:

[tex]x + 1 - 2 = 0[/tex].

[tex]x = 1[/tex].

In other words,

[tex]\left\{\begin{aligned}&x = 1\\ & y = 1 \\&z = 2\end{aligned}\right.[/tex].

Answer: k=−1,452

Step-by-step explanation:

k/22 x 22 = −66 x22

The value of 'k' can be determined by isolating 'k' in the equation. This results in k = 22 * -66, simplifying to k = -1452.

The equation conveyed in the question can be written as k/22 = -66. To find the variable k's value, we need to isolate k in the equation. This can be done by keeping the inverse operation on both sides of the equation balanced. Since k is currently divided by 22, we must multiply both sides of the equation by 22 to get k independently.

When we do this, the equation becomes k = 22 * -66. Then, solve for k by multiplying 22 and -66 together. So, k equals -1452.

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Answer:

14000 lbs.

Step-by-step explanation:

7 tons = 14000 lbs

1 ton = 2000 lbs.

7 x 2000 = 14000 Lbs.

Answer:

Last choice

Step-by-step explanation:

V means or.

So we have x<0 or y<0.

This means we want the quadrant that have negative x's and we want the quadrants that have negative y's

x is negative to the left of the y-axis so it's negative in quadrants 2 and 3

y is negative below the x-axis so it's negative in quadrants 3 and 4.

So we are looking at all quadrants except quadrant 1.

Answer:

A) a = 1050 and b = 0.81

B) 3.3

Step-by-step explanation:

Original price of the computer = $ 1050

Rate of decrease in price = r = 19%

This means, every year the price of the computer will be 19% lesser than the previous year. In other words we can say that after a year, the price of the computer will be 81% of the price of the previous year.

Part A)

The exponential model is:

[tex]v(t)=a(b)^{t}[/tex]

Here, a indicates the original price of the computer i.e. the price at time t = 0. So for the given case the value of a will be 1050

b represents the multiplicative rate of change i.e. the percentage that would be multiplied to the price of previous year to get the new price. For this case b would be 81% or 0.81

So, a = 1050 and b = 0.81

The exponential model would be:

[tex]v(t)=1050(0.81)^{t}[/tex]

Part B)

We have to find after how many years, the worth of the computer will be reduced to half. This means we have the value of v which is 1050/2 = $ 525

Using the exponential model, we get:

[tex]525=1050(0.81)^{t}\\\\ 0.5=(0.81)^{t}\\[/tex]

Taking log of both sides:

[tex]log(0.5)=log(0.81)^{t}\\\\ log(0.5)=t \times log(0.81)\\\\ t = \frac{log(0.5)}{log(0.81)}\\\\ t = 3.3[/tex]

Thus, after 3.3 years the worth of computer will be half of its original price.

The initial value of the computer (a) is $1,050 and the depreciation rate (b) is 0.81. After approximately 4.1 years, the computer's value will reduce to half its original price.

In this question, we have an exponential decay problem. In the formula v(t) = a*b^t, a is the initial value of the computer, and b is the rate of depreciation per year.

(A) In this problem, a = $1,050 (the initial cost of the computer), and b = 0.81 (1 - 0.19, since the computer loses 19% of its value per year), so the equation becomes v(t) = 1050 * (0.81)^t.

(B) To find when the computer will be worth half its original value, we can set up the equation 1050 * (0.81)^t = 525. Solving this equation for t (using a logarithm), we find that t ≈ 4.1 years.

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Answer: -2z+2

Step-by-step explanation:

Simplify brackets

-3z + z + 2

Collect like terms

(-3z + z) + 2

Simplify

-2z + 2

Answer:

Step-by-step explanation:

[tex](-)(-)=(+)\\\\-3z-(-z-2)=-3z+z+2\qquad\text{combine like terms}\\\\=(-3z+z)+2=-2z+2[/tex]

Answer:

x + 10 = x² + 2x + 1

Step-by-step explanation:

[tex]\sqrt{x + 10}[/tex] - 1 = x

x + 1 = [tex]\sqrt{x + 10}[/tex]

Squaring both sides gives;

(x + 1)² = ([tex]\sqrt{x + 10}[/tex])²

x + 10 = x² + 2x + 1

Answer:

option B

Step-by-step explanation:

the given equation is,

[tex]\sqrt{x+10}-1 =x[/tex].................................(1)

adding  both side by 1 in equation (1)

[tex]\sqrt{x+10}= x + 1[/tex]

squaring both side              

x + 10 = ( x + 1 )²                

we know,

( a + b )²  = a² + b² + 2 a b

x + 10 = x² + 2 x + 1

hence, the correct answer is option B.

Answer:

D describes the concept of natural price accurately

Step-by-step explanation:

Adam Smith said that the natural price is the price which covers all the costs to produce it for instance, rent of land, wages of labour, cost of machinery.

A. The price of any item that is less than costs of producing it

This is incorrect since natural price covers all costs of production,

B. The price of any item that is equal to its market price.

C. The price of any item that is less than its market price

Both B and C are incorrect because market price is determined by the forces of demand and supply and changes accordingly whereas the natural price is the everyday normal price.

D. The price of any item that is equal to the costs of producing it.

This is correct because the natural price covers all costs involved in producing a product and is neither low nor high.

!!

Answer:

The answer is D.

Step-by-step explanation:

Answer:

Part A) The system of inequalities is

[tex]x\geq2[/tex]  and  [tex]y\geq2[/tex]

Part B) In the procedure

Part C) The schools that Natalie is allowed to attend are A,B and D

Step-by-step explanation:

Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions

we have

Points C(2,2), F(3,4)

The system of inequalities could be

[tex]x\geq2[/tex] -----> inequality A

The solution of the inequality A is the shaded area at the right of the solid line x=2

[tex]y\geq2[/tex] -----> inequality B

The solution of the inequality B is the shaded area above of the solid line y=2

see the attached figure N 1

Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

Verify point C

C(2,2)    

Inequality A

[tex]x\geq2[/tex] -----> [tex]2\geq2[/tex] ----> is true

Inequality B

[tex]y\geq2[/tex] ------> [tex]2\geq2[/tex] ----> is true

therefore

Point C is a solution of the system of inequalities

Verify point D

F(3,4)    

Inequality A

[tex]x\geq2[/tex] -----> [tex]3\geq2[/tex] ----> is true

Inequality B

[tex]y\geq2[/tex] ------> [tex]4\geq2[/tex] ----> is true

therefore

Point D is a solution of the system of inequalities

Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.

we have

[tex]y < -2x+2[/tex]

The solution of the inequality is the shaded area below the dotted line [tex]y=-2x+2[/tex]

The y-intercept of the dotted line is the point (0,2)

The x-intercept of the dotted line is the point (1,0)

To graph the inequality, plot the intercepts and shade the area below the dotted line

see the attached figure N 2

therefore

The schools that Natalie is allowed to attend are A,B and D

Step-by-step explanation:

Taking left hand side:

[tex]\frac{1+tan\ x}{sin\ x+cos\ x}\\=\frac{1+\frac{sin\ x}{cos\ x} }{sin\ x+cos\ x}\\=\frac{\frac{cos\ x+sin\ x}{cos\ x} }{sin\ x+cos\ x}\\=\frac{cos\ x+sin\ x}{cos\ x} * \frac{1}{sin\ x+cos\ x}\\=\frac{1}{cos\ x}[/tex]

1/cos x is equal to sec x.

So,

[tex]\frac{1}{cos\ x} = sec\ x[/tex]

Hence proved ..

Answer:

22cm,24cm,24cm

Step-by-step explanation:

Let us call one of the other sides x

the shortest side = 2x-26

in an isosceles, 2 sides are equal (x in this case)

so we now have sides of x,x and 2x-26

form an eqution from this.

4x-26=70

4x=96

x=24

24 x 2 = 48 - 26 = 22

thus, the shortest side is 22cm and the other sides are both 24cm

Answer:

The lengths of the three sides in ascending order is.

_22__cm, __24__cm, __24__cm

Step-by-step explanation:

The perimeter of a triangle is equal to the sum of the length of its three sides.

By definition, an isosceles triangle has two equal sides.

We know that the short side measures  26 cm less than twice as long as the other sides, and that the other two sides are of equal length.

We also know that the perimeter of the triangle is 70 cm

Then we propose the following equation

[tex]P = b + 2s[/tex]

Where P is the perimeter, b is the shortest side of the triangle and s is the length of the equal sides.

Then:

[tex]b= 2s -26[/tex]

We substitute this equation in the first equation and solve for s

[tex]P = 2s -26 + 2s[/tex]

[tex]P = 4s -26=70[/tex]

[tex]4s -26=70[/tex]

[tex]4s=70 +26[/tex]

[tex]4s=96[/tex]

[tex]s=\frac{96}{4}[/tex]

[tex]s=24[/tex]

Then

[tex]b= 2(24) -26[/tex]

[tex]b= 22[/tex]

Answer:

The inequality that represent the problem is [tex]80x+60y \geq 6,800[/tex]

The solution in the attached figure

Step-by-step explanation:

Let

x ----> the number of laptops sold

y ----> the number of smartphones sold

we know that

The inequality that represent the problem is equal to

[tex]80x+60y \geq 6,800[/tex]

The solution of the inequality is the shaded area

Remember that the number of laptops or the number of smartphones must be  a whole positive number

The graph in the attached figure

Answer:

the 2nd one isss x+y< 100

Step-by-step explanation:

First find the decreased value,

[tex]777-777\cdot0.12=777-93.24=683.76[/tex]

Then from the value found, find increased value,

[tex]683.76+683.76\cdot0.04\approx\boxed{711.11}[/tex]

Hope this helps.

r3t40

Answer:

GCF is 4ab

And the expression will be: 4ab ( 3a^2+2ab-5b^2)

Step-by-step explanation:

Factor the GCF :

12a^3b + 8a^2b^2-20 ab^3

We need to find the common terms that are common in each of the term given above

12,8 and 2 are all divisible by 4

a is common in all terms and b is also common in all terms,

So, GCF is 4ab

Taking 4ab common

12a^3b + 8a^2b^2-20 ab^3=4ab ( 3a^2+2ab-5b^2)

Answer:

5(-9+1)

= -45+5

= -40 (answer)

✌Pls mark my answer as brainliest ✌

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Answer is provided in the image attached.

Answer:

[tex]x^6+x^4+4x^3-2x^2-x+3[/tex]

Step-by-step explanation:

[tex]x^3+2x+3[/tex]

[tex]\times(x^3-x+1)[/tex]

---------------------------------

First step multiply your terms in your first expression just to the 1 in the second expression like so:

[tex]x^3+2x+3[/tex]

[tex]\times(x^3-x+1)[/tex]

---------------------------------

[tex]x^3+2x+3[/tex]  Anything times 1 is that anything.

That is, [tex](x^3+2x+3) \cdot 1=x^3+2x+3[/tex].

Now we are going to take the top expression and multiply it to the -x in the second expression. [tex]-x(x^3+2x+3)=-x^4-2x^2-3x[/tex].  We are going to put this product right under our previous product.

[tex]x^3+2x+3[/tex]

[tex]\times(x^3-x+1)[/tex]

---------------------------------

[tex]x^3+2x+3[/tex]

[tex]-x^4-2x^2-3x[/tex]  

We still have one more multiplication but before we do that I'm going to put some 0 place holders in and get my like terms lined up for the later addition:

[tex]x^3+2x+3[/tex]

[tex]\times(x^3-x+1)[/tex]

---------------------------------

[tex]0x^4+x^3+0x^2+2x+3[/tex]

[tex]-x^4+0x^3-2x^2-3x+0[/tex]  

Now for the last multiplication, we are going to take the top expression and multiply it to x^3 giving us [tex]x^3(x^3+2x+3)=x^6+2x^4+3x^3[/tex]. (I'm going to put this product underneath our other 2 products):

[tex]x^3+2x+3[/tex]

[tex]\times(x^3-x+1)[/tex]

---------------------------------

[tex]0x^4+x^3+0x^2+2x+3[/tex]

[tex]-x^4+0x^3-2x^2-3x+0[/tex]  

[tex]x^6+2x^4+3x^3[/tex]

I'm going to again insert some zero placeholders to help me line up my like terms for the addition.

[tex]x^3+2x+3[/tex]

[tex]\times(x^3-x+1)[/tex]

---------------------------------

[tex]0x^6+0x^4+x^3+0x^2+2x+3[/tex]

[tex]0x^6-x^4+0x^3-2x^2-3x+0[/tex]  

[tex]x^6+2x^4+3x^3+0x^2+0x+0[/tex]

----------------------------------------------------Adding the three products!

[tex]x^6+x^4+4x^3-2x^2-x+3[/tex]

[tex]\bf \begin{cases} f(x)=&10x+25\\ g(x)=&x+8 \end{cases}~\hspace{5em} \begin{array}{llll} f(~~g(x)~~)=&10[g(x)]+25\\\\ f(~~g(x)~~)=&10[x+8]+25\\\\ f(~~g(x)~~)=&10x+80+25\\\\ f(~~g(x)~~)=&10x+105 \end{array}[/tex]

Answer:

f(g(x)) = 10x + 105

Step-by-step explanation:

Start with f(x) = 10x + 25.  Replace this x with (x + 8), which is g(x):

f(g(x)) = 10(x + 8) + 25, or

         = 10x + 80 + 25, or 10x + 105

f(g(x)) = 10x + 105