If f(x) = 3x2 - 2x+4 and g(x) = 5x + 6x - 8, find (f-g)(x).

ANSWER

The solution is (1,-3)

EXPLANATION

The system of Equations are;

[tex]x=4+y[/tex]

and

[tex]-10x+6y=-28[/tex]

We substitute the first equation into the second equation to get:

[tex]-10(4 + y)+6y=-28[/tex]

We expand the parenthesis to get:

[tex]-40 - 10y+6y=-28[/tex]

Group similar terms to get:

[tex]- 10y+6y=-28 + 40[/tex]

Simplify the similar terms to get;

[tex] - 4y = 12[/tex]

Divide both sides -4.

[tex]y = \frac{12}{ - 4} [/tex]

[tex]y = - 3[/tex]

We put y=-3 into the first equation to get:

[tex]x = 4 + - 3 = 1[/tex]

Therefore the solution is (1,-3)

Answer:

(-4, -4)

Step-by-step explanation:

Look for the vertex / minimum point on the graph.  If you read the x- and y-axis scales correctly, you'll see that the vertex is located at (-4, -4).  Not all the divisions on the x- and y-axes are marked;  you have to mark them in your imagination.

Answer:

A.

Step-by-step explanation:

As in the picture we have that the parabola opens up, then the vertex will be the minimum point in the graph. Now, the minimum point of the parabola in the picture is in x= -4 and y = -4 (the points go two by two), I show you that values in the picture below. Then, the vertex of the graph showed in the picture is (-4,-4). Then, the answer is A.

Answer:

Step-by-step explanation:

Recall any base that is raised to a negative power is simply the reciprocal of the base.

i.e [tex]x^{-1}[/tex] = [tex]\frac{1}{x}[/tex]

Using this knowledge, we can start simplifying the equation (see attached)

Answer:

[tex]\frac{a^3b^2}{a^{-1}b^{-3}}=a^{4}b^{5}[/tex]  

Step-by-step explanation:

Given : Expression [tex]\frac{a^3b^2}{a^{-1}b^{-3}}[/tex]

To find : Multiply or divide as indicated. Leave your answer with no factors in the denominator.

Solution :

We know when two same term are in divide then their power get subtracted.

So, [tex]\frac{a^m}{a^n}=a^{m-n}[/tex]

Applying in the expression,

[tex]\frac{a^3b^2}{a^{-1}b^{-3}}=a^{3-(-1)}b^{2-(-3)}[/tex]

Solve the power,

[tex]\frac{a^3b^2}{a^{-1}b^{-3}}=a^{3+1}b^{2+3}[/tex]

[tex]\frac{a^3b^2}{a^{-1}b^{-3}}=a^{4}b^{5}[/tex]

Therefore, The solution is [tex]\frac{a^3b^2}{a^{-1}b^{-3}}=a^{4}b^{5}[/tex]

Answer:

Explanation of the above answer: “One less than the quotient of four and a number x. ""One less"" means you will subtract 1 from it. For that reason the overall expression is 4x-1.

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer: the answer is C. Range :D

Step-by-step explanation:

Answer:

The standard deviation of the data set is 5.7 to the nearest tenth

Step-by-step explanation:

* Lets explain how to find the standard deviation

# Step 1: find the mean of the data set

∵ The mean = the sum of the data ÷ the number of the data

∵ The data set is 3 , 17 , 18 , 15 , 12 , 21 , 9

∵ Their sum = 3 + 17 + 18 + 15 + 12 + 21 + 9 = 95

∵ They are seven

∴ The mean = 95 ÷ 7 = 13.6

# Step 2: subtract the mean from each data and square the answer

∴ (3 - 13.6)² = 112.36

∴ (17 - 13.6)² = 11.56

∴ (18 - 13.6)² = 19.36

∴ (15 - 13.6)² = 1.96

∴ (12 - 13.6)² = 2.56

∴ (21 - 13.6)² = 54.76

∴ (9 - 13.6)² = 21.16

# Step 3: find the mean of these squared difference

∵ The mean = the sum of the data ÷ the number of the data

∵ The sum = 112.36 + 11.56 + 19.36 + 1.96 + 2.56 + 54.76 + 21.16 = 223.72

∴ The mean = 223.72 ÷ 7 = 31.96

# Step 4: the standard deviation is the square root of this mean

∴ The standard deviation = √(31.96) = 5.6533 ≅ 5.7

* The standard deviation of the data set is 5.7 to the nearest tenth

Answer:

$9.00

Step-by-step explanation:

4x + 12 = 48         - First, subtract 12 from each side of the equation.

4x = 36                 - Then, divide each side by 4 to get x by itself.

x = 9                     - After dividing by 4, we are left with x = 9, so 1 ticket costs

                              $9.00

For this case we have the following equation:

[tex]4x + 12 = 48[/tex]

Where the variable "x" represents the cost of a performance ticket.

Clear "x" of the equation to know the cost of a ticket.

Subtracting 12 on both sides of the equation:

[tex]4x = 48-12\\4x = 36[/tex]

Dividing between 4 on both sides of the equation:

[tex]x = \frac {36} {4}\\x = 9[/tex]

So, the cost of a ticket is $ 9.00

Answer:

Option C

Answer:

x=0, x=-6

Step-by-step explanation:

Answer: -33

Step-by-step explanation:

Final answer:

To find the quotient of x + 4x² divided by 2x, divide each term inside the numerator by the denominator. Simplify the expression by dividing each term by 2x.Simplifying further, we get: 1/2 + 2x

Explanation:

To find the quotient of x + 4x² divided by 2x, we divide each term inside the numerator by the denominator.

This gives us: (x + 4x²) ÷ 2x

Next, we can simplify the expression by dividing each term by 2x:

x ÷ 2x + 4x² ÷ 2x

Simplifying further, we get: 1/2 + 2x

Answer:

Table B

Step-by-step explanation:

we know that

A relationship between two variables, a, and b, represent a proportional variation if it can be expressed in the form [tex]b/a=k[/tex] or [tex]b=ka[/tex]

In this problem the table B shows a proportional relationship because

For a=20, b=25 -----> b/a=25/20=1.25

For a=24, b=30 -----> b/a=30/24=1.25

For a=32, b=40 -----> b/a=40/32=1.25

The constant of proportionality k is 1.25

Answer:

Im pretty sure its B :)

Step-by-step explanation:

Answer:

y=-2x+14

Step-by-step explanation:

If we are looking for a line parallel to 2x+y=5.

Then we are looking for an equation with the same slope as the equation 2x+y=5.

To obtain the slope of equaiton 2x+y=5 I will put it in slope-intercept form.

Luckily there is only one step which is to subtract 2x on both sides.

y=-2x+5

The slope of this line is -2

The slope of parallel line will also be -2.

So we know our equation is in the form y=-2x+b

To find b we will just use the point (x,y)=(5,4) we know is on the line.

Plug in and solve for b.

4=-2(5)+b

4=-10+b

14=b

So the equation that is parallel to 2x+y=5 and goes through (5,4) is y=-2x+14

Answer:

g(x)=40x+4x^2

Step-by-step explanation:

[tex]g(x) = 40x + 4 {x }^{2} [/tex]

Answer: 14x-7u+14

Step-by-step explanation:  multiply parenthesis by -7

Answer:

14x -7u+14

Step-by-step explanation:

-7(-2x+u-2)

Multiply -7 by each term in the parentheses

-7*-2x + -7*u + -7*-2

14x -7u+14

There are a few ways to do it; the easiest is just to follow the pattern of taking away two from the average.

The next lines of the table are

6 to 7  -13

7 to 8   -15

8 to 9   -17

Answer: C. -17

Let's find the equation and do it that way.

We have a vertex at (0,3) so we can fill out the vertex form a bit.  In general for vertex (p,q) it's

y = a(x-p)^2+q

We have

f(x) = ax^2 + 3

f(1) = 2

a+3 =2

a = -1

So we found our equation,

y = -x^2 + 3

Let's check it at x=5, y=-5^2+3=-25+3=-22, good

We want the rate of change from 8 to 9, which is

[tex]r = \dfrac{f(9)-f(8)}{9-8}=f(9)-f(8)=-9^2 - -8^2 = -17[/tex]

Answer: -17 again, that checks

The average rate of change for the interval from x=8 to x=9 is -17.

The correct option is (C)

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

We have a vertex at (0,3).

In general let us take vertex (p,q) then

y = a(x-p)²+q

We have,

f(x) = ax² + 3

as x=1, f(x)=2

so,

f(1) = 2

a+3 =2

a = -1

Now, the equation

y = -x² + 3

Thus, the rate of change from 8 to 9

= f(9)-f(8)/9-8

= -9²-(-8)²

=-81+64

=-17

Hence,  the average rate of change for the interval from x=8 to x=9 is -17.

Learn more about this concept here:

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Answer:

50

Step-by-step explanation:

half of polygon A is 50          the sides of polygon A are twice the length

                                                 of the corresponding sides of polygon B.

It's the sum of the length of the sides used to make the given figure. The perimeter of Polygon A is 50 units.

It's the sum of the length of the sides used to make the given figure.

Given Polygon A is similar to polygon B. Also, The perimeter of polygon Ais 100.  Now, let the number of sides in Polygon A be n, while the length of a side is 2x. Therefore, the perimeter of the polygon A is,

n × 2x = 100

Given the length of the side of the polygon B is half the length of the side of polygon A. Therefore, the perimeter of polygon B is,

n × x = Perimeter

Now, if the ratio of the two equations is taken then,

(n × 2x)/ (n × x) = 100/ Perimeter

2 = 100/Perimeter

Perimeter = 50 units

Hence, the perimeter of Polygon A is 50 units.

Learn more about Perimeter:

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Answer:

169

Step-by-step explanation:

Answer: -2

Step-by-step explanation:

The slope of a line passing through points (a,b) and (c,d) is given by :-

[tex]m=\dfrac{d-b}{c-a}[/tex]

From the given graph , the line is passing from points (6,33) and (15,15).

Now, the of a line passing through points (6,33) and (15,15) is given by :-

[tex]m=\dfrac{15-33}{15-6}=\dfrac{-18}{9}\\\\\Rightarrow\ m=-2[/tex]

Hence, the slope of the line = -2

- 3 + 3x = 2x – 13

Bring -3 to the right side of the equation by adding 3 to both sides

(- 3 + 3) + 3x = 2x – 13 + 3

0 + 3x = 2x - 10

3x = 2x - 10

Bring 2x to the other side by subtracting 2x to both sides

3x - 2x = 2x - 2x - 10

x = -10

Check:

-3 + 3(-10) = 2(-10) - 13

-3 + (-30) = -20 - 13

-33 = -33

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Step-by-step explanation:

2 - 3y + 3t = -x - 2yz

I don't think you can actually solve the equation. You are not given any information about the letters (variables).

Answer:

its 17.4

Step-by-step explanation:

if you add all the numbers up then divide it by the amount of numbers you added together you get this answer

Answer 17.4

Explanation: you add them all up so 13+18+20+25+11 then divide by how many numbers there are so divide by 5 you will end up with 17.4

The number 0.58 produces a rational number when added to 0.42.

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. It can be expressed as a whole number or in the fractional format.

Let us find the nearest rational number which can be expressed in the whole number format.

For 0.42, the nearest rational number is 1 .

Thus the number added to 0.42 is (1 - 0.42) = 0.58 .

Therefore, the number 0.58 produces a rational number when added to 0.42.

To learn more about rational number, refer -

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Answer:40 %

Step-by-step explanation:

Given

Debt=5,446,772,143,940,528 $

Gross domestic product(GDP)=13,647,498,222,417,097 $

Debt to GDP ratio is

=[tex]\frac{5,446,772,143,940,528}{13,647,498,222,417,097}[/tex]

=0.399104

[tex]39.91 \%\approx 40\%[/tex]

Answer:

Table 3 and Table 5

Step-by-step explanation:

y = 3/5 x

The slope is 3/5

3/5 = .6

We want a slope that is lower

We want to find the slope for each table

Slope is found by

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

Table 1

    = (12-4)/(9-3) = 8/6 = 4/3 =1.33

Table 2

   = (12-4)/(15-5) = 8/10 = 4/5=.8

Table 3

   = (54-18)/(93-31) = 36/62=18/31=.58

Table 4

= (33-11)/(54-18) = 22/36 = 11/12=.92

Table 5

 = (21-7)/(36-12) =14/24 = 7/12 =.58

Answer:

y=-2/5x^2-3x+63

Step-by-step explanation:

Use y=mx+b

Answer:

one solution: (2.5, 0)

Step-by-step explanation:

y = 2x – 5  

–8x – 4y = –20

Solve the second equation for y

Add 8x to each side

–8x+8x – 4y =8x –20

-4y = 8x-20

Divide by -4

-4y/-4 =8x/-4 -20/-4

y = -2x+5

The two equations are

y = 2x-5

y = -2x+5

Both equations are solved for y so set them equal

2x-5 = -2x+5

Add 2x to each side

2x+2x-5 = -2x+2x+5

4x-5 = 5

Add 5 to each side

4x-5+5 = 5+5

4x=10

Divide by 4

4x/4 = 10/4

x = 2.5

y = 2x-5

Substitute x=2.5 in

y = 2(2.5) - 5

y=5-5

y=0

There is one solution (2.5,0)

Answer: B (2.5, 0)

B: - One solution: (2.5, 0)                  

Step-by-step explanation:

Given : Two linear equation -

Equation 1 -  

Equation 2 -  

To find : How many solutions does this linear system have?

Solution :

We solve the given equations,

Substitute the value of y from equation 1 in equation 2

Now, put value of x in equation 1

There is one solution (x,y) = (2.5, 0)

B is correct.

Answer:

4

Step-by-step explanation:

4 - 2 = 4 + -2 = -2 + 4

Answer:

Last option: [tex]3+(-7)=-4[/tex]

Step-by-step explanation:

The number line can help us to make additions and subtractions.

To add a positive number we need to move the point to the right and to add a negative number we need to move the point to the left.

You can observe in the figure that the point on the number line is moved from 3 to -4, then it is moved 7 places to the left. Therefore, you can express it in the following form:

[tex]3+(-7)[/tex]

This is:

[tex]3+(-7)=3-7=-4[/tex]

Then the number line represents this number sentence:

[tex]3+(-7)=-4[/tex]

Answer:

5.80

Step-by-step explanation:

How much was the total profit

1412 -1006

406

She sold 70 puppets

The profit per puppet is the profit divided by the number of puppets

406/70

5.80

Answer:

π(4)²(16)

Step-by-step explanation:

Given r = 4, h = 16

Use formula for cylinder:

Volume of cylinder,

V = πr²h

= π(4)²(16)

Answer:

Answer:

π(4)²(16)

Step-by-step explanation:

Given r = 4, h = 16

Use formula for cylinder:

Volume of cylinder,  

V = πr²h

= π(4)²(16)

Step-by-step explanation: