The domain for f(x) and g(x) is the set of all real numbers.
Let f(x)=3x+5 and g(x)=x^2 .
Find g(x)-f(x)

A.) 3x^2-5
B.) x^3-5
C.) 3x^3-5x^2
D.) x^2-3x-5

Please an explanation too:) Thank you!

Answer:

Step-by-step explanation:

Simply by comparing the given

f(x)=(x-2)^2-3   to

f(x) = (x-h)^2 + k, we see that h = 2 and k = -3, which tells us that the vertex of the graph is (2, -3).  This parabola opens up because the coefficient of (x-2)^2 is +1.

Evaluating f(x)=(x-2)^2-3 at x = 4 (an arbitrary value), we see that

                 f(4) = (4-2)^2 - 3 = 4 - 3 = 1.

The point (4, 1) is also on the graph of this parabola.

Graph the vertex (2, -3) and the arbitrarily chosen point (4, 1).  Remember that (2, -3) is the minimum of this function, so for x other than 2, the y-value is greater than -3.

Answer:

f(x) = 2x+1​

Step-by-step explanation:

Equation in slope intercept form y = mx + b where m = slope b = y-intercept

To find slope ,

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

m = (3 - 1) / (1 - 0)

m = 32/1

m = 2

y-intercept b = 1

In this case y = 2x + 1 or f(x) = 2x+1​

Answer:

2 and a half @ 2.5 inches (sorry i can't type the fraction)

Step-by-step explanation:

(1/2, 1/4)=(x,y)

based on the graph shown that each grid on the y axis represents 1/4, that is the smallest scale stood in the y axis.

this means 2 grid= 1/4 x 2 = 1/2 @ 0.5 inches.

since the '5 months-hair-length' is above about 2 grid above 2 inch:

2 inch + 0.5 inch= 2.5 inch

Answer:

D

Step-by-step explanation:

Answer:

option B

Step-by-step explanation:

(6x^2-x+8) - (x^2+2)

6x^2-x+8 - x^2-2

5x^2-x+6

Answer:

box contains - 3

Step-by-step explanation:

a(x - 3) + 2x = -(x - 5) +4              Remove the brackets on both sides

ax - 3a + 2x = -x + 5   + 4             Subtract 2x from both sides.

ax - 3a + 2x - 2x = -x - 2x + 9

ax - 3a = - 3x + 9

ax - 3(-3) = - 3x + 9

ax + 9 = - 3x + 9

Now if you make a = -3 then both sides with have - 3 for the x coefficient.

Any number could be put in for x and it will make the answer on both sides equal. Notice you could subtract 9 from both sides and it will not change the condition of the problem.

Answer:

c = -3

Step-by-step explanation:

Call the unknown c

c(x-3) +2x = -(x-5) +4

Distribute the negative sign

c(x-3) +2x = -x+5+4

Combine like terms

c(x-3) +2x = -x +9

Subtract 2x from each side

c(x-3) +2x-2x = -x-2x +9

c(x-3) = -3x+9

Factor a -3 from the right side

c(x-3) = -3(x-3)

Divide by (x-3)

c = -3

The right and left hand side need to be equal for there to be infinite solutions, so c = -3

Answer:

P = 4 / 6 = 2/3 = 0.66 = 66%

Step-by-step explanation:

Assuming the die is numbered 1 to 6.

To answer the question, we first need to know many prime numbers can be represented on the die.  What are the prime numbers equal to 6 or lower?

We have 2, 3 and 5.  (since 4 and 6 are not prime numbers).  So we have 3 prime numbers, plus the number 1... so there are 4 possibilities valid for rolling a 1 or a prime number: 1,2,3 and 5.

4 possibilities out of 6 total possible outcomes, so...

P = 4 / 6 = 2/3 = 0.66 = 66%

Answer:

The probability of rolling a 6 sided die and getting a 1 or a prime number = 2/3

Step-by-step explanation:

The numbers on the die are 1, 2, 3, 4, 5 and 6

To find the probability

Total outcomes of rolling a die = 6

Prime numbers less than 6 are 2, 3 and 5

Possible outcomes(getting 1 or a prime number) =  1, 2, 3 and 5

Probability of getting 1 or prime number when rolling a die = 4/6 = 2/3

Answer:

a. I=5350E +37100

Step-by-step explanation:

The trend line does not start at the origin so we can immediately rule out option C

The equation should be in slope intercept form so we can rule out option D, since E is the x axis and we are looking for y = mx + b not x = mx + b.

Option B is ruled out because if we plug in the value of E = 2 then we get:

I = 5350(2) - 37100

I = 10700 - 37100

I = -16400

Which is wrong since we are not in the negative so your answer is A

Answer:

wdawdwd

Step-by-step explanation:

Answer:

C, D,F

Step-by-step explanation:

Answer:

Its C

Step-by-step explanation:

Answer:

Yes, [tex]y=-x[/tex]  describes "y" as a funcion of "x", because  each input value (value of "x") has only one ouput value (value of "y").

 Step-by-step explanation:

By definition, a relation is a function if  each input value (value of "x")has only one ouput value (value of "y").

We need to remember that "y as a function of x" means that  "x" is the independent variable and "y" is the dependent variable or, in other words,  the value of the variable "y" depends upon the value of the variable "x".

Then, [tex]y=-x[/tex] is a function, because each input value has one and only one output value. For example:

If [tex]x=-2[/tex], then:

[tex]y=-(-2)=2[/tex]

If [tex]x=1[/tex], then:

[tex]y=-(1)=-1[/tex]

If [tex]x=5[/tex], then:

[tex]y=-(5)=-5[/tex]

Therefore,  [tex]y=-x[/tex]  describes "y" as a funcion of "x".

C. A non-equilateral triangle does not have three congruent sides. True

Answer: B is correct, 40 degrees.

Step-by-step explanation:

70 is the given angle, z is equivalent to that angle, so z is 70. So add those together, and you have 140. According to the rule, a triangle will always add up to 180. So 180-140=40 and there's your answer. Hope this helps!

Domain means all the x - values included in a set of data:

{(3, 5), (8, 6), (2, 1), (8, 6)}

It is unnecessary to put two of the same numbers. You only need to put one.

{2, 3, 8}

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer: Last option.

Step-by-step explanation:

By definition, the Domain is the set of all the x-coordinates of the ordered pairs (input values) and the Range is the set of all the y-coordinates of the ordered pairs (output values)

In this case you have the following relation:

[tex]R:[/tex]{[tex](3, 5), (8, 6), (2, 1), (8, 6)[/tex]}

You can identify that the set of all the x-coordinates is:

{[tex]3,8,2,8[/tex]}

You can observe that the input value 8 appears twice, but you only need to write it once.

Therefore, the Domain of that relation is:

[tex]Domain:[/tex]{[tex]2,3,8[/tex]}

Answer:

D. Malik substituted 60 for y instead of x.

Step-by-step explanation:

Look closely at the step by step process.

Answer:Answer:

D. Malik substituted 60 for y instead of x.

Step-by-step explanation:

Look closely at the step by step process.

Step-by-step explanation:

Check the picture below.

Answer:

[tex] f ( x ) = 2 . 2 5 ( 1 + 0 . 4 ) ^ x [/tex]

Step-by-step explanation:

We are given that the price of gas started at $2.25 and increased at a rate of 4% per year.

We are to write a function which models this situation using numerical values of A and r into the expression.

A = $2.25

r = 4%

Assuming x to be the time in years, the function would be:

[tex] f ( x ) = 2 . 2 5 ( 1 + 0 . 4 ) ^ x [/tex]

Answer:

x = 53, y = 33

Step-by-step explanation:

Let one of the numbers = x, & the other = y. Set the equations:

x + y = 86

x - y = 20

This is a system of equation, in which the variables must be true for both of them.

First, choose a equation to use. In this case, I will choose x + y = 86. Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract y from both sides.

x + y = 86

x + y (-y) = 86 (-y)

x = 86 - y

Now, note the other equation: x - y = 20. You now know that x = 86 - y. Plug in 86 - y for x in the "other" equation:

x - y = 20

(86 - y) - y = 20

Simplify. Combine like terms:

86 - y - y = 20

86 - 2y = 20

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS (Parenthesis, Exponents (& Roots), Multiplication, Division, Addition, Subtraction):

First, subtract 86 from both sides:

86 (-86) - 2y = 20 (-86)

-2y = 20 - 86

-2y = -66

Isolate the variable, y. Divide -2 from both sides:

(-2y)/-2 = (-66)/-2

Note: Before we go any further, I want to remind you of division & multiplication rules. There are 3 kinds, when you are multiplying two positive numbers (+/+), when you are multiplying a positive number with a negative number (+/-), and when you are multiplying a two negative numbers (-/-). Note the "table" in the bottom:

________________________________________________________

(+/+) : Two positive numbers multiplied/divided with each other will always result in a positive answer:

Examples:

10/5 = 2

20/10 = 2

(+/-) : One positive number and one negative number multiplied/divided with each other will always result in a negative answer:

Examples:

20 x -5 = -100

50 x -3 = -150

(-/-) : Two negative numbers multiplied/divided with each other will always result in a positive answer:

Examples:

-30 x -5 = 150

-200/-10 = 20

________________________________________________________

Now, solve the equation:

(-2y)/-2 = (-66)/-2

y = -66/-2

Divide.

y = 33

One of your numbers (y) is 33. Plug in 33 for y in one of the equations:

x + y = 86

x + (33) = 86

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 33 from both sides.

x + 33 (-33) = 86 (-33)

x = 86 - 33

x = 53

Your answers: x = 53, y = 33.

Check: Plug in 53 for x, 33 for y in the equations:

x + y = 86:

(53) + (33) = 86

86 = 86 (True)

x - y = 20:

(53) - (33) = 20

20 = 20 (True)

Your answers: x = 53, y = 33

~

Answer: 53 and 33

Step-by-step explanation:

Let be "x" the first number and "y" the second number.

Based on the information provided we can set up a system of equations:

[tex]\left \{ {{x+y=86} \atop {x-y=20}} \right.[/tex]

Applying the Elimination method, we can add both equations and solve for the variable "x":

[tex]\left \{ {{x+y=86} \atop {x-y=20}} \right.\\................\\2x=106\\\\x=\frac{106}{2}\\\\x=53[/tex]

Now we can substitute [tex]x=53[/tex] into one of the original equations and solve for the variable "y":

[tex]53+y=86\\\\y=86-53\\\\y=33[/tex]

Answer:

Option d) all real numbers

Step-by-step explanation:

we have

[tex]y=\log8^x[/tex]

using a graphing tool

The graph of the equation is a line that represent a direct variation ( the line passes through the origin)

therefore

The domain is all real numbers ---->interval (-∞,∞)

The range is all real numbers ---->interval (-∞,∞)

see the attached figure to better understand the problem

Answer:

(x-2) (x-7)

Step-by-step explanation:

x^2 -9x+14

What two numbers multiply to 14 and add to -9

-2*-7 = 14

-2+-7 = -9

(x-2) (x-7)

Answer:

(1) x= 5, y = 3

(2) x = -27, y = -29

Step-by-step explanation:

If the frist equation is 16x - 2y = 74

[tex]\\\\\left\{\begin{array}{ccc}8x-y=37\\x-y=2&\text{add y to both sides}\end{array}\right\\\\\left\{\begin{array}{ccc}8x-y=37&(1)\\x=2+y&(2)\end{array}\right\\\\\\\text{substitute (2) to (1):}\\\\8(2+y)-y=37\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\16+8y-y=37\qquad\text{subtract 16 from both sides}\\7y=21\qquad\text{divide both sides by 7}\\\boxed{y=3}[/tex]

[tex]\text{put the value of y to (2):}\\\\x=3+2\\\boxed{x=5}[/tex]

If the first equation is 16 - 2y = 74

[tex]\left\{\begin{array}{ccc}16-2y=74&\text{divide both sides by 2}\\2-2y=4&\text{divide both sides by 2}\end{array}\right\\\left\{\begin{array}{ccc}8-y=37&\text{subtract 8 from both sides}\\x-y=2\end{array}\right\\\left\{\begin{array}{ccc}-y=29&\text{change the signs}\\x-y=2\end{array}\right\\\left\{\begin{array}{ccc}y=-29&\text{put it to the second equation}\\x-y=2\end{array}\right\\\left\{\begin{array}{ccc}y=-29\\x-(-29)=2\end{array}\right\\\left\{\begin{array}{ccc}y=-29\\x+29=2&\text{subtract 29 from both sides}\end{array}\right[/tex]

[tex]\left\{\begin{array}{ccc}y=-29\\x=-27\end{array}\right[/tex]

For this case we have that the variable "s" represents the quantity of slices for each pizza.

In total, 9 pizzas were purchased and 72 slices were obtained. Then we can raise the following equation:

[tex]9s = 72[/tex]

To know the amount of slices of each pizza we clear "s":

[tex]s = \frac {72} {9} = 8[/tex]

Answer:

[tex]9s = 72\\s = 8[/tex]

Answer:

1) 33.33%

2) 16.66%

Step-by-step explanation:

1) Since multiples of 3 in 1,2,3,4,5,6 include and limited to 3 and 6.  This means that 2 / 6 or 1 / 3.  This fraction is equal to 33.33%.

2) Since multiples of 4 in 1,2,3,4,5,6 include and limited to only 4.  This means that 1/6 and this fraction is equal to 16.66%.

Answer:

1/2.

Step-by-step explanation:

A multiple of 3 is 3 or 6 and a multiple of 4 is 4.

Probability(3 or 6) = 2/6 = 1/3.

Probability(4 ) = 1/6.

So Probability ( multiple of 3 or a multiple of 4) = 1/6 + 1/3

= 1/2.

Answer:

b=128

Step-by-step explanation:

Answer:

Option D b = 128°

Step-by-step explanation:

There are two parallel lines p and q

These lines are crossed by a transversal m

then ∠b and ∠128° are the alternate angles.

which should be equal in measure.

Therefore, ∠b = 128°

Option D b = 128° is the answer.

Answer:

The correct option B) 4.

Step-by-step explanation:

Consider the provided equation.

[tex]5x - 20 = 0[/tex]

To find the zero simplify the above equation as shown

Add 20 from both the sides.

[tex]5x - 20+20 = 20[/tex]

[tex]5x= 20[/tex]

Divide 5 from both the sides.

[tex]\frac{5x}{5}=\frac{20}{5}[/tex]

[tex]x=4[/tex]

Thus, the zero of the equation is [tex]x=4[/tex].

Hence, the correct option B) 4.

For this case we have by definition, that the area of a square is given by:

[tex]A = l ^ 2[/tex]

While the perimeter is given by:

[tex]p = 4l[/tex]

Where:

l: It's the side of the square.

Square 1: [tex]l = 2.5[/tex]

[tex]A = (2.5) ^ 2 = 2.5 * 2.5 = 6.25\\p = 4 (2.5) = 10[/tex]

Square 2: [tex]l = 5[/tex]

[tex]A = (5) ^ 2 = 5 * 5 = 25\\p = 4 (5) = 20[/tex]

We can see that the perimeter of the second square is double that of the first. In addition, the second area is four times that of the first square.

Answer:

[tex]p_ {2} = 2p_ {1}\\A_{2} = 4A_ {1}[/tex]

Answer:

A

Step-by-step explanation:

Answer:

180 voted in favor

Step-by-step explanation:

To find out how many people vote for the new town hall, take the number of people who voted and multiply by the percent who voted in favor

2000 * 9%

2000 * .09

180

180 voted in favor

For this case we have the following expression:

[tex]-1.5x-3.1 <5.5[/tex]

Adding 3.1 to both sides of the inequality:

[tex]-1.5x <5.5 + 3.1\\-1.5x <8.6[/tex]

Dividing between -1.5 on both sides of the inequality, keeping in mind that the sign changes direction:

[tex]x> \frac {8.6} {- 1.5}\\x> -5.73333[/tex]

Answer:

[tex]x> -5.73333[/tex]

Answer:

So value of x = -1 and value of y = 1

Solution Set (-1,1)

Step-by-step explanation:

x+y =0

x-y +2 =0

We need to solve these equations to find value of x and y

x+y =0 eq(1)

Add -2 on both sides

x-y = -2 eq(2)

Add equation 1 and 2

x+y = 0

x-y =-2

______

2x = -2

x = -2/2

x = -1

Now, put value of x = -1 in equation 1

x+y = 0

-1 +y =0

Adding +1 on both sides

-1+1+y = 0+1

y = 1

So value of x = -1 and value of y = 1

Solution Set (-1,1)

We would plot the values of x= -1 and y = 1 on the graph.

Graph is attached in the figure below.

Answer:

Step-by-step explanation:

Total cost here is a sum that increases with the number of eggs produced.

TC(x) = $1000 + ($0.05/egg)x, where x is the number of eggs produced.

The y-intercept is $1000; it is independent of the number of eggs produced.

The slope is $0.05/egg.

Answer C is correct.

The equation that represents the monthly cost y for producing x eggs is y = 0.05x + 1000, where 0.05 (the cost per egg) is the slope, and 1000 (the monthly upkeep cost) is the y-intercept. Thus, the correct answer is option C.

In the given scenario, the cost per egg is $0.05, which makes this the slope of the equation, as this is the cost that changes with the number of eggs produced, represented by x. The fixed cost of $1000 per month for the upkeep of the farm is the y-intercept because this cost does not change regardless of the quantity of eggs produced. Therefore, using y = mx + b (slope-intercept form), where y is the total cost, m is the cost per egg, x is the number of eggs, and b is the monthly upkeep cost, we get:

y = 0.05x + 1000

Hence, the correct answer is C: The slope is 0.05 because this is the cost per egg. The equation is y = 0.05x + 1000.

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Answer:

W, I believe

Step-by-step explanation:

Answer:

W

Step-by-step explanation:

The y intercept is where the graph crosses the y axis (where x=0)

This is the point W