If g(x) is the inverse of f(x), what is the value of f(g(2))?
0-6
O-3
02
O 5

Answers

Answer 1

Answer:

2

Step-by-step explanation:

When a function and its inverse are composed, the output is equal the input.


Related Questions

please help me to find the answer Y=2X 3X+4Y=22 Y=2X 3X+4Y=22 ​

Answers

System of equations.

[tex]\left\{\begin{array}{ccc}y=2x&(1)\\3x+4y=22&(2)\end{array}\right[/tex]

Put (1) to (2):

[tex]3x+4(2x)=22\\3x+8x=22\\11x=22\qquad|\text{divide both sides by 11}\\\boxed{x=2}[/tex]

Substitute the value of x to (1):

[tex]y=2\cdot2\\\boxed{y=4}[/tex]

Solution:

[tex]\huge\boxed{\left\{\begin{array}{ccc}x=2\\y=4\end{array}\right}[/tex]

-(x − 2)(3x2 + 4x − 5)

Answers

The simplification of the algebraic expression to its simplest form is -3x³ + 2x² + 13x - 10

What is the simplest form of an algebraic expression?

The simplest form of an algebraic expression is a stage at which the expression can no longer be further simplified.


From the given expression:

= -(x − 2)(3x² + 4x − 5)

= (-x +2)(3x² + 4x − 5)

Open brackets

= -3x³ - 4x² + 5x +6x² + 8x - 10

= -3x³ + 2x² + 13x - 10

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If it is already 110F degrees below zero, and the temperature drops another 40 F degrees, how cold is it now?

Answers

Answer:

-150

or 150 degrees below 0

Step-by-step explanation:

The temp is -110. Dropping another 40 degrees means subtracting 40.

-110 - 40 = -150

Find the value of x.

Answers

Answer:

x=21°

Step-by-step explanation:

40°+5x+14°+x=180°

5x+x=180°-40°-14°

6x=126°

x=21°

Answer:

x = 21

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

x + 40 + 5x+14 = 180

Combine like terms

6x+54 =180

Subtract 54 from each side

6x+54-54 = 180-54

6x =126

Divide each side by 6

6x/6 =126/6

x = 21

URGENT, please help I am so lost

Answers

Answer:

Using the concept of linear equations, we find that we need 40 gallons of the 65% antifreeze and 10 gallons of the 90% antifreeze.

Step-by-step explanation:

Let x = amount of 20% antifreeze

Let y = amount of 70% antifreeze

Given that the total amount of antifreeze is 80 gallons

So, x + y = 80

Also given that the purity of the total antifreeze is 60%.

0.65x + 0.90y = 0.70(x + y)

65x + 90y = 70(x + y)

Simplify and solve the system of equations

65x + 90y = 70x + 70y      

65x -70x+ 90y-70y = 0    

-5x + 20y = 0      

Now we have the following system of equations:

x + y = 50

-5x + 20y = 0

Multiply the first equation by 5 to get opposite coefficients for x;  

add the equations to eliminate x

5x + 5y - 5x + 20y = 250

25y = 250

y = 10              

Since the total mixed gallons is 50,

x = 50 - 10 = 40

So we need 40 gallons of the 65% antifreeze and 10 gallons of the 90% antifreeze

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Determine the linear function for a graph that is a line with a slope of 1/7
and contains the point
(−4, 1).

Answers

The linear equation is y = (1/7)*x + 11/7.

How to get the linear equation?

The general linear equation is:

y = a*x + b

Where a is the slope.

Here we know that a = (1/7), then the line is:

y = (1/7)*x + b

We also know that the line contains the point (-4, 1), this means that when x = -4, we must have y = 1.

Replacing that, we get:

1 = (1/7)*(-4) + b

1 + 4/7 = b

7/7 + 4/7 = b

11/7 = b

So the linear equation is:

y = (1/7)*x + 11/7.

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The equation of the linear function of the line is: y = 1/7x + 11/7.

What is a Linear Function Equation?

A linear function equation is modelled as, y = mx + b, where m is the slope and b is the y-intercept.

Slope (m) = 1/7, and the line passes through (-4, 1), therefore, substitute (x, y) = (-4, 1) and m = 1/7 into y = mx + b:

1 = 1/7(-4) + b

1 = -4/7 + b

1 + 4/7 = b

11/7 = b

b = 11/7

Plug in the values of m and b into y = mx + b:

y = 1/7x + 11/7

The equation of the linear function is: y = 1/7x + 11/7

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The star shape is made from a regular hexagon and six congruent equilateral triangles The area of the star shape is 96cm squared Work out the area of the regular hexagon.

Answers

Answer:

48 Square Centimeters

Step-by-step explanation:

The red triangular exterior pieces are all equilateral triangles with some side length.

We don't need to know what that side length is. It doesn't matter.

The area of one red equilateral triangle is some area A.

There are 6 of these red triangles, so the red exterior triangular parts combine to a total area of 6*A.

The hexagon is composed of equilateral triangles as well.

Each of these blue equilateral triangles is congruent to any outer red triangle because the side length is the same.

Therefore, the 6 blue equilateral triangles composing this hexagon combine to get a total area of 6*A

The area of the star overall is 12*A because we have 6 blue triangles combining with the 6 red triangles.

There is a total of 12 triangles.

HEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEELP

Answers

Answer:

C.

Step-by-step explanation:

Adding 2 fractions results in a fraction.

Answer:

B: The sum is a non-terminating and a non-reapeating decimal

Step-by-step explanation:

-11/4 +5/g

There is 15 steps you have to do after (look in the picture)


but this is what you get:

[tex]-\frac{11g-20}{4g}[/tex]

Which graph represents this equation?

5y = x + 5

A.
A line is graphed in an x y plane, where the x and the y axes range from negative 8 to 8 in increments of 2. The line rises through (negative 8, negative 0.5), (negative 5, 0), (0, 1), and (5, 2).
B.
A line is graphed in xy plane ranging from negative 8 to 8 in increament of 1. The line raises through (negative 8, negative 2) ,(0,1) and (1,5).
C.
A line is graphed in an x y plane, where the x and the y axes range from negative 8 to 8 in increments of 2. The line rises through (negative 5, 4), (0, 5), and (5, 6).
D.
A line is graphed in an x y plane, where the x and the y axes range from negative 8 to 8 in increments of 2. The line rises through (negative 2, negative 5), (negative 1, 0), and (0, 5). need answer quick

Answers

Graph (A) represents the equation of the line 5y = x + 5 shown in the graph option (A) is correct.

What is a straight line?

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the equation of the line:

5y = x + 5

After plotting the line on the coordinate plane.

The above line passes through:

(-5, 0), (0,1), and (5,2)

And the line rises from (-8, -0.5), (-5, 0), (0,1), and (5,2)

Thus, graph (A) represents the equation of the line 5y = x + 5 shown in the graph option (A) is correct.

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Answer:  A. A line is graphed in an x y plane, where the x and the y axes range from negative 8 to 8 in increments of 2. The line rises through (negative 8, negative 0.5), (negative 5, 0), (0, 1), and (5, 2).

Step-by-step explanation:

Solve the simultaneous equations below.
7x-6y = 30
2x+6y= 24

Answers

Answer:

(x,y)—>(6,2)

Step-by-step explanation:

Add both equations to eliminate y

9x=54

x=6

plug x=6 into either equation

2(6)+6y=24

6y=24-12

y=12/6=2

What is the length of the line?
Choose 1 answer: A. 7 B. The square root of 10 C. Square root of 29 D.Square root of 21

Answers

Answer:

C

Step-by-step explanation:

= The square root of (5^2+2^2)= The square root of 29 ---> C

Hi my name is aughhhhhhhhhhh

Answers

Answer:

Hello auggggh nice to meet you!

Step-by-step explanation:

how to figure out pythagoras theorem?

Answers

Any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

What is the Pythagoras Theorem?

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In △ABD and △ACB,

∠A = ∠A (common)

∠ADB = ∠ABC (both are right angles)

Thus, △ABD ∼ △ACB (by AA similarity criterion)

Similarly, we can prove △BCD ∼ △ACB.

Thus △ABD ∼ △ACB,

Therefore, AD/AB = AB/AC.

We can say that AD × AC = AB².

Similarly, △BCD ∼ △ACB.

Therefore,

CD/BC = BC/AC.

We can also say that

CD × AC = BC².

Adding these 2 equations, we get

AB² + BC² = (AD × AC) + (CD × AC)

AB² + BC² =AC(AD +DC)

AB² + BC² = AC²

Hence proved

Thus, any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

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A half-marathon is 13 miles, how many kilometers is that?
26 km

82.36 km
20.92 km
209.31 km

Answers

Answer:

The correct answer would be 20.92

the answer is 20.92 because one mile is 1.60 and 1.60 x 13 is 20.92

Select the graphs that show a proportional relationship between x and y

Answers

Hey there could you please show an image of said graphs!


What are the solutions of 2x² - 6x+5=0?

Answers

Answer:

no solutions

Step-by-step explanation:

we use the quadratic formula.

for an equation ax²+bx+c=0, the solutions for x are:

x = (-b±sqrt(b²-4ac))/2a

in our case, a=2, b=-6 and c=5, so:

x= (6±sqrt(36-40))/4

we see that we get a negative number inside the sqrt, so we have no real solutions

Answer:

No solution

Step-by-step explanation:

1) Use the quadratic formula

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

[tex]2x^2-6x+5=0[/tex]

[tex]a=2\\b=-6\\c=5[/tex]

[tex]x=\frac{-(-6)\pm\sqrt{(-6)^2-4*2*5} }{2*2}[/tex]

2) Simplify

Evaluate the exponent:

[tex]x=\frac{6\pm\sqrt{(-6)^2-4*2*5} }{2*2}[/tex]

[tex]x=\frac{6\pm\sqrt{36-4*2*5} }{2*2}[/tex]

Multiply the numbers:

[tex]x=\frac{6\pm\sqrt{36-4*2*5} }{2*2}[/tex]

[tex]x=\frac{6\pm\sqrt{36-40} }{2*2}[/tex]

Subtract the numbers:

[tex]x=\frac{6\pm\sqrt{36-40} }{2*2}[/tex]

[tex]x=\frac{6\pm\sqrt{-4} }{2*2}[/tex]

Multiply the numbers

[tex]x=\frac{6\pm\sqrt{-4} }{2*2}[/tex]

[tex]x=\frac{6\pm\sqrt{-4} }{4}[/tex]

3) No real solutions because the discriminant is negative

The square root of a negative number is not a real number

[tex]d=-4[/tex]

Result

No solution

Given the quadrilateral below is a rhombus, solve for the length of the side of the rhombus.

Answers

Answer:

7.21

Step-by-step explanation:

There is a formula to find the area of a side of a rhombus given 2 diagonals.

It is:  [tex]\frac{\sqrt{p^{2}+q^{2} } }{2}[/tex]

64 + 144 = 208

[tex]\sqrt{208}[/tex] = 14.42

14.42 / 2 =

7.21

The diagonals of the rhombus meet perpendicularly, so you have four right triangles. Because of this you can use the Pythagorean theorem with 8 and 12 to find the side.

Theorem: a^2 + b^2 = c^2

8^2 + 12^2 = c^2
64+144 = c^2
c^2 = 208
c = sqrt208

What is the range of this function?

OA. (3, 5, 7, 11)
OB. (-3, 4, 5, 7)
OC. (-3, 0, 3, 4, 5, 6, 7, 11)
OD. (-3, 0, 4, 6)

Answers

Answer:

(-3, 0, 4, 6) (option D)

Step-by-step explanation:

The "range" of a function is all possible y-values. In this image, there are x's entered on the left side--which I know to be x values because a function, f(x) is essentially the outcome of what happens when x is entered.

So, the y-values are featured on the right. All of these values are the possible values for y, or, what we call the range.

Meaning that the range of this function is (-3, 0, 4, 6)

Henry recorded the number of miles he biked each day for a week. His milles were 25,40,35, 25, 40, 60, and 75.
Enter the data into the statistics calculator
What is the standard deviation of the milles Henry bilked to the nearest tent?

Answers

The answer is 17.1 if i did my math correctly

5) A restaurant menu has 6 starters, 10 mains and 6 desserts.
A customer can choose from the following meals
a starter and a main,
a main and a dessert,
a starter, a main and a dessert.
Show that there are 480 different ways of choosing a meal at this restaurant.

Answers

Answer: 360

Step-by-step explanation: 6 times 6 times 10 = 360

X-intercept (3,0) and y-intercept (0, -6).

Answers

What’s the actual question
What’s the question lol

Simplify the expression.

Answers

Answer:

D

Step-by-step explanation:

Just a question about the problem, dont need the answer if you dont want to solve it, but would 15 be negative? Thats all, Thanks!
[tex]f(x)=x^{2} +15x+3[/tex]

Answers

Answer:

[tex]x = -\frac{15}{2}[/tex]

Step-by-step explanation:

Hello!

The formula for the AOS is given to you, and you simply have to plug in the information given by the equation.

Equation of a Parabola (Standard): [tex]y = ax^2 + bx + c[/tex]

Comparing it to our equation:

a = 1b = 15c = 3

Plug it in to the AOS formula:

[tex]x = \frac{-b}{2a}[/tex][tex]x = \frac{-15}{2(1)}[/tex][tex]x = -\frac{15}{2}[/tex]

You only have to input 15 in to the correct box since the negative sign is already placed for you.

Rewrite the expression in the form z^n. z x z x z x z x z x z/z x z

Answers

Answer:

z⁴

Step-by-step explanation:

(z x z x z x z x z x z) / (z x z)

z⁶ / z² = z⁴

A table of data is given.

x: -2, -1, 0, 1, 2
f(x): 128, 27, 5, 1, 0.1

Which exponential model best represents the data?

A. f(x) = 5(1.2)^x

B. f(x) = 5(0.2)^x

C. f(x) = 2(5)^x

D. f(x) = 2(0.5)^x

Answers

The exponential model best represents the data is B. f(x) = 5(0.2)^x

How to determine the exponential model?

From the table of values, we have the following points:

(x, y) = (0,5) and (1,1)

An exponential model is represented as:

y = ab^x

Substitute (x, y) = (0,5)

5 = ab^0

5 = a

This gives

a = 5

So, we have:

y = 5b^x

Substitute (x, y) = (1,1)

1 = 5b^1

This gives

5b = 1

Divide by 5

b = 0.2

Substitute b = 0.2 in y = 5b^x

y = 5(0.2)^x

Hence, the exponential model best represents the data is B. f(x) = 5(0.2)^x

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The diagram below shows a square inside a regular octagon. The apothem of the octagon is 15.69 units. To the nearest square unit, what is the area of the shaded region? 13 U 13 U Apothem length: 15.69 O A. 1463 square units B. 816 square units C. 647 square units OD. 764 square units ​

Answers

perimeter of octagon

8(13)104units

Now area

perimeter×apothem /2104(15.69)/252(15.69)815.88units²

Area of square

13²169units²

Area of shaded region

815.88-169646.88units²647units²

Answer:

C.  647 square units

Step-by-step explanation:

To find the shaded area, subtract the area of the unshaded square from the area of the octagon.

Area of the octagon

[tex]\textsf{Area of a regular polygon}=\dfrac{n\:l\:a}{2}[/tex]

where:

n = number of sidesl = length of one sidea = apothem

Given:

n = 8l = 13a = 15.69

Substitute the given values into the formula and solve for A:

[tex]\implies \textsf{Area}=\sf \dfrac{8 \cdot 13 \cdot 15.69}{2}[/tex]

[tex]\implies \textsf{Area}=\sf \dfrac{1631.76}{2}[/tex]

[tex]\implies \textsf{Area}=\sf 815.88\:\:square \:units[/tex]

Area of the square

[tex]\implies \textsf{Area}=\sf 13^2=169 \:\:square \:units[/tex]

Area of the shaded region

= area of the octagon - area of the square

= 815.88 - 169

= 646.88

= 647 square units (nearest square unit)

If you receive a 20% DISCOUNT off an item costing $20.00, how much money do you save?

Answers

It’s easy just convert the percentage to decimal by dividing by 100 and you get 0.2

Now you multiply 20x0.2= 4

You save $4
20% off of $20 would be $4.
I know this because all you have to do while finding percentages is to take the first number of the % and the first number of the cost which will be 2x2= $4 saved

Solve the equation:
1-2 lnx = -4
~ [?]
X~
Round your answer to the nearest thousandth.

Answers

Answer:

x ≈ 12.182

Step-by-step explanation:

1 - 2lnx = - 4 ( subtract 1 from both sides )

- 2lnx = - 5 ( divide both sides by - 2 )

lnx = 2.5

x = [tex]e^{2.5}[/tex] ≈ 12.182 ( to the nearest thousandth )

Answer:

x = 12.182  (nearest thousandth)

Step-by-step explanation:

Given equation:

[tex]1-2 \ln x=-4[/tex]

Subtract 1 from both sides:

[tex]\implies 1-1 -2 \ln x =-4-1[/tex]

[tex]\implies -2 \ln x=-5[/tex]

Divide both sides by -2:

[tex]\implies \dfrac{-2 \ln x}{-2}=\dfrac{-5}{-2}[/tex]

[tex]\implies \ln x = \dfrac{5}{2}[/tex]

[tex]\textsf{As }\: \ln x=\log_ex \:\:\textsf{}[/tex], the natural logarithm can be canceled by giving both sides a base of e (Euler's number):

[tex]\implies e^{\ln x}= e^{\frac{5}{2}[/tex]

[tex]\implies x= e^{\frac{5}{2}[/tex]

[tex]\implies x=12.182\:\: \sf (nearest\:thousandth)[/tex]

State the value of 'x' in this equation, and explain why you know this to be true without doing any calculations.

[tex]5^x = 5^9[/tex]

Answers

Answer:

x=9

if

a^b = a^c

then b=c

so in this case x=9

what it the answer to 1 ÷ 4 1/2=

Answers

Its 2/9 which is 0.22222

Answer:

2/9 or 0.22222

Step-by-step explanation:

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