f(x)=2x^2
g(x)=x+1
prove fg(x)=gf(x)

Answer:

Step-by-step explanation:

y varies directly with x then, y=kx

for x = 2 and y= -10 we get:

-10 = 2k

k= -5

when x = 12

y = -5 * (12) = -60

D

Answer:

thus: x = 5, y = -3

Step-by-step explanation:

Solve the following system:

{y + x = 2 | (equation 1)

-4 y + 3 x = 27 | (equation 2)

Swap equation 1 with equation 2:

{3 x - 4 y = 27 | (equation 1)

x + y = 2 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:

{3 x - 4 y = 27 | (equation 1)

0 x + (7 y)/3 = -7 | (equation 2)

Multiply equation 2 by 3/7:

{3 x - 4 y = 27 | (equation 1)

0 x + y = -3 | (equation 2)

Add 4 × (equation 2) to equation 1:

{3 x + 0 y = 15 | (equation 1)

0 x + y = -3 | (equation 2)

Divide equation 1 by 3:

{x + 0 y = 5 | (equation 1)

0 x + y = -3 | (equation 2)

Collect results:

Answer: {x = 5, y = -3

Answer: No, it works out to a different number. The 1st will end up with 605 bison.

Step-by-step explanation:

1st Herd: (550 x 10%) = 55 Bison

550 + 55 = 605   Thus 550 with a 10% increase is 605 Bison.

2nd herd: if you take 10% of 605 bison that number of (60.5) will give you a greater loss when taken away from 605.

605 - 60.5 = 544.5 bison remaining if 605 has a 10% loss.

Herd 2 started with approximately 611 bison. Check your math by multiplying 611 by 10% = 61.1

then subtract (611 - 61.1) = 549.9

So Herd 1 Does Not Equal Herd 2.

Answer:

5.083

Step-by-step explanation:

[tex]V=\frac{1}{3}Bh=(1/3)(1/2)(1.7)(3.9)(4.6)=5.083[/tex]

Answer: [Rational function definition]In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. In other words, it's a function that is the ratio of two polynomials. It is "Rational" because one is divided by the other, like a ratio.

Answer: he reads 52 chapters in 2 hours.

Step-by-step explanation:

Since he reads 26 chapters per hour, multiply the number of chapters by the number of hours which is two.

26 * 2 = 52

he reads 52 chapters in 2 hours.

Answer:

52 chapters

Step-by-step explanation:

Because he reads 26 chapters in 1 hour and his rate is constant (never changing), multiply 26 by 2 to find how many chapter for 2 hours.

26 x 2 = 52

when a person's test performance can be compared with that of a representative and pretested sample of people, the test is said to be norm-referenced.

Norm-referenced tests are assessments that measure an individual's performance against a predetermined group, or norm. A norm-referenced test is designed to evaluate how a person performs in comparison to a representative and pretested sample of people. This type of testing is especially common with achievement tests, such as the SAT or IQ tests, where the scores are meant to represent how the individual compares to others of the same age or in the same educational setting. The results of norm-referenced tests can be used to rank individuals according to their performance on the test, allowing for an easy comparison between individuals. Norm-referenced tests are designed to provide a comprehensive view of an individual’s strengths and weaknesses in comparison to a predetermined group.

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Answer:

8 < f

Step-by-step explanation:

Because it says the cooler could hold less than eight large fish

Less than mean <

So the equation is 8<f

Answer: b  8 < f

Step-by-step explanation:

Answer:

I believe the answer is y=3

Step-by-step explanation:

If you were to graph y=0, the line would be horizontal through the origin. Since the lines are parallel, you cannot have the answer being x=-3 or x=3 as they would intersect. Now that we have eliminated two answers, we have to choose between y=-3 and y=3. In the question, it says that the line passes through (-3,3). Because of the (x,y) coordinates, you can see that y does indeed equal 3.

I hope this helps!

Answer:

y = 3

Step-by-step explanation:

y = 0(x)

3 = 0(- 3)

y = 3

Answer:

D) $3,264.00

Step-by-step explanation:

I = Prt

I = $1600 × 0.0325 × 32 = $1664

total = $1600 + $1664 = $3264

Answer: 167/30

Step-by-step explanation:

1/6 + 5.4

5.4 = 54/10

So we have 1/6 + 54/10

The common factor is 60

10/60 + 324/60

334/60

167/30

Answer:

1/6 + 5.4 = 167/30 = 5  17/30

Step-by-step explanation:

Conversion of a decimal number to a fraction: 5.4 = 54/

10

= 27/5

a) Write down the decimal 5.4 divided by 1: 5.4 = 5.4/

b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

5.4/1

= 54/10

Note: 54/10

is called a decimal fraction.

c) Simplify and reduce the fraction

54/10

= 27 * 2/5 * 2

= 27 * 2/5 * 2 = 27/5

Add: 1/6 + 5.4 = 1/6 + 27/5 = 1 · 5/

6 · 5 + 27 · 6/

5 · 6

= 5/30 + 162/30 = 5 + 162/30

= 167/30

The linear equality for the given graph is x > 0.

Option (B) is correct.

What is linear equality?

In mathematics, a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

The hollow circle in the linear equality shows that the point should be excluded and the line is going towards the positive x-axis.

So we can prepare the linear equality as

                       x > 0

Hence, the linear equality for the given graph is x > 0.

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The equation of the line would be 7x - 2y = 6.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                    y - y1 = m(x - x1)

The required line passes through (0, -3) and the slope is 7/2.

By using the slope-point form of the line, we get

          y - (-3) = (7/2)(x-0)

          y + 3 = 7/2x

          2y + 6 = 7x

         7x - 2y = 6

Hence, the equation of the line would be 7x - 2y = 6.

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Question: Find the equation of the line passing through the point (0, -3) having slope 7/2.

Answer:

The expression represents a cubic polynomial with 3 terms. The constant term is -1, the leading term is x^3, and the leading coefficient is 1.

Step-by-step explanation:

Answer:

A. 145 degree

Step-by-step explanation:

A triangle has 180 degree

109 + 36 = 145 degree

180 - 145 = 35 degree

35 degrees is the missing angle of the triangle. This angle must add with angle 1 equal to 180 degrees.

180 - 35 = 145 degree

So, the answer is A

Answer:

ANGLE 1 = 145°

Step-by-step explanation:

Angle 1 is right next to the EMPTY interior angle of the triangle and they are on a straight line!

This means, these two angles (angle 1 and the empty angle next to it) are supplementary angles!

Supplementary angles are angles on a straight line and they always add up to 180°

To find it, we need to find the degrees of the empty angle.
To find it, we need to look at the whole triangle.

Remember, all triangles equal 180°

Let's find this empty angle

180° - 109 - 36 = 35°

The empty angle = 35°

BUT WE ARE NOT DONE!

We are looking for angle 1, not the empty angle.

To find angle 1, we must remember that the empty angle (which we found was 35°) and angle 1 make a supplementary angle (which totals up to 180°)

Let's find angle 1, using subtraction.

180° - 35 = 145°

ANGLE 1 = 145°

Answer:

y = -3z - 3

Step-by-step explanation:

y=mz+b  ==> slope-intercept form where m=slope

9z + 3y = -9​  

9z - 9z + 3y = -9z - 9  ==> solve for y

3y = -9z - 9

(3y = -9z - 9)/3  ==> divide equation by 3 to isolate y

y = -3z - 3

Answer: 3a

Step-by-step explanation:

(4a*6a)/8a

24a^2/8a

3a

[tex]4a\times6a[/tex]

[tex]4\times6=24\\4a\times6a=24a[/tex]

[tex]\dfrac{24a}{8a}[/tex]

[tex]=\fbox{3a}[/tex]

Answer:

  10 pounds

Step-by-step explanation:

You want to know the number of pounds of peanuts in a mix of $5/lb peanuts and $6/lb almonds that gives 14 pounds of nuts for $74.

Let p represent the number of pounds of peanuts in the mix. The (14-p) is weight of almonds, and the total cost is ...

  5p +6(14 -p) = 74

Simplifying the equation gives ...

  -p +84 = 74

  10 = p . . . . . . . . add p-74

You should buy 10 pounds of peanuts to make the 14 lb bag cost $74.

__

Additional comment

You notice that simplifying the equation gives p a negative coefficient. If you choose the variable to represent the more expensive contributor, then the coefficient of that comes out positive. (We like positive coefficients, as they tend to reduce errors.)

Here, the problem is requesting the amount of the lower cost contributor, so we used the variable to represent that.

Often, you are asked to solve mixture problems using a system of equations. Those would use a variable for each of the quantities, and the equations would be ...

You notice that substituting for 'a' gives the equation we used above.

Jumping directly to this step saves a bit of written work, though the mental work is the same.

Answer:

The item that shows what Kenneth has left is [B] Net Worth: $1,050.

Net worth is a person's assets minus their liabilities. In this case, Kenneth's assets include the $2,000 lottery prize and the money he deposited in his bank account. His liabilities include the car payment he paid off and the gift card he bought for his nephew. Subtracting these liabilities from his assets gives us his net worth of $1,050.

Net cash is the amount of cash a person has available, which would not include any assets such as the money in Kenneth's bank account. Net income is the total amount of income a person has earned, which would not include the lottery prize in this case.

Answer: The answer would be 9.125.

Step-by-step explanation:

I can't really find an explanation for it.  Sorry.

The remaining angles are 80 and 30

The sum of angles of a triangle = 180

One angle is given as                 = 70

The sum of the remaining angles= 110

Now we apply the theory of ratios

The ratio between the angles are given as 3:8

So one angle will be 3 parts of 110 and other eight parts of 110

Total number of parts = 3+8 = 11

Angle 1                         = (3*110)/11

                                     =  30

Angle 2                        = (8*110)/11

                                     = 80

So the other two angles are 30 and 70.

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The equation of a line parallel to -3x - y= -4  and passing through a point  (1,4) is y = -3x + 7.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the line is parallel to  -3x - y = -4 and it passes through (1, 4).

Parallel lines have the same slope.

Hence,

-3x - y = -4

y = -3x + 4

The slope of the line is -3.

Let's find y-intercept using (1, 4)

y = -3x + b

4 = -3(1) + b

4 + 3 = b

b = 7

Therefore, the equation of the line is y = -3x + 7.

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Answer:

11.25

Step-by-step explanation:

(1.35 × 10^7) / (1.2 × 10^6) =

= 135/12

= 11.25

Answer: 11.25 is the answer

The unexplained sum of squares measures variation in the dependent variable Y about the estimated Y values. The correct answer is option D.

The unexplained variation is the sum of the squared of the differences between the y-value of each ordered pair and each corresponding predicted y-value. The sum of the explained and unexplained variations is equal to the total variation.

Unexplained variance is also known as error variation or residual variation. It refers to the random fluctuations around the regression line which show as variation. This type of variation is the sum of squared differences among each ordered pair's y-value and the predicted corresponding y-value.

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The integer that makes the inequality 3(n − 6) < 2(n + 12) false is

The integer that makes the inequality false is solved by substituting the values and solving the inequality

3(n − 6) < 2(n + 12)

for n = -5

substituting the value of n

3(-5 − 6) < 2(-5 + 12)

= -33 < 14

3(n − 6) < 2(n + 12)

for n = 3

substituting the value of n

3(3 − 6) < 2(3 + 12)

= -9 < 30

3(n − 6) < 2(n + 12)

for n = 12

substituting the value of n

3(12 − 6) < 2(12 + 12)

= 18 < 48

3(n − 6) < 2(n + 12)

for n = 42

substituting the value of n

3(42 − 6) < 2(42 + 12)

= 108 < 108 wrong

This is the only wrong solution since 108 = 108

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The values of X ∩ Y are 1, 3, 5, and 7.

A set is a collection of items where there are operations such as:

Union of sets, the intersection of sets, complements of sets.

We have,

X = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }

Y = {-3, -1, 1, 3, 5, 7, 20}

Now,

X ∩ Y

= The values common to both sets.

= {1, 3, 5, 7 }

Thus,

X ∩ Y = {1, 3, 5, 7 }

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The largest right circular cone that can fit within a cube has a volume of 718.67 cm3.

When a cone's axis is the line from the vertex to the circular base's midpoint, the cone is said to be right circular. In other words, a right angle is formed when the center of the circular base joins the cone's peak.

A three-dimensional form called an inverted frustum that resembles a conical cylinder. When the vertex of a cone is inverted after being sliced by a plane parallel to the shape's base, it is said to have this shape.

The formula r2+rl, where r is the radius of the circular base, h is the height of the cone, l is the slant height, and is an approximation, is used to determine the surface area of a cone as 3.14

Side of cube: 14 cm

Cube's radius is 14/2 cm, or 7 cm.

h=14cm for height

Volume'=1/3piR x 2hM =1/3 x 22 x 7 x 7 x7

= 718.67 cm3.

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To change a greater than or equal to type constraint into an equality constraint, a variable is removed from the left side. It also goes by the name "negative slack variable."

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The unit rate of change of flour (y) with respect to sugar (x) will be 2.25.

        r = Δy/Δx

        [tex]\lim_{x \to \;0} (r) = \lim_{x \to \;0}[/tex] (Δy/Δx) = dy/dx

Given is that Melissa made three batches of oatmeal cookies. Her recipe calls for amounts of sugar (in cups) and flour (in cups) in the following ratios as shown in the question.

We can write the rate of change as -

r = Δy/Δx

r = (y₂ - y₁)/(x₂ - x₁)

y₂ = [tex]$6\frac{3}{4}[/tex] = 27/4

y₁ = [tex]$4\frac{1}{2}[/tex] = 9/2

x₂ = 3

x₁ = 2

Using the values -

r = (27/4 - 9/2)/(3 - 2)

r = (27 - 18)/4

r = 9/4

r = 2.25

Therefore, the unit rate of change will be 2.25.

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In the △IGH, the measurement of the angles are m∠G = 114°, m∠H = 49°, and m∠I = 17°.

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Given that,

m∠G = (7x - 5)°, m∠H = (3x - 2)°, and m∠I = x°.

The sum of interior angles of a triangle is 180°.

Therefore,

m∠G + m∠H + m∠I = 180°

Putting m∠G = (7x - 5)°, m∠H = (3x - 2)°, and m∠I = x°:

(7x - 5)° + (3x - 2)° + x° = 180°

Combine like terms:

(7x + 3x + x) - (5 + 2) =180

11x - 7 = 180

Add 7 on both sides:

11x = 187

Divide both sides by 11:

x = 187/11

x = 17

Now putting x = 17 in m∠G = (7x - 5)°, m∠H = (3x - 2)°, and m∠I = x°:

m∠G = (7×17 - 5)° = 114°

, m∠H = (3×17  - 2)° = 49°

m∠I =  17°

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The partial derivative of function f(x, y) = xy/cos(x) is  ∂/∂y [xy/cos(x)] = x sec(x)

In this question we have been given a function y′ = f(x,y) = xy/cos(x)

We need to find the partial derivative of function f(x, y) with respect to y, ∂f/∂y

Consider the partial derivative of function

∂f/∂y = ∂/∂y [xy/cos(x)]

∂f/∂y = ∂/∂y [xy * 1/cos(x)]

we know that 1/cos(x) = sec(x)

∂f/∂y = ∂/∂y [xy * sec(x)]

∂f/∂y = x sec(x)  ∂/∂y (y)

∂f/∂y = x sec(x) * 1

∂f/∂y = x sec(x)

Therefore,  ∂/∂y [xy/cos(x)] = x sec(x)

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