How does the graph of g(x) = (x + 2)3 − 6 compare to the parent function of f(x) = x3? g(x) is shifted 2 units to the right and 6 units down. g(x) is shifted 6 units to the right and 2 units up. g(x) is shifted 2 units to the left and 6 units down. g(x) is shifted 6 units to the left and 2 units down.

Answer:

To fill in the table of values for the equation y = 2x + 1, we can choose different values of x and substitute them into the equation to find the corresponding values of y. For example:

x y

0 1

1 3

2 5

3 7

4 9

To get the value of y, we substitute each value of x into the equation and simplify:

When x = 0:

y = 2(0) + 1 = 1

When x = 1:

y = 2(1) + 1 = 3

When x = 2:

y = 2(2) + 1 = 5

When x = 3:

y = 2(3) + 1 = 7

When x = 4:

y = 2(4) + 1 = 9

Therefore, the table of values for the equation y = 2x + 1 is:

x y

0 1

1 3

2 5

3 7

4 9

If Jake whittles little wooden figurines and begins to sell them. If the demand function for his figurines is given by D(q) = 80 - 1.25q and the supply function is S(q) = 0.75g. The equilibrium quantity is  40 units.

Given the demand function D(q) = 80 - 1.25q and the supply function S(q) = 0.75q, we can find the equilibrium quantity by setting these two functions equal to each other and solving for q:

D(q) = S(q)

80 - 1.25q = 0.75q

Simplifying this equation, we get:

2q = 80

q = 40

Therefore, the equilibrium quantity is q = 40. At this quantity, the quantity demanded is:

D(q) = 80 - 1.25q = 80 - 1.25(40) = 30

And the quantity supplied is:

S(q) = 0.75q = 0.75(40) = 30

Thus, the equilibrium quantity of Jake's wooden figurines is 40 units.

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Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.

This common convenience, already-existing variables, or all important elements from the original Diocesan customizable survey that followed a particular event methodology can all be used to achieve the goal. If it does, there will be another chance to get in touch with the entity. If it doesn't, each of the crucial elements of a term proof outcome will surely be lost.

Here,

The quantity of punch produced by the recipe is:

If the punch bowl has an 8-quart capacity and the recipe fills it 3/4 full.

=> 6 pints =  8 * 3/4.

The formula yields 6 quarts of punch as a result.

Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.

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We need a piece of wood that is approximately 8.1 inches long to replace AD. So, the answer is option A.

In geometry, a triangle is a three-sided polygon consisting of three line segments that connect three non-collinear points. These three points are called the vertices of the triangle, and the line segments connecting them are called sides. The sum of the angles of a triangle is always 180 degrees.

Triangles can be classified based on their sides and angles. A triangle with all three sides of equal length is called an equilateral triangle, while a triangle with two sides of equal length is called an isosceles triangle. A triangle with no sides of equal length is called a scalene triangle.

Triangles can also be classified based on their angles. A triangle with all three angles less than 90 degrees is called an acute triangle, while a triangle with one angle greater than 90 degrees is called an obtuse triangle. Finally, a triangle with one angle equal to 90 degrees is called a right triangle.

First, we can use trigonometry to find the length of side AC. Since angle BCD is 30 degrees and BC = 14, we have:

sin(30) = AC/14

AC = 14*sin(30)

AC = 7 inches

Next, we can use the fact that triangle ACD is a 15-75-90 triangle to find the length of AD. Since angle CAD is 75 degrees, we have:

tan(75) = AD/AC

AD = ACtan(75)

AD = 7tan(75)

Using a calculator, we get:

AD ≈ 8.09 inches

Therefore, we need a piece of wood that is approximately 8.1 inches long to replace AD. So, the answer is option A.

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Answer:

5.9

Step-by-step explanation:

segment BD was 8.1 so segment AD cant be 8.1

Answer:

[tex]k = - 3[/tex]

Step-by-step explanation:

[tex]y = kx[/tex]

[tex]k \times ( - 1) = 3[/tex]

[tex] - k = 3[/tex]

[tex]k = - 3[/tex]

Answer:

[tex]k = -3[/tex]

Step-by-step explanation:

Step 1: Substitute

To solve this problem you are going to need to substitute the values of y and x into the problem y=kx.  Which would give you the problem of 3=-1k or 3 = -k to make things easier.

Step 2: Using properties of equality

In order to isolate the value of k you would need to divide both sides by -1 because division cancels out multiplication. You would get [tex]\frac{3}{-1} = \frac{-k}{-1}[/tex] or [tex]-3 = k[/tex]

Step 3: Check

In order to check this problem you would need to insert the values back into the original equation and solve. So that would be 3= -1*-3 which does equal 3. So the answer is correct

By adding all the numbers in the line plot, we conclude that she will have enough olive oil.

To check this, we just need to add the 13 numbers and see if it is more than 16.

Each point above the line plot means how many times that number will apear in our sum, then the sum will be:

(2*0 + 4*(4/8) + 3*(6/8) + 3*1 + (1 + 2/8))

Now we need to solve that:

(2*0 + 4*(4/8) + 3*(6/8) + 3*1 + (1 + 2/8))

= 2 + 9/4 + 3 + 1 + 1/4

= 2 + 3 + 1 + 9/4 + 1/4

= 6 + 10/4

= 6 + 8/4 + 2/4

= 6 + 2 + 1/2

= 8 + 1/2

That is the amount of ounces of oil that she needs for the 13 recipes, it is less than 16 ounces, so she will have enough oil.

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The x- and y-coordinates of AJ'K'L' are related to the x- and y-coordinates of AJKL, as x-coordinate of AJ'K'L' = -y-coordinate of AJKL and y-coordinate of AJ'K'L' = x-coordinate of AJKL.

We create the x-axis and y-axis in the coordinate plane. the origin, where the x- and y-axes cross, and the coordinates ( 0,0 ). The horizontal axis represents the x-axis. The vertical axis represents the y-axis. The first and second coordinates are for the horizontal and vertical axes, respectively. On the coordinate plane, coordinates are expressed by ( x ,y ). The x-coordinate stands for the first coordinate.

When a point is rotated 90° clockwise about the origin, its x-coordinate becomes the negative of its original y-coordinate, and its y-coordinate becomes the positive of its original x-coordinate.

So, for point A(x,y), its new coordinates after a 90° clockwise rotation about the origin would be A'(-y,x). Similarly, for point J, K, and L, their new coordinates would be J'(-yj,xj), K'(-yk,xk), and L'(-yl,xl) respectively.

Therefore, the x- and y-coordinates of AJ'K'L' are related to the x- and y-coordinates of AJKL as follows:

x-coordinate of AJ'K'L' = -y-coordinate of AJKL

y-coordinate of AJ'K'L' = x-coordinate of AJKL

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Answer:

3n + 5n = 8n = 95

n = 11

$95 - $88 = $7

(11 paint brushes, 11 boxes of colored pencils)

Answer:

5

Step-by-step explanation:

S1=R1²=*3²=9 (the outer circle)

S2=R2²=*2²=4 (the inner circle)

S=S1-S2=9-4=5 (the shaded ring)

Two equivalent expressions to  3x + 3(x+y) are:

Two expressions are equivalent if we can rewrite one into the other, in such a way that  we only use algebra to do so.

Here we start with the expression:

3x + 3(x + y)

If we take 3 as a common factor, then we can write:

3x + 3(x + y) = 3*(x + (x + y)) = 3*(x + x + y)

That is an equivalent expression, now if we simplify this:

3*(x + x + y) = 3*(2x + y)

Distribute that product.

3*(2x + y) = 6x + 3y

These is other equivalent expression.

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To determine the profit earned from selling 250 shares worth $4.50 each with a 7% fee charged by the stock broker, we need to calculate the total revenue earned and the total cost incurred.

Total revenue earned from selling 250 shares at $4.50 per share:

Revenue = 250 x $4.50 = $1,125

Total cost incurred for buying and selling the shares, including the 7% fee charged by the broker:

Cost = 2 x 250 x $4.50 x 0.07 = $157.50

Here, we are multiplying the number of shares (250) by the price per share ($4.50) to get the total value of the shares. Then we multiply this by 2, since we need to account for both the buying and selling transactions, and then multiply by the broker fee rate of 7% (0.07) to get the total cost incurred.

Therefore, the profit earned from the sale of 250 shares is:

Profit = Revenue - Cost

Profit = $1,125 - $157.50

Profit = $967.50

Hence, the profit earned from selling 250 shares worth $4.50 each with a 7% fee charged by the stock broker is $967.50.

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According to the solution we have come to find that, 48% of the teas served were caffeinated.

A percentage is a way of expressing a proportion or a fraction as a number out of 100. The symbol used for percentage is the "%" sign. For example, if you have 10 apples and you want to express how many of them are red, you can say that 20% (or 2 out of 10) of the apples are red.

To find the percentage of caffeinated teas served, we need to divide the number of caffeinated teas by the total number of teas served, and then multiply by 100 to get the answer as a percentage.

Total number of teas served = 36 + 39 = 75

Percentage of caffeinated teas served = (36/75) x 100%

                                                                = 48%

Therefore, 48% of the teas served were caffeinated.

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Fionna and Anuar each had 349 cards, bringing the total to 417. Fionna alone had 145 cards.

A mathematical concept known as the unitary approach entails calculating the value of a single unit in order to calculate the value of a given quantity. Finding the value of one unit and utilising that value to determine the value of a given quantity is an approach for solving problems. For instance, you can use the unitary technique to determine the price of 10 apples if you know that 5 apples cost $10. Now, divide $10 by 5, which equals $2, to determine the price of one apple. The cost of 10 apples is then determined by multiplying the price of one apple ($2) by 10, giving you a final cost of $20.

given

145 total cards with Fionna

349 total cards with Fionna and Aura

Card count with Anuar: 349 - 145

= 204

Rizza's number of cards equals 1/3 of 204.

= 204 / 3

= 68

Total number of cards: 68, 204, and 145

= 417

Fionna and Anuar each had 349 cards, bringing the total to 417. Fionna alone had 145 cards.

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Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

A value or combination of values that satisfy an equation, inequality, system of equations, or system of inequalities are known as solutions in mathematics. Take the equation x2 - 3x + 2 = 0, for instance. This equation has a solution in the form of an x value that makes the equation true. The quadratic formula allows us to determine that this equation has two solutions, x = 1 and x = 2. According to this, a solution for a system of equations is a set of values that simultaneously satisfy every equation in the system. Mathematical problem-solving, which has many applications in areas like engineering, physics, economics, and more, is a crucial component of the subject.

given

We must identify the point(s) at where the two lines intersect in order to obtain the solution(s) to the system of equations depicted by the graph. The graph demonstrates that the lines cross at the location (-3, 3).

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

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Answer:

85 degrees.

Step-by-step explanation:

These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.

Answer:

28 people

Step-by-step explanation:

21 / 3 = 25

7 = 25%

25 x 4 = 100%

so

7 x 4 = 28

28 people are in the class

Answer:

The answer would be 14 miles!

The image of the point B after the rotation by 180 degrees about point C is (0, 0)

Given that

B = (4, 4)

C = (3, 1)

The rotation rule is given as

Rotation by 180 degrees counterclockwise around vertex C

The rule of 180 degrees counterclockwise about the origin is

(x,y) = (-x,-y)

If the center of rotation is (a, b), then we have

(x,y) = (-(x - a) + b, -(y - b) + a)

So, we have

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

Evaluate

B' = (0, 0)

Hence, the image of the point is (0, 0)

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The variable term can be added to both sides to solve an inequality with a positive coefficient when it is solved with a negative coefficient.

In mathematics, inequalities specify the connection between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol (≠)" to indicate that two values are not equivalent. But various inequalities are used to compare the values, whether it is less than or larger than.

A coefficient in mathematics is a multiplicative component in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. When the coefficients are themselves variables, they may also be termed parameters.

Recognize that the variable term can be added to both sides to solve an inequality with a positive coefficient when it is solved with a negative coefficient; in this instance, the relationship between the variable and the inequality symbol has flipped.

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Up to 180 degrees

Your Welcome

Answer: 5 1/2 hours

Step-by-step explanation:

for every 2 nights he reads he will gain an hour of time so the easiest way to solve is to divide 11 by 2 for an answer of 5.5 or 5 1/2 hours.

If the unit rate is 1/2 hours per night,

Carlos will read for 5.5 hours in 11 nights.

We have,

If Carlos reads for 1/2 hour every night,

This is the unit rate.

Now,

In 11 nights he will read for:

(1/2) x 11 = 11/2

= 5.5 hours

Therefore,

Carlos will read for 5.5 hours in 11 nights.

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Answer: 9x^2y

the gcf of -63 , 9 and 90 is 9

And the gcf of the variables is x^2 and y

So, 9x^2y

By answering the question using the information provided, we can conclude that in order to arrive at the general solution, we must take into account the scenario in which [tex]y-1\neq 0 , y \neq 1[/tex], by constructing equations.

Two equations are said to be equivalent when their bases and solutions line up. To create an equivalent equation, the same quantity, symbol, or expression must be added to or removed from both of the equation's two sides.

We can also create an analogous equation by multiplying or dividing both sides of an equation by a nonzero integer.

Solving differntial calculus

[tex](1+x)y'=( x+2) (y-1)[/tex]

We will first employ varying separation. The variables y and x will be placed on the opposite sides of the equation, and both sides will be integrated.

[tex](1+x)y'/(y-1) = (x+2)dx[/tex]

We will integrate both sides using the substitution[tex]u= y-1,\frac{du}{dy} =y'[/tex]

∫[tex](x+2)dx[/tex] =∫[tex](1+x)\frac{du}{u}[/tex]

㏑l[tex]u[/tex]l +[tex]x[/tex]㏑l[tex]u[/tex]l= [tex]\frac{1}{2} x^{2}+2x+c[/tex]

Substituting [tex]u= y-1[/tex]

㏑l[tex]y-1[/tex]l+ [tex]x[/tex]㏑l[tex]y-1[/tex]l= [tex]\frac{1}{2x^{2} } +2x+c[/tex]

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The complete question is: Find the general solution to the differential equation (1+x)y' = (x + 2)(y − 1).

Answer:

Step-by-step explanation:

0.08*X >= 100000,   i.e.   X >= 100000%2F0.08 = 1,250,000 dollars.

Then each year he will draw 100000, but the bank will return  equal or even greater amount than 0.08*1250000 = 100000,

so his balance will only increase from year to year.

It is a rough estimation.

If we want to consider more realistic case, when he withdraws 100000 at the first day of the year and the bank compounds 8% at the end of the year,

then the unknown starting amount X must satisfy inequality

0.08*(X-100000) >= 100000,   which gives

0.08X - 0.08*100000 >= 100000,

0.08X > (1+0.08)*100000

x >= %28%281%2B0.08%29%2A100000%29%2F0.08 = 1350000.

Answer.  Having  $1,350,000 or more initially on the account provides the sough condition.

Answer:

$26421.76

Step-by-step explanation:

We have to calculate final value i.e. balance to earn $50,000 annually from interest.

[tex]= \dfrac{50,000}{0.08} = \$625,000[/tex]

Now, N = n × y  = 12 × 25 = 300

        I  = 8% =  APR = 0.08

       PV = 0  = PMT = 0

      FV = 625,000 = A

[tex]\text{A}=\dfrac{\text{PMT}\times[(1+\frac{\text{apr}}{\text{n}})^{\text{ny}}-1 }{\frac{\text{apr}}{\text{n}} }[/tex]

[tex]\text{PMT}=\dfrac{\text{A}\times(\frac{\text{APR}}{\text{n}}) }{[(1+\frac{\text{APR}}{\text{n}})^{\text{ny}}-1 }[/tex]

[tex]\text{PMT}=\dfrac{625,000\times(\frac{0.08}{12}) }{[(1+\frac{0.08}{12})^{12\times25}-1] }[/tex]

[tex]\text{PMT}=\dfrac{625,000\times(0.006667) }{[(1+\frac{0.08}{12})^{12\times25}-1] }[/tex]  

[tex]\text{PMT}=\dfrac{625,000\times(0.006667) }{[(1+0.006667)^{300}-1] }[/tex]

[tex]\text{PMT}=\dfrac{\frac{33335}{8} }{[1.006667^{300}-1]}[/tex]

[tex]\text{PMT}=\dfrac{\frac{33335}{8} }{6.34090515}[/tex]

Monthly payment (PMT) = $26421.7591469 ≈ $26421.76

$26421.76 is required monthly payment in order to $50,000 interest.

Step-by-step explanation:

The volume of a cone can be calculated using the formula:

V = (1/3)πr^2h

where r is the radius of the base, h is the height of the cone, and π is a constant approximately equal to 3.14.

In this case, the diameter of the base of the cone is 8 cm, which means the radius is half of that, or 4 cm. The height of the cone is given as 10 cm. Substituting these values into the formula, we get:

V = (1/3)π(4 cm)^2(10 cm)

V ≈ 167.55 cubic centimeters

Therefore, the volume of the paper drinking cone is closest to 167.55 cubic centimeters.

Answer: To solve this problem, we can use the formula for simple interest:

I = P * r * t

where I is the interest earned, P is the principal, r is the interest rate as a decimal, and t is the time in years.

We are given that the interest rate is 1.95% = 0.0195, the time is 30 years, and the final amount in the account is $800. Let P be the principal we are trying to find.

First, we can use the formula to find the total interest earned over the 30-year period:

I = P * r * t

I = P * 0.0195 * 30

I = 0.585P

Next, we can use the fact that the final amount in the account is the sum of the principal and the interest:

800 = P + 0.585P

800 = 1.585P

P = 504.71

Therefore, the principal was $504.71 and the interest earned over the 30-year period was:

I = 0.585P

I = 0.585 * 504.71

I = 294.29

So the interest earned was $294.29.

Step-by-step explanation:

As a result, the cylinder's capacity is roughly 11,088 cubic metres.

The diameter of a circular is the distance measured through its middle. The radius of a circle is the distance to the middle to any spot on the edge. Diameter divided by radius equals two, or 2r=d. 2 r = d .

First, we need to find the radius of the cylinder. We know that the diameter is 28 meters, so the radius is half of that, which is 14 meters.

Using the formula for the volume of a cylinder, V = πr²h, we can now substitute the given values:

V = (22/7) x 14² x 4.5

Simplifying this expression:

V = (22/7) x 196 x 4.5

V = 11,088 cubic meters

Therefore, the volume of the cylinder is approximately 11,088 cubic meters.

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The measure of the angle A in the given right angled triangle is found as: A = 64.82°

Applying the sin function in the given right angled triangle.

Sin A = 77/85

Sin A = 0.905

A = Sin⁻¹ (0.905)

A = 64.82°

Thus, the measure of the angle A in the given right angled triangle is found as: A = 64.82°

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