quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (4, -4)(4,−4). What is the vertex of the function defined as g(x)=f(x-2)g(x)=f(x−2)?

Answer:

None

Step-by-step explanation:

Evaluate each answer option, following the order of operations (PEMDAS).

[tex]\begin{aligned}\textsf{A.} \quad (6^2+2)-18\sqrt{81}&=(36+2)-18\sqrt{81}\\&=(36+2)-18(9)\\&=38-18(9)\\&=38-162\\&=-124\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{B.} \quad 6^2(2-8)\sqrt{81}&=36(2-8)\sqrt{81}\\&=36(2-8)(9)\\&=36(-6)(9)\\&=(-216)(9)\\&=-1944\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{C.} \quad (6^2+2-8)\sqrt{81}&=(36+2-8)\sqrt{81}\\&=(36+2-8)(9)\\&=(38-8)(9)\\&=(30)(9)\\&=270\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{D.} \quad 6^2 +2(8\sqrt{81})&=36+2(8\sqrt{81})\\&=36+2(8\cdot 9)\\&=36+2(72)\\&=36+144\\&=180\end{aligned}[/tex]

Therefore, none of the answers has a value of -18.

A line segment has two specific endpoints in a line. The length of the line segment is set, that is the distance between two fixed points.

The length here can be measured by metric units such as centimeters (cm), and millimeters (mm), or by conventional units like feet or inches.

A closed line segment contains both endpoints, but an open line segment is exclusive of the two endpoints. A line segment that has just one endpoint is called a half-open line segment.

A line segment has two endpoints. Now if we know the coordinates of the endpoints, then we calculate the length of the line segment by distance formula.

[tex]D = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} -y_{1})^{2} }[/tex]

Let a line segment has coordinates (2, –3) and (–1, –2). What is the length of a line segment?

Therefore, by distance formula,

[tex]D = \sqrt{(2 - (-1))^{2} + (-3 -(-2)^{2} }[/tex]

[tex]D = \sqrt{(2 + 1))^{2} + (-3 +2)^{2} }[/tex]

[tex]D = \sqrt{(3)^{2} + (-1)^{2} }[/tex]

[tex]D = \sqrt{10}[/tex] = 3.16

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The solution to the system of equations is x = 0, y = 0.

What is substitution algebraic expression?

Substitution means replacing the variables in an algebraic expression with their numerical values. We can then work out the total value of the expression.

To use algebraic substitution to solve for x and y, we can substitute one equation into the other and solve for one of the variables.

Given that y = -8x, we can substitute this into the second equation, 2x + 4y = 0

So, 2x + 4(-8x) = 0

Simplifying this we get,

2x - 32x = 0

30x = 0

Dividing both sides by 30

x = 0

Now we have x = 0, we can substitute this value back into the equation y = -8x

So y = -8(0)

y = 0

Hence, the solution to the system of equations is x = 0, y = 0.

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Answer: Simplified

Step-by-step explanation: The question is already as simplified as it can get.

Answer:

x-y=4, 3x-5y=-4

Step-by-step explanation:

step (1)

write the equation in the form ax+by=c

step (2)

put the equations below each other

x-y=4....(1)

3x-5y=-4....(2)

Multiply (1) by (-5) then add (1) and (2)

-5x+5y=-20

3x-5y=-4

-2x=-24 then x=12 from (1) y=8

S.S.={(12,8)}

Answer:

10x^2 - 11x -6

Step-by-step explanation:

1/ First, distribute the brackets:

( multiply 5x to the other bracket, then 2 multiply it also to the other bracket)

After the distribution you'll get this:

10x^2 - 15x + 4x - 6

2/ finally, to simplify you'll have to combine the like terms:

( as you can see the only like terms we have are -15x and +4x)

combine them and you'll get:

10x^2 - 11x -6  ( this is the final answer)

Answer:

Step-by-step explanation:

p=12 q=4 r=10

The formula for [tex]R_{N}[/tex] for the function f(x) is [tex]& R_N=\sum_{j=1}^N f\left(x_j\right) \Delta x[/tex] and the value of [tex]R_{N}[/tex] =  2688.

As per the given data, the given function f(x) is:

f(x) = [tex](8 x)^2[/tex]  on [-1, 5]

Here we have to determine the formula for [tex]R_{N}[/tex]

Let us consider the interval [a, b]

Then the value of a is -1 and the value of b is 5.

[tex]& \Delta x=\frac{b-a}{N}=\frac{5+1}{N}=\frac{6}{N} \\[/tex]

[tex]& x_j=a+\Delta x_j=-1+\frac{6 i}{N} \\[/tex]

Area Using Riemann Sum:

The Riemann sum of a function f(x) over a given interval [a, b] is given by:

[tex]$$S_n=\sum_{k=1}^n f\left(c_k\right) \Delta x$$[/tex]

When the points are chosen randomly, then the sum is called a Riemann sum and will give an approximation for the area of R that is in between the lower and upper sums.

Split the area into vertical slices then use the Riemann sum formula.

[tex]& R_N=\sum_{j=1}^N f\left(x_j\right) \Delta x[/tex]

[tex]=\sum_{j=1}^N f\left(-1+\frac{6 j}{N}\right) \frac{6}{N} \\[/tex]

[tex]& =\sum_{j=1}^N 64\left(-1+\frac{6 j}{N}\right)^2 \frac{6}{N} \\[/tex]

[tex]& R_N=\sum_{j=1}^N 64\left(1+\frac{6 j}{N}\right)^2 \frac{6}{N} \\[/tex]

[tex]& =\sum_{j=1}^N 64\left(1+\frac{36 j^2}{N^2}-\frac{12 J}{N}\right) \frac{6}{N} \\[/tex]

[tex]& =384 \sum_{j=1}^N\left(1+\frac{36 j^2}{N^2}-\frac{12 j}{N}\right) \frac{1}{N} \\[/tex]

[tex]& =384\left(N+\frac{36}{N^2}\left(\frac{N(N+1)(2 N+1)}{6}\right)-\frac{12}{N}\left(\frac{N(N+1)}{2}\right)\right) \frac{1}{N} \\[/tex]

[tex]& =384\left(1+6\left(\frac{N(N+1)(2 N+1)}{N^3}\right)-6\left(\frac{N(N+1)}{N^2}\right)\right) \\[/tex]

[tex]& \lim _{V \rightarrow \infty} R_N=384 \lim _{N \rightarrow \infty}\left(-1+6\left(\frac{N(N+1)(2 N+1)}{N^3}\right)-6\left(\frac{N(N+1)}{N^2}\right)\right) \\[/tex]

= 384 (1 + 6(2) - 6)

= 384 (7)

= 2688

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The graph of the resulting line of y = 1/2 x + 4 will be a line passing through P(0, 4), Q (-8, 0) and R (2, 5).

A graph is a pictorial representation of a figure formed by connecting set of points.

We have to find the points through which the line y = 1/2 x + 4 passes through to draw the graph of the line.

Let x = 0 ⇒ y = 4

A point P is found as P (0, 4), which is the y intercept where the line touches with the Y axis.

Let y = 0, then 1/2 x = -4 or x = -8

A point Q is found as Q (-8, 0) which is the x intercept where the line touches with the X axis.

Let x = 2, then y = 5

A point R is found as R (2, 5).

So graph of y = 1/2 x + 4 will be a line passing through P(0, 4), Q (-8, 0) and R (2, 5).

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Funsters inc. , the largest toy company in canada, sells its most popular doll for $35. It has just learned that its leading competitor toysorama is mass producing an excellent copy and plans to flood the market with their $10 doll in 6 weeks. Funsters should increase the supply of its doll now before the other doll hits the market.

1. Addressing Customer Needs

Often business competition motivates brands and businesses to meet customer needs, vying to be more effective than their competitors. This encourages brands to develop an understanding of audience needs.

This competition resulted in a focus on meeting customer needs including higher quality products, increased service value, and increased customer satisfaction.

2. Analyze Strengths and Weaknesses

Business competition can drive an evaluation of strengths and weaknesses, as well as optimizing sales strategies based on these findings. This enables a business to maximize resources, make informed decisions about marketing and sales strategies, and tailor offerings according to their strengths.

3. Increasing Demand

Business competition is an effective way to increase demand for a product or service. As more companies invest in their marketing and advertising efforts, the consumer demand for their products and services may increase as brand awareness increases.

3. Encouraging Innovation

In order to gain an advantage in the market, business competition can drive to innovate strategies and improve their products or services in creative ways. This is an important contribution to continuously improving the quality of goods and services, advancing product and service technology, and adapting to changing consumer needs.

4. Show Excellence

A business often tracks and analyzes competitors' performance to gain insight into their business strategy. By studying competitors' tactics, a business will be able to demonstrate their superiority in the market. So that many businesses can develop strategies that will result in success.

5. Promoting Business

Continuous business development can be an important factor in long-term success. Business competition is often challenging to continue to increase brand awareness, promote, analyze success, and develop new methods to achieve even bigger goals.

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Using ratio, the length of the tree is 1.9m

Ratio is a comparison of two or more related quantities, expressed as a fraction or a proportion. Ratios are used to compare values and to look for relationships between them. For example, if you have five friends and two of them are girls, the ratio of girls to boys is 2:3 (2 out of 5).

We can set up two ratio as a proportion to find the length of the tree.

1.2 / x = 4.2 / 6.5

Cross multiply both sides and solve for x

x = (1.2 * 6.5) / 4.2

x = 1.85m ≅ 1.9m

The height of the tree is 1.9m

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Answer:

The shadow cast by the building is of the length 11.8 m.

Step-by-step explanation:

We consider the height of the building as the height of the triangle and the length of the shadow as the base of the triangle, then the distance from the top of the building to the tip of the shadow would be the hypotenuse of the triangle.

Using the Pythagorean theorem:

c^2 = a^2 + b^2

Where c is the hypotenuse, which is 36m, a is the height of the building, which is 34m and b is the base of the triangle, which is the length of the shadow.

So by plugging the given numbers in:

b^2 = c^2 - a^2

b^2 = 36^2 - 34^2

b = √(36^2 - 34^2)

b ≈ 11.8m (if rounded to the nearest tenth)

So the length of the shadow in this scenario is approximately 11.8 m.

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Answer:

Step-by-step explanation:

The payments each month do not cover all interest and no principal. The correct answer would be an option (B).

A credit card trap occurs when the minimum payments required each month do not cover all the interest charges and do not reduce the principal balance. This means that even if the cardholder makes the minimum payments on time, they will still be paying only the interest charges and not reducing the amount of debt. This can result in a cycle of high-interest debt that is difficult to escape from.

Option A is incorrect as it's describing a common way payments work on credit cards.

Option C is not a trap, as it's describing a credit card issuer with a low-interest rate.

Option D is also incorrect, as it's describing a common way payments work on credit cards.

Hence, the correct answer would be an option (B).

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The simplified form of the radical is 9i

A complex number is the sum of a real number and an imaginary number. A complex number is of the form a + ib and is usually represented by z. Here both a and b are real numbers. The value 'a' is called the real part which is denoted by Re(z), and 'b' is called the imaginary part I'm (z).  Also, it is called an imaginary number.

Given here, √-81 and we know √-1 = i

√-81 = √9² × √-1

        = 9 ×i

        = 9i

Hence 9i is the correct answer.

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Answer: 9i is the correct answer.

Step-by-step explanation:

Solving the given work.

2x< x+22 is the inequality equation which satisfy that x=20 the other inequality equation does not satisfy the condition.

Given that,

We have to find which inequality is true for x=20

The inequality equations are

a. x-5 < 2x-35

b. 2x < x+22

c. x/4 > x-12

d. x+30 >3x

We know that,

We have to substitute x=20 in the inequality equation to check which equation is true.

a. 20-5 < 2(20)-35

15 < 40-35

15< 5

NO, the inequality is not true

b. 2(20) < 20+22

40 < 42

Yes, the inequality is true

c. 20/4 > 20-12

5>8

NO, the inequality is not true

d. 20+30 > 3(20)

50 > 60

NO, the inequality is not true

Therefore, 2x< x+22 is the inequality equation which satisfy that x=20 the other inequality equation does not satisfy the condition.

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Answer:

Step-by-step explanation:

positive

The distance between the two cities located at latitude 19 degrees N, and the other has a latitude 26 degrees S is 5011 km

The distance between the two cities is calculated using the formula

= x/360 * 2 * pi * r

where

r = radius

x = the angle subtended by the distance

From the question we have that

x = 19 degrees N + 26 degrees S

x = 45 degrees

radius of the earth = 6380 km

distance between the points = x/360 * 2 * pi * r

distance between the points = 45/360 * 2 * pi * 6380

distance between the points = 0.125 * 12760 * pi

distance between the points = 5010.84 km

distance between the points = 5011 km

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The measure of ∠5 is 35degree

Linear pair of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.

Given:

In Quadrilateral ABCD, AB||CD

<M2=35

If a transversal line intersects two parallel lines then the alternate interior angles are congruent.

In the given figure In Quadrilateral ABCD, AB||CD<M2=35  .

So,

<5≅<2 (Alternate interior angles)

M<5=M<2

M<5=35degree

Therefore, the angle measure of M<5 will be 35degree

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Answer:

45%

Step-by-step explanation:

5% owns both so you remove that 5% from both the 40% and 10% because it's already in the "both" category. For example if Sara has both, then it also means that Sara is among the 5% that has both but also in the 40% that owns a bike and the 10% that owns a skateboard. You need to remove Sara from those two categories (skateboard and bike) because she's already in the "both" category.

So when you remove it, it's not 40 and 10 percent but 35 and 5 percent.

The answer is 35+5+5 = 45%

The statements that complete the blanks are underlined as follows

From the question, we have the following parameters that can be used in our computation:

The graph

The given graph is a quadratic graph

All quadratic graphs are functions

So, the relation is a function

This statement is false,

This is so because one y value points to two different x values, as evident on the graph

As a general rule, the inverse of a quadratic function is not a function

This means that the inverse of the given relation is not a function

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1/8 is the slope of the line that represents the relationship and 1/4  the slope and the y-intercept represent

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Given, Anton realizes there is a linear relationship between the weight of the pet and the amount of food the pet should be fed.

The slope the slope of the line that represents the relationship is 1/8 cups.

the y-intercept of the line that represents the relationship is 1/4.

The slope is the value that will be multiplied by the weight of the cat  so as to know the amount of food that will be given to the cat.

The y intercept represent the fixed food that should be given to the cat after it has been using.

Hence, 1/8 is the slope of the line that represents the relationship and 1/4  the slope and the y-intercept represent

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The amount to be paid by Chet if The flight he selected was $229.99, but he got 20% off because he booked it online through a new travel website, is $184.

A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance.

Given:

The flight he selected was $229.99 but he got 20% off because he booked it online through a new travel website,

Calculate the amount of discount as shown below,

Discount = 20% of 229.99

Discount = 20 / 100 × 229.99

Discount = 0.2 × 229.99

Discount = 45.998

Thus, the amount to be paid = 229.99 - discount

the amount to be paid = 229.99 - 45.99

the amount to be paid = 184

Thus, the amount to be paid is $184.

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Answer:

Foci:  (±5, 0)

Vertex: ( ±4 , 0)

Eccentricity: e = 5/4

Step-by-step explanation:

   Write the equation of hyperbola in the form,

              [tex]\boxed{\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1}[/tex]

9x² - 16y² = 144

Divide the entire equation by 144,

          [tex]\sf \dfrac{9x^2}{144}-\dfrac{16y^2}{144}=\dfrac{144}{144}\\\\\\ \dfrac{x^2}{16}-\dfrac{y^2}{9}=1\\\\\\\dfrac{x^2}{4^2}-\dfrac{y^2}{3^2}=1[/tex]

a = 4 and b =3

  Eccentricity: e

           [tex]\boxed{e=\sqrt{1+\dfrac{b^2}{a^2}}}[/tex]

                [tex]\sf = \sqrt{1+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{16}{16}+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{25}{16}}=\sqrt{\dfrac{5*5}{4*4}}\\\\\\=\dfrac{5}{4}[/tex]

Foci:

         (ae, 0)  & (-ae , 0)

          [tex]\sf \left(4*\dfrac{5}{4},0 \right) \ ; \ \left( -4*\dfrac{5}{4},0 \right)\\\\\\(5, 0) \ ; \ (-5,0)[/tex]

Vertex of hyperbola:

       The vertex of the hyperbola is a point where the hyperbola cuts the axis.  (-a , 0)  ; (a , 0)

 Vertex : (-4 , 0) ; (4 , 0)

The solution for this question is as follows:

Vertices ≈ (±4 , 0)

Foci ≈ (±5 , 0)

Eccentricity: e = 5/4

Asymptotes: y=  ±(3/4)x

Hyperbola:

The location of all the points on a plane where the distance between them and two fixed points in the plane is always equal to zero is called a hyperbola.

Step by step solution:

Given: [tex]9x^{2} -16y^{2} =144[/tex]      

The given equation of hyperbola can be written as:

⇒[tex]\frac{x^{2} }{16} -\frac{y^{2} }{9} =1[/tex]

On comparing with standard equation of hyperbola; [tex]\frac{x^{2} }{a} -\frac{y^{2} }{b} =1[/tex]

We get; a=4 and b=3

The eccentricity of hyperbola is given by:

      9=16(e^2 - 1)

So; e^2 = (9/16) + 1

       e^2 = 25/16

       e = 5/4

The vertices of hyperbola are given by (±a , 0) ≈ (±4 , 0)

The foci of hyperbola are given by (±ae , 0) ≈ (±5 , 0)

The asymptotes of hyperbola are given by y= ± (b/a)x  

                                                                        y=  ±(3/4)x

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The formula for Area of Hexagon is written as : [tex]\frac{3\sqrt{3} a^{2} }{2}[/tex]

The formula for Perimeter of Hexagon is written as : [tex]6a[/tex] .

A Regular Hexagon is defined as a two dimensional shape which has 6 sides, 6 angles and 9 diagonals, and sum of its interior angles is 720°.

When one side length of the regular hexagon is given as "a" units ,

A regular hexagon comprises of six equilateral triangles, formula for finding area of a hexagon is derived from formula of area of equilateral triangle .

So,  the Area can be calculated by the formula : [tex]\frac{3\sqrt{3} a^{2} }{2}[/tex]  square units ;

and Perimeter of hexagon be calculated by the formula : [tex]6a[/tex] units .

The given question is incomplete , the complete question is

What is the formula for area and perimeter of a hexagon ?

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the volume of rectangular shape is 8 cm³ and density is 4 gm/cm³

What is cube?

The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6-sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.

Given sides of the rectangular cube are 1 cm, 2c.m, and 4c.m

The volume will be the product of all three sides = 1*2*4 = 8 cube cm

The density will be mass/volume.

= 32gm/8 = 4 gm/cm³

Hence volume of the rectangular shape is 8 cm³ and density is 4 gm/cm³

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The rate of change of the amount of gasoline in a storage tank at t=3 hours is -0.75 thousand gallons per hour, and the amount of gasoline in the storage tank is increasing at an increasing rate between t=5 and t=10.

(a) To estimate the rate of change of the amount of gasoline in the storage tank at time t=3 hours, we can use the formula for the average rate of change over an interval: (G(b) - G(a)) / (b - a).

We can choose two points on the table that are closest to t=3 hours, such as t=2 and t=4. Using these points, we have:

G(2) = 22

G(4) = 20.5

Substituting these values into the formula, we get:

(G(4) - G(2)) / (4 - 2) = (20.5 - 22) / (4 - 2) = -1.5 / 2 = -0.75

The units of measure for this rate of change would be thousands of gallons per hour.

(b) Since G′′(t)>0 for 5≤t<10, this means that the second derivative of G(t) is positive for all values of t within this interval. The second derivative represents the rate of change of the rate of change, or the acceleration. A positive second derivative indicates that the rate of change is increasing, or that the function is accelerating. This means that the amount of gasoline in the storage tank is increasing at an increasing rate between t=5 and t=10.

We can also conclude that G′(t)>0 for 5≤t<10 since the second derivative represents the rate of change of the first derivative, which is positive. This means that the first derivative, or the rate of change of the function, is also positive for this interval. This confirms that the amount of gasoline in the storage tank is increasing between t=5 and t=10.

Complete Question:

'A gasoline storage tank is filled by a pipeline from a refinery. At the same time, gasoline flows from the tank into trucks that will make deliveries to gasoline stations. The amount of gasoline in the storage tank at time t is given by the twice-differentiable function G, where t is measured in hours and 0≤t≤10. Values of G(t), in thousands of gallons, at selected times t are given in the table above. It is known that G′′(t)>0 for 5≤t<10.

(a) Use the data in the table to estimate the rate of change of the amount of gasoline in the storage tank at time t=3 hours. Show the computations that lead to your answer. Indicate units of measure.

(b) For 0 t (hours) 0 5 8 10 G (0 (thousands of gallons 22 18.5 19.5 22 24'

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