For the function below, find the vertex, axis of symmetry, maximum or minimum value, and the graph of the function.

f(x)=(x^2/2) + 2x +1 ...?

Answer:

Scale factor is 2

Step-by-step explanation:

A rectangle has an area of 16ft²

That is

            Length₁ x Breadth₁ =  16 ft²

Every dimension is multiplied by a scale factor, let the scale factor be s.

New dimensions are

                  Length₂ = s x Length₁

                  Breadth₂ = s x Breadth₁

New area is given by

                 Area = Length₂ x Breadth₂ = s x Length₁ x s x Breadth₁

                 Area = s² x Length₁ x Breadth₁

                 64 = s² x 16

                  s² = 4

                  s = 2

So scale factor is 2

In fraction,

175% = 35/20

In mixed fraction,

175%  = [tex]1\frac{15}{20}[/tex]

In simplest form,

175%  = 1.75

The given percentage is,

175%

Now to write it into fraction,

Divide it by 100 we get

175% = 175/100

         = 35/20

Thus,

175% = 35/20

Now divide 35 by 20 to write it into mixed fraction

20  ) 35 ( 1

     - 20

     ___

        15

Hence in simple fraction

175%  = [tex]1\frac{15}{20}[/tex]

Now again proceed the division,

20  ) 35 ( 1.75

     - 20

     ___

        15  0

      - 14 0

     _____

           10 0

         - 10 0

           ____

               x

Hence in simplest form,

175%  = 1.75

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Answer:

The student's conclusion is incorrect because the solution to the system of equations 3x + 4y = 32 and 5x + 5y = 50 is (8, 2).

Step-by-step explanation:

To see if the answer to an equation is right, you just have to put the value of X and Y into the equation system, since we don´t have the equation system that the student used, we will make our own, so we will start by stating that Notebooks are represented by X and index cards are represented by Y.

Your equation would look like this:

3x+ 4y=34

The student said that the price of the notebook is $5 and the index card would be $1, now we put those values into the equation.

3(5)+4(1)=32

15+4=32

19=32

Since 19 is not equal to 32, the equation is wrong, therefore the student is wrong.

Now to solve it you get your other equation, since if he had bought 5 and 5 he would have needed 18 extra dollars that means that

5x+5y= 32 +18

5x+5y=50

With the two equations you just use elimination process to create a single equation:

(5x+5y=50)-3=  -15x-15y=-150

(3x+4y=32)5 =   15x+20y= 160

You eliminate the x from the equation and are left with:

-15y+20y= -150+160

5y=10

y=[tex]\frac{10}{2}[/tex]

y=2

Now that you have the value of Y you just put it into the equation to know the value of x:

5x + 5(2) = 50

5x+10=50

You clear the x and the result would look like this:

x= [tex]\frac{50-10}{8}[/tex]

x=8

Answer:

360 texts

Step-by-step explanation:

Given,

The points given for 3 texts = 15,

So, the points given for 1 text = [tex]\frac{15}{3}[/tex] = 5,

If x text are sent,

Then the number of points earned = x × points for 1 text

= 5x

According to the question,

5x = 1800

[tex]\impilies x = \frac{1800}{5} = 360[/tex]

Hence, 360 texts needs to send to get 1800 points.

Answer:

Options A & B

Step-by-step explanation:

Given is a triangle XYZ in the I quadrant.  There are four more triangles A, B,C and D given.

We have to find that which one is the translation of XYZ

We know that by translation we must get a congruent triangle as XYZ.

By simply seeing we can say that C and D are not congruent with XYZ.

So these two are eliminated

Remaining are A and B.

Both A and B are right

This is because XYZ is transformed into B by shifting 7 units horizontal to the left.

A is the reflection of B about x=-5.5

Thus both A and B are right

The mode of this set is 19.

1. **List the Numbers**: Start by listing out all the numbers in the set.

  [tex]\[ 19, 1, 17, 19, 3, 20, 5, 2 \][/tex]

2. **Count Frequency**: Count how many times each number appears in the list.

  - 19 appears twice.

  - 1 appears once.

  - 17 appears once.

  - 3 appears once.

  - 20 appears once.

  - 5 appears once.

  - 2 appears once.

3. **Identify the Most Frequent Number**: The mode is the number that appears most frequently. In this case, 19 appears twice, which is more than any other number in the set. Therefore, the mode of this set is 19.

P = the principal

t = 25 years the time in years

r = 0.0525 or 5.25% annual rate

m = 1 compounding periods per year

i = 0.0525 or 5.25% interest rate per period

n = t*m = 25 total number of compounding periods

A = $75,000 future value

A = P(1 + i)^n

P(1 + i)^n = A

P(1 + 0.0525)^25 = 75000

by solving we find:

P = $20,869.34

The correct statements for this question would be:

a) The point (1, 1) is on the graph of the equation."

d) The graph of the equation is the set of all points that are solutions to the equation.

Option (a) and (d) are true.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The linear equation;

y = 4x - 3

Now, By option a;

To check the point (1, 1) is on the graph of the equation.

We can substitute x = 1 and y = 1 in the equation of line as;

y = 4x - 3

1 = 4 × 1 - 3

1 = 4 - 3

1 = 1

Thus, The point (1,1) is on the graph of the equation.

For option b;

Since, The point (0, 3) is not satisfy the equation y = 4x - 3.

Hence, Option b is not true.

For option c;

Since, The y - intercept of the line 4x - y = -3 and line y = 4x - 3 is not same.

Hence, Both have different graph.

Clearly, By the graph of y = 4x - 3 is is the set of all points that are solutions to the equation.

So, Option d is true.

Thus, The correct statements for this question would be:

a) The point (1, 1) is on the graph of the equation."

d) The graph of the equation is the set of all points that are solutions to the equation.

Option (a) and (d) are true.

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By applying the PEMDAS rule, the coefficient of x is equal to 7.

In Mathematics and Euclidean Geometry, a coefficient simply refers to a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.

Based on the information provided, we have the following mathematical expression:

[tex]10x^2+8x-6x^3+4x^2+12x^3-x+20\\\\12x^3-6x^3+10x^2+4x^2+8x-x+20\\\\6x^3+14x^2+7x+20[/tex]

In this context, we can reasonably and logically deduce that the coefficient of x is 7.

Complete Question:

When this polynomial is simplified, what is the coefficient of x?

[tex]10x^2+8x-6x^3+4x^2+12x^3-x+20[/tex]

The question requires solving various problems involving projectile motion, a physics topic, using kinematic equations and algebraic techniques to determine height, flight time, and impact speeds.

The question involves calculating various aspects of projectile motion, which is a topic in physics. In these problems, equations of motion are used to determine the maximum height, time of flight, and speed at impact of objects thrown or released from certain heights.

Example Calculations

Each of these problems requires an understanding of the kinematic equations for vertical projectile motion and the ability to apply algebraic and calculus techniques.

Answer:

$623

Step-by-step explanation:

Let us suppose that the

Earning = y

Fixed payment = c

Commission paid = m per unit

Case 1.

When 500 units are sold, Earning y = $385

Earning = Fixed Payment + Commission paid per unit * Number of units

385=c+m*500

385=c+500m   ________(a)

Case 2.

When 1000 units are sold  earning y = $470

Earning = c+m*1000

470=c+1000m _________(b)

Subtracting (a) from (b) we get

85=500m

[tex]m=\frac{85}{500}\\=0.17[/tex]

Putting this value of m in (a)

[tex]385=c+\frac{85}{500} * 500[/tex]

385=c+85

c=300

Hence the fixed payment is $300 and the commission given is $0.17 per unit

Case 3 :

Number of Units sold = 1900

Earning = 300+0.17*1900

Earning = 300+323

Earning = 623

Hence The earning will be $623

Answer:

The answer is the option B

y varies inversely as x.

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]yx=k[/tex] or [tex]y=k/x[/tex]

In this problem we have

[tex]3xy=5[/tex] -----> rewrite

[tex]xy=5/3[/tex]

The value of k is equal to [tex]k=\frac{5}{3}[/tex]

therefore

y varies inversely as x.

To determine the number of copies made per minute, the total time of 4 minutes and 45 seconds is first converted to 4.75 minutes. Dividing the total copies (114) by the total time in minutes (4.75) gives us 24 copies per minute.

Calculating Copies Per Minute

To find out how many copies the machine makes per minute, we need to convert the total time into minutes. There are 4 minutes and 45 seconds. Since there are 60 seconds in a minute, we can convert 45 seconds into minutes by dividing by 60, which gives us 0.75 minutes. Therefore, the total time in minutes is 4 + 0.75 = 4.75 minutes.

Now, we use the given information that the copy machine makes 114 copies in 4.75 minutes to calculate the number of copies it makes per minute:

Copies per minute = Total copies / Total time in minutes

Copies per minute = 114 copies / 4.75 minutes

Copies per minute = 24 copies per minute (rounded to the nearest whole number)

Answer:

(D)

Step-by-step explanation:

Given: Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angle ADE is 28°.

To prove: The measure of angle ECB is 62°.

Proof:

Step1. Segment DE joins the mid points of segments AB and AC (GIVEN).

Step 2. Segment DE is parallel to segment BC (MIDSEGMENT THEOREM)

Step3. Angle ECB is congruent to angle AED (CORRESPONDING ANGLES ARE CONGRUENT) that is ∠AED≅∠ACB.

Step 4. Measure of angle DAE is 90° (Definition of right angle)

Step 5.  Measure of angle ADE is 28° (Given)

Step 6. Thus, by triangle sum theorem, we have

∠DAE+∠ADE+∠AED=180°

∠AED=180-118

∠AED=62°

Step 7. Thus, by substitution, we have

∠AED≅∠ACB that is ∠ECB=62°

Hence proved.

Answer:

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Step-by-step explanation:

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