Write a quadratic function f whose zeros are 2 and 9 .

The functions f(x)=x² and g(s)=s² are essentially the same function with different variable notations. The f(x)=2x graph is linear, and the red graph g(x) with the same shape would also be linear, involving a transformation that retains the proportional relationship between x and y.

Based on the provided information, the equation of f(x) is given as f(x) = x². If the blue graph represents this function, and we are looking for the red graph equation g(x), which has the same shape, we need to understand the transformation involved.

Regarding the equations provided in the examples, functions f and g are both defined as taking an input, squaring it, and outputting the result. Although they use different variable names (x for f and s for g), they are effectively the same function. When you have a transformation such as f(x-2), the graph of the function shifts to the right without changing its shape. Similarly, if the red graph were g(x) = 2x, the transformation applied would be to double the output, stretching the graph vertically relative to f(x).

Since the blue graph equation is given as f(x) = 2x and the red graph has the same shape, it means the red graph, g(x), also has a linear relation with a proportional transformation applied. Common linear transformations include multiplying by a scalar to scale the graph or adding/subtracting a number to shift the graph along the x-axis or y-axis.

Final answer:

To evaluate the function for x = m/4, substitute m/4 for x in the function[tex]f(x) = 8x^2 - 4x[/tex]and simplify to get the result [tex]m^2/2 - m.[/tex]

Explanation:

To evaluate the function [tex]f(x) = 8x^2 - 4x[/tex] for x = m/4, we substitute m/4 for x in the function and simplify.

Substitute x with m/4:

[tex]f(m/4) = 8(m/4)^2 - 4(m/4)[/tex]

Simplify the equation:

[tex]f(m/4) = 8(m^2/16) - m[/tex]

[tex]f(m/4) = (8/16)m^2 - m[/tex]

[tex]f(m/4) = m^2/2 - m[/tex]

Therefore, the correct answer is D.  [tex]m^2/2 - m.[/tex]

To find the distance Laura lives from the mountains, calculate her average speed when driving to the mountains and use the time taken during the trip. With the given speeds and travel times, the distance can be determined using a simple equation.

To find the distance Laura lives from the mountains:

Answer:

Part 1) [tex]-3x^4+3x^3+8x^2-2x-5[/tex]

Part 2) The graph in the attached  figure

Part 3) [tex]16y^8-24y^7+40y^5[/tex]

Part 4) [tex]x1=\frac{-1+\sqrt{139}i} {14}[/tex]  and [tex]x2=\frac{-1-\sqrt{139}i} {14}[/tex]

Part 5) Harold reads more than [tex]90[/tex] pages, but less than [tex]180[/tex] page

Part 6)  [tex](30,68)[/tex], [tex](40,60)[/tex]

Part 7) [tex]\$576[/tex]

Part 8) [tex]23 + 2i[/tex]

Step-by-step explanation:

The complete answers in the attached figure because is too long  

Part 1) Subtract (enter answer is standard form)

we have

[tex](-2x^4-2x^3+8x^2+2)-(x^4-5x^3+2x+7)[/tex]

Eliminate parenthesis

[tex]-2x^4-2x^3+8x^2+2-x^4+5x^3-2x-7[/tex]

Combine like terms

[tex](-2x^4-x^4)+(-2x^3+5x^3)+8x^2-2x+(2-7)[/tex]

[tex]-3x^4+3x^3+8x^2-2x-5[/tex] ------> standard form

Part 2) Which graph represents the inequality?

we have

[tex]2x-3y\leq 6[/tex]

Rewrite the inequality ------> [tex]3y\geq2x-6[/tex]

the solution is the shaded area above the solid line

the equation of the line is equal to [tex]3y=2x-6[/tex]

the slope of the line is positive

the y-intercept of the line is the point [tex](0,-2)[/tex] ---> value of y when the value of x is equal to zero

the x-intercept of the line is the point [tex](3,0)[/tex] ---> value of x when the value of y is equal to zero

The solution in the attached figure

Part 3) Multiply

we have

[tex]8y^4(2y^4-3y^3+5y)\\=( 8y^4*2y^4)-(8y^4*3y^3)+(8y^4*5y)\\=16y^8-24y^7+40y^5[/tex]

Part 4) Solve for x

we have

[tex]0=7x^2+x+5[/tex]

we know that

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

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

in this problem we have

[tex]7x^2+x+5=0[/tex]

so

[tex]a=7\\b=1\\c=5[/tex]

substitute in the formula

[tex]x=\frac{-1(+/-)\sqrt{1^{2}-4(7)(5)}} {2(7)}[/tex]  

[tex]x=\frac{-1(+/-)\sqrt{-139}} {14}[/tex]

remember that

[tex]i=\sqrt{-1}[/tex]

so

[tex]x=\frac{-1(+/-)\sqrt{139}i} {14}[/tex]

[tex]x1=\frac{-1+\sqrt{139}i} {14}[/tex]

[tex]x2=\frac{-1-\sqrt{139}i} {14}[/tex]

Part 5) Harold and Helen both spend [tex]3[/tex] hours reading a novel. Helen reads [tex]30[/tex] more pages than Harold. Helen reads at least [tex]40[/tex] pages in [tex]1[/tex] hour, but no more than [tex]70[/tex]pages in  [tex]1[/tex] hour.  

Which statement correctly describes the range of pages Harold reads?

Let

x------> the number of pages that Harold read

y------> the number of pages that Helen read

we know that

[tex]y=30+x[/tex] -----> equation A

[tex]y\geq 40\ pages[/tex] ------> in one hour

so

in three hours -------> [tex]y\geq 120\ pages[/tex] ------> inequality B

[tex]y\leq 70\ pages[/tex] ------> in one hour

so

in three hours ------->[tex]y\leq 210\ pages[/tex] ------> inequality C

Substitute equation A in the inequality B

[tex]x+30\geq 120\ pages[/tex] ------>  [tex]x\geq 90\ pages[/tex]

Substitute equation A in the inequality C

[tex]x+30\leq 210\ pages[/tex] ------> [tex]x\leq 180\ pages[/tex]

therefore  

Harold reads more than [tex]90[/tex] pages, but less than [tex]180[/tex] page

Part 6) Let

x------>  the number of Standard Specials sold last Monday  

y------>  the number of Deluxe specials sold last Monday

we know that

[tex]2x+4y\geq 200[/tex] -----> inequality A

[tex]0.50x+1.25y\leq100[/tex] -----> inequality B

[tex]x\geq30[/tex] -----> inequality C

Remember that

If a ordered pair representing a combination  of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation

then

the ordered pair must satisfy all restrictions

Verify

A) [tex](30,68)[/tex]  

Substitute the value of x and y in each inequality

Inequality A

[tex]2(30)+4(68)\geq 200[/tex]

[tex]332\geq 200[/tex] ------> is true

Inequality B

[tex]0.50(30)+1.25(68)\leq100[/tex]

[tex]100\leq100[/tex] -----> is true

Inequality C

[tex]30\geq30[/tex] -----> is true

The ordered pair [tex](30,68)[/tex]  represent a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation

B) [tex](80,40.5)[/tex]  

The value of [tex]y=40.5[/tex] not make sense in the context of the situation, because is not a whole number

C) [tex](60,70)[/tex]  

Substitute the value of x and y in each inequality

Inequality A

[tex]2(60)+4(70)\geq 200[/tex]

[tex]400  \geq 200[/tex] ------> is true

Inequality B

[tex]0.50(60)+1.25(70)\leq100[/tex]

[tex]117.5\leq100[/tex] -----> is not true

therefore

the ordered pair [tex](60,70)[/tex] is not a solution

D) [tex](40,60)[/tex]  

Substitute the value of x and y in each inequality

Inequality A

[tex]2(40)+4(60)\geq 200[/tex]

[tex]320\geq 200[/tex] ------> is true

Inequality B

[tex]0.50(40)+1.25(60)\leq100[/tex]

[tex]95\leq100[/tex] -----> is true

Inequality C

[tex]40\geq30[/tex] -----> is true

The ordered pair[tex](40,60)[/tex]   represent a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation

E) [tex](50.5,40)[/tex]  

The value of [tex]x=50.5[/tex] not make sense in the context of the situation, because is not a whole number

When functions are defined by more than one equation, they are called Piecewise defined functions.

What is Piecewise- defined function?

A Piecewise defined function is one which is defined not by a single equation, but by two or more.

Hence,

When functions are defined by more than one equation, they are called Piecewise defined functions.

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55(t-2) =45t

55t-110 = 45t

-110 = -10t

t = 11 hours

 2 pm plus 11 hours = 1 am

Answer: mathematics, central tendency is the tendency of data values to cluster around some central value. What does a measure of variability tell you about the central tendency of a set of data? ... If the range and IQR are small, the values are clustering around some central value.

Step-by-step explanation:

Let

x--------> the number

we know that

1) the phrase, "the sum of 12 and a number"

represent the expression --------> [tex](12+x)[/tex]

and

2) the complete phrase, "one third the sum of 12 and a number"

represent the expression --------> [tex]\frac{1}{3}(12+x)[/tex]

therefore

the answer is

[tex]\frac{1}{3}(12+x)[/tex]

The Standard Form: -w¹² + 4w¹¹,

Degree: 12 degree

Leading Coefficient: -1

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given equation

4w¹¹ - w¹²

Standard form of polynomial,

List the exponents in decreasing order of importance.

-w¹² + 4w¹¹

Degree of polynomial,

The degree, or the exponent in the first term, if it is in standard form, is the biggest exponent.

degree is 12.

Leading coefficient,

the first term's standard form coefficient Before the w in the first phrase, there is and understood 1.

for equation coefficient is -1,

Hence degree = 12, and leading coefficient is -1.

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The complete Question is

Write the polynomial in standard form. Identify the degree and leading coefficient of the polynomial.

Then classify the polynomial by the number of terms.

4w11 - w12

standard form

degree

leading coefficient.

Her gross pay was the amount of $450 for last week.

The commission is determined by the product of the commission rate and the total sales.

Commission = Commission rate x Total sales

As per the question, we have data :

Commission rate = 12 %

Total sales = $3,000

The base salary = $90

We know that,

Commission = Commission rate x Total sales

= 12% x $3,000

= 0.12 x $3,000

= $360

The total pay is then the base salary increased by the commission:

Total pay = base salary + Commission

Total pay = $90+ $360

Total pay = $450

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Answer:

Given,

Set speed of car = 55,

∵ The speed of the car within 3 miles per hour of the set speed.

So, the maximum speed of car = 55 + 3,

And, the minimum speed of car = 55 - 3

Let x shows the current speed of car,

x ≤ 55 + 3 or x ≥ 55 - 3

x - 55 ≤ 3 or x - 55 ≥ - 3

x - 55 ≤ 3 or -(x-55) ≤ 3

⇒ | x-55 | ≤ 3

Which is the required compound inequality,

Now, 55 - 3 ≤ x ≤ 55 + 3

52 ≤ x ≤ 58

⇒ [52, 58]

Which is the solution of the above compound inequality.

Also, the graph is shown below.

Answer:

If you want to build a good credit history

Step-by-step explanation:

Buying something in order to build a good credit history does not benefit in the short run such as any financial or non-financial benefit.

However, when need arises to make request for a large sum of loan in the long run (such as buying house, purchasing vehicle or capital for investing in business) from the financial institution or any other credit providers, then the good credit history would be winning key factor for obtaining the loan.

Final answer:

The area of a circular mirror with a radius of 10 cm is calculated using the formula πr², which results in an area of 314.16 cm².

Explanation:

The area of a circular mirror can be calculated using the formula πr², where π (pi) is approximately 3.1416 and r is the radius of the circle. Given the radius of the circular mirror as 10 cm, we can substitute this value into the formula to find the area.

Area = π × (10 cm)²
A = 3.1416 × 100 cm²
A = 314.16 cm²

Therefore, the area of the circular mirror is 314.16 cm².