If a polynomial function f(x) has roots 3 and StartRoot 7 EndRoot, what must also be a root of f(x)?Negative StartRoot 7 EndRoot
i StartRoot 7 EndRoot
–3
3i

Answer:

To find the difference between the highest and lowest temperatures in Chicago while using absolute values, you can calculate it as follows:

|Highest Temperature| - |Lowest Temperature| = |105°F| - |-27°F|

|105| - |-27| = 105 + 27 = 132

So, the absolute difference between the highest and lowest temperatures in Chicago is 132 degrees Fahrenheit.

Step-by-step explanation:

Kris' gross pay is $689.50.

What is Kris' gross pay?

The gross pay is the total income she receives from her work before any deductions. If she is paid biweekly, it means she is paid every two weeks.

Gross pay = (per per hour x total hours worked x 2)

= (9.85 x 35 x 2)

= $689.50

Answer:

The best option is;

A triangle with three equal sides all longer than 12 inches

Step-by-step explanation:

The cross sectional area of the square prism that passes through points A, B and C is found as follows;

Shape of cross section ABC = Triangle

Base, AB of the triangle is given by;

AB = √(8² + 8²) = √128 = 8·√2

Side, AC of the triangle is given by AC = √(8² + 12²) = 4√13

Therefore, the height of the triangle is given as follows;

Height, h = √(4·√13)²-(4·√2)² = 4·√11

The area of the cross section then is 0.5 × Base × Height

= 0.5 × 8·√2 × 4·√11  = 16·√22

A triangle with 3 equal sides of 8 inches has an area of 4×8×sin(60) = 16√3

A triangle with 2 equal sides of 12 inches and one side of 8 inches has an area of 4×12×sin(60) = 24√3

Therefore since 16·√22 > 24√3 >  16√3, the best option is a triangle with three equal sides of   all longer than 12 inches.

Final answer:

The formula for the circumference of a circle can be rewritten in terms of its diameter by replacing the '2r' with 'd', given that the diameter is twice the radius. This yields the new formula: C = πd.

Explanation:

The original formula for the circumference of a circle is C = 2πr, where 'C' represents the circumference, 'π' is a mathematical constant approximately equal to 3.14, and 'r' is the radius of the circle.

• To rewrite this formula in terms of the diameter, we need to know the fundamental relationship between the radius and the diameter of a circle. In every circle, the diameter 'd' is simply twice the radius: d = 2r.
• Substituting this into the original formula, we replace the '2r' in 'C = 2πr' with 'd'. This gives us the new formula: C = πd.

So, the formula for the circumference of a circle in terms of its diameter is C = πd.

Learn more about Circumference of a Circle here:

brainly.com/question/31844715

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Declaration

Let the original amount of the paycheck be x

Equation

Paycheck - cost of mower - cost of chainsaw - 180 = 270

x - [(3/8)x + (2/5)x + 180] =  270

Solve

Change 3/8 and 2/5 to a common denominator and add.

3*5/8*5 + 2*8/5*8 = 15/40 + 16/30 = 31/40

x - [(31/40)x + 180] = 270                 Remove the outer brackets

x - (31/40)x - 180 = 270                    Evaluate the "x"s

40/40x - 31/40x - 180 = 270        

9x/40 - 180 = 270                          Add 180 to both sides

9x/40 = 180 + 270

9x/40 = 450                                  Multiply by 40

9x = 18000                                    Divide by 9

x = 18000/9

x = 2000

His paycheck was 2000 dollars.