Part A: The area of a square is (9x2 − 18x + 9) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work.

Part B: The area of a rectangle is (25x2 − 4y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work.

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

△ABC ≅ △WRS

So, Perimeter of △ABC is given by

AB+BC+CA

here, AB = 3 units

BC = 4 units

AC = x

By pythagorus theorem, we get that

[tex]AC^2=AB^2+BC^2\\\\x^2=3^2+4^2\\\\x^2=9+16\\\\x^2=25\\\\x=\sqrt{25}\\\\x=5\ units[/tex]

So, perimeter of △ABC is

3+4+5=12 units

So, the perimeter of △WRS is also 12 units as they are similar triangles .

Hence, Third option is correct.

Answer:

The Answer Is 12

Step-by-step explanation:

Answer:

xyz⋅xyz

x•x•y•y•z•z

Step-by-step explanation:

Select all that apply.

(xyz)2 = _____

The expression without exponents is?

xyz⋅xyz

x•x•y•y•z•z

x2 •y2 •z2

xy•xy•xy

Odyssey

Answer:

5.5

Step-by-step explanation:

3.8 is misinformation

The approximate percentage of change will be 43.24%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

An antique car was purchased for $7400 and is not worth $10,600.

Then the approximate percent of change will be given as,

P = [(10600 - 7400) / 7400] x 100

P = (3200 / 7400) x 100

P = 0.4324 x 100

P = 43.24%

The approximate percentage of change will be 43.24%.

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Domingo made $14.25 per hour last year by dividing his annual income of $29640 by the total hours worked in the year, which is 2080 hours (40 hours/week  imes 52 weeks).

To calculate how much Domingo made per hour, divide his annual income by the total number of hours worked in a year. Domingo works 40 hours per week, and there are 52 weeks in a year, so the total hours worked in a year is 40 hours/week  imes 52 weeks/year = 2080 hours/year.

The formula to find the hourly wage is:

Hourly Wage = Annual Income / Total Hours Worked

Thus, Domingo's hourly wage would be:

$29640 / 2080 hours = $14.25 per hour.

Therefore, the correct answer is A. $14.25.

The cubic polynomial equation which passes through the coordinate (0,-5) and whose zeroes are (2 , 0), (3 , 0), and (5 , 0) is: [tex]y = \dfrac{1}{6}(x-2)(x-3)(x-5)[/tex] and it can be determine by arithmetic operations.

Given :

Arithmetic operations can be used to determine the cubic polynomial equation. The generalised cubic polynomial equation is given by:

[tex]y = K(x-a)(x-b)(x-c)[/tex]

Where, K is constant and a, b, and c are the zeroes of the cubic polynomial equation. Therefore, the value of a, b, and c are 2, 3, and 5 respectively.

[tex]y = K(x-2)(x-3)(x-5)[/tex]   ----- (1)

It is given that cubic polynomial equation passes through (0 , -5). So, put x = 0 and y = -5 in equation (1) to evaluate the value of K.

[tex]-5=K(0-2)(0-3)(0-5)[/tex]

[tex]5=30K[/tex]

[tex]K = \dfrac{1}{6}[/tex]

Therefore the cubic polynomial equation is given by:

[tex]y = \dfrac{1}{6}(x-2)(x-3)(x-5)[/tex]

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Step [tex]1[/tex]

Find the slope of the line perpendicular to the given line

we have

the equation of the given line is

[tex]y=\frac{1}{2}x+7[/tex]

we know that

if two lines are perpendicular

then

the product of their slopes is equal to minus one

so

[tex]m1*m2=-1[/tex]

in this problem the slope m1 of the given line is

[tex]m1=\frac{1}{2}[/tex]

so

[tex]m2=-\frac{1}{m1}[/tex]

[tex]m2=-2[/tex]

Step [tex]2[/tex]

Find the equation of the line with slope m2 and passes through the point [tex](6, 2)[/tex]

we know that

the equation of the line is

[tex]y-y1=m*(x-x1)\\ y-2=-2*(x-6)\\y=-2x+12+2\\ y=-2x+14[/tex]

therefore

the answer is the option A

the equation of the line is [tex]y=-2x+14[/tex]

see the attached figure to better understand the problem

Answer:

The dimensions of the box are (b+3), (b-2) and (b+2).

Step-by-step explanation:

The volume of a rectangular box is

[tex]V=l\times w\times h[/tex]    

The volume of a certain box is

[tex]V=b^3+3b^2-4b-12[/tex]

First of all find the factors of above expression by grouping method.

[tex]V=b^2(b+3)-4(b+3)[/tex]

[tex]V=(b+3)(b^2-4)[/tex]

[tex]V=(b+3)(b^2-2^2)[/tex]

[tex]V=(b+3)(b-2)(b+2)[/tex]                 [tex][\because a^2-b^2=(a+b)(a-b)][/tex]  

Volume of a rectangle is the product of its dimensions, therefore the dimensions of the box are (b+3), (b-2) and (b+2).

The solution is, the race ends at 12h50 (noon)

It can be stated as, Addition is a way of combining things and counting them together as one large group.We know that, Addition in math is a process of combining two or more numbers.

here, we have,

Anna started a race at 9:30am. She ran for 3 hours and 47 minutes.

so we know the time she start and how many time the race was so let's add them together to get the end time

now,

9:03+3h47

=12h50

so the race ends at 12h50 (noon)

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Step 1: Assign variable for the unknown that we need to find.

Let ' x ' be the number of applicants received by University Law School.

Step 2: Set up an equation based on the information given.

"University Law School accepts 2 out of every 15 applicants. If the school accepts 180 students, find how many applicants they received"

[tex] \frac{Accepted \; application}{Applied \; applicants} =\frac{2}{15} =\frac{180}{x} [/tex]

Step 3: Solving the equation

[tex] \frac{2}{15} =\frac{180}{x} \\ Cross \; Multiply\\ \\ 2x=15(180)\\ 2x=2700\\ Divide\; by\; 2\; on\; both\; sides\\ \\ \frac{2x}{2} =\frac{2700}{2} \\ Simplifying\; fraction\; on\; both\; sides\\ \\ x=1350 [/tex]

Conclusion:

The number of applicants received by University Law School is 1350.

Answer: 50

Step-by-step explanation: