Question 2 (Essay Worth 10 points)
(03.01 MC)

Look at the rectangle and the square:

A rectangle PQRS and square LMNO are drawn side by side. The length SR of the rectangle is labeled as 12 inches, and the width QR is labeled as 6 inches. The side LM of the square is labeled as 6 inches.

Sam says that the length of diagonal SQ is two times the length of diagonal OM.

Is Sam correct? Justify your answer and show all your work. Your work should state the theorem you used to find the lengths of the diagonals.

Answer:

The answer is A

Step-by-step explanation:

C’(4, –2)

The coordinates of C' are (1, 0)

A translation moves a shape up, down or from side to side, but it does not change its appearance in any other way.

Given that, On a coordinate plane, triangle A B C has points (-2, -1), (-2, -3), (-5, -1).

When Triangle ABC is translated 6 units to the right and 1 units up.

We know that rule for translating b unit up and a unit right is

(x, y) → (x+a, y+b)

Hence, the coordinates for C' =

(-5, -1) = (-5+6, -1+1) = (1, 0)

Hence, the coordinates of C' are (1, 0)

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Answer:

∠a=∠b

Step-by-step explanation:

Alternate exterior angles are congruent

Answer:

164.4

Step-by-step explanation:

m<ABC = m<ABK + m<KBC

17x + 8 = 42 + 12x - 4

17x - 12x = 42 - 4 + 8 add like terms

5x = 46 divide both sides by 5

x = 9.2 now replace x with 9.2 in 17x + 8

17*9.2 + 8 = 164.4

Answer:

This question is asking for the pattern , not the factoring of it...

this is the [tex](a+b)^{2} pattern = a^{2} + 2ab + b^{2}[/tex]

Step-by-step explanation:

Answer:

(x - 8)²

Step-by-step explanation:

This is in the form of a perfect square, that is

(x + b)² = x² + 2bx + b²

with x = x - 3 and by comparison of like terms

2b = - 10 ⇒ b = - 5

Then

(x + b)²

= (x - 3 - 5)²

= (x - 8)² ← in factored form

Answer:

It is mainly used while doing scientific notation. If two numbers differ by one order of magnitude, one is about ten times larger than the other. If they differ by two orders of magnitude, they differ by a factor of about 100.A quarter is 0.25 dollars so the ratio between 1 dollar and a quarter is 1/0.25(it means the dollar and the quarter which is 0.25 dollars) and that equals =4

Answer: -3

Step-by-step explanation:

-l-7+4l = -l-3l = - 3

ll means anything inside there is positive, so for example if -3 was in there, l-3l = 3

Answer:

- 3

Step-by-step explanation:

-|-7 + 4|

Simplify inside the absolute values first( like parentheses)

-|-3|

Take the nonnegative value for the absolute value

- 3

Answer:

what are the options...

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Given that the equation of the revenue is R=2x2+55x+10 and the equation of the cost is C=2x2 – 15x – 40, you will get the profit by subtracting the revenue from the cost: R-C=P. Therefore, P=(2x2+55x+10)-(2x2 – 15x – 40). You will get P=70x+50 where x is is the number of cellphones sold. If 240 cellphones are sold, then the profit is 16850 dollars.

The profit, if 240 cell phones are sold, is $16,850.

Profit = 70x + 50

Option C is the correct answer.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example: so

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The profit, in dollars, can be found by subtracting the cost from the revenue:

Profit = Revenue - Cost

= (2x² + 55x + 10) - (2x² - 15x - 40)

= 70x + 50

The expression for profit is 70x + 50.

To find the profit if 240 cell phones are sold, we substitute x = 240 into the expression for profit:

Profit = 70x + 50

= 70(240) + 50

= 16,850

Therefore,

The profit, if 240 cell phones are sold, is $16,850.

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Using it's concept, the probability that a student liking music given they already like art is of 10/17 = 0.5882 = 58.82%.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, from the Venn Diagram, there are 17 students who like art, and of those, 10 like music, hence the probability is given by:

10/17 = 0.5882 = 58.82%.

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Answer:

The domain of the function are values of x that respect the following condition: [tex]x \geq 7[/tex]

Step-by-step explanation:

We are given the following function:

[tex]f(x) = \sqrt{x - 7}[/tex]

Domain of the square root function:

The square root does not exist for negative values, so the domain of a square root function:

[tex]g(x) = \sqrt{h(x)}[/tex]

Is [tex]h(x) \geq 0[/tex]

In this question:

[tex]f(x) = \sqrt{x - 7}[/tex]

Then:

[tex]h(x) = x - 7[/tex]

[tex]x - 7 \geq 0[/tex]

[tex]x \geq 7[/tex]

The domain of the function are values of x that respect the following condition: [tex]x \geq 7[/tex]

Answer:

the answer is 8 and x>or equal 7 and the only option greater than 7 is 8

Step-by-step explanation:

Answer:

68.9 in^2

Step-by-step explanation:

first lets find the height of the blue triangle

hypotenuse = 15 in

one side is 12 in whereas other has to be find.

take 50 degree as reference angle

using sin rule

sin 50 = opposite/hypotenuse

0.76 = opposite/15

0.766*15 = opposite

11.49 = opposite

area of triangle = base*height/2

=12*11.49/2

=136.88/2

=68.94

=68.9 in^2

Answer:

A = 68.9 in²

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = [tex]\frac{1}{2}[/tex] ab sinC ( a, b are 2 sides and C the angle between them )

Here a = 12, b = 15 and C = 50° , then

A = [tex]\frac{1}{2}[/tex] × 12 × 15 × sin50°

   = 6 × 15 × sin50°

   = 90 × sin50° ≈ 68.9 in² ( to the nearest tenth )

Step-by-step explanation:

given pi value= 3

radius=7

we know,

area of a circle(A)= πr²

= 3×7²

=147cm²

Answer:

A = 147 cm²

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Geometry

Area of a Circle Formula: A = πr²

Step-by-step explanation:

Step 1: Define

Identify

r = 7 cm

Step 2: Find Area

Answer:

x = 83

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360

75+x+97+105 = 360

Combine like terms

x+277=360

Subtract 277 from each side

x+277-277=360-277

x = 83

Answer:

whichever one looks like the screenshot i have of the graph-

Answer:

Graph B

Step-by-step explanation:

Took the test and got it right on EDGE22

Answer:

y < - 12

Step-by-step explanation:

Given

y + 15 < 3 ( subtract 15 from both sides )

y < - 12

Answer:

36 sq units

Step-by-step explanation:

the area of shaded part =

(½×12×12) - (6×6)

= 72-36

= 36 sq units

Answer:

The sum of two non-zero even numbers is even and greater than the addends

Step-by-step explanation:

The solution to the whole number equation is sum of two non-zero even numbers is even and greater than the addends

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the first number be p

Let the second number be q

Now , the values of p and q are even

So , when p = 2 and q = 4

The sum of two non-zero even numbers is even and greater than the addends

p + q > q   be equation (1)

p + q > p   be equation (2)

2 + 4 > 4

2 + 4 > 2

6 > 4 and 6 > 2

Hence , the equation is true and sum of two non-zero even numbers is even and greater than the addends

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Answer:

$500

Step-by-step explanation:

f(x) = 0 + 10h

f(x) = $C

$C = 0 + 10(50)

55-5 = 50

$C = 10(50)

$C = $500

Answer:

hope this will help you more

Answer:

[tex]x^2-5x+6[/tex]

x = 3, x = 2

[tex]x^2-11x+28[/tex]

x = 7, x = 4

Step-by-step explanation:

One is asked to solve two quadratic equations. Both of these quadratic equations are in standard form. This means that the two equations follow the following general format;

[tex]ax^2+bx+c[/tex]

The quadratic formula is a method of solving a quadratic equation using the coefficients of the terms in the equation. The quadratic equation is the following,

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

Substitute in each of the terms and solve for the roots in each equation;

[tex]x^2-5x+6[/tex]

Substitute, and solve

[tex]\frac{-(-5)(+-)\sqrt{(-5)^2-4(1)(6)}}{2(1)}\\\\=\frac{5(+-)\sqrt{25-25}}{2}[/tex]

[tex]=\frac{5+1}{2}[/tex]          [tex]=\frac{5-1}{2}[/tex]

[tex]=3[/tex]               [tex]=2[/tex]

[tex]x^2-11x+28[/tex]

Substitute, and solve

[tex]\frac{-(-11)(+-)\sqrt{(-11)^2-4(1)(28)}}{2(1)}\\=\frac{11(+-)\sqrt{121-112}}{2}[/tex]

[tex]=\frac{11+\sqrt{9}}{2}[/tex]           [tex]=\frac{11-\sqrt{9}}{2}[/tex]

[tex]=\frac{11+3}{2}[/tex]              [tex]=\frac{11-3}{2}[/tex]

[tex]=7[/tex]                     [tex]=4[/tex]

Answer: I think a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

question a is technically 7.5 and question b is 7.5

Step-by-step explanation:

half half

Answer:

A.

Step-by-step explanation:

If R(-2), then x = -2. Just plug in -2 for x. -2^2 - 3(-2) - 1 = 4 + 6 - 1 = 10 - 1 = 9. The answer is 9.

Answer:

y = 2/3x + 1 1/3

Step-by-step explanation:

As y increases by 2, x increases by 3, so 2/3. The y - intercept is 1 and 1/3 so plus 1 1/3

Answer:

(15,9)

Step-by-step explanation:

The solution to the system is where the two graphs intersect

The intersect at x=15 and y =9

(15,9)

Answer:

12cm

Step-by-step explanation:

Area of square = Area of rectangle

Area of square = length x breadth

Area of square = 9 x 16 = 144(cm)^2

(side)^2 = 144

side = √144

side = 12cm

12cm

Step-by-step explanation:

area of square=area of rectangle

s^2=L*W

area of rectangle=length * width

area of rectangle=9cm*16cm=144cm^2

s^2 =144cm^2

s=12 cm

Answer:

[tex] { \boxed{ \tt{f(x) = 5 \cos3x \degree}}} \\ { \green{f(x) = f(60) : x = 60}}\\ f(60) = 5 \cos(3 \times 60) \degree \\ f(60) = 5 \cos(180 \degree) \\ but \: \cos(180 \degree) = - 1\\ { \boxed{ \bf{answer : f(60) = - 5}}} \\ \\ { \underline{ \blue{becker \: jnr}}}[/tex]

Answer:

post the question i can do it

Step-by-step explanation:

-pi/4 is the same thing as 7pi/4.

The sine function will get us the y-value we need.

Keep in mind that our y-value will be negative (based on the position of the line), and pi/4 and 3pi/4 will both have positive y-values.

Therefore, the correct expression is sin(7pi/4).

Hope this helps!! :)

Answer: the total number of milk chocolate is 6

Step-by-step explanation: