What is the property shown below

Angle ECD and Angle FDC are same-side interior angles. They lie on the same side of the transversal and are on the inside of the two parallel lines. Same-side interior angles are supplementary, meaning that they add up to 180.

(40x + 15) + (5x + 30) = 180

45x + 45 = 180

45x = 135

x = 3

Angle ECD = 40(3) + 15 = 120 + 15 = 135

Angle FDC = 5(3) + 30 = 15 + 30 = 45

Hope this helps!

Step-by-step explanation:

x-3y=6

-3y=6-x

3y=x-6

y=x/3-2

option 4 is the answer

Answer:

what the product of 2 and 3

Answer:

[tex] MN= \boxed{15}[/tex]

Step-by-step explanation:

refer the attachment

therefore Let,

according to the question

[tex] \displaystyle (x - 3 ) (x + 13) =( x + 3 {)}^{2} [/tex]

simplify square and Multiplication:

[tex] \displaystyle {x}^{2} + 10x - 39 = {x}^{2} + 6x + 9[/tex]

cancel x² from both sides:

[tex] \displaystyle 10x - 39 = 6x + 9[/tex]

cancel 6x from both sides:

[tex] \displaystyle 4x - 39 = 9[/tex]

add 39 to both sides:

[tex] \displaystyle 4x = 48[/tex]

divide both sides by 4:

[tex] \displaystyle \boxed{x = 12}[/tex]

given that,

[tex] MN= x + 3[/tex]

substitute the got value of x:

[tex] MN= 12 + 3[/tex]

simplify addition hence,

[tex] MN= \boxed{15}[/tex]

Answer:

it will be the correct answer..

because

The median is the most informative measure of central tendency for skewed distributions or distributions with outliers. For example, the median is often used as a measure of central tendency for income distributions, which are generally highly skewed.

Answer:

32 years

Step-by-step explanation:

8x12 because there are 12 inches in a foot

8x12=96

96/3

96/3=32

Answer:

32 years

Step-by-step explanation:

y = years

1 foot  = 12 inches

12 × 8 = 96

Now, plug in random numbers into the expression below to find how long it takes for the tree to grow 8 feet.

3y

3 × 10 = 30

3 × 20 = 60

3 × 30 = 90

3 × 31 = 93

3 × 32 = 96

It will take the pine tree 32 years to grow 8 feet, or 96 inches.

Answer:

[tex]x(qr + pr + pq) > pqr \: \: \: by \: dividing \: both \: sides \: by \: (qr + pr + pq)[/tex]

we get that

Step-by-step explanation:

[tex]x > \frac{qr + pr + pq}{pqr} [/tex]

Answer:

30 words per minute

Step-by-step explanation:

Take the number of words and divide by the number of minutes

150/5 = 30

300/10 =30

450/15 = 30

600/20 = 30

30 words per minute

Answer:

janae types 30 words each minutes.

Step-by-step explanation:

if 5minutes = 150 words

[tex]1 \: minute = \frac{150words}{5minutes} [/tex]

[tex] = \: 30words[/tex]

Answer:

[tex]4x^3-2x^2+5x-6+\frac{1}{x}[/tex] is a polynomial

Step-by-step explanation:

a polynomial is a set of numbers with multiple terms that are not simplify able

[tex]9x^7y^{-3} z[/tex] is not a polynomial because its actually one term, there is no addition/subtraction of different terms.

-13 is a single number, so not a polynomial

13x^-2 is also a single number, not a polynomial

Answer:

7. 35-(2*3+5*4.5)

8. 6.5

Answer:

21x+4

Step-by-step explanation:

X’s: 21x

#’s: 4

So it will be 21x+4

Answer:

A is the correct answer

Step-by-step explanation:

Answer:

A is the correct answer

Answer:

50.7

Step-by-step explanation:

38+1.3+90 from the right angle=129.3

180-129.3=50.7

Answer:

Step-by-step explanation:

Patrick thinks that when 'a' is a negative integer and 'b' is a positive,

Let "a = -2" and "b = 3"

a). a - b is positive.

a - b = -2 - 3

            = -5 {negative]

Therefore, statement is False.

(a - b) is negative.

b). b - a is positive.

b - a = 3 - (-2)

       = 3 + 2

       = 5 [Positive]

Statement is True.

c). a - (-b) is negative.

a - (-b) = a + b

          = -2 + 3

          = 1 [Positive]

False.

But it's true when a = -5 and b = 3

a - (-b) = -5 - 3

           = -8 [Negative]

Answer:

x = 8

Step-by-step explanation:

The angles shown are vertical angles

Vertical angles are congruent hence 8x + 36 = 5x + 60

( Notice that we just created an equation that we can use to solve for x )

We now solve for x algebraically

8x + 36 = 5x + 60

Step 1: Subtract 5x from both sides

8x - 5x + 36 = 5x - 5x + 60

Outcome: 3x + 36 = 60

Step 2: Subtract 36 from both sides

3x + 36 - 36 = 60 - 36

Outcome: 3x = 24

Step 3: Divide both sides by 3

3x/3 = 24/3

Outcome: x = 8

The values of x between which the relative maximum occurs is between the x-values; -1 and 1

The known parameters;

The table of the partial set of the polynomial values is presented as follows;

[tex]\begin{array}{rcr}\mathbf{x}&&\mathbf{g(x)}\\-2&&-14\\-1&&-2\\0&&0\\1&&-4\\2&&-6\\3&&2\end{array}[/tex]

From the table above, we have that g(x) is maximum (g(x) = 2) when x = 3

Method;

Define and find the relative maximum

The relative maximum of a function, is given by a point where the graph of the function changes direction from 'continuously' increasing values of the function before the point to 'continuously' decreasing values of the function after the point

From the table, at x = -2, -1, 0, g(x) = -14, -2, 0, and is therefore, increasing

Where, x = 0, 1, 2, we have g(x) = 0, -4, -6, therefore, g(x) is decreasing

The maximum value of g(x), in the region where g(x) changes from increasing to decreasing is g(x) = 0, which is given between the x-values of -1 and 1

Therefore, the relative maximum is most likely to occur between the values of x = -1, and x = 1, which is the option -1 and 1

Learn more about relative maximum here;

https://brainly.com/question/2321623

Answer:

[tex]x=4\sqrt{2}\\y=7[/tex]

Step-by-step explanation:

In order to solve this problem, the easiest approach is to draw a line connecting the vertex between the side with a measure of (y) and (3) to the side with the length (x). This side should be parallel to the side with a length of (4).

Since the new side constructed (call this side (b)), is parallel to the side with a length of (4) and is intersected by segments that are perpendicular to the side with a length of (4), the side (b) and (4) must have the same measure. Therefore (b = 4).

The triangle formed with sides (x) and (b) is a (45 - 45 - 90) triangle. Meaning that its angles have the following measure, (45 - 45- 90). This means that its sides follow the following ratio:

angle : side opposite

[tex]45:x\\45:x\\90:x\sqrt{2}[/tex]

Apply this logic to the given situation.

[tex]x=b*\sqrt{2}\\x = 4\sqrt{2}[/tex]

The side (b) divides the side (y) into two parts. Call the part that is a side of the triangle ([tex]y_1[/tex]) the side that is a part of the rectangle is called ([tex]y_2[/tex]). As per the logic used to find the lengths of side (b), one can use similar logic to find the length of side ([tex]y_2[/tex]). The sides ([tex]y_2[/tex]) and (3) are parallel and are intersected by the sides with a measure of (4) and (b), therefore  ([tex]y_2[/tex]) and (3) are cognrunet. Thus ([tex]y_2[/tex] = 3).

The base angles converse theorem states that when two angles in a triangle are congruent, the triangle is isosceles, and the sides opposite the congruent angles are also congruent. Thus, one can state the following:

[tex]y_1=b\\y_1=4[/tex]

Now add up the measurement of ([tex]y_2[/tex]) and ([tex]y_1[/tex]) to find the measure of (y):

[tex]y_2+y_1=y\\4+3=y\\7=y[/tex]

Answer: 1⅓ batch of cookies

Step-by-step explanation:

From the question, we are given the information that a cook has 4 cups of raisins to make oatmeal cookies and that the recipe requires 3 cup of raisins for each batch of cookies.

Therefore, the number of batches of cookies that the cook can make will be the number of cups of rasins that the cook has divided by the number of reasons needed for each cookie. This will then be:

= 4/3

= 1⅓ batch of cookies

Answer:

Yes

Step-by-step explanation:

Statistics can perdict cyclones for example lets say that somewhere a cyclone happens almost every February then its statistically likely to happen this February too.

Answer:

i) 2160

ii) 1800

Step-by-step explanation:

so, the retailer sold the item for 2052, if I understand the problem description correctly.

and with this sale price, he actually made a loss of 5%.

so, 2052 are actually only 95% of what he himself paid the wholesaler for it.

2052 = 95%

1% = 2052/95 = 21.60

100% (the whole price the retailer paid to the wholesaler) = 21.60 × 100 = 2160

so, now, these 2160 have the wholesaler a profit from his perspective of 20%.

that means this price includes the 20% profit margin.

2160 = 120%

1% = 2160 / 120 = 18

100% (the price the wholesaler originally paid) = 18 × 100 = 1800

Answer:

(4, 0)

(-1, 3)

(2, -1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

Point (2, 1)

Point (-3, 4)

Point (0, 0)

Rule (x + 2, y - 1)

Step 2: Translate

Substitute in points into rule.

Point (2, 1) → (2 + 2, 1 - 1) = (4, 0)

Point (-3, 4) → (-3 + 2, 4 - 1) = (-1, 3)

Point (0, 0) → (0 + 2, 0 - 1) = (2, -1)

Answer:

There are 8 bottles in each box.

Step-by-step explanation:

Victor has 12 boxes with 'n' number of water bottles in each box.

A dozen is same as 12.

Now, 12 boxes and each with 'n' number of bottles. Total number of bottles in '12' boxes is 12n bottles.

Now, it is removing 12(a dozen) bottles from 12n bottles which gives 84.

So, 12n -12=84

Add both sides 12

12n= 96

Divide both sides by 12

n=8

So, there are 8 bottles in each box.

Answer:

1,2, and 4

Step-by-step explanation:

I attached a picture with the graph

y= -4 is a straight horizontal line (red line) and  

y≤10 will give a horizontal line passing trough y=10 (blue line)

the solution is all points under and on the line  y=10

1, 2, and 4 are part of the solution set

(the blue area is the solution of the system of equations)

Answer:

( - 2, 7 )

Step-by-step explanation:

Step-by-step explanation:

1. The length is one more thrice it's width. The height is 4 more than it width. We can represent the

[tex](3x + 1)(x + 4)[/tex]

[tex](3 {x}^{2} + 13x + 4)x = 720[/tex]

Multiply it by x.

[tex]3 {x}^{3} + 13 {x}^{2} + 4x = 720[/tex]

[tex] 3{x}^{3} + 13 {x}^{2} + 4 x - 720[/tex]

The possible roots

The possible roots are plus or minus is1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720. By a long list of substitution, 5 is a root. So this means that x=5. So the width has to be

[tex]x = 5[/tex]

2. First. we apply the Rational Root Theorem so the possible roots are plus or minus 1,2,3,6.

Let check via synethic division to see which are roots.

Let try 1 and -1 first. If we plug 1 into the equation, we get

[tex]1 - 2 - 5 + 6 = 0[/tex]

So 1 or (x-1) is a solution. Since it's a solution we can divide this into our original polynomial to get us a new polynomial that is more simplified. If we apply synthetic division, we get a new polynomial in

[tex] {x}^{2} - x - 6[/tex]

We can then factor this into

[tex](x - 3)(x + 2)[/tex]

So our roots or factors is

[tex](x - 1)(x - 3)(x + 2)[/tex]