polynomial function
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Proved that ΔABC ≅ ΔDEC

SAS rule of congruent states that if two sides and one angle of the triangle is equal to the two sides and one angle of the another triangle, then the both triangles are congruent

The line BE and AD intersect at point C

The measure of the angle BCA = The measure of the angle ECD

The length of the side BC = The length of the side EC

The length of the side AC = The length of the side DC

Consider the triangle ABC and triangle DEC

Two sides and one angle of the triangle ABC is equal to the two sides and one angle of the triangle DEC, according to SAS rule of congruent the triangle ABC and triangle DEC are congruent

Hence, proved that ΔABC ≅ ΔDEC

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A. The length of the side of original garden is 4 m

B. The width of the new garden is 5m

C. The length of the new garden is 7m

D. The area of the new garden is 35 m²

Let the side of the garden = x m.

area = x² m²

From the question, we have

The new length is (x+3) m and the new width is (x+1) m.

Then the new area = (x+3)(x+1) m².

(x+3)(x+1)=x²+19

⇒ x²+3x+x+3=x²+19

⇒ 4x+3=19

⇒ 4x=19-3

⇒ 4x=16

⇒ x = 4 m

The length of the side of original garden is 4 m

new length = (x+3) m = (4+3)m = 7 m

new width = (x+1) = (4+1) = 5 m

new area = (x+3)(x+1) m² = 7*5 = 35 m²

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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Answer:

x = 2

Step-by-step explanation:

The image shows a large rectangle with a similar, smaller triangle inside of it. The small leg on the small rectangle is 4, and the small leg on the large rectangle is 12. This tells me that the scale factor is 3.

If the scale factor is 3, then

[tex]6*3=6+6x[/tex]

Simplify

[tex]18=6+6x\\12=6x\\x=2\\[/tex]

If the team buys 18 jerseys for a total of (18x-36) dollars then we can conclude that the discount the team has received is $36.

According to the question,

We have the following information:

A soccer team receives a discount on each jersey purchased. The original price of each jersey is x dollars. The team buys 18 jerseys for a total of (18x-36) dollars.

Now, the original price of 18 jerseys will be 18x.

Now, when 36 is subtracted from 18x to find the total cost then it means that this is the discount from the original price.

Hence, if the team buys 18 jerseys for a total of (18x-36) dollars then we can conclude that the discount the team has received is $36.

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If Emily's family loves to work together in the garden . The number of vegetable plants they have is :20.

Using this formula to determine the number of vegetable plants

Number of vegetable plants = Percentage of vegetable plants  × Number of plants

Let plug in the formula

Number of vegetable plants = 40% × 50

Number of vegetable plants = 20

Therefore we can conclude that  the number of vegetable plants is 20.

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The correct question is :

Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60 percent of their plants are flowers and 40 percent are vegetables. They have 50 plants growing in the garden.

How many vegetable plants do they have?

The y-coordinate of the point that divides the directed line segment from J to K into a ratio of is 5.

The coordinates of point that divides the line segment into m:n ratio can be obtained as follows,

Coordinates of point = [tex](\frac{mx_{2}+ nx_{1} }{m+n} \frac{my_{2}+ ny_{1}}{m+n} )[/tex]

The coordinate of point J is (-3,1)

The coordinate of point K is (-8,11)

Consider the point that divides the line segment into 2:3 ratio as P(x,y).

The coordinates of point that divides the line segment into 2:3 ratio can be calculated as follows,

[tex]Coordinates of P = (\frac{3(-3)+2(-8)}{2+3}, \frac{3(1)+2(11)}{2+3} )[/tex]

[tex]= (\frac{-9-16}{5}, \frac{3+22}{5} )\\\\= (\frac{-25}{5} \frac{25}{5} )[/tex]

= (-5,5)

Hence the answer is The y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3 is 5.

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Answer:answer is 20

Step-by-step explanation:9/3=3 then add that to 2 times 6 which is 12+3=15 then 15+5+20

$135 is markup price when cost is $450.

What is the cost price and an example?

selling price of item = $600

       cost = $450

10%×$650=$585

$585-$450=$135

$135 is markup price .

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The number that represents the shoe rental charge is $3 and the price per game is $2.5.

Given:

The function y=2.5x+3 represents the cost y of bowling x games.

y = 2.5x+3

In the equation the 2.5 represents additional fee.

For 1 game = 2.5*1 = 2.5

For 2 games = 2.5 * 2

= 5

3 is the flat fee for renting the shoes.

Therefore the number that represents the shoe rental charge is $3 and the price per game is $2.5.

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Answer:

y = - [tex]\frac{3}{4}[/tex] x - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 12, 4 ) and (x₂, y₂ ) = (0, - 5 ) ← coordinates of 2 end stars

m = [tex]\frac{-5-4}{0-(-12)}[/tex] = [tex]\frac{-9}{0+12}[/tex] = [tex]\frac{-9}{12}[/tex] = - [tex]\frac{3}{4}[/tex]

the lowest star is on the y- axis at (0, - 5 ) ⇒ c = - 5

y = - [tex]\frac{3}{4}[/tex] x - 5

Answer:

x = 12, y = 15

Step-by-step explanation:

x + y = 27

1 / 2 x + 1 / 3 y = 11

y = 27 - x

1 / 2 x + (27 - x) / 3 = 11

1 / 2 x + 9 - 1 / 3 x = 11

1 / 6 x = 2

x = 12

12 + y = 27

y = 15

Answer:

-7

Step-by-step explanation:

Given inequality:

[tex]4x - 12 \leq 16 + 8x[/tex]

Subtract 4x from both sides:

[tex]\implies 4x - 12-4x \leq 16 + 8x -4x[/tex]

[tex]\implies -12\leq 16+4x[/tex]

Subtract 16 from both sides:

[tex]\implies -12-16\leq 16+4x-16[/tex]

[tex]\implies -28\leq 4x[/tex]

[tex]\implies 4x \geq -28[/tex]

Divide both sides by 4:

[tex]\implies 4x \div 4 \geq -28 \div 4[/tex]

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

This means that x is equal to or greater than -7.

Therefore, the value of x that is in the solution set of the inequality is -7 as -10, -9 and -8 are all less than -7.

Answer:

x ≥ -7

Step-by-step explanation:

Given inequation,

→ 4x - 12 ≤ 16 + 8x

Then the value of x will be,

→ 4x - 12 ≤ 16 + 8x

→ 4x - 8x ≤ 16 + 12

→ -4x ≤ 28

→ x ≥ 28/-4

→ [ x ≥ -7 ]

Hence, the value of x is -7.

The value of x is 15 and the value of y is 4 for the given triangle.

According to the question,

We have the following information:

We have a figure of triangle and a line parallel to the base is drawn. Some measurements of the sides are given.

Now, to find the values of x and y, we will use Basic Proportionality theorem which states that the ratio of the corresponding sides are equal.

For the larger triangle, we have:

12/y = 18/6

Using the cross multiplication method:

y = 12*6/18

y = 4

Now, using the same theorem for the smaller triangle:

12/y = x/5

12/4 = x/5

Using the cross multiplication method:

x = 15

Hence, the value of x is 15 and the value of y is 4 for the given triangle.

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The value of the linear expression quantity negative 1 over 4 times r minus 8 minus 5 over 7 times r end quantity minus the linear expression quantity negative 3 over 4 times r plus 9 end quantity is B. negative 3 over 14 times r plus negative 17

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Based on the information given, the expression will be:

= (-1/4r - 8 - 5/7r) - (-3/4r + 9)

Collect like terms

-1/4r - 5/7r + 3/4r - 8 - 9.

= - 3/14r - 17

In conclusion, the correct option is B.

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Answer:

Step-by-step explanation:

b

The value of x and y in the vector matrix are 2 and 5

If a matrix has only one row or only one column it is called a vector.

A matrix having only one row is called a row vector.

A matrix having only one column is called a column vector.

The matrix for two equations

3 - x/4 = 5/2 ---------------------1

8 - 12/4 = y ----------------------2

From equation 1,

collect like terms

x/4 = 3-5/2

x/4 = 1/2

cross multiply

2x = 4

x = 4/2

x = 2

From equation 2,

8 - 3 = y

y = 5

In conclusion, the value of x = 2 and the value of y = 5

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Answer:

1/10 or 0.1 m^3

Step-by-step explanation:

V = 1/4 * 2/3 * 3/5 = 6/60 = 1/10 m^3 = 0.1 m^3

Answer:

q = 4

Step-by-step explanation:

Step 1: Set up the equation

Step 2: Solve for q

Answer:

The bill after tipping 21 percent would be $104.30.

Step-by-step explanation:

$86.20 x 0.21 = $18.102

$86.20 + $18.102 = $104.302

$104.302 ≈ 104.30

Hope my answer helped! Have a great afternoon.

Step-by-step explanation:

I suspect you mean

11³ × 11 = ?

11³ ÷ 11 = ?

11³ × 11 = 11⁴

11³ ÷ 11 = 11²

why ?

11³ = 11×11×11

11³ × 11 = 11×11×11 × 11 = 11×11×11×11 = 11⁴

11³ ÷ 11 = 11×11×11 / 11 = 11×11 × 1 = 11×11 = 11²

The slope will be 1, for the right.

What is the slope of line?

Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.

We know that formula two find the slope of the line joining two points which is

m = (4-3)/(4-3)

m = 1

Hence the slope of the line is shown in the graph is 1.

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Step-by-step explanation:

120 ft relate to 24 inches.

120/80 must be the same ratio as 24/model width.

120/80 = 3/2

so,

24/width = 3/2

48/width = 3

48 = 3width

width = 48/3 = 16 inches

I will have to reject the offer of the rival company since it's lesser than $40560.

From the information, the person works a basic week of 40 hours and the basic rate is $19.50 per hour. It should be noted that there are 52 weeks in a year. The total amount will be:

= 40 × 19.50 × 52

= $40560

The rival company offers you an annual salary is $36000.

I'll reject the rival company's offer since it's lower.

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The number needed to multiply the amount of each ingredient by to adjust the recipe is 5. It's determined by dividing the number of people that needs to be served by the number of people the provided ingredients will serve.

1 ¼ teaspoons salt

3 ¾ cups sugar

5 eggs

10 tablespoons milk

10 ½ cups chocolate chips

1. Number needed to multiply the amount of each ingredient by to adjust the recipe = Number of people that needs to be served ÷ The ingredients provided serves

= 60/12

= 5

2. Steps involved in finding out how much flour you will need to make 60 servings of chocolate chip cookies.

Quantity of flour provided = 1 ¼ cups

Flour needed for 60 servings = Quantity of flour provided × number needed to multiply each ingredients with

= 1 ¼ × 5

= 5/4 × 5

= 25/4

= 6 ¼

3. Steps involved in finding out how much baking soda you will need to make 60 servings of chocolate chip cookies

baking soda needed for 60 servings = Quantity of baking soda provided × number needed to multiply each ingredients with

= ½ × 5

= 5/2

= 2 ½

4. Teaspoons salt = ¼ × 5 = 5/4 = 1 ¼

Cups sugar = ¾ × 5 = 15/4 = 3 ¾

Eggs = 1 × 5 = 5

tablespoons milk = 2 × 5 = 10

Cups chocolate chips = 1 ¾ × 6 = 7/4 × 6 = 42/4 = 10 ½

5. The number of eggs needed for 60 servings than 12 servings = eggs needed for 60 servings - ieggs needed for 60 servings

= 5 - 1

= 4

6. Number needed to multiply the amount of each ingredient by to adjust the recipe to 78 servings = Number of people that needs to be served ÷ The ingredients provided serves

= 78/12

= 6 ½

7. One time I made a mistake of keeping bad company, it really affected my studies because I lost concentration in school. My parents were disappointed in me but they helped me get back on the right track.

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Answer: <1=104 degrees, <2=76 degrees, <4=104 degrees, <5=104 degrees, <6= 76 degrees, <7= 76 degrees, <8= 104 degrees

Step-by-step explanation:

<76 & < 2 are vertical angles, which means they are congruent. <1 & <2 are supplements, meaning when you add them up they equal 180 degrees (180-76=104 degrees). <1 & <4 are vertical angles. Using the Alternating Exterior Angles Theorem (AIA), <2 & <7 are congurent. Using the same theorem, <1 & < 8 are congruent. <7 & <5 are supplements, and so is <8 & <6.

The constraints for this situation in the form of a system of inequalities is 6x + 10 y = 60.

Given:

you receive a $60 gift card to a move theater. a ticket to an afternoon show costs $6 and a ticket to an evening show costs $10. the rules of the gift card state that you can only buy a maximum of 8 total tickets with the card.

x =  the number of afternoon tickets and y = the number of evening tickets.

6x ≤ 60

10y ≤ 60.

so

6x + 10 y = 60.

Therefore the constraints for this situation in the form of a system of inequalities is 6x + 10 y = 60.

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Answer:

[tex]x=6, y=-2[/tex]

Step-by-step explanation:

[tex]-2=3x-20 \\ \\ 3x=18 \\ \\ x=6 \\ \\ \therefore x=6, y=-2[/tex]

Answer:

The answer is x = 6. If you want to solve the equation by inputting the x and y value, then take the x value and input it into the equation as well as the y value.

Step-by-step explanation:

To solve this equation, plug in the value equal to y and solve for x. The first thing you have to do is make the equation -2 = 4x - 20, since we already have the value for y which is given in the question. Then add 20 to both sides of the equation. We now have 18 = 3x, divide both sides by 3 and you have your answer.

Hence, X = 6.

The (i,j) minor of a matrix A is the matrix Aij obtained by deleting row i and column j from A it is true.

The (i,j) minor of a matrix A is the matrix Aij obtained by deleting row i and column j from A. A determinant of an n×n matrix can be defined as a sum of multiples of determinants of (n−1)×(n−1) sub matrices.

This is done by deleting the row and column which the elements belong and then finding the determinant by considering the remaining elements. Then find the co factor of the elements. It is done by multiplying the minor of the element with -1i+j. If Mij is the minor, then co factor, [tex]c_{ij}[/tex] [tex]= -1^{i+j}[/tex] + [tex]m_{ij}[/tex].

Each element in a square matrix has its own minor. The minor is the value of the determinant of the matrix that results from crossing out the row and column of the element .

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