Find the measure of each numbered angle.





Fill in your answers below:

m<1 =

m<2 =

m<3 =

m<4 =

Answer:

3 berries

Explanation:

Opportunity costs for the Orange group:

Opportunity cost of pumping 1 gallon of water = 3/1 = 3 berries

Opportunity cost of picking 1 berry = 1/3 = 0.333 gallons of water

Opportunity costs for the Yellow group:

Opportunity cost of pumping 1 gallon of water = 8/2 = 4 berries

Opportunity cost of picking 1 berry = 2/8 = 0.25 gallons of water

Opportunity cost for both groups combined:

Opportunity cost of pumping 1 gallon of water = 3 berries (Orange group should pump water since opportunity cost is lower)

Opportunity cost of picking 1 berry = 0.25 gallons of water (Yellow group should pick berries since opportunity cost is lower)

Opportunity costs are the extra costs or benefits lost resulting from choosing one investment or activity over another alternative. In this case, people can either pump water or pick berries, but they cannot do both at the same time. When they are pumping water, the opportunity cost is the amount of berries that they will not be able to collect, and vice versa.

Answer:

Its AA similarity theorem

Step-by-step explanation:

correct on edge 2021

The triangles ABC and EDC are similar by AA similarity theorem.

Two triangles are said to be similar if their corresponding sides are in equal ratio and corresponding angles are congruent.

Given is a proof of showing △ ABC ~ △ EDC

The proof is as follows :-

           Statement                                                Reason

            AB ∥ DE                                                     Given

         ∠ ACB = ∠ ECD                           definition of vertical angles  

         ∠ BDE ≅ ∠ DBA                   alternate interior angles are congruent

         △ ABC ~ △ EDC                                 AA similarity theorem

AA similarity theorem :-

AA similarity theorem states that when two corresponding angles of two triangles are found congruent then the triangles are similar by AA similarity theorem.

Hence, the missing reason is AA similarity theorem.

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Answer:

13.5

Step-by-step explanation:

Answer:

The perimeter of triangular sign is 12x+3

Step-by-step explanation:

Length of side1 of triangle = x inches

Length of side2 of triangle = 4x-5 inches

Length of side3 of triangle = 7x+8 inches

We need to find perimeter of triangular sign.

The formula used is: [tex]Perimeter \ of \ triangle = Sum \ of \ all \ three \ sides[/tex]

Now, finding perimeter of triangular sign:

[tex]Perimeter \ of \ triangle = Sum \ of \ all \ three \ sides\\Perimeter \ of \ triangle = x+4x-5+7x+8\\Perimeter \ of \ triangle = x+4x+7x-5+8\\Perimeter \ of \ triangle = 12x+3[/tex]

The perimeter of triangular sign is 12x+3

Answer:

b is correct

Step-by-step explanation:

The product of the functions M(x) and n(x) is x³+ 4x².

To find the product of the two functions, M(x) = x² + 4x and n(x) = x, we need to multiply them together.

So, (mn)(x) = M(x) × n(x)

Substituting the given functions:

(mn)(x) = (x² + 4x) × x

Now, we can simplify the expression by applying the distributive property of multiplication:

(mn)(x) = x × x² + x × 4x

Simplifying further:

(mn)(x) = x³ + 4x²

Therefore, the product of the functions M(x) and n(x) is x³+ 4x².

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Answer:

9

Step-by-step explanation:

DB^2=AD^2+AC^2

15^2=12^2+AC^2

AC^2=225-144

AC^2=81

AC=√81

AC=9

Answer:

f(x)=60c * 24h

Step-by-step explanation:

Hope this helped!

Answer:

Step-by-step explanation:

Given sequence:

This is not AP as the difference in terms is not common

This is GP with the common ratio of -2 as:

Correct choice is (C)

Answer:

Step-by-step explanation:

Chen is 44 inches tall

Answer:

7?

Step-by-step explanation  :

yo creo que si

Answer:

The present age of the artifact is 1,600 years

Step-by-step explanation:

let the present age of the artifact = x

let the present age of the book, = y

x = 4y ---- equation (1)

x + 200 = 3(y + 200) ------equation (2)

x + 200 = 3y + 600

substitute in the value of x into the equation;

4y + 200 = 3y + 600

4y - 3y = 600 - 200

y = 400

Then, x = 4 x 400

x = 1,600 years

Therefore, the present age of the artifact is 1,600 years

Answer:

The present age of the artifact is 1,600 years  

Step-by-step explanation:  

let the present age of the artifact = x  

let the present age of the book, = y  

x = 4y ---- equation (1)  

x + 200 = 3(y + 200) ------equation (2)  

x + 200 = 3y + 600  

substitute in the value of x into the equation;  

4y + 200 = 3y + 600  

4y - 3y = 600 - 200  

y = 400  

Then, x = 4 x 400

x = 1,600 years

Answer:

John has 357 marbles left.

Step-by-step explanation:

120 marbles went to Bob

48 went to Pat

and 75 to Matt.

Answer:

Number of hamburgers sold each day at Hamburger Mary's because it's counting a number of something, not measuring a quantity with respect to a variable like temperature or weight. If this is still unclear let me know what I need to clarify. Have a nice night.

Answer:

24x

Step-by-step explanation:

Multiply  − 6  by  − 4 .

Answer:

24

Step-by-step explanation:

you multiply negative 4 by negative 6

If there are 3 boys for every 4 girls in a class, there would be 12 boys because 16 ÷4 us 4, and 4×3 is 13.

Answer:

8 large glasses can be filled by a large bottle.

Step-by-step explanation:

First we calculate the volume of a small bottle:

Now we calculate the volume of a small glass:

" A small bottle fills 6 small glasses with no juice left over.", this means that

Then we calculate the volume of a large glass:

Finally we divide the volume of a large bottle by the volume of a large glass:

So 8 large glasses can be filled by a large bottle with juice left over.

Answer:

ill Put the answer in the comments if you give a pic of the image for this problem

Step-by-step explanation:

Answer:

-7 and 7

Step-by-step explanation:

Answer:

The sum of the first 12 terms of the sequence is 2703.673096

Step-by-step explanation:

The nth term of a geometric progression is a(n) = [tex]ar^{n-1}[/tex], where

The sum of n terms of the geometric progression is s(n) = [tex]\frac{a(r^{n}-1)}{r-1}[/tex]

∵ The third term of a geometric progression is [tex]\frac{63}{4}[/tex]

∴ a(3) = [tex]\frac{63}{4}[/tex]

∵ a(3) = ar²

→ Equate its two right sides

∴ ar² =  [tex]\frac{63}{4}[/tex] ⇒ (1)

∵ The sixth term is [tex]\frac{1701}{32}[/tex]

∴ a(6) = [tex]\frac{1701}{32}[/tex]

∵ a(6) = a[tex]r^{5}[/tex]

→ Equate its two right sides

∴ a[tex]r^{5}[/tex] =  [tex]\frac{1701}{32}[/tex] ⇒ (2)

→ Divide (2) by (1)

∴ r³ = [tex]\frac{27}{8}[/tex]

→ Take ∛  for both sides

∴ r = [tex]\frac{3}{2}[/tex] = 1.5

→ Substitute the value of r in (1) to find a

∵ a(1.5) = [tex]\frac{63}{4}[/tex]

∴ 1.5a = 15.75

→ Divide both sides by 1.5

∴ a = 10.5

→ Let us find the sum of the first 12 terms

∵ n = 12, a = 10.5, and r = 1.5

→ Substitute them in the rule of the sum above

∵ s(12) = [tex]\frac{10.5(1.5^{12}-1)}{1.5-1}[/tex]

∴ s(12) = 2703.673096

∴ The sum of the first 12 terms of the sequence is 2703.673096

The measure of one side of a square is (s + 3) inches long. The pair of expressions which both represents the perimeter of this square is:

d) 4( s + 3 ) and (s + 3) + (s + 3) + (s + 3) + (s + 3)

Answer:

D is the correct answer.

Answer:

its the 4/7x 28

Step-by-step explanation:

you count by 2 and then you look for the numbers

Answer:

THE OTHER PERSON IS WRONG DO NOT LISTEN YOUNG ONE

Step-by-step explanation:

THE ANSWER IS D, 2/7 x 28

Answer: