A principal evenly distributes 6 reams of copy paper to 8 fifth-grade teachers.
a. How many reams of paper does each fifth-grade teacher receive? Explain how you know using pictures, words, or numbers.
b. If there were twice as many reams of paper and half as many teachers, how would the amount each teacher receives change? Explain how you know using pictures, words, or numbers.

The properties of triangle side lengths follow the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side, leading to three correct inequalities for Triangle EFG.

The question presented is related to the properties of triangle sides, specifically in relation to the inequality theorems that apply to triangles.

By understanding these properties, we can determine which statements about the lengths of the sides in triangle EFG are true.

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

This theorem gives rise to three inequalities that must hold true for any triangle:

To assess which statements about Triangle EFG are true, we can compare them against the principles derived from the Triangle Inequality Theorem.

The following are the correct statements based on this theorem:

Any statement that contradicts these principles is false.

Therefore, the three true statements regarding Triangle EFG are that EF + FG is greater than EG, EG + FG is greater than EF, and EG - FG is less than EF.

The three true statements regarding Triangle EFG are:
- EF + FG > EG
- EG + FG > EF
- EG + EF < FG

Let's go through each option one by one:

1. E F + F G greater-than E G: To determine if this statement is true, we need to compare the lengths of EF and EG combined with FG. Let's say EF is 5 units long, FG is 3 units long, and EG is 7 units long. In this case, 5 + 3 is equal to 8, which is greater than 7. Therefore, this statement is true.

2. E G + F G greater-than E F: Similarly, to determine if this statement is true, we need to compare the lengths of EG and FG combined with EF. Using the same lengths as before, 7 + 3 is equal to 10, which is greater than 5. Therefore, this statement is true as well.

3. E G minus F G less-than E F: For this statement, we need to subtract the length of FG from EG and compare it to EF. Using the same lengths as before, 7 - 3 is equal to 4, which is less than 5. Therefore, this statement is false.

4. E F minus F G greater-than E G: Here, we need to subtract the length of FG from EF and compare it to EG. Using the same lengths as before, 5 - 3 is equal to 2, which is less than 7. Therefore, this statement is false.

5. E G + E F less-than F G: To check this statement, we need to compare the lengths of EG and EF combined with FG. Using the same lengths as before, 7 + 5 is equal to 12, which is greater than 3. Therefore, this statement is true.

Complete question :-

Answer:

Input

Independent variable

Step-by-step explanation:

we know that

Independent variables, are the values that can be changed or controlled in a given model or equation

Dependent variables, are the values that result from the independent variables

we have the function

[tex]d(t)=50t[/tex]

In this problem

The function d(t) represent the dependent variable or the output

The variable t represent the independent variable or input

Answer:

input and independet variable                                        

Step-by-step explanation:

Answer:

7,497.50 OR, 7,497 &1/2 in fraction form

Step-by-step explanation:

I got this answer by dividing 14,995 by 2 and got $7,497.50 hope this helps you mark as brailiest if best answer if any questions comment on this question below!! ThNks !!

Answer:

7,497.50

Step-by-step explanation:

Answer:

no. it is not because 0.6 is a decimal

Answer:

d=1/2

Step-by-step explanation:

9(8d-5)+13=12d-2

1) Use the distributive property:

72d-45+13=12d-2

2) Combine alike terms:

72d-32=12d-2

3) Add 32 to both sides:

72d=12d+30

4) Subtract 12d on both sides:

60d=30

5) Divide both sides by 60:

d=30/60

6) Simplify 30/60 to 1/2

Answer:

x = 10

Step-by-step explanation:

collect like terms, so add 5 to both sides: 2x = 20

divide both sides by 2 to get the value of x: x = 10

Answer:

x=10

Step-by-step explanation:

first, add 5 to both sides. the -5 and +5 cancel out, and 15 + 6 is 20. 2x=20. now divide 2 on both sides. the 2s cancel out and 20/2 is 10, so x=10.

Answer:

x = - 3 is extraneous

Step-by-step explanation:

Given

[tex]\sqrt{x+7}[/tex] - 1 = x  ( add 1 to both sides )

[tex]\sqrt{x+7}[/tex] = x + 1 ( square both sides )

x + 7 = (x + 1)² ← distribute right side

x + 7 = x² + 2x + 1 ( subtract x + 7 from both sides )

0 = x² + x - 6 ← in standard form

0 = (x + 3)(x - 2) ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

As a check

Substitute these values into the equation and if both sides are equal then they are the solutions.

x = - 3 : [tex]\sqrt{-3+7}[/tex] - 1 = [tex]\sqrt{4}[/tex] - 1 = 2 - 1 = 1 ≠ - 3

x = 2 : [tex]\sqrt{2+7}[/tex] - 1  = [tex]\sqrt{9}[/tex] - 1 = 3 - 1 = 2

x = 2 is a solution and x = - 3 is extraneous

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____________________

Step-by-step explanation:

Look at the photo below for the answer.

:)

Answer:

Step-by-step explanation:

Answer:

For points :  (2, 12) and (6, 11)

, option A. is correct.

For points : (6, –1) and (–3, –1), option B. is correct

Step-by-step explanation:

We are given points in both the questions and we need to find the slope.

Slope refers to steepness of curve .It is basically change in y with change in x.

For two points [tex]P\left ( x_1,y_1 \right )\,,\,Q\left ( x_2,y_2 \right )[/tex], slope of line PQ is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

For points : (2, 12) and (6, 11)

Let [tex]P\left ( x_1,y_1 \right )=(2, 12)\,,\,Q\left ( x_2,y_2 \right )=(6, 11)[/tex],

Slope is [tex]\frac{11-12}{6-2}=\frac{-1}{4}[/tex] i.e, - 1 over 4

So, option A. is correct.

For points : (6, –1) and (–3, –1)

Let [tex]P\left ( x_1,y_1 \right )=(6, -1)\,,\,Q\left ( x_2,y_2 \right )=(-3, -1)[/tex]

Slope is [tex]\frac{-1+1}{-3-6}=\frac{0}{-9}=0[/tex]

So, option B. is correct

The required slope of the lines with the given coordinates are as follow,

For first line option A. -1/4

For second line option B.0.

For the first set of coordinates of the line,

Points  are (2, 12) and (6, 11)

let (x₁ , y₁ ) = (2, 12 )

( x₂ , y₂ ) = (6, 11 )

Slope of the line for the two coordinates (x₁ , y₁ ) = (2, 12 ) and

( x₂ , y₂ ) = (6, 11 ) is equal to

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substitute the value ,

m = ( 11 - 12 ) / ( 6 - 2 )

   = -1 / 4

For the second set of coordinates of the line,

Points  are (6, -1) and (-3, -1)

let (x₁ , y₁ ) = (6, -1 )

( x₂ , y₂ ) = (-3, -1 )

Slope of the line for the two coordinates (x₁ , y₁ ) = (6, -1 ) and

( x₂ , y₂ ) = (-3, -1 ) is equal to

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substitute the value ,

m = ( -1 - (-1) ) / ( -3 - 6 )

   =0 / -9

   = 0

Therefore, slope of the lines are option A. -1/4 and option B.0.

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Answer:

60 cm

Step-by-step explanation:

Parallelogram ABCD is shown in attached diagram. The diagonals of the parallelogram bisect each other, so

AE = EC

BE = ED

Ib DE = 3y + 6 cm, BE = 5y - 10 cm, then

[tex]3y+6=5y-10\\ \\3y-5y=-10-6\\ \\-2y=-16\\ \\2y=16\\ \\y=8\ cm[/tex]

Now, EC = 2y + 4, so

[tex]EC=2\cdot 8+4=16+4=20\ cm[/tex]

Since AE = EC, then AE = 20 cm

The brace that connects points B and D has the length

[tex]BD=BE+ED=3y+6+5y-10=8y-4=8\cdot 8-4=64-4=60\ cm[/tex]

The brace that connects points A and C has the length

[tex]AC=AE+EC=20+20=40\ cm[/tex]

Answer:

60cm

Step-by-step explanation:

Answer:

number of servings = 5 servings

Explanation:

We are given that each serving is 3/10 of a pint. To know the number of servings of 1.5 pints, we will simply use cross multiplication as follows:

1 serving ....................> 3/10 pint

?? servings ................> 1.5 pints

number of servings = (1.5*1) / (3/10)

number of servings = 5 servings

Hope this helps :)

Answer:

11/2-3/4

11-6/2=5/2

Step-by-step explanation:

Answer:

9 = x; (9, -1)

Step-by-step explanation:

-y₁ + y₂\-x₁ + x₂ = m

-5 - 1\-8 + x

-8 + x = 1

+8 + 8

_________

x = 9

The denominator is set to equal one because the numerator already equals negative six, and all we have to do is divide it by a POSITIVE one to stay at negative six.

I am joyous to assist you anytime.

The other number could be 6. The GCF of 6 and 24 is 6, and 6 is less than 30.

[tex]\huge\boxed{\text{A.}\ x=-3}[/tex]

Start by subtracting [tex]2x[/tex] from both sides of the equation. Our goal is to isolate the variable. [tex]5+4x=-7[/tex]

Now, subtract [tex]5[/tex] on both sides. [tex]4x=-12[/tex]

Finally, divide both sides by [tex]4[/tex]. [tex]x=\boxed{-3}[/tex]

Answer:

A. x = -3

Step-by-step explanation:

5 + 6x = 2x - 7

5 + 7 = 2x - 6x

12 = -4x

12/-4 = x

-3 = x

Answer:

-12

Step-by-step explanation:

3(x-4)+2x^2

when x =5 , sub 5 into x

3(5-4)+2(5)-(5)^2

=15-12+10-25

=-12

Answer:

Step-by-step explanation:

3(x-4)+2x-x^2 first you should eliminate the parentheses

3x-12+2x-x^2 now replace x for 5

3(5)-12+2(5)-(5)^2

15-12+10-25

-12

Answer:

Step-by-step explanation:

Answer:

the new height will be:

d.168 inches

Answer:

168 inches

Step-by-step explanation:

First, 12.6 times 9 is 113.4. So withouth the space, that is how long the busses are. Then you do 2meters times 8 is 16 meters between the busses. 113.4+16 equals 129.4, the final answer.

Answer:  The total length from the front of the first bus to the end of the last bus is 129.4 meters.

Step-by-step explanation:

Hi, to answer this question we have to multiply:

The number of buses by the length of each one

The number of spaces between buses by the length of each space.

Since there is no space in front of the first bus and behind the last bus, there are 8 spaces in between.

Feel free to ask for more if needed or if you did not understand something.  

Answer:

5x^2 − 2x

Step-by-step explanation:

Let's simplify step-by-step.

=3x + 6x^2 + − 5x + − x^2

Combine Like Terms:

=3x + 6x^2 + − 5x + − x^2

=( 6x^2 + − x^2 ) + ( 3x + − 5x )

= 5x^2 + − 2x

Answer:

5x^2 − 2x

hope this helps!!

Answer:

8ft.

Step-by-step explanation: If you are finding he area, 2 times 4 equals 8, so the answer would be 8 feet.

Answer:

x = - 7, x = 1

Step-by-step explanation:

Given

x² + 6x = 7

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(3)x + 9 = 7 + 9

(x + 3)² = 16 ( take the square root of both sides )

x + 3 = ± [tex]\sqrt{16}[/tex] = ± 4 ( subtract 3 from both sides )

x = - 3 ± 4

x = - 3 - 4 = - 7

x = - 3 + 4 = 1

Solution set = { - 7, 1 }

Answer:

a = 7/2

Step-by-step explanation:

2x - y - 5 = 0

2x = y + 5

y = 2x - 5

m = -1/2

y - 5 = -1/2(x - (-2))

y - 5 = -1/2(x + 2)

y - 5 = -x/2 - 1

y = -x/2 + 4

a = -1/2 + 4

a = 7/2

Answer:

divide it using a calculator

Answer:

Step-by-step explanation:

0.65 is your answer

Answer:

25.

Step-by-step explanation:

2/3 of 300 is 200

1/4 of 300 is 75

Answer:

25

Step-by-step explanation:

2/3 of 300 is 200  

1/4 of 300 is 75

Answer:

4700

Step-by-step explanation:

4 thousands = 4000

7 hundreds = 700

Add those numbers together and you get 4700

Hope this helps

88.6 as a mixed number is 14 2/3

-615

I'm assuming you meant this. (6*7) - (3^2) *(9+4^3)

(42) - (3^2) * (9+4^3)

(42) - (9) * (9+4^3)

(42) - (9) * (9+64)

(42) - (9) * (73)

42 - 657

-615

Hope this helps!

Answer: Line slopes:

m1= 3/2 defined by points (5,3) and (7,6)

m2= -2/3 defined by points (7,6) and (4,8)

m3 = 3/2 defined by points (4,8) and (2,5)

m4 = -2/3 defined by points (2,5) and (5,3)

All comply the orthogonal slopes rule (90º)

Step-by-step explanation:

As those 4 point define a polygon, to check is that polygon is a rectangle, you need to compare the slopes of the lines defined by the 4 points and check that accomplish the following rule:

m1 = -(1/m2). this shows that the slopes are intersected in 90º angle.

Final answer:

By calculating the dot products of the direction vectors for adjacent sides, all of which are zero, and checking the distances of opposite sides, which are equal, we prove that the given quadrilateral is a rectangle.

Explanation:

To prove that a quadrilateral with given vertices is a rectangle, we must show that the quadrilateral has four right angles and opposite sides are equal. A right angle exists between two sides if the dot product of their direction vectors is zero, as this indicates perpendicularity. Equal length of opposite sides can be shown by the distance formula. We are given the vertices of the quadrilateral: (2,5), (4,8), (7,6), and (5,3).

Calculate the direction vectors of adjacent sides:

AB: (4-2, 8-5) = (2,3)

BC: (7-4, 6-8) = (3,-2)

CD: (7-5, 6-3) = (2,3)

DA: (2-5, 5-3) = (-3,2)

Check the dot products of the direction vectors of adjacent sides to confirm right angles:

AB · BC = (2)(3) + (3)(-2) = 6 - 6 = 0

BC · CD = (3)(2) + (-2)(3) = 6 - 6 = 0

CD · DA = (2)(-3) + (3)(2) = -6 + 6 = 0

DA · AB = (-3)(2) + (2)(3) = -6 + 6 = 0

Use the distance formula to confirm equal lengths of opposite sides:

AB = √((4-2)² + (8-5)²) = √(13)

CD = √((7-5)² + (6-3)²) = √(13)

BC = √((7-4)² + (6-8)²) = √(13)

DA = √((2-5)² + (5-3)²) = √(13)

Since all adjacent sides are perpendicular and opposite sides are of equal length, the quadrilateral is a rectangle.

Answer:

240 liters

Step-by-step explanation:

because the tank holds 240 liters so if it's full then it will be the same

In the tank, there are 240 liters of water, as mentioned in the given condition. Option A is correct.

Given that

A tank holds 240 liters of water.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
As mentioned in the condition the tank can hold 240 liters of water, so as of the given data when the tank is full there can only be 240 liters of water.

Thus, In the tank, there are 240 liters of water, as mentioned in the given condition. Option A is correct.

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Answer:

[tex]2^3(2^4)=2^{3+4}=2^7=2(2)(2)(2)(2)(2)(2)[/tex]

Step-by-step explanation:

You can write 2 as a factor of [tex]2^3 \times 2^4[/tex] 7 times

The given expression can be written mathematically as:

[tex]2^3 \times 2^4[/tex]

We can simplify the expression by using the rule of indices shown below:

[tex]a^b \times a^b = a^{b+c}[/tex]

Applying the rule above to the given expression:

[tex]2^3 \times 2^4\\\\2^{3+4}\\\\2^7[/tex]

Therefore [tex]2^3 \times 2^4 = 2^7[/tex]

You can write 2 as a factor of [tex]2^3 \times 2^4[/tex] 7 times

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