Write each proof. Finish the table.

Using proportion, the number of liters of soda needed would be 52.5 liters.

Proportion can be described as an equation that relates two equal ratio to each other.

If you need 7 liters of soda for every 12 guests, and you have 90 guests, you can use the proportion:

7 liters / 12 guests = x liters / 90 guests.

To find the number of liters of soda you need, you can cross-multiply and solve for x:

12x = 7(90)

12x = 630

x = 630/12

x = 52.5

So, you need 52.5 liters of soda for 90 guests.

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The equation is 2x + 6x = 48. Then the unknown number will be 6.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The sum of double a number and six times a number is 48.

Let the unknown number be 'x'. Then the equation is given as,

2x + 6x = 48

Simplify the equation, then the value of 'x' is given as,

2x + 6x = 48

8x = 48

x = 48 / 8

x = 6

The equation is 2x + 6x = 48. Then the unknown number will be 6.

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5518 is the quotient of 154,504 divided by 28.

A division is a process of splitting a specific amount into equal parts.

The quotient of 154, 504 divided by 28 is 5518 after applying the arithmetic operation.

Long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals that is simple enough to perform by hand.

Hence, 5518 is the quotient of 154,504 divided by 28.

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Let x be the cost of each drink.

The total cost for all four teachers' meals can be represented using the distributive property:

4(3.99 + x) = 20.32

Expanding and solving for x:

15.96 + 4x = 20.32

Subtracting 15.96 from both sides:

15.96 -15.96 + 4x = 20.32 -15.96

4x = 4.36

Dividing both sides by 4:

x = 1.09

Hence, each drink cost $1.09

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Answer:

Step-by-step explanation:

grew graph B for graph A

If the shaded area is 112 cm², then the length x in the figure is 7cm.

The area of Rectangle is length times of width.

Split the shape into two rectangles:

then you have two areas:

x×10 and x×6

the shaded area is given as 112cm²

10x+6x=112

Add the like terms

16x=112

Divide both sides by 16

x=112/16

x=7 cm

Hence, if the shaded area is 112 cm², then the length x in the figure is 7cm.

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The average number of yards per completed pass is 11.

In order to determine the number of yards per completed pass, divide the total yards completed by the total number of passes.

Division is the process of dividing a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

Number of yards per completed pass = total number of yards / total number of passes = 286 / 26 = 11

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see attachment..........

Answer:

  x = 4 . . . cm

Step-by-step explanation:

You want the measure of the segment CE from external point C to circle O, given several other dimensions of chords and segments in the circle.

As in the attachment, we can extend segment DO across the circle to make diameter DX. Then we can use the relation for chord lengths to find the radius of the circle (r).

Segments of crossing chords have the same product:

  FA·FE = FD·FX

  7·4 = 2·(2r -2) . . . . . use given segment values

  14 = 2r -2 . . . . . . divide by 2

  16 = 2r . . . . . . . add 2

  r = 8 . . . . . . . divide by 2

The radius of the circle is 8 cm.

We can also extend radius EO across the circle to make diameter EY, as shown in the attachment.

The relation involving the product of secant segments can be used to find x:

  CE·CY = CB·CA

  x(x +16) = 5(5+4+7)

  x² +16x = 80 . . . . . . . . simplify

  x² +16x +64 = 144 . . . . . . . add 64 to complete the square

  (x +8)² = 12² . . . . . . . . . write as squares

  x +8 = 12 . . . . . . . . positive square root

  x = 4 . . . . . . . . subtract 8

The value of x is 4.

__

Additional comment

The attachment is accurately drawn.

For the given case, the  the range of values for the length of the run using inequalities is  4 < l < 8.5.The equation for the area of a rectangle is A = w x l, where w is the width and l is the length.

To find the range of values for the length of the run, we need to set up an inequality equation. We know the width is 4cm, so A = 4l > 50m2. This can be rearranged to 4l > 50m2, and then divided by 4 to get l > 50/4m2, which gives us l > 12.5m. This means that the length of the run must be greater than 12.5m.  

We also know that Ben has a maximum of 34m of fencing to use, so l < 34/4m, which gives us l < 8.5m. This means that the length of the run must be less than 8.5m.  Therefore, the range of values for the length of the run using inequalities is 4 < l < 8.5m.

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The solution of the system of equations:

is (-3, 6)

Here we want to solve the system of equations below:

y = -5x + 21

-4x + y = 6

We can use the elimination method to solve this if we take the difference between the two equations, we will get:

y - (-4x + y) = -5x - 21 - 6

4x = -5x - 27

Now we can solve this for x.

4x + 5x = -27

9x = -27

x = -27/9 = -3

And the value of y is given by:

y = -5x - 21  (we need to evaluate that on x = -3)

y = -5*-3 - 21

y =  15 - 21 = 6

The solution is (-3, 6).

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Answer: Elimination : (-3,-6) Substitution : (5/3,38/3)

Step-by-step explanation: Elimination : y = -5x + 21;-4x + y = 6                                                   y - (-4x + y) = -5x - 21 - 6                                     4x = -5x - 27                                                                       4x + 5x = -27                                                           9x/9 = -27/9                                                                           x = -3                                                                                          y = -5x - 21 y = (-5) (-3) - 21   y = 15 - 21                                                                               y = -6                                                                                       (-3,-6) Substitution : y = -5x + 21;-4x + y = 6 −4x + −5x + 21 = 6 −9x + 21 - 21 = 6 - 21 -9x/-9 = -15/-9 x = 5/3 y = −5x + 21 y = −5 (5/3) + 21 (-25) (1) + (21) (3) / (3) (1) -25/3 + 63/3 y = 38/3 (5/3,38/3)

The line crosses the vertical axis at 400, so the equation has to be "C = something + 400".

If you pick any point and go up 100 and over 200, you get back on the line, so the slope is 100/200 or 1/2

Option C: C = 1/2 N + 400

Answer:

C. 1/2N +400

Step-by-step explanation:

So the 400 is reqiured in the equation as

x =0 , y= 400.

To find the slope you can do rise over run:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex] =

[tex]\frac{500-400}{200-0} =\frac{100}{200} =\frac{1}{2}[/tex]

Answer: its A

Step-by-step explanation:

Answer:

step 6

Step-by-step explanation:

The work done by student is 145.9 W.To calculate the work done by the student:

Work = Force x Distance = 565 N x 3.25 m = 1841.25 J

Calculate the power output:

Power = Work/Time = 1841.25 J/12.6 s = 145.9 W

Power is the quantity of energy that is transported or transformed per unit of time in physics. The watt, or one joule per second, is the unit of power in the International System of Units. Power is also referred to as activity in ancient writings. A scalar quantity is power.

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Step-by-step explanation:

-13 on both sides

/ by -7 on both sides

flip the ineq sign bcus u divided by a negative

x < -5.86

The equation which is required to solve how many of each board John needs is x + x - 7 = 23.

The number of 20-foot boards is 15.

The number of 16-foot boards is 8.

As per the given data, John needs 23 boards to build rafters for his house.

He can use 16-foot or 20-foot length boards.

He needs seven fewer 16-foot boards than 20-foot boards.

Here we have to determine how many of each board John needs.

Let the number of 20-foot boards be x.

Then the number of 16-foot boards be x - 7.

Total number of boards are 23.

Equation to determine how many of each board John needs:

x + x - 7 = 23

2x - 7 = 23

2x = 23 + 7

2x = 30

x = 15

The number of 20-foot boards are 15.

The number of 16-foot boards are x - 7

= 15 - 7

= 8

The number of 16-foot boards are 8.

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The solution set for the given graph is (2,1). The solution has been obtained using linear equations.

What is a linear equation?

It is a linear equation that has the greatest degree of one. In a linear equation with an exponent greater than one, this indicates that there are no variables. A straight line is produced on the graph by this equation.

We are given two lines on the graph

The points of the red line are (3,0) and (0,3)

So, the equation of the line comes out to be

y=−x+3      ...(1)

The points of the blue line are (3,2) and (-1,-2)

So, the equation of the line comes out to be

y=x−1     ...(2)

To find the solution set, we need to solve the equations

Substituting (1) in (2), we get,

⇒−x+3 = x−1

⇒−2x = -4

⇒x = 2

So, y = 1

Hence, the solution set for the given graph is (2,1).

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N(u) = 4, where N is the function and u is the independent variable, is the function that is provided.

The input values for a particular function are shown by the independent variable (x).An experiment involves controlling the independent variables while it is being conducted.

The results of the function are shown by the dependent variable (y). In an experiment, a variable that stands in for a variable being changed is known as an independent variable.As the independent variable in an equation, x is frequently employed as its symbol.

N(u) = 4, where N is the function and u is the independent variable, is the function that is provided.

Since u is no longer a variable, the value of the function N(u) is now a constant.

As a result, the N(u) function will always equal 4 for all values of the variable u, making it a constant function.

Thus, N(4) = 4. ( Answer )

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The total number of boys enrolled in the course is 170.

Here are 374 children, are there are 5 boys to every 6 girls.

If the ratio of boys to girls is 5 to 6, then 5 out of every 11 students are boys and 6 out of every 11 students are girls.

Set up a proportion for the boys, where b = the total number of boys.

5/11 = b/374

11b = 1870

b = 1870/11

b = 170

There are 170 boys.

The total number of student is 374, so the number of girls, is 374 -b.

There are 374-170= 204 girls.

Finding a proportionality constant would be another algebraic solution to this issue. The total number indicated by the ratio is 5 + 6 or 11, which is equal to the total number of children when multiplied by the proportionality constant.

Let x = the proportionality constant

11x=374

x=34

The number of boys is 5x and the number of girls is 6x.

5x=5×34 =170 boys

6x=6×34 =204 girls.

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The point at which the triangle's three interior angle bisectors intersect appears to be the incenter.

The incenter of a triangle seems to be the point at which the triangle's three interior angle bisectors intersect. This point is equidistant from the triangle's sides.

∠ARU angle = 40°

AU length = 20°

∠QPA = 35°

A diagram is included here.

AR is the angle bisector of angle URK.

As a result, ∠ARU = ∠ARK = 40°.

Because the incenter point is equidistant from the triangle's sides.

As a result, AT = AU = AK = 20.

Because PA is the angle bisector of angle QPU.

As a result, ∠QPA = ∠UPA.

3x + 2 = 4x - 9

4x - 3x = 9 + 2

x = 11

Changing the value of x in the angle 3x + 2

We obtain ∠QPA = 3(11) + 2 = 35°.

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Answer:

7units

Step-by-step explanation:

The quadrilateral is parallelogram because the opposite sides are parallel and congruent

What is a parallelogram?

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. The Sum of all the interior angles equals 360 degrees.

Since WZ and XY are congruent and XW and YZ are congruent and Also, WZ and XY are parallel and XW and YZ are parallel, we can therefore say that the quadrilateral obeys the property of a parallelogram.

parallel lines are two straight lines that can not meet at a point.

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If Mccay purchased a home in a flood zone for $26500 , and the value depreciates by 2.5% , then the value of house after 5 years will be $23349     .

the current value of Mccay's house is = $26500  ;

the percent decrease in the value of the house is = 2.5% per year ;

let the number of years be = "n" years ;

we know that 2.5% is = 0.025 ;

the Depreciated Value(V) of the house can be written as :

V = 26500(1 - 0.025)ⁿ ;

to  find the value of house after 5 years we substitute n = 5 ;

V = 26500(0.975)⁵ = 23349.035

V = 23349 .

Therefore , the value of the house after 5 years will be $23349  .

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The bakery will not have enough time to bake 10 batches of bagels in 6 hours.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

Given that,

There is a time limit of 6 hours to make 10 batches of bagel.

Time needed to make 1 batch of bagel = 3/4 hour

Time needed to make 10 batches of bagel = 10 × (3/4)

                                                                        = 30 / 4

                                                                        = 7.5 hours

Hence at least 7.5 hours is needed to make 10 batches of bagel.

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This post is about the author's experience at an alternative school, which they have been attending since freshman year. They have had the opportunity to explore their interests and develop their own unique learning style with the support of teachers. The atmosphere of the school is friendly and encouraging and the author is very grateful for the experience they have had. They recommend the school to anyone looking for an alternative learning experience.

My name is _________, and I'm a senior at an alternative school. I've been attending this school since my freshman year, and it has been an amazing experience.

At this school, I've been able to explore my interests and develop my own unique learning style. The teachers are supportive and caring, and they encourage students to actively participate in their education. I've had the opportunity to take classes that I'm passionate about and have even been able to design my own coursework.

The atmosphere of the school is also a great one. Everyone is friendly and willing to help each other out. There's no judgement or pressure. We all come from different backgrounds, but that doesn't stop us from working together and having a great time.

I'm so grateful for the experience I've had at this school. It has been an incredible journey, and I am so proud of what I have accomplished. I have grown so much as a person and have had so many opportunities to explore my interests.

I would highly recommend this school to anyone looking for an alternative learning experience. It has been a great place to learn, and I will miss it when I graduate.

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The required Product of the given two expression is  x³ - 9x² - 22x - 24.

The process of multiplying two provided expressions made up of variables and constants is known as the multiplication of algebraic expressions. An expression that uses integer constants and variables together is called an algebraic expression.

We have given,

(x+6)(x²-3x-4)

= x(x²) - x(3x) - 4x + 6x² - 6(3x) - 24

= x ³ - 3x² - 4x - 6x² - 18x - 24

=  x³ - 9x² - 22x - 24

Thus, required product of the given two expression is  x³ - 9x² - 22x - 24.

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The two expression given has a necessary Product of x3 - 9x2 - 22x - 24.

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The volume of a pyramid with a base area of 15 square inches and a height of 7 inches will be 35 cubic inches.

Suppose the base of the pyramid has length = L units and width = W units, slant height = K units, and the height of the pyramid is of H units.

Then the volume of the pyramid will be

V = (L × B × H) / 3

V = (Base area x H) / 3

The volume of a pyramid varies jointly with the base area of the pyramid and its height.

The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches.

Then the volume of a pyramid with a base area of 15 square inches and a height of 7 inches will be

V = (15 x7) / 3

V = 35 cubic inches

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Answer: With 4/3 cups of sugar, Kris can make (4/3) / (2/3) = 2 batches of cookies.

Step-by-step explanation: