What do i put in the boxes ?…

a) The value of x from the proportion is x = 2/5

b) The value of x from the proportion is x = 8

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the value of A is

a)

3 / ( x + 2 ) = ( 5 / 4 )   be equation (1)

On simplifying the equation , we get

Multiply by ( x + 4 ) on both sides of the equation , we get

( 5/4 ) ( x + 2 ) = 3

Multiply by 4 on both sides of the equation , we get

5 ( x + 2 ) = 12

On further simplification , we get

5x + 10 = 12

Subtracting 10 on both sides of the equation , we get

5x = 2

Divide by 5 on both sides of the equation , we get

x = 2/5

Therefore , the value of x is 2/5

b)

( x + 2 ) / 5 = ( x - 2 ) / 3   be equation (2)

On simplifying the equation , we get

Multiply by 5 on both sides of the equation , we get

( x + 2 ) = 5( x - 2 ) / 3

Multiply by 3 on both sides of the equation , we get

3 ( x + 2 ) = 5 ( x - 2 )

On further simplification , we get

3x + 6 = 5x - 10

Subtracting 3x on both sides of the equation , we get

2x - 10 = 6

Adding 10 on both sides of the equation , we get

2x = 16

Divide by 2 on both sides of the equation , we get

x = 8

Therefore , the value of x is 8

Hence , the proportion is solved

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The term "solution set" refers to the collection of all possible solutions to an equation thus  {x|x≤4.5} holds it . The value is a solution because the equation holds true if both sides are equal.

Option B is correct.

The distinct items that make up a set are referred to as the set's members or elements. Set notation is a method for representing a set using a combination of symbols and numbers, and it can be used to define sets. "x | -5 x 4.5" is another way to show the solution set of the inequality -5 x 4.5 on a number line. Interval notation is the method by which all real numbers between two given values can be represented. The solution set can be read as "x such that -5 is less than x and x is less than or equal to 4.5" because "|" denotes "such that" and the vertical line denotes "and."

When the lines coincide and have the same y-intercept, the number of solutions to an equation system is infinite. If the slope and y-intercept of the two lines are the same, they are in fact on the same exact line.

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The equation in the problem is in slope intercept form. The slope-intercept form of a linear equation is: y = mx + b

What is meant by slope?

The slope-intercept form of a linear equation is: y = mx + b

Where m is the slope and b is the y-intercept value.

Therefore, for this equation y = -2x - 7

The Slope is: m = -2

The Y=Intercept is b = -7 (or)

slope and y-intercept from the graph: (0, -7)

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Let x be the number of acres of Farm A planted with pine trees and birch trees, and let y be the number of acres of Farm B planted with pine trees and birch trees.

The system of equations would be as follows:

25x + 50y = 200 (the total number of pine trees planted)

75x + 75y = 450 (the total number of birch trees planted)

To solve this system of equations, we can use the method of substitution. Solving the first equation for x in terms of y:

x = (200 - 50y) / 25

We can substitute this expression for x into the second equation:

75((200 - 50y) / 25) + 75y = 450

Simplifying and solving for y:

(200 - 50y) + 75y = 450

25y = 250

y = 10

So 10 acres of Farm B are planted with pine and birch trees. To find the number of acres of Farm A that are planted with pine and birch trees, we can substitute this value of y back into the first equation:

25x + 50(10) = 200

25x = 50

x = 2

So 2 acres of Farm A are planted with pine and birch trees.

Therefore, the company will plant 25x = 50 pine trees and 75x = 225 birch trees on Farm A, and 50y = 500 pine trees and 75y = 750 birch trees on Farm B.

Answer:

--------------------------

We know that corresponding sides of similar figures are proportional.

Thus we have equal ratios:

Solve it for x:

Answer:

see explanation

Step-by-step explanation:

A translation of [tex]T_{(5,2)}[/tex] means

add 5 to the original x- coordinate and add 2 to the original y- coordinate.

A (1, - 2 ) → A' (1 + 5, - 2 + 2 ) → A' (6, 0 )

B (- 3, - 3 ) → B' (- 3 + 5, - 3 + 2 ) → B' (2, - 1 )

C (3, 5 ) → C' (3 + 5, 5 + 2 ) → C' (8, 7 )

Answer:

see explanation

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

  = 3x(x + 4) ← distribute parenthesis by 3x

A = 3x² + 12x

when x = 1 , then

A = 3(1)² + 12(1) = 3 + 12 = 15 yd²

Answer: I need help with this what is the answer

Step-by-step explanation:

[tex] \pmb{ \underline{\color{green} \huge{Αηςωεr : ∼}}}[/tex]

[tex] \large \frak{ \red{x } - 4 = 8}[/tex]

[tex] \: [/tex]

[tex] \large \frak{ \red{x } = 8 + 4}[/tex]

[tex] \: [/tex]

[tex] \underline{ \boxed{ \large \frak{ \red{x } = \green{12}}}}[/tex]

[tex] \: [/tex]

hope it helps!

Subtract the given angle from 180° and the missing angle measurements is 42°.

What is meant by angle ?

A+B+C=180°

57°+81°+C°=180°

138°+C=180°

C=138°-180°

C=42°.

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The number of different sandwiches that Javier can order, given the number of types of meat and cheeses, is 12 sandwiches.

Javier has 3 choices for the type of meat and 4 choices for the cheese, so the total number of different sandwiches he can order is the product of the number of choices for each ingredient.

To find the total number of different sandwiches, you can multiply the number of meat choices by 4 the number of cheese choices.

The number of sandwiches Javier can order are:

= 3 x 4

= 12 sandwiches

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Answer:

T < 5

Step-by-step explanation:

High School A: A(t) = 800 + 35t

High School B: B(t) = 550 + 85t

To find the interval of years in which High School A will have more students than High School B, we need to find the years in which A(t) > B(t).

So, we need to solve the inequality A(t) > B(t)

800 + 35t > 550 + 85t

250 > 50t

t < 5

Therefore, High School A will have more students than High School B for the first five years.

The interval of years, t, for which High School A will have more students than High School B is t < 5

Answer:

Step-by-step explanation:

i dont knpw

Answer:

Step-by-step explanation:

For the cat's heart to beat 45 times in 15 seconds

for 1 second, we must divide 45 by 15

the answer will be 3 beats per second

The correct explaination to calculate the total number of miles that Cody hiked in two days is Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Add the two products.

First of all, we must know the formula of average speed. The formula is as follows -

Average speed = distance ÷ time

Using this formula, we can calculate distance for Saturday and Sunday and subsequently add the distance to find the number of miles that Cody hiked in two days.

For Saturday -

Distance = 1 × 5

Performing multiplication

Distance = 5 miles

For Sunday -

Distance = 3 × 2

Performing multiplication

Distance = 6 miles

Total distance hiked = 5 + 6

Performing addition

Total distance hiked = 11 miles

Thus, the correct explaination is Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Add the two products.

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The complete question is -

Cody hiked at an average speed of 1 mile per hour for 5 hours on Saturday. He hiked an average speed of 2 miles per hour for 3 hours on Sunday. Which explanation correctly tells how to calculate the total number of miles that Cody hiked in two days? Step 1: Divide 1 ÷ 5. Step 2: Divide 2 ÷ 3. Step 3: Subtract the two quotients. Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Add the two products. Step 1: Divide 1 ÷ 5. Step 2: Divide 2 ÷ 3. Step 3: Add the two quotients. Step 1: Multiply 1 × 5. Step 2: Multiply 2 × 3. Step 3: Subtract the two products.

When the line to be examined's slope is known, and the provided point also serves as the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b).

When should you use point-slope form?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.

One of the three ways we can express a straight line is using the point slope form, also known as the point-gradient form. By merely knowing one point on the line and the slope of the line, we may use this form to get the equation of the line.

The slope and y-intercept of the matching line can be rapidly determined when we have a linear equation in slope-intercept form. This enables us to graph it as well.

The equation of a line can be represented in either slope-intercept form or point-slope form.

Slope-intercept form:

The slope-intercept form of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the equation of the line passing through the points (3,5) and (6,11) in slope-intercept form, we can use the point-slope formula to find the slope and then use one of the points to find the y-intercept.

Point-slope form:

The point-slope form of a line is given by y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

To find the equation of the line passing through the points (3,5) and (6,11) in point-slope form, we can use the point-slope formula and one of the points.

Using the point-slope formula, the slope of the line is (11 - 5) / (6 - 3) = 6/3 = 2.

So, the equation of the line in slope-intercept form is:

y = 2x + b

We can use the point (3,5) to find the y-intercept:

5 = 2 * 3 + b

Solving for b, we get b = -1.

So the equation of the line in slope-intercept form is:

y = 2x - 1

In point-slope form, using the point (3,5), the equation of the line is:

y - 5 = 2(x - 3)

Both forms represent the same line, just in different ways.

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Answer:

Step-by-step explanation:

4x + 3 + 2x + 9 = 180°

6x + 12 = 180

6x = 180 - 12

6x = 168

x = 168 : 6

x = 28°

-------------------------------

4 × 28 + 3 + 2 × 28 + 9 = 180    (remember PEMDAS)

112 + 3 + 56 + 9 = 180

180 = 180

The point (4, 3) is a viable solution.

At least two linear inequalities in the same variables make up a system of linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

Given:

A basket holds at most 14 pounds of apples and oranges.

There are at least 3 pounds of apples in the basket.

This graph shows the system that represents this scenario, where x is the weight of the apples and y is the weight of the oranges.

That means, we have the system of inequalities,

x + y ≤ 14,

x ≥ 3

Option B and C are discarded.

And y ≥ 0.

Option A is also discarded.

Substituting (4, 3),

x + y ≤ 14,

7  ≤ 14.

Therefore, (4, 3) is a solution.

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The complete question:

A basket holds at most 14 pounds of apples and oranges. There are at least 3 pounds of apples in the basket. This graph shows the system that represents this scenario, where x is the weight of the apples and y is the weight of the oranges. Which point represents a viable solution?

The solutions of each expression for n are given as follows:

1. n = 1.5972.

2. n = 11.4688.

3. n = 6.5025.

4. n = 1.81.

5. n = 28.9835.

All the five expressions in this problem are multiplication operations involving two decimal numbers.

Hence, to obtain the solution for n of each expression, we must simply apply the multiplication operation of the two decimals, using a calculator.

The result of each expression is given at the beginning of the answer.

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Answer:

Refer to the step-by-step

Step-by-step explanation:

∠1 and ∠2 lie in the alternate interior of the parallel lines and are on opposite sides of the transversal. So, ∠1 and ∠2 are equal angles.

Answer:

C

Step-by-step explanation:

Lets use process of elimination.
A would result in biased results as Lin is on the basketball team herself and thus, her teammates would be inclined to vote for her.

B would result in biased results as well. It doesn't say every third person in the line but rather every third girl. The girls might be inclined to vote for a female candidate.

That leaves C as the only viable option.

The error interval due to rounding:

71.25 ≤ t < 71.35

Now, According to the question:

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

"Information available from the question"

Paul won a race with a time of 71. 3 seconds.

The time, t, is to the nearest tenth of a second.

So, Rounding off to nearest tenth

Rounded to the nearest 0.1 or the Tenths Place will be

The error interval due to rounding:

So, 71.25 ≤ t < 71.35

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The inequality statement j/6 > 3 is true when j = 24.

To substitute the value of j into the inequality statement, you will replace j with 24 and then simplify the expression.

j / 6 > 3

24 / 6 > 3

Simplifying, we get

4 > 3

Since 4 is greater than 3, the inequality statement is true.

You can also check by multiplying both sides of inequality by 6

j > 18

24 > 18

This is true because 24 is greater than 18. Therefore, the inequality statement j/6 >3 if j =24 is true.

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The number line inequality that best represents the possible number of shirts the company can ship in a package without playing extra for shipping is given by the image presented at the end of the answer.

Before putting any T-shirts in the box, the package weighs 1.5 oz. Each shirt weighs 5 oz, hence the total weight function for x shirts is given as follows:

y = 1.5 + 5x.

The maximum weight without needing to pay extra is of 13 ounces, hence the inequality is given as follows:

5x + 1.5 <= 13

x <= 11.5/5

x <= 2.3.

Which can be simplified as:

x <= 2.

(as the number of shirts is a countable amount).

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Answer:

b.  20°

Step-by-step explanation:

Find the missing angle in the top triangle:

180 - 40 - 20 = 120

because, the sum of interior angles of a triangle is 180.

The top angle of the bottom triangle = 120 because it is a vertical angle to the one you just found.

Now find the missing angle (x) on the bottom:

x = 180 - 120 - 40 = 20

Answer: 16x^38y^22

Step-by-step explanation:

Re-order terms so constants are on the left
(−xy)2(2x9y5)4(−)2(295)4

Distribute exponent

(−xy)2(2x9y5)4(−)2(295)4

Evaluate the exponent

(−1)2(xy)2⋅(2x9y5)4(−1)2()2⋅(295)4

Encoding simply means the process of putting a sequence of characters like letters, numbers and other special characters into a specialized format.

It should be noted that a type of code, that is extremely difficult to break, and one which makes use of a large matrix to encode a message is the encoding matrix.

Here, the receiver of the message decodes it by using the inverse of the matrix. In their case, the first matrix is the encoding matrix and the inverse is the decoding matrix.

To decode the message, we simony have to take the string of coded numbers and then multiply it by the inverse of the matrix in order to get the original string of numbers.

Encoding simply means the process of putting a sequence of characters like letters, numbers and other special characters into a specialized format.

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Answer:

We can find two other points on the line passing through (1,5) and (3,-1) by using the slope-intercept form of a line: y = mx + b where m is the slope of the line, and b is the y-intercept.

To find the slope (m) of the line, we can use the formula: m = (y2 - y1) / (x2 - x1)

Plugging in the coordinates of the two given points: m = (-1 - 5) / (3 - 1) = -6 / 2 = -3

To find the y-intercept (b) of the line, we can use one of the given points and substitute the values of x, y and m into the equation y = mx + b.

Plugging in the coordinates of the point (1,5) and the value of m: 5 = -3(1) + b, b = 8

So the equation of the line is y = -3x + 8

We can use this equation and any x value to find two other points on the line. For example, if we choose x = -2, we get y = -3(-2) + 8 = 2

so the point (-2,2) is on the line.

If we choose x = 0, we get y = -3(0) + 8 = 8

so the point (0,8) is on the line.

So two other points on the line passing through (1,5) and (3,-1) are (-2,2) and (0,8)

If I helped you, could you please make my answer best?

Answer:

x + y = 4

m = -1

Step-by-step explanation:

(3 - 5) / (1 - (-1))

m = -2/2

(y - 5) = -1 × (x - (-1))

y - 5 = - x - 1 = 0

The number of tables for 15 guests will be 3 tables.

The number of tables for 25 guests will be 5 guests

The number of tables for 50 guests will be 10.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, Trey is having a party. He'll have 2 tables for every 10 guests. This means that 1 table will be for 10/2 = 5 guest

The number of tables for 15 guests will be:

= 15 / 5.

= 3 tables.

The number of tables for 25 guests will be:

= 25 / 5

= 5 guests

The number of tables for 50 guests will be:

= 50 / 5

= 10

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