You can also write an equation for equivalent ratios. The equation at the right can be used to find the actual length x of the sculpture room in the museum. Complete the equation and explain what each part represents

Answer:

Should be B

Step-by-step explanation:

5 + 2 ( x-4[3x+7(2-x)]

5+2 (x-4[ 4x + 14])

5+2 (17x - 56)

5 + 34x - 112

34x - 107

Answer:

Your final answer is 15x+12

Step-by-step explanation:

Remove parathenes ( ) group like terms add similar elements add the numbers 5 + 7 = 12

Answer: x = 623

Step-by-step explanation: In this problem, notice that x is being divided by 7 so to get x by itself,

we need to multiply both sides of the equation by 7.

Notice that on the left side, the 7 and 7 cancel each other out so we're just left with x. On the right side we have

89 x 7 which is 623 so x = 623.

Finally, we can check our answer by plugging a 623 back into the original equation. So we have [tex]\frac{(623)}{7} = 89[/tex] or 89 = 89. Since this is true, our answer checks.

Answer:

No, because 3x+9/2 isn't equivalent to 3x+3/2.

Step-by-step explanation:

1 1/2=3/2

3(x+3/2)=3x+9/2

The area of the frame not covered by the painting is 192 square inches

Solution:

Given that, A rectangular painting is 24 inches wide and 20 inches tall without the frame

The area of rectangle is given as:

[tex]Area = length \times width[/tex]

Find the area of painting without frame:

Length = 20 inches

Width = 24 inches

[tex]Area\ Without\ Frame = 20 \times 24 = 480[/tex]

Thus area of painting without frame is 480 square inches

With the frame, it is 28 inches wide and 24 inches tall

Find the area of painting with frame:

Length = 24 inches

Width = 28 inches

[tex]Area\ with\ frame = 24 \times 28 = 672[/tex]

Thus area of painting with frame is 672 square inches

What is the area of the frame not covered by the painting

Area of the frame not covered by the painting = Area with farme - Area without frame

Area of the frame not covered by the painting = 672 - 480 = 192

Thus the area of the frame not covered by the painting is 192 square inches

Answer:

1.125

Step-by-step explanation:

the unit cost is how much it cost per wheel

dozen is 12

so 12 times 6 is 72

so then you do 81/72 to get your answer

and you are probably wondering how i got the divison from was because i'm supposed to divide to find a unit cost.

the 81 was the total for the 72 packages of toy wheels

Answer:

first find how much a dozen of 6 is, so 6*12=72

next to get the cost of one divide 81/72=$1.125

$1.13

Step-by-step explanation:

the first situation goes with the first equation

the second situation goes with the third equation

the third situation goes with the third equation

The equation for Statement 1 is 4+5x=16, the equation for Statement 2 is (5-4)x=16 and the equation for Statement 3 is 16-4x=5.

For the given statements we need to match the given equations.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Statement 1: An adults and 5 children rent skates. It costs $4 per adult for stakes and a total of $16.

Let the cost of 5 children rent skates be 5x.

Now, 4+5x=16

Statement 2: It costs Mikael $4 to make a bike bag, and he sells each for $5. He has made a profit of $16 so far.

Profit=Selling Price-Cost Price

⇒Profit=5-4

⇒(5-4)x=16

Statement 3: It was 16° C. It began falling 4° C per hour until it reached 5° C.

It began falling 4° C per hour, which can be written as 4x.

Now, 16-4x=5

Therefore, the equation for Statement 1 is 4+5x=16, the equation for Statement 2 is (5-4)x=16 and the equation for Statement 3 is 16-4x=5.

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Step-by-step explanation:

if x=1/4 then y=1/4-1/4=0

if x=13/4 then y=13/4-1/4=12/4=3

if x=2 then y=2-1/4=8/4-1/4=7/4=1 3/4

Answer:

To find area of irregular shapes you need to divide the irregular shape to get a new shape (for instance: rectangle); then you have to find the area of that particular shape using its formula (for instance: area of square = side*side)

Final answer:

A recursive rule for the sequence 243, 81, 27, 9, 3, ... is to multiply each term by one-third (⅓) of the previous term. The first term is 243, and the rule can be expressed as an = ⅓ × an-1 for n >= 2.

Explanation:

To write a recursive rule for the sequence 243, 81, 27, 9, 3, ... we must first identify the pattern. Observing the sequence, we see that each term is one-third of the previous term. Therefore, to get from one term to the next, we multiply by ⅓ (which is the same as dividing by 3).

The recursive formula for this sequence can be written as follows:

This recursive rule clearly indicates that every term is a fraction of the preceding term, which is consistent with the pattern of division by three observed in the original sequence.

For this case we have the following equation:

[tex]2m + 4s = 16[/tex]

We solve for each of the variables:

For m:

We subtract 4s from both sides of the equation:

[tex]2m = 16-4s[/tex]

We divide by 2 on both sides of the equation:

[tex]m = \frac {16-4s} {2}\\m = \frac {16} {2} - \frac {4s} {2}\\m = 8-2s[/tex]

For s:

We subtract 2m from both sides of the equation:

[tex]4s = 16-2m[/tex]

We divide between 4 on both sides of the equation:

[tex]s = \frac {16} {4} - \frac {2m} {4}\\s = 4- \frac {m} {2}[/tex]

Answer:

[tex]m = 8-2s\\s = 4- \frac {m} {2}[/tex]

Without additional information or a second equation, the values for 'm' and 's' cannot be specifically determined from the equation 2m+4s=16 due to the infinite number of solutions.

The question 2m+4s=16 asks us to find the values of m and s. However, with a single equation and two variables, there are infinite solutions. This is because without additional information or constraints, each variable can take on many different values as long as the equation balances out to 16. Therefore, we cannot determine specific values for m and s without additional equations or information.

To find the values of M and S in the equation 2M + 4S = 16, we can use algebraic methods to solve for the variables.

Step 1: Start by isolating M in the equation. Subtract 4S from both sides of the equation: 2M = 16 - 4S.

Step 2: Divide both sides by 2 to solve for M: M = (16 - 4S)/2.

Now you have an equation that expresses M in terms of S. You can substitute different values for S to find the corresponding values for M. For example, if S = 2, then M = (16 - 4(2))/2 = 4. So, when S = 2, M = 4. Repeat this process for different values of S to find the corresponding values of M.

Answer:3 weeks

Step-by-step explanation:The reason for that is because if Kayla is taking 3 tests each week then 3 times 3 is 9 so three weeks.

Each game costs 1.25 and each ride costs 3.75

Step-by-step explanation:

Let,

Cost of each game = x

Cost of each ride = y

According to given statement;

5x+6y=28.75        Eqn 1

4x+3y=16.25         Eqn 2

Multiplying Eqn 2 by 2

[tex]2(4x+3y=16.25)\\8x+6y=32.50\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 1 from Eqn 3

[tex](8x+6y)-(5x+6y)=32.50-28.75\\8x+6y-5x-6y=3.75\\3x=3.75[/tex]

Dividing both sides by 3

[tex]\frac{3x}{3}=\frac{3.75}{3}\\x=1.25[/tex]

Putting x=1.25 in Eqn 1

[tex]5(1.25)+6y=28.75\\6.25+6y=28.75\\6y=28.75-6.25\\6y=22.50[/tex]

Dividing both sides by 6

[tex]\frac{6y}{6}=\frac{22.50}{6}\\y=3.75[/tex]

Each game costs 1.25 and each ride costs 3.75

Keywords: linear equation, elimination method

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Final answer:

The cost of one game is 1.25 dollars and the cost of one ride is 3.75 dollars at the carnival. This was determined by setting up and solving a system of equations based on the expenses of Owen and Kayden.

Explanation:

To determine the cost of each game and each ride at the carnival, we can set up a system of equations based on Owen and Kayden's expenses. Let x represent the cost of one game and y represent the cost of one ride.

Owen played 5 games and went on 6 rides for a total cost of 28.75 dollars. This can be represented by the equation:
5x + 6y = 28.75

Kayden played 4 games and went on 3 rides for a total cost of 16.25 dollars. This can be represented by the equation:
4x + 3y = 16.25

We now have a system of linear equations:
5x + 6y = 28.75

4x + 3y = 16.25

To solve the system, we can multiply the second equation by 2 to align the y-terms:
5x + 6y = 28.75

8x + 6y = 32.50
Subtracting the first equation from the multiplied second equation, we get:

3x = 3.75
Dividing both sides by 3, we find that x = 1.25, which is the cost of one game.

To find the cost of one ride, we substitute x = 1.25 into either of the original equations. If we use the second equation 4(1.25) + 3y = 16.25, we get:
3y = 16.25 - 5

3y = 11.25

y = 3.75

Therefore, the cost of one ride is 3.75 dollars.

Answer:

80 students

Step-by-step explanation:

Let the number of voters in the election for class president is x.

So, given that 40% of the voters voted for Gerardo,35% of the voters voted for Leonardo, and 25% of the voters voted for Juju.

So, the number of voters for Leonardo was [tex]x \times \frac{35}{100} = 0.35x[/tex]

Given that, 0.35x = 70

⇒ x = 200

Now, the number of voters for Gerardo was [tex](x \times \frac{40}{100}) = 0.4x = 0.4(200) = 80[/tex].

(Answer)

The reflection transformation of the triangles is C) [tex]( rx-axis(x, y) \rightarrow (x, -y) )[/tex].

The points of the original triangle are:

The points for the reflected triangle are:

Identify the transformation

From the pairs of coordinates, we can observe how each point has changed from the original triangle to the reflected triangle:

Analyze the change in coordinates

We see that for each point, the x-coordinates remain unchanged while the y-coordinates change sign from positive to negative. This indicates that the reflection is across the x-axis.

Reflection rule

The general rule for reflection across the x-axis can be stated as follows:

If a point is given by (x, y), then the reflected point will be (x, -y).

Reflection across the x-axis :
[tex]( rx-axis(x, y) \rightarrow (x, -y) )[/tex]

Complete question

On a coordinate plane, 2 triangles are shown. The first triangle has points M (negative 5, 4), N (negative 2, 3), and L (negative 4, 2). The second triangle has points L prime (negative 4, negative 2), M prime (negative 5, negative 4), and N prime (negative 2, negative 3). What is the rule for the reflection?

a. rx-axis(x, y) → (–x, y)

b. ry-axis(x, y) → (–x, y)

c. rx-axis(x, y) → (x, –y)

d. ry-axis(x, y) → (x, –y)

The given sequence is not geometric because they don't have a common ratio.

A geometric sequence is set of numbers which have a common ratio. The next number in a geometirc sequence is the multiple of the previous  number.

-1/1 = -1

4/1 = 4

8/4 = 2

The numbers don't have a common ratio.

Thus, we can conclude that the given sequence is not geometric because they don't have a common ratio.

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The common ratio is not the same for all pairs of consecutive terms, so the sequence is not geometric.

To determine if a sequence is geometric, we need to check if there is a common ratio between consecutive terms.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant value called the common ratio.

Let's check the given sequence: -1, 1, 4, 8.

To find out if it is geometric, we need to check if the ratio of consecutive terms is constant:

Common Ratio (r) = (Second Term) / (First Term)

= 1 / (-1)

= -1

Now, let's check if the common ratio is the same for the other pairs:

1st and 2nd terms: 1 / (-1) = -1

2nd and 3rd terms: 4 / 1 = 4

3rd and 4th terms: 8 / 4 = 2

The common ratio is not the same for all pairs of consecutive terms. Since the common ratio is not constant, the given sequence (-1, 1, 4, 8) is not a geometric sequence.

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Answer:

Graphing Linear Inequalities differs from graphing regular linear equations. That is it has certain rules to be followed to draw the graph.

Thus if the equation has y < or y > then we use broken line and y= , y≤ and y≥ then we use solid line.

Answer:

both of The answers are equal to Zero

Answer:

Step-by-step explanation:

1.  sin37xcsc37

For this use the recipricol identity.  csc37 = 1/sin37

sin37x(1/sin37)  =  (sin37)/(sin37) = 1

2.  sec^2(23) - tan^2(23)

For this one use the pythagorean identity

sec^2(23) = 1+tan^2(23)

1+tan^2(23) - tan^2(23) = 1

Answer:

1788

Step-by-step explanation:

The number of students who graduates from college is multiplied by a factor of 1.045 every year since 1999.

So, the number of students graduated every year can be modeled as

[tex]G(x) = 924(1.045)^{x}[/tex] where x is the number of the year since 1999.

Now, in 2014, the x value is (14 + 1) = 15 years.

So, the number of students who will graduate in 2014 is given by

[tex]G(15) = 924(1.045)^{15} = 1788.2[/tex] ≈ 1788. (Answer)

Answer:

Step 3 because when dividing 7y=-9, you divide by 7, not 9. Kendra divided the whole thing by 9, which is incorrect. You want to get the Y by itself(as in y, not a fraction of y) to solve the rest of the problem.

Step-by-step explanation:

Step 1.

-3x+7y=-15

-2x-7y=5

-5x=10 and x=2

Step 2.

-5x =-10. x = 2.

Step 3.

-3 (2) + 7 y = - 15. - 6 + 7 y = - 15. 7 y = - 9. y = -9/7  = - 1  2/7

Answer:

The solution is the point (-2,1)

Step-by-step explanation:

we have

[tex]-2x+3y=7[/tex] ----> equation A

[tex]5x+8y=-2[/tex] ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system is the intersection point both lines

using a graphing tool

The solution is the point (-2,1)

see the attached figure

Answer:

Number of instructors are 225.

Step-by-step explanation:

Given:

Total number of employees at bright mind learning = 300

Number of instructors = 75%

We have to convert this percentage and find the number.

So,

[tex]75\%[/tex] can be written as [tex]\frac{75}{100}=0.75[/tex]

Now 75% of 300 employees are the instructors at Bright mind learning.

Can be written as [tex]0.75*300=225[/tex]

Number of instructors at Bright mind learning =225

Answer:

y ≈ 242.4 ft

Step-by-step explanation:

The lower angle in the triangle is 29° ( alternate angles )

Using the sine ratio in the right triangle

sin29° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{500}[/tex]

Multiply both sides by 500

500 × sin29° = y, thus

y ≈ 242.4 ft ( to the nearest tenth )

Answer:

7-4+6=7 + 2

Step-by-step explanation:

The original equation 7-4+6=7 is incorrect because it simplifies to 9, not 7. There is no simple way to adjust the equation with the given numbers to make the equation balance correctly. It's crucial to check your work and make sure the equation balances, just like ensuring a chemical equation has equal numbers of atoms on both sides.

To complete the equation 7-4+6=7 to make it equal, we need to perform the operations on the left side of the equation and see if the result is indeed 7, the same as the right side. Let's solve it step by step:

The original equation 7-4+6=7 is incorrect because 7-4+6 equals 9, not 7. To make the equation correct, we would need to change a number or an operation. One possible solution could be adding parentheses: (7-4)+6=7+2, which simplifies to 3+6=9, but again that does not equal 7. Therefore, there is no simple way to correct the equation using basic operations without changing the numbers given.

To make sure the charge and atoms on both sides of an equation balance or to ensure the correctness of a mathematical operation, eliminating terms where possible to simplify the algebra and checking the answer to see if it’s reasonable are important steps.

When balancing equations, whether they are chemical equations or mathematical ones, it's essential to make sure each side is equal to maintain the balance, as seen in the example: 7 carbon atoms, 16 hydrogen atoms, and 22 oxygen atoms on each side of a balanced chemical equation.

Answer: 3.35 in 3 significant figures.

Step-by-step explanation:

According to question,

Perimeter ∝ length

Here, ∝ means directly proportional.

To remove symbol, introduce a constant. Let the constant be k.

Perimeter ∝ length

Perimeter = k × length

Now, perimeter = 17.7 and length = 5.29

Perimeter = k × length

k = perimeter / length

k = 17.7 / 5.29

k = 3.35 in 3 significant figures.

Answer:

3

Step-by-step explanation:

k=y/x

k=17.75/5.29

k= 3.345

=3

Answer:

The closest you would get is (8*2)-6+3=13

Step-by-step explanation:

Answer:

20x−18

Step-by-step explanation:

Apply the distributive property.

8x−6⋅3−6(−2x)8x-6⋅3-6(-2x)

Multiply −6-6 by 33.

8x−18−6(−2x)8x-18-6(-2x)

Multiply −2-2 by −6-6.

8x−18+12x

Add 8x8x and 12x12x.

20x−18

The given expression 8x - 6(3 - 2x) simplifies to 20x - 18.

The expression is given as follows:

8x - 6(3 - 2x)

As we know that algebraic expressions are mathematical statements that comprise at least two variables or integers.

Start by distributing the -6 to the terms inside the parentheses:

⇒ 8x - 6 × 3 + 6 × 2x

Simplify the above expression to get:

⇒ 8x - 18 + 12x

Combine like terms in the above expression to get:

⇒ 20x - 18

Therefore, the given expression 8x - 6(3 - 2x) simplifies to 20x - 18.

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Answer:

New Deal

Explanation:

In order to bring an end to the Great Depression, Franklin Delano Roosevelt (the 32nd President of the United States) proposed the "New Deal."

The "New Deal" was a set of programs which allowed the government to have a direct role in making the American lives easier. This mainly supported the poor people, especially the farmers and those who lost their jobs or who were unemployed.

The programs started with the First New Deal, followed by the Second New Deal. The First New Deal focused on reformation while the second one was directed towards protecting the people.

Thus, this explains the answer.