The dimensions of a rectangular floor in a floor plan are 4 cm by 6 cm. In actuality, the shorter side of the floor is 5m. Find the length of the longer side.

The expressions rewritten using the distributive property are:

1. -12x + 24

2. 4x - 24y

3. 30 - 6q

4. [tex]\(\frac{c}{2} - 4\)[/tex]

5. -15 + 3b

6. -7D - 14

To rewrite each expression using the distributive property:

1. 3(-4x + 8):

  [tex]\[3 \cdot (-4x) + 3 \cdot 8\][/tex]

  -12x + 24

2. 4(x - 6y):

  [tex]\[4 \cdot x - 4 \cdot 6y\][/tex]

  4x - 24y

3. 6(5 - q):

  [tex]\[6 \cdot 5 - 6 \cdot q\][/tex]

  30 - 6q

4. [tex]\(\frac{1}{2}(c - 8)\)[/tex]:

  [tex]\[\frac{1}{2} \cdot c - \frac{1}{2} \cdot 8\\ \[\frac{c}{2} - 4\][/tex]

5. -3(5 - b):

  [tex]\[-3 \cdot 5 + 3 \cdot b\][/tex]

  -15 + 3b

6. (D + 2)(-7):

  [tex]\[D \cdot (-7) + 2 \cdot (-7)\][/tex]

  -7D - 14

So, the expressions rewritten using the distributive property are:

1. -12x + 24

2. 4x - 24y

3. 30 - 6q

4. [tex]\(\frac{c}{2} - 4\)[/tex]

5. -15 + 3b

6. -7D - 14

Answer:

Step-by-step explanation:

The picture that shows the needed information is attached.

According to the graph, the distance showed between Gendet and Montrose is 1.5cm with a scale of 1 centimeter = 16 kilometers.

This scale means that each centimeter on the paper represents 16 kilometers of the real distance. So, what we need to do is just multiply the 1.5 cm by 16 km, because that's the scale:

[tex]1.5(16)=24[/tex]

Therefore, the actual distance is 24 kilometers.

Answer:

7.7

Step-by-step explanation:

Its 7.7 kilograms

Answer

Find out the how much of each metal is needed to make 3.6 kg of this alloy .

To proof

As given

An alloy consists of nickel, zinc, and copper in the ratio 2:7:9 .

This shows that an alloy contains 18 parts and assume one part of alloy be u .

Thus

An alloy consists of nickel = 2u

An alloy consists of zinc = 7u

An alloy consists of copper = 9u

As given

Total weight of alloy = 3.6 kg

Thus equation becomes

2u + 7u + 9u = 3.6

18u = 3.6

[tex]u = \frac{3.6}{18}[/tex]

u = 0.2 kg

An alloy consists of nickel = 2 × 0.2

                                           = 0.4 kg

An alloy consists of zinc = 7 × 0.2

                                        = 1.4 kg

An alloy consists of copper = 9 × 0.2

                                             = 1.8 kg

Hence proved

To make 3.6 kg of alloy in the given ratio, 400 grams of nickel, 1400 grams of zinc and 1800 grams of copper are required.

The question is asking how much of each metal, namely nickel, zinc, and copper, is needed to make 3.6 kg of an alloy with a ratio 2:7:9. To solve this, first, we have to understand that the ratio represents relative amounts of each metal, not their exact weights. The entire alloy is made up of 2 parts nickel, 7 parts zinc, and 9 parts copper - a total of 18 parts. We can find the weight equivalent to one part by dividing the total weight of the alloy - 3.6 kg or 3600 grams - by 18. This gives us 200 grams as the weight of one part. To find the weight of each metal needed, we multiply the weight of one part by the number of parts in the ratio: nickel is 2 * 200 = 400 grams, zinc is 7 * 200 = 1400 grams, and copper is 9 * 200 = 1800 grams.

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Answer:

1. Using Backwards Method, we get,

We have the inequality 2n+5<13.

So, we subtract both the sides by 5,

i.e. 2n+5-5<13-5

i.e. 2n < 8

Now, divide both sides by 2, we get,

[tex]\frac{2n}{2} <\frac{8}{2}[/tex]

i.e. n < 4.

So, using the Backwards method, we get the solution is n<4.

2. Now, we use the Algebraic method,

We have, 2n+5<13

Take 5 to the right side of the inequality,

i.e. 2n<13-5

i.e. 2n < 8

Now, take the 2 on the right side of the inequality.

i.e. [tex]n<\frac{8}{2}[/tex]

i.e. n < 4.

So, again using the Algebraic Method, we get that the solution is n<4.

To convert from pounds to tons, divide the number of pounds by 2,000. A Class 2 truck, which weighs between 6,000 and 10,000 pounds, would weigh between 3 and 5 tons.

To convert the weight range of a Class 2 truck from pounds to tons, we must know the unit equivalence that 2,000 pounds is equal to 1 ton. Since we're converting from a smaller unit (pounds) to a larger unit (tons), we need to divide.

The lower end of the range:

6,000 pounds / 2,000 pounds per ton = 3 tons

The upper end of the range:

10,000 pounds / 2,000 pounds per ton = 5 tons

Therefore, a Class 2 truck weighs between 3 and 5 tons.

Answer:

The cube root of 9

Step-by-step explanation:

The true statement are as follows:

Here's a breakdown of why each statement is true or false:

True:

If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective. As the painting time increases, the hourly rate becomes a bigger factor, and Splash of Color's lower rate outweighs Interior Designs USA's initial fee advantage.

If it takes 3 hours to paint the rooms, both companies will charge the same amount. Both companies will charge 3 hours of labor at their respective rates: $35/hour * 3 = $105 for Interior Designs USA and $55/hour * 3 = $165 for Splash of Color.

False:

If it takes 7 hours to paint the two rooms, Interior Designs USA will charge the least. Interior Designs USA will cost $60 + $35/hour * 7 = $315, while Splash of Color will cost $55/hour * 7 = $385.

Splash of Color will always charge the least. This is not true because Interior Designs USA can be cheaper for smaller jobs due to their lack of an initial fee (e.g., 1 hour painting time).

If it takes 10 hours to paint the rooms, Splash of Color will charge $200 more than Interior Designs USA. Splash of Color will cost $55/hour * 10 = $550, while Interior Designs USA will cost $60 + $35/hour * 10 = $410. The difference is actually $140, not $200.

Complete question:

Mary having her living room and bedroom painted. Interior Designs USA charges $60.00 to evaluate the space plus $35.00 per hour of labor. Splash of Color charges $55.00 per hour with no initial fee. Which of the following are true? Select all that apply.

Answer:

$10.

Step-by-step explanation:

We have been given a function [tex]y=10.00x+35[/tex], where  y represents the cost of cabin lodging per occupant and x represents the number of occupants.

Since slope of a line is also known as unit rate, so the cost increase for every occupant will be equal to the slope of line.

We can see from our given expression that 10.00x represents the slope of line, so the cost increase for every occupant is $10.