Two bicyclists are 180 miles apart when they start racing towards each other. If their speeds are 14 mph and 16 mph respectively, how long will it be before they are twenty miles apart?

(6d + 5) - (2 - 3d)

Remove the parenthesis. This will help the question look more clear

6d + 5 - 2 + 3d

Add like terms.

(6d + 3d) + (5 - 2)

Simplify.

9d + 3

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To find the difference between (6d+5) and (2-3d), distribute the negative sign and combine like terms to get 9d + 3.

To find the difference between (6d+5) and (2-3d), we first distribute the negative sign to the terms inside the second parentheses. This gives us:

(6d+5) - (2-3d) = 6d+5 - 2 + 3d

Next, we combine like terms by adding the coefficients of d:

(6d + 3d) + (5 - 2) = 9d + 3

So, the difference between (6d+5) and (2-3d) is 9d + 3.

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Answer:

[tex]1\frac{1}{4}[/tex]gallon/hour

Step-by-step explanation:

After [tex]2\frac{1}{4}[/tex] hour a chainsaw has used [tex]2\frac{13}{16}[/tex] gallons of fuel.

[tex]2\frac{1}{4}[/tex] hours = [tex]\frac{9}{4}[/tex] hours

[tex]2\frac{13}{16}[/tex] gallons = [tex]\frac{45}{16}[/tex] = 2.8125 gallons

The chainsaw used fuel after [tex]\frac{9}{4}[/tex] hours = [tex]\frac{45}{16}[/tex] gallons

The chainsaw used fuel in 1 hour = [tex]\frac{\frac{45}{16}}{\frac{9}{4}}[/tex]

= [tex]\frac{45}{16}[/tex] ÷ [tex]\frac{9}{4}[/tex]

=  [tex]\frac{45}{16}[/tex] × [tex]\frac{4}{9}[/tex]

= [tex]\frac{180}{144}[/tex]

= [tex]\frac{90}{72}[/tex]

= [tex]\frac{30}{24}[/tex]

= [tex]\frac{15}{12}[/tex]

= [tex]\frac{5}{4}[/tex]

= [tex]1\frac{1}{4}[/tex] gallons of fuel

Chainsaw used [tex]1\frac{1}{4}[/tex] gallons of fuel in each hour

Answer:

2.04

Step-by-step explanation:

1. I make an estimate

2. I regroup some of the numbers.

3. then subtract it all and you get...

                       2.04

16-10 = 6 inches

24-15  = 9 ounces

it stretches 6 inches when 9 ounces are added

 divide 6 inches by 9 ounces

6 / 9 = 0.67 inches per ounce

Answer:

-1

Step-by-step explanation:

We are given that an expression

[tex]\frac{5}{6}-\frac{11}{6}[/tex]

We have to find the correct value of given expression on the number line.

[tex]\frac{11}{6}=1\frac{5}{6}[/tex]

[tex]\frac{5}{6}-\frac{11}{6}[/tex]

[tex]\frac{5-11}{6}=\frac{-6}{6}[/tex]

[tex]\frac{5}{6}-\frac{11}{6}=-1[/tex]

[tex]\frac{5}{6}+(-1\frac{5}{6})[/tex]

When an integer positive and other integer negative and add them .If negative integer is greater and positive integer is small then we go from left to right.

We go [tex]\frac{5}{6}[/tex] step from [tex]-1\frac{5}{6}[/tex]towards right  then we reach at [tex]{-1}[/tex].

Hence, -1 is the correct value of given expression.

The greatest number of side dishes they can buy is 5, as per linear equation.

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation."

The family has $35 to spend on dinner.

They spend $18 on entrees.

Therefore, they are left with $(35 - 18) = $17.

Side dishes are $3 each.

Therefore, the most number of side dishes they can buy is

($17/$3)

= 5.67

≈ 5

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Answer:

-7

Step-by-step explanation:

First, start at zero. Now, because we are multiplying -4 by 3, we will jump over by 4 to the left  ; 3 times on the number line. We should reach -12, and if we check our work, 3 x -4 = -12.                                            

Final answer:

To model the multiplication of 3 and -4 on a number line, start at zero and make three moves to the left by 4 units, ending up at -12. This demonstrates the rule that multiplying numbers with opposite signs results in a negative product.

Explanation:

To model the multiplication of 3 and -4 on a number line, you can follow these steps:

Start at zero on the number line.

Since you are multipling a positive number by a negative number, you will move in the negative direction (to the left).

Make three moves (corresponding to multiplying by 3), each 4 units to the left. This represents adding -4 three times.

Where you end up on the number line is the product of 3 and -4, which is -12.

This method of multiplication on a number line illustrates the rule that when two numbers multiplied have opposite signs, the answer has a negative sign, such as in the example ( -4) x 3 = -12.

It would take Gali approximately 7.5 hours to drive from Cleveland, Ohio, to Washington, D.C. on the interstate highways.

To find Gali's average driving speed, we can divide the distance she can travel by the time it takes her:

140 miles / 3 hours = 46.67 miles per hour (approx).

Now that we know her average driving speed, we can calculate the time it would take her to drive 350 miles from Cleveland to Washington, D.C.

Time = Distance / Speed

Time = 350 miles / 46.67 miles per hour

Time ≈ 7.5 hours

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To solve this problem, we set up a proportion based on the provided information: 132 pounds correlates to 143 milligrams. We then use cross multiplication to find the required dosage for the patient with the weight of 156 pounds, which results to about 169.3 milligrams.

The method to solve this issue is to use the concept of proportionality. First, we set up a proportion based on the given information: 132 pounds (patient weight) correlates to 143 milligrams (medicine dosage). Secondly, we could use cross multiplication to find the unknown medicine dosage for the patient weighting 156 pounds. Here's the mathematical process:

Carrying out the multiplication and division should result in x ≈ 169.3 milligrams. So a patient weighing 156 pounds would require approximately 169.3 milligrams of the medicine.

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I took the test and this was the answer