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Tamiku [17]
2 years ago
7

A car uses 3t gallons of gasoline to travel 5 miles.

Mathematics
1 answer:
Nadusha1986 [10]2 years ago
6 0

Answer: a) \frac{24}{5}t gallons are needed to travel 8 miles

b) Town X and town Y are 15 miles apart.

Step-by-step explanation:

Given : Gasoline used to travel 5 miles = 3t gallons

a) To find: Gasoline used to travel 8 miles = ?

Using unitary method:

If Gasoline used to travel 5 miles = 3t gallons

Thus Gasoline used to travel 8 miles = \frac{3t}{5}\times 8=\frac{24}{5}t gallons

\frac{24}{5}t gallons are needed to travel 8 miles

b) when 3t gallons of gasoline are used , distance covered = 5 miles

Thus when 9t gallons of gasoline are used , distance covered = \frac{5}{3t}\times 9t=15 miles

Thus town X and town Y are 15 miles apart.

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In a function, y varies inversely with x. The constant of variation is 4. Which table could represent the function?
Nimfa-mama [501]
The equation will be y=4/x. u can make the table of variables by inserting the values of x in the equation. for suppose here, if x=1 then y=4 , x=2 then y=2 and so on.
5 0
2 years ago
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According to the Rational Root Theorem, the following are potential fox) 2x2 +2x 24.roots of -4, -3, 2, 3, 4Which are actual roo
aksik [14]

Correct Answer: First Option

Explanation:

There are two ways to find the actual roots:

a) Either solve the given quadratic equation to find the actual roots

b) Or substitute the value of Possible Rational Roots one by one to find out which satisfies the given equation.

Method a is more convenient and less time consuming, so I'll be solving the given equation by factorization to find its actual roots. To find the actual roots set the given equation equal to zero and solve for x as given below:

2x^{2} +2x-24=0\\ \\ 2(x^{2} +x-12)=0\\ \\ x^{2} +x-12=0\\ \\ x^{2} +4x-3x-12=0\\ \\ x(x+4)-3(x+4)=0\\ \\ (x-3)(x+4)=0\\ \\ x-3=0, x=3\\ \\ or\\\\x+4=0, x=-4

This means the actual roots of the given equation are 3 and -4. So first option gives the correct answer.

7 0
2 years ago
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A puppy finds a rawhide bone and begins to pull it with a force, Ft. The free-body diagram is shown. A free body diagram with 4
Drupady [299]

Answer:

  • <em><u> It begins to move toward the right</u></em>

Explanation:

The given information can be summarized in this way:

  • First force vector: Fg = - 8N (vertical down)
  • Second force vector: Ft = 6N (horizonal right)
  • Third force vector: FN = 8N (vertical up)
  • Fourth vector: Ff = - 4N (horizontal left)

Following Newton's second law, net force equal mass times acceleration:

  • Net force = mass × acceleration

To predict the motion, you apply Newton's second law in each direction (vertical and horizontal)

  • <u>Vertical force balance:</u>

        Net vertical force = 8N - 8N = 0. This means there is not motion in the vertical direction.

  • <u>Horizontal force balance:</u>

         Net horizontal force = 6N - 4N = 2N. This means there is a net force of 2N to the right, which lets you predict that the bone starts to accelerate to the right; this is, the bone begins to move toward the right.      

6 0
2 years ago
When you select a random person, the probability that this person will go to Ches
insens350 [35]

Answer: a= 0.0231

Step-by-step explanation:

n=8

p=0.75

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(p=x)

p(5) = 8C5 (0.25)^5 (0.75)^8-5

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6 0
2 years ago
A recipe calls for 5 ounces of vinegar and 10 ounces of oil. Daren is making dressing with 9 ounces of vinegar using the same ra
g100num [7]

Answer:

Step-by-step explanation:

Set this up as ratio of vinegar to oil in fraction form:

\frac{v}{o}:\frac{5}{10}

That's what we're given.  If we are looking to find how much oil he needs if he's using 9 ounces of vinegar, then 9 goes on top with the vinegar stuff and x goes on bottom as the unknown amount of oil:

\frac{v}{o}:\frac{5}{10}=\frac{9}{x}

Cross multiply to get

5x = 90 and

x = 18

Which you probably could do without the proportions.  If he is using 5 ounces of vinegar and double that amount of oil, then it just makes sense that if he uses 9 ounces of vinegar he will double that amount in oil to use 18 ounces.

6 0
2 years ago
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