A car has 15 gallons of gas in its tank. The car travels 35 miles per gallon of gas. It uses 1/35 of gas to go 1 mile. How much gas dose the car use to 100 miles? Show your reasoning.

Note: Consider we need to find the solution of given equation.

Given:

The equation is

[tex]\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}[/tex]

To find:

The solution of the equation.

Solution:

We have,

[tex]\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}[/tex]

[tex]\dfrac{2+x^2}{2x}=\dfrac{11}{6}[/tex]

By cross multiplication, we get

[tex]6(2+x^2)=11(2x)[/tex]

[tex]12+6x^2=22x[/tex]

[tex]6x^2-22x+12=0[/tex]

[tex]2(3x^2-11x+6)=0[/tex]

Divide both sides by 2.

[tex]3x^2-11x+6=0[/tex]

Splitting the middle term, we get

[tex]3x^2-9x-2x+6=0[/tex]

[tex]3x(x-3)-2(x-3)=0[/tex]

[tex](x-3)(3x-2)=0[/tex]

Using zero product property, we get

[tex]x-3=0[/tex] and [tex]3x-2=0[/tex]

[tex]x=3[/tex] and [tex]x=\dfrac{2}{3}[/tex]

Therefore, the solutions of the given equation are [tex]x=3[/tex] and [tex]x=\dfrac{2}{3}[/tex].

Quadratic equations are algebraic equations that can be factored or broken down into simpler forms(factors).

Transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0

We are given the algebraic equation:  1/x+x/2=11/6

Transforming it into a quadratic equation, we find the Lowest common denominator of the fractions in the quadratic equations.

LCD(x,2,6) = 6x

Multiply all through the fractions by 6x

(1/x * 6x)+ (x/2 * 6x) = (11/6 * 6x)

6 + 3x² = 11x

Rewriting the equation:

3x² - 11x + 6 = 0

Therefore, transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0

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Step-by-step explanation:

do you want to find r?

so do 4252.50/ (18000*54)

Answer:

80

Step-by-step explanation:

Answer:

B (also known as 30)

Step-by-step explanation:

hope this helps!

Answer:

2

Step-by-step explanation:

ez any thing else just hit me up of so

Answer:

0.7 lap per minute

Step-by-step explanation:

Answer:

Step-by-step explanation:

1) The newly opened Mario's Trattoria is expected to produce a continuous income stream at the rate of

R(t) = 130,000 to generate income at the rate of

R(t) = 200,000 Camille purchased a 14-year franchise for a computer outlet store that is expected to generate income at the rate of

R(t) = 400,000

Answer:

i believe its C

Step-by-step explanation:

Answer:

52 degree angle

Answer:

12

Step-by-step explanation:

27 times2 is 54 -200 =146           12 times 12 is 144 and you cant go over 146 for 13                 please mark brianly

Answer:

300g

Step-by-step explanation:

Given parameters:

Mass of carbohydrate in the cereal meal  = 18g

Unknown:

Grams of carbohydrate recommended each day = ?

Solution:

The 18grams of the carbohydrate is just 6% of the total carbohydrate need per day;

         6% x total carbohydrate recommendation  = 18

       [tex]\frac{6}{100}[/tex] x total carbohydrate  = 18

       Total carbohydrate = 18 x [tex]\frac{100}{6}[/tex]   = 300g

Answer:

The answer is 300 grams of carbs on a 2000-calorie diet!

Step-by-step explanation:

Mass = 18g

daily allowance: ???

6% x total carbohydrate recommendation  = 18

x total carbohydrate  = 18

Total carbohydrate = 18 x    = 300g on a 2000-calorie diet

Answer:

3y

Step-by-step explanation:

Answer:

The third one is the answer. if you ever need help hit me up.

Step-by-step explanation:

Answer:

83, 84, 85

Step-by-step explanation:

Answer:

n/4 + 1 =5

n/4 = 5-1

n/4 = 4

n = 4*4

n = 16

Answer:

So do this,

Step-by-step explanation:

stand up and go ask your mom!

Answer: I don't see the amount per football

Step-by-step explanation:

Answer:

What is this about?

Step-by-step explanation:

What topic?

Answer:

False

Step-by-step explanation:

Cause the graphs show false instead of being true

Answer:

there is none

Step-by-step explanation:

Answer:

No solutions

Step-by-step explanation:

Real number solutions only or real and complex solutions. A solution to the system:

y=-2x+2

y=x2-2x+4

is the value of x such that when you plug it into both equations, they both produce the same value of y, or the value of x such that

-2x+2=x2-2x+4

solving this equation----------> x2=-2, taking square root of both sides gives x= ±√2i, or the system has no real solutions but has 2 complex solutions. If you graph both functions in the xy-plane, where x, y are real numbers, you' ll see they do not intersect, which implies there is no real number solutions.

Answer:

here is the answer in photo form

Answer:

Step-by-step explanation:

Simple and best practice solution for (c-5)d=2 equation. ... If it's not what You are looking for type in the equation solver your own equation and let us solve it. ... 2 + 5d cd = 2 + 5d Divide each side by 'd'. c = 2d-1 + 5 Simplifying c = 2d-1 + 5 Reorder ... 11/4-t8 | | (3x^2+5x+2)+(4x^2+3x+2)= | | 4Y+7-Y=4+2Y-8 | | 10x+190=360 ...

For example, let's say with have the equation x+5 ... If we evaluate the same expression when x=10 , we get: 3(10)+7=30+7=37 . Here's a variable expression with two variables : 3x−2y ... How do you express the phrase "a number z divided by 19" as an algebraic expression? ... How do you simplify 11c+5d−9c−9d?Let the number of cows be x and their legs be 4x. ... or, x = 7 [dividing by 2 on both sides]. ... The roots of the equation ax2 + bx + c = 0 will be reciprocal if: ... A circle of radius 10 inches has its center at the vertex C of an equilateral triangle ABC ... (a) 15, (b) 30, (c) 60, (d) 90, (e) 120. Circle Problem Answers. Answer: (b) 5.

Answer:

7*-4=-28

Step-by-step explanation:

7*-4=-28

Answer:

sarah can buy 88 songs

Step-by-step explanation:

filler fbjebdjsndjen

Answer:

sarah has to give her 15.99 from 75 after that she will be left with 59.01 and with that she can buy 74 songs

Answer:

X=-3

Step-by-step explanation:

2x+15=-3x

15=-5x

x=15/-5

x=-3

Answer:

x = -3

Step-by-step explanation:

2x + 15 = -3x

15 = -5x

x = -3

Answer:

wut i cannot see the question

Step-by-step explanation:

Answer:

25 inches

Step-by-step explanation:

Given

Son:

[tex]Height = 40\ inch[/tex]

[tex]Shadow = 24\ inch[/tex]

Woman:

[tex]Height = 41.4\ inch[/tex]

Required

Determine the height of the woman's shadow

From the question, the height is directly proportional to the height of the shadow:

So, we have:

[tex]40\ inch = 24\ inch[/tex] --- For the son

and

[tex]41.4\ inch = x[/tex]

Where x represents the shadow of the woman

Cross Multiply:

[tex]x * 40 = 24 * 41.4[/tex]

[tex]x * 40 = 993.6[/tex]

[tex]40x = 993.6[/tex]

Make x the subject

[tex]x = 993.6/40[/tex]

[tex]x = 24.84[/tex]

[tex]x = 25[/tex] ---- approximated

Hence, the woman's shadow is 25 inches tall

Answer:

3 - 0.75x= .625

Step-by-step explanation:

3/4=0.75

5/8=0.625

Step-by-step explanation:

4x^2+2x-5

4(-1)^2+2(-1)-5

4-2-5

2-5= -3

Answer:

The expected value of lateness [tex]\frac{7}{20}[/tex] hours.

Step-by-step explanation:

The probability distribution of lateness is as follows:

  Lateness             P (Lateness)

  On Time                     4/5

1 Hour Late                  1/10

2 Hours Late                1/20

3 Hours Late                1/20​

The formula of expected value of a random variable is:

[tex]E(X)=\sum x\cdot P(X=x)[/tex]

Compute the expected value of lateness as follows:

[tex]E(X)=\sum x\cdot P(X=x)[/tex]

         [tex]=(0\times \frac{4}{5})+(1\times \frac{1}{10})+(2\times \frac{1}{20})+(3\times \frac{1}{20})\\\\=0+\frac{1}{10}+\frac{1}{10}+\frac{3}{20}\\\\=\frac{2+2+3}{20}\\\\=\frac{7}{20}[/tex]

Thus, the expected value of lateness [tex]\frac{7}{20}[/tex] hours.

An expected value is the theoretical mean value of a numerical experiment over many repetitions of the experiment.

Expected value of lateness is  [tex]\frac{7}{20}[/tex] hours.

Let us consider, P(x) is represent that probability of lateness and x represent number of hours late.

So, below a table is formed.

         x       0             1            2           3

      P(x)      4/5         1/10      1/20       1/20

From formula of expected value,

        E(x) = ∑ x P(x)

[tex]E(x)=(0*\frac{4}{5} )+(1*\frac{1}{10} )+(2*\frac{1}{20} )+(3*\frac{1}{20} )\\\\E(x)=0+\frac{1}{10}+\frac{1}{10}+\frac{3}{20} \\\\E(x)=\frac{7}{20}[/tex]

So, expected value of lateness is 7/20 hours.

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Answer:

(There are so many answers to this question) she could have gotten 13 glitter boxes and none of the other boxes.

Step-by-step explanation:

13x10=130

Answer: 13 glitter cardboard boxes that are $10

Step-by-step explanation:

We have to divide the number $130 by both numbers each cardboard box costs, designed glitter boxes that are $10 and plain cardboard boxes are 6 each. So, let's do that right now.

130 ÷ 6 = 23.333

Sara only bought 13 cardboard boxes, so it is no the answer.

Now, let's try the second number that is $10. We have to remember that the answer has to be 13. So, let's do that as well right now.

130 ÷ 10 = 13

We see that we get 13 while we divide 130 by 10, so Sara bought 13 designed glitter cardboard boxes.

The answer to the question is 13 glitter cardboard boxes that are $10.

Hope this helps you!