1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Oksana_A [137]
3 years ago
5

A vehicle 1 1/8 uses gallons of gasoline to travel 13 1/2 miles. At this rate, how many miles can the vehicle travel per gallon

of gasoline?
Mathematics
2 answers:
alexgriva [62]3 years ago
3 0

Answer: 12 miles per gallon

trust

me

on

my

mama

this

is

correct

my

g

Ivan3 years ago
3 0

Answer:

<em>The vehicle can travel 12 miles per gallon of gasoline</em>

Step-by-step explanation:

<u>Proportions</u>

A vehicle uses 1 1/8 gallons of gasoline to travel 13 1/2 miles.

It's required to find the rate of miles per gallon of gasoline consumption of the vehicle.

First, we convert all the mixed fractions to improper fractions:

1\frac{1}{8}=1+\frac{1}{8}=\frac{9}{8}

13\frac{1}{2}=13+\frac{1}{2}=\frac{27}{2}

The rate of consumption is:

\displaystyle \frac{\frac{27}{2}}{\frac{9}{8}}

Operating:

\displaystyle \frac{\frac{27}{2}}{\frac{9}{8}}=\frac{27}{2}\cdot\frac{8}{9}=12

The vehicle can travel 12 miles per gallon of gasoline

You might be interested in
3f+3&lt;6 or 7f-20 &gt;50 I don't understand this
OLga [1]
The answers to the questions

7 0
3 years ago
The denominator of a fraction is two more than the numerator. If both numerator and denominator are decreased by six, the simpli
ira [324]

Answer:

\dfrac{40}{42}

Step-by-step explanation:

Let the numerator of the fraction=x

Since the denominator of a fraction is two more than the numerator.

Denominator=x+2

The fraction is therefore:

\dfrac{x}{x+2}

If both numerator and denominator are decreased by six, the fraction becomes:

\dfrac{x-6}{x+2-6}

The simplified result is \dfrac{17}{18}

Therefore:

\dfrac{x-6}{x+2-6}=\dfrac{17}{18}\\$Next, we solve for x\\Cross multiply\\18(x-6)=17(x+2-6)\\18(x-6)=17(x-4)\\Expand the bracket\\18x-108=17x-68\\Collect like terms\\18x-17x=-68+108\\x=40

Substituting x=40 into the initial fraction

\dfrac{x}{x+2}=\dfrac{40}{40+2}=\dfrac{40}{42}

Therefore, the original fraction is \dfrac{40}{42}

4 0
3 years ago
Which function is the same as y = 3 cosine (2 (x startfraction pi over 2 endfraction)) minus 2? y = 3 sine (2 (x startfraction p
kirza4 [7]

The function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

<h3>How to convert sine of an angle to some angle of cosine?</h3>

We can use the fact that:

\sin(\theta) = \cos(\pi/2 - \theta)\\\sin(\theta + \pi/2) = -\cos(\theta)\\\cos(\theta + \pi/2) = \sin(\theta)

to convert the sine to cosine.

<h3>Which trigonometric functions are positive in which quadrant?</h3>
  • In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.
  • In second quadrant(π/2 < θ < π), only sin and cosec are positive.
  • In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.
  • In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.

(this all positive negative refers to the fact that if you use given angle as input to these functions, then what sign will these functions will evaluate based on in which quadrant does the given angle lies.)

Here, the given function is:

y= 3\cos(2(x + \pi/2)) - 2

The options are:

  1. y= 3\sin(2(x + \pi/4)) - 2
  2. y= -3\sin(2(x + \pi/4)) - 2
  3. y= 3\cos(2(x + \pi/4)) - 2
  4. y= -3\cos(2(x + \pi/2)) - 2

Checking all the options one by one:

  • Option 1: y= 3\sin(2(x + \pi/4)) - 2

y= 3\sin(2(x + \pi/4)) - 2\\y= 3\sin (2x + \pi/2) -2\\y = -3\cos(2x) -2\\y = 3\cos(2x + \pi) -2\\y = 3\cos(2(x+ \pi/2)) -2

(the last second step was the use of the fact that cos flips its sign after pi radian increment in its input)
Thus, this option is same as the given function.

  • Option 2: y= -3\sin(2(x + \pi/4)) - 2

This option if would be true, then from option 1 and this option, we'd get:
-3\sin(2(x + \pi/4)) - 2= -3\sin(2(x + \pi/4)) - 2\\2(3\sin(2(x + \pi/4))) = 0\\\sin(2(x + \pi/4) = 0

which isn't true for all values of x.

Thus, this option is not same as the given function.

  • Option 3: y= 3\cos(2(x + \pi/4)) - 2

The given function is y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2

This option's function simplifies as:

y= 3\cos(2(x + \pi/4)) - 2 = 3\cos(2x + \pi/2) -2 = -3\sin(2x) - 2

Thus, this option isn't true since \sin(2x) \neq \cos(2x) always (they are equal for some values of x but not for all).

  • Option 4: y= -3\cos(2(x + \pi/2)) - 2

The given function simplifies to:y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2

The given option simplifies to:

y= -3\cos(2(x + \pi/2)) - 2 = -3\cos(2x + \pi ) -2\\y = 3\cos(2x) -2

Thus, this function is not same as the given function.

Thus, the function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

Learn more about sine to cosine conversion here:

brainly.com/question/1421592

4 0
2 years ago
Read 2 more answers
Select each expression that has a value of 36 when x = 12.
pogonyaev

Answer:

Option c

Step-by-step explanation:

if x = 12

12^2 = 144

144/18 = 8

28 + 8 = 36

6 0
3 years ago
Meaghan and Lily are dividing 43.61 by 7. Meaghan says that the first digit of the quotient is in the ones place. Lily says it i
Ivahew [28]

Answer: Meaghan is right.

Step-by-step explanation:

For a number like:

123.45

the tens place would be the "2" (second number at the left of the decimal point)

The ones place would be the "3" (first number at the left of the decimal point)

Let's suppose that Lily is correct.

Then the quotient of:

43.61/7

Will be a number with two digits in the left of the decimal point.

The smallest number that meets this condition, is the number 10.

Then let's see:

7*10 = 70

then:

70/7 = 10

and:

43.61 < 70

(70 is larger than 43.61)

then:

43.61/7 < 70/7 = 10

Then:

(43.61/7) < 10

This means that our quotient is smaller than 10, then the first digit of the quotient can not be on the tens place.

Then Meaghan is the correct one.

We also could perform the quotient to find:

43.61/7 = 6.23

So yes, Meaghan is correct.

5 0
2 years ago
Other questions:
  • *One half of two fifths of x.
    7·1 answer
  • Next two sets of numbers after 3-6, 7-14
    6·1 answer
  • Look at picture plz help I’m dumb
    7·1 answer
  • Huong is cooking cupcakes. The recipe calls for three and five sixths cups of sugar. She accidentally puts in three and nine eig
    5·1 answer
  • Find the Area of the figure.<br> 4x - 3<br> 2x + 1
    9·1 answer
  • Katie earned $1890 in 7 years on an investment at a 6% annual simple interest rate. How much was Katie’s investment?
    8·2 answers
  • A popular beach erodes 4 inches per year on average.
    5·1 answer
  • HELPPPP!!!!!
    5·2 answers
  • Plzzzzzss answer quickly !!!!!
    7·1 answer
  • Location Score Factor (100 points each) Weight A B C Convenience 0.15 89 78 84 Parking facilities 0.20 75 93 98 Display area 0.1
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!