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
Goryan [66]
3 years ago
11

PLEASE HELP!!!!!!! A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a

fuel efficiency of 20 miles per gallon of gas. During one particular week, the two cars went a combined total of 1450 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?
Mathematics
1 answer:
Marianna [84]3 years ago
4 0

Answer:

The answer to your question is car 1 = 30 gal and car 1 = 20 gal

Step-by-step explanation:

car 1 = a

car 2 = b

Efficiency of car 1 = 35 mi/gal

Efficiency for car 2 = 20 mi/gal

Total distance = 1450

Total gas consumption = 50 gal

Equations

                          35a + 20b = 1450            ------- (I)

                             a   +     b =  50               ------- (II)

Solve by elimination

Multiply equation II by -35

                          35a  + 20b  = 1450

                         -35a  - 35b   = -1750

Simplify

                            0    - 15b    =  -300

Solve for b

                                        b =  -300/-15

Result

                                        b = 20

Substitute b in equation II to find a

                               a +  20  = 50

Solve for a

                               a  = 50 -20

Result

                               a  = 30

You might be interested in
5+5 divded by 6 multiplied by 100 divded by 25 +1000 - 3456 multiplied by 60 and divded by 23 = what
Paladinen [302]

Answer:-9,015.23 i think plz dont come at me if wrong

Step-by-step explanation:

5+5=10/6=1.6*100=166.6/(25+1000=1025)=0.16-3456=-3,455.84*60=-207,350.4/23=-9,015.23

3 0
3 years ago
Y=5x-4
anyanavicka [17]

Answer:

\displaystyle -5x + y = -92\:or\:y = 5x - 92

Step-by-step explanation:

−12 = 5[16] + b

80

\displaystyle -92 = b \\ \\ y = 5x - 92

If you want it in <em>Standard</em><em> </em><em>Form</em>:

y = 5x - 92

- 5x - 5x

__________

\displaystyle -5x + y = -92

I am joyous to assist you anytime.

7 0
3 years ago
Please help me with this one
ruslelena [56]

Answer:

3.9375

Step-by-step explanation:

3 0
3 years ago
Find the remaining trigonometric ratios of θ if csc(θ) = -6 and cos(θ) is positive
VikaD [51]
Now, the cosecant of θ is -6, or namely -6/1.

however, the cosecant is really the hypotenuse/opposite, but the hypotenuse is never negative, since is just a distance unit from the center of the circle, so in the fraction -6/1, the negative must be the 1, or 6/-1 then.

we know the cosine is positive, and we know the opposite side is -1, or negative, the only happens in the IV quadrant, so θ is in the IV quadrant, now

\bf csc(\theta)=-6\implies csc(\theta)=\cfrac{\stackrel{hypotenuse}{6}}{\stackrel{opposite}{-1}}\impliedby \textit{let's find the \underline{adjacent side}}&#10;\\\\\\&#10;\textit{using the pythagorean theorem}\\\\&#10;c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a&#10;\qquad &#10;\begin{cases}&#10;c=hypotenuse\\&#10;a=adjacent\\&#10;b=opposite\\&#10;\end{cases}&#10;\\\\\\&#10;\pm\sqrt{6^2-(-1)^2}=a\implies \pm\sqrt{35}=a\implies \stackrel{IV~quadrant}{+\sqrt{35}=a}

recall that 

\bf sin(\theta)=\cfrac{opposite}{hypotenuse}&#10;\qquad\qquad &#10;cos(\theta)=\cfrac{adjacent}{hypotenuse}&#10;\\\\\\&#10;% tangent&#10;tan(\theta)=\cfrac{opposite}{adjacent}&#10;\qquad \qquad &#10;% cotangent&#10;cot(\theta)=\cfrac{adjacent}{opposite}&#10;\\\\\\&#10;% cosecant&#10;csc(\theta)=\cfrac{hypotenuse}{opposite}&#10;\qquad \qquad &#10;% secant&#10;sec(\theta)=\cfrac{hypotenuse}{adjacent}

therefore, let's just plug that on the remaining ones,

\bf sin(\theta)=\cfrac{-1}{6}&#10;\qquad\qquad &#10;cos(\theta)=\cfrac{\sqrt{35}}{6}&#10;\\\\\\&#10;% tangent&#10;tan(\theta)=\cfrac{-1}{\sqrt{35}}&#10;\qquad \qquad &#10;% cotangent&#10;cot(\theta)=\cfrac{\sqrt{35}}{1}&#10;\\\\\\&#10;sec(\theta)=\cfrac{6}{\sqrt{35}}

now, let's rationalize the denominator on tangent and secant,

\bf tan(\theta)=\cfrac{-1}{\sqrt{35}}\implies \cfrac{-1}{\sqrt{35}}\cdot \cfrac{\sqrt{35}}{\sqrt{35}}\implies \cfrac{-\sqrt{35}}{(\sqrt{35})^2}\implies -\cfrac{\sqrt{35}}{35}&#10;\\\\\\&#10;sec(\theta)=\cfrac{6}{\sqrt{35}}\implies \cfrac{6}{\sqrt{35}}\cdot \cfrac{\sqrt{35}}{\sqrt{35}}\implies \cfrac{6\sqrt{35}}{(\sqrt{35})^2}\implies \cfrac{6\sqrt{35}}{35}
3 0
3 years ago
John’s friend told him that he could earn $49 for handing out flyers at a local concert John wants to calculate the hourly rate
son4ous [18]

\frac{3.5x}{3.5}  =  \frac{49}{3.5}
x = 14
5 0
4 years ago
Other questions:
  • The graph of an equation representing a direct variation passes through the point (6, 10). Give another point with integral coor
    12·1 answer
  • Blue cassettes hold 45 minutes of music. Green cassettes hold 55 minutes of music. If Niko has 16 cassettes containing 830 minut
    15·2 answers
  • Dwayne starts assembling marketing packets at 11 a.m. Ashlie starts assembling marketing packets at 11:30 a.m. and assembles at
    7·1 answer
  • It has 3 more vertices than a triangle
    5·2 answers
  • Miss Penny inherits £910.
    11·2 answers
  • Deshaun deposited $4000 into an account with 5.1% interest, compounded semiannually. Assuming that no withdrawals are made, how
    14·2 answers
  • What are the multiples of the factors of 15
    6·1 answer
  • If Kathy walks 3 miles in 80 minutes how far will she in 120 minutes
    10·1 answer
  • 1. The Venn diagram shows Set T, a subset of real numbers. Real numbers Rational numbers Irrational numbers Whole numbers Based
    13·1 answer
  • Please help lol!!!!!!!
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!