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
Temka [501]
2 years ago
13

Solve the following system by the elimination method.1/3x+y=0/3 and 1/6x+1/5y=9/10

Mathematics
1 answer:
tatiyna2 years ago
6 0

Answer:

<h2>x = 9 and y = -3 → (9, -3)</h2>

Step-by-step explanation:

\left\{\begin{array}{ccc}\dfrac{1}{3}x+y=\dfrac{0}{3}&\text{multiply both sides by 3}\\\\\dfrac{1}{6}x+\dfrac{1}{5}y=\dfrac{9}{10}&\text{multiply both sides by 30}\end{array}\right\\[tex]\left\{\begin{array}{ccc}x+3y=0&\text{multiply both sides by (-2)}\\5x+6y=27\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-2x-6y=0\\5x+6y=27\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad3x=27\qquad\text{divide both sides by 3}\\.\qquad\boxed{x=9}\\\\\text{Put the value of x to the first equation:}\\\\9+3y=0\qquad\text{subtract 9 from both sides}\\3y=-9\qquad\text{divide both sides by 3}\\\boxed{y=-3}[/tex]

You might be interested in
A farmer wants to fence a rectangular area of 72 square feet next to a river. Find the length and width of the rectangle which u
Arlecino [84]

Answer:

  • 12 ft parallel to the river
  • 6 ft perpendicular to the river

Step-by-step explanation:

The least fence is used when half the total fence is parallel to the river. That is, the shape of the rectangle is twice as long as it is wide.

72 = W(2W)

36 = W²

6 = W . . . . . . the width perpendicular to the river

12 = 2W . . . .  the length parallel to the river

_____

<em>Development of this relation</em>

Let T represent the total length of the fence for some area A. Then if x is the length along the river, the width is y=(T-x)/2, and the area is ...

  A = xy = x(T -x)/2

Note that the equation for area is that of a parabola with zeros at x=0 and at x=T. That is, for some fence length T, the area will be a maximum at the vertex of this parabola. That vertex is located halfway between the zeros, at ...

 x = (0 +T)/2 = T/2

The corresponding area width (y) is ...

  y = (T -T/2)/2 = T/4

Equivalently, the fence length T will be a minimum for some area A when x=T/2 and y=T/4. This is the result we used above.

8 0
3 years ago
Help meeeeeeeeeeeeeeeeeee <br><br> &gt;_
nignag [31]

Answer:

good news, the second one is relatively easy because it can be factored to (2x+1)(2x-3) which means that number two has solutions of -1/2 and 3/2

but for number one you have to either use the quadratic equation cause I've tried using synthetic division or just use the second equation to derive the first solutions so I tried move the graph up by two units and found that the intercepts are approximately (1+-√2)/2 or 1/2+-1/√2 for 4x^2-4x-1

7 0
3 years ago
180 miles in 3 hours, what's the unit rate?
Oliga [24]

Answer:

60 or 60:1

Step-by-step explanation:

You will have to divide 180 by 3 which is 60 or you can divide 160 / 3 = 60 & divide 3 / 3 = 1.

6 0
3 years ago
Read 2 more answers
Evaluate F(x) = x^2 + 1 for f(-1)
Aleks04 [339]

Answer:

2

Step-by-step explanation:

f(x) = x^2 + 1

f(-1) = (-1)^2 + 1

f(-1) = 2

3 0
2 years ago
Read 2 more answers
What is the factored form of x^3 - 1?
qaws [65]
X³ - 1 = x³ - 1³ = (x-1)(x²+x+1)
7 0
3 years ago
Other questions:
  • This is the problem<br> Dan says 3/5 Is the same as 3.5. Is he correct? Explain
    5·2 answers
  • Plz help MATH HW<br>explain/answer
    15·1 answer
  • The graph of the equation y=x^2-7 is symmetric with respect to which of the following?a.the line y=-x+7b.the y-axis c.the x axis
    6·1 answer
  • Is this equation an identity?<br><br> -5w − 8 = 1 − 2w
    8·1 answer
  • Im having a really bad day help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
    11·2 answers
  • S^2t - 10 if s= -8 and t = 3/4
    9·2 answers
  • PLEASE HELP!!!!
    10·2 answers
  • Richard is $15 overdrawn on his checking account. He writes a check for $7. What is the balance in his checking account now?​
    10·1 answer
  • What is the slope of the line that contains these points?
    6·1 answer
  • GOOD REVIEW IF BOTH OF THE ANSWERS ARE CORRECT
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!