answer.
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
nexus9112 [7]
2 years ago
8

Solve the linear equation 31x + 29y = 33 29x + 31y = 27

Mathematics
1 answer:
Temka [501]2 years ago
6 0

Answer:

x = 2

y = -1

Step-by-step explanation:

Make the coefficient of x the same

Multiply the first equation by 29

31x + 29y = 33 becomes

899x + 841y = 957

Multiply the second equation by 31

29x + 31y = 27 becomes

899x + 961y = 837

Subtract the equations

(899x + 841y) - (899x + 961y) = 957 - 837

(899x - 899x) + (841y - 961y) = 120

841y - 961y = 120

-120y = 120

y = 120/-120 = -1

Substitute the value of y into both equations to find the value of x and check its right.

31x + 29y = 33

31x + 29(-1) = 33

31x - 29 = 33

31x = 33 + 29

31x = 62

x = 62/31 = 2

29x + 31y = 27

29x + 31(-1) = 27

29x - 31 = 27

29x = 27 + 31

29x = 58

x = 58/29 = 2

You might be interested in
Cameron buys 2.45 pounds of apples and 1.65 pounds of pears. Apples and pears each cost c dollars per pound. If the total cost a
Leto [7]

Answer:

2.45c + 1.65c = 4.12 + 0.75

Step-by-step explanation:

To write an equation to find the value for c, we need to declare what c is first.

c = price of fruit

2.45c + 1.65c = 4.12 + 0.75

Now we multiplied c to 2.45 and 1.65 and added them together, because whatever the value of c is will give us the equivalence of the sum of 4.12 + 0.75.

Now to check if the equation is right, let's solve for c.

2.45c + 1.65c = 4.12 + 0.75

4.1c = 4.87

Now to get the value of c, we divide both sides of the equation by 4.1.

\dfrac{4.1c}{4.1}=\dfrac{4.87}{4.1}

c = 1.19

Now let's substitute the value of c in the equation to see if we got it right.

2.45(1.19) + 1.65(1.19) = 4.12 + 0.75

2.92 + 1.96 = 4.87

4.87 = 4.87

Therefore concluding that the value of c is 1.19.

7 0
2 years ago
Which part of the proof does the fourth statement and reason represent?
denis-greek [22]

Answer:

Option B is correct.

Reason:It is an argument

Step-by-step explanation:

Given: AB \cong BC  and BC \cong EF

By transitive property:  a = b  and b = c then, a =c

⇒AB \cong EF

AB = EF                                [def of \cong segment]

By Segment Addition Postulate states that given  two points A and C, and a third point B lies on the line segment AC if and only if the distances between the  points satisfy the equation

AB + BC = AC.

Since, the line segment EG , F lies on the line segment;

then, by segment addition postulates we have;

EG = EF + FG

By substitution AB=EF

⇒ EG = AB + FG                     hence proved!

Since, in the fourth statement reason is:  It is an argument

3 0
2 years ago
Two window washers start at the heights shown. (A: 21 ft high rising 8 in per second. The other is 50 feet high descending 11inc
babunello [35]

For this case, the first thing we are going to do is write the generic equation of motion for the vertical axis.

We have then:

h = \frac {1} {2} gt ^ 2 + vo * t + h0

Where,

  • <em>g: acceleration of gravity </em>
  • <em>vo: initial speed </em>
  • <em>h0: initial height </em>

For the first body:

h1 = \frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21

For the second body:

h2 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50

By the time both bodies have the same height we have:

h1 = h2\\

\frac {1} {2} gt ^ 2 + \frac {8} {12} * t + 21 = \frac {1} {2} gt ^ 2 - \frac {11} {12} * t + 50

Rewriting we have:

\frac {8} {12} * t + 21 = - \frac {11} {12} * t + 50

\frac {8} {12} * t + \frac {11} {12} * t = 50 - 21

\frac {19} {12} * t = 29

Clearing time:

t = 29 (\frac {12} {19})\\t = 18.31s

Answer:

 it takes 18.31s for the two window washers to reach the same height

6 0
2 years ago
Read 2 more answers
HURRY PLEASE When 5 and 6 are multiplied by the same factor, how do the ratios compare to the ratio 5:6? The ratios are equivale
erma4kov [3.2K]

Answer:

The ratios are equivalent.

Step-by-step explanation:

If you multiply both 5 and 6, the ratio stays the same.

5:6 = 10:12 = 15:18 = 20:24 etc.

You can try this by dividing the larger number by the smaller number. You'll always get 1.2 as the "relationship", or ratio, is preserved.

24/20 = 1.2

15/18 = 1.2

10/12 = 1.2

6/5 = 1.2

6 0
2 years ago
The rectangular playground in tim's school is three times as long as it is wide. the area of the playground is 75 square meters.
qwelly [4]
Let x be the width of the playground, then 3x is the length of the 
<span>playground

х * 3х = 75
3x</span>² = 75
x² = 25
x = 5 m (width)
5*3=15 m (length)

Perimeter = 2(5+15) = 2*20 = 40 meters.
8 0
2 years ago
Other questions:
  • This box has the same length , width, and height as the 2 basketballs. Which expression gives the volume of the empty space enci
    8·2 answers
  • There are four defenders on a soccer team. if this represents 20 percent of the players on the team, which equation can be used
    14·2 answers
  • A company borrowed $40,000 cash from the bank and signed a 6-year note at 7% annual interest. The present value of an annuity fa
    8·1 answer
  • The graph of y=|x| is transformed as shown in the graph below. Which equation represents the transformed function?
    12·2 answers
  • A sample with M = 85 and s = 12 is transformed into z-scores. After the transformation, what are the values for the mean and sta
    7·2 answers
  • A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Find the lengths of the median o
    7·1 answer
  • The graph shows a vertical translation of y = RootIndex 3 StartRoot x EndRoot.
    9·2 answers
  • Q: Angelica uses the point (4,3) to represent the location of her house and uses the point (10,8) to represent the location of a
    12·2 answers
  • On a game show, contestants shoot a foam ball toward a target. The table includes points along OnePath the ball can take to hit
    5·1 answer
  • Maple street is 3 times as long as pine street. how long is pine street?
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!