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
Inessa [10]
3 years ago
7

Use properties to rewrite the given equation. Which equations have the same solution as 3/5x +2/3 + x = 1/2– 1/5x? Check all tha

t apply.
a. 8/5x+2/3=1/2-1/5x
b. 18x + 20 + 30x = 15 – 6x
c. 18x + 20 + x = 15 – 6x
d. 24x + 30x = –5
e. 12x + 30x = –5
Mathematics
2 answers:
VMariaS [17]3 years ago
5 0

Answer:

Only options a ,b,d have the same solution as \frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x

Step-by-step explanation:

Given:

An equation:  \frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x    ....[1]

Like terms states that contain the same variables raised to the same power.

Combine like terms on left hand side in equation [1] we get,

\frac{3}{5}x+x +\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x

\frac{8}{5}x +\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x

we get option (a) as the same solution.

Using LCM(Least Common ) to change each fraction to make their denominators the same as the least common denominator

Taking LCM both sides in Equation (1) ,

\frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x

As LCM(3,5)=15 and LCM(2,5)=10 we have,

\frac{9x+10+15x}{15}= \frac{5-2x}{10}

On simplifying we get,

10(9x+10+15x)= 15(5-2x)=

Dividing both sides by 5 we get,

\frac{10(9x+10+15x)}{5} =\frac{15(5-2x)}{5}

On simplify:

2(9x+10+15x)=3(5-2x)

∴ 18x+20+30x=15-6x

which is same solution as given in option (b).

Now,

Use Additive Property of Equality states that allows one to add the same quantity to both sides of an equation.

Further, using the above property add 6x both sides  in  18x+20+30x=15-6x we get,

18x+20+30x+6x=15-6x+6x

On simplifying we get,

18x+20+30x+6x=15

Subtract 20 from both the sides we get,

18x+20+30x+6x-20=15-20

Simplify:

18x+30x+6x=-5

or, 24x+30x=-5 which is same solution  as given in option(d)

But, options c and e equation doesn't have same solution as \frac{3}{5}x +\frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x










lorasvet [3.4K]3 years ago
3 0

Answer:

a,b,d

Step-by-step explanation:

You might be interested in
What the y-intercept of (8,0) and (3,7)
Anettt [7]

Answer:

\sf \bf y - intercept = \dfrac{56}{5}

Step-by-step explanation:

Y-intercept:

   (8,0)  ; x₁ = 8 & y₁ = 0

   (3,7)   ; x₂= 3  & y₂ = 7

  • First find the slope of the line.

      \sf \boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}

                  \sf = \dfrac{7 - 0}{3 - 8}\\\\ =\dfrac{7}{-5}\\\\=\dfrac{-7}{5}

 slope y-intercept form of the line:  y = mx + b

Substitute the slope and x and y in the above equation. We can choose anyone of the given points.

     0 = \dfrac{-7}{5}*8 + b\\\\0=\dfrac{-56}{5}+b\\\\\dfrac{56}{5}=b\\\\ \boxed{\bf b = \dfrac{56}{5}}

3 0
1 year ago
Jejdhsgeuekdskdjduuwwoiehrddujeejdhxu
Dimas [21]
Jssjsjsjsjsjdjidjebsvabbxjxjufiwiwj .
3 0
3 years ago
Read 2 more answers
The midpoint of chord AB is ( , ), and the slope of chord AB is
kykrilka [37]

Answer:

See solution below

Step-by-step explanation:

Let the coordinate's of A and B be (1, 0) and (2,4) respectively

midpoint M (X, Y) = [(x1+x2/2, y1+y2/2)]

X = x1+x2/2

X = 1+2/2

X = 3/2

X = 1.5

Y = y1+y2/2

Y = 0+4/2

Y = 4/2

Y = 2

Hence the required midpoint (X, Y) is (1.5, 2)

Slope m = y2-y1/x2-x1

m = 4-0/2-1

m = 4/1

m = 4

Hence the slope is 4

<em>Note that the coordinates are assumed but the same calculation can be employed for any other coordinates</em>

7 0
2 years ago
Which is a perfect square? 5, 8, 44, 36
agasfer [191]

Answer:

The answer is 36.

Step-by-step explanation:

   36

    /\

6      6

/\      /\

3 2   3 2

4 0
3 years ago
Read 2 more answers
The tuition at a certain college was $29,793 last year and increased 5.3% from last year to the current year. How much is this y
SCORPION-xisa [38]

Answer:

the answer is 67

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • Lilianna has $68. She needs at least $194 for a new cell phone. Write an inequality to fit this situation. What's the least amou
    12·1 answer
  • in a repeating musical pattern,there are 56 beats in 7 measure.How many measures are there after 104 beats
    12·1 answer
  • The graph of the parent function f(x) = x is translated to form g(x) = (x - 7) + 9. The point (0,0) on the graph of
    10·1 answer
  • 1) What is the length of the garden in this blueprint?<br> 1”=4 feet <br> 1/4
    6·1 answer
  • In a chocolate chip cookie recipe flour,brown sugar, and chocolate chips are mixed in the ratio 5:3:4 if the total volume of the
    8·1 answer
  • When rolling two number cubes, what is the probability of rolling a sum that is 6 or a sum that is odd?
    9·1 answer
  • A bin of 50 manufactured parts contains 3 defective parts and 47 non-defective parts. A sample of size 6 parts is selected from
    6·1 answer
  • Michael, Leo and JuWoong collect stamps. The ratio of the number of Michael's stamps to JuWoong's stamps is 2:7. The number of J
    5·1 answer
  • A car is traveling at a rate of 72 miles per hour. What is the car's rate in feet per second? How many feet will the car travel
    9·1 answer
  • Help ill give brainly
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!