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Allisa [31]
4 years ago
9

Determine whether or not the two equations below have the same solution. In two or more complete sentences, explain your rationa

le

Mathematics
1 answer:
Artist 52 [7]4 years ago
8 0

Answer:

Yes, they have the same solution.

Step-by-step explanation:

The steps in solving a two-step equation are to simplify by using

  1. The inverse of addition or subtraction and then
  2. The inverse of multiplication or division

Equation 1

\dfrac{2}{3}x + \dfrac{3}{4} = 8

(a) Inverse of addition

\begin{array}{rcl}\dfrac{2}{3}x + \dfrac{3}{4} - \dfrac{3}{4}& = & 8 - \dfrac{3}{4}\\\\\dfrac{2}{3}x & = & \dfrac{29}{4}\\\end{array}

(b) Inverse of multiplication

\begin{array}{rcl}\left (\dfrac{2x}{3}\right ) \left (\dfrac{3}{2}\right ) & = & \left (\dfrac{29}{4}\right ) \left ( \dfrac{3}{2} \right ) \\\\x & = & \dfrac{87}{8}\\\end{array}

Equation 2

8x = 87

(a) Inverse of multiplication

\begin{array}{rcl}\dfrac{8x}{8} & = & \dfrac{87}{8}\\\\x & = & \dfrac{87}{8}\\\end{array}

The two equations have the same solution.

For the first equation, I used the inverse of addition and then the inverse of multiplication to get the value of x.

The second equation needed only the inverse of multiplication.

Both solutions were the same.

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a wall is 8 feet tall and 36 feet wide. tom wants to cover it with white paint that costs 2 dollars per ounce. if each ounce of
arlik [135]

Answer:

1152

Step-by-step explanation:

First we need to find the area of the wall in square inches

8 ft = 8*12 = 96 inch tall

36 ft = 36 * 12 = 432 inches wide

The area = 96 * 432 =41472 in^2

Each ounce of paint cover 72 in^2 so divide by 72

41472/72 =576

We need 576 ounces to cover the wall

At 2 dollars per ounces

576*2 =1152 dollars to paint the wall

8 0
3 years ago
Brandon has 1 jill has 3 mark has 2 need Nicole has 4 and steve has 0 what is the mean​
Anna [14]

Answer: The mean is 2.

Step-by-step explanation:

The mean number is a group of numbers is the average. In this group, the numbers are 1, 3, 2, 4 and 0. The total of all of the numbers is 10. In order to calculate the average/mean you need to divide the total by the number of values, which is 10/5 = 2. The mean is 2.

8 0
3 years ago
Read 2 more answers
Solve Quantity x plus 6 end quantity over 2x is equal to three-fourths. Show all work.
Jet001 [13]

The expression described is translated into the following formula:


\frac{x+6}{2x} = \frac{3}{4}


Note that this implies that x \neq 0


Cross-multiply denominators to get rid of the fractions:


4(x+6) = 3(2x)


Expand both sides:


4x+24 = 6x


Subtract 4x from both sides:


24 = 6x - 4x = 2x


Divide both sides by 2:


12 = x


Check:


\frac{12+6}{24} = \frac{18}{24} = \frac{3}{4}


Which is true because


18 \cdot 4= 24\cdot 3


since both sides evaluate to 72

5 0
3 years ago
How many 20 cm by 30 cm rectangular tiles would you need to tile the outdoor are shown below?
svetlana [45]
What answer did you get.



4 0
4 years ago
Match each statement to the reasons given for the geometric proof.
Savatey [412]

Answer:  5, 3, 1, 2, 6, 4

<u>Step-by-step explanation:</u>

The proof should be written as follows (which is a different order than provided):

  <u>Statement                       </u>                         <u>Reason                                         </u>

1. ABCD is a parallelogram                     1. Given

2. AB||DC and AD||BC and AB ≅ DC     2. Definition of parallelogram

3. ∠ABD ≅ ∠CDB                                    3. Alternate Interior Angles Theorem

4. ∠DEC ≅ ∠BEA                                     4. Vertical Angles Theorem

5. ΔABE ≅ ΔCDE                                    5. AAS Congruency Theorem

6. AE = CE and BE = DE                         6. CPCTC

This is the order provided in your question:

5. ΔABE ≅ ΔCDE                                    5. AAS Congruency Theorem

3. ∠ABD ≅ ∠CDB                                    3. Alternate Interior Angles Theorem

1. ABCD is a parallelogram                     1. Given

2. AB||DC and AD||BC and AB ≅ DC     2. Definition of parallelogram

6. AE = CE and BE = DE                         6. CPCTC

4. ∠DEC ≅ ∠BEA                                     4. Vertical Angles Theorem

5 0
3 years ago
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