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garik1379 [7]
3 years ago
8

Given: ⅓ (18x + 27) = 81 Prove: x = 12

Mathematics
1 answer:
sasho [114]3 years ago
4 0

Answer:

Firstly, rewrite the equation:

⅓ (18 + 27) = 81

Substitute x for the given number of it's supposed equivalent.

In this case x = 12.

⅓ (18(12) + 27) = 81

Solve using PEMDAS and simplify what is in the parenthesis first. Then, multiply.

(18 x 12) + 27 = 243

Now, solving using PEMDAS, multiply the total of what you got that was originally in the parenthesis by ⅓ .

⅓ (243) = 81

When you multiple these number they are equivalent to 81.

81 = 81

Since the equation given, when substituted x for 12, is equivalent to 81, this proves that substituting x for 12 makes this equation true.

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The equation d = 3t gives the distance, d, in meters that Liam swims with respect to time, t, in seconds.
Natasha_Volkova [10]

Answer:

Liam's rate = 3 meters per second

Edgar's rate = 3.2 meters per second

Edgar swims faster

Step-by-step explanation:

<u>Liam:</u>

The equation d=3t gives the distance, d, in meters that Liam swims with respect to time, t, in seconds.

When t=0,\ d=0.

When t=1,\ d=3.

Rate of change:

\dfrac{3-0}{1-0}=3

Liam's rate is 3 metres per second.

<u>Edgar:</u>

When t=20, \ d=64.

When t=40,\ t=128.

Rate of change:

\dfrac{128-64}{40-20}=\dfrac{64}{20}=3.2

Edgar's rate is 3.2 metres per second.

Edgar swims faster.

5 0
3 years ago
What is the result of subtracting the second equation from the first?<br> -2x+y=0<br> -7x+3y=2
Mashutka [201]

Answer:

If you subtract -2x+y=0 and -7x+3y=2 you will get 5x-2y=-2

Step-by-step explanation:

Subtract -2x and -7x which is 5x

Subtract y and 3y which is -2y

Subtract 0 and 2 which is -2

Result: 5x-2y=-2

Hope this helps!

8 0
3 years ago
Read 2 more answers
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California.
pishuonlain [190]

Answer:

The 80% confidence interval for the mean per capita income in thousands of dollars is between $21.3 and $21.9.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.8}{2} = 0.1

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.1 = 0.9, so z = 1.28

Now, find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.28*\frac{12.5}{\sqrt{3839}} = 0.3

The lower end of the interval is the sample mean subtracted by M. So it is 21.6 - 0.3 = $21.3.

The upper end of the interval is the sample mean added to M. So it is 21.6 + 0.3 = $21.9.

The 80% confidence interval for the mean per capita income in thousands of dollars is between $21.3 and $21.9.

7 0
3 years ago
Read 2 more answers
Your group has $60 altogether for pizza. The tax is 5% and you want to leave 15% tip on the price of the food before sales tax
Tems11 [23]

Answer:

48

Step-by-step explanation:

8 0
3 years ago
1.) Find the distance between the points at (2, 3) and (-4,6)
Elza [17]

Answer:

6.7082

Step-by-step explanation:

Distance Formula=√(x2−x1)^2+(y2−y1)^2

                                √(-4-2)^2+(6-3)^2

                                 -4 - 2= -6 squared is -36

                                 6-3= 3 squared is 9

                                 add 36 and 9 which = 45

                                 √45 = 6.7082

7 0
3 years ago
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