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krok68 [10]
2 years ago
6

Suppose you first want to eliminate the fraction in 4n=1/2(2n-12). What would your first step be? Is -2 still the solution when

you start by eliminating the fraction first? Explain
​
Mathematics
1 answer:
Lisa [10]2 years ago
7 0

Answer:

Step-by-step explanation:

Recognize that the (1/2) in  4n=1/2(2n-12)  is a coefficient, the coefficient of the (2n - 12) term.

Thus, multiply both sides of this equation 4n=1/2(2n-12) by 2, to obtain:

8n = 2n - 12

Combining like terms, we get 6n = -12, so that n = -2.  

Multiplying both sides of the equation by a constant does not in any way affect your ability to find a solution and does not change the solution.

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Rewrite the given expression in the form 3^u where u is a constant or an algebraic expression.
lawyer [7]
Simplifying the given expressions we proceed as follows:
(5sqrt3)^x
=5^x*(3^1/2)^x
=5^x*3^x/2
=5^x3^u
where u=x/2


(1/2)^(x-3)
=1/2^(x-3)
=2^-(3-x)
=2^u
where u=-(3-x)

9/3sqrt(3)
=3/(3)^(1/2)
=3(3)^(-1/2)

16/(3sqrt (2^x))
=1/3*(2^4*2^(-x/2))
=1/3*2^(4-x/2)
=1/3*2^u
where:
u=4-x/2

8 0
1 year ago
Read 2 more answers
Find the gradient of the line segment between the points (2,3) and (-3,8).
fiasKO [112]

Answer:

m = -1

Step-by-step explanation:

Given

Points (2,3) and (-3,8)

Required

Determine the gradient

Gradient (m) is calculated by dividing the change in y values by the change in x values.

i.e.

m = \frac{y_2 - y_1}{x_2 - x_1}

Where:

(x_1,y_1) = (2,3)

(x_2,y_2) = (-3,8)

m = \frac{y_2 - y_1}{x_2 - x_1} becomes

m = \frac{8 - 3}{-3 -2}

m = \frac{5}{-5}

m = -1

<em>Hence, the gradient is -1</em>

7 0
1 year ago
The orbit of the planet Venus is nearly circular. An astronomer develops a model for the orbit in which the sun has coordinates
klio [65]
Since the Venus orbits round the sun, the sun is the center of the circular path of the revolution of the planet, Venus.

Thus, the distance of the planet, Venus fron the sun is given by the distance between the points (0, 0) and (41, 53).

Recall that the distance between two points (x_1, y_1) and (x_2, y_2) is given by d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Thus, the distance between the points (0, 0) and (41, 53) is given by:

d= \sqrt{(41-0)^2+(53-0)^2}  \\  \\ = \sqrt{41^2+53^2} = \sqrt{1,681+2,809}  \\  \\ = \sqrt{4,490} =67 \ units

Given that each unit of the plane represents 1 million miles, therefore, the distance from the sun to the Venus is 67 million miles.
8 0
1 year ago
The state of Wisconsin would like to understand the fraction of its adult residents that consumed alcohol in the last year, spec
leonid [27]

Answer:

The answer is below

Step-by-step explanation:

What we should do is the following:

First, from the random sample of 852 researchers, it is necessary to obtain the number of adult residents who consumed alcohol in the past year.

After the above, we must calculate the proportion of adult residents who consumed alcohol in the last year by dividing the number of adult residents who consumed alcohol in the last year by 852.

After this, we must compare if the proportion is exactly 70% or different from it.

We have the following hypotheses:

Null Hypothesis: The proportion of adult residents who consumed alcohol in the last year in the state of Wisconsin is exactly 70%

Alternative hypothesis: The proportion of adult residents who consumed alcohol in the last year in the state of Wisconsin is not equal to 70%

4 0
1 year ago
Jonathan borrowed $475 at a simple annual interest rate of 2%. How many years will it take him to repay the loan if he wants to
vovikov84 [41]
Firstly you would times 475 by the percentage, which you can convert to a decimal my multiplying the percentage by 100.

475 * 0.02 = 9.50

Then divide the interest by the amount of interest per year:
38 / 9.5 = 4.

The answer would be 4 years.

Hope this helps.
3 0
1 year ago
Read 2 more answers
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