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3 years ago

What is the solution to 2(6x+10)-3x=10-(x-2)

Mathematics

1 answer:

creativ13 [48]3 years ago

3 0

Answer:

The value of x is -4/5.

Step-by-step explanation:

First, you have to get rid of brackets, by expanding out :

2(6x+10) - 3x = 10 - (x-2)

2(6x) + 2(10) - 3x = 10 - x + 2

12x + 20 - 3x = 10 - x + 2

Next, is to bring all the x variable to one side :

12x + 20 - 3x = 10 - x + 2

12x - 3x + x = 10 + 2 - 20

10x = -8

Lastly, is to solve it by dividing 10 to both sides :

10x = -8

10x ÷ 10 = -8 ÷ 10

x = -4/5

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Solve for x. leave your answer in simplest radical form.

adell [148]

Answer:

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1 year ago

A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained p

Oliga [24]

Answer:

no of sample within two percentage points is 5409

no of sample not use prior estimates is 8321

Step-by-step explanation:

Given data

E = 2% = 0.02

male m = 21.2 % = 0.212

female f = 19.7 % = 0.197

to find out

no of sample within two percentage points and if does not use any prior estimates

solution

first we calculate no of sample within two percentage points

we know Z critical value for 99% is 2.58

so no of sample will be

n = (Z / E )² × m(1-m) + f ( 1-f )

put all the value we get no of sample

n = (2.58 / 0.02 )² × 0.212 ( 1 - 0.212 ) + 0.197 ( 1 - 0.197 )

n = 16641 ×0.3250

no of sample within two percentage points is 5409

in 2nd part no of sample not use prior estimates

here than f and m will be 0.5

than

n = (Z / E )² × m(1-m) + f ( 1-f )

put all value

n = (2.58 / 0.02 )² × 0.5 ( 1 - 0.5 ) + 0.5 ( 1 - 0.5 )

n = 16641 × 0.5

no of sample not use prior estimates is 8321

7 0

3 years ago

Latrell took one of his friends out to lunch. The lunches cost $60 and he paid 5% sales tax. If Latrell left a 15% tip on the $6

VladimirAG [237]

Answer:

$72

Step-by-step explanation:

Cost of the lunch = $60

Sales tax = 5% of $60

= 5/100 × 60

= 0.05 × 60

= $3

Tip = 15% of $60

= 15/100 × 60

= 0.15 × 60

= $9

how much in total did he pay?

Total amount paid = cost of the lunch + sales tax + tip

= $60 + $3 + $9

= $72

Latrell paid $72 in total for the lunch

4 0

3 years ago

Find the indefinite integral using the substitution provided.

Nady [450]

Answer: $7\text{Ln}\left(e^{2x}+10\right)+C$

This is the same as writing 7*Ln( e^(2x) + 10) + C

=======================================================

Explanation:

Start with the equation $u = e^{2x}+10$

Apply the derivative and multiply both sides by 7 like so

$u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\$

The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)

This way we can do the following substitutions:

$\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\$

Integrating leads to

$\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\$

Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.

To verify the answer, you can apply the derivative to it and you should get back to the original integrand of $\frac{14e^{2x}}{e^{2x}+10}$

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2 years ago

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miv72 [106K]

The area of the kite in the picture is 5m

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2 years ago

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