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3 years ago

The sum of twice a number n and 8 at most 25

Mathematics

1 answer:

mezya [45]3 years ago

6 0

2n + 8 ≤ 25 |subtract 8 from both sides

2n ≤ 17 |divide both sides by 2

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PLEASE HELP!! Algebra 2

lawyer [7]

Answer:

Edit:

Yes, based on original equation. (Credit to greenpumpkin for correction)

Step-by-step explanation:

For this problem, we simply need to find the values of x that can make the equation true. So, let's begin by isolating the "x" variable.

sqrt(2x + 13) = x + 5

[sqrt(2x + 13)]^2 = (x + 5)^2

2x + 13 = x^2 + 10x + 25

0 = x^2 + 8x + 12

Note, we can remove the sqrt method by squaring both sides of the equation. Doing this, we see we have a quadratic equation meaning we can apply the quadratic formula to find solutions for x.

[-b +/- sqrt( b^2 - 4(a)(c) ) ] / 2a

Let a = 1, b = 8, and c = 12

[-8 +/- sqrt( (8)^2 - 4(1)(12) ) ] / 2(1)

= [-8 +/- sqrt( 64 - 48 ) ] / 2

= [-8 +/- sqrt(16) ] / 2

= [ -8 +/- 4 ] / 2

So, x = [ -8 + 4 ] / 2 and x = [-8 - 4 ] / 2

x = [-4] / 2 = -2 and x = [-12] / 2 = -6

Hence, the two values of x that can solve this quadratic equation are x = -2 and x = -6.

Therefore, we know that x = -6 is not extraneous, meaning it is a solution to our equation.

Cheers.

----------------------------------------------------

Edit:

Plugging the value of -6 back into the original equation, we get the following:

sqrt(2x + 13) = x + 5

sqrt(2(-6) + 13) = (-6) + 5

sqrt (1) = -1

1 != -1

Given that 1 cannot equal negative 1, we can say that x = -6 is an extraneous solution. (Credit to greenpumpkin for correction)

8 0

3 years ago

The smallest positive integer value of n for which 168n is a multiple of 324

Nikitich [7]

Answer:

n = 27

Step-by-step explanation:

168n is a multiple of 324

168(27) = 4536 is a multiple of 324

BRAINLIEST?

6 0

3 years ago

Read 2 more answers

Evaluate the expression for v = –3 and w = –4.<br><br> vw + w =

kolbaska11 [484]

Answer:

Step-by-step explanation:

v = -3, w = -4,

vw + w,

Subsitute in (-3) for (v), and (-4) for (w).

(-3)(-4) + (-4)

Simplfiy,

12 + (-4)

12 - 4

8 0

3 years ago

What would the area be for a circle with the diameter of 7

Marina86 [1]

Answer:

The answer is 38.48

Step-by-step explanation:

Picture with explanation provided below.

3 0

3 years ago

The total number of people at a football game was 5600. Field-side tickets were 40 dollars and end-zone tickets were 20 dollars.

rewona [7]

Answer:

1100 field-side tickets and 4500 end-zone tickets.

Step-by-step explanation:

Let x represent number of field side tickets and y represent number of end-zone tickets.

We have been given that the total number of people at a football game was 5600. We can represent this information in an equation as:

$x+y=5600...(1)$

$y=5600-x...(1)$

We are also told that Field-side tickets were 40 dollars and end-zone tickets were 20 dollars.

Cost of x field side tickets would be $40x$ and cost of y end-zone tickets would be $20y$ .

The total amount of money received for the tickets was $134000. We can represent this information in an equation as:

$40x+20y=134000...(2)$

Upon substituting equation (1) in equation (2), we will get:

$40x+20(5600-x)=134000$

$40x+112000-20x=134000$

$20x+112000=134000$

$20x+112000-112000=134000-112000$

$20x=22000$

$\frac{20x}{20}=\frac{22000}{20}$

$x=1100$

Therefore, 1100 field side tickets were sold.

Upon substituting $x=1100$ in equation (1), we will get:

$y=5600-1100$

$y=4500$

Therefore, 4500 end-zone tickets were sold.

3 0

3 years ago