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4 years ago

What is the missing reason for line 5 in this proof?

Mathematics

1 answer:

Molodets [167]4 years ago

5 0

Line 5 shows the division property of equality.

The division property of equality states that you can divide both sides of the equation by the same number and the equation remains the same. This equation is being divided by 4 on both sides.

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A fence is to be built to enclose a rectangular area of 260 square feet. The fence along three sides is to be made of material t

Nat2105 [25]

Answer:

Length of the rectangle = 9.58 feet and width = 27.14 foot

Step-by-step explanation:

Let the length of the rectangular area is = x feet

and the width of the area = y feet

Area of the rectangle = xy square feet

Or xy = 260

y = $\frac{260}{x}$ -------(1)

Cost to fence the three sides = $3 per foot

Therefore cost to fence one length and two width of the rectangular area

= 3(x + 2y)

Similarly cost to fence the fourth side = $14 per foot

So, the cost of the remaining length = 14x

Total cost to fence = 3(x + 2y) + 14x

Cost (C) = 3(x + 2y) + 14x

C = 3x + 6y + 14x

= 17x + 6y

From equation (1)

C = $17x+\frac{260\times 6}{x}$

Now we take the derivative,

C' = 17 - $\frac{1560}{x^{2} }$

To minimize the cost of fencing,

C' = 0

17 - $\frac{1560}{x^{2} }$ = 0

$\frac{1560}{x^{2} }$ = 17

$x^{2} =\frac{1560}{17}$

$x=\sqrt{\frac{1560}{17} }$

x = 9.58 foot

and y = $\frac{260}{9.58}$

y = 27.14 foot

4 0

3 years ago

The graph below shows the balance in Steven's savings account as a function of time. Please Helpp

zhuklara [117]

Answer:

Steven starts with an account balance of $300

And with each passing month his balance increases by $150

Step-by-step explanation:

300 is you're start value

On the graph you can see that Feb. 1 hits the line on the graph between $300 and $600. You want to find half of $300, So you divide 300 by 2, And that give you 150.

Then with you can add 150 to 300 to give you 450. Then add 150 to 450 to give you 600. And repeat the process.

Hope This Helps :)

3 0

3 years ago

Jake bought 3 drawing pens for $8.07. Each pen costs the same amount. About how much did he spend for one pen? * 2 points

Marina86 [1]

Given:

Jake bought 3 drawing pens for $8.07.

Each pen costs the same amount.

To find:

How much did he spend for one pen?

Solution:

Let x be the cost of each pen. Then

Cost of three pens = 3x

Jake bought 3 drawing pens for $8.07.

$3x=8.07$

Divide both sides by 3.

$x=\dfrac{8.07}{3}$

$x=2.69$

Therefore, he spend $2.69 for one pen.

3 0

3 years ago

4x2 - 12x + 9 can be factored as (2x - 3)(2x - 3)<br><br> True<br><br> False

azamat

Answer:

(2 x - 3)^2 thus it's True

Step-by-step explanation:

Factor the following:

4 x^2 - 12 x + 9

Factor the quadratic 4 x^2 - 12 x + 9. The coefficient of x^2 is 4 and the constant term is 9. The product of 4 and 9 is 36. The factors of 36 which sum to -12 are -6 and -6. So 4 x^2 - 12 x + 9 = 4 x^2 - 6 x - 6 x + 9 = 2 x (2 x - 3) - 3 (2 x - 3):

2 x (2 x - 3) - 3 (2 x - 3)

Factor 2 x - 3 from 2 x (2 x - 3) - 3 (2 x - 3):

(2 x - 3) (2 x - 3)

(2 x - 3) (2 x - 3) = (2 x - 3)^2:

Answer: (2 x - 3)^2

6 0

3 years ago

Read 2 more answers

After 5 throws in a game of darts, Brent's mean score was 32. Calculate his total score.

ehidna [41]

1.To know this answer, we need to know some vocabulary that's used in t. Most people don't know how to solve questions if they have hard Vocabulary and what the question is Asking

Mean=The average of all his throws

It's asking us to calculate his total score

2. Find Clues to help you solve word problems

Finding clues in Word Problems is a very important part a lot of people skip but this helps you solve the question easier

5 throws and Mean Score is 32 are the clues

3. Guess and check

The method to this thingy is called guess and check. There is another method which is slightly harder and i just don't want to do it.

Let's just say his scores were... 5, 6, 4, 5,10Add them up and you get 30Then 30/5

Let's try bigger numbers

20+25+20+20

If you like this method, you may try it another method is called work Backwards

5x32=160

Then divide 160 by 5 to double check and you get 32!!

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

Therefore, the answer s 160 as his total score

hope this gives you a clue to what we are doing and when you have a question like this, I really hope you understand the concept

Hope this helped (:

5 0

3 years ago