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4vir4ik [10]
3 years ago
7

The length of a rectangle is 8 feet more than it's width. The area of the rectangle is 84 square feet. Find it's length and widt

h.
Mathematics
1 answer:
S_A_V [24]3 years ago
3 0

Length of the rectangle is 14 ft and width is 6 ft

Step-by-step explanation:

  • Step 1: Let the width of the rectangle be x, then length = 8 + x. Find dimensions if area = 84 ft²

⇒ Area of the rectangle = length × width

⇒ 84 = x(8 + x) = 8x + x²

⇒ x² + 8x - 84 = 0

⇒ x² + 14x - 6x - 84 = 0 (Using product sum rule to factorize)

⇒ x(x + 14) - 6(x + 14) = 0

⇒ (x + 14)(x - 6) = 0

⇒ x = -14, +6 (negative value is neglected)

∴ x = 6 and x + 8 = 14

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Help pls I'll give 25 points
RideAnS [48]

Answer:

\text{C. }60

Step-by-step explanation:

<u>Question from image</u>:

"The digits 1, 2, 3, 4, and 5 can be formed to arrange 120 different numbers. How many of these numbers will have the digits 1 and 2 in increasing order? For example, 14352 and 51234 are two such numbers."

Let's start by taking a look with the number 1. There are four possible places 1 could be, because there needs to be space for the 2 after it.

Checkmarks mark where the 1 can be, the <em>x</em> marks where it cannot be.

\underline{\checkmark}\:\underline{\checkmark}\:\underline{\checkmark}\:\underline{\checkmark}\:\underline{X}

Let's start with the first position:

\underline{\checkmark}\:\underline{\#}\:\underline{\#}\:\underline{\#}\:\underline{\#}

There are four places the 2 can be. For each of these four places, we can arrange the remaining 3 digits in 3!=6 ways. Therefore, there are 4\cdot 6=\boxed{24} possible numbers when 1 is the first digit of the number.

Continue this process with the remaining possible positions for 1.

Second position:

\underline{X}\underline{\checkmark}\:\underline{\#}\:\underline{\#}\:\underline{\#}

There are three places the 2 can be, since the 2 must be behind the 1. For each of these three places, the remaining 3 digits can be arranged in 3!=6 ways. Therefore, there are 3\cdot 6=\boxed{18} possible numbers when 1 is the second digit of the number.

The pattern continues. Next there will be 2 places to place the 2. For each of these, there are 3!=6 ways to rearrange the remaining 3 digits for a total of 2\cdot 6=\boxed{12} possible numbers when 1 is the third digit of the number.

Lastly, when 1 is the fourth digit of the number, there is only 1 place the 2 can be. For this one place, there are still 3!=6 ways to rearrange the remaining three numbers. Therefore, there are 1\cdot 6=\boxed{6} possible numbers when 1 is the fourth digit of the number.

Thus, there are 24+18+12+6=\boxed{60} numbers that will have the digits 1 and 2 in increasing order, from a set of 120 five-digit numbers created by the digits 1 through 5, where no digit may be repeated.

5 0
2 years ago
Which of the following is a fifth degree binomial?
Anna11 [10]

Answer:

C)

Step-by-step explanation:

2xy^{2}-5y^{5}

Binomial should have two terms. Five degree binomial means highest degree of the binomial should be 5

5 0
3 years ago
Question
Vlada [557]

Answer:

(-6,4)

Step-by-step explanation:

You started at (-4,2)  The first number in the ordered pair moves the number left and right and the second number moved the point up and down.

We are first told to move the point 2 units to the left.  -4 is my left right number.  If I am at -4 and I go to unites to the left, I will be at -6.  My new point is now (-6,2).  Next we are told to go up 2.  The 2 number in my ordered pair tells me that I am 2 above the x axis.  Now I am going to go two more units up.  I am now at 4, so my new ordered pair after the translation is (-6,4)

8 0
2 years ago
The measures of ∠1, ∠2, and ∠3 are 40%, 12.5%, and 25% of the sum of the angle measures of the quadrilateral. Find the value of
sweet [91]

The value of x is 81

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360°

  • The measure of ∠1 is 40% of the sum of the angle measures of the quadrilateral
  • The measure of ∠2 is 12.5% of the sum of the angle measures of the quadrilateral
  • The measure of ∠3 is 25% of the sum of the angle measures of the quadrilateral
  • We need to find the value of x

∵ The figure have 4 sides

∴ The figure is a quadrilateral

∵ The sum of the measures of the interior angles of a

    quadrilateral is 360°

- Add the four angles and equate the sum by 360

∴ m∠1 + m∠2 + m∠3 + x = 360

∵ m∠1 = 40% of the sum of the angle measures of the quadrilateral

∴ m∠1 = 40% × 360 = \frac{40}{100} × 360 = 144°

∵ m∠2 = 12.5% of the sum of the angle measures of the quadrilateral

∴ m∠2 = 12.5% × 360 = \frac{12.5}{100} × 360 = 45°

∵ m∠3 = 25% of the sum of the angle measures of the quadrilateral

∴ m∠3 = 25% × 360 = \frac{25}{100} × 360 = 90°

- Substitute these values in the equation above

∴ 144 + 45 + 90 + x = 360

- Add the like terms in the left hand side

∴ 279 + x = 360

- Subtract 279 from both sides

∴ x = 81°

The value of x is 81

Learn more:

You can learn more about the polygons in brainly.com/question/6281564

#LearnwithBrainly

5 0
3 years ago
What is the area of the figure? A) 18 in2 B) 24 in2 C) 30 in2 D) 36 in2
Annette [7]
Hello!

You need to separate this into two rectangles and add their areas together

first rectangle

3 * 6 = 18

rectangle 2

3 * 2 = 6

18 + 6 = 24

the answer is 24in squared


5 0
3 years ago
Read 2 more answers
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