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viktelen [127]
3 years ago
9

Perform the operation indicated, then place the answer in the proper location on the grid. The perimeter of a triangle is 7a - 1

1b. If two of its sides are 2a + b and a - 9b, what is the third side?

Mathematics
1 answer:
vlada-n [284]3 years ago
3 0

Answer: 4 a - 3 b

Step-by-step explanation:

Since, the perimeter of the triangle = sum of all the three side of the triangle.

Here, two sides of the triangle are 2a + b and a - 9b,

And, the perimeter of the triangle = 7 a - 11

Let third side = x

Therefore, 2 a + b + a - 9 b + x = 7 a - 11 b

⇒ 3 a - 8 b + x = 7 a - 11 b

⇒ x = 7 a - 11 b - 3 a + 8 b

⇒ x = 4 a - 3 b  ( by operating like terms)

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solve this problem by using a 5d process or writing and solving an equation. No matter which method you use, be sure to define y
marysya [2.9K]

Answer:

width of the rectangle=x=4in and length of the rectangle=11in

Step-by-step explanation:

Let the width of the rectangle be x, then according to the question, length is one less than three times its width that is l=3x-1.

Now, width=b=x and length=l=3x-1, thus

Perimeter of the rectangle= 2(l+b)

⇒30=2(3x-1+x)

⇒15=(3x-1+x)

⇒15=4x-1

⇒16=4x

⇒x=4in

Thus, width of the rectangle=x=4in and length of the rectangle=l=3x-1=3(4)-1=12-1=11in.

5 0
3 years ago
A researcher was testing the number of popcorn kernels that popped out of a mini bag of 100 kernels after being cooked for the s
Lelechka [254]

Answer:

The percentage of the bag that should have popped 96 kernels or more is 2.1%.

Step-by-step explanation:

The random variable <em>X</em> can be defined as the number of popcorn kernels that popped out of a mini bag.

The mean is, <em>μ</em> = 72 and the standard deviation is, <em>σ</em> = 12.

Assume that the population of the number of popcorn kernels that popped out of a mini bag follows a Normal distribution.

Compute the probability that a bag popped 96 kernels or more as follows:

Apply continuity correction:

P( X\geq 96)=P( X>96+0.50)

                 =P( X>96.50)\\=P(\frac{X-\mu}{\sigma}>\frac{96.50-72}{12})\\=P(Z>2.04)\\=1-P(Z

*Use a <em>z</em>-table.

The probability that a bag popped 96 kernels or more is 0.021.

The percentage is, 0.021 × 100 = 2.1%.

Thus, the percentage of the bag that should have popped 96 kernels or more is 2.1%.

3 0
3 years ago
A. 7/3 <br> B. 3/7<br> C. -3/7 <br> D. -7/3
77julia77 [94]
Your Answer is -3/7 so C
3 0
2 years ago
The length of a rectangular deck is five times it's width if the decks perimeter is 24 feet what is the decks area
miv72 [106K]

Answer:

20 square feet

Step-by-step explanation:

The length of a rectangular deck is five times it's width if the decks perimeter is 24 feet what is the decks area

Step 1

We find the Length and Width of the deck

Perimeter of a rectangle = 2L + 2W

The length of a rectangular deck is five times it's width

W = Width

L = Length = 5W

P = 24 feet

Perimeter = 2(5W) + 2W

24 = 10W + 2W

24 = 12 W

W = 24/12

W = 2 feet

Solving for L

L = 5W

L = 5 × 2 feet

L = 10 feet

Step 2

We find the area of the deck

Area of the deck(Rectangle) = Length × Width

= 10 feet × 2 feet

= 20 square feet

4 0
2 years ago
Select the correct graph of −4x + 3y = 6. (1 point)
mojhsa [17]

Answer:

Line\ passing\ through\ (-1.5,0)\ and\ (0,2).\\\\Correct\ graph\ is\ attached.

Step-by-step explanation:

The\ given\ equation\ represents\ a\ line\\\\

y-intercept:

Substitute\ x=0\\\\-4\times 0+3y=6\\\\3y=6\\\\y=\frac{6}{3}\\\\y=2\\\\The\ line\ passes\ through\ the\ point\ (0,2).

x-intercept:

Substitute\ y=0\\\\-4x+3\times 0=6\\\\-4x=6\\\\x=-\frac{6}{4}\\\\x=-1.5\\\\The\ line\ passes\ through\ the\ point\ (-1.5,0).

The correct graph is attached.

6 0
3 years ago
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