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3 years ago

Line l is the perpendicular bisector of AB. What is the perimeter of ABC

Mathematics

1 answer:

saveliy_v [14]3 years ago

3 0

Answer:

Perimeter = 60

Step-by-step explanation:

because l bisects AB:

3y+1 = 5y-5

reduce:

2y = 6

y = 3

and:

2x+4 = 4x-12

reduce:

2x = 16

x = 8

AB = (3y+1) + (5y-5)

AB = 8y-4

substitute for y

AB = 8(3)-4

AB = 20

Perimeter = (2x+4) + (4x-12) + 20

reduce:

perimeter = 6x+12

substitute for x:

Perimeter =6(8)+12

reduce:

Perimeter = 60

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Find the 6th term in the expansion of (x + 2)9.

Masja [62]

Answer:

$4032x^4$

Step-by-step explanation:

Use the 10th row of Pascal's Triangle to get you where you need to be. You need 10 rows because any polynomial raised to the 9th power has 10 terms. Those 10 terms are, in order:

1, 9, 36, 84, 126, 126, 84, 36, 9, 1

Setting up for the first 6 terms:

$1(x^9)(2^0)+9(x^8)(2^1)+36(x^7)(2^2)+84(x^6)(2^3)+126(x^5)(2^4)+126(x^4)(2^5)+...$

The 6th term is the last one. It goes on from there, but I stopped at the 6th term, since that is what you need.

Simplifying gives us:

$126(x^4)(32)$

and multiplying gives us:

$4032x^4$

4 0

3 years ago

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard devi

alexira [117]

Answer: 0.8490

Step-by-step explanation:

Given : The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.0 inches and a standard deviation of 0.9 inches.

i.e. $\mu=30$ and $\sigma=0.9$

Let x denotes the lengths of aluminum-coated steel sheets.

Required Formula : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For n= 36 , the probability that the average length of a sheet is between 29.82 and 30.27 inches long will be :-

$P(29.82$

∴ Required probability = 0.8490

3 0

4 years ago

A model of a tractor-trailer is shaped like a rectangular prism and has width 3 in., length 10 in., and height 4 in. The scal

aleksandr82 [10.1K]

33 plus 4 is 37 and 10plus 1 is 12 so add that and get 49

7 0

4 years ago

What is the probability of rolling a 5 on the first number cube and rolling a 6 on the second number cube? Assume the number cub

scoundrel [369]

Answer:

The probability of rolling a 5 on the first number cube and rolling a 6 on the second number cube is 1/36

Step-by-step explanation:

There are total 6 possible outcomes of rolling a six sided fair cube. Therefore, the probability of rolling each number (1,2,3,4,5,6) is fair = 1/6

In this way,

The probability of rolling a 5 on the first number cube = p(A) = 1/6

The probability of rolling a 6 on the second number cube = p(B) = 1/6

The probability of rolling a 5 on the first number cube and rolling a 6 on the second number cube is = p(A) * p(B) = 1/6*1/6 = 1/36

3 0

4 years ago

5x+4y=16 -2x-4y=-4 <br>Show your step by step process.<br>Solve the system of linear equations.

slava [35]

Answer:

x=1 and y= 5 $\frac{1}{4}$

Step-by-step explanation:

To solve this, lets take the first equation and find the x value.

Because it is ordered in standard form, we need to convert to slope-intercept form, and isolate the y.

5x+4y=16

-5x -5x

4y=-5x+16

÷4 ÷4 ÷4

y= $\frac{-5}{4}$ +4

y=-1 $\frac{1}{4}$ +4

y= 5 $\frac{1}{4}$

Now that we have the y value, we can use this to find the x value by inserting it into either equation, since they both have y values in them. Going with the first one again, lets try it:

5x+4( $\frac{-5}{4}$ +4)=16

5x-5+16=16

5x+11=16

-11 -11

5x=5

÷5 ÷5

x=1 and y= 5 $\frac{1}{4}$

7 0

3 years ago