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3 years ago

PLEASE HELP!!

2 answers:

8 0

<span>Let x = the width
:
It says,"The length of a rectangle is 4 less than 3 times the width." write that as:
L = 3x - 4
:
If the perimeter is 40, find the dimensions of the rectangle.
:
We know: 2L + 2W = 40
:
Substitute (3x-4) for L and x for W
2(3x-4) + 2x = 40
:
6x - 8 + 2x = 40; Multiplied what's inside the brackets
:
6x + 2x = 40 + 8; do some basic algebra to find x; (added 8 to both sides)

:
8x = 48
:
x = 48/8
:
x = 6 which is the width
:
It said that L = 3x - 4, therefore:
L = 3(6) - 4
L = 18 - 4
L = 14; is the length
:
Check our solutions in the perimeter:
2(14) + 2(6) =
28 + 12 = 40</span>

Arada [10]3 years ago

4 0

Length= 3x-4
width= x
perimeter= 72 feet
2(3x-4)+2x=72
6x-8+2x=72
8x-8=72
8x=80
x=10
The width is 10 and the length is 26.

Hope this helps!

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Line A passes through the points (-5, 1) and (5, 11).

11111nata11111 [884]

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y - y₁ = m(x - x₁)
y - 1 = 1(x - (-5))
y - 1 = 1(x + 5)
y - 1 = 1(x) + 1(5)
y - 1 = x + 5
   + 1    + 1
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Line B: $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{20 - (-1)}{-3 - 4} = \frac{20 + 1}{-7} = \frac{21}{-7} = -3$
   y - y₁ = m(x - x₁)
y - (-1) = -3(x - 4)
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   y + 1 = -3x + 12
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y = x + 6
y = -3x + 11

   x + 6 = -3x + 11
+ 3x     + 3x
   4x + 6 = 11
       - 6   - 6
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The answer is B.

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4 years ago

What is the result of subtracting the second equation from the first? 5x-y=6 and -2x+y=8

Travka [436]

Answer:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(2,−4)

Equation Form: x= 2, y = −4

Step-by-step explanation:

I did the math

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3 years ago

The number of defective circuit boards coming off a soldering machine follows a Poisson distribution. During a specific ten-hour

Alexus [3.1K]

Answer:

a) the probability that the defective board was produced during the first hour of operation is $\frac{1}{10}$ or 0.1000

b) the probability that the defective board was produced during the last hour of operation is $\frac{1}{10}$ or 0.1000

c) the required probability is 0.2000

Step-by-step explanation:

Given the data in the question;

During a specific ten-hour period, one defective circuit board was found.

Lets X represent the number of defective circuit boards coming out of the machine , following Poisson distribution on a particular 10-hours workday which one defective board was found.

Also let Y represent the event of producing one defective circuit board, Y is uniformly distributed over ( 0, 10 ) intervals.

f(y) = $\left \{ {{\frac{1}{b-a} }\\\ }} \right _0$ ; ( a ≤ y ≤ b ) $_{elsewhere$

= $\left \{ {{\frac{1}{10-0} }\\\ }} \right _0$ ; ( 0 ≤ y ≤ 10 ) $_{elsewhere$

f(y) = $\left \{ {{\frac{1}{10} }\\\ }} \right _0$ ; ( 0 ≤ y ≤ 10 ) $_{elsewhere$

Now,

a) the probability that it was produced during the first hour of operation during that period;

P( Y < 1 ) = $\int\limits^1_0 {f(y)} \, dy$

we substitute

= $\int\limits^1_0 {\frac{1}{10} } \, dy$

= $\frac{1}{10} [y]^1_0$

= $\frac{1}{10} [ 1 - 0 ]$

= $\frac{1}{10}$ or 0.1000

Therefore, the probability that the defective board was produced during the first hour of operation is $\frac{1}{10}$ or 0.1000

b) The probability that it was produced during the last hour of operation during that period.

P( Y > 9 ) = $\int\limits^{10}_9 {f(y)} \, dy$

we substitute

= $\int\limits^{10}_9 {\frac{1}{10} } \, dy$

= $\frac{1}{10} [y]^{10}_9$

= $\frac{1}{10} [ 10 - 9 ]$

= $\frac{1}{10}$ or 0.1000

Therefore, the probability that the defective board was produced during the last hour of operation is $\frac{1}{10}$ or 0.1000

no defective circuit boards were produced during the first five hours of operation.

probability that the defective board was manufactured during the sixth hour will be;

P( 5 < Y < 6 | Y > 5 ) = P[ ( 5 < Y < 6 ) ∩ ( Y > 5 ) ] / P( Y > 5 )

= P( 5 < Y < 6 ) / P( Y > 5 )

we substitute

$= (\int\limits^{6}_5 {\frac{1}{10} } \, dy) / (\int\limits^{10}_5 {\frac{1}{10} } \, dy)$

$= (\frac{1}{10} [y]^{6}_5) / (\frac{1}{10} [y]^{10}_5)$

= ( 6-5 ) / ( 10 - 5 )

= 0.2000

Therefore, the required probability is 0.2000

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3 years ago

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3 years ago