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3 years ago

14

Angles X and Y are supplementary. Angle X is 3 times the measure of angle Y. What is the measure of angle X?

2 answers:

Leona [35]3 years ago

6 0

3x + x = 180

4x = 180

x = 45

Angle y = 45

Multiply 45 * 3 = 135

<x = 135

Andreas93 [3]3 years ago

4 0

we know that

Supplementary angles are those angles whose sum is equal to $180$ degrees

In this problem

$x+y=180$ --------> equation $1$

$x=3y$ --------> equation $2$

Substitute the equation $2$ in equation $1$

$[3y]+y=180$

$4y=180$

$y=45$ °

<u>Find the value of x</u>

$x=3*45$

$x=135$ °

therefore

<u>the answer is </u>

The measure of angle x is $135$ °

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Answer:

26.8cm²

Step-by-step explanation:

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Answer:

Binomial distribution requires all of the following to be satisfied:

1. size of experiment (N=27) is known.

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3. probability (p=0.14) remains constant through trials.

4. trials are independent, and random.

Binomial distribution can be used as a close approximation, with the usual assumption that a sample of 27 in thousands of stock is representative of the population., and is given by the probability of x successes (defective).

P(x)=C(N,x)*p^x*(1-p)^(n-x)

where N=27, p=0.14, and C(N,x) is the number of combinations of x items out of N.

So we need the probability of <em>at most one defective</em>, which is

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2 years ago

Find three positive numbers whose sum is 140 and whose product is a maximum. (Enter your answers as a comma-separated list.)

Paladinen [302]

Answer:

$\frac{140}{3}, \frac{140}{3}, \frac{140}{3}$

Step-by-step explanation:

Let the numbers be $x, y\ and\ z.$

Such that:

$x + y + z = 140$

Make z the subject

$z = 140 -x - y$

For their product to be maximum, we have:

$f(x,y,z) = xyz$

Substitute $z = 140 -x - y$ in $f(x,y,z) = xyz$

$f(x,y) = xy(140 - x - y)$

Open bracket

$f(x,y) = 140xy - x^2y - xy^2$

Differentiate w.r.t x and y

$f_x=140y - 2xy - y^2$

$f_y=140x - x^2 - 2xy$

Since the products are maximum, then $f_x = f_y = 0$

For $f_x=140y - 2xy - y^2$

$140y - 2xy - y^2 = 0$

Factorize:

$y(140 - 2x - y) = 0$

Split

$y = 0\ or\ 140 - 2x - y = 0$

Make y the subject

$y = 0\ or\ y = 140 - 2x$

For $f_y=140x - x^2 - 2xy$

$140x - x^2 - 2xy = 0$

---------------------------------------------------

Substitute y = 0

$140x - x^2 -2x*0 = 0$

$140x - x^2 = 0$

Factorize

$x(140 - x)= 0$

$x = 0\ or\ 140-x = 0$

$x = 0\ or\ x = 140$

---------------------------------------------------

Substitute $y = 140 - 2x$

$140x - x^2 - 2xy = 0$

$140x - x^2 - 2x(140 - 2x) = 0$

$140x - x^2 - 280x + 4x^2 = 0$

Re-arrange

$4x^2 -x^2 +140x - 280x = 0$

$3x^2 -140x = 0$

Factor x out

$x(3x - 140) = 0$

Divide through by x

$3x - 140 = 0$

$3x = 140$

$x = \frac{140}{3}$

Recall that: $y = 140 - 2x$

$y = 140 - 2 * \frac{140}{3}$

$y = 140 - \frac{280}{3}$

Take LCM

$y = \frac{140*3-280}{3}$

$y = \frac{140}{3}$

Recall that:

$z = 140 -x - y$

$z = 140 - \frac{140}{3} - \frac{140}{3}$

Take LCM

$z = \frac{3 * 140- 140 - 140}{3}$

$z = \frac{140}{3}$

Hence, the numbers are:

$\frac{140}{3}, \frac{140}{3}, \frac{140}{3}$

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2 years ago