(SEE PICTURE) Which choice is equivalent to the quotient shown here when x>0?

16. Prove that the sum of three angles of triangle is two right angles.

Reptile [31]

Answer:

Two right angles = 180 degrees

Step-by-step explanation:

A right angle = 90 degrees

The sum of the interior angles of a triangle = 180 degrees

Two right angles (2 * 90) = 180

180 = 180

Therefore, the sum of the interior angles of any triangle is equal to two right angles.

3 0

2 years ago

AB = 6x + 2 and<br> BC = 5x + 3<br> Find AC.

uranmaximum [27]

Answer:

AC = 3x + 3 (answers may vary)

Step-by-step explanation:

AB = 6x + 2

Answers may vary for this question,

Let's say that,

B = 4x + 1

So that means that,

A = 2x + 1

BC = 5x + 3

Since we chose

B = 4x + 1,

we must subtract B from BC to get C,

C = x + 2

Now we add A and C to get AC,

A = 2x + 1

C = x + 2

AC = 3x + 3

5 0

3 years ago

The function f (x comma y )equals 3 xy has an absolute maximum value and absolute minimum value subject to the constraint 3 x sq

zmey [24]

Answer:

The maximum value of f is 363, which is reached in (11,11) and (-11,-11) and the minimum value of f is -33, which is reached in (√11,-√11) and (-√11,√11)

Step-by-step explanation:

f(x,y) = 3xy, lets find the gradient of f. First lets compute the derivate of f in terms of x, thinking of y like a constant.

$f_x(x,y) = 3y$

In a similar way

$f_y(x,y) = 3x$

Thus,

$\nabla{f} = (3y,3x)$

The restriction is given by g(x,y) = 121, with g(x,y) = 3x²+3y²-5xy. The partial derivates of g are

[ŧex] g_x(x,y) = 6x-5y [/tex]

$g_y(x,y) = 6y - 5x$

Thus,

$\nabla g(x,y) = (6x-5y,6y-5x)$

For the Langrange multipliers theorem, we have that for an extreme (x0,y0) with the restriction g(x,y) = 121, we have that for certain λ,

$f_x(x_0,y_0) = \lambda \, g_x(x0,y0)$
$f_y(x_0,y_0) = \lambda \, g_y(x_0,y_0)$
$g(x_0,y_0) = 121$

This can be translated into

$3y = \lambda (6x-5y)$
$3x = \lambda (-5x+6y)$
$3 (x_0)^2 + 3(y_0)^2 - 5\,x_0y_0 = 121$

If we sum the first two expressions, we obtain

$3x + 3y = \lambda (x+y)$

Thus, x = -y or λ=3.

If x were -y, then we can replace x for -y in both equations

3y = -11 λ y

-3y = 11 λ y, and therefore

y = 0, or λ = -3/11.

Note that y cant take the value 0 because, since x = -y, we have that x = y = y, and g(x,y) = 0. Therefore, equation 3 wouldnt hold.

Now, lets suppose that λ=3, if that is the case, we can replace in the first 2 equations obtaining

3y = 3(6x-5y) = 18x -15y

thus, 18y = 18x

y = x

and also,

3x = 3(6y-5x) = 18y-15x

18x = 18y

x = y

Therefore, x = y or x = -y.

If x = -y:

Lets evaluate g in (-y,y) and try to find y

g(-y,y) = 3(-y)² + 3y*2 - 5(-y)y = 11y² = 121

Therefore,

y² = 121/11 = 11

y = √11 or y = -√11

The candidates to extremes are, as a result (√11,-√11), (-√11, √11). In both cases, f(x,y) = 3 √11 (-√11) = -33

If x = y:

g(y,y) = 3y²+3y²-5y² = y² = 121, then y = 11 or y = -11

In both cases f(11,11) = f(-11,-11) = 363.

We conclude that the maximum value of f is 363, which is reached in (11,11) and (-11,-11) and the minimum value of f is -33, which is reached in (√11,-√11) and (-√11,√11)

5 0

3 years ago

Margie divided 24 by 3

Levart [38]

Answer:

24 divided by 3 is 8

Step-by-step explanation:

3 goes into 24, 8 times

3 0

3 years ago

Read 2 more answers

Last year, 46% of business owners gave a holiday gift to their employees. A survey of business owners indicated that 20% plan to

alisha [4.7K]

Answer:

Part a: So the number of business owners giving holiday gift to their employees from survey is 12.

Part b: p-value is 0.00003

Part c: value of p is less that a we reject the null hypothesis.

Step-by-step explanation:

Part a

number of business owners=20% x n

number of business owners= 0.2x 60

number of business owners=12

Part b

H0: p=0.46

H1: p<0.46

Here

n=60, $\hat{p}$ =0.2, p=0.46

So test statistics is given as

$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\\z=\frac{0.20-0.46}{\sqrt{\frac{0.46(1-0.46)}{60}}}\\z=\frac{-0.26}{0.064}\\z=-4.04$

p-value is P(z<-4.04)= 0.00003

Part c

As value of p is less that a we reject the null hypothesis.

4 0

3 years ago