Look at the diagram. Which angle is supplementary to 60°

10 5/12- 12 7/12 = in simplest form

Alika [10]

Answer:

-13/6 or (in mixed number form) -2 1/6

Step-by-step explanation:

Rewriting our equation with parts separated

=10+512−12−712

Solving the whole number parts

10−12=−2

Solving the fraction parts

512−712=−212

Reducing the fraction part, 2/12,

−212=−16

Combining the whole and fraction parts

−2−16=−216

Another way to do it:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

125/12−151/12

Applying the fractions formula for subtraction,

=(125×12)−(151×12) / 12×12

=1500 − 1812/ 144

=−312/144

Simplifying -312/144, the answer is

=−2 1/6

3 0

3 years ago

What is 2x^2+9x-18 in vertex form?

atroni [7]

Complete the square:

2x² + 9x - 18

2(x² + 9/2 x) - 18

2(x² + 9/2 x + 81/16 - 81/16) - 18

2(x² + 2 (9/4) x + (9/4)²) - 81/8 - 18

2(x + 9/4)² - 225/8

If you're not familiar with the method, the idea is to get a quadratic from the standard form

ax² + bx + c

into its vertex form

a (x - h)² + k

where (h, k) is the vertex of the parabola associated with the quadratic.

Expand the vertex form to get

a (x² - 2xh + h²) + k

ax² - 2ahx + ah² + k

For the two forms to be equivalent, we must have

-2ah = b

ah² + k = c

which means

h = -b/(2a)

k = c - ah² = c - b²/(4a)

In this case, a = 2, b = 9, and c = -18, so

h = -9/(2 • 2) = -9/4

k = 18 - 9²/(4 • 2) = -225/8

7 0

4 years ago

<img src="https://tex.z-dn.net/?f=%20%20%5Crm%5Csum%20%5Climits_%7Bn%20%3D%200%7D%5E%7B%20%5Cinfty%20%7D%20%20%5Carcsin%20%5Clar

sineoko [7]

Recall that over an appropriate domain,

$\arcsin(x) \pm \arcsin(y) = \arcsin\left(x \sqrt{1-y^2} \pm y \sqrt{1-y^2}\right)$

Let $x=\frac1{n+1}$ and $y=\frac1{n+2}$ (these belong to the "appropriate domain", so the identity holds). We have

$\dfrac{\sqrt{n+3}}{(n+2)\sqrt{n+1}} = \dfrac1{n+1} \sqrt{\dfrac{(n+3)(n+1)}{(n+2)^2}} = \dfrac1{n+1} \sqrt{1 - \dfrac1{(n+2)^2}} = x \sqrt{1-y^2}$

and

$\dfrac{\sqrt n}{(n+1)\sqrt{n+2}} = \dfrac1{n+2} \sqrt{\dfrac{n(n+2)}{(n+1)^2}} = \dfrac1{n+2} \sqrt{1 - \dfrac1{(n+1)^2}} = y \sqrt{1-x^2}$

Then the sum telescopes, as

$\displaystyle \sum_{n=0}^\infty \arcsin\left(x \sqrt{1-y^2} - y \sqrt{1-x^2}\right) = \sum_{n=0}^\infty \left( \arcsin(x) - \arcsin(y) \right) \\\\ = \left(\arcsin(1) - \arcsin\left(\frac12\right)\right) + \left(\arcsin\left(\frac12\right) - \arcsin\left(\frac13\right)\right) + \cdots \\\\ = \arcsin(1) = \boxed{\frac\pi2}$

3 0

2 years ago

A gas station sells unleades regular petrol and preminum charged by station for regular is$1.299

sergey [27]

Answer:

a. Assuming gallons of unleaded regular is denoted by r; and unleaded premium by p.

Revenue from one gallon of unleaded regular is $1.299 and from unleaded premium is $1.379.

Revenue function = 1.299r + 1.379p

b. Cost of one gallon of unleaded regular is $1.219 and for unleaded premium is $1.289.

Cost function = 1.219r + 1.289p

c. Total profit = Revenue - Cost

= 1.299r + 1.379p - 1.219r - 1.289p

= 1.299r - 1.219r + 1.379p - 1.289p

= 0.08p + 0.09p

d. If station sells 100,000 gallons of unleaded regular and 40,000 of unleaded premium;

= (0.08 * 100,000) + (0.09 * 40,000)

= 8,000 + 3,600

= $11,600

7 0

3 years ago

The balance on your business credit card was $215 before you purchased 5 new chairs for the office. Each chair cost $75.

STatiana [176]

Answer:

$590

Step-by-step explanation:

The credit card balance on the card is : $215.

You put on his charge 5 chairs that each cost $75.

So 75 * 5 = 375.

You have now added to your credit card balance of $375 and before you bought the chairs, it was $215. You must add these totals to get your new balance after purchasing 5 new chairs for the office.

375 + 215 = 590.

4 0

3 years ago

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