Solve for B<br> 12B+12C=5

Zoe paid $18.60 in sales tax and tips for dinner. The sales tax rate is 11%, and she had tipped 20%. (the sale tax does not appl

zlopas [31]

Answer:

$60

Step-by-step explanation:

To find how much Zoe paid before the sales tax and tip, we first need to consider the amount she paid in sales tax and tips.

Sales tax + Tips = $18.60

Let x = original price

Sales tax = 11% * original price

Sales tax = 0.11 * x

x= 0.11x

Tips = 20% * original price

Tips = 0.20 * x

x = 0.2x

Now that we have a value for both the sales tax and tips, we can then proceed to find the original price by:

0.11x + 0.2x = 18.60

0.31x = 18.60

Now we need to divide both sides by 0.31 to find x.

x = 60

Zoe's dinner before the sales tax and tips was $60.

7 0

3 years ago

Given that sec (x) = 2 and cosec (x) is negative,

weeeeeb [17]

Answer:

i) sin(2x) = $-\frac{\sqrt{3}}{2}$

ii) cot(x+360) = $-\frac{\sqrt{3}}{3}$

iii) sin(x-180) = $\frac{\sqrt{3}}{2}$

Step-by-step explanation:

sec(x) = 2

Since cos(x) is reciprocal of sec(x), this means:

cos(x) = $\frac{1}{2}$

cosec(x) is negative , this means sin(x) is also negative. The only quadrant where cos(x), sec(x) are positive and sin(x), cosec(x) are negative is the 4th quadrant. Hence the terminal arm of the angle x is in 4th quadrant.

Part i)

sin(2x) can be simplified as:

sin(2x) = 2 sin(x) cos(x)

First we need to find the value of sin(x). According to Pythagorean identity:

$sin^{2}(x)=1-cos^{2}(x)\\\\ sin(x)=\pm \sqrt{1-cos^{2}(x)}$

Since, angle is in 4th quadrant, sin(x) will be negative. So considering the negative value of sin(x) and substituting the value of cos(x), we get:

$sin(x)=- \sqrt{1-cos^{2}(x)}\\\\ sin(x)=-\sqrt{1-(\frac{1}{2})^{2}}\\\\ sin(x)=-\frac{\sqrt{3}}{2}$

So,

$sin(2x)=2 \times -\frac{\sqrt{3} }{2} \times \frac{1}{2}\\\\ sin(2x)=-\frac{\sqrt{3}}{2}$

Part ii)

We have to find cot(x + 360)

An addition of 360 degrees to the angle brings it back to the same terminal point. So the trigonometric ratios of the original angle and new angle after adding 360 or any multiple of 360 stay the same. i.e.

cot(x + 360) = cot(x)

$cot(x) = \frac{cos(x)}{sin(x)}\\$

Using the values, we get:

$cot(x)=\frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2} }\\\\ cot(x)=-\frac{\sqrt{3}}{3}$

Part iii)

We need to find the value of sin(x - 180)

sin(x - 180) = - sin(x)

Addition or subtraction of 180 degrees changes the angle by 2 quadrants. The sign of sin(x) becomes opposite if the angle jumps by 2 quadrants. For example, sin(x) is positive in 1st quadrant and negative in 3rd quadrant.

So,

sin(x - 180) = $-(-\frac{\sqrt{3}}{2}) = \frac{\sqrt{3}}{2}$

6 0

3 years ago

An item is regularly priced at $40. It is on sale for 30% off the regular price. What is the sale price?

morpeh [17]

40$ - 100% (full price)

x$ - 70% (100-30=70%)

40 * 70 = 100x

2800 = 100x

x = 28

Answer 28$

or

40$ = 100%

then 1% = 40/100 = 0.4$

so 70% will be 0.4 * 70 = 28$

8 0

3 years ago

Find the missing value.

Blizzard [7]

Answer:

x=3

Step-by-step explanation:

x-6=-3

x=3

4 0

2 years ago

A hat is on sale for h dollars. The regular price is 7 times as much. Charlie has enough money to buy two hats at the regular pr

Nostrana [21]

Answer:

Charlie can buy 14 hats at the sale price

Step-by-step explanation:

Let

h ----> the sale price of the hat

x ---> the regular price of the hat

we know that

$x=7h$ ----> equation A

so

Two hats at the regular price is equal to multiply 2 by x

Multiply by 2 equation A both sides

$2x=(7h)*2$

$2x=14h$

2 hats at the regular price cost the same that 14 hats at the sale price

therefore

Charlie can buy 14 hats at the sale price

8 0

3 years ago

Solve for B 12B+12C=5