Factor

10. RP3-M

SashulF [63]

Answer:

Jeannette's ticket was less than the original pice by 30%

Step-by-step explanation:

original price = $75

percentage discount = 20% of original price = 20% of $75

discounted price = $\frac{20}{100} \times\ 75\ =\ 15$

discounted price = $15

website service fee = 10% of original price

website service fee = $\frac{10}{100}\times 75 = \$7.5$

New discounted price = discount price + website service fee

= 15 + 7.5 = $22.5

Next, let us calculate what percentage of the original price that will give the new discount price.

Let the percentage of the original price = x%

x% of 75 = $22.5

$\frac{x}{100} \times\ 75\ = 22.5\\\\\frac{75x}{100} = 22.5\\\\75x = 2250\\\\x = \frac{2250}{75} \\\\x = 30$

Therefore, Jeannette's ticket was less than the original pice by 30%

5 0

3 years ago

Determine the period of this function

Salsk061 [2.6K]

<h3>Answer: C) 6</h3>

Explanation:

The function is somewhat sinusoidal but not entirely. Its composed of piecewise line segments when we should have a single continuous smooth curve; however, it's still periodic since it repeats itself.

Let's start at the top at the left most corner. This point has x coordinate of x = 1.

The other endpoint of this top left flat portion is when x = 2. Then the function curve goes downhill until it reaches x = 4. From x = 4 to x = 5, we're at the flat bottom part. From x = 5 to x = 7 is when the function increases.

Once we get to x = 7, the process described earlier starts all over again. So this is when the cycle ends and the length of the period is 7-1 = 6 units. The function repeats itself every 6 units, or you can say the length of each cycle is 6 time units (eg: 6 seconds).

5 0

3 years ago

Find all the solutions in there interval (0,2pi) for cos5x=-1/2

oee [108]

Answer:

$\frac{2\pi}{15},\frac{4\pi}{15},\frac{8\pi}{15},\frac{2\pi}{3},\frac{14\pi}{15}, \frac{16\pi}{15}, \frac{4\pi}{3},\frac{22\pi}{15}, \frac{26\pi}{15}, \frac{28\pi}{15}$

Step-by-step explanation:

Solving trigonometric equations.

We are given a condition and we must find all angles who meet it in the provided interval. Our equation is

$cos5x=-\frac{1}{2}$

Solving for 5x:

$5x=\frac{2\pi}{3}+2n\pi$

$5x=\frac{4\pi}{3}+2n\pi$

The values for x will be

$x=\frac{\frac{2\pi}{3}+2n\pi}{5}$

$x=\frac{\frac{4\pi}{3}+2n\pi}{5}$

To find all the solutions, we'll give n values of 0, 1, 2,... until x stops belonging to the interval $(0,2\pi)$

For n=0

$x=\frac{\frac{2\pi}{3}}{5}=\frac{2\pi}{15}$

$x=\frac{\frac{4\pi}{3}}{5}=\frac{4\pi}{15}$

For n=1

$x=\frac{\frac{2\pi}{3}+2\pi}{5}=\frac{8\pi}{15}$

$x=\frac{\frac{4\pi}{3}+2\pi}{5}=\frac{2\pi}{3}$

For n=2

$x=\frac{\frac{2\pi}{3}+4\pi}{5}=\frac{14\pi}{15}$

$x=\frac{\frac{4\pi}{3}+4\pi}{5}=\frac{16\pi}{15}$

For n=3

$x=\frac{\frac{2\pi}{3}+6\pi}{5}=\frac{4\pi}{3}$

$x=\frac{\frac{4\pi}{3}+6\pi}{5}=\frac{22\pi}{15}$

For n=4

$x=\frac{\frac{2\pi}{3}+8\pi}{5}=\frac{26\pi}{15}$

$x=\frac{\frac{4\pi}{3}+8\pi}{5}=\frac{28\pi}{15}$

For n=5 we would find values such as

$x=\frac{\frac{2\pi}{3}+10\pi}{5}=\frac{32\pi}{15}$

$x=\frac{\frac{4\pi}{3}+10\pi}{5}=\frac{34\pi}{15}$

which don't lie in the interval $(0,2\pi)$

The whole set of results is

$\frac{2\pi}{15},\frac{4\pi}{15},\frac{8\pi}{15},\frac{2\pi}{3},\frac{14\pi}{15}, \frac{16\pi}{15}, \frac{4\pi}{3},\frac{22\pi}{15}, \frac{26\pi}{15}, \frac{28\pi}{15}$

6 0

3 years ago

In triangle xyz what is the cosine ratio of angle x

Jobisdone [24]

<span>Data:
</span><span>Hypotenuse is 7.5
Opposite of angle x is 6</span><span>

Cosine = Side opposite (S.O) the angle on the hypotenuse (h)

We have:

</span> $Cos (\alpha)x = \frac{S.O}{h}$
$Cos (\alpha)x = \frac{6}{7.5}$
$\boxed{Cos (\alpha)x = 0.8}$

<span>For better understanding, see the annex:

</span>

6 0

3 years ago

A cake is created by assembling two layers as shown in the diagram below. The exposed surfaces of the cake require frosting. Ass

joja [24]

The total cake frosted would be 352

3 0

4 years ago

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