Answer:
m∠x = 10°
Step-by-step explanation:
Since we are dealing with a <u>right triangle</u> and its two sides and one angle, we can use <u>trigonometry ratios</u>. Remember them all with the acronym SohCahToa.
"o" is for opposite side, "a" is for adjacent side, "h" is for hypotenuse side.
The ratios are:
sinθ = opposite/hypotenuse
cosθ = adjacent/hypotenuse
tanθ = opposite/adjacent
θ means the "angle of reference", or the angle you know or want to find. This determines which side is adjacent (touching) or opposite (not touching). The hypotenuse (longest side) does not change.
In this triangle, θ = x. The sides we know are hypotenuse and opposite. Therefore, we will use the sinθ ratio.
sinθ = opposite/hypotenuse
sinx = CB/AB Substitute the labels in the diagram
sinx = 4/23 Substitute known values (side lengths)
x = sin⁻¹(4/23) Isolate 'x'. Use calculator to solve.
x = 10.015....° Exact answer
x ≈ 10° Round to the nearest degree
Therefore the measure of angle x (m∠x) is 10°.
Answer:
22.2%
Step-by-step explanation:
Probability is the chance of an event happening, it can be found by using the following formula,

Where the word (desired) represents the outcomes one wants, and (total) represents the total number of outcomes.
In this case, one is asked to find the probability of the sum of two numbers the results from rolling two dice, not being a multiple of (3) or (2). In this case, it is easier to list out the number of numbers between (1) and (12) that are not a multiple of three or two. Please note, the largest sum of number one can get when rolling two dice is (12), since the largest value on a dice is (6), and (6+6) equals (12).
Not multiples of (3) or (2):
1, 5, 7, 11
There are (4) numbers that are not multiples of (2) or (3). This means that there are (8) multiples of (2) or (3) between the numbers of (1) and (12), since (12 - 4 = 8)
The total number of outcomes is the following:

This is because there are (6) sides on a die, the number of outcomes is equal to (6) times (6), thus (
) or (
).
Now set up the probability equation:

Substituted,

Write as a decimal:
0.222
As a percent:
22.2%
Answer:
![\frac{\sqrt[3]{5} }{3x}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B5%7D%20%7D%7B3x%7D)
Step-by-step explanation:
Ok, let's do this step by step....
![\sqrt[3]{\frac{10x^{5} }{54x^{8} } }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B10x%5E%7B5%7D%20%7D%7B54x%5E%7B8%7D%20%7D%20%7D)
Let's first simplify the x's:
![\sqrt[3]{\frac{10}{54x^{3} } }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B10%7D%7B54x%5E%7B3%7D%20%7D%20%7D)
Then we breakdown the 54 as 2 * 27 then simplify with the 10 above.
![\sqrt[3]{\frac{10}{2 * 27x^{3} } } = \sqrt[3]{\frac{5}{27x^{3} } }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%5Cfrac%7B10%7D%7B2%20%2A%2027x%5E%7B3%7D%20%7D%20%7D%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B5%7D%7B27x%5E%7B3%7D%20%7D%20%7D)
Now, we can rewrite this as the following and solve the bottom part:
![\frac{\sqrt[3]{5} }{\sqrt[3]{27x^{3} } } = \frac{\sqrt[3]{5} }{3 \sqrt[3]{x^{3} } } = \frac{\sqrt[3]{5} }{3x}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B5%7D%20%7D%7B%5Csqrt%5B3%5D%7B27x%5E%7B3%7D%20%7D%20%7D%20%3D%20%5Cfrac%7B%5Csqrt%5B3%5D%7B5%7D%20%7D%7B3%20%5Csqrt%5B3%5D%7Bx%5E%7B3%7D%20%7D%20%7D%20%3D%20%5Cfrac%7B%5Csqrt%5B3%5D%7B5%7D%20%7D%7B3x%7D)
The solution is
![\frac{\sqrt[3]{5} }{3x}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B5%7D%20%7D%7B3x%7D)
Answer:
4(x + 2)
Step-by-step explanation:
Factor out common factors from each term. Note the factors for each number
4: 1, 2, 4
8: 1, 2, 4, 8
The largest factor for each is 4, and so divide 4 from both terms.
(4x + 8)/4 = (x + 2)
4(x + 2) is your factored expression.
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