<h3>
Answer: 60</h3>
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Explanation:
Multiply the two values to get 4*15 = 60
Then divide by the GCF 1 to get 60/1 = 60. The GCF being 1 means the result hasn't changed.
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Another example would be: "Find the LCM of 6 and 8". We would first do 6*8 = 48, then divide by the GCF 2 to get 48/2 = 24. The LCM of 6 and 8 is 24.
Step-by-step explanation:
we see f(x), which is |x|.
and we see g(x), which is clearly the same basic graph, it is just shifted 3 units down in y direction.
shifts are simply done by keeping the original function definition and then add it subtract a certain constant that then adapts every original functional value.
so, a shift down by 3 units is done by adding -3.
therefore, C is the correct answer (the original f(x) - 3).
Answer:
![y-\frac{1}{3}=\frac{3}{4}(x-4)](https://tex.z-dn.net/?f=y-%5Cfrac%7B1%7D%7B3%7D%3D%5Cfrac%7B3%7D%7B4%7D%28x-4%29)
Step-by-step explanation:
we know that
The equation of the line into point slope form is equal to
![y-y1=m(x-x1)](https://tex.z-dn.net/?f=y-y1%3Dm%28x-x1%29)
In this problem we have
![point\ (4,\frac{1}{3})](https://tex.z-dn.net/?f=point%5C%20%284%2C%5Cfrac%7B1%7D%7B3%7D%29)
![m=\frac{3}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B3%7D%7B4%7D)
substitute the given values
![y-\frac{1}{3}=\frac{3}{4}(x-4)](https://tex.z-dn.net/?f=y-%5Cfrac%7B1%7D%7B3%7D%3D%5Cfrac%7B3%7D%7B4%7D%28x-4%29)
y minus StartFraction one-third EndFraction equals StartFraction 3 Over 4 EndFraction left-parenthesis x minus 4 right-parenthesis.(x – 4)
Answer:
d) 4 ± 5i
Step-by-step explanation:
Here we have to use the quadratic formula.
x = ![\frac{-b +/- \sqrt{b^2 - 4ac} }{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%20%2B%2F-%20%5Csqrt%7Bb%5E2%20-%204ac%7D%20%7D%7B2a%7D)
In the given equation x^2 - 8x + 41 = 0, a =1, b = -8 and c = 41
Now plug in the given values in the above formula, we get
x = ![\frac{-(-8) +/- \sqrt{(-8)^2 - 4*1*41} }{2*1}](https://tex.z-dn.net/?f=%5Cfrac%7B-%28-8%29%20%2B%2F-%20%5Csqrt%7B%28-8%29%5E2%20-%204%2A1%2A41%7D%20%7D%7B2%2A1%7D)
Simplifying the above, we get
x = ![\frac{8 +/- \sqrt{64 - 164} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B8%20%2B%2F-%20%5Csqrt%7B64%20-%20164%7D%20%7D%7B2%7D)
x = ![\frac{8 +/- \sqrt{-100} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B8%20%2B%2F-%20%5Csqrt%7B-100%7D%20%7D%7B2%7D)
[√-100 = √-1 *√100 = i*10 = 10i] because the value of √-1 = i]
x = (8 ± 10i )/2
Now dividing by 2, we get
x = 4 ± 5i
The answer is d) 4 ± 5i
Hope you will understand the concept.
Thank you.
Answer:
Sum of the interior angles of the triangle is 180°.
According to the above problem,
![4y + (y + 11) + 39 = 180 \\ 5y + 50 = 180 \\ 5y = 130 \\ y = \frac{130}{5} \\ \boxed{y = 26}✓](https://tex.z-dn.net/?f=4y%20%2B%20%28y%20%2B%2011%29%20%2B%2039%20%3D%20180%20%5C%5C%205y%20%2B%2050%20%3D%20180%20%5C%5C%205y%20%3D%20130%20%5C%5C%20y%20%20%3D%20%5Cfrac%7B130%7D%7B5%7D%20%20%5C%5C%20%20%5Cboxed%7By%20%3D%2026%7D%E2%9C%93)
<h3><u>y=26</u><u>°</u> is the right answer.</h3>