The missing side and angles are 16.8 , 23.33 degree and 123.7 degree respectively.
<h3>What is a Triangle ?</h3>
Triangle is a polygon with three sides , three angles and three vertices.
Given is triangle ABC , with sides a = 8, c = 11, and m∠C=33 degree
The missing angle and side is given by Cosine rule of triangle
c² = a² + b² - 2ab cosC
11² = 8² + b² - 2* 8 * b * cos 33
57 = b² -13.42 b
b² -13.42b -57 = 0
b = 16.8
By sine rule
a / sin A = b/sin B = c/sinC
8 / sin A = 11 / sin 33
A = 23.33 degree
Similarly
B = 123.7 degree
Therefore the missing side and angles are 16.8 , 23.33 degree and 123.7 degree respectively.
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Answer:
-3 and -2
Step-by-step explanation:
7x² + 19x + 21 = 4x² + 4x + 3
combine like terms:
3x² + 15x + 18 = 0
3(x² + 5x + 6) = 0
(x + 3)(x + 2) = 0
x = -3
x = -2
Let the missing term <span>be y
</span><span>(x^12)^5 x (x^-2)^9 x y = (x^40)^5
(x</span>∧60) x (x∧-18) x y = x∧200 (just multiply the powers together)
x∧60 ÷ x∧18 x y = x∧200 (just put the x∧-18 as divider (is that what it called) and the power will be positive)
x∧42 x y = x∧200 (cross out the x∧18 by minusing power 60 by 18)
y = x∧200 ÷ x∧42 (swapping the place)
y = x∧158
<span>1. slope = (n-k)/(m-j)
2. slope = (n-k))/(m-j)
3. P" = (m,n+e-3)
1. The slope of a line is the ratio between the change in y in regard to the change in x. Since we have two known points on the line r, we can simply subtract their respective x and y coordinates and divide. So
slope = (n-k)/(m-j)
One thing to pay attention to is to do the subtraction IN THE SAME ORDER. The actual order doesn't matter as long as it's the same for both top and bottom. For instance, this is another equation for the slope that's just as valid.
slope = (k-n)/(j-m)
2. This is the exact same way. Just subtract the different y coordinates and divide by the difference between the x coordinates.
slope=((n+e)-(k+e))/(m-j)
Now because of the associative property, we can do some rearrangement of the expression to get
slope=(n+e-k-e))/(m-j)
and the "e" terms cancel each other, giving
slope=(n-k))/(m-j)
And you'll see that the slope is the same as for problem #1 above.
3. For this, let's look at the coordinates of point P'
P' = (m,n+e)
Since we want to move it 3 units down, just subtract 3 from the y coordinate, so
P" = (m,n+e-3)</span>
