Answer:
35cm²
Step-by-step explanation:
Area = trapezium + triangle
Trapezium = ½×(8+4)×2 = 12
Triangle = ½×8×5.75 = 23
Area = 12+23 = 35 cm²
It sounds like everything is being described in reference to angle A, so a good starting point is to pick a variable to represent the measure of angle A. I'm going to use "a" for that.
Next, I'm going to take the verbal descriptions in the problem and "translate" them into "math language". They say angle B is 5 times angle A, so that means the measure of angle B is actually 5a. The size of angle C is 5 degrees less than 4 times the size of A, so that translates to 4a-5.
We now know the following:
Angle A: a
Angle B: 5a
Angle C: 4a-5
Now, to find the value of a, we need to remember that all the angles in a triangle add up to 180 degrees.
So we have: a+5a+4a-5 = 180
We can solve that equation by combining like terms to get: 10a-5=180
We can add 5 to both sides: 10a =185
And divide by 10: a = 18.5
That tells us the measure of angle A! (It's 18.5 degrees). Now we can go back and find B by multiplying A by 5. We get 92.5 degrees for that.
Finally, we can find C by taking 4*18.5-5. We get 69 degrees for that.
One last thing-- let's check that they really do add up to 180! 69+92.5+18.5 = 180. Yep!
Hope that helps you!!
The measure of the longer diagonal is 24.31 units
<h3>How to determine the longer diagonal?</h3>
The side lengths are given as;
a = 16
b = 10
The shorter diagonal is represented as d1, and it is given as
d1 = 11
The longer diagonal is represented as d2, and it is calculated using
d1^2 + d2^2 = 2 * (a^2 + b^2)
Substitute the known values in the above equation
11^2 + d2^2 = 2 * (16^2 + 10^2)
Evaluate the sum
121 + d2^2 =2 * 356
Evaluate the product
121 + d2^2 = 712
Subtract 121 from both sides
d2^2 = 591
Take the square root of both sides
d2 = 24.31
Hence, the measure of the longer diagonal is 24.31 units
Read more about parallelograms at:
brainly.com/question/970600
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Answer:
point C (-1, -3)
Step-by-step explanation:
The line you are looking for already has two givens: m = 2 and it has coordinate (2,3) on it. You can plug these in to find the equation of the line and then see which of the 4 points it must pass through.
3 = 2(2) + b
-1 = b
the line you are looking for is y = 2x - 1
First, you can rule out points D and B, because after a quick look, you can see that a line with a slope of 2 wouldn't come close to the point (2,3). Now you can choose between C (-1, -3) and A (-2, -3).
Now you can plug in the points C and A into the equation of the line that was obtained in the first part of this answer.
checking point A: -3 = 2(-2) - 1
-3= -5
not true, so now we check point C
checking point C: -3 = 2(-1) - 1
-3 = -2 - 1
-3 = -3
true, so the point must be C
