Answer:
k =2.57
Step-by-step explanation:
3.1+k=5.67
Subtract 3.1 from each side
3.1-3.1+k=5.67-3.1
k =2.57
Let S=larger square side and s=smaller square side. The area between the larger and smaller is simple the larger area minus the smaller area. The area of any square being s^2. So our remaining area is:
A=S^2-s^2
A=144-49=95 cm^2
Answer:
<em>No, he should have set the sum of ∠AED and ∠DEC equal to 180°, rather then setting ∠AED and ∠DEC equal to each other</em>
Step-by-step explanation:
Find the diagram attached
If line AC and BD intersects, then m<AED + m<DEC = 180 (sum of angle on a straight line is 180 degrees)
Given
m<AED = 16x+8
m<DEC = 76 degrees
16x + 8 + 76 = 180
16x + 84 = 180
16x = 180-84
16x = 96
x = 96/16
x = 6
Hence the value of x is 6
Hence the correct option is <em>No, he should have set the sum of ∠AED and ∠DEC equal to 180°, rather then setting ∠AED and ∠DEC equal to each other</em>
Answer: The lines through the pairs of points are perpendicular.
Step-by-step explanation: The lines when graphed do not have the same slope so they can not be parallel. However, when graphed the points (-3, 5) and (-1, 0) goes through the midpoint of the points (-3,1) and (2,3) meaning that the above points are perpendicular! Hope this makes sense and helps.
Answer:
Answer d)
,
, and 
Step-by-step explanation:
Notice that there are basically two right angle triangles to examine: a smaller one in size on the right and a larger one on the left, and both share side "b".
So we proceed to find the value of "b" by noticing that it the side "opposite side to angle 60 degrees" in the triangle of the right (the one with hypotenuse = 10). So we can use the sine function to find its value:

where we use the fact that the sine of 60 degrees can be written as: 
We can also find the value of "d" in that same small triangle, using the cosine function of 60 degrees:

In order to find the value of side "a", we use the right angle triangle on the left, noticing that "a" s the hypotenuse of that triangle, and our (now known) side "b" is the opposite to the 30 degree angle. We use here the definition of sine of an angle as the quotient between the opposite side and the hypotenuse:

where we used the value of the sine function of 30 degrees as one half: 
Finally, we can find the value of the fourth unknown: "c", by using the cos of 30 degrees and the now known value of the hypotenuse in that left triangle:

Therefore, our answer agrees with the values shown in option d)