Answer:
Step-by-step explanation:
Nice summary problem.
<AEC
- AEC = 360 - 243.5 = 116.5
- The number of degrees in 1 rotation of a circle = 360o. You have accounted for 243.5 degrees. What is left over is the answer.
<EAD and <ECD
Both of these are tangents to a circle. Tangents meet radii at 90 degree angles.
<EAD = <ECD = 90 degrees
<ABC
<ABC is 1/2 the central angle. The Central angle is <AEC
- < AEC = 116.5
- <ABC = 1/2 * 116.5
- <ABC = 58.25
<ADC
There are 2 ways of doing this. You should know both of them.
<em><u>One</u></em>
All quadrilaterals = 360 degrees. You know three of the angles. You should be able to find ADC
- <ADC + 90 + 90 + 116.5 = 360 Add the four angles together.
- <ADC + 296.5 = 360 Combine terms on the left
- <ADC = 360 - 296.5 Subtract 238.25 from both sides
- <ADC = 63.5 Answer
<em><u>Method Two</u></em>
<ADC = 1/2 (major Arc - Minor Arc) This formula is fundamental to circle / tangent properties. The Major arc is the larger of the two parts of the circumference of a circle. The Minor arc is the smaller.
- <ADC = 1/2(243.5 - 116.5)
- <ADC = 1/2(127)
- <ADC = 63.5
Answer:
40%
Step-by-step explanation:
10000 = 5000 = 50% + 9000 = 40%
1/2in = 16 mi
2 3/4 in without whole numbers [(denominator ×whole) + numerator] / denominator
4×2 = 8 +3 = 11/4
Find common denominator for 1/2 and 11/4 (common D Is 4)
Multiply 1/2 by 2/2
2/4 in = 16 mi divide this by 2
2/4 ×1/2 = 1/4
16 /2 = 8
1/4 = 8
1/4 goes into 11/4 11 times
Multiply 8 times 11
88 miles (D)
End zone to end zone is = length so his scale is 6 in and in real life it is 360 ft
To find scale divide 360 by 6
1in = 60 ft (B)
160 ft wide
(divide 160 by 60 ft ) fraction
160/60 is a fraction now simplify
16/6
Common factors of both numbers is 2
Simplify by 2
8/3
Make into whole number fraction
3 goes into 8 two times (2×3=6)(2 becomes whole number) while there's is 2 left over( 8 -6=2) (becoming the numerator)
2 2/3 in (B)
120 ft long
80 ft wide
24 in is scale of "long"
Divide 120 by 24
120÷24=5
So 5in in scale equals 1ft in real life
To find width in scale divide 80 by 5
80/5= 16in (A)
If you have any trouble understanding feel free to let me know I will try to explain as best as I can :)
The answer for number 3 is 3.c
We are given two binomials: x+4 , x^2-9.
x+4 can't be factored. Therefore, it is a prime.
Let us work on x^2-9.
9 could be written as 3^2.
Therefore, x^2-9 = x^2 - 3^2.
Now, we can apply difference of the squares formula to factor it.
We know a^2 -b^2 = (a-b) (a+b).
Therefore, x^2 - 3^2 can be factored as (x-3) (x+3).
So, x^2-9 is not a prime binomial because it can be factored as (x-3) (x+3).
