It's an isosceles triangle so angles A and BCA are congruent.
Angle BCA is the supplement of BCD, so 180-109 = 71.
Angle A is congruent to that, so A=71 degrees.
Let's see if we can get that in the format they want, kind of as a proof.
1. ∠BCD=109° Reason: Given
2. AB ≅ BC Reason: Given
3. ∠BCA = 71° Reason: Linear pairs are supplementary
4. ΔABC is isosceles. Reason: Definition of isosceles
5. ∠A ≅ ∠BCA Reason: Isoceles triangle theorem
6. ∠A = 71° Reason: Def congruent
Answer: 71 degrees
Answer:
The correct options are (1), (3) and (5).
Step-by-step explanation:
The two triangles are shown below.
The measure of ∠F corresponds to ∠F'.
The distance between the points D and origin is of 9 units.
And the distance between the points D' and origin is 3 units.
Thus, the distance from point D' to the origin is One-third the distance of point D to the origin.
Check for similarity:
Thus, the △DEF is similar to △D'E'F'.
Thus, the correct options are (1), (3) and (5).
⓵ To calculate the volume of a right circular cylinder, the formula is π times the radius of the circular base² time the height of the cylinder.
⓶ Now that we know that the equation to calculate the volume of a right circular cylinder is :
V = π x (r²) x h
You need to find the numbers to replace the volume (V) and the height (h) in the formula.
We already know that the volume is 320 square feet and that the height is 20 feet.
So we are left with a formula looking like this :
320 = π x (r²) x 20
⓷ Now we need to find the radius of the circular base! To do so, you need to solve this equation and isolate the “r”. Start by simplifying the right side :
320 = π x (r²) x 20
÷20 ÷20
↓
16 = π x r²
÷π ÷π
↓
5,09 ⋍ r²
√ √
↓
2,26 feet ⋍ r
⓸ Now that we knoe the value of the radius of the circular base, all there’s left to do is multiply this number by two in order to find the diameter of the water tank :
2,26 x 2 = d
↓
4,51 feet ⋍ d
So your final answer is : the diameter of the water tank is about 4,51 feet.
** Since I devided by “π”, all the answers I wrote from that point are rounded to the nearest hundredths just to make things easier to visualize, but I kept all of the decimals when doing the calculations. So it is possible that your answer might differ slightly from mine if you use the rounded numbers to calculate everything. Just keep that in mind!
I hope this helped, if there’s anything just let me know! ☻
Answer:
89414,89416,89418
Step-by-step explanation:
Let n bet the positive integer and then 2n is an even integer because multiplying n with 2 makes it an even integer.
Now, 2n+2, 2n+4 are the next integers.
Therefore, three consecutive integers are: 2n, 2n+2, 2n+4.
It is given that twice the first integer added to the second is 268,244 that means:
Therefore, three consecutive integers are:
2n=89414, 2n+2=89416, 2n+4=89418
Answer:
[x-h]^2 + [y-k]^2 =r^2
Step-by-step explanation:
Let x and y be an arbitrary point along the circle
The equation of the circle is given as:
[x-h]^2 + [y-k]^2 =r^2
