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:
Option D (7).
Step-by-step explanation:
The formula for gradient of the straight line is given by:
m = (y2 - y1)/(x2 - x1); where (x1, y1) and (x2, y2) are two fixed points on the straight line. It is given that (x1, y1) = (4, r) and (x2, y2) = (r, 2). The gradient of the straight line is given by -5/3. To find the value of r, simply substitute all the values in the gradient equation. Therefore:
-5/3 = (2 - r)/(r - 4).
Cross Multiplying:
-5*(r - 4) = 3*(2 - r).
-5r + 20 = 6 - 3r.
-2r = -14.
r = 7.
Therefore, Option D is the correct answer!!!
The best batch size is 1053.
Since 5% have failed, this means 95% have passed the test.
95% = 95/100 = 0.95
We can set up an equation to answer this:
0.95x = 1000
Divide both sides by 0.95:
0.95x/0.95 = 1000/0.95
x = 1052.6 ≈ 1053
We know that
If the scalar product of two vectors<span> is zero, both vectors are </span><span>orthogonal
</span><span>A. (-2,5)
</span>(-2,5)*(1,5)-------> -2*1+5*5=23-----------> <span>are not orthogonal
</span><span>B. (10,-2)
</span>(10,-2)*(1,5)-------> 10*1-2*5=0-----------> are orthogonal
<span>C. (-1,-5)
</span>(-1,-5)*(1,5)-------> -1*1-5*5=-26-----------> are not orthogonal
<span>D. (-5,1)
</span>(-5,1)*(1,5)-------> -5*1+1*5=0-----------> are orthogonal
the answer is
B. (10,-2) and D. (-5,1) are orthogonal to (1,5)
