Answers:
- Angle A = 76
- Angle B = 37
- Angle C = 67
Triangle ABC is an acute triangle. It's also a scalene triangle.
====================================================
Work Shown:
x = measure of angle B
2x+2 = measure of angle A, since we're told its "2 more than twice angle B"
2x-7 = measure of angle C, for similar reasoning
The three angles add to 180. This is true for any triangle
A+B+C = 180
(2x+2)+(x)+(2x-7) = 180
5x-5 = 180
5x = 180+5
5x = 185
x = 185/5
x = 37
This means angle B is 37 degrees. The other two angles are
A = 2x+2 = 2*37+2 = 74+2 = 76
C = 2x-7 = 2*37-7 = 74-7 = 67
----------------
In summary, we have these three interior angles
As a way to check, note how A+B+C = 76+37+67 = 180. This confirms the answer. All three angles mentioned are smaller than 90 degrees, so this triangle is acute.
Furthermore, because all three angles are different measures, this means all three sides are different lengths. This leads to triangle ABC being scalene.
Do cross-multiplication
<span>72/x = 60/100 </span>
<span>so </span>
<span>60 times x = 72 times 100 </span>
<span>so </span>
<span>60x = 7200 </span>
<span>then divide both sides by 60 </span>
<span>x = 120</span>
Answer:
£3.6
Step-by-step explanation:
24 = 100% ; x = 15%
Let's make it simple
Answer:
(-0.607 ; 1.757)
Step-by-step explanation:
Student: __ 1 ___ 2 ___ 3 ___ 4
Fall _____2.6__ 3.0__ 1.5 __1.4
Spring___ 1.7__ 2.2 __1.4 __0.90
Using calculator :
Fall:
Xbar1 = 2.125
Sample size, n1 = 4
Standard deviation, s1 = 0.8
Spring :
Xbar2 = 1.55
Sample size, n2 = 4
Standard deviation, s2 = 0.54
Confidence interval :
(xbar1 - xbar2) ± Tcritical * Sp* √1/n1 + 1/n2
Sp = √[(df1*s1² + df2*s2²) ÷ (n1 + n2 - 2)]
df = n - 1
(xbar1 - xbar2) = 2.125 -1.55 = 0.575
Hence,
Sp = √(((3*0.8^2) + (3*0.54^2)) / 6)
Sp= √2.7948 ÷ 6
Sp = √0.4658
Sp= 0.682
Tcritical at 95%, df = 4 = 2.45
Error margin = 2.45 * 0.682 * √1/4 + 1/4 = 1.182
Confidence Interval:
Lower boundary = 0.575 -1.182 = -0.607
Upper boundary = 0.575 + 1.182 = 1.757
(-0.607 ; 1.757)