Answer:
largest angle = 92°
Step-by-step explanation:
Since the measurement of the angles are;
x°, ( x + 6)°, (2x + 10)°
And we know that sum of angles in a triangle is 180. Thus;
x + (x + 6) + (2x + 10) = 180
x + x + 6 + 2x + 10 = 180
4x + 16 = 180
4x = 180 - 16
4x = 164
x = 164/4
x = 41°
The other two angles will be;
(41 + 6)° and (2(41) + 10)°
Which gives;
47° and 92°
So,largest angle = 92°
The equations used to find the measure of each angle in degrees is x + y = 90 and x = 6y - 1
The two complementary angles are 77 degrees and 13 degrees
<em><u>Solution:</u></em>
Given that two angles are complementary angles
Complementary angles are two angles whose sum is 90 degrees
Let one of the angle be "x" and the other angle be "y"
Therefore,
x + y = 90 ------ eqn 1
Also given that,
One angle is one less than six times the measure of another
one angle = six times the other angle - 1
x = 6y - 1 ------ eqn 2
Substitute eqn 2 in eqn 1
6y - 1 + y = 90
Thus the above equation is used to find the measure of each angle in degrees
Solve the above equation
6y + y - 1 = 90
7y - 1 = 90
7y = 91
y = 13
Substitute y = 13 in eqn 2
x = 6(13) - 1
x = 78 - 1
x = 77
Thus the two complementary angles are 77 degrees and 13 degrees
Answer:
12 months
Step-by-step explanation:
Given data:
Before joining club 6 books read
3 books every month
total books read 42
books read after joining the club = 42 - 6
books read after joining the club = 36
Months she has in book club = 36/3
Months she has in book club = 12 months
Answer:
x = 3.67
Step-by-step explanation:
Simplify both expressions
14x - 18 = 5x + 15
Subtract the bigger (n)x by the smaller
14x - 5x = 9x
Plus the smallest by itself, giving you:
9x - 18 = 15
+18 +18
9x = 33
Simplify ( divided by 3 )
3x = 11
x = 3.67
Answer:
Step-by-step explanation:
The hypothesis is written as follows
For the null hypothesis,
µd ≤ 10
For the alternative hypothesis,
µ > 10
This is a right tailed test
Since no population standard deviation is given, the distribution is a student's t.
Since n = 97
Degrees of freedom, df = n - 1 = 97 - 1 = 96
t = (x - µ)/(s/√n)
Where
x = sample mean = 8.9
µ = population mean = 10
s = samples standard deviation = 3.6
t = (8.9 - 10)/(3.6/√97) = - 3
We would determine the p value using the t test calculator. It becomes
p = 0.00172
Since alpha, 0.01 > than the p value, 0.00172, then we would reject the null hypothesis. Therefore, At a 1% level of significance, there is enough evidence that the data do not support the vendor’s claim.
