we know that
In the right triangle ABC
∠
∠
------> by complementary angles
so
Step 
Find the measure of angle B
we know that
in this problem
so
Step 
Find the measure of angle A
therefore
the answer is the option
35.5° and 54.5°
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line is
7x+4y=3
4y = - 7x + 3
y = -7x/4 + 3/4
Comparing with the slope intercept form, slope = -7/4
If the line passing through the given point is perpendicular to the given line, it means that its slope is the negative reciprocal of the slope of the given line.
Therefore, the slope of the line passing through (6,-9) is 4/7
To determine the intercept, we would substitute m = 4/7, x = 6 and y = -9 into y = mx + c. It becomes
- 9 = 4/7×6 + c = 24/7 + c
c = - 9 - 24/7 = -87/7
The equation becomes
y = 4x/7 - 87/7
Answer:
Since it took Juan 16 hours to wrap 2 presents, it will take Juan 32 hours.
1 present- 8 hours
2 present- 16 hours
3 present- 24 hours
4 present- 32 hours
To check if a relation is a function, given a mapping diagram of the relation, use the following criterion: If each input has only one line connected to it, then the outputs are a function of the inputs.
Given that,
Sample size= 83
Mean number= 39.04
Standard deviation= 11.51
We know the critical t-value for 95% confidence interval which is equal to 1.989.
We also know the formula for confidence interval,
CI=( mean number - critical t-value*standard deviation/(sample size)^(1/2), mean number + critical t-value*standard deviation/(sample size)^(1/2))
So, we have
CI= (39.04 - 1.989*11.51/83^(1/2), 39.04 + 1.989*11.51/83^(1/2)
CI= (39.04 - 2.513,39.04 + 2.513)
CI= (36.527,41.553)
Therefore, 95% confidence interval for these data is (36.527,41.553), and this result interpret that the true value for this survey sample lie in the interval (36.527,41.553).
