two nonoverlapping acute angles that share a ray form an obtuse angle if one of the acute angles have a a measure of 50 degres w
hat could be the measure of the other acute angle?
2 answers:
Answer:
The measure of other acute angle has to be less than 40°
Step-by-step explanation:
Let a and b denote the two acute angle that is formed by a same ray.
such that a=50 degree.
Let c be the obtuse angle that is formed.
i.e. m∠c >90°
So, we get a triangle such that the three angles of a triangle are a , b and c.
As we know that the sum of all the angles of a triangle is 180°.
Hence,
m∠a+m∠b+m∠c=180°
Hence,
50+m∠b+m∠c=180°
m∠b+m∠c=180°-50°
m∠b+m∠c=130°
Hence,
m∠b=130°-m∠c
As,
m∠c>90°
⇒ -m∠c<-90°
⇒ 130°-m∠c<130°-90°
⇒ 130°-m∠c<40°
⇒ m∠b<40°
Hence, the measure of the other acute angle has to be less than 40°
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The equation for the line passing through point A and perpendicular to AB will be y-0.5x=6, the gradient of line AB is -2, and the gradient of a line perpendicular to AB is 0.5.
<h3 /><h3>What is the slope or gradient?</h3>A numerical assessment of a line's angle relative to the ground is known as the slope.
Given data;
m₁ is the slope of line AB
m₂ is the slope of a line perpendicular to AB
The coordinate points are,
A,(x₁,y₁)= (0, 6)
B,(x₂,y₂)=(3, 0).
The gradient of line AB;
The slope of the lines has a perpendicular relation is -1;
m₁ × m₂ = -1
(-2) × m₂ = -1
m₂ = 1/2
m₂ = 0.5
The equation of the line passing through point A and perpendicular to AB;
(y - y₁) = m₂(x-x₁)
(y-6)=0.5(x-0)
y-6 = 0.5 x
y-0.5x=6
Hence, the gradient of line AB, the gradient of a line perpendicular to AB, and the equation of the line passing through point A and perpendicular to AB will be -2,0.5 and y-0.5x=6.
To learn more about the slope, refer to the link;
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Answer:
a) For this case we need to use a t distribution since we know the information about a sample and we don't know the population deviation.
b)
So on this case the 90% confidence interval would be given by (118.904;133.096)
c) For this case since confidence interval include tha value of 130 so then we don't have enough evidence to conclude that the claim by the consultant is incorrect.
Step-by-step explanation:
Part a
For this case we need to use a t distribution since we know the information about a sample and we don't know the population deviation.
Part b
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
represent the sample mean
population mean (variable of interest)
s=15 represent the sample standard deviation
n=14 represent the sample size
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.90 or 90%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,13)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 90% confidence interval would be given by (118.904;133.096)
Part c
For this case since confidence interval include tha value of 130 so then we don't have enough evidence to conclude that the claim by the consultant is incorrect.