Answers
Step-by-step explanation:
you should have measured the lengths of the sides and added that information here to the picture.
because we here cannot measure this from a picture that is inclined and has no size scale.
I can give you a hint how to get the angles, when you have all 3 sides :
start with the extended Pythagoras for non right-angled triangles:
c² = a² + b² - 2ab×cos(C)
with c being the side opposite of the angle you are aiming for.
then
2ab×cos(C) = a² + b² - c²
cos(C) = (a² + b² - c²)/(2ab)
for example, to get the angle at T, its opposite side is SE.
cos(T) = (ST² + ET² - SE²)/(2×ST×ET)
you can do the same thing for all 3 angles (you need to always pay attention to what sides you have to use in what combination for the angle).
or you can switch after getting the first angle to the laser of sine :
a/sin(A) = b/sin(B) = c/sin(C)
where the sides and the disposing angles are always opposite of each other.
for your triangle that looks like
ET/sin(S) = ST/sin(E) = SE/sin(T)
from there (once you have one angle via the Pythagoras approach) you get all other angles.
Related Questions
The temperature of a cup of coffee varies according to Newton's Law of Cooling: dT dt equals negative k times the quantity T minus A, where T is the temperature of the coffee, A is the room temperature, and k is a positive constant. If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25°C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes.
74
67
60
42
Answers
Answer:
(b) 67
Step-by-step explanation:
A solution to the differential equation describing the temperature according to Newton's Law of Cooling could be written as ...
T = (final temp) + (initial difference)×(decay factor)^t
where the decay factor is the fraction of change during 1 unit of time period t.
__
Here, the initial difference of 100-25 = 75 degrees decays to 90-25 = 65 degrees in 1 minute. So, the units of t are minutes, the decay factor is 65/75, the initial difference is 75 degrees, and the final temperature is 25 degrees. That lets us write the equation as ...
T = 25 +75(65/75)^t
Then for t=4, the temperature is ...
T = 25 +75(13/15)^4 ≈ 67.3 . . . . degrees
After 4 minutes the temperature of the coffee is about 67 degrees.
8. A tree on a 30° slope grows straight up. What are the measures of the
greatest and smallest angles the tree makes with the hill? Explain.
Answers
the slope makes a 30-degree w/ the horizon, then we can draw it out by making a right triangle out of it
we'll get a 30-60-90 triangle
the tree will make 2 angles w/ the slope, one on each side.
so draw the tree on the slope, then you'll get a 60 and 120 degree
it'd be easier if you visualize this problem
hope it helps! I know I sound confusing
The measure of the smallest angle of a tree with a hill is 60°.
The measure of the greatest angle of a tree with a hill is 120°.
Given:
A tree on a 30° slope grows straight up.
To find:
The measures of the
greatest and smallest angles the tree makes with the hill.
Solution:
In figure drawn:
[tex]\angle PQR = 30^o[/tex]
AB= Straight three
Construction:
Draw a parallel line CA to QR through point A.
Now,
[tex]\angle PQR = \angle PAC = 30^o\\\\\angle PAC +\angle PAB = 90^o \text{(Complimentary angles)}\\\\\angle PAB = 90^o -\angle PAC\\\\angle PAB=90^o-30^o=60^o[/tex]
The measure of the smallest angle of a tree with a hill is 60°.
[tex]\angle PAB + \angle BAQ= 180^o\text{(Supplementary angles)}\\\\ \angle BAQ= 180^o-\angle PAB \\\\ \angle BAQ=180^o-60^o=120^oC[/tex]
The measure of the greatest angle of a tree with a hill is 120°.
Learn more about complementary and supplementary angles here:
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Use the appropriate conversions listed to convert 80 cups into gallons. Round to the nearest hundredth
Answers
Answer:
5 gallons
Step-by-step explanation:
You divide the number of cups by 16 to find how many gallons are there in a certain amount of cups.
f(x) = 1?-1.9(x) = x - 2. Find
(a) ( + g)(3)
Answers
Answer: f(x)=1-1.9x=x-2
Step-by-step explanation:
Big brain time.
Solve. Use the discount equation
S = R − rR, where S is the sale price, R is the regular price, and r is the discount rate.
An exercise bike is on sale for $320, having been marked down 20% off the regular price. Find the regular price.
Answers
Answer:
[tex]\$ 400[/tex].
Step-by-step explanation:
In this question, [tex]S[/tex] (sales price) and [tex]r[/tex] (discount rate) are both given. The unknown is the regular price, [tex]R[/tex].
Rearrange the discount equation to solve for [tex]R[/tex] in terms of [tex]S[/tex] and [tex]r[/tex].
[tex]S = R - r\, R[/tex].
[tex]S = (1 - r)\, R[/tex].
Divide both sides by [tex](1 - r)[/tex]:
[tex]\displaystyle \frac{S}{1 - r} = \frac{(1 - r)\, R}{1 - r}[/tex].
[tex]\begin{aligned}R &= \frac{S}{1 - r}\end{aligned}[/tex].
It is given that [tex]S = 320[/tex]. A mark-down of [tex]20\%[/tex] is equivalent to a discount rate of [tex]r = 20 / 100 = 0.20[/tex]. Substitute in [tex]S[/tex] and [tex]r[/tex] to find the value of [tex]R[/tex]:
[tex]\begin{aligned}R &= \frac{S}{1 - r} \\ &= \frac{320}{1 - 0.2} \\ &= \frac{320}{0.8} \\ &= 400\end{aligned}[/tex].
Thus, the regular price would be [tex]\$ 400[/tex].
White 4x+y=8 in slope intercept form
Answers
Answer:
y=-4x+8
Step-by-step explanation:
Solve: x2 - 2x + 1 = 4
Please help me
Answers
Let's solve your equation step-by-step.
x2−2x+1=4
Step 1: Subtract 4 from both sides.
x2−2x+1−4=4−4
x2−2x−3=0
Step 2: Factor left side of equation.
(x+1)(x−3)=0
Step 3: Set factors equal to 0.
x+1=0 or x−3=0
x=−1 or x=3
Answer:
x=−1 or x=3
A triangular bandana has an area of 78 square inches. The height of the triangle is 9 3 4 inches. Enter and solve an equation to find the length of the base of the triangle. Use b to represent the length of the base. An equation to find the length of the base of the triangle is 78= The length of the base of the triangle is inches.
Answers
Area of triangle = 1/2 x base x height:
78 = 1/2 x base x 9 3/4
Multiply both sides by 2:
156 = base x 9 3/4
Divide both sides by 9 3/4:
Base = 16 inches
Is (-1,2) a solution to the following system of equations? Show and explain why or why not.
f(x)=x^2+3x+4
g(x)=2x+4
Answers
Answer:
It is a solution.
Step-by-step explanation:
Plug in (-1,2) to both equations:
Plug in -1 to see if 2 comes out:
f(x)=x^2+3x+4
y=(-1)^2+3(-1)+4
y=1-3+4
y=-2+4
y=2
(yes it works)
g(x)=2x+4
y=2(-1)+4
y=-2+4
y=2
(yes it works)
The mass of the apples harvested from a particular orchard follows a nearly normal distribution with a mean of 94 grams and a standard deviation of 27 grams. What size sample is needed to get a standard error of 3
Answers
The sample size needed to get a standard error of 3 is 81
How to determine the sample size?The given parameters are:
Mean = 94Standard deviation = 27Standard error = 3The standard error is calculated using:
[tex]SE = \frac{\sigma}{\sqrt n}[/tex]
So, we have:
[tex]3= \frac{27}{\sqrt n}[/tex]
Divide both sides by 3
[tex]1= \frac{9}{\sqrt n}[/tex]
Square both sides
1 = 81/n
Multiply both sides by n
n = 81
Hence, the sample size needed to get a standard error of 3 is 81
Read more about standard errors at:
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help me please i dont get it
Answers
Answer:
Q11 part a
Q12 part b
Step-by-step explanation:
You have been asked to develop a composite measure of the quality of life on your campus.
1. Outline the social indicators you would use to develop such a measure. Be specific. Explain why you selected these indicators?
2. Now suppose data on your social indicators have been collected over a ten-year period. What might you be able to do with these data?
Answers
The social indicators that can be used to know the quality of life in campus are the number of hours spent in school, extra curricular activities, etc.
What are social indicators?It should be noted that social indicators are used to monitor the social system.
The social indicators that can be used to know the quality of life in campus are the number of hours spent in school, extra curricular activities, etc. They're important to assess ones social life.
In conclusion, after necessary data has been collected m, a research can be made to know how the quality of life is affected by the data.
Learn more about indicators on:
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6+8x/2=5x solve for X
Answers
6+8x = 5x(2)
6+8x = 10x
6=10x-8x
6=2x
6/2=x
3=x
x=3
1. A certain small factory employs 98 workers. Of these, 10 receive a wage of $150 per day and the rest receive $85.50 per day. To the management, a week is equal to 6 working days. How much does the factory pay out for each week
Answers
Answer:hello I'm from Philippines
Step-by-step explanation:
Dana is making a seating chart for an awards banquet. There are 120 people coming to the banquet.If 8 guests can be seated at each table, how many tables will be needed for seating for the awards banquet?
Answers
Explanation: 120/8 will give you 15 tables.
What is nineteen minus twelve divided by six
19 - 12 / 6
Answers
Answer:
17
Step-by-step explanation:
Using PEMDAS you divide first and get 2
19-2
then you get 17 as your final answer
Please answer this correctly without making mistakes
Answers
Answer:
The answer is 10 months
Step-by-step explanation:
solve the equation for x 5x squared - 4x = 6
Answers
Joyce purchased 84.92 in groceries and gives the clerk $100 bill how much change should the clerk give back to her
Answers
Answer:
$15.08
Step-by-step explanation:
When subtract 84.92 from 100 you get 12.08 which is how much he clerk should give back
Answer:
15.08
Step-by-step explanation:
Given: ∠P ≅ ∠Q and Line Segment RS bisects ∠PQR. Prove: Line segments PR≅QR . Supply the missing statement in Statement 5 of the proof of the the Converse of the Isosceles Triangle Theorem.
Begin with isosceles ∆PRQ with ∠P ≅ ∠Q. Construct Line Segment RS a bisector of ∠PRQ.
A. ∆PRS ≅ ∆PRQ
B. ∆PRS ≅ ∆PRS
C. ∆PRS ≅ ∆SRQ
D. ∆PRS ≅ ∆QRS
Answers
Answer:
D
Step-by-step explanation:
Vertices P and Q correspond, vertices R and S correspond to themselves.
By the property of (Angle-Angle-Side)AAS postulates ΔPRS≅QRS
Option (D) is correct.
It is required to find the missing statement in Statement 5 of the proof.
What is congruence in Triangle?Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.
Given that:
∠P ≅ ∠Q and Line Segment RS bisects ∠PQR.
In ΔPRS≅QRS ,
∠P≅∠Q (Given)
∠PRS≅∠QRS (Definition of angle bisector)
RS≅RS (reflexive property of congruence)
so,ΔPRS≅QRS (By AAS congruence)
Therefore, by the property of (Angle-Angle-Side)AAS postulates ΔPRS≅QRS
Learn more about the congruence in triangle here:
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What is 84, percent of 300?
Answers
Answer:
252
Step-by-step explanation:
.84 times 300 = 252
Answer:
252%
Step-by-step explanation:
I did the Khan Academy.
When a result from a simple is extended to the population
Answers
Answer:
You can opt to study the entire population when the population is well defined(Complete sampling frame) and small.
It can eliminate any potential bias occurring through sampling technique, but other than that it is really not justified to consume more resources and time.
A circle with the center C (4, -2) contains the point D (8,1). What is the equation of the line perpendicular to the radius of the circle passing through point C?
Answers
Answer:
y = -4x/3 + 10/3
Step-by-step explanation:
We find the slope of CD and get (-2 - 1)/(4 - 8) = -3/-4 = 3/4
The slope of a perpendicular line is the opposite reciprocal of the slope of the line it's perpendicular to, so we get a slope of -4/3.
We can use point-slope form and get (using point C):
y - (-2) = (-4/3)(x - 4) -->
y + 2 = -4x/3 + 16/3 -->
y = -4x/3 + 10/3
**NOTE** I can't see the picture (because of a problem on my computer) so if there is any info given there that isn't given in the text, then my answer will be incorrect.
the area of a rectangle is 30 to the square root of 3750 square inches, and the length is 3 to the square root of 250 inches. what is the width of the rectangle?
Answers
We are given that:
Area of rectangle is 30√3570Length of the rectangle is 3√250Area of rectangle is given by:
[tex] \implies\quad{\pmb{ \sf{Area = length\times width}} }[/tex]
Hence, putting the values in the formula:
[tex] \implies\quad \sf{ A = l\times w}[/tex]
[tex] \implies\quad \sf{ 30\sqrt{3750}=3\sqrt{250}\times w}[/tex]
[tex] \implies\quad \sf{3\sqrt{250}\times w = 30\sqrt{3750} }[/tex]
[tex] \implies\quad \sf{ w =\dfrac{30\sqrt{3750}}{3\sqrt{250}}}[/tex]
[tex] \implies\quad \sf{ w =10\dfrac{\sqrt{3750}}{\sqrt{250}}}[/tex]
[tex] \implies\quad \sf{ w = 10\times\sqrt{\dfrac{3750}{250}}}[/tex]
[tex] \implies\quad \underline{\underline{\pmb{\sf{ w =10\sqrt{15}}}}}[/tex]
A t-shirt that was originally priced at $14 is marked down to $10.
About what is the percent decrease?
A. 40%
B. 28.6%
C. 71.4%
D. 140%
Answers
plss help mee
Show your work plss not just the answer
If two people share one soda, how much of the soda should each person get?
Answers
Answer:
1/2 of the soda:) sure yan
Answer:
sorry i dont know
Step-by-step explanation:
They need to park the Mystery Machine. They could
either park in the lot that charges $5 and then $2 an
hour, or they could park using the meter on the street
that charges $3.75 per hour.
Write an equation that describes when the cost is the
same at both locations (the parking lot and on the
street).
Answers
Answer:
12 hours in the street=20 hours in the lot
Step-by-step explanation:
Well basically if you're at the street for 12 hours it will add up to 45 dollars. subtract the 5 starting dollars and you get 40. Divide 40 by 2 and you get 20. What does this mean? This means that in 12 hours on the street you can match the same amount of money if you were in the lot for 20 hours.
Pls help with this it’s easy
If u click there will be pic
Answers
Answer:
15, the second one.
Step-by-step explanation:
We can use this proportion:
[tex]\frac{centimeters}{meters}[/tex]
So, in this case:
[tex]\frac{5 centimeters}{20 meters}[/tex]=[tex]\frac{x centimeters}{60 meters}[/tex]
We can cross multiply, resulting in:
[tex]20x = 300 centimeters[/tex]
Divide both sides by 20, resulting in:
[tex]x = 15 centimeters[/tex]
a chess club has 20 girls and 15 boys. seven of the girls and 7 of the boys in the chess club are also in the math club.
what percent of the students in the chess club are also in math club?
Answers
Answer:
40% why? because 20+15=35 that is the total but they are saying 7 boys and 7 girls are in math and chees so is 14 14/35 is 40%
An airplane on autopilot took 5 hours to travel 3540 kilometers. What is the unit rate for kilometers per hour?
Answers
Answer:
708 km.
Step-by-step explanation:
3540/5=708
Answer:
708 km/h
Step-by-step explanation:
3540 / 5 = 708