The three sides of AXYZ
measure 13 feet, 17 feet, and
21 feet. IS AXYZ an acute,
right, or obtuse triangle?
Answers
9514 1404 393
Answer:
acute
Step-by-step explanation:
I like to think of this in terms of the "form factor" (a term I made up). It is computed as ...
f = a² +b² -c²
where a, b, c are the side lengths, and c is the longest.
The interpretation is ...
f > 0 . . . acute
f = 0 . . . right
f < 0 . . . obtuse
Here, we have ...
f = 13² +17² -21² = 17 . . . . . the triangle is acute
_____
Additional comment
The measure of the largest angle is ...
arccos(f/(2ab)) = (17/(2(13·17)) = arccos(1/26) ≈ 87.8°
You can see that (2ab) is always positive, so the sign of f matches the sign of the cosine of the angle. That is what leads to the above interpretation.
This formula comes from the Law of Cosines, of which the Pythagorean theorem is a special case.
Related Questions
what is the area of the shaded region in the figure below
Answers
Answer:
4 cm^2
Step-by-step explanation:
2 x 2 x 0.5 x 2 = 4 cm^2
Hi there!
[tex]\huge\boxed{4 \text{ cm}^{2}}[/tex]
Find the area of the shaded area using the given dimensions:
The shaded area is divided up into two triangles, each with a base of 2 cm and a height of 2 cm. Use the following equation to solve for area:
A = 1/2(bh)
A = 1/2(2 · 2)
A = 1/2(4) = 2 cm²
There are two triangles, therefore:
2 × 2 = 4 cm²
This is due in 10 minutes please help me
Answers
Given:
The rate of interest on three accounts are 7%, 8%, 9%.
She has twice as much money invested at 8% as she does in 7%.
She has three times as much at 9% as she has at 7%.
Total interest for the year is $150.
To find:
Amount invested on each rate.
Solution:
Suppose x be the amount invested at 7%. Then,
The amount invested at 8% = 2x
The amount invested at 9% = 3x
Total interest for the year is $150.
[tex]x\times \dfrac{7}{100}+2x\times \dfrac{8}{100}+3x\times \dfrac{9}{100}=150[/tex]
Multiplying both sides by 100, we get
[tex]7x+16x+27x=15000[/tex]
[tex]50x=15000[/tex]
Dividing both sides by 50, we get
[tex]x=\dfrac{15000}{50}[/tex]
[tex]x=300[/tex]
So, the amount invested at 7% is [tex]300[/tex].
The amount invested at 8% is
[tex]2(300)=600[/tex]
The amount invested at 9% is
[tex]3(300)=900[/tex]
Hence, the stockbroker invested $300 at 7%, $600 at 8%, and $900 at 9%.
which of the following is NOT a property of all parallelograms
(1) the diagonals are perpendicular
(2) the diagonals bisect each other
(3) opposite sides are congruent
(4) adjacent angles are supplementary
Answers
I already know the answer but I want to see if people get it right :) will give brainiest to correct answer.
There is a patch of lily pads on a lake. Every day, the patch doubles in size.
If it takes 48 days for the lily pads to cover the entire lake how much days does it take for the lily pads to cover half the lake.
Answers
Answer:
is it 47? I'm not sure
if not can you explain it to me
Answer:
47 days
Step-by-step explanation:
Since the patch of lily pads double each day, the day before day 48 would cover half of the lake.
You put $500 in a savings account. The account earns $20 simple interest in 6 months. What is the annual interest rate? Write your answer as a percent
Answers
Answer:
8%
Step-by-step explanation:
For simple interest, we use the equation I = PRT, where I is the interest earned, P is the principal/amount invested, R is the rate as a decimal, not percentage, and T is the time in years.
For this problem, we have to use 0.5 for T, because 6 months is 1/2 a year.
20 = (500)(r)(0.5)
20 = 250r
r = 0.08 = 8%
Answer pls is mathematically is due today in 1 m
Answers
Answer:
200.96 units^2 or 64π units^2
Step-by-step explanation:
8^2(3.14) = 200.96 units^2 or 64π units^2
(multiplied by 2 to change the radius to diameter)
Please solve this pleaseeeeeeeeeee
Answers
Answer:
x = 45
Step-by-step explanation:
x + 2x + x = 180
4x = 180
x = 45
Answer:
Since its a triangle, all the angles must add to 180. So x+x+2x=180. Solve for x and you got your answer.
Step-by-step explanation:
A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them. Previously research has shown the variability in the number to be σ = 2. The researchers wish the margin of error to be no larger than 0.5 for a 99% confidence interval. To obtain such a margin of error the researchers need at least:
A. 53 observations.
B. 107 observations.
C. 106 observations.
D. 54 observations.
2.
A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them. The number of enteroliths is determined by surgery or ultrasound. This requires the participation of a radiologist and a surgeon in the study. The researchers decide that they should only enroll horses seen at the best veterinary hospital in the country to ensure correct counts. Such a hospital will typically see the most severe cases. The researchers will enroll the first 100 horses seen beginning on the day the study is funded. The resulting interval is likely biased because:
A. the first 100 horses seen is not an SRS of all horses with enteroliths and therefore never representative.
B. a sample of 100 horses is too small to obtain an unbiased estimate.
C. the best veterinary hospital is likely to see the most severe cases with larger number of enteroliths.
D. All of the above
3.
A group of veterinary researchers plan a study to estimate the average number of enteroliths in horses suffering from them. The number of enteroliths is determined by surgery or ultrasound. This requires the participation of a radiologist and a surgeon in the study. The researchers decide that they should only enroll horses seen at the best veterinary hospital in the country to ensure correct counts. Such a hospital will typically see the most severe cases. The researchers will enroll the first 20 horses seen beginning on the day the study is funded. The researchers will calculate a 95% confidence interval. The procedure is not valid because the:
A. sample size is too small for the central limit theorem to apply.
B. average number is not an integer and does not reflect any actual observation.
C. None of the above. The procedure is valid.
D. data are counts and, therefore, not Normally distributed.
4.
In a test of hypothesis for a mean, which statement is CORRECT?
A. The test requires that the sample mean is normally distributed; this requires that either the population distribution is Normal or the sample size exceeds 30.
B. As long as the population distribution consists only of positive values, sample size does not matter.
C. The population distribution can be any distribution because the sample mean is always Normally distributed.
D. The population must be normal because that is the only case when the sample mean is Normally distributed.
5.
A "false negative," in which no effect is detected when in reality one exists, is an example of:
A. a Type I error.
B. the power of the test.
C. a Type II error.
D. None of the above
Answers
Answer:
1.) 107 observations
2.) the best veterinary hospital is likely to see the most severe cases with larger number of enteroliths
3.) A. sample size is too small for the central limit theorem to apply.
4.) The test requires that the sample mean is normally distributed; this requires that either the population distribution is Normal or the sample size exceeds 30.
5.) a Type I error
Step-by-step explanation:
n = [(Zcritical * σ) ÷ E]²
n = sample size
Zcritical at 99% = 2.58
E = error margin = 0.5
Standard deviation, σ = 2
n = [(2.58 * 2) ÷ 0.5]²
n = [5.16 ÷ 0.5]²
n = (10.32)²
n = 106.5024
n = 107 observations
B.) The thought or decision that the best veterinary hospital is likely to see the most severe cases with larger number of enteroliths will introduce a bias in the study.
C.) For central limit theorem ; sample size must be considerably large ; at least sample size, n ≥ 30
D.) Distribution must be normal it approximately normal, obeying the central limit theorem ; sample size must be considerably large ; at least sample size, n ≥ 30
HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
help din HDKE EJFNQKEHWHQODBEHQVEIFNFJRNSJEBSG
Step-by-step explanation:
di ko din alam e AHAHAHAHAHAHAHAHAHA NSKFBWJF S DJEBEJS
JSHEBEJS IF JENSKS.DJWKW
SBWUKWVEUEBJQBRJDNDJXBDJDBDKW
EBEJE KD DJWKQKQBWHS
Pls help, thank you :)
Answers
3,500,000 divided by 100
That equals
=35000
So (3)
Hope this helped ^^
Answer:
(3)
Step-by-step explanation:
Which equation is an identity?
Answers
I need to know how many more there are.
Answers
Wdym????????????????
please help i don't know this one
Answers
Answer:
Hey do you know the answer to the question you wrote a while ago?
Step-by-step explanation:
(02.05)
Two similar triangles are shown on the coordinate grid:
A coordinate plane is shown. Triangle XYZ has vertices X at negative 5 comma negative 1, Y at negative 6 comma negative 2, and Z at negative 3 comma negative 2. Triangle X double-prime Y double-prime Z double-prime has vertices X double-prime at 10 comma negative 2, Y double-prime at 12 comma negative 4, and Z double-prime at 6 comma negative 4.
Which set of transformations has been performed on triangle XYZ to form triangle X′′Y′′Z′′?
Do you?? :(
Find the distance between (−9, 7) and (−6, 7).
Answers
Answer:
(6,7),(9,6)
Step-by-step explanation:
HOPE THIS HELPS!!!!
I NEED HELP NOW PLZ!!!
Answers
Answer:
A) P' (0, -9)
Step-by-step explanation:
Which of the following is the product of (3x − 5) and (3x + 5)?
Answers
Answer:
[tex] {9x}^{2} - 30x + 25[/tex]
[tex]\huge\underline\bold\blue{ƛƝƧƜЄƦ}[/tex]
(3x + 5)(3x - 5)
By using identity
(a + b)(a - b) = a² - b²
3x² - 5²
9x² - 25
Give the domain and range of the relation then determine if the relation is a function (-3,3), (1, 1), (0, -2), (1, -4), (5, -1)
Domain:_____
Range:_____
Function?_____
PLEASE HURRY
Answers
*domain is the x-value, input, independent
Ranges: {-4, -2, -1, 1, 3}
*range is the y-value, output, dependent
LIST BOTH FROM LEAST TO GREATEST
Functions are when each input(x) has one and only one output(y)
If you were to graph a function, no points would line up vertically with one another.
This question would not be a function because an input (number 1 in this case) has more than one output (1 AND -4)
So function? No.
A number is divided by 3 and decreased by 5 is 6. What is the number???
Answers
Answer:
Given : x/3-5=6
answer = 23
Step-by-step explanation:
x-5=6*3
x-5=18
x=18+5
x=23
Answer:
33
Step-by-step explanation:
let the number be n , then the number divided by 3 is [tex]\frac{n}{3}[/tex] and decreased by 5
[tex]\frac{n}{3}[/tex] - 5 = 6 ( add 5 to both sides )
[tex]\frac{n}{3}[/tex] = 11 ( multiply both sides by 3 )
n = 33
The number is 33
For f (x) = 2x+1 and g(x) = x2 - 7, find (fºg)(2).
Answers
Answer:
Step-by-step explanation:
Your first step will be to set up the problem:
f(x) - g(x)
Next you will substitute in your values:
(2x + 1) - (x2 - 7)
The easiest way to do the subtraction problems is to distribute your negative into your second set of parenthesis, so your expression would become:
2x + 1 - x2 + 7
Then combine your like terms:
2x - x2 + 8
Lastly put your expression in standard form (highest exponent to lowest)
-x2 + 2x + 8
Hope this helped!
10
Sara was thinking of a number. Sara adds 19 to it, then doubles it and gets an answer of 39.2. What was the original number?
Answers
Answer:
0.6
Step-by-step explanation:
2(x+19)=39.2
x+19=19.6
x=0.6
Answer right get brainiest !!!! 12 points
Two trains on opposite tracks leave the same station at the same
time. One train travels at an average speed of 80 kilometers per
hour and the other travels at an average speed of 70 kilometers
per hour. How long after they leave the station will they be 50
km apart?
Answer right get brainiest
Answers
t = .33 hours =20 minutes
This assumes the trains are going opposite directions (opposite tracks so I’m assuming opposite directions)
Hi i need help with this please?!??!!
Answers
Answer:
May be your answer is option 3
Solve the equation. Show the steps of the solution process.
Solve: -14 = -3(6 + 6k) + 4
Answers
Answer:
very easy just simplify and solve
Step-by-step
k=0
Best luck with your studying
The diameter of a circle is 18 cm. Find the circumference to the nearest tenth to the nearest tenth.
Answers
c=2πr. r=18/2=9
=2 ×22/7 ×9
=56.6 to the nearest tenth
if x degree + x + 10 degree + x + 15 degree + x + 20 degree + x + 25 degree + x + 30 degree
Answers
Answer:
x° + x° + 10° + x° + 15° + x° + 20° + x° + 25° + x° + 30°
= 6x° + (10 + 15 + 20 + 25 + 30)°
= 6x° + 100
0 = 6x + 100
6x = 100
X = 100/6
X = 16.66
ILL GIVE U BRAINLIST!! PLEASE HELP :(
Answers
Answer:
5 faces, 8 edges, 5 vertices
PLEASE HELP!!! I WILL GIVE BRAINLIEST
Answers
Answer:x=2y=3
Step-by-step explanation: I did this before
what is the density of the oak board? it is 5.5 inches wide, 1.5 inches thick and 3 feet long
Answers
multiply 5.5 the width with 1.5 by 3 which gives you 24.75 inches feet long.
5.5 x 1.5 x 3=24.75 that's your answer.
Answer:297 cubic inches, other person is incorrect.
Step-by-step explanation:5.5 inches* 1.5inches * 3 feet
Convert 3 feet to inches and you have 36 inches. So now it becomes 5.5inches*1.5inches*36inches = 297 cubic inches
Cual es la ley que establece que la suma o producto de dos números reales no dependen del orden en que se presentan los factores en la multiplicación y los sumados en la aducción ?
Answers
Answer:
Conmutativa
Step-by-step explanation:
Propiedad conmutativa : El orden de los factores no varía el producto o la suma. Un ejemplo seria 3 x 10 da lo mismo que 10 x 3 que es 30.
Con la suma 3+ 5 es lo mismo que 5+3 que es 8.
Nada mas funciona con SUMA o MULTIPLICACION. Nunca en la resta.
Please help I’m on a test
“Given the triangle below, what is the longest side length?”
Answers
~11.31
Pythagorean Theorem because it is a right triangle.