Given a right triangle with sides of length a, b, and c and area a²+b²-c², find c/b, the ratio of the legs of the right triangle.
Answers
Answer:
4
Step-by-step explanation:
Looking at the sketch we can formulate 2 equations:
Pythag: [tex]b^{2} +c^{2} =a^{2}[/tex]
Area of triangle= [tex]\frac{1}{2} bc[/tex]
But area also = [tex]a^{2} +b^{2} -c^{2}[/tex] (from the question)
Therefore [tex]\frac{1}{2} bc[/tex] = [tex]a^{2} +b^{2} -c^{2}[/tex]
But we can sub in the expression for [tex]a^{2}[/tex] from pythag. ([tex]b^{2} +c^{2} =a^{2}[/tex])
[tex]\frac{1}{2} bc= b^{2} +c^{2} +b^{2} -c^{2}[/tex]
[tex]\frac{1}{2} bc=2b^{2}[/tex]
[tex]bc=4b^{2}[/tex]
[tex]c=4b[/tex]
[tex]c/b= 4b/b=4[/tex]
Related Questions
Solve the equation. Then check your solution.
1. 1/4 = a +3/8
Answers
-1/8+3/8=1/4
estimated answer for 3 3/7 x 1 3/4 simplify and type a whole number
Answers
Answer:
6
Step-by-step explanation:
I solved the equation, but you can't simplify 6.
During the Computer Daze special promotion, a customer purchasing a computer and printer is given a choice of seven free software packages. There are 10 different software packages from which to select. How many different groups of software packages can be selected?
Answers
Answer:
120 ways
Step-by-step explanation:
To solve the question above, we use combination formula:
Where ;
nCr = n! / (n-r)! r!
10C7 = 10! / (10 - 7)! 7!
10C7 = 10! / 3! 7!
10C7 = (10 * 9 * 8) / 3 * 2 * 1
10C7 = 720 / 6
= 120 ways
Find the value of a in the relation Cov(2X,−3Y+2)=a⋅Cov(X,Y) .
a=
c) Suppose that X , Y , and Z are independent, with a common variance of 5 . Then,
Cov(2X+Y,3X−4Z)=
Answers
Answer:
a = -6
Cov (2X+Y, 3X-4Z) = 30
Step-by-step explanation:
Key points:
Cov (aX, bY) = a·b·Cov (X, Y)Cov (X, X) = V (X) Cov (X, a) = 0If X and Y are independent then Cov (X, Y) = 0.Cov(2X, -3Y+2) = a⋅Cov (X,Y)
Cov (2X, -3Y) + Cov (2X, 2) = a⋅Cov (X,Y)
(2)⋅(-3)⋅Cov (X, Y) + 0 = a⋅Cov (X,Y)
-6⋅Cov (X, Y) + 0 = a⋅Cov (X,Y)
⇒ a = -6.
(c)
Suppose that X, Y, and Z are independent, with a common variance of 5, i.e. V (X) = V (Y) = V (Z) = 5
Cov (2X+Y, 3X-4Z) = Cov (2X, 3X) + Cov (2X, -4Z) + Cov (Y, 3X) + Cov (Y, -4Z)
= 6⋅Cov (X, X) - 8⋅Cov (X, Z) + 3⋅Cov (Y, X) - 4⋅Cov (Y, Z)
= (6 × 5) - 0 + 0 - 0
= 30
Thus, the value of Cov (2X+Y, 3X-4Z) is 30.
The value of a = -6. And, Cov (2X+Y, 3X-4Z) = 30.
Calculation of the value of a and cov:Since
Cov (aX, bY) = a·b·Cov (X, Y)
Cov (X, X) = V (X)
Cov (X, a) = 0
In the case when X and Y are independent so Cov (X, Y) = 0.
Now
Cov(2X, -3Y+2) = a⋅Cov (X,Y)
Cov (2X, -3Y) + Cov (2X, 2) = a⋅Cov (X,Y)
(2)⋅(-3)⋅Cov (X, Y) + 0 = a⋅Cov (X,Y)
-6⋅Cov (X, Y) + 0 = a⋅Cov (X,Y)
a = -6.
(c)
here
Suppose that X, Y, and Z are independent, with a common variance of 5, i.e.
V (X) = V (Y) = V (Z) = 5
So,
Cov (2X+Y, 3X-4Z) = Cov (2X, 3X) + Cov (2X, -4Z) + Cov (Y, 3X) + Cov (Y, -4Z)
= 6⋅Cov (X, X) - 8⋅Cov (X, Z) + 3⋅Cov (Y, X) - 4⋅Cov (Y, Z)
= (6 × 5) - 0 + 0 - 0
= 30
Thus, the value of Cov (2X+Y, 3X-4Z) is 30.
Learn more about variance here: https://brainly.com/question/24138432
Find the value of. -
[(-4) + (-8)] = [(-4)=2x2
(a) 3
(b)-3
(C) 4
(d) - 4
Answers
Answer:
d
Step-by-step explanation:
Consider the set of whole numbers from 3 to 30, inclusive.
List the numbers that meet the condition: less than six or prime
List the numbers, separated by commas.
Answers
The numbers less than 6 or prime are [tex]4,5,6,7,11,13,17,19,23,29[/tex]
Whole and prime numbers:Whole numbers are a set of numbers including all natural numbers and 0. They are a part of real numbers that do not include fractions, decimals, or negative
A prime number is a number that has only two factors, that is, 1 and the number itself.
The prime numbers between 3 to 30 are,
[tex]7,11,13,17,19,23,29[/tex]
We have to find the numbers that are less than 6 or prime.
Numbers are, [tex]4,5,6,7,11,13,17,19,23,29[/tex]
Learn more about prime numbers here:
https://brainly.com/question/145452
Lisa Has 17 cookie she subtracts 19 and adds 156 then she divides by 4.
Answers
Answer:
38.5
Step-by-step explanation:
17-19= -2
-2+156=154
154 divided by 4= 38.5
it should be 17 - 19 + 154 then divided by 4
so 38.5 cookies
cual es el valor de 7 3/4 + 1 7/8 fraccionado
Answers
A particular fruit's weights are normally distributed, with a mean of 720 grams and a standard deviation of 38 grams. The heaviest 19% of fruits weigh more than how many grams? Give your answer to the nearest gram.
Answers
Answer: The heaviest 19% of fruits weigh more than 753grams.
Step-by-step explanation:
Let X = fruit's weights that are normally distributed.
Given: [tex]\mu=720,\ \ \ \sigma=38[/tex]
To find : x such that P(X>x)=19%
i.e. P(X<x) = 81% [100%-19%=81%]
i.e. P(X<x) = 0.81
[tex]P(\dfrac{X-\mu}{\sigma}<\dfrac{x-720}{38})=0.81[/tex]
Since, [tex]Z=\dfrac{X-\mu}{\sigma}[/tex] and from z-table the z value for p-value of 0.81 (one -tailed) = 0.8779
[tex]\dfrac{x-720}{38}=0.8779\\\\\Rightarrow\ x-720 =38\times0.8779\\\\\Rightarrow\ x-720 =33.36\\\\\Rightarrow\ x = 33.36+720=753.36\approx753[/tex]
Hence, the heaviest 19% of fruits weigh more than 753grams.
Can anyone that is good at math please help me with all my math questions. I will Mark Brainliest to whomever can help. ( Just click on my name and then hit question button and you should see them all working on them and can't figure them out.
Answers
Answer:
i will
Step-by-step explanation:
1. Find y, A. and B.
Answers
3A=120 degrees (bcoz they are alternate exterior angles)
A= 40 degrees
5B= 120 degrees( bcoz they're alternate exterior angles)
B= 24 degrees
to find value of y I equalized
8+15=29/3 + y
y= 23-29/3
y=17/3
ok so if someone needs 2 1/4 cups of water for 1 cup of rice then if they use 1/3 cup of rice how much water would they need
Answers
You would need 3/4 cups of water.
if a distibution has a mean of 50 and a standard devation of 25, how many standard deviation is 0 from the mean
Answers
Answer:
2
Step-by-step explanation:
Here, we have a mean of 50 and a standard deviation of 25, we now need to find out in terms of standard deviation how 0 is far from 50.
Firstly, we subtract 0 from 50
That gives 50. Now, we need to divide this difference by the standard deviation
That will be 50/25 and that makes it 2
So 0 is two deviations away from 50
PLEASE help. Will give brainliest.
Answers
Answer:
y=5
x=10 and
z=2
Step-by-step explanation:
since they are equivalance then,
for
triangle ABC and triangle DFE
AB=DF,BC=FE and AC= DE
So, AB=DF
8y-20= 4y
or, y=5
Then, BC= FE
2x+5=x+15
or, x=10
and
AC=DE
3z+9=10z-5
or, z= 2
hope u got ut.
The triangles are parallel thus their sides are equal to each other peer to peer.
So ;
[tex]x + 15 = 2x + 5[/tex]
Subtract sides -5
[tex]x + 15 - 5 = 2x + 5 - 5[/tex]
[tex]x + 10 = 2x[/tex]
Subtract sides -x
[tex]x - x + 10 = 2x - x[/tex]
[tex]x = 10[/tex]
_________________________________
[tex]4y = 8y - 20[/tex]
Subtract sides -8y
[tex]4y - 8y = 8y - 8y - 20[/tex]
[tex] - 4y = - 20[/tex]
Negatives simplifies
[tex]4y = 20[/tex]
Divided sides by 4
[tex] \frac{4}{4}y = \frac{20}{4} \\ [/tex]
[tex]y = 5[/tex]
_________________________________
[tex]10z - 5 = 3z + 9[/tex]
Plus sides 5
[tex]10z - 5 + 5 = 3z + 9 + 5[/tex]
[tex]10z = 3z + 14[/tex]
Subtract sides -3z
[tex]10z - 3z = 3z - 3z + 14[/tex]
[tex]7z = 14[/tex]
Divided sides by 7
[tex] \frac{7}{7}z = \frac{14}{7} \\ [/tex]
[tex]z = 2[/tex]
_________________________________
And we're done....♥️♥️♥️♥️♥️
Which number is equal to 10^3
Answers
Answer: is 0.001
10^-3 = (1)/(10^3) move the negative exponent to the denominator (1)/(1000) simplify 10^3 in the denominator (1)/(1000) = 0.001
Step-by-step explanation:
Hope you have a great night
Answer: 0.001
Step-by-step explanation:
show your work
16 = k/11
Answers
You’re going to need to get K by itself
So you need to multiply 11 on both sides
to remove the denominator of 11
16 x 11 = 176
k/11 x 11 = k
So now the answer would be
176 = k
Hope this helped :)
Find the square root of each number.
40=
Answers
Answer:
6.32455532034
is the square root of 40
This is my last question.
Answers
Answer:
NOM and POR
(so so sorry if it's wrong, I tried my best to help you but I had to look up an image of a angle like that but i hope you have a wonderful day, sorry again if i am wrong, i hope i help in a way, in i did not, sorry)
A baker makes 51 loaves of bread in 8 1/2 hours. What is the unit rate for the number of loaves in one hour. I need a answer pleaseee
Answers
Answer:
6
Step-by-step explanation:
51 divided by 8.5
A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the lengths of two different pipes produced by the process. h)What is the probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X)
Answers
The probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is approximately 2.6092%.
Here,
Since the length of the pipes follows a uniform distribution on the interval [10 feet, 10.57 feet], the probability density function (PDF) for each pipe is:
f(x) = 1 / (10.57 - 10) = 1 / 0.57 ≈ 1.7544 for 10 ≤ x ≤ 10.57
Since the lengths of the pipes are independent, the joint probability density function (PDF) of X and Y is the product of their individual PDFs:
f(x, y) = f(x) * f(y) = 1.7544 * 1.7544 = 3.0805 for 10 ≤ x ≤ 10.57 and 10 ≤ y ≤ 10.57
Now, we want to find the probability that the second pipe (Y) is more than 0.11 feet longer than the first pipe (X).
Mathematically, we want to find P(Y > X + 0.11).
Let's set up the integral to calculate this probability:
P(Y > X + 0.11) = ∬[10 ≤ x ≤ 10.57] [y > x + 0.11] f(x, y) dx dy
We integrate with respect to x first and then with respect to y:
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] ∫[10 ≤ x ≤ y - 0.11] f(x, y) dx dy
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [∫[10 ≤ x ≤ y - 0.11] 3.0805 dx] dy
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [3.0805 * (x)] from x = 10 to x = y - 0.11 dy
P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [3.0805 * (y - (10 - 0.11))] dy
P(Y > X + 0.11) = 3.0805 * ∫[10 ≤ y ≤ 10.57] (y - 9.89) dy
P(Y > X + 0.11) = 3.0805 * [(y² / 2) - 9.89y] from y = 10 to y = 10.57
P(Y > X + 0.11) = 3.0805 * [((10.57)² / 2) - 9.89 * 10.57 - (((10)² / 2) - 9.89 * 10)]
P(Y > X + 0.11) = 3.0805 * [((111.7249 / 2) - 104.9135 - (50 / 2 - 98.9)]
P(Y > X + 0.11) = 3.0805 * [(55.86245 - 104.9135 + 49.9)]
P(Y > X + 0.11) = 3.0805 * [0.84895]
P(Y > X + 0.11) ≈ 2.6092
Therefore, the probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is approximately 2.6092%.
To learn more on probability click:
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What is the difference between –12 and –5?
Answers
Answer:
-7
Step-by-step explanation:
(-12)-(-5)
negative and negative make a positive
-12+5
= -7
Answer:
-7
Step-by-step explanation:
What is m<KNL?
Enter your answer in the box
Answers
The measurement of ∠KNL is 102°
First, you must set up an equation to find x.
[tex]5x+2=[3(x+14)[/tex]
Then, you must simplify both sides of the equation.
[tex]5x+2=3x+42[/tex]
Next, subtract 3x on both sides.
[tex]2x+2=42[/tex]
Then, subtract 2 on each side.
[tex]2x=40[/tex]
Next, divide 2 on each side.
[tex]x=20[/tex]
Now that we have the value of x, we can substitute it in for angle KNL.
[tex][3(20+14)][/tex]
[tex][3(34)][/tex]
[tex]102[/tex]
[tex]102[/tex]°
An engine pulls four identical carriages. The engine is the length of 2/3
a carriage and the total length of the train is 86.8 m. Find the length
of the engine.
Answers
Answer:
12.4m
Step-by-step explanation:
In order to solve this equation, we can use the length of a carriage as our unknown value (using the engine is a bit more difficult). The questions says that the whole train: 4 carriages and an engine = 86.8m
If we represent carriage length as 'x', we can write the following equation:
4x (length of 4 carriages) + (2/3)x (length of engine as it is 2/3 of a carriage) = 86.8m
4x+(2/3)x = 86.8
From here we can combine into one fraction:
[tex]4x+\frac{2}{3} x=\frac{14}{3}x[/tex]
So now our equation looks like this:
[tex]\frac{14x}{3}=86.8[/tex]
Now all we need to do is multiply both sides by 3 and then divide both sides by 14 to isolate and solve x:
[tex]\frac{14x}{3}*3=86.8*3\\ 14x=260.4\\\frac{14x}{14}=260.4/14\\ x=18.6\\[/tex]
Now that we know the carriage length, we can use it to find the engine length:
Engine length = 2/3 Carriage length
[tex]E=\frac{2}{3}x\\ E=\frac{2}{3} (18.6)\\E = 12.4m[/tex]
Hope this helped!
Length of a carriage = x
Length of four carriages = 86.8 m
Length of each carriage =
[tex]86.8 \div 4 \: m \\ = \: 21.7 \: m[/tex]
Length of one carriage = 21.7 m
Length of the engine =
[tex] = \frac{2}{3} x[/tex]
[tex] = \frac{2}{3} \times 21.7[/tex]
[tex] = 43.4 \: m[/tex]
[tex]43.4 \div 3 \: m \\ = 14.4666666667 \: m[/tex]
∴ The length of the engine is 14.4666666667 m .
what is the Quotient: 3/4divided1/4
Answers
Answer:
3
Step-by-step explanation:
Select the expression that shows the value of three hundred and eighty two thousandths
Answers
Answer:
Step-by-step explanation:
To write the value of three hundred and eighty two thousandths in words, we can follow the steps below:
Split the expression based on the place values
The statement is expressed as:
[tex]\frac{382}{1000}[/tex] = 0.382
three hundred thousandth = 0.300 (thousandth)
eighty thousandth= 0.080
two thousandth = 0.002
Add the values gotten
= 0.300 + 0.080 + 0.002
= (3*10⁻¹) + (8*10⁻²) + (2*10⁻³)
= 0.382
What is the value of (4 minus 2) cubed minus 3 times 4?
Negative 20
Negative 4
4
20
Answers
Answer:
yes the last person is correct
Step-by-step explanation:
Which sequence can be defined by the recursive formula f (1) = 4, f (n + 1) = f (n) – 1.25 for n ≥ 1?
1, –0.25, –1.5, –2.75, –4, . . .
1, 2.25, 3.5, 4.75, 6, . . .
4, 2.75, 1.5, 0.25, –1, . . .
4, 5.25, 6.5, 7.75, 8, . . .
Answers
Answer:
4, 2.75, 1.5, 0.25, –1, . . .
Step-by-step explanation:
edge2020
Two angles are complementary. One angle measures 22 degree more than the other angle. Find the measure of the larger angle
Answers
Answer:
[tex]\theta = 56[/tex]
Step-by-step explanation:
Represent the angles with [tex]\theta[/tex] and [tex]\alpha[/tex]
Such that:
[tex]\theta = 22 + \alpha[/tex]
Since both angles are complementary, we have:
[tex]\theta + \alpha = 90[/tex]
Substitute [tex]\theta = 22 + \alpha[/tex]
[tex]22 + \alpha + \alpha = 90[/tex]
[tex]22 + 2\alpha = 90[/tex]
Collect Like Terms
[tex]2\alpha = 90 - 22[/tex]
[tex]2\alpha = 68[/tex]
[tex]\alpha = 68/2[/tex]
[tex]\alpha = 34[/tex]
Recall that:
[tex]\theta = 22 + \alpha[/tex]
[tex]\theta = 22 + 34[/tex]
[tex]\theta = 56[/tex]
Hence:
The larger angle is 56
can someone help me please with 582 x 23 ≈ __________ x __________ = 12,000
Answers
Answer:
Step-by-step explanation:
582×23≈600×20=12,000
Please help with this question I really need help
Answers
Answer/Step-by-step explanation:
Part A: In the table given above, every input value has exactly one output value. No input value gives two different output value. Therefore, the data in the table represents a function.
Part B: in the table given, when x = 4, y = 9. That is, f(4) = 9.
Given the relation f(x) = 2x - 8, to find what value it would give us, when x = 4, substitute x = 4 into the relation.
f(4) = 2(4) - 8 = 8 - 8
f(4) = 0
Therefore, the relation in the table has a greater value when x = 4.
Part C: using, f(x) = 2x - 8, when f(x) = 34, value of x would be calculated as shown below:
34 = 2x - 8
Add 8 to both sides
34 + 8 = 2x
42 = 2x
Divide both sides by 2
42/2 = x
21 = x
x = 21
