Answers
Answer:
P1P2 = P1P3 = 2√2P2P3 = 4isosceles right triangle (both)Step-by-step explanation:
The length of a side can be found using the distance formula:
d = √((x2 -x1)^2 +(y2 -y2)^2)
For P1P2, this gives ...
d = √((0-(-2))^2 +(1-(-1))^2) = √(4+4) = √8
P1P2 = 2√2
__
The same ∆x and ∆y apply to P1P3, so we know ...
P1P3 = 2√2
__
The lengths of P1P2 and P1P3 are the same, so the triangle is isosceles.
__
The length of P2P3 can be found by subtracting the y-coordinates:
P2P3 = 1 -(-3)
P2P3 = 4
__
We note that the slope of P1P2 is 2/2 = 1, and the slope of P1P3 is -2/2 = -1. The product of these slopes is (1)(-1) = -1, so we know those lines are perpendicular. The triangle is a right triangle.
Related Questions
Simplify 3-8 divided by 3-2
Answers
Answer:
-5
Step-by-step explanation:
[tex] \frac{3 - 8}{3 - 2} [/tex]
[tex] \frac{ - 5}{1} [/tex]
[tex] - 5[/tex]
3-8= -5
3-2=1
-5/1= -5
Hope this helps
What is the equation for a line with slope = 3 that passes through point (2, 5)?
a. y = 3x - 13
b. y = 3x - 1
C. y = 3x - 5
Answers
select the correct answer which equation has no solution
Answers
Answer:
C: 7(x+2)-3x = 2/3(6x+3)
Step-by-step explanation:
Graphing both lines shows that they are parallel to each other.
Answer:
There ya go love
Step-by-step explanation:
2. Find the distance between (-2,1) and (3,4).
Answers
Answer:
[tex]\sqrt{34}[/tex] or 5.83095
Step-by-step explanation:
Use the distance formula [tex]\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1} )^2 }[/tex]
Make sure to round the answer appropriately if not asked for in square root form!!
Which of the following list contains exactly 2 composite numbers and 2 prime numbers?
Answers
How much is 2/3 - 1/6 =
Answers
Answer:
1/2
Step-by-step explanation:
First create like dominators
2/3 -1/6 = 4/6 - 1/6
simplify using subtraction
4/6 - 1/6 = 3/6
Simplify the answer
3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
2/3 - 1/6
Subtract the two fractions:
2/3 - 1/6 = 1/2
The answer we get is:
1/2
Divide the numerator by the denominator for the decimal form:
1 ÷ 2 = 0.5
0.5 is our decimal form.
1/2 and 0.5 are our answers.
Hope you learned from this answer!
There are 35 students in art class and 57 students in dance class. Find the number of students who are either in art class or in dance class. Find
When two classes meet at different hours and 12 students are enrolled in both activities. ( 2marks)
When two classes meet at the same hour. ( 2 marks)
Answers
Answer:
a. 80 students
b. 92 students
Step-by-step explanation:
Represent arts students with A and Dance students with D.
So, we have,
n(A) = 35
n(D) = 57
Required
Determine n(A or D)
Solving (a):
Here, we have:
n(A and D) = 12
n(A or D) is calculated as thus:
n(A or D) = n(A) + n(D) - n(A and D)
n(A or D) = 35 + 57 - 12
n(A or D) = 80
b. From the given details
n(A and D) = 0 because both students are not mixed up as in (a) above
Using the same formula as (a).
n(A or D) = n(A) + n(D) - n(A and D)
n(A or D) = 35 + 57 - 0
n(A or D) = 92
The biggest zucchini from Joe’s Farm is 2. 5/8 pounds,which is 1 1/12 pound more than the average weight from his farm.what is the average weight of zucchini’s from his farm?
Answers
Answer:
1 13/ 24
Step-by-step explanation:
2-1=1
5/8 - 1/12=26/48 =13/24
The concentration of particles in a suspension is 50 per mL. A 5 mL volume of the suspension is withdrawn. a. What is the probability that the number of particles withdrawn will be between 235 and 265? b. What is the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52? c. If a 10 mL sample is withdrawn, what is the probability that the average number per mL of particles in the withdrawn sample is between 48 and 52? d. How large a sample must be withdrawn so that the average number of particles per mL in the sample is between 48 and 52 with probability 95%?
Answers
Answer:
(a) 0.6579
(b) 0.2961
(c) 0.3108
(d) 240
Step-by-step explanation:
The random variable X can be defined as the number of particles in a suspension.
The concentration of particles in a suspension is 50 per ml.
Then in 5 mL volume of the suspension the number of particles will be,
5 × 50 = 250.
The random variable X thus follows a Poisson distribution with parameter, λ = 250.
The Poisson distribution with parameter λ, can be approximated by the Normal distribution, when λ is large say λ > 10.
The mean of the approximated distribution of X is:
μ = λ = 250
The standard deviation of the approximated distribution of X is:
σ = √λ = √250 = 15.8114
Thus, [tex]X\sim N(250, 250)[/tex]
(a)
Compute the probability that the number of particles withdrawn will be between 235 and 265 as follows:
[tex]P(235<X<265)=P(\frac{235-250}{15.8114}<\frac{X-\mu}{\sigma}<\frac{265-250}{15.8114})[/tex]
[tex]=P(-0.95<Z<0.95)\\=P(Z<0.95)-P(Z<-0.95)\\=P(Z<0.95)-[1-P(Z<0.95)]\\=2P(Z<0.95)-1\\=(2\times 0.82894)-1\\=0.65788\\\approx 0.6579[/tex]
Thus, the value of P (235 < X < 265) = 0.6579.
(b)
Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{5}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{5}})[/tex]
[tex]=P(-0.28<Z<0.28)\\=P(Z<0.28)-P(Z<-0.28)\\=P(Z<0.28)-[1-P(Z<0.28)]\\=2P(Z<0.28)-1\\=(2\times 0.64803)-1\\=0.29606\\\approx 0.2961[/tex]
Thus, the value of [tex]P(48<\bar X<52)=0.2961[/tex].
(c)
A 10 mL sample is withdrawn.
Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{10}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{10}})[/tex]
[tex]=P(-0.40<Z<0.40)\\=P(Z<0.40)-P(Z<-0.40)\\=P(Z<0.40)-[1-P(Z<0.40)]\\=2P(Z<0.40)-1\\=(2\times 0.65542)-1\\=0.31084\\\approx 0.3108[/tex]
Thus, the value of [tex]P(48<\bar X<52)=0.3108[/tex].
(d)
Let the sample size be n.
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{n}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{n}})[/tex]
[tex]0.95=P(-z<Z<z)\\0.95=P(Z<z)-P(Z<-z)\\0.95=P(Z<z)-[1-P(Z<z)]\\0.95=2P(Z<z)-1\\P(Z<z)=\frac{1.95}{2}\\\\P(Z<z)=0.975[/tex]
The value of z for this probability is,
z = 1.96
Compute the value of n as follows:
[tex]z=\frac{\bar X-\mu}{\sigma/\sqrt{n}}\\\\1.96=\frac{48-50}{15.8114/\sqrt{n}}\\\\n=[\frac{1.96\times 15.8114}{48-50}]^{2}\\\\n=240.1004\\\\n\approx 241[/tex]
Thus, the sample selected must be of size 240.
Once cup of instant rice makes 1.5 cups of cooked rice. How many cups of cooked rice will 3 cups of instant rice make?
Answers
Answer:
2
Step-by-step explanation:
If 1 = 1.5
2 = 3
That is the answer
Answer: 3 cups will make 4.5 cups of cooked rice.
Step-by-step explanation: 3 * 1.5
Please help me answer this question:
Answers
Answer:
Total area = 141,
the trapezoid = 117, the triangle=24
I need help with 20 please thank you.
Answers
Answer:
IM BACK!!!!
The answer is *DRUMROLLLLLLLL* B
jk
its 1 lol
Step-by-step explanation:
Plug in -8 to x and you end up multiplying -8 by 1/2 which is pretty simple but the Muhammad ibn Musa al-Khwarizmi guy invented Algebra, Gottfried Wilhelm Leibniz invented functions, and Brahmagupta of India invented addition, so thanks to them, you can solve this question. -8 times 1/2 is -4 and -4 plus 5 equals 1.
Hope this helps
Given m || n, find the value of x and y.
(3x-4)
(6x-5)
Answers
Answer:
X=21 and Y=121
Step-by-step explanation:
With these types of problems, we need to know our vertical angles and that lines are 180° when two angles on a line are next to each other.
To solve this problem algebraically we want to add (3x-4) and (6x-5) together so that they equal 180. The reason we do this is that they lie on the same line which is 180°. The equation would look like [tex]3x+6x-5-4=180[/tex]. We then want to add like terms which will leave us with [tex]9x-9=180[/tex]. Now we want to get 9x by itself by adding 9 on each side which leaves us with [tex]9x=189[/tex]. To isolate x we need to divide on each side by 9 which finally leaves us with [tex]x=21[/tex]
Now that we have the value of x (21) we can now utilize our knowledge of vertical angles (angles that are completely across and equal to one another.) We can find y by doing this equation: [tex]y=6x-5[/tex] and with the value of x found we can plug in the value to get [tex]y=6(21)-5[/tex] which simplifies to [tex]y=126-5[/tex] then to [tex]y=121[/tex].
A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 31% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled and asked if they believe their company president has low ethical standards and their years of experience at the company. Could the probability distribution for the number of years of experience be modelled by a binomial probability distribution?
Answers
Answer:
Explained below.
Step-by-step explanation:
A Binomial experiment has the following properties:
There are a fixed number of trials (n). Each trial are independent of the others. Each trial has only two outcomes: Success and Failure Each trial has the same probability of success (p).If a random variable X is used in an experiment and the experiment has all the above mentioned properties, then the random variable X is known as a binomial random variable.
The number of employees selected is, n = 20.
Every employees response is independent of the others.
Each employees response is either: Yes or No.
The probability of an employee responding as "yes" is, p = 0.31.
Thus, the experiment being performed is a binomial experiment.
So, the probability distribution for the number of employees believing their company president has low ethical standards can be modelled by a binomial probability distribution.
But the number of years of experience cannot be modelled by a binomial probability distribution. Because every employee will have different answer for this question.
Someone plz help me
Answers
Answer:
The first order.
Step-by-step explanation:
What do these symbols mean?
The funny shaped line is a square root, meaning what times itself (so for example, 3 x 3) gets that number. So the square root of 9=3.
The small 2 in the top right of the big numbers means square. The opposite. This means multiply that big number by itself twice. If the small number was say, 7, you would multiply the big number by itself 7 times. A common mistake is propel multiply the big number by the small number. The square used in these is 2 to the power of 3, the small number. This means you do 2x2x2, as the small 3 determines how many time you multiply the big number, 2. The result of 2x2x2=8.
The fraction is 11/9. The 9 means how many parts are in a whole number. The 11 means how many of those parts you actually have. Like a pizza-if you had a pizza (the whole) split into 7 parts, 7 would be your bottom number (as the 9 is here). If you are 4 parts and were left with 3 parts, 3 would be your top number (as the 11 is here). Seeing as 11 is bigger than 9, you have to imagine 2 pizzas. Each is split into 9, and you have 11 parts altogether. Thsi is 1 whole pizza and 2 extra parts, making the fraction 1 and 2/9. This is jaut another way to write 11/9 but I find it easier to look at.
The answer?
So. We have established that 11/9 = 1 & 2/9
And that 2 cubed (with the small 3 on it) = 8.
Amd the square roots of 5, 11 and 20 are approximately (Not exactly, but close enough) the following:
5. 2.2
11. 3.3
20. 4.4
So this leaves us a bunch of numbers to put in order from smallest to largest. This is fairly easy. It's not the second one. 8>3.3. It's not the third one. 8>2.2. It's not the fourth one. 1 & 2/9 may be smaller than 8, but 2.2 isn't. So this leaves the first order.
*Note that the symbol > means greater than or bigger than. So 8>2 means 8,is bigger than 2.
true or false? y=x^2 - 1 defines y as a function of x
Answers
Answer:
true
Step-by-step explanation:
it equals to
x1= -1
and
x2= 1
Answer:
Step-by-step explanation:
y=x²-1 is not a function for every value of y , x has more than one value
ex: if x=-1 , y=(-1)²-1 then y=0
if x=1 then y=0
The norman h.s. math club has twice as many male members as female members twenty percent of the male members and 30 female members participated in a math contest. What fraction of those members participating in the math contest were female? express your answer as a common fraction
Answers
Answer:
[tex]\frac{3}{7}[/tex]
Step-by-step explanation:
20% male and 30% female. 20% + 30%= 50% It is asking us what members participating was female. *50% out of 100%
> [tex]\frac{30}{70}[/tex] reduce or divide by 10 we get our fraction and answer, [tex]\frac{3}{7}[/tex].
Listed below are the heights from a sample of male students (in inches). 75 72 72 73 74 65 69 74 70 70 71 75 71 75 69 75 78 70. How many students are measured?
Answers
Answer:
18
Step-by-step explanation:
count
The number of students measured in this sample is 18.
The number of students measured is the number of heights that were acquired for the sample.
Looking at the question, the number of heights acquired were 18 which means that there were 18 students.
Knowing the number of students is important as it can help you calculate things such as mean:
Mean = Sum of heights / Number of students
= (75 + 72 + 72 + 73 + 74 + 65 + 69 + 74 + 70 + 70 + 71 + 75 + 71 + 75 + 69 + 75 + 78 + 70) / 18
= 72.11
In conclusion, the number of students measured is 18.
Find out more at https://brainly.com/question/20855935.
which is the equation of the line that passes through the points (-4,-8) and (1,3)
Answers
Answer:
−5x+13y=84
Step-by-step explanation:
I hope this is good :)
f(x) = x^3 translate 3 units left translate 1 unit down
Answers
Answer:
the function would look like: f(x)=(x³+3)-1
the graph would literally look like the cubic parent graph, just shifted 3 left and 1 down
Which of the following expressions is not equivalent to -4.5 • -8?
-8 • -4.5
8 • 4.5
(8)(-4.5)
(4.5)(8)
Answers
Answer: (8)(-4.5)
Step-by-step explanation:
If you were to multiply-4.5 • -8 that would equal a positive number but if you were to divide (8)(-4.5) it would equal a negative number
Answer:
(8)(-4.5)
Step-by-step explanation:
please mark brainliest
Which of the following is the equation of the line that is parallel to
y= 3/5x+ 8 and goes through point (-10,4)?
Select one:
a. y = 5/3x + 20 2/3
b. y=-5/3x – 12 2/3
c.y= 3/5x + 10
d. y = -3/5x-2
Answers
Answer:
C
Step-by-step explanation:
We want to write the equation of a line that is parallel to:
[tex]y=\frac{3}{5}x+8[/tex]
And also passes through (-10, 4).
Remember that parallel lines have the same slope.
The slope of our old line is 3/5.
Therefore, the slope of our new line is also 3/5.
We know that it passes through (-10, 4). So, we can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
So, let's substitute 3/5 for m and let (-10, 4) be our (x₁, y₁). This yields:
[tex]y-(4)=\frac{3}{5}(x-(-10))[/tex]
Simplify:
[tex]y-(4)=\frac{3}{5}(x+10)[/tex]
Distribute on the right:
[tex]y-4=\frac{3}{5}x+6[/tex]
Add 4 to both sides:
[tex]y=\frac{3}{5}x+10[/tex]
So, our answer is C.
And we're done!
Step-by-step explanation:
Hey there!
The equation of a st.line passing through point (-10,4) is ;
(y-y1)= m1(x-x1) [one point formula]
Put all values.
(y - 4) = m1( x + 10)..........(i)
Another equation is; y = 3/5 + 8.............(ii)
From equation (ii)
Slope (m2) = 3/5 [ By comparing equation with y = mx+c].
As per the condition of parallel lines,
Slope of equation (i) = slope of equation (ii)
(i.e m1 = m2 )
Therefore, the value of m1 is 3/5.
Putting value of slope in equation (i).
[tex](y - 4) = \frac{3}{5} (x + 10)[/tex]
[tex](y - 4) = \frac{3}{5} x + \frac{3}{5} \times 10[/tex]
[tex](y - 4) = \frac{3}{5} x + 6[/tex]
[tex]y = \frac{3}{5} x + 10[/tex]
Therefore the required equation is y = 3/5x + 10.
Hope it helps...
. A triangle has one angle measuring 3x degrees. A second angle measures 2x+20 degrees and the third angle measures 4x-20 degrees. What is the value of x
Answers
Answer:
Step-by-step explanation:
You know that all of the angles of a triangle have to add to equal 180°.
Therefore, (3x)+(2x+20)+(4x-20)= 180°
If you combine like terms you get:
9x=180°
Divide both sides by 9 to get:
X=20
NEED HELP PLEASEE!!!!!
Answers
Answer:
x=1
Step-by-step explanation:
i believe its asking at which point is the output the same and when x=1 they both output 3
A = 2/3 * (B + C)
Solve for C
Answers
a=2(b+c)/3
Multiply both sides by 3
a * 3 = 2(b+c)
Regroup terms
3a=2(b+c)
Divide both sides by 2
3a/2 = b+c
Subtract c from both sides
3a/2 - c = b
Switch sides
b = 3a/2 - c
What is the answer to 6x + 7= -x + 70
Answers
Answer:
x = 9
Step-by-step explanation:
6x + 7 = -x + 70
~Subtract 7 to both sides
6x = -x + 63
~Add x to both sides
7x = 63
~Divide 7 to both sides
x = 9
Best of Luck!
Corey earned
$3,200 working over the summer. If he
made $400 each week, how many weeks
did he work? How many weeks would he
need to work to earn $6,400? $8,800?
Answers
Answer:
He would need to work 8 weeks for 2300, 16 for 6400, and 22 for 8800
Step-by-step explanation:
You have to divide 3,200 by 400 since thats how much he makes in a week
that gives you 8
and you do the same for the rest
equation:
money wanted/400=weeks
Answer:)
he work for 8 weeks to earn 3,200
he needs to work 8 more weeks to earn 6,400
he needs to work 14 more weeks to earn 8,800
Step-by-step explanation:
Determine whether the lines are parallel, perpendicular, or neither. EM has the
slope of 5/6 and TC has the slope of 6/5
Answers
Answer:
Not sure, not good with lines, but I think I did it correctly. EM = Neither TC= Perpendicular.
Classify the following triangle. Check all that apply.
A. Right
B. Acute
C. Equilateral
D. Scalene
E. Obtuse
F. Isosceles
Answers
Need help on this pleaseeeeee
Answers
Answer:
I think it's C
Step-by-step explanation:
I just rotated point K 180 degrees and C was the only one with the coordinate points I got for K'