Determine whether the given coordinates are the vertices of a triangle. Explain.
L(–24, –19), M(–22 ,20), N(–5, –7)
A:
yes:
LM + MN > LN,
LM + LN > MN,
LN + MN > LM
B:
no:
LM + MN = LN
C:
no:
LM + MN < LN
D:
yes:
LM + MN < LN,
LM + LN < MN,
LN + MN < LM
Answers
yes
LM + MN > LN,
LM + LN > MN,
LN + MN > LM
Explanation:
In any triangle, the sum of any two sides MUST BE GREATER than the third side.
Therefore, to decide whether the given coordinates can form a triangle or not, we will simply get the length of each side and then check the above condition.
The length can be calculated using the distance formula attached in the image.
LM = [tex] \sqrt{(-24--22)^2+(20--19)^2} [/tex] = 39.05 units
MN = [tex] \sqrt{(-5--22)^2+(-7-20)^2} [/tex] = 31.906 units
NL = [tex] \sqrt{(-5--24)^2+(-7--19)^2} [/tex] = 22.4722 units
Now, let's check:
LM + MN = 39.05 + 31.906 = 70.956 units > NL
MN + NL = 31.906 + 22.4722 = 54.3782 > LM
LM + NL = 39.05 + 22.4722 = 61.5222 > MN
Therefore,, the given coordinates can form a triangle
Hope this helps :)
Final answer:
After computing the distances between the points L, M, and N using the distance formula and comparing them, it is clear that the sum of the lengths of any two sides is greater than the length of the third side, satisfying the conditions of a triangle.
Explanation:
To determine whether the given coordinates are the vertices of a triangle, we can check if the sum of the lengths of any two sides is greater than the length of the third side, which is a principle derived from the triangular inequality theorem. First, we calculate the distances between the points L(–24, –19), M(–22, 20), and N(–5, –7) using the distance formula: √((x2-x1)² + (y2-y1)²).
For LM: √((-22 + 24)² + (20 + 19)²) = √(4 + 1521) = √(1525)
For MN: √((-5 + 22)² + (-7 - 20)²) = √(289 + 729) = √(1018)
For LN: √((-5 + 24)² + (-7 + 19)²) = √(361 + 144) = √(505)
Now we compare the lengths:
LM + MN > LN
LM + LN > MN
LN + MN > LM
Since all three conditions are satisfied, the points L, M, and N form a triangle.
Related Questions
Kill bought items costing $3.45,$1.99,$6.59 ,and $12.98. She used a coupon worth $2.50 .if Jill had $50.00 when she went into the store,how much did she have when she left?
Answers
ASAP
A central angle θ in a circle with a radius of 3.5 centimeters intercepts an arc with a length of 6.3 centimeters.
What is the radian measure of θ ? Enter your answer, as a decimal, in the box.
Answers
S = r * θ
Where,
r: radio
θ: central angle
Clearing θ we have:
θ = S / r
Substituting the values we have:
θ = 6.3 / 3.5
θ = 1.8 radians
Answer:
the radian measure of θ is:
θ = 1.8 radians
The frequency of the musical not B3 is about 246.94 Hz. What is the frequency of the note a perfect fifth below B3
370.42 Hz
246.94 Hz
241.94 Hz
164.63 Hz
Answers
The frequency of the note a perfect fifth below B3 will be
246.94×2/3 = 164.62667
The appropriate choice is ...
164.63 Hz
David, Mike, and Anne are friends. As a hobby, the friends collect baseball cards. Mike owns 9 less than 9 times the number of cards that Anne owns. David owns 27 more than 3 times the number of cards that Anne owns. If David and Mike own the same number of baseball cards, how many baseball cards does Anne own?
Answers
Sal is making bracelets for a fundraiser.he uses 6 inches of yarn per bracelets.how many bracelets can sal make with 5 feet of yarn
Answers
5 feet = 5 x 12 = 60 inches
1 braclet = 6 inches, find nnumber of bracelets:
60 ÷ 6 = 10
Answer: Sal can make 10 bracelets
What is the value of y?
Please enter your answer, as an exact value
Answers
y = tan(60) * 5
and you know tan(60) = √3
so
y = 5√3
answer
5√3 (exact value)
So to Solve this we are going to be using Tangent.
Tangent: opposite/adjacent
Tan60 = y/5
Tan60 * 5 = y/5 *5
Tan60 * 5 = y
8.66 = y
1. ______________ is process that you can do over and over, where each result does not affect the next.
Ex. Flipping a coin, rolling dice, choosing a card, etc.
Answers
Probability experiment or a trail is process that you can do over and over, where each result does not affect the next
Explanation: Trail is defined as a procedure that can repeated any number of times and the result of one trial does not affect the next. This mean each trail or a probability experiment is independent and not associated with the last result.
What is the volume of a sphere if the radius is 9?
Answers
Answer is 3053.63
Answer: [tex]Volume = 972\pi units^{3}[/tex]
Step-by-step explanation: To find the volume of a sphere, start with the formula for the volume of a sphere.
[tex]Volume = \frac{4}{3} \pi r^{3}[/tex]
Notice that our sphere has a radius of 9 units so we can plug 9 into our formula.
[tex]Volume = (\frac{4}{3})(\pi)(9 units)^{3}[/tex]
Now, let's simplify the exponent. 9 units³ is equal to 9 units × 9 units × 9 units or 729 units³.
[tex]Volume = (\frac{4}{3}) (729 units^{3}) (\pi)[/tex]
Notice that we can cross cancel [tex]3[/tex] in [tex]\frac{4}{3}[/tex] and [tex]729[/tex] to [tex]1[/tex] and [tex]243.[/tex]
[tex]Volume = (4) (243units^{3}) (\pi)[/tex]
[tex]Volume = 972\pi units^{3}[/tex]
HELP PLEASE!!!
Base your answer to the question on the diagram shown below.
Fernando is going to draw a marble from the bag, replace it, and then draw another marble. What is the probability that Fernando will get a green or blue marble on the first draw and a pink on the second draw?
(3 green, 4 yellow, 5 blue, 8 pink)
1.) 4/5
2.) 4/25
3.) 3/100
Answers
The answer is actually the second choice 4/25 hope this helps...
Answer: The correct option is (2) [tex]\dfrac{4}{25}.[/tex]
Step-by-step explanation: Given that there are 3 green, 4 yellow, 5 blue and 8 pink marbles in a bag. Fernando is going to draw a marble from the bag, replace it, and then draw another marble.
We are to find the probability that Fernando will get a green or blue marble on the first draw and a pink on the second draw.
Let, S be the sample space for the experiment of drawing a marble from the bag.
Then, n(S) = 3 + 4 + 5 + 8 = 20.
Let E denotes the event of drawing a green or blue marble and F denote the event of drawing a pink marble.
Then, we have
n(E) = 3 + 5 = 8 and n(F) = 8.
Since the second marble is drawn after replacing the first marble,
so the required probability of Drawing a green or blue marble on the first draw and a pink marble on the second draw is
[tex]P\\\\=P(E)\times P(F)\\\\\\=\dfrac{n(E)}{n(S)}\times \dfrac{n(F)}{n(S)}\\\\\\=\dfrac{8}{20}\times\dfrac{8}{20}\\\\\\=\dfrac{4}{25}.[/tex]
Thus, the required probability is [tex]\dfrac{4}{25}.[/tex]
Option (2) is CORRECT.
The sum of two numbers is 66. the larger number is 2 more than 3 times the smaller. what are the two numbers?
Answers
66 = l + s
l = 2 + 3s
66 = 2 + 3s + s
66 = 2 + 4s
66 - 2 = 64
64 = 4s
64 / 4 = 16
66 = l + 16
66 - 16 = 50
50 - 2 = 48
16 + 2 = 18
66 = 48 + 18
What are the solutions of the equation 4x2 + 3x = 24 – x?
a.)–3, 2, or 4
b.)–3 or 2
c.)–2, 3, or 4
d.)–2 or 3
Answers
Answer:
Its B
Step-by-step explanation:
Write 8 square root of z to the 3 in exponential form
Answers
A basketball is thrown upwards. The height f(t), in feet, of the basketball at time t, in seconds, is given by the following function:
f(t) = -16t^2 + 16t + 32
Which of the following is a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground?
A: 0.5 < t < 1
B: 0.5 < t < 2
C: 1 < t < 2
D: 1 < t < 1.5
Answers
Remember that to find the vertex [tex](h,k)[/tex] of a parabola of the form [tex]a x^{2} +bx+c[/tex] we use the vertex formula: [tex]h= \frac{-b}{2a} [/tex], and then, we evaluate our function at [tex]h[/tex] to find [tex]k[/tex].
We can infer for our parabola that [tex]a=-16[/tex] and [tex]b=16[/tex], so lets replace those values in our formula:
[tex]h= \frac{-b}{2a} [/tex]
[tex]h= \frac{-16}{2(-16)} [/tex]
[tex]h= \frac{-16}{-32} [/tex]
[tex]h=0.5[/tex]
Now we now that the ball reaches its maximum height in 0.5 seconds.
Next, we are going to determine how long it takes for the ball to hit the ground. To do that we are going to set the time [tex]f(t)[/tex] equal to zero and solve for [tex]t[/tex]:
[tex]0=-16t^2+16t+32[/tex]
[tex]16t^2-16t-32=0[/tex]
[tex]16(t^2-t-2)=0[/tex]
[tex]t^2-t-2=0[/tex]
[tex](t+1)(t-2)=0[/tex]
[tex]t=-1[/tex] or [tex]t=2[/tex]
Since time cannot be negative, the answer is [tex]t=2[/tex]
We can conclude that a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground is B: 0.5 < t < 2
Answer:
A basketball is thrown upwards. The height f(t), in feet, of the basketball at time t, in seconds, is given by the following function:
f(t) = −16t2 + 16t + 32
Which of the following is a reasonable domain of the graph of the function when the basketball falls from its maximum height to the ground?
B is correct!
:)
Which expression is equivalent to 60x^20 y^24/30x^10 y^12
Answers
= (60/30) · (x^20/x^10) · (y^24/y^12)
= 2 · x^(20-10) · y^(24-12)
= 2 · x^10 · y^12
Answer: 2 x^10 y^12
The answer is B on edg :)
How do u find the median of 4 numbers?
Answers
QS is the perpendicular bisector of PR solve for x
Answers
3x - 20 = 70
3x = 90
x = 30
The term 'perpendicular bisector' means QS cuts PR into two equal parts at a 90-degree angle. If PR is '2x', then each half is 'x'. To solve for x, we would need data about the lengths of the line segments.
Explanation:Given that QS is the perpendicular bisector of PR, it implies two things. Firstly, QS intersects PR at a 90-degree angle. Secondly, QS splits PR into two equal segments. So, if PR is represented as '2x', then PQ and QR are both 'x'.
Unfortunately, missing information prevents a specific solution for x. We'd need additional data about the lengths of these line segments to solve the equation for x. For instance, if PR = 10, then '2x = 10' which gives us 'x = 5'.
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What are the cordinates
Answers
The cordinates are, The third one.
Plz give Brainlist If right.
Convert. If necessary, round to the nearest tenth. (Recall: 1 mi ≈ 1.61 km) km/h ~ 10 mi/h
Answers
Answer:
10 mile per hour = 16.1 kilometers per h our
Step-by-step explanation:
We know that
1 mile = 1.61 kilometers
We are supposed to convert speed given in miles per hour (mph) to kilometers per hours (kmph)
In order to do so ,
1 mile = 1.61 kilometers
1 mile per hour = 1.61 kilometers per hour
Multiplying both sides by 10 we get
10 miles per hour = 1.61 *10 kilometers per hour
10 miles per hour = 16.1 kilometers per hour
Hence our speed in kilometers per hour is 16.10 kmph
Harry was given an assignment. He had 42 days to get 336 tasks done at work.Which operation would he use to figure out how many tasks he needs to complete each day
Answers
42divided by 336 that is it
Hope this Helped :D
Is the following relation a function ? Yes or no
Answers
The table shows the height, in feet, of the tide over time, in hours.
I know the answer is that it should be cosine instead of sine, but I don't how to determine that. I'd like to know so I could solve questions like these in the future.
Answers
f (x) = - 4sine ((pi / 6) x) + 5
We evaluate the function for x = 0
f (0) = - 4sine ((pi / 6) 0) + 5
f (0) = -4 * (0) + 5
f (0) = 5
We note that the result does not correspond to the table.
Let's rewrite the function:
f (x) = - 4cosine ((pi / 6) x) + 5
We evaluate the function for x = 0
f (0) = - 4cosine ((pi / 6) 0) + 5
f (0) = -4 * (1) + 5
f (0) = 1
The result corresponds to the table
Answer:
The student's mistake is to use the sine function instead of using the cosine function.
The correct function is:
f (x) = - 4cosine ((pi / 6) x) + 5
What is the area of this polygon?
units²
5-sided polygon on a coordinate plane with vertices F, N, S, C, W. Point f is at (negative 4, negative 2), point N is at (2, 4), point s is at (5, negative 2), point c is at (5, negative 4), and point w is at (negative 4, negative 4)
Answers
Step 2) Find the area of this rectangle. The area is 18 square units because it is 2 units high and 9 units across (9*2 = 18). You can count out the spaces or you can note how we go from x = -4 to x = 5 so subtracting the values gives -4-5 = -9 which has an absolute value of 9.
Step 3) Find the area of triangle FSN. The base is 9 units and the height is 6 units (count out the spaces or subtract y values). So the area is A = b*h/2 = 9*6/2 = 54/2 = 27
Step 4) Add up the area of the rectangle to the area of the triangle: 18+27 = 45
Final Answer: 45 square units
note: another way to find the answer is to find the area of rectangle WABC where point A is at (-4,4) and point B is at (5,4). Then subtract off the triangular areas of AFN and BNS
In this exercise we have to use the knowledge of polygon area to calculate the area of a trapezoid, in this way we find that:
[tex]45 units[/tex]
So find the area of this rectangle, this area will be:
[tex]9*2 = 18[/tex]
Find the area of triangle FSN, this area will be:
[tex]A = b*h/2 = 9*6/2 = 54/2 = 27[/tex]
Sum all the areas will be:
[tex] 18+27 = 45[/tex]
See more about area at brainly.com/question/1631786
You have 23 coins, including nickels, dimes, and quarters. if you have two more dimes than quarters, and the total value of the coins is $2.50. how many of each kind of coin do you have?
Answers
n + d + q = 23 . . . . . . . there are 23 coins total
0n +d -q = 2 . . . . . . . . .there are 2 more dimes than quarters
5n +10d +25q = 250 . .the total value is $2.50
The collection includes 11 nickels, 7 dimes, and 5 quarters.
_____
I used the matrix function of my calculator to solve these equations. You can find q by subtracting from the last equation five times the sum of the first two equations.
(5n +10d +25q) -5((n +d +q) +(d -q)) = (250) -5(23 +2)
25q = 125 . . . . . . . simplify
q = 5
From the second equation,
d = q +2 = 7
And from the first,
n = 23 -5 -7 = 11
Hi there i hope this will help
n + d + q = 23 . . . . . . . there are 23 coins total
0n +d -q = 2 . . . . . . . . .there are 2 more dimes than quarters
5n +10d +25q = 250 . .the total value is $2.50
The collection includes 11 nickels, 7 dimes, and 5 quarters.
I used the matrix function of my calculator to solve these equations. You can find q by subtracting from the last equation five times the sum of the first two equations.
(5n +10d +25q) -5((n +d +q) +(d -q)) = (250) -5(23 +2)
25q = 125 . . . . . . . simplify
q = 5
From the second equation,
d = q +2 = 7
And from the first,
n = 23 -5 -7 = 11
answer is 11Find the volume of the figure the diameter of the base is 4 cm
The figure is a cylinder that has d= 4 cm and h= 2.5 with a hemisphere on the top that has the same diameter as the cylinder (4 cm)
Please help! Thanks!
Answer Choices:
A. 22π cm^3
B. 152/3 π cm^3
C. 62/3 π cm^3
D. 46/3 π cm^2
Answers
D
Total volume = volume of cylinder + volume of hemisphere
Total volume = pi * r^2 * h + 2/3 * pi * r^3, where r = 2 and h = 2.5
total volume = 46/3 pi cm^2
How do I do this? Show all work please! THANKS
RANDOM ANSWERS WILL BE MODERATED!
Answers
the medians are of course the segments going from a vertex to the middle of the opposite side.
now, one thing about the centroid, it cuts all medians in a 2:1 ratio.
by looking at the graph, we can see that BP is the longer, so BP : PM are on a 2:1 ratio, thus
[tex]\bf \cfrac{BP}{PM}\implies \cfrac{7x+4}{2x+5}=\cfrac{2}{1}\implies 7x+4=4x+10 \\\\\\ 3x=6\implies x=\cfrac{6}{3}\implies x=2\qquad \qquad \qquad\qquad \boxed{PM=2(2)+5}[/tex]
A certain number of bacteria are in a petri dish. If the growth rate is 2.7 percent per hour, how many hours will it take the bacteria to double in number?
Answers
Using the rule of 70, which states that the doubling time in hours is equal to 70 divided by the growth rate percentage, it will take approximately 25.93 hours for the bacteria to double in number at a growth rate of 2.7 percent per hour.
Explanation:To calculate the time it will take for the bacteria to double in number with a growth rate of 2.7 percent per hour, we can use the rule of 70. The rule of 70 states that we can find the doubling time by dividing 70 by the percentage growth rate.
Doubling time = 70 ÷ growth rate percentage = 70 ÷ 2.7 ≈ 25.93
Therefore, it will take approximately 25.93 hours for the bacteria to double in number.
The local weather report states that the probability that it will snow today is 20% and the probability that it will snow tomorrow is 40%. Which of the following is a true statement?
A.
It is not very likely that it will snow both today and tomorrow.
B.
It is very likely that it will snow both today and tomorrow.
C.
It is impossible that it will snow both today and tomorrow.
D.
It is certain that it will snow both today and tomorrow.
Answers
The probability of it snowing both today and tomorrow is 8%, based on the given probabilities for individual days. Therefore, the most accurate statement is that it's not very likely for it to snow on both days.
Explanation:The question revolves around understanding the concept of probability. In the context of probability, you multiply the probabilities of two independent events (like it snowing on two different days) to get the probability of both occurring.
To find out if it will snow both today and tomorrow, we multiply the probability it will snow today (20% or 0.2) by the probability it will snow tomorrow (40% or 0.4). This gives us a probability of 0.08 or 8%, which means that it's not very likely that it will snow both today and tomorrow.
So, the correct answer would be Option A: It is not very likely that it will snow both today and tomorrow.
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plz help in the picture below
Answers
= 4(1/4) + 18
= 1 + 18
= 19
answer
A) 19
What is the surface area of a rectangular prism whose base is 5 inches by 6 inches and whose height is 5 inches? 150 square inches 150 cubic inches 170 square inches 170 cubic inches
HELPPPP
Answers
Answer:
Option (3) is correct.
The surface area of a rectangular prism of given dimension is 170 square inches.
Step-by-step explanation:
Given : a rectangular prism whose base is 5 inches by 6 inches and whose height is 5 inches.
We have to find the surface area of a rectangular prism of given dimension.
Since a rectangular prism whose base is 5 inches by 6 inches
That is length (l)= 5 inches
Width (w) = 6 inches
and height (h) = 5 inches.
Also . [tex]\text{surface area of a rectangular prism}=2(lw+wh+hl)[/tex]
Substitute, we have,
[tex]\text{surface area of a rectangular prism}=2(5\cdot 6+5\cdot 5+5\cdot 6)[/tex]
simplify , we have,
surface area of a rectangular prism = 170 inches²
Thus, the surface area of a rectangular prism of given dimension is 170 square inches
Identify the parameters in y = a*bkx.
Answers
Thus the parameters here are a, b and k. k is the constant of proportionality.