Determine if a triangle can be formed with given length if yes classify as acute right or obtuse
Answers
1) cos α = 0.8, cos β = 0.6, cos γ = 0. The triangle exists and is right.
2) cos α ≈ 0.882, cos β ≈ 0.471, cos γ ≈ 0.441. The triangle exists and is acute.
3) cos α ≈ 0.977, cos β ≈ 0.324, cos γ ≈ -0.115. The triangle exists and is obtuse.
4) cos α = 1, cos β = 1, cos γ = -1. The triangle does not exist.
How to determine if a triangle may exist and the existence of given angles
Triangles are geometric figures formed by three line segments and internal angles, whose sum is equal to 180°, which can be three acute angles or an obtuse angle and two acute angles or a right angle and two acute angles. The possibility is determined by applying the law of cosine:
[tex]\cos \theta = -\frac{x^{2}-y^{2}-z^{2}}{2\cdot y\cdot z}[/tex] (1)
The triangle if and only if the cosine of each angle is between -1 and 1 with the following characteristics:
If the cosine of the angle is between 0 and 1, then it is acute.If the cosine of the angle is 0, then it is right.If the cosine of the angle is between 0 and -1, then it is obtuse.Now we proceed to determine the existence of each triangle:
1) cos α = 0.8, cos β = 0.6, cos γ = 0. The triangle exists and is right.
2) cos α ≈ 0.882, cos β ≈ 0.471, cos γ ≈ 0.441. The triangle exists and is acute.
3) cos α ≈ 0.977, cos β ≈ 0.324, cos γ ≈ -0.115. The triangle exists and is obtuse.
4) cos α = 1, cos β = 1, cos γ = -1. The triangle does not exist.
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Related Questions
What is the surface area of this composite solid? Show your work.
Answers
Answer:
357.5ft^3
Step-by-step explanation:
solve for bottom reticular prism
8 * 10 * 4
320ft^3
solve for top triangular prism
((3*5)/2)*5
37.5ft^3
add top and bottom
320+37.5
357.5ft^3
Answer: 268ft^3
Step-by-step explanation: To solve, find the area of each side and add them all together.
8*4=32*2=64
10*4=40*2=80
10*5=50*2=100
8*3/2=12*2=24
64+80+100+24=268
Hope I helped <3
Kobe's overtime pay is $5 an hour more than his regular pay. He worked 8 hours at his regular wage and 3 hours at his overtime wage. He earned $114.
What is Kobe's regular wage per hour?
Answers
Answer:
anwer 9$ and hour
Step-by-step explanation:
9×8=72
9+5=14
14×3=42
42+72=114
Shondra was unsure about what career to go into. Her high school counselor suggested a personal assessment to point out Shondra’s interests. The assessment revealed that Shondra is very passionate about justice and making sure that people stay safe and treat each other fairly. Shondra also enjoys physical fitness and can handle risky high-pressure situations well.
Shondra would be well suited for which career cluster. Select three options.
Answers
Answer:
lawer, Police officer criminal justice
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
option ( c ) [tex]\huge\pink{1 \frac{2}{5} }[/tex]
step by step explanation -
well , the question asks us to find the difference between the two terms given as mixed fractions ~
tho it's not that difficult to simplify a problem in mixed fraction , but solving the problem by first converting it to an improper fraction reduces the risk of mistakes ! so let's do the question by that way ~
[tex]4 \frac{4}{5} - 3 \frac{2}{5} \\ \\ converting \: into \: improper \: fraction \: we \: get \\ \\ \implies \: \frac{5 \times 4 + 4}{5} \: \: - \: \: \frac{5 \times 3 + 2}{5} \\ \\ \implies \: \frac{24}{5} \: \: - \: \: \frac{17}{5} \\ \\ since \: the \: denominators \: are \: same \: we \: can \: simply \: subtract \: the \: terms \\ \\ \implies \: \frac{7}{5} [/tex]
we're done with our solution tho , but since the options given are in mixed fraction , so let's convert the improper fraction , obtained as the answer , into a mixed fraction !
[tex] \frac{7}{5} = 1 \frac{2}{5} \\ [/tex]
hope helpful :D
Answer:
1 2/5
Step-by-step explanation:
subtract it and then add it and u will have your answer
Answer please and leave an explanation too! thank you!
1. If the arc angle of a sector is doubled, then the area of the sector......
A. is half
B. remains the same
C. doubles (increases by a factor of two)
D. triples (increases by a factor of three)
E. quadruples (increases by a factor of four)
2. If the radius of a sector is doubled, then the area of the sector......
A. is half
B. remains the same
C. doubles (increases by a factor of two)
D. triples (increases by a factor of three)
E. quadruples (increases by a factor of four)
Answers
Answer:
1-C; 2-D.
Step-by-step explanation:
0) the common formula is:
area=π*r²;
1) according to the formula above the area of the sector C. doubles (increases by a factor two);
2) according to the formula the area of the sector D. quadruples (increases by a factor four).
Alex is 12 years older than George.
Carl is three times older than Alex
The sum of their ages is 68
Find the ratio of George's age to Carl's age to Alex's age.
Answers
Answer:
George : Carl : Alex = 1 : 12 : 4
Step-by-step explanation:
let a = Alex's age in years
let g = George's age in years
let c = Carl's age in years
Given:
Alex is 12 years older than George⇒ a = 12 + g
⇒ g = a - 12
Given:
Carl is three times older than Alex⇒ c = 3a
Given:
The sum of their ages is 68⇒ a + g + c = 68
Substitute the first two equations in the last equation and solve for a:
⇒ a + (a - 12) + 3a = 68
⇒ 5a - 12 = 68
⇒ 5a = 80
⇒ a = 16
Substitute the found value of a into the other equations to find g and c:
⇒ g = 16 - 12 = 4
⇒ c = 3(16) = 48
Therefore:
Alex = 16 years oldGeorge = 4 years oldCarl = 48 years oldRatio
George : Carl : Alex = 4 : 48 : 16
Reduce by dividing by 4 → 1 : 12 : 4
Which statement best describes the equation (x+5)^2+4(x+5)+12=0
Answers
Answer:
x^2 + 14x + 57 = 0
Step-by-step explanation:
(x+5)^2+4(x+5)+12 = 0
x^2 +10x + 25 + 4x + 20 + 12 = 0
x^2 + 14x + 57 = 0
Vlad spent 20 minutes on his history homework and then completely solved x math problems that each took 2 minutes to complete. what is the equation that can be used to find the value of y, the total time that vlad spent on his homework, and what are the constraints on the values of x and y? y=2x 20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20. y=2x 20; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20. y=20x 2; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20. y=20x 2; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 20.
Answers
The expression for y is y = 2x +20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
What is domain and range of a function?Domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
We're given that:
Time spent by Vlad on history homework = 20 minutesTime spent by Vlad on math homework (x math problems) = 2 minutes on each problemy = time he spent on doing overall homeworkThen we have:
y = time on math homework + history homework
y = 2 +2 +2 ... (x times) + 20 minutes
[tex]y = 2x + 20[/tex]
x is "number of math problems". Thus, x can be 0,1,2,... These numbers are called non-negative integers(or integers greater or equal to 0) or whole numbers.
y is the time taken, but we see that
y = 2 times (non-negative integer) + 20
y = positive integer times non-negative integer + positive integer
Thus, we have:
y = non-negative integer + positive integer = positive integer
Thus, y assumes positive integral values only (in minutes).
Also, y is always going to be at least 20 (as history homework is going to take 20 minutes, even if math homework is nill ).
Thus, the expression for y is y = 2x +20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20
Learn more about domain here:
https://brainly.com/question/20073127
14
Select the correct answer from each drop-down menu.
A scientist conducted an experiment to measure the effect of apple cider vinegar on blood sugar levels. The scientist randomly selected
200 adults and randomly assigned them to two subject groups. The first subject group received an apple cider vinegar supplement, and the
second subject group received a placebo. The scientist was aware of which subjects were assigned to each group.
This experiment is
because
know which treatment group each subject is in
Answers
Answer:
The first one is blinded. I didn't get the other one though. The one that says "neither the subjects nor the researchers" is wrong.
Step-by-step explanation:
I use Plato.
The experiment is blindeded because the scientist know which treatment group each subject is in.
What is experiment?Experiment is the scientific approach to determine the properties of some sample by doing some research on it eg. By adding another material, or determination of hypothesis.
What is hypothesis?Hypothesis is the assumption which is made under some evidence which can be proceed further verification or by doing experiment on it.
From the question it is clear that the scientist wants to meassure the effect of apple cider vinegar subject on the blood sugar level.
So here the effect of apple cider vinegar subject on the blood sugar level is hypothesis.
From 200 randomly choosen young groups one half have taken apple cider where other half have taken placebo in order to clarify and study which group has taken which treatment and their effect in their blood sugar level.
Learn more about experiment
Here : https://brainly.com/question/5397388
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The formula for the perimeter of a rectangle is P = 2w + 2l. Write a formula that can be used to find the length, 1, in terms of P, and w.
Answers
Length = P/2-w
II. Let us see what you have learned in this module by
completing the following statements.
The Central Limit Theorem implies the following important
ideas in statistics:
1. The sample mean can be considered approximately
normally distributed if the sample size is
2. If the population is not normally distributed, or if we don't
know of its distribution, the
allows us to
conclude that the distribution of the sample mean will be
normal if the sample size is sufficiently large.
3. The population mean is equal to the
of the
sampling distribution. That is u = ur.
4. Mean of the sampling distribution of the sample mean is
equal to the population mean: H. - = H and the
of the sampling distribution of the sample
mean (sampling with replacement)
is equal to: 0,7
5. The Central Limit Theorem describes the
of the sample mean taken from a
population that is not normally distributed
o
Answers
Write an equation in point-slope form of the line that passes through the point (-6,6) and has a slope of m=3/2
Answers
Answer:
y-6=(3/2)(x+6)
Step-by-step explanation:
Given:
slope = m = 3/2point = (x1,y1) = (-6,6)Point-Slope:
[tex]\displaystyle \large{y-y_1=m(x-x_1)}[/tex]
Substitute m = 3/2, x1 = -6 and y1 = 6:
[tex]\displaystyle \large{y-6=\dfrac{3}{2}[x-(-6)]}\\\displaystyle \large{y-6=\dfrac{3}{2}(x+6)}[/tex]
Therefore, the equation is y-6=3/2(x+6)
Solve the equation to find X.
2.5+5.5-0.6x
Answers
Answer:
40/3
Step-by-step explanation:
-0.6X=-8
X=-8/-06
X=40/3
This is not multiple-choice, I need steps and how we found the answer, help I've been stuck for 2 days now!!!!
Find the surface area of the figure. Be sure to show all of your work and steps in solving for your answer.
Answers
Answer:
The surface area of a figure is the sum of all the sides that consist of it.
Let's first find the base's area, using the formula for the area of a rectangle, L · W:
9(6)
= 54 is the area of the base.
Now let's find the entire front side of this figure's area and double it so we get both the areas of the front and back side (using the formula for the area of a rectangle):
4(9)[bottom front rectangle] + 4(5)[upper front rectangle]
36 + 20
= 56, now double that area to get the area of both the front and back side:
56(2)
= 112 is the area of both the entire front and back side of this figure.
Now let's figure out the area of the right whole side of this figure then double it so we get both the areas for the left and right sides.
But, if we look at the middle rectangle to the right and left sides, we can see that there is no value, so let's find the value first.
The total length across the figure is 9 inches.
And we are given that the rectangle above intersects with the total length, so let's exclude that from 9 inches.
9 - 4 = 5, so now the total length of the two rectangles beside the above rectangle is 5.
But we want to find the value of one side, so divide 5 by 2.
5/2 = 2.5 inches.
Now let's find the whole entire area of the right side to this figure.
5(6)[upper right rectangle] + 2.5(5)[flat middle right rectangle] + 6(4)[bottom right rectangle)
30 + 12.5 + 24
= 66.5, now double that area to get both the area of the right and left side.
66.5(2)
= 133, is the area of both the right and left side of this entire figure.
Finally, we add all those areas together to get the surface area:-
54 + 112 + 133
= 299 inches is the surface area for this figure.
Answer:The surface area of a figure is the sum of all the sides that consist of it.
Let's first find the base's area, using the formula for the area of a rectangle, L · W:
9(6)
= 54 is the area of the base.
Now let's find the entire front side of this figure's area and double it so we get both the areas of the front and back side (using the formula for the area of a rectangle):
4(9)[bottom front rectangle] + 4(5)[upper front rectangle]
36 + 20
= 56, now double that area to get the area of both the front and back side:
56(2)
= 112 is the area of both the entire front and back side of this figure.
Now let's figure out the area of the right whole side of this figure then double it so we get both the areas for the left and right sides.
But, if we look at the middle rectangle to the right and left sides, we can see that there is no value, so let's find the value first.
The total length across the figure is 9 inches.
And we are given that the rectangle above intersects with the total length, so let's exclude that from 9 inches.
9 - 4 = 5, so now the total length of the two rectangles beside the above rectangle is 5.
But we want to find the value of one side, so divide 5 by 2.
5/2 = 2.5 inches.
Now let's find the whole entire area of the right side to this figure.
5(6)[upper right rectangle] + 2.5(5)[flat middle right rectangle] + 6(4)[bottom right rectangle)
30 + 12.5 + 24
= 66.5, now double that area to get both the area of the right and left side.
66.5(2)
= 133, is the area of both the right and left side of this entire figure.
Finally, we add all those areas together to get the surface area:-
54 + 112 + 133
= 299 inches is the surface area for this figure.
Step-by-step explanation:
Write an algebraic expression The product of c and 3
Answers
c x 3 = 3c
Answer:
The answer is c3 or c x 3.
Step-by-step explanation:
Because the product in math is multiplication, the product of c and 3 would be c x 3.
Arrange the following fraction in ascending order 4/12 , 5/6 , 2/3 5/6
Answers
Answer:
4/12 2/3 5/6 5/6
Step-by-step explanation:
The perimeter of a rectanglular pool is 294 m. If thr width of the pool is 54 m what is its length
Answers
Answer:
L=93
Step-by-step explanation:
So basically you need to know the formula beforehand the formula to find the length of a rectangle what is P=2(l+w) so to find for L the equation will be L=P/2-W=294-54=93 Therefore 93 is L
-4x-4y=24, 3x+10=y
since y is already isolated in the second equation, we can substitute the y value subs 2 into 1.
Next I have to combine like terms????
Answers
[tex]-4x-4y = 24~~...(i)\\\\3x +10 = y~~....(ii)\\\\\text{Substitute}~ y = 3x +10~ \text{in eq (i):}\\\\-4x -4(3x+10) = 24\\\\\implies -4x -12x -40=24\\\\\implies -16x =24+40\\\\\implies -16x = 64\\\\\implies x =- \dfrac{64}{16}\\\\\implies x = -4\\\\\text{Substitute}~ x = -4 ~ \text{in equation (ii) to find y:} \\\\y=3(-4) +10 = -12 +10 = -2\\\\\text{Hence,}~(x,y) = (-4,-2)[/tex]
Anyone know the Answer???
A figure has a vertices W(-2,4), and X(1,4. Find the coordinates of the figure after a dilation with a scale factor of 2. W(-4,83), X(2,8) W(-4,8), X(2,8)
Answers
Answer:
Step-by-step explanation:
The radius of a circle is 4 m. Find its area in terms of
π
π.
Answers
Answer:
16π
Step-by-step explanation:
Given:
[tex]\text{Radius of circle}: 4 \ \text{m}[/tex]
Formula:
[tex]\text{Area of circle} = \pi r^{2}[/tex]
Replace the radius in the formula:
[tex]\implies \text{Area of circle} = \pi (4)^{2}[/tex]
Evaluate the area:
[tex]\implies \text{Area of circle} = \pi (4)(4)[/tex]
[tex]\implies \text{Area of circle} = 16\pi[/tex]
Since the question says to determine the area in terms of π, the final answer is 16π.
what is the measure of XWV?
Answers
Answer:
Then the vertex is at (h, k) = (2, –3) and the value of p is –3. Since y is squared and p is negative, then this is a sideways parabola that opens to the left. This puts the focus 3 units to the left of the vertex.
vertex: (2, –3); focus: (–1, –3)
Step-by-step explanation:
The total amount of deductions from an employee’s gross pay is $83.20. if the gross pay is $378.18, what percent of their gross pay is being withheld? a. 21% b. 22% c. 23% d. 24% please select the best answer from the choices provided a b c d
Answers
The total amount of deduction in percentage is 22%. Then the correct option is B.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
The total amount of deductions from an employee’s gross pay is $83.20. if the gross pay is $378.18.
Then the percentage will be given as
[tex]\rm P = \dfrac{83.20}{378.18}\times 100\\\\P = 0.220 \ or \ 22\%[/tex]
More about the percentage link is given below.
https://brainly.com/question/8011401
Which orders pair is the solution to the system of equations
Answers
Answer: C) (12, -14)
Step-by-step explanation:
I am going to solve by elimination.
Start by subtracting one equation from the other
[tex]y=-x-2\\-(y=-\frac{1}{2} x-8)\\0=-\frac{1}{2} x+6[/tex]
Now solve for x
[tex]0=-\frac{1}{2} x+6\\0-6=-\frac{1}{2} x+6-6\\-6=-\frac{1}{2} x\\(-6)(-2)=(-2)(-\frac{1}{2} x)\\12=x[/tex]
Now sub in x into one of the equations to find the value of y
[tex]y=-(12)-2\\y=-14[/tex]
mean absolute deviation of 290
Answers
Answer:
3.5555555555556
Step-by-step explanation:
you cannot find the Mean Absolute Deviation of one number. This answer is the data set 2, 9, and 0. 3.5555555555556 is the Mean Absolute Deviation of 2, 9, 0.
laura bought a square canvas to paint a picture of her cat. One side measures 22 centimeters. What is the area of the canvas?
Answers
Answer
The area will be 484 square centimeters.
Find The distance between (5,2) and (5,0) on the coordinate Plane
Answers
Answer:
2
Step-by-step explanation:
2 is 2 away from 0
Help me in math please
Answers
Answer:
1. 27.5
2.32.5
3.30
6.22.5
11. 17.5
16.12.5
21. 7.5
7.27.5
12.22.5
17.17.5
22.12.5
8.25
13.20
18.15
23.10
ratio of passenger cars to cargo cars in
the rail yard is 18:4. If there are 8 cargo
cars, how many cars are there altogether?
Answers
passenger cars = 36
total no. of cars = 36 + 8 = 44
hope it helps...!!!
find tow rational number between –2 and 2
Answers
Answer:
i got you explain
Step-by-step explanation:
Two rational numbers between -2 and 2 are : 0 and 1.
or The two rational no are -1 and +1
[tex]\qquad \qquad \huge \pink {\sf{☁Answer☁}} \\ \\ [/tex]
→ first rational number
[tex] \tt{⇒ \frac{ ( { \cancel{-2}}+{ \cancel 2)}} {\cancel{2}}} \\ \\ \tt{⇒ \frac{ 0}{2} }\\ \\ \tt{⇒0} [/tex]
[tex] \pink{ \rule{60mm}{2.2pt}}[/tex]
→ Second rational number
[tex]\\ \tt{⇒ \frac{(-2+0)}{2}} \\ \\ \tt{⇒ \frac{ \cancel{-2}}{ \cancel{2}} }\\ \\ \tt{⇒-1} [/tex]
[tex]\rule{70mm}{3.9pt}[/tex]
[tex]\sf{\:мѕнαcкεя\: ♪...}[/tex]
To solve the following problem, use the 5-D Process. Define
a variable and write an expression for each column of your
table. In the first three football games of the season, Carlos gained three times as many yards as Alston. Travis gained ten yards
more than Carlos. Altogether, the three players gained a total
of 430 yards. How many yards did Carlos gain?
Answers
Answer:
c=3a=180
Step-by-step explanation:
c=3a,t=c+10 and a +t=430
a+3a+3a+10=430
7a=420
a=60
c=3a=180