Use vectors to find the interior angles of the triangle with the given vertices. (Enter your answers as a comma-separated list. Enter your answers in terms of degrees. Round your answers to two decimal places.) (−6,-9), (2,7),(7,2)
Answers
Answer:
23.20°, 71.57°, 85.24°
Step-by-step explanation:
The angle between two vectors can be found by making use of the definition of the dot product. The computed angle is the angle between the vectors when they are placed tail-to-tail.
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setupvector definition
The second attachment shows the given points plotted as A, B, C in the order given. In the diagram, the vectors a, b, c are defined as BA, CB, AC, respectively. That is, the vector a is ...
a = A -B = (-6, -9) -(2, 7) = (-6-2, -9-7) = (-8, -16)
The vectors are defined in counterclockwise order around the triangle, though that makes no difference to the calculation.
dot product definition
The definition of the dot product of vectors A and B is ...
A·B = |A|×|B|×cos(θ) . . . . . where θ is the angle between the vectors
Solving for the angle, we find it to be ...
[tex]\theta=\arccos\left(\dfrac{\vec{A}\cdot\vec{B}}{|\vec{A}|\,|\vec{B}|}\right)[/tex]
__
computationBecause of the way the vectors in this solution are defined, the angle between any given pair of vectors will be an exterior angle of the triangle. In order to find the measure of the interior angle, we must reverse one of the vectors. That is, the dot product used in our computation will be the opposite of the dot product of the vectors we have found.
The spreadsheet shown in the first attachment does the necessary computations.
Each vector is the difference of successive points. (x1 -x2, y1 -y2)Each dot product shown is the opposite of the dot product of successive vectors. -(x1x2 +y1y2)The magnitude is computed in the usual way: the root of the sum of the squares of the components of the vector. √(x²+y²)The cosine is the dot product of successive vectors, divided by each of the vector magnitudes.The spreadsheet shows the angle in degrees, having converted it from the radian value produced by the ACOS function.As a check, the spreadsheet shows the sum of the angle values. (The rounded values add up to 180.01°.)
The interior angles of the triangle are 23.20°, 71.57°, 85.24°.
_____
Additional comment
Another way to find the interior angles from coordinates is to consider the slope of each side of the triangle as being the tangent of the angle it makes with the x-axis. The difference of these angles can be used to find the interior angles of the triangle. Less work is involved because there is no dot-product or magnitude computation.
Related Questions
Mario has captured many yellow spotted slalmaders. He weighs each and then counts the number of yellow spots on its back. This trend line is a ___ fit for these data.
Answers
Question 29 of 49
The pattern below follows the rule, "starting with a value of 3, every
consecutive row has a value that is 2 less than twice the value of the previous
row."
Value
Row 1
3
Row 2
4
Row 3
6
What is the value for the 6th row?
Answers
34.............................. ........
Simplify
x² - 7x - 30
x² + 5x + 6
Answers
Answer:
(X+3)(x-10)
(X+3)(X+2)
Which type of data would be best displayed in a dot plot. (Help fast)
Answers
The type of data that would be best displayed in a dot plot is the correspondent to the third option.
Which type of data would be best displayed in a dot plot?
A dot plot is a plot where in the horizontal axis different numbers or properties (discrete set, usually we want smaller ranges, just so the graph are easier to read.) are marked, and above these, we mark dots, that represents how many times these are repeated on the data set.
We don't want large ranges (like in the first option 725 to 2450) because it means that we need to mark 725 points, or we need to find a common factor so each point represents more than one unit.
So, we need to have discrete data and with ranges not to large. The only option that meets both conditions is the third one, where on the horizontal axis we would have each of the 15 school dental clinics, and the dots would represent the number of dentist volunteering on each of them.
Then the correct option is the third one.
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Answer:
3rd option
Step-by-step explanation:
what is 5 x 9/10 (fraction)
help me please asap
Answers
Answer=
5x9
10
Cut 5 with 10 as it’s possible
5 x 1 =5 and 5x 2=10
So the answer is
9/2
~30 PTS, BRAINLIEST, AND 5 STARS TO BEST ANSWER!~
1.) Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8).
2.)Find point Z that partitions the directed line segment XY in the ratio of 2:1 where X(1, 2) and Y(7, 5).
(PLS PROVIDE A DETAILED RESPONSE, ALONG WITH AN EASY
STEP BY STEP PROCESS. TY!)
Answers
For both problems, we can use the section formula.
1) [tex]P=\left(\frac{(1)(1)+(5)(-9)}{6}, \frac{(1)(8)+(5)(3)}{6} \right)=\boxed{\left(-\frac{22}{3}, \frac{23}{6} \right)}[/tex]
2) [tex]Z=\left(\frac{(2)(7)+(1)(1)}{3}, \frac{((2)(5)+(1)(2)}{3} \right)=\boxed{(5, 4)}[/tex]
1) A survey asked 200 Grade 4 students about their reading preferences. Based on Graph #1, about how many of them would you expect prefer comic books?
x
A. 10
B. 20
C. 60
D. 80
E. 100
help please
Answers
Answer:
First send the graph then we can help you in your answer
Answer:
D. 80
Step-by-step explanation:
The graph shows that about 3/8 ( 37.5% ) of the students enjoy comic books.
200 × .375 = 75
75 rounded to the nearest tens value is 80
For anyone wondering, the graph was on a different question that this person asked.
Find the quotient.
48a3bc2 ÷ 3abc
16 ac2
16 a2c
18 a2c
16 a4b2c 3
Answers
The quotient when 48a³bc²is divided by 3abc will be 16a²c.
How to explain the quotient?The information given is that we should find the quotient of 48a³bc² ÷ 3abc.
This can be expressed as:
48a³bc² ÷ 3abc = (3 × 16 × a³ × b × c²) / (3 × a × b × c)
= 16a²c
In this case, the quotient when 48a³bc²is divided by 3abc will be 16a²c.
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What is the value of x?
Enter your answer in the box.
Answers
Answer:
25
Step-by-step explanation:
c^2=a^2+b^2
where c = hypotenuse
so, x^2 = 24^2+7^2
x^2 = 576 + 49
x^2 = 625
x = square root of 625
x = 25
24x24 + 7x7 = 625
Square root of 625 is 25
What is the factored form of 4x2 23x – 72? (4x 8)(x – 9) (4x – 8)(x 9) (4x 9)(x – 8) (4x – 9)(x 8)
Answers
Answer:
(x+8)(4x-9)
Step-by-step explanation:
Rewrite expression 4x^2 + 32x - 9x - 72
Factor out 4x 4x(x+8) - 9x - 72
Factor out x+8 4x(x+8) - 9(x+8)
Simplify (x+8)(4x-9)
Q38: Rearrange g=2hm to make m
the subject
Answers
The expression g = 2hm can be written as in terms of g and h when m is the subject is m = g/2h.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
g = 2hm
To make m as the subject and solve it:
Divide the above expression by 2h on both sides:
g/2h = m or
m = g/2h
Thus, the expression g = 2hm can be written as in terms of g and h when m is the subject is m = g/2h.
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Which point is on the circle centered at the origin with a radius of 5 units?
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
(2, StartRoot 21 EndRoot)
(2, StartRoot 23 EndRoot)
(2, 1)
(2, 3)
Answers
At a diner, the lunch special gives you three choices. For the starter, you can pick from 3 choices (soup or salad or fries) For the main item, you can pick from 2 choices (burger or sandwich) For the drink, you can pick from 2 choices (coke or pepsi) If the staff chooses all items for you randomly, figure these probabilities.
1. Probability of getting (soup, burger, coke)
2. Probability of getting (fries, burger, any drink)
Answers
Answer:
1/12; 1/6
Step-by-step explanation:
1. the chance of getting soup is 1/3, the chance of getting a burger is 1/2, and the chance of getting coke is 1/2, multiply these chances to get (1/3) *(1/2) * (1/2) = 1/12
2. the chance of getting fries is 1/3, the chance of getting a burger is 1/2, and the chance of getting any drink is 1, multiply these chances to get (1/3) * (1/2) * 1 = 1/6
The inverse of a quadratic parent function with a limited domain is a
function.
A. negative
B. cubed
C. square root
D. hyperbolic
Answers
The inverse of a quadratic parent function with a limited domain is given by the square root function, hence option C is correct.
How to find the inverse of a function?Supposing we have a function y = f(x), to find the inverse, we exchange x and y, and isolate y.
The quadratic function is:
[tex]y = x²[/tex]
Exchanging and isolating y:
[tex]x = y^2[/tex]
[tex]y^2 = x[/tex]
[tex]y = \sqrt{x}[/tex]
[tex]f^{-1}(x) = \sqrt{x}[/tex]
Hence option C is correct.
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Lakeridge health oshawa is a 423 beds hospital with 463 doctors and 4058 staff comprised of nurses and technologists. it is planning to open another 35-bed wing. assuming the same proportionate staffing levels, how many more doctors will need to be hired?
Answers
The number of doctors that would be needed for the 35-bed wing is 38.
How many more doctors are needed?The first step is to determine the number of doctors needed for one bed : 463 / 423
The second step is to multiply the ratio gotten in the first step by the number of beds in the new wing: (463 / 423) x 35 = 38.21 = 38
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Banana
23
Apple
18
Orange
34
Peach
27
Pear
18
Using proportional reasoning, about how many students out of the 2,000 would you expect to select an orange as their favorite fruit?
Answers
Answer:
almost 567 students
Step-by-step explanation:
all fruits = 23+18+34+27+18 = 120
possibility of selecting an orange as favourite fruits by one student = 34/120 = 17/60
possibility of selecting an orange as favourite fruits by 2000 students = 17/60×2000 =1700/3 = 566.6666...=567 students
please help me (show ur solution)
Answers
Answer:
See below ~
Step-by-step explanation:
Q9
x = 200° (arc measure = central angle measure)The inscribed angle y is half of the arc length xy = 1/2xy = 1/2(200°)y = 100°Q10
x + 112 = 180x = 68°y + 81 = 180y = 99°Answer:
9. x = 200 and y = 100
10. x = 68 and y = 99
Step-by-step explanation:
Question 9
The measure of an arc is the measure of its central angle.
⇒ x = 200
This is a non-cyclic quadrilateral as not all its vertices touch the circumference of the circle.
The angle at the center is twice the angle at the circumference.
⇒ y = 200 ÷ 2
⇒ y = 100
Question 10
This is a cyclic quadrilateral as all its vertices touch the circumference of the circle.
The opposite angles in a cyclic quadrilateral add up to 180°.
⇒ x + 112 = 180
⇒ x = 68
⇒ y + 81 = 180
⇒ y = 99
Find the range.
3 -9 7 -1 5 -4 2
Answers
Answer:
16
Step-by-step explanation:
The range is the distance between the largest number and the smallest number. To find the range, you take the smallest number and subtract it from the largest number. In this case, the smallest number is -9 and the largest number is 7. 7 minus -9 is a double negative, so you can also do 7+9=16. 16 is the range.
What is the value of the expression?
-16+12
Answers
Answer:12-16=-4
Step-by-step explanation:the answer is the same way it’s just flipped
What is the y-intercept of the function f(x) = -2/-9x+1/3?
Answers
Answer:
b = 1/3
Step-by-step explanation:
The general structure of equations in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept.
The given equation is already in slope-intercept form. In other words, you have already been given "m" and "b". Therefore, the value which corresponds with the y-intercept is (1/3).
f(x) = mx + b
f(x) = -(2/9)x + 1/3
Consider the equation -5\cdot e^{10t}=-30−5⋅e
10t
=−30minus, 5, dot, e, start superscript, 10, t, end superscript, equals, minus, 30.
Solve the equation for ttt. Express the solution as a logarithm in base-eee.
t=
Approximate the value of ttt. Round your answer to the nearest thousandth.
t=
Answers
The approximate equation is n = (ln 6)/10 and approximate value is n = 0.179.
What is Exponential equation?In mathematics, an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
Here, given equation; (we are using n in place of t)
-5.e¹⁰ⁿ = -30
On dividing -5 both sides, we get
-5.e¹⁰ⁿ/-5 = -30/-5
e¹⁰ⁿ = 6
Taking 'ln' on both side, we get
10n = ln 6
n = (ln 6)/10
n = 1.791759/10
n = 0.179
Thus, the approximate equation is n = (ln 6)/10 and approximate value is n = 0.179.
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which sequence of transformations could be used to move triangle RST so it completely covers triangle R”S”T?
Answers
Triangle RST is reflected across the x-axis and translated 5 units to the left to form triangle R"S"T"
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Triangle RST is reflected across the x-axis and translated 5 units to the left to form triangle R"S"T"
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There is a bag filled with 5 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
Answers
5 blue, 4 red = 9 total
Probability (Blue, Blue) = 5/9 x 5/9 = 25/81 = 0.30864
Probability (Red, Red) = 4/9 x 4/9 = 16/81 = 0.19753
Probability (Blue,Blue) or (Red,Red) = 25/81 + 16/81 = 41/81 = 0.506173
Fraction answer = 41/81
Decimal answer = 0.506173 (round off as needed)
can you help me figure of the value of y?and possible x (I think I got it)
Answers
The values of x and y from the figure are 22.5 and 10 respectively
Vertical anglesThe angles that meet at a point X are equal and vertically opposite
From the diagram shown
6x - 5 = 8x - 50
6x - 8x = -50 + 5
-2x = -45
x = 22.5
Similarly
2y + 30 = 3y + 20
2y - 3y = 20 - 30
-y = -10
y = 10
Hence the values of x and y from the figure are 22.5 and 10 respectively
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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
Since the two lines intersects each other we can conclude that :
6x - 5 = 8x - 50and
2y + 30 = 3y + 20[ That's because they form vertical opposite angle pair ]
So, let's solve for x and y ~
[tex]\qquad \sf \dashrightarrow \:6x - 5 = 8x - 50[/tex]
[tex]\qquad \sf \dashrightarrow \:8x - 6x = - 5 + 50[/tex]
[tex]\qquad \sf \dashrightarrow \:2x = 45[/tex]
[tex]\qquad \sf \dashrightarrow \:x = \dfrac{45}{2} [/tex]
[tex]\qquad \sf \dashrightarrow \:x = 22.5[/tex]
And
[tex]\qquad \sf \dashrightarrow \:2y + 30 = 3y + 20[/tex]
[tex]\qquad \sf \dashrightarrow \:3y - 2y = 30 - 20[/tex]
[tex]\qquad \sf \dashrightarrow \:y = 10[/tex]
I hope the steps are clear ~ let me know if you have doubts ~
Needs help no bots please
Directions: Solve each of the following problems. Round answers to the nearest hundredths when applicable.
1) If the height of a parallelogram is 27.3 m and the base is 6.3 m, what is the area of the parallelogram?
2) If the base of a rectangle is 27.4 mm and the area is 420.92 mm2, what is the height of the rectangle?
3) What is the height of a rectangle with perimeter 133.2 mm and base length 30.6 mm?
4) If the base of a parallelogram is 61 m and the area is 645 m2, what is the height of the parallelogram?
5) What is the perimeter of a parallelogram with base 32 cm and side length 34 cm?
6) What is the area of a parallelogram with base 40 mm and height 18 mm?
7) If the height of a rectangle is 8.8 m and the base is 7.9 m, what is the perimeter of the rectangle?
8) If the base of a rectangle is 23 cm and the area is 354 cm2, what is the height of the rectangle?
9) What is the area of a square with a perimeter of 44 mm?
10) What is the area of a square with a perimeter of 55 cm?
11) What is the area of a parallelogram with a height 43 m and base 18 m?
12) What is the perimeter of a parallelogram with side length 35 m and base 25 m?
13) If the base of a rectangle is 16 m and the area is 600 m2, what is the height of the rectangle?
14) What is the area of a rectangle with perimeter 125.6 cm and base length 40.5 cm?
15) If the height of a parallelogram is 64.3 m and the base is 4.3m, what is the area of the parallelogram?
Answers
6.3x27.3=171.99m^2
2) 420.92/27.4= 15.36mm to 2 decimal places
3) 133.2x30.6=4075.92mm^2
4) 651/61=10.57m to 2 decimal places
5) (32x2)+(34x2)=132mm
6) 40x18=720mm^2
7) (8.8x2)+(7.9x2)=33.4m
8)354/23= 15.39cm to 2 decimal places
9) 44/4=11
11x11=121mm^2
10)55/4=13.75
13.75x13.75=1890.0625cm^2
11) 43x18=774m^2
12) 25x35=875m^2
13)600/16=37.5m
14) 125-(40.5x2)=44.6
44.6/2=22.3
22.3x40.5=903.15cm^2
15) 64.3x4.3=276.49m^2
Can someone help me?
Answers
Answer:
It's the third one hun :>
Answer:
yup third one
Step-by-step explanation:
parabolas are ALWAYS a U shape ;-)
its so hard can you guys help
Answers
Answer:
1593 pandas 13 years ago.
Difference? ≈271 pandas
Keyword:
"Increase"
Step-by-step explanation:
Use the equation:
x + (x × P%) = y
x(1 + P%) = y
x = 1864/(1 + 17%)
x = 1864/(1 + 0.17(17%))
x = 1864/1.17
x = 1593.1624 ≈ 1593
please help me find answer for this question
Answers
Answer:
The answer with 4 cubes 2x2
Step-by-step explanation:
D it has 5 cubs in all,if you see A,B,C,they do not have cuds
which of the following equations will produce the graph shown below?
Answers
A circle can be characterized by its center's location and its radius' length. The correct option is A.
What is an equation of a circle?A circle can be characterized by its center's location and its radius' length. Let the center of the considered circle be at (h,k) coordinate and the radius of the circle be 'r' units. Then, the equation of that circle would be:
(x-h)² + (y-k)² = r²
The given graph is the graph of a circle that has its origin at (0,0) and has a radius of 4 units, therefore, the equation will be,
(x-0)² + (y-0)² = 4²
x² + y² = 16
Multiply both the sides of the equation by 2,
2x² + 2y² = 32
Hence, the correct option is A.
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(2⁄3)3 the 3 is a exponent a answer would help but i would also like a step by step explanation so i can solve it on my own next time
Answers
Answer:
8/27
Step-by-step explanation:
So an exponent is basiclly when you multiply the number as many times as the exponent says. In this case it saying 3 so you would do 2/3*2/3*2/3 and then you would get 8/27. I hope this helps.