Answer:
[tex]A = 74.7^\circ[/tex]
[tex]B = 42.5^\circ[/tex]
[tex]C = 62.8^\circ[/tex]
Step-by-step explanation:
Given
[tex]A = (-1,2) \to (x_1,y_1)[/tex]
[tex]B = (2,8) \to (x_2,y_2)[/tex]
[tex]C = (4,1) \to (x_3,y_3)[/tex]
Required
The measure of each angle
First, we calculate the length of the three sides of the triangle.
This is calculated using distance formula
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2[/tex]
For AB
[tex]A = (-1,2) \to (x_1,y_1)[/tex]
[tex]B = (2,8) \to (x_2,y_2)[/tex]
[tex]d = \sqrt{(-1 - 2)^2 + (2 - 8)^2[/tex]
[tex]d = \sqrt{(-3)^2 + (-6)^2[/tex]
[tex]d = \sqrt{45[/tex]
So:
[tex]AB = \sqrt{45[/tex]
For BC
[tex]B = (2,8) \to (x_2,y_2)[/tex]
[tex]C = (4,1) \to (x_3,y_3)[/tex]
[tex]BC = \sqrt{(2 - 4)^2 + (8 - 1)^2[/tex]
[tex]BC = \sqrt{(-2)^2 + (7)^2[/tex]
[tex]BC = \sqrt{53[/tex]
For AC
[tex]A = (-1,2) \to (x_1,y_1)[/tex]
[tex]C = (4,1) \to (x_3,y_3)[/tex]
[tex]AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2[/tex]
[tex]AC = \sqrt{(-5)^2 + (1)^2[/tex]
[tex]AC = \sqrt{26[/tex]
So, we have:
[tex]AB = \sqrt{45[/tex]
[tex]BC = \sqrt{53[/tex]
[tex]AC = \sqrt{26[/tex]
By representation
[tex]AB \to c[/tex]
[tex]BC \to a[/tex]
[tex]AC \to b[/tex]
So, we have:
[tex]a = \sqrt{53[/tex]
[tex]b = \sqrt{26[/tex]
[tex]c = \sqrt{45[/tex]
By cosine laws, the angles are calculated using:
[tex]a^2 = b^2 + c^2 -2bc \cos A[/tex]
[tex]b^2 = a^2 + c^2 -2ac \cos B[/tex]
[tex]c^2 = a^2 + b^2 -2ab\ cos C[/tex]
[tex]a^2 = b^2 + c^2 -2bc \cos A[/tex]
[tex](\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A[/tex]
[tex]53 = 26 +45 - 2 * 34.21 * \cos A[/tex]
[tex]53 = 26 +45 - 68.42 * \cos A[/tex]
Collect like terms
[tex]53 - 26 -45 = - 68.42 * \cos A[/tex]
[tex]-18 = - 68.42 * \cos A[/tex]
Solve for [tex]\cos A[/tex]
[tex]\cos A =\frac{-18}{-68.42}[/tex]
[tex]\cos A =0.2631[/tex]
Take arc cos of both sides
[tex]A =\cos^{-1}(0.2631)[/tex]
[tex]A = 74.7^\circ[/tex]
[tex]b^2 = a^2 + c^2 -2ac \cos B[/tex]
[tex](\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B[/tex]
[tex]26 = 53 +45 -97.67 * \cos B[/tex]
Collect like terms
[tex]26 - 53 -45= -97.67 * \cos B[/tex]
[tex]-72= -97.67 * \cos B[/tex]
Solve for [tex]\cos B[/tex]
[tex]\cos B = \frac{-72}{-97.67}[/tex]
[tex]\cos B = 0.7372[/tex]
Take arc cos of both sides
[tex]B = \cos^{-1}(0.7372)[/tex]
[tex]B = 42.5^\circ[/tex]
For the third angle, we use:
[tex]A + B + C = 180[/tex] --- angles in a triangle
Make C the subject
[tex]C = 180 - A -B[/tex]
[tex]C = 180 - 74.7 -42.5[/tex]
[tex]C = 62.8^\circ[/tex]
In an arithmetic sequence, the 10th term is 37, and the 21st term is 4. Find the common difference and the first term
Answer:
Common difference is 3. And the first term is 64.
Step-by-step explanation:
The differnce between 21 and 10 is 11. So there are 11 unknown numbers in between. And the difference between 37 and 4 is 33. 33/11 is equal to 3. So the pattern is minus three. the first term is 9 terms before 37. 9 times 3 is 27. 37+27 is equal to 64. so the first term is 64
What is the equation of the trend line in the scatter plot?
Use the two yellow points to write the equation in slope-intercept form. Write any coefficients
as integers, proper fractions, or improper fractions in simplest form.
Answer:
y = 5/8x + 9
Hope this helps!
Maria wants to huy some coffe mugs and plastic plates. The total cost of five coffe mugs and four plastic olayed is $28 and tge total cost of two coffe mugs and two plastic olates is $12 Write a system of equations and ise it to determine the cost of one coffe mug
Answer:
$4
Step-by-step explanation:
5c + 4p=28 equation 1
2c + 2p=12 equation 2
-2(2c +2p)=-2(12) multiply equation 2 by -2 so you can solve by elimination.
-4c-4p=-24 equation 2 multiplied by -2
5c+4p=28. Equation 1
c=4 added above 2 equations
solve for plates:
2c + 2p=12
2(4)+ 2p=12
8+2p=12
2p=4
p=2
check answer:
5c+4p=28. Equation 1
5(4)+4(2)=28
20+8=28
28=28
AREA OF CIRCLES PLS HELPP
Answer:
r = 3 ft
Step-by-step explanation:
A = πr²
9π = πr²
9π/π = r²
9 = r²
√9 = r
3 = r
Hope this helps!
Brenna is constructing a circle inscribed in a triangle. She has partially completed the construction, as shown below. What should be her next step in the construction?
Connect vertex B to the arc marking to complete the angle bisector
Find the angle bisectors for angles A and B
Connect three arc markings together to form the triangle
Use the incenter to determine the center to construct the circle
The construction is missing, so i have attached it.
Answer:
Use the incenter to determine the center to construct the circle.
Step-by-step explanation:
From the attached image, we can see that the 3 bisector of the three interior angles in the triangle intersect at a point. This point is known as the incentre of the triangle.
Now, to draw an inscribed circle inside the triangle, we will draw a perpendicular line from the incentre to any of the 3 sides and we will use the incentre as centre to draw the circle to touch each of the 3 perpendicular points.
13. Each edge of a cube is the same length. What is the surface area of the 1
cube represented by the net shown?
Answer:
6 is the answer
Step-by-step explanation:
what number goes into the missing space
Answer:
12
Step-by-step explanation:
mrk me brainliest plzzzzzzzzzz
Answer:
b) 12
Step-by-step explanation:
The first image shows the top 2 numbers as 5 and 2 = 5 * 2
=> 10
The Second image shows the top 2 numbers as 3 and 3 = 3 * 3
=> 9
So, the third image shows the top 2 numbers as 2 and 6 = 2 * 6
=>12
Therefore, the missing space in the third circle is b) 12
Hope it helps :)
3x-8y=24
y=x-8
Please show
work
Answer:
3x - 8y = 24 --------(1)
y = x - 8 ---------(2)
substitute y in (1)
3x - 8( x - 8) = 24
3x - 8x + 64 = 24
-5x = 24 - 64
-5x = -40
5x = 40
x= 8
substitute x in (2)
y = 2 - 8
y = - 6
Answer:
x = 8, and y = 0
Step-by-step explanation:
We can solve this by taking y as (x-8), as it states there.
Since y is equal to x-8, we can rearrange the system of equations into one single equation.
We can multiply y by 8, as it shows in the first equation, which is something like 8x-64.
Since it is a negative 8 being multiplied by y, it would be the inverse of 8x-64, which is -8x+64.
We can now organize our equation here.
3x - 8x + 64 = 24.
We can use subtraction property of equality by subtracing 64 from both sides to get rid of it.
We will get something like:
3x - 8x + 64 - 64 = 24 - 64.
Simplify by solving like terms like the x value and the integers.
-5x = -40
Divide both sides with division property of equality:
-5/5x = -40/5
x = 8
We can then plug the 8 back into x, lets use the second equation because I'm lazy and it looks the easiest to solve for.
y = (8) - 8
y = 0
Therefore, x = 8, and y = 0.
Help please I don’t understand this! Giving brainliest!
Answer:
200
Step-by-step explanation
100+400=500 BUS
300+400=700 SPORTS
sports-bus
700-500=200
Answer:
300 + 400 = 700
Step-by-step explanation:
Play sports, : 300 + 400 = 700
Don't play, : 200 + 100 = 300
Triangle ABC has side lengths a=74.1, b= 60.8, c=114.2. What is the measure of angle C?
a. 35.9°
b. 28.8°
c. 96.4°
d. 115.3°
Given:
In triangle ABC, a=74.1, b= 60.8, c=114.2.
To find:
The measure of angle C.
Solution:
According to the Law of cosine:
[tex]\cos C=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
Substituting [tex]a=74.1,b= 60.8,c=114.2[/tex], we get
[tex]\cos C=\dfrac{(74.1)^2+(60.8)^2-(114.2)^2}{2(74.1)(60.8)}[/tex]
[tex]\cos C=\dfrac{5490.81+3696.64-13041.64}{9010.56}[/tex]
[tex]\cos C=\dfrac{-3854.19}{9010.56}[/tex]
[tex]\cos C=-0.42774145[/tex]
Taking cos inverse on both sides, we get
[tex]C=\cos^{-1}{-0.42774145}[/tex]
[tex]C=115.324312[/tex]
[tex]C=115.3^\circ[/tex]
Therefore, the correct option is d.
Find the sum of the given geometric series: n = 8, r = 3, a = 1/2
Answer:
a⁸=112 is the answer.
Step-by-step explanation:
a⁸=32(1/2)⁷
a⁸=32(7/2)
a⁸=112
f(x)=∣x∣
g(x)=∣x−1∣+9
We can think of g as a translated (shifted) version of f
Complete the description of the transformation.
Answer:
Step-by-step explanation:
There are two transformations, one vertical, one horizontal.
The + 9 part outside the absolute value sign moves the graph up 9 units.
Replacing x with x - 1 moves the graph right 1 unit.
Comment: The horizontal shifts sometimes appear backwards: x - 1 looks like a shift to the left, but it's not.
Example: f(4) = |4| = 4. To get the same output (4) from g(x), you have to use a value for x that is 1 unit larger than 4. g(5) = |5 - 1| = 4.
THIS IS URGENT PLZ HELP!!!
Find three consecutive EVEN numbers such that: The sum of one sixth of the first number, two sevenths of the second number and one half of the third number equals 54
Answer:
12
Step-by-step explanation:
2
4
6
8
10
12
14
16
18
20
22
24
26
A volume of the cone is (1/3) the volume of a cylinder. The volume of the sphere is what fraction of the volume of the cylinder?
Answer:
4/3
Step-by-step explanation:
To know this, let's write down the formulas for the volume of cylinder and sphere.
Vs = 4/3πr³ (1)
Vc = π r² h (2)
Now, we do have a little problem here and its the fact that the sphere do not have a height like the cylinder do. But in this case so if you want to have an idea of the fraction of the volume, we will assume that the cylinder has the same height as its radius. Assuming this we have the following:
Vs / Vc = 4πr³ / 3πr²h
Vs/Vc = 4πr³ / 3πr³
From here, we can cancel out the values of π and r³:
Vs/Vc = 4/3
Vs = 4/3 VcThus we can conclude that the volume of the sphere is 4/3 the volume of a cylinder.
Hope this helps
its math algebra 1 i need help
Answer:
The 3rd one which is C
Step-by-step explanation:
It's the 3rd one because if you look at the orange like where the 2 and the 4 is you will see the orange line is between them two which that's where the 3 will go and the others don't have that, so it C hope this helps you!
Use the distributive property to write an equivalent expression.
10(2x + 8y - 6)
Answer:
20x +80y -60 hope this helped:)
Step-by-step explanation:
Find the surface area of the regular pyramid.
PLS HELP ME
Answer:
The surface area equals 45.
Solve the equation:
2 + y/3 =8
plsss anybody help no links more files they are viruses
Answer:
1- B & C (Same answer and also I'm not that sure)
2- B: y = 8x (I'm sure of this ^^)
3- Option 3
4- 108 degrees
Answer:
1. C
2. B
3. Option 3
4. 108 degrees
Step-by-step explanation:
1. There cannot be less than 0 people or more then 25 people, but the theatre capacity can be equal to both of these numbers.
2. x is multiplied by 8 to create y, so the equation is y=8x
3. There can't be over 8 refrigerators on the truck, and you can't have a fraction of a refrigerator.
4. One line is 180 degrees. 36+36=72, 180-72= 108 degrees
I need help with math
Answer:
Its the second one
Step-by-step explanation:
Stephen was thinking of a number. Stephen adds 2, then divides by 7 to get an answer of 11. What was the original number?
Answer:
75
Step-by-step explanation:
Let x = number thought of
(x + 2) / 7 = 11
multiply both sides of the equation by 7
11 x 7 = x+ 2
collect like terms
77 - 2 = x
x = 75
alright hear me out... why is the word dictionary in the dictionary? ಠ_ಠ
cause a dictionary contains all known words including dictionary..my turn!.look in the comments!
6. Find both solutions by factoring
): 3x^2 + 10x + 7 = 0
Help meeeeeeee!!!!!!!
Answer:
the answer is c
Step-by-step explanation:
If u add the values of the dots on set A it would be greater than set B.
!!!!!I NEED HELP ASAP!!!!!
1
What is the product оf (9)(-9. (-1)
-81
-1
1
81
Answer:
81
Step-by-step explanation:
(-81)(-1) = 81
2
Type the correct answer in the box.
212 units
2 units
2 units
8 units
2 units
2 units
2 units
6 units
The area of the figure is
square units.
Reset
Next
Answer:
212×2×2×8×2×2×2×6= 325636
I hope the answer is correct. I hope I will get 5points
Answer:
2 units i hope this helps you
The triangle below is equilateral. Find the length of side x in simplest radical form with a rational denominator.
Answer:
x = 8
Step-by-step explanation:
If a triangle is equilateral, each vertex has an angle that is equal to 60 degrees
As we can see, we have two sets of similar right triangles
The value x faces the right angle and that makes it the hypotenuse
Also, the side measure 4 is the adjacent side to the angle 60
The trigonometric identity that relates the hypotenuse and the adjacent is the cosine
it is the ratio of the adjacent to the hypotenuse
Mathematically;
cos 60 = 4/x
x = 4/cos 60
x = 8
20 points pls answer
A bag contains n counters. one counter is blue and the rest are red. Two counters are taken at random from the bag. a) express, in terms of n, the probability that a counter of each colour is taken. Give your answer as a fraction. b) the probability that a counter of each colour is taken is 0.125. How many red counters are in the bag?
Answer:
A] Probability = 1/n ; B] Number = 8
Step-by-step explanation:
Total counters = n , Blue counter = 1 , Red counters (remaining) = n -1
A] Prob (One blue, & One red counter) = (Blue counter / Total counters) x (Red counters / Total remaining counters) = [1 / n] x [ (n -1) / (n-1)] = 1 / n
Alternative, Prob (One red, & one blue) = (Red counter / Total counters) x (Blue counters / remaining counters) = [ (n-1) / n ] x [1 / (n-1) ] = 1 / n
B] Prob (each color , a blue & red counter taken) = 0.125 {Given}
By A], this Prob = 1/n.
So, 0.125 = 1/n → n = 1 / 0.125 = 8
Find the slope of the line and that passes through (7, 2) and (-7, 48)
Answer:
-23/7
Step-by-step explanation:
y2 - y1 / x2 - x1
48 - 2 / -7 - 7
46 / -14
= -23/7