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]
Evaluate the expression when a=6 and b = 50.
b-4a
Answer:
26
Step-by-step explanation:
sub it it
50-(4×6)
50-24
Find the length of the boldest arc. Rounded answer to the nearest hundredth (use 3.14 for pie)
State if the triangles in each pair are similar.
What is the correct answer?
Answer:
pink
Step-by-step explanation:
,pink is the only logical option
Cards in a pack are black or red in the ratio
black: red = 2:5
What fraction of the cards are red?
The midpoint of AB is M(0,3). If the coordinates of A are (4, -1), what are the
coordinates of B?
Answer:
Submit Answer
attempt 1 out of 2
A camera has a listed price of $511.99 before tax. If the sales tax rate is 7.75%, find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary,
Answer:
$551.70
Step-by-step explanation:
Price before tax= $511.99
Cost of the tax= 7.75/100×511.99
= $39.679
Total cost of the camera= $511.99+$39.679
= $551.669
≈ $551.70
What is the value of s?
Identify the volume of a regular hexagonal pyramid with base edge length 8 in. and height 10 in.,
rounded to the nearest tenth.
Answer:
554.3 m^2
Step-by-step explanation:
https://brainly.com/question/17542967?referrer=searchResults
The volume of a regular hexagonal pyramid will be 554.3 cubic inches.
What is the volume of the pyramid?Let h be the height of the pyramid, l be the slant height, and A be the base area of the pyramid. Then the volume of the pyramid will be given as,
Volume = (1/3) × A × h
The base area is calculated as,
A = 6 x (1/2) x 8 x 8 x sin 60°
A = 3 x 8 x 8 x 0.866
A = 166.28 square inches
The volume of a regular hexagonal pyramid is calculated as,
V = 1/3 x 166.28 x 10
V = 554.3 cubic inches
More about the volume of the pyramid link is given below.
https://brainly.com/question/17615619
#SPJ2
Please HEELLPPP!!!!!!!!!
Answer:
C) 56
Step-by-step explanation:
These angles are supplementary (they add up to 180):
3x + 31 + 2x - 6 = 180
5x + 25 = 180
5x = 180 - 25
5x = 155
x = 31
<FEG:
2x - 6
2(31) - 6
62 - 6
56
If sin 52° = 0.788, what is the approximate value of
cos 38°?
No link pls
Answer:
0.788
Step-by-step explanation:
Sin 52° = 0.788
Therefore
Cos 38° Is 0.788
The approximate value for 38° is 0.788
WHAT IS 1/2 + 1/9 PLEASE ANSWER! AND EXPLAIN I NEED MY GRADE UP!!!
Answer:
11/18
Step-by-step explanation:
1 2 + 1 9 = ? The Least Common Multiple (LCM) of 2 and 9 is 18. Multiply the numerator and denominator of each fraction by whatever value will result in the denominator of each fraction being equal to the LCM: 1 2 + 1 9 = 1 × 9 2 × 9 + 1 × 2 9 × 2 = 9 18 + 2 18 Now that the fractions have like denominators, add the numerators: 9 18 + 2 18 = 9 + 2 18 = 11 18 The result is: 1 2 + 1 9 = 11 18
so 11/18 is you answer
Answer:
11/18
Step-by-step explanation:
Get the common denominator by multiplying 2 and 9.
Multiply both sides of 1/2 by 9 to get 9/18, and both sides of 1/9 by 2 to get 2/18.
[tex]\frac{1}{2} +\frac{1}{9} = \frac{9}{18} + \frac{2}{18} = \frac{11}{18}[/tex]
After adding both fractions you'll get 11/18. That's your answer.
Solve 3x2 + x - 10 = 0. Round solutions to the nearest hundredth. (5 points) a x ≈ −5 and x ≈ 2 b No real solutions c x ≈ −2 and x ≈ 1.67 d x ≈ −1.67 and x ≈ 2
Answer:
c) x ≈ −2 and x ≈ 1.67
Step-by-step explanation:
Solve 3x²+ x - 10 = 0.
We solve using Almighty formula
-b ± √b² - 4ac/2a for equation: ax² + bx + c
where a = 3, b = 1, c = -10
Hence
-1 ± √1² - 4 × 3 × -10/2 × 3
-1 ± √1 - (-120)/6
-1 ± √1 + 121/6
-1 ± √121/6
-1 ± 11/6
Hence:
-1 - 11/6
-12/6 = -2
-1 + 11/6
= 10/6
= 1.67
Therefore, x = -2, x = 1.67
Option c) x ≈ −2 and x ≈ 1.67 is the correct answer
Which polynomial is a perfect square trinomial?
36x2 − 18x − 9
4a2 − 28a − 49
25b2 − 40b + 16
4x2 − 6x + 9
Answer:
The third one
Step-by-step explanation:
The process would be figuring out the square root of the first and last term of each equation, after doing so, you would take that number (square root of first and last number) then you do 2(a)(b) which would be which should be the middle term. In this case 2(5)(4) = 40 which is correct.
Step-by-step explanation:
my calculator got 36x*2-18-27/4
Name all the expressions that are equivalent to 3x+6y+7x-14
Select all
A.) -10x-14
B.)2(2x + 3y - 7)
C.)4x - 6y + 14
D.)4x+6y - 14
E.)10x + 6y - 14
Answer:
The answer to the question is E
Step-by-step explanation:
E is the only answer out of the choices to be equivalent to 3x+6y+7x-14
Someone please help with this question I need an answer no longer than 5 minutes
NO LINKS
Answer:
radius: 8.4 Area: 221.5
Step-by-step explanation:
16.8 divided by 2 = 8.4
The Formula for finding the area of circle= R₂ (radius squared: radius times itself) Multiplied by pi. pi = 3.14
8.4₂ multiplied by 3.14
Write the first five terms of the geometric sequence, given a1= -16 and r= -1/4
Answer: -16, 4, -1, 1/4,?
Step-by-step explanation: the nth term of a GP is given by Un= ar^n-1
Where n= the term.
So substituting the values for each term will give you the answer above. I don't know if it's tiredness or what but my fifth term gives me the same value as my fourth term.
Are the two Rectangles congruent? How do you know?
A. No, Sides are diffrent length and do not have a corresponding part.
B. Yes, each side and each angle has a congruent corresponding part.
Yes each side and each angle has a congruent corresponding part
(add. write your answer as a fraction, as a whole or as a mixed number)
PLEASE HELP . WILL GIVE BRAINLIEST !
Answer:
3 and 1/12
Step-by-step explanation:
hope this helps! :)
Reflect the function f(x)=x^4 about the x-axis and translate it 3 units to the left to produce g(x). A. G(x)=-x^4+3 B. G(x)=-x^4-3 C. G(x)=-(x-3)^4 D. G(x)=-(x+3)^4
Answer:(d)
Step-by-step explanation:
Given
Function is [tex]f(x)=x^4[/tex]
If it is reflected about the x-axis it becomes [tex]-x^4[/tex]
To shift it 3 units to the left it becomes
[tex]-(x+3)^4[/tex]
option (d) is correct
This is shown in the figure below
Pls help is it; (1.5, 2) or no solution
Answer:
no solution?
Step-by-step explanation:
can someone please help its my 2 to last one
Answer:
x= -7 because when you add 60+45+82 you get 187. The interior angles of a triangle add up to 180
Step-by-step explanation:
28 out of the 50 students in the 4th grade love chocolate ice cream. What percentage of the 4th graders DO NOT love chocolate ice cream?
Answer:20%
Step-by-step explanation: multiply 40 x 50=2,000
2,000 divided by 100= 20%
Which is the best estimate for √34 to the nearest whole number
Answer:Other than using a calculator to get an approximate value (
5.83
) for
√
34
,
√
34
can not be simplified
Step-by-step explanation:The only factors (
>
1
) of
34
are
2
and
17
Since neither of these are a square,
√
34
has no simplification.
Round your answer to the nearest hundredth.
A
4.
?
B
С
3
Answer:
a. 4.00
b. 3.00
I hope this helps
Please please please help me with this
Answer:
Apparently the picture is pitch black so I don't understand what you need help with. Sorry.
Step-by-step explanation:
Where do people and animals get the oxygen they breathe?
From plants
From other animals
From water
From the sun
Answer:
From plants hope it helps you have a good day keep smiling be happy stay safe ☺️Answer:
From Plants
Hope it will help you
What is m X to the nearest degree?
Help plssss
Answer:
A
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos X = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{XY}{XZ}[/tex] = [tex]\frac{13}{18}[/tex] , then
∠ X = [tex]cos^{-1}[/tex] ([tex]\frac{13}{18}[/tex] ) ≈ 44° ( to the nearest degree ) → A
The slating palace charges a $6.00 shoe rental fee plus $2.00 an hour to skate.Mathland skating rink charges $4.00 an hour to skate . what equation represents situation on;the skating palace
Answer:
Equation for the skating palace
= 6 + 2x
Step-by-step explanation:
Let the number of hours = x
For skating palace, the equation is written as:
The slating palace charges a $6.00 shoe rental fee plus $2.00 an hour to skate.
$6 + $2 × x
= 6 + 2x
For Mathland , the equation is written as:
Mathland skating rink charges $4.00 an hour to skate .
$4 × x
= 4x
Therefore, the equation that represents the situation on the skating palace is :
6 + 2x
The box plots show the weights in pounds of the dogs in two different animal shelters
Weights of Dogs in Shelter A
6
8
10
12
14
16
18
20
22
24
26
28
Weights of Dogs in Shelter B
One-half of the dogs in each shelter are between which weights?
between 8 and 30 pounds in shelter A between 10 and 28 pounds in shelter B
benveen 8 and 17 pounds in shelter A between 10 and 16 pounds in shelter B
between 21 and 30 pounds in shelter A between 18 and 28 pounds in shelter B
between 28 and 30 pounds in shelter A between 20 and 28 pounds in shelter B
Answer:
between 21 and 30 pounds in shelter A between 18 and 28 pounds in shelter B
Step-by-step explanation:
One half of the dogs in each shelter points at the the upper 50% of the dog weight. This point is marked by the median value up to the maximum weight value.
The median value is the point marked inside the box on a boxplot and the maximum value is the upper end or the endpoint of the whisker.
For SHELTER A:
Median = 21
Maximum = 30
Hence, For shelter A, it is the interval between 21 and 30
For shelter B:
Median = 18
Maximum = 28
Hence, it is the interval between 18 and 28
Answer:
it's c
Step-by-step explanation:
:)