Answers
Answer:
a 120
Step-by-step explanation:
Related Questions
Item 7
△ABC has vertices A(−1, 2), B(2, 8), and C(4, 1). Find the measure of each angle of the triangle. Round decimal answers to the nearest tenth.
Answers
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]
i have a geometry question.
Answers
Answer:
Step-by-step explanation:
You already have the area for your triangle. Substract that from the entire area of the rectangle.
To get the area of the rectangle, multiply the length by the height.
15*20 = 300
Now substract your triangle from that :)
i need this done rn plz help
Answers
Answer:
answer for yes total, is 5, the answer for no total is 20, the total for junior is 17, and the total for senior is 8.
Step-by-step explanation:
What you do is you add the 2 values. for example, to find the total for the juniors, you would add 1 to 16.
Can someone please help me with math.
Answers
Answer:
Vertical Angles
Step-by-step explanation:
Hope this helps
Help ASAP! It’s due and thanks
Answers
Answer:
C
Step-by-step explanation:
It can't be B or D, because there is only a difference in the X axis (Meaning it goes either left or right)
It can't be A because 2 is less than 11, so (2, -1) would be left 9 units in relation to (11, -1)
please help and show work
Answers
Answer:
Step-by-step explanation:
3) JH is the length of the radius
def. of midpoint
def. of < bisector
4) The missing length is 15
Given a=8 and c=17,
b = 30
∠α = 28.072° = 28°4'21" = 0.48996 rad
∠β = 61.928° = 61°55'39" = 1.08084 rad
area = 60
perimeter = 40
h =
120
17
= 7.0588235294118
Which statements apply to the expression (3/5^3) cubed? Check all that apply.
Answers
Answer:
The true statements are
3/5 is the base
3 is the exponent
(3/5)³ = 3/5 × 3/5 × 3/5
(3/5)³ = 27/125
Step-by-step explanation:
Let a and b be any integer, given the expression;
[tex]a^b[/tex]
a is the base
b is the exponent
Similarly if we have;
[tex]a^3[/tex]
This means we can multiply a in three places as shown;
[tex]a^3 = a \times a \times a[/tex]
Applying this to the given expression
[tex](\frac{3}{5} )^3 = \frac{3}{5} \times \frac{3}{5} \times \frac{3}{5} \\Also\\(\frac{3}{5} )^3 = \frac{3 \times 3 \times 3}{5 \times 5 \times 5} \\(\frac{3}{5} )^3 = \frac{27}{125}[/tex]
The base value will be 3/5 and the exponent is 3
20 points.
Find the area of a right triangle whose hypotenuse is 20 units long and the altitude drawn from the Right angle divides the hypotenuse into 5 units and 15 units.
Answers
Step-by-step explanation:
the height of the triangle = √(5×15)= √75
=5√3 units
the base of triangle= 20 units
so, the area = ½×20×5√3= 50√3 units
or 86.60 units
please help! answer correct for 10 points and brainliest.
Answers
Answer:
14 square cm Should be the answer, plz do correct me if im wrong!!
Step-by-step explanation:
The right side which is triangle is 2x3 is 6 but because there is only half 6/2
it is 3!
Th middle portion which is square is 2 to the 4th power or 2x2x2x2 or just 2x4(2^4)!! Which is 8!
Finally the last triangle is the same as the first 3
8+6(the to triangles 3+3)=14
Mark brainliest plz, it was nice helping you if im wrong plz tell me immdiately i dont want to cause any problems good day ;)
Simplify the expression using long division.
(412 - 13x - 4)+(-2)
A. quotient 4x - 13 and remainder 2 B, quotient 4x - 5 and remainder-6
C. quotient 4x +5 and remainder 6 D. quotient 4x - 5 and remainder
Answers
Step-by-step explanation:
(4x^2 - 13x - 4) + (x - 2)
Remove the parentheses
4x^2 - 13x - 4 + x - 2
Add -13x and x
4x^2 - 12x - 4 - 2
Subtract 2 from -4
4x^2 - 12x - 6
I know this isn’t fully the correct answer but try option B
Mark me as brainliest!
Line BC is a tangent line to the circle centered at A. If angle BAC is 64 degrees, what is the
measure of angle ACB? Explain/show your reasoning.
Answers
Answer:
Here.
Step-by-step explanation:
Step-by-step explanation:
BC is tangent to the circle at point B.
Therefore, by tangent-radius theorem:
Step-by-step explanation:
BC is tangent to the circle at point B.
Therefore, by tangent-radius theorem:
for the bud to see... and one person to get poi.nts XD
so addison got banned yesterday but got her account back today and then drake got banned today
Answers
Answer:
WHAT!? THEY BOTH GOT BANNED?! HOW
solve the inequality for x
2x+5<5x-4
Answers
Answer:
x is greater than 3
Step-by-step explanation:
Answer:
2x + 5 < 5x - 4
5 + 4 < 5x -2x
9 < 3x
3 < x
hi! please help i’ll give brainliest
Answers
Answer:
give brainliest
Step-by-step explanation:
then i help
h(v)=5v2–28v+11, use synthetic division to find h(4).
Answers
Answer:
h(4)=-21
Step-by-step explanation:
h(v)=5x^2-28v+11
h(4)=5(4)^2-28(4)+11
h(4)=5(16)-112+11
h(4)=80-101
h(4)=-21
If this helps please mark as brainliest
Colton has a stone paperweight composed of a triangular pyramid on top of a triangular
prism with the dimensions shown below. Use the drop-down menus to explain how to
determine the volume of the paperweight.
Answers
Answer:
1/2 * 5 * 5
4
1/3, 7
79 in³
Step-by-step explanation:
The area of the base : base is shaped like a triangle ;
Area of triangle = 1/2 base * height :
Base and height = 5
Area of base = 1/2 * 5 * 5 = 12.5 in²
Volume of triangular prism = Area of base * height
Volume of triangular prism = 12.5 * 4 = 50 in³
For the triangular pyramid :
Area of base * height of pyramid *1/3
12.5 * 7 * (1/3) = 29.17
The volume of the paperweight :
Volume of triangular pyramid + volume of triangular prism
29.17 + 50
79.17 = 79 in³
What is the value of x if 2x - 3 = 15?
Answers
You add 3 to both sides which leaves you with 2x=18 and then divide by two and that gives you x=9
In a standard deck of card there are 52 cards total. Find the number of possible 5 hand cards that contain 3 queens and 2 kings.
Answers
Answer:
The probability of choosing 3 kings and 4 queens out of the 8 (4+4) kings and queens is given by 0.42857
Step-by-step explanation:
There are 4 queens and 4 kings in a deck of 52 cards. So we have to choose 5 cards having 3 queens and 2 kings out of the 52
Therefore the combinations can be written like this 8C5= 56 ways
And the probability this can be chosen is given by
4C3*4C2/8C5
=4*6/56
=24/56
=0.42857
The probability of choosing 2 kings and 3 queens out of the 8 (4+4) kings and queens is given by 0.42857 or 24/56
What is the measure of the unknown angle?
Answers
Answer:
55 degrees is the measure of the unknown angle
c(n) = -6(-1/3)^n-1 Which is the 2 or term of the succession?
Answers
Answer:
the first term will be n=1 and the second term is n=2
Step-by-step explanation:
Hope this is Helpful! :)
Have a nice day!
Can you plz help me!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
10 ft
Step-by-step explanation:
This is the Pythagorean theorem. a²+b²=c².
8²=64
6²=36
Now we add 64+36=100. Square root 100 to get 10 ft. (The answer is squared before so we have to square root it)
Please help thanks!!!
Answers
Answer:
Parallelogram
Step-by-step explanation:
Find the area of a triangle with base of 10 inches and a height of 5 inches.
100 square inches
B 50 square inches
C) 25
square inches
D 12.5 square inches
Answers
Answer:
25 square inches
Step-by-step explanation:
just divide your base by 2 and then multiply it by the height
math question please help
Answers
Answer:
a. 4
b. 132
Step-by-step explanation:
Plugg in the equation in desmos graphing calculator and the find the vertex to find the answer.
(Are you doing this in pearson?)
help please ill give you brainliest if it’s right
Answers
Answer:
[tex] \frac{1 }{3} \times \pi \times {4}^{2} \times 10 + \frac{1}{2} \times \frac{4}{3} \times \pi \times {4}^{3} = 6 \times \pi \times {4}^{2} = 301.44[/tex]
Classify this triangle by its sides.
Answers
Step-by-step explanation:
The answer is scalene triangle
what times twelve is exactly 30
the answer is most likely a mixed number
Answers
Answer:
2.5 or 2 and 1/2
Step-by-step explanation:
30/12 = 2.5
There are two wholes that fit in 30 with a remainder of half of a whole.
2.5 translates to 2 and 1/2
Answer:
Hello! answer: 2½
Step-by-step explanation:
Assuming you mean mixed number as in fraction I did 30 ÷ 12 = 2.5 and converted it to a mixed number and since 2½ × 12 = 30 the answer is 2½ Hope that helps!
12. Solve for x. (6x-21) P Q T S R
Answers
Answer:
x=4
Step-by-step explanation:
since its a square, the diagonals cut the right angle in half, so 45
6x - 21 = 45
6x = 24
x=4
6x-21=0
6x=21
Divide both side by 6 to leave x alone,
x=3.5
a debt that the company or entity enters into with the investors that pays the investors interest on that debt is refer as
Answers
Answer:
dividend,
Step-by-step explanation:
The population of a swarm of killer bees multiplies
10 fold in 50 days. Determine the correct
expression to calculate the number of bees after t
days if the initial swarm had 1000 bees.
Answers
Answer:
The correct expression to calculate the number of bees after t days if the initial swarm had 1000 bees is [tex]P = 1000 *e^{0.2*t}[/tex]
Step-by-step explanation:
Given -
The population of a swarm of killer bees increases by 10 times in 50 days
The rate of increase of population is [tex]r = \frac{10}{50} = 0.2[/tex] per day
As we now the equation of population projection is
[tex]P= P_0 *e^{rt}\\[/tex]
Where P0 = initial population
P is the population after time t
and r is the rate of increase of population
Substituting the given values in above equation, we get -
[tex]P = 1000 *e^{0.2*t}[/tex]