WILL GIVE BRAINLIEST! Given: ∆ABC, AB =√2. M ∈ AC, AM = 1. BM = 1, BC = 2. Find: m∠ABC
The measurement of ∠ ABC in [tex]\triangle ABC[/tex], When AB =√2, AM = 1. BM = 1, BC = 2 will be [tex](\cos^{-1}{5)[/tex].
The measures of angle ∠ ABC can be calculated as:
The Law of Cosines, states that:
[tex]c^2 = a^2+ b^2 - 2ab \cos (C)[/tex]
Where, c is the side opposite angle C, and a and b are the other two sides of the triangle.
The sides of ∆ ABC will be :
AB = [tex]\sqrt{2}[/tex] (given)
BC = 2 (given)
[tex]AC = 1 + \sqrt{MC}[/tex]
∆ ABC is a triangle and according to the triangle inequality theorem, the The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
So:
BC+AB > AC
[tex]2+\sqrt 2 > 1 + {\overline{MC}}[/tex]
[tex]\sqrt 2 +1 > \overline{MC}[/tex]
The law of cosines for [tex]\angle ABC[/tex] can be calculated as:
[tex]{BC}^2 = {AB}^2 + {AC}^2 - 2.AB.AC.cos(\angle ABC)[/tex]
The values can be obtained by the substitution.
[tex]2^2 = (\sqrt2)^2 + (1+{\overline {MC)}^2 - 2.\sqrt2 > (1 +{\overline{MC}).cos (\angle ABC)[/tex]
[tex]4 = 3 +2.\overline{MC} + \overline{(MC})^2 - 2. (\sqrt2. (1+ \overline{MC}).cos (\angle ABC)[/tex]
This can be simplified as:
[tex]0 = 3 + 2.\overline{MC} + \overline{MC})^2 - 2. (\sqrt2. (1+ \overline{MC}).cos (\angle ABC)[/tex]
The value of [tex]\overline{MC}[/tex] can be calculated as:
[tex]\sqrt 2+1 > \overline{MC}[/tex]
Substitute the value in the equation,
[tex]0 = 3+2.(\sqrt2+1) + (\sqrt2+1)^2 - 2.\sqrt2. (1+ \sqrt2+ 1).cos (\angle ABC)[/tex]
[tex]0 = 3+2 \sqrt2+4+2\sqrt2+1-2\sqrt2-2-2\sqrt2-2\sqrt2- 2.cos (\angle ABC)[/tex]
[tex]0 = 10 - 2.cos (\angle ABC)[/tex]
Thus, the value of cos [tex](\angle ABC)[/tex] is calculated as:
[tex]cos (\angle ABC) = \dfrac{10}{2}[/tex]
[tex]cos(\angle ABC) = 5[/tex]
Thus, the value of[tex](\angle ABC)[/tex] is [tex](\cos^{-1}{5)[/tex].
Learn more about angles here:
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Use the original price and the markdown to find the retail price.
Original price: $80; Markdown: 16%
Answer:
its b
Step-by-step explanation:
Answer:
The answer would be $67.2.
Step-by-step explanation: The answer would be $67.2. Take 80, divide it by 100 to get 1% of 80, 0.80. Now since you are taking 16% off the original price (100%), you multiply 0.80 (1%) by 84 (for 84% price), to get $67.2. This means, after the markdown, the 80$ item is now $67.2
Is there a proportional relationship between category 1 and Category 2 in the table below
Answer: Please upload the image or PDF.
if the tank length is 24 inch and width is 12 inch then how much litre of water is in it?
Answer:
Step-by-step explanation:
How to Estimate Aquarium Water Volume
You can estimate the amount of water that a tank can hold by using the volume formula for the shape of your tank. The process is similar to calculating tank volume for other tanks, but the formulas are a bit different for different aquarium shapes.
You’ll need a different formula to find the volume for rectangular, bow front, cylindrical, and other aquarium shapes.
Tank Volume Formulas
See the volume formulas for various aquarium fish tank styles below.
Rectangular Tank Formula
tank volume = l × w × h
l = tank length
w = tank width
h = tank height
1) Find the area of the shaded region
if the big diameter is 12 in, and the
small diameter is 8 in.
Answer:
the answer in 12 x 8÷2 =48
Help please serious answers only
Step-by-step explanation:
1 Use the Quadratic Formula.
x=\frac{2+2\sqrt{14}\imath }{30},\frac{2-2\sqrt{14}\imath }{30}
x=
30
2+2
14
,
30
2−2
14
2 Simplify solutions.
x=\frac{1+\sqrt{14}\imath }{15},\frac{1-\sqrt{14}\imath }{15}
x=
15
1+
14
,
15
1−
14
Done
Using pennies, nickels, and dimes, how many
ways can you make 16 cents?
Answer:
16 pennies, one dime and 1 nickel and 1 penny, 3 nickels and 1 penny.
Step-by-step explanation:
Answer:
1 dime, 1 nickel, 1 penny
Step-by-step explanation:
1 dime= 10 cents
1 nickel= 5 cents
1 penny= 1 cent
Help me with my math work please! Whoever helps gets 50 points! Thnx!
Answer:
6) y=-2
7) w=15
8) x=1
Help please (50 points)
Provide the missing statements and reasons for the following proof.
Theorem opposite slides of parallelograms are congruent
Answer:
R3. alternate interior angles
( alternate interior angles are always congruent )
S4. AC = CA
R5. ASA triangle congruence property
( you have 2 angles and the included side, so you know they're congruent )
lmk if you want an actual explanation
4000 families were randomly selected for a survey. 50% of them read the newspaper in nepali language, 45% read it in English language and 25% read in neither of these languages. How many families read the newspaper in both the languages? Also find the number of families who read exactly one of these papers.
Answer:
2000 families read the newspaper in the Nepali language.
1800 families read it in the English language.
3800 families read the newspaper in both.
Step-by-step explanation:
#1. individual
convert % to decimal ( x ÷ 100 )
0.5 x 4000 = 2000
0.45 x 4000 = 1800
#2. together
2000 + 1800 = 3800
OR
50 + 45 = 95
95 ÷ 100 = 0.95
0.95 x 4000 = 3800
HELP ME GUYS THANKS !
Answers:
-32
-8
-2
4
Step-by-step explanation:
[tex]y = 6x - 2[/tex]
[tex]y_1 = 6(-5) - 2 = -30 -2 = -32[/tex]
[tex]y_2 = 6(-1) - 2 = -6 -2 =-8[/tex]
[tex]y_3 = 6(0) - 2 = 0 -2 = -2[/tex]
[tex]y_4 = 6(1) - 2 = 6 -2 = 4[/tex]
Step-by-step explanation:
Ok so the function rule is: y=6x-2
We have 4 sets of numbers under the value "x." That means we have to input the given values into the function.
First is x=-5. We input -5 into the function so we get y=6(-5)-2. We multiply 6 and -5 and we get -30, then we subtract 2 from -30. Then for the answer for the first column, we get -32 for the y value.
Now we have x=-1. We input the number for x in the function and we get y=6(-1)-2. We multiply 6 and -1 and we get -6, then we subtract -2 from -6 and we get -8. So out y value for the second row is -8.
Try the next two on your own to see if you understand. If you still don't understand please comment under this answer. I'll try to respond as quickly as I can.
A line passes through the points (9,6) and (6,5). What is its equation in slope-intercept form?
Answer:
Y=X/3+3
Step-by-step explanation:
M= Y2-Y1/X2-X1
= 5-6/6-9
= -1/-3
= 1/3
sub x=6, y=5, M=1/3 into Y=MX+C
5=6/3+C
5=2+C
5-2= 2+C-2
3=C
any one is good at math can help :(
can somebody help me/tell me how to do these?
Hi! I'll try to help
It gives you two equations, one for "x" and one for "y"
All you have to do is replace the variable "y" with its value in the second equation. Might be kind of confusing so let's do one.
y=4x
3x-y=1
Since we know that "y" is the same as 4x, you can rewrite the equation as
3x-4x=1
Next, all you have to do is combine like terms as solve "3x-4x" which is -x
Let's rewrite the equation, then:
-x=1
You can simplify it to
x=-1
by dividing both sides by negative one, in other words swapping the negative sign so that "x" is positive
Find the total surface area of the cone in the figure. (Use π = 3.14.)
A) 219.8 cm2
B) 266.9 cm2
C) 314.0 cm2
D) 282.6 cm2
Answer:
282.6 cm^2
Step-by-step explanation:
typed it into a surface area calculator and I got the answer right
1) Derrick is sharing pizza with his 3 friends. They have 6/8 of a pizza. If they split the pizza evenly, how much pizza does each person get? Show your work with both a model and an equation.
Answer:
3/16
Step-by-step explanation:
So Derrick is sharing pizza with 3 friend, so in total, there are 4 people.
There is 6/8 pizza in current total pizza.
[tex]\frac{\frac{6}{8}}{4} =6/32=3/16[/tex]
Answer:
2/8
Step-by-step explanation:
each person would get 2/8
I need help. what is the slope?
(The bottom one says : (-1, -6)
what is the solution to the system of equations graphed below? y=-x+3 y=x-3
Answer:
x-3=-x+3
2x=6
x=3 y=0
the solution is the intersection of those two lines!
Set of ordered pairs: Is it a function? (yes no ) Why or why not? (0,3),(-1,4),(2,4),(0,8),(5,7)
Answer:
No
Step-by-step explanation:
A function cannot have two different points with the same x-coordinate. For instance in this one, (0,3) & (0,8) share the same value of x
PLEASE HELP!!!!!!.....
Answer:
x=2
Step-by-step explanation:
hope this helps! :D
to everyone reading this: have a miraculous day!! <3
Answer:
x=2
Step-by-step explanation:
..............
✌️❤️✌️
The rectangle and the trapezoid have the same area. What is the length l of the rectangle?
Please show work
Answer:
length = 18 ft
Step-by-step explanation:
A(rect) = 9l
A(trap) = 1/2(9)(24+12) → 4.5(36) → 162
9l = 162
l = 162/9
l = 18
=====================================================
How to get the answer:
We first need to compute the area of the trapezoid
area of trapezoid = height*(base1+base2)/2
A = h*(b1+b2)/2
A = 9*(12+24)/2
A = 9*(36/2)
A = 9*18
A = 162
The trapezoid has an area of 162 square feet.
---------
The rectangle also has an area of 162 sq ft.
area of rectangle = length*width
A = L*W
A/W = L
L = A/W
L = 162/9
L = 18
The length of the rectangle is 18 feet.
---------
Side note: both rectangle and trapezoid have the same height (9 feet). Notice how the average of the 12 ft and 24 ft sides leads to 18 ft, which is exactly the value of L. It's not a coincidence these two facts line up.
A 2 inch pulley on an an electric motor that runs at 600 rpm is connected by a non slip belt to a 4 inch radius pulley on a saw arbor. The radius of the saw blade is 8 inches.
A) Which of these quantities is the same for both the 2 inch and 4 inch radius pulleys? V, The Translational Speed OR W, The Rotational Speed.
B) Find the value of W in rads/min for the 2 inch radius pulley. Answer in terms of pi.
C) Find the value of W for the 4 inch radius pulley. Answer in terms of pi.
D) Find the Translational Speed, V, of a saw tath in inches/min. Answer in terms of pi.
B no ........................
how does 9 + 9 = 6 ?
Answer:
it does not, it equals 18
Step-by-step explanation:
9+9=18 - true
9+9=6 - false
What forms of the following equation in?
2x+3y=15
What is the value of t?
t − 122 = 2t − 3
A. t = -2
B. t = -6
C. t = 6
D. t = 2
Answer:
-39 2/3
Step-by-step explanation:
t - 122= 2t - 3
subtract 't' from each side to get:
-122 = 3t - 3
add 3 to each side to get:
-119 = 3t
divide each side by 3 to get:
t = -39 2/3
Adelita, Elena, Betina, and Bianca each work as a doctor, lawyer, teacher, or banker. From these clues, decide who is the doctor.
Answer: Adelita
Step-by-step explanation:
because if its going in order of the names by jobs then its adelita
For f(x) = 2x+1 and g(x) = x2 - 7, find (f+ g)(x).
=
A. x2 + 2x - 6
B. 2x3 - 6
C.x2 + 2x+8
D. 2x2 – 15
Answer:
the answer is A. it good answer
Which is the graph of y = [x]-2?
Answer:
Step-by-step explanation:
number 1
what is the number of terms for 1000z + 800y
Answer:
2 terms
Step-by-step explanation:
hope this helps! :D
have a MIRACULOUS day!! <3
Find the value of x for the following triangle. Give your answer to a whole number. (No decimal)
Answer:
12
Step-by-step explanation: