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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What is the measure of
Answer:
∠B = 82°Step-by-step explanation:
To find out ∠B, we need to find out what is ∠A. We are given one clue that the outer angle of ∠A is 143°. Can we use this clue and find out ∠A? Let's find out!
=> 180 - 143 = ∠A=> ∠A = 37°Since we have found ∠A, we can now find ∠B.
=> 61 + 37 + ∠B = 180=> 98 + ∠B = 180=> ∠B = 180 - 98=> ∠B = 82°Conclusion:
We have finally found out our answer and our answer is '∠B = 82°'.
[tex]GeniusUser[/tex]
You might need: 3 Calculator
2
Find the area of the shape.
Either enter an exact answer in terms of t or use 3.14 for it and enter your answer as a decimal.
units?
Answer:
90/360 x 3.14 x [tex]2^{2}[/tex]. (put into calculator)
Step-by-step explanation:
This is a sector of a circle we can see that there is a right angle (90 degrees) so we can say there is 90/360 of a circle.
The formula for the area of a circle is pi times radius squared.
We can use this but also need to use 90/360.
We can say the area of the shape is 90/360 x 3.14 x [tex]2^{2}[/tex].
Alesia reads 12 books over 6 months. After 8 months, how many books will she have read in all?
18 books
16 books
22 books
20 books
Solve the inequalities d/13_>-3
Answer:
d > -39
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
In mosquito, more itchy bites are dominate to less itchy bites. If a male mosquito with a heterogeneous, more itchy bite mates with a less itchy, homologous female, what will the offspring likely be like?
4 Points Total:
Key (assign letters and traits) 1
Correct Punnet square 1
Correct phenotype 1
Correct prototypes 1
Answer:
a rash
Step-by-step explanation:
Pls help: Write 2^100 as a power with the following base. For example: 4^50
1)16 2)32 3)1024
[tex]2^{100} = 16^{25} =32^{20} =1024^{10}[/tex]
P/s: [tex]2^{100} = 2^{4.25} =16^{25}[/tex] ......
ok done. Thank to me :>
∠A and \angle B∠B are vertical angles. If m\angle A=(2x-10)^{\circ}∠A=(2x−10) ∘ and m\angle B=(x+8)^{\circ}∠B=(x+8) ∘ , then find the measure of \angle A∠A.
Answer:
m∠B=52
∘
Step-by-step explanation:
Two or more angles are said to be complementary if they sum up to 90 degrees.
Given that angles A and B are complementary, then:
\begin{gathered}\angle A+\angle B=90^\circ\\m\angle A=(2x+18)^{\circ}\\m\angle B=(6x-8)^{\circ}\\$Therefore:\\(2x+18)^{\circ}+(6x-8)^{\circ}=90^\circ\\2x+6x+18-8=90^\circ\\8x+10^\circ=90^\circ\\8x=90^\circ-10^\circ\\8x=80^\circ\\$Divide both sides by 8\\x=10^\circ\\$Therefore:\\m\angle B=(6x-8)^{\circ}\\m\angle B=(6(10)-8)^{\circ}\\=60-8\\m\angle B=52^{\circ}\end{gathered}
The measure is the angles of a triangle are shown in the figure below. Solve for x
Answer:
30+48+x=180
x=102 ..........
..................
determine the intercepts of the line
Answer:
x-intercepts(-7,0)
y-intercepts(0,-2)
Step-by-step explanation:
Step-by-step explanation:
The x-intercept is (-7,0)
The y-intercept is (0,2)
Two parallel lines are crossed by a transversal. Vertical and parallel lines h and i are cut by transversal g. At the intersection of lines h and g, the uppercase right angle is 70 degrees and the bottom left angle is x degrees.
Answer:
x = 70
Step-by-step explanation:
803 to 2:12
1,460 to 4:00
753 to 1:30
are these proportional?!?
Answer:
no
Step-by-step explanation:
In terms of area per hour, Bob's works at the rate of ...
1460 ft²/(4 h) = 365 ft²/h
Rhonda's rate is ...
753 ft²/(1.5 h) = 502 ft²/h
The rates are different, so they are not proportional.
___
Additional comment
Toni's rate is 803 ft²/(2.2 h) = 365 ft²/h . . . the same as Bob's
Bob's and Toni's rates are proportional.
Allen's daily regular wage is P1,420. This coming Christmas, his boss is asking him to work for 14 hours. How much is his DAILY RATE on that particular day?
Php 1,420
Php 2,840
Php 2,420
Php 1,840
Using proportions, it is found that his DAILY RATE on that particular day is of Php 2,420 .
This question is solved by proportions, using a rule of three.In a regular 8-hour day, Allen earns Php 1420. How much will he earn on a 14 hour day?The rule of three is:
8 hours - Php 1420
14 hours - x
Applying cross multiplication:
[tex]8x = 1420 \times 14[/tex]
[tex]x = \frac{1420 \times 14}{8}[/tex]
[tex]x = 2485[/tex]
The closest option is Php 2,420.
A similar problem is given at https://brainly.com/question/24372153
Find the area of the trapezoid
Answer:
18000Step-by-step explanation:
Given,
Back of lot of the trapezoid = 175
Front of lot of the trapezoid = 185
Length of lot of the trapezoid = 100
Therefore,
Area of the given trapezoid
[tex] = \frac{a + b}{2} c[/tex]
[On putting values][tex] = \frac{175 + 185}{2} \times 100[/tex]
[On Simplification]= 360 × 50
[On multiplying]= 18000
Hence,
The required area of the given trapezoid is 18000 (Ans)
Jodie made a New Year's resolution to learn how to play the violin. She bought an
Introduction to Violin class pack from the Noble Notes music shop, which covers the cost of
12 violin lessons. She also paid $25 to rent a violin. In all, Jodie paid $385. How much does
each violin lesson cost?
Answer:
$30
Step-by-step explanation:
If x is the cost of a lesson, the total cost of Jodie's purchase is ...
cost of lessons + rental cost = total cost
12x + 25 = 385
12x = 360 . . . . . . . subtract 25
x = 30 . . . . . . . . . . divide by 12
Each violin lesson costs $30.
my Christmas present to you
Answer: ty
Step-by-step explanation:
1 lb = 0.45 kg
How many pounds are in 90.9 kilograms?
Answer:
200.4002 pounds
Step-by-step explanation:
Answer:
The answer is 200.4002
If you have to round to the nearest thousandth then it is 200.400
If you have to round to the nearest hundredth then it is 200.40
If you have to round to the nearest tenth then it is 200.4
I only need help on Question D
The ratio of United States gold medals to Russia gold medals was about to 1. If the US has 46 and Russia has 24, then what is the ratio
Answer;
23:12
Step-by-step explanation:
if USA has 46medals and Russia had 24medalso 46 : 24lowest term method 2in 46 23and 24/2is 12 answer 23 : 12The ratio between the US and Russia is 23:12
What is a ratio?The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given here US has 46 and Russia has 24 and thus the ratio is
46:24=23:12
Hence, the required ratio is 23:12
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Martin drank 2/3 liter of water Monday before going jogging.He drank 3/7 liter of water after his jog.How much water did Martin drank altogether?Write your answer as a mixed number.
I really need help it’s due in two days
Answer:
Step-by-step explanation:
The answer is "Impossible to solve" , because there is no rule for function at point x = 7 . The given function has domain ( - ∞ , 2 ) ∪ { 2 } ∪ ( 2 , 7 ) ⇒ 7 is not a part of domain!!!
What is 6x + 5x - 6 = 32 + 9x
Answer:
x = 19
Step-by-step explanation:
Step-by-step explanation:
6x + 5x - 6 = 32 + 9x
11x - 6 = 32 + 9x
Bringing like terms on one side
11x - 9x = 32 + 6
2x = 38
x = 38/2 = 19
Given the function below find f(0).
f(x)=x2−3x+5
Group of answer choices
-5
0
5
10
Answer:
5
Step-by-step explanation:
f(x) = x² - 3x + 5
f(0)
putting x as 0 in the equation
f(0) = 0² - 3(0) + 5
= 0 - 0 + 5
= 5
Solve for y.
y + 3 = 8y + 3
y =
[tex]y + 3 = 8y + 3[/tex]
Subtract both sides 3
[tex]y + 3 - 3 = 8y + 3 - 3[/tex]
[tex]y + 0= 8y + 0[/tex]
[tex]y = 8y[/tex]
Subtract both sides y
[tex]y - y = 8y - y[/tex]
[tex]0 = 7y[/tex]
Divide both sides by 7
[tex] \frac{0}{7} = \frac{7y}{7} \\ [/tex]
[tex]y = 0[/tex]
There you go....
Ah
Have a great day ♡
Lily hereeeeeeee (Rose's younger sister))))))))))
Please help me with mathhhhhh
the equation is 1 5/6 - 3/4
This is for a important test for advanced math in middle school
Answer:
1 1/12
Step-by-step explanation:
Make 1 5/6 improper fraction ( 1 times 6, then add 5 = 11)
Find common denominator, which is 24
6 times 4 equals 24; 11 times 4 equals 44
4 times 6 equals 24; 3 times 6 equals 18
44/24 - 18/24 (subtract only top numbers (44-18) = 26
26/24 simplified is 13/12 or 1 1/12
Hope it's right :)
43. Write a system of equations that is equivalent to each of the systems of equations below
2x + 3y = 4
12x+3y=1
X-7y=8
5x+4y=20
1.
The new system of equivalent equations are 4x + 6y = 8 and 12x + 3y = 1
To get an equivalent equation, we multiply the original equation by a constant and replace it with the new equation.
So, 2x + 3y = 4 (1)
12x + 3y = 1 (2)
We multiply equation (1) by 2
So, 2x + 3y = 4 (1) × 2
⇒4x + 6y = 8 (3)
Replacing (1) by (3), we have
4x + 6y = 8 (3)
12x + 3y = 1 (2)
So, the new system of equivalent equations are 4x + 6y = 8 and 12x + 3y = 1.
2.
The new system of equivalent equations are 3x - 21y = 24 and 5x + 4y = 20
To get an equivalent equation, we multiply the original equation by a constant and replace it with the new equation.
So,
x - 7y = 8 (1)
5x + 4y = 20 (2)
We multiply equation (1) by 3, we have
So, x - 7y = 8 (1) × 3
⇒3x - 21y = 24 (3)
Replacing (1) by (3), we have
3x - 21y = 24 (3)
5x + 4y = 20 (2)
So, the new system of equivalent equations are 3x - 21y = 24 and 5x + 4y = 20.
Learn more about equivalent equations here:
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HELPP PLEASEE! pleaseeeeee
Answer:
a = 14 km
Step-by-step explanation:
The area of a triangle is
A = 1/2 bh where b is the base and h is the height
112.7 = 1/2 ( a) 16.1
112.7 = 8.05a
Divide each side by 8.05
112.7/8.05 = a
14 =a
a = 14 km
bri bought a sweater for $7 for a 20% discount what was the original price?
Answer:
$200
Step-by-step explanation:
20% =$40; Since 5x20%=100% just multiply 5x $40 to get the total (before discount) cost of $200
One group of carolers goes to every 6th house in a neighborhood, another goes
to every 8th house. At which house will the first meet?
The carolers would meet first at the 24th house.
In order to determine in which house the carolers would meet, the multiple of 6 and 8 have to be determined. They would first meet at the first common multiple of 6 and 8.
A multiple of a number is the product of an integer and that number.
First ten multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54 and 60First ten multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, Least common multiple = 24To learn more about multiplies, please check: https://brainly.com/question/10520264
The sum of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?
Answer:
34
Step-by-step explanation:
Answer:
b=4 a=3
The first digit is 3 and the second 4 so the original number is 34
To be honest! It would be much quicker to solve by trial and error.
Explanation:
Building the equations
Let the first digit be
a
Let the second digit be
b
The first condition
a
+
b
=
7
...............................(1)
Step-by-step explanation:
What is 10Million divided 10Million its a very hard question you know.