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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#SPJ12
PLEASE HELP! IT'S A GRAPH-TYPE QUESTION!
Answer:
Step-by-step explanation:
tell me numbersin order
Part 1:-
cost to park of a day is= $25+$43+$61+$79 =$208and the hourly rate to a paddle boat =208÷24=$8.6 per hour______________________
What will Lin pay if she rents a paddleboat for 3.5 hours and splits the total cost with a friend? Completethe explanation.The total cost to rent the boat will be
3.5 hours x $ 12 per hour + $ 5 =$47
if she spilt cost with a friend ,they will each pay$47 ÷ 2= $ 23.5
Which of these sets is a function ?
Answer:
A. trust me I did it and got 100
Answer:
D
since all the other 1st elements (Domains) of each ordered pairs are repeated in all options except D they are not functions.
In conclusion, a function is defined as a set of ordered pairs with wich each element of the domain has one unique y value.
6/7 is in simplest form
Answer:
6/7 is the simplest form.
Hope this helps :)
Jamal finds some dimes and quarters in his change purse. How much money (in dollars) does he have if he has 9 dimes and 4 quarters? How much money (in dollars) does he have if he has xx dimes and yy quarters?
Answer:
$1.90
10xx+25yy cents
Step-by-step explanation:
9 dimes (10 cents each) = 90 cents = 0.9 dollars
4 quarters (25 cents each) = 100 cents = 1 dollar
Making $1.90
xx dimes (10 cents each) = 10xx cents
yy quarters (25 cents each) = 25yy cents
Making 10xx+25yy cents in total I believe..
Hope this helps :)
Pls answer these questions
Answer:
I believe the answers are
B) 1
D) $1,000
Step-by-step explanation:
Answer plz I need the answer
Answer:
D) 3x + 33
Step-by-step explanation:
3(x + 11)
3x + 33
Hope this helps! Pls give brainliest!
PLEAAAAASSEEEEEEEEEEE
im held captive._.
The inequality that models the situation is:
[tex]15000 + 4s \geq 450000[/tex]
Solving it, it is found that they need to sell at least 108,750 shirts.
During the day:
They earned 15000 in mask sales.They will sell s shirts, and earn a total of of 4s.Hence, the earnings are:
[tex]T = 15000 + 4s[/tex]
They want to earn at least 450,000, hence:
[tex]T \geq 450000[/tex]
[tex]15000 + 4s \geq 450000[/tex]
Solving it:
[tex]15000 + 4s \geq 450000[/tex]
[tex]4s \geq 435000[/tex]
[tex]s \geq \frac{435000}{4}[/tex]
[tex]s \geq 108750[/tex]
They need to sell at least 108,750 shirts.
A similar problem is given at https://brainly.com/question/24514895
what is cosec32°/sec58°=
Answer:
1
Step-by-step explanation:
Using the cofunction identity
sec(90 - x) = cosecx , then
sec(90 - 58)° = cosec32° , so
[tex]\frac{cosec32}{sec58}[/tex]
= [tex]\frac{cosec32}{cosec32}[/tex]
= 1
Which pair of triangles must be similar?
Triangle 5 has a 30∘ angle and a 90∘ angle. Triangle 6 has a 30∘ angle and a 70∘ angle.
Triangles 1 and 2 each have a 35∘ angle.
Triangle 7 has a 50∘ angle and a 25∘ angle. Triangle 8 has a 50∘ angle and a 105∘ angle.
Triangles 3 and 4 are both isosceles. They each have a 40∘ angle.
Brendan says that the negative of - 1/3
is 3 because they are on opposite sides of zero when they are plotted on the number line.
Is Brendan correct? Explain your answer.
Answer:
No! Brendan has totally got the wrong idea.
Step-by-step explanation:
Numbers on the right hand side of zero are said to be positive, while, the numbers on the opposite side are said to be negative.
That means Brendan's correct in saying that -1/3 lies on the opposite side of 3, since negative numbers lie on the opposite side of the positives.
But,
Negative "of" a number is the same number with opposite sign.
That is, if a number is 3 units away from the zero, it's negative will also be 3 units away from zero, but on the opposite side.
-1/3 and 3 do not lie at the same distance from zero.
-1/3 would be approached before -1 by walking in the negative direction whereas 3 would be approached after 1.
Therefore, Brendan is wrong as the negative of a number has opposite sign but same "magnitude".
Just help me on 6 and 7 please
6) [tex]\frac{9}{4}[/tex] ÷ [tex]\frac{5}{8} \\[/tex] = [tex]\frac{9}{4} . \frac{8}{5} = \frac{9.4.2}{4.5} =\frac{18}{5}[/tex]
7) [tex]2\frac{1}{2}[/tex] ÷ [tex]4\frac{1}{2}[/tex] = [tex]\frac{5}{2}[/tex] ÷ [tex]\frac{9}{2}[/tex] = [tex]\frac{5}{2} .\frac{2}{9}=\frac{5.2}{2.9} =\frac{5}{9}[/tex]
ok done. Thank to me :>
Mrs. Owens had to call the local plumber to install a hot water heater. the equation y= 50x+75 is the relationship between his hours worked (x) and the amount of the bill (y).A. How much money did the plumber charge for the service call? How can you tell from the equation?B. How much is the plumber charging per hour? How can you tell from the equation?
Answer:
A. He charges 75 dollars for the service call because the y-intercept of the equation is 75.
B. He charges 50 dollars per hour because the slope of the equation is 50.
Step-by-step explanation:
8x-5y=15
6x+4y=43
solve the system by any method
Answer:
[tex]x=\frac{275}{62}[/tex] , [tex]y=\frac{127}{31}[/tex]
Step-by-step explanation:
I will use the elimination method.We want to make the X's the same:
[tex]24x-15y=45[/tex]
[tex]24x+16y=172[/tex]
Because the signs of the X's are the same we subtract the 2 equations to make:
(I put the second one on top of the 1st)
[tex]31y=127[/tex]
So:
[tex]y=\frac{127}{31}[/tex]
Substitute y into either equation 1 or 2:
(I chose equation 1)
[tex]8x-5(\frac{127}{31})=15[/tex]
[tex]8x=5(\frac{127}{31}) + 15[/tex]
[tex]x=\frac{5(\frac{127}{31})}{8}[/tex]
So:
[tex]x=\frac{275}{62}[/tex]
this is the question.
solve (3.4)x(0.2)
Answer:
0.68
Step-by-step explanation:
Answer:
0.68
Step-by-step explanation:
In the accompanying diagram, overline BA perp overline BD and overline BC perp overline BE Which statement is true?
The measure of angle 1 is equal to angle 3
From the diagram, if BA is perpendicular to BD, then;
m<1 + m<2 = 90 degreesSimilarly, if BC is perpendicular to BE, then;
m<2 + m<3 = 90 degreesEquating both expressions will give:
m<1 + m<2 = m<2 + m<3Subtract m<2 from both sides
m<1 + m<2 - m<2= m<2 + m<3 - m<2
m<1 = m<3
Hence the measure of angle 1 is equal to angle 3
learn more on perpendicular lines here: https://brainly.com/question/1202004
please help ! 20 pts please
The given ratios expresses the number of time a value is larger or smaller
than another value.
The correct responses are;
3. (B) 12 and 244. (D) 6, 9, 215. [tex]\underline{(E) \ \displaystyle \frac{11}{2}}[/tex]6. [tex]\underline{(E) \ \displaystyle \frac{5}{14}}[/tex]7. (B) [tex]\overline{EF}[/tex] = 6, [tex]\overline{AC}[/tex] = 9·√58. (C) The values are equal9. (A) The value in column A is greaterReasons:
3. Given that the perimeter of the rectangle = 72
The ratio of the lengths of the sides = 1:2
Let a and b represent the sides, we have;
2·a + 2·b = 72
[tex]\displaystyle \frac{a}{b} = \mathbf{\frac{1}{2}}[/tex]
Which gives;
2·a = b
2·a + 2·(2·a) = 72
6·a = 72
a = 72 ÷ 6 = 12
b = 2·a = 2 × 12 = 24
The lengths of the sides are; (B) 12 and 24
4. Extended ratio = 2:3:7
The perimeter = 36
The lengths of the sides are;
[tex]\displaystyle \frac{2}{2 + 3 + 7} \times 36 = \mathbf{6}[/tex]
[tex]\displaystyle \frac{3}{2 + 3 + 7} \times 36 = \mathbf{9}[/tex]
[tex]\displaystyle \frac{7}{2 + 3 + 7} \times 36 = \mathbf{21}[/tex]
The lengths are; (D) 6, 9, 21
5. The given equation is presented as follows;
[tex]\displaystyle \frac{5}{x + 7} = \mathbf{\frac{3}{x + 2}}[/tex]
5 × (x + 2) = 3 × (x + 7)
5·x + 10 = 3·x + 21
5·x - 3·x = 21 - 10
2·x = 11
[tex]\displaystyle x = \mathbf{ \frac{11}{2}}[/tex]
The correct option is; [tex]\displaystyle \underline{(E) \ \frac{11}{2}}[/tex]
6. The width to length ratio is [tex]\displaystyle \mathbf{\frac{2.5}{7.0}}[/tex]
The simplified ratio is therefore;
[tex]\displaystyle \frac{2.5}{7.0} = \frac{2 \times 2.5}{2 \times 7.0} = \mathbf{\frac{5}{14}}[/tex]
The correct option is (E) [tex]\displaystyle \underline{(E) \ \frac{5}{14}}[/tex]
7. The given ratio of the lengths is 3:1
Therefore;
[tex]\overline{BC}[/tex]:[tex]\overline{EF}[/tex] = 3:1
Which gives;
[tex]\displaystyle \mathbf{\frac{\overline{BC}}{\overline{EF}}} = \frac{3}{1}[/tex]
[tex]\overline{BC}[/tex] = 18
Therefore;
[tex]\displaystyle \frac{18}{\overline{EF}} = \frac{3}{1}[/tex]
18 × 1 = 3 × [tex]\overline{EF}[/tex]
[tex]\displaystyle \overline{EF} = \frac{18 \times 1}{3} = 6[/tex]
[tex]\overline{EF}[/tex] = 6
By Pythagorean theorem, we have;
[tex]\overline{DF}[/tex]² = [tex]\mathbf{\overline{DE}}[/tex]² + [tex]\mathbf{\overline{EF}}[/tex]²
Which gives;
[tex]\overline{DF}[/tex]² = 3² + 6² = 45
[tex]\overline{DF}[/tex] = √(45) = 3·√5
Using the given ratio, we have;
[tex]\overline{AC}[/tex] = 3 × [tex]\mathbf{\overline{DF}}[/tex]
Which gives;
[tex]\overline{AC}[/tex] = 3 × 3·√5 = 9·√5
[tex]\overline{AC}[/tex] = 9·√5
The correct option is; (B) [tex]\overline{EF}[/tex] = 6, [tex]\overline{AC}[/tex] = 9·√5
8. EF = 1, AB = 2
CD = 2, CE = 4
Therefore;
[tex]\displaystyle \mathbf{\frac{EF}{AB}} =\frac{1}{2}[/tex]
[tex]\displaystyle \mathbf{\frac{CD}{CE}} =\frac{2}{4} = \frac{1}{2}[/tex]
Which gives;
[tex]\displaystyle \frac{EF}{AB} =\displaystyle \mathbf{\frac{CD}{CE}}[/tex]
(C) The values are equal
9. AC = 6, BE = 8
DF = 3, BD = 6
Column A
[tex]\displaystyle \frac{AC}{BE} =\displaystyle \mathbf{\frac{6}{8}} = \frac{3}{4}[/tex]
Column B
[tex]\displaystyle \frac{DF}{BD} =\displaystyle \mathbf{\frac{3}{6}} = \frac{1}{2}[/tex]
[tex]\displaystyle \frac{3}{4} > \mathbf{\frac{1}{2}}[/tex]
Therefore;
Column A is greater than column B
(A) The value in column A is greater
Learn more about ratios here:
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-233.2 - 25.8
Please help.
Answer:
-259
Step-by-step explanation:
brainliest
Answer:
-259
Step-by-step explanation:
Subtracting a negative number is the same as adding a positive number — that is, go up on the number line. This rule works regardless of whether you start with a positive number or a negative number.
When subtracting a negative number, remember that the two back-to-back minus signs cancel each other out, leaving you with a plus sign.
Subtracting Negative and Positive Integers
To subtract integers, change the sign on the integer that is to be subtracted.
If both signs are positive, the answer will be positive.
Example: 14 - (-6) = 14 + 6 = 20
If both signs are negative, the answer will be negative.
Example: -14 - (+6) = -14 - 6 = -20
If the signs are different subtract the smaller absolute value from the larger absolute value. The sign will be the sign of the integer that produced the larger absolute value.
Example: 14 - (+6) = 14 - 6 = 8
Example: -14 - (-6) = -14 + 6 = -8
What does: 8w+22=34 equal?
Answer:
3/2
HOPE I HELPEDD
Answer:
w= 1 1/2
I dont know if thats the question youre asking, if its not tell me.
The length of a rectangle exceeds its width by four inches. Find the dimensions of the rectangle if its area is 96 square inches.
Answer:
the width is 8
Step-by-step explanation:
I know this because 12×8 is 96
and 12 exceeds 8 by 4, that's how I came up with it
Length-12 in
Width-8 in
Area-96 square inches
can someone help me with this
Answer:
equation: (4x +8)° = (2x +3)° +51°exterior angle: 100°Step-by-step explanation:
The relevant relation is "the exterior angle is equal to the sum of the remote interior angles." That means ...
(4x +8)° = (2x +3)° +51° . . . equation to solve for x
2x = 46 . . . . . . . . . . . . . divide by °, subtract 8+2x
x = 23 . . . . . . . . . . . . divide by 2
Then the exterior angle is ...
(4x +8)° = (4(23) +8)° = 100°
_____
Additional comment
Instead of solving for x, we can solve for (2x+3). We can do that by subtracting 5+2x from both sides to get 2x+3 = 49. Then the exterior angle is the sum 49+51 = 100 degrees. (We don't actually care about the value of x.)
What’s the difference between an event and in event handler
Answer:
There’s a subtle, but important difference between these 2 methods of handling events. If you’ll use the first method, event handlers, the difference is that if you add two event handlers for the same button click, the second event handler will overwrite the first and only that event will trigger
Step-by-step explanation:
i hope this answer your questions
There are 70 students in the school band. 40% of them are sixth graders, 20% are seventh graders, and the rest are eighth graders.
1. How many band members are sixth graders?
band members
2. How many band members are seventh graders?
band members
3. What percentage of the band members are eighth graders?
Answer:
1=28 students 2=14students 3=40%
Step-by-step explanation:
1. 70 students = 100%
7 students = 10%
28 students = 40%
28 students are sixth graders!
2.70 students = 100%
7 students = 10%
14 students = 20%
14 students are seventh graders!
3.Percentage of band that is eighth graders: 40+20=60% 100%-60%=40%
40% are eighth graders!
What is the degree measure of the angle formed by the hands of a clock at 7:30 PM?
Which choice is similar to the figure shown?
m is a positive integer and n is a negative integer. Which of these is always positive?
(picture posted below)
A. Only (i)
B. Only (ii)
C. Both (i) and (ii)
D. Cannot say
S ANSWER ASAP!! ILL MARK U BRAINLIEST!!!♡♡♡
Answer:
n
Step-by-step explanation:
it's simple mathematics that's the way it is
As promised I I will be doing 100 points now please do NOT do anything that is not pertaining to the picture
what are 43.6÷8 use compatible numbers using the quotient
Answer:
7.3
Step-by-step explanation:
Regan cycles 78 miles in 6 hours.
His average speed for the first 30 miles is 15 mph.
Work out Regan's average speed for the last 48 miles.
Answer:
12 mph
Step-by-step explanation:
First 30 miles while cycling at 15 mph. This means he spent 2 hours here.
Thus the 4 hours on the last 48 miles.
Average speed = distance / time
Average speed = 48 miles / 4 hours
Average speed = 12 mph
Therefore Regan's average speed is 12 mph for the last 48 miles.
Please help other people are saying different answers and I 'm confused
Answer:
x ≈ 35.6
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos16° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{37}[/tex] ( multiply both sides by 37 )
37 × cos16° = x , then
x ≈ 35.6 ( to the nearest tenth )
