Solve the triangle, find m∠A and m∠C. Round angles to the nearest degree.
m∠A= __∘
m∠C= __∘
Answers
Answer:
[tex]m\angle A=63^\circ\\m\angle C=26^\circ[/tex]
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of the triangle is called the hypotenuse and the other two sides are called the legs.
Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.
The cosine ratio is defined as:
[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]
Note the angle A of the figure has 17 as the adjacent leg and 38 as the hypotenuse, so we can directly apply the formula:
[tex]\displaystyle \cos A=\frac{17}{38}[/tex]
[tex]\cos A=0.4474[/tex]
Using a scientific calculator, we get the inverse cosine:
[tex]A=\arccos(0.4474)[/tex]
[tex]A\approx 63^\circ[/tex]
Since A+B+C=180°, we can solve for C:
C = 180° - A - B
C = 180° - 63° - 90°
C = 26°
Thus:
[tex]m\angle A=63^\circ\\m\angle C=26^\circ[/tex]
In the given right triangle ABC, m∠A ≈ 26.44° and m∠C ≈ 63.56°.
To solve the right triangle ABC, we can use trigonometric ratios. In a right triangle, the three main trigonometric ratios are:
1. Sine (sin): [tex]\(\sin(\theta) = \frac{{\text{opposite side}}}{{\text{hypotenuse}}}\)[/tex]
2. Cosine (cos): [tex]\(\cos(\theta) = \frac{{\text{adjacent side}}}{{\text{hypotenuse}}}\)[/tex]
3. Tangent (tan): [tex]\(\tan(\theta) = \frac{{\text{opposite side}}}{{\text{adjacent side}}}\)[/tex]
Given:
AC = 38
AB = 17
To find the angles m∠A and m∠C, we can use the sine and cosine ratios, respectively.
1. For m∠A:
[tex]\(\sin(m\angle A) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle A= \sin^{-1}\left(\frac{{17}}{{38}}\right)\)[/tex]
2. For m∠C:
[tex]\(\cos(m\angle C) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle C = \cos^{-1}\left(\frac{{17}}{{38}}\right)\)[/tex]
Let's calculate the angles:
[tex]1. \(m\angle A \approx \sin^{-1}\left(\frac{{17}}{{38}}\right) \approx 26.44^\circ\)\\\\2. \(m\angle C \approx \cos^{-1}\left(\frac{{17}}{{38}}\right) \approx 63.56^\circ\)[/tex]
Therefore, m∠A ≈ 26.44° and m∠C ≈ 63.56° (rounded to the nearest degree).
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Plz plz help help help plz plz help plz
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since your adding to hours each time youll have 11, then the answer would be d the last one :)
Step-by-step explanation:
Answer:25.50 an hour
Step-by-step explanation:
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The answer is A because a number on it's own is a constant (30) and a number with a variable is a coefficient (12h)
16/21 decimal rounded to the nearest hundreth
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Answer:
0.76
Step-by-step explanation:
Hundredth is just the 2nd decimal point
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical. (3.-5) and (2-2)
А. -3, falls
В. 1/3, rises
C. 3, rises.
D. -1/3, falls
Answers
Answer:
Slope of line having points (3,-5) and (2,-2) is 3 and since the slope is positive do it rises. Option C is correct option.
Step-by-step explanation:
The formula calculate to find slope is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given points (3,-5) and (2,-2) so,
[tex]x_1=3, y_1=-5, x_2=2, y_2=-2[/tex]
Putting values in formula and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{-2-(-5)}{2-3}\\Slope=\frac{-2+5}{1}\\Slope=3[/tex]
So, Slope of line having points (3,-5) and (2,-2) is 3 and since the slope is positive do it rises. Option C is correct option.
What is the sum of the first five prime numbers?
18
26
28
39
Answers
Answer for brainliest and 15 points
Answers
Answer:
1) C
2) O
3) P
4) T
5) I
6) C
7) P
8) S
9) A
10) L
11) T
12) E
13) L
Step-by-step explanation:
What is the answer to the following question?
1.8
2.2
3.3
4.12
?
Answers
Answer:
1.8
Step-by-step explanation:
1.8
please help .thanks
Answers
Answer:
2 and 1/5 is greater than 2.15
Step-by-step explanation:
This is true because 1/5 is equal to .20 which is greater than .15
Answer:
B, >
Step-by-step explanation:
2 1/5
2*5= 10+1= 11
11/5 vs 2.15
2.2 vs 2.15
2.2 > 2.15
find the slope
13. y=-x+0
14. y=(7/14)x+2
15. y=(2/4)x+1
16. y=3x-4
Answers
13) -1
14) 7/14
15) 2/4 or 1/2
16) 3
3x^2 + 2x^2=
6x^3 - 2x^3=
first answer gets brainiest :)
Answers
Answer:
1) [tex]13x^{2}[/tex]
2) [tex]208x^{6}[/tex]
Step-by-step explanation:
(3*3(x)^2) + (2*2(x)^2) = 9x^2 + 4x^2 = 13x^2
(6*6*6(x)^3) - (2*2*2(x)^3) = 216x^3 - 8x^3 = 208x^3
Line M is represented by the following equation: x − y = 8
Which equation completes the system that is satisfied by the solution (18, 10)? (4 points)
a
2x − y = 26
b
x + y = 18
c
2x − 2y = 36
d
x − y = −28
Answers
Answer:Let's plug in (18,10) into each answer choice until we find the one that has it as a solution.
A) 2x - y = 26
2(18) - 10 = 26
36 - 10 = 26
26 = 26
Your answer is A.
I'll just do the rest to show that you the they are incorrect.
B) x + y = 18
18 + 10 = 18
28 ≠ 18
C) 2x - 2y = 36
2(18) - 2(10) = 36
36 - 20 = 36
16 ≠ 36
D) x - y = -28
18 - 10 = -28
8 ≠ -28
Your answer is A) 2x - y = 26.
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
2(18) - (10) = 26
36 - 10 = 26
Describe the transformation that moved Figure A to Figure B?
A) Reflect over the x-axis
B) Reflect over the y-axis
C) Rotate 90 degrees clockwise about the origin
D) Rotate 180 degrees about the origin
Answers
Answer:
D
Step-by-step explanation:
Its kinda hard to explain but its the answer
What does (f+g)x mean?
Answers
Answer:
(f + g)(x) means f(x) + g(x)
General Formulas and Concepts:
Alg I
Function NotationCombining like termsAlg II
Composite FunctionsStep-by-step explanation:
(f + g)(x) is the number form of "f plus g of x", meaning that we add the functions f and g together respect to x.
Another way to write (f + g)(x) is f(x) + g(x), which is the number form of "f of x plus g of x", still meaning that we are adding the 2 functions together.
how many solutions are there to this problem
|m-2|=2
Answers
Answer:
2 solutions
-4 and 4 are possible answers
Step-by-step explanation:
The sum of the digits of a two-digit number is 12. The number formed by reversing the digits is 54 more than the original number. What is the original number?
Answers
Answer:
39
Step-by-step explanation:
let the 2 digit number be ab = 10a + b ( considering place value )
The reversed 2 digit number is ba = 10b + a
The sum of the 2 digit number is
a + b = 12 ( subtract b from both sides )
a = 12 - b → (1)
Expressing as an equation
ba = ab + 54 , that is
10b + a = 10a + b + 54
Substitute a = 12 - b into the equation
10b + 12 - b = 10(12 - b) + b + 54 , simplify both sides
9b + 12 = 120 - 10b + b + 54
9b + 12 = - 9b + 174 ( add 9b to both sides )
18b + 12 = 174 ( subtract 12 from both sides )
18b = 162 ( divide both sides by 18 )
b = 9
Substitute b = 9 into (1)
a = 12 - 9 = 3
Thus
the original 2 digit number = ab = 39
The reversed 2 digit number = ba = 93
which is 54 more than the original number
The number of scares a clown will get for the night can be modeled with the equation `y=2x`. Vampires have an equation that is parallel to clowns and passes through the point (4, 11). What is the vampire's equation?
Answers
Answer:
ghvucycygifud5duvufysyvkcyxhvucydycibkx
Step-by-step explanation:
huh gg xtdy"#gicyfufucyxyhhjv ycyf cyst
Answer:
the answer is 3×2+2
Step-by-step explanation:
3x2=9+2=11
For Emily’s birthday, her father treated her and five friends to a dinner at a restaurant at the mall. Emily and her friends ordered three pizza dinners at $6.25 each and three chicken baskets at $7.50 each. All six people ordered soft drinks costing $1.25 each. The sales tax on the meal was 4.5%, and the tip was 15%. What was the total cost of the meal, including the sales tax and the tip?
Answers
Answer:
58.25
Step-by-step explanation:
C is the total cost of the meal, fifty-eight dollars and twenty-five cents.
First, find the cost of the meal, which is forty-eight dollars and seventy-five cents.
To calculate the amount of the sales tax, use the proportion, amount of sales tax divided by cost of meal equals sales tax rate divided by one hundred.
Substitute the known values. Amount of sales tax divided by forty-eight dollars and seventy-five cents equals four point five divided by one hundred.
Cross multiply. One hundred times amount of the sales tax equals forty-eight dollars and seventy-five cents times four point five.
Divide both sides by one hundred to find that the sales tax equals two dollars and nineteen cents.
Then, to calculate the amount of the tip, use the proportion, amount of tip divided by cost of meal equals tip percent rate divided by one hundred.
Again, substitute the known values into the proportion, amount of tip divided by forty-eight dollars and seventy-five cents equals fifteen divided by one hundred.
Then, cross multiply. One hundred times amount of tip equals forty-eight dollars and seventy-five cents times fifteen.
And, divide both sides by one hundred to find that the tip equals seven dollars and thirty-one cents.
Finally, add the amounts together to find the total cost of the meal was fifty-eight dollars and twenty-five cents.
Answer: 56.25
Step-by-step explanation:
Colton bounces a ball 3.268 feet infront of his feet. The path of the ball from the time it hits the ground until it lands on the floor is represented by
Answers
here is the complete and correct question. Colton bounces a ball 3.268 feet in front of his feet. The path of
the ball from the time it hits the ground until it lands on the floor is represented by
f(x) =-4(x - 5)2 + 12
Assuming that Colton's feet are located at the origin, (0, 0), what is the maximum height of the ball (in feet)?
Answer:
12ft
step by step explanation:
This equation has been written in vertex form, and it has its vertex at (5, 12). Because the scale factor is not positive, it has a negative value, the graph for the question is going to open downward, such that the vertex,
that is the maximum height is 12 ft.
we have The equation of a parabola with vertex (h, k) to be
f(x) = a(x -h)² + k
when put in Comparison to your question function, we get that
a=-4
h=5
k=12
so the vertex (h, k) = (5, 12).
The equation of the line in the graph is y= (blank) x+ (blank)
Answers
Q4. Find the range, standard deviation, and variance for the following sample data:
33, 55, 29, 40, 8, 90, 61, 41, 17, 80, 56, 17, 59, 21,78
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Answer:
40 I think but no I think
Why do people pretend they have depression, Depression is not something to joke about
Answers
Answer:
they want more attention than they already have,or they think its funny
Step-by-step explanation:
Answer:
It seems like most people joke about depression for attention.
Step-by-step explanation:
PLS HELP DUE TODAY i will give brailest if you show all work please help
Answers
Answer:
15) 3(4+r)=-18
3x4+3xr
12+3r= -18
-12 -12
3r= -30
/3 /3
r= -10
Step-by-step explanation:
distribute the 3 to the 4 and the r you should then have 12+3r=-18 and so subtract from both sides 12 and you should have 3r=-30 divide both sides by 3 and you get your answer r=-10
Answer:
(7) n=9
8) x=8
9) m=-7
10) b= -6
11) r=6
12)b=10
13)v=8
14)k=-8
15)r=-10
16)p=20
17)v=10
18)x=21
19)a=28
20)b=10
Step-by-step explanation:
Four identical right triangles whose sides measure 5x, 12x, and 13x are arranged to form a small square inside a large square, as shown. The perimeter of the large square is 17 units. What is the perimeter of the small square? Explain.
Answers
Answer:
The perimeter of the small square is approximately 9.154 units
Step-by-step explanation:
The given parameters are;
The sides of the four identical right triangles = 5·x, 12·x, and 13·x,
The perimeter of the large square = 17 units
Therefore, we have;
The hypotenuse side of the right triangles = The longest side = 13·x
The sides of the large square are formed by the hypotenuse sides of the right triangle
Therefore, the perimeter of the large square = 4 × 13·x = 52·x = 17 units
x = 17/52 ≈ 0.3269
x ≈ 0.3269 units
The sides of the small square = The difference between the longer and the shorter of the two legs = 12·x - 5·x = 7·x
∴ The sides of the small square = 7·x = (7 × 0.3269) units ≈ 2.2885 units
The perimeter of the small square = 4 × The sides of the small square
The perimeter of the small square ≈ (4 × 2.2885) units ≈ 9.154 units
The perimeter of the small square ≈ 9.154 units.
Anyone know how to do this, I’m lost!
Answers
Total angle degree for a parallelogram is 360 degrees
The angles added up is 6x
So 6x=360
X=60
The 4 angles inside EVERY 4-sided figure ALWAYS add up to 360 degrees.
Now you have been found !
A mixture of green paint contains 9 pints of blue paint and 12 pints of yellow paint. To make the same shade of green paint using using 21 pints of blue paint, how much yellow would you need?
Answers
Answer:
28 pints of yellow paint needed
Step-by-step explanation:
Mixture of green paint = 9 pints of blue paints : 12 pints of yellow paint
Blue paint : yellow paint = 9 : 12
To make the same shade of green paint using using 21 pints of blue paint, how much yellow would you need?
Let
x = pints of yellow pint needed
Blue paint : yellow paint = 21 : x
Equate the ratios to find x
Blue paint : yellow paint
9 : 12 = 21 : x
9/12 = 21/x
Cross multiplication
9 * x = 12 * 21
9x = 252
Divide both sides by 9
x = 252 / 9
= 28
pints of yellow pint needed = x
= 28
HELP PLS LOL !!!!!!!!!!!!!!
Answers
Answer:
try 137
Step-by-step explanation:
it may be congruent since they're parallel
Put these in order starting from the smallest
5^2 2^4 3^3 1^8
Answers
Answer:
1^8, 2^4, 5^2, 3^3 is the answer.
The numbers ordered from the smallest to the largest is [tex]1^{8} , 2^{4} , 5^{2} , 3^{3}[/tex].
What is the order of the numbers?In order to determine the order of the numbers, we have to solve for the numbers. The power of a number can be solved by multiplying a number by its number of power.
[tex]5^{2}[/tex] = 5 x 5 = 25
[tex]1^{8}[/tex] = 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 1
3³ = 3 x 3 x 3 = 27
[tex]2^{4}[/tex] = 2 x 2 x 2 x 2 = 16
To learn more about perfect squares, please check: https://brainly.com/question/22947195
Cody rented a bicycle from Cycle Factory for $65. How many hours did Cody rent the bike for if their cost is $16 to rent the bike plus $7 per hour?
Answers
Answer: Cody rented the bike for 7 hours.
Step-by-step explanation:
$65-$16=$49
$49/$7=7 hours
(2,-4), (x,\ y), A, and B all lie on the line. Find an equation relating x and y.
Answers
Answer:
I can't see the picture, sorry. :(
Step-by-step explanation:
Answer:
y=3/4x-5.5
Step-by-step explanation:
y=mx+b
B=starting point 5.5
x= variable
M=slope 3/4
Find m∠BOC in the figure if m∠AOC = 77°.
Question 18 options:
A)
71°
B)
18°
C)
65°
D)
59°
Answers
Answer:
Answer of this is... D... 59
According to the figure the value of ∠BOC is 59. So, the correct option is option D.
Given:
∠AOC = 77°
According to the figure ∠AOB = 3X and ∠BOC = 7X + 17
∠AOC = ∠AOB + ∠BOC.
Plugging the values in this equation.
Then we get,
77 = 3X + 7X + 17
Subtract 17 on both sides.
77 - 17 = 3X + 7X + 17 - 17
60 = 3X + 7X
After simplify we get,
60 = 10x.
X = 6
To find the ∠BOC.
∠BOC = 7X + 17.
Plugging the value of X in this equation.
∠BOC = 7 * 6 + 17
∠BOC = 42 + 17
∠BOC = 59.
Therefore, the value of ∠BOC is 59.
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