in triangle ABC, AC=13, BC=84, and AB=85. find the measure of angle C.
Answers
in triangle ABC, AC=13, BC=84, and AB=85. the measure of angle is C.5.1 degrees,
How can the angle be found?Using the The Law of Cosines in any triangle which can be expressed as;
[tex]c^2 = a^2 + b^2 - 2ab * cos(C)[/tex]
Then if we expressed the given sides in the cosine formula we have
[tex]13^2 = 85^2 + 84^2 - 2 * 85 * 84 * cos(C)[/tex]
Then we have [tex]169 = 7225 + 7056 - 14280 * cos(C)[/tex]
[tex]14280 * cosC = (7225 + 7056 - 169)[/tex]
[tex]cosC = \frac{14212}{ 14280}[/tex]
cos 0.9947
[tex]C = cos^-1(0.9947)[/tex]
C = 5.1 degrees
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Related Questions
PLEASE HELP WORTH 14 POINTS!
Answers
Answer:
180°
cuz when a line (I forgot the name) and radius meet at the circumference they from an angle of 90°
if a = { 1,2,3,...,10} and U={1,2,4,8} then find A'
Answers
Answer:
U-A empty
Step-by-step explanation:
all in a is in u in u is in a therfore empty is found on u but not in a
The solving to this question
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a) The resultant force on the particle is equal to - 225 · x, where x is measured in meters.
b) The particle moves with simple harmonic motion.
c) The motion has a period of approximately 1.257 seconds.
d) The particle has an approximate speed of 2.488 meters per second when it is 0.05 metres from C.
e) The equation for the position of the particle is x(t) = 0.5 · cos 25t, where t is in seconds.
How to analyze a system with a particle and two springs
In this case we have a system with a particle under periodic motion due to two reactive forces from two springs. a) The system is represented by the following formula based on Newton's laws:
∑F = - k₁ · x - k₂ · x = m · a (1)
Where:
k₁, k₂ - Spring constantsx - Distance of elongation, in metres. m - Mass of the particle, in kilograms.a - Net acceleration, in metres per square second.If we know that k₁ = k₂ = 112.5 N/m, then the resultant force on the particle is equal to - 225 · x, where x is measured in meters.
b) The particle is under simple harmonic motion has a differential equation of the form:
x'' + ω² · x = 0 (2)
Where:
x'' - Net acceleration, in metres per square second.x - Position of the particle, in metres.ω - Angular frequency, in radians.By some algebraic handling on (1), we find the following differential equation:
x'' + [(k₁ + k₂) / m] · x = 0 (3)
Thus, the particle moves with simple harmonic motion.
c) The period of the motion (T), in seconds, is determined by T = 2π / ω. Then, the period is described by the following expression:
T = 2π · √[m / (k₁ + k₂)]
T = 2π · √(9 kg / 225 N /m)
T ≈ 1.257 s
The motion has a period of approximately 1.257 seconds.
d) The speed of the particle (v), in metres per second, can be found by the principle of energy conservation:
(1 / 2) · k · A² = (1 / 2) · k · x² + (1 / 2) · m · v² (4)
v = √[k · (A² - x²) / m]
Where:
A - Amplitude, in metres.x - Particle position with respect to equilibrium position, in metres.If we know that k = 225 N / m, A = 0.5 m, x = 0.05 m and m = 9 kg, then the speed of the particle is:
v = √[(225 N / m) · [(0.5 m)² - (0.05 m)²] / (9 kg)]
v ≈ ± 2.488 m / s
The particle has an approximate speed of 2.488 meters per second when it is 0.05 metres from C.
e) The function position for a particle under simple harmonic motion:
x(t) = A · cos ω · t (5)
If we know that A = 0.5 m and ω = 25 rad / s, then the equation for the position of the particle is:
x(t) = 0.5 · cos 25t
The equation for the position of the particle is x(t) = 0.5 · cos 25t.
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Lisa has $7.80 to spend on some tomatoes and a loaf of bread. Tomatoes cost $1.20 per pound, and a loaf of bread costs $1.80.The inequality 1.20x + 1.80 ≤ 7.80 models this situation, where x is the number of pounds of tomatoes.Solve the inequality. How many pounds of tomatoes can Lisa buy
Answers
Answer:
At maximum, she can buy 5 tomatoes.
Step-by-step explanation:
If you solve the inequality, as so:
1.2x+1.8 <=7.8
1.2x <= 6
x <= 5
Which of the following is The function f(x)=2x2−1 is/has
A. order 2 rotational 2 symmetry about the origin
B. symmetry about the y-axis
C. neither symmetric about the y-axis nor has order 2 rotational symmetry about the origin
D. odds a good way to get someone to participate in a group?
Answers
The given function has symmetry about the y - axis.
Symmetry of the Function
If we reflect a function's graph about the y-axis, we will get the same graph since if the function is symmetrical about the y-axis. We can reflect a function about the x- and y-axis and obtain the same graph. These two symmetry kinds are known as the even function and odd function.
The given function is,
f(x) = 2x² - 1
It is an even function since the function remains same for both x and -x.
Putting f(x) = 0, we get,
2x² - 1 = 0
2x² = 1
x² = 1/2
x = ±1/2
⇒ Axis of symmetry is, x=0
Hence, the function f(x) is symmetric about y-axis.
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HELP ASAP
Question
Garret studies number of hours sleep per night among students who have a grade point average of 3.0–4.0 versus students who have a grade point average of 2.0–3.0.
His theory is that students who get more sleep will have a higher grade point average than students who get less sleep because they are more rested and, therefore, better able to concentrate.
In his samples, the mean number of hours of sleep students with a grade point average of 3.0–4.0 received each night was 6.8. The mean number of hours of sleep students with a grade point average of 2.0–3.0 received each night was 6.4.
Assuming there are no outliers or skew, do the results support Garret's theory?
Select from the drop-down menus to correctly complete the statements.
Since the samples were large and randomly chosen, we can use the samples to understand the populations.
Because the sample mean for students with a grade point average of 3.0–4.0 is
Choose...
a. less than
b. about the same
c.greater than
the sample mean for students with a grade point average of 2.0–3.0, the results
Choose...
a. tend to
b. do not tend to
Answers
The sample mean for students with a grade point average of 3.0–4.0 is greater than students with grade point average of 2.0 - 3.0, the results tend to
How to interpret Garret studies?From the question, we have the following highlights
The sample size is large enoughThe sample is at randomStudents who have a grade point average of 3.0 - 4.0 sleep for an average of 6.8 hoursStudents who have a grade point average of 2.0–3.0 sleep for an average of 6.4 hoursThere are no outliersFrom the above highlights, the sample mean for students with a grade point average of 3.0–4.0 is greater than students with grade point average of 2.0 - 3.0
This is because 6.8 is greater than 6.4
This means that Garret's theory about the hours of sleep is correct
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Sequence: 15, 19, 23, 27,...
an an-1 +4
C
a1
=
Answers
The recursive function o f the given sequence will be an = an-1 + 4
Recursive functionThe formula for calculating the recursive function of n arithmetic sequence is expressed as
an = an-1 + d
Determine the common difference
d = 19 - 15 = 23 -19
d = 4
The recursive function o f the given sequence will be an = an-1 + 4
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I need to see the steps to the problem for me to fully get it
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The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)
How to find the result of a multiplication of two matrices
In this question we must apply the operation of multiplication of two matrices, whose definition is shown below:
[tex]\vec B\, \cdot \, \vec A[/tex], where [tex]\vec B \in \mathbb {R}_{n \times p}[/tex] and [tex]\vec A \in \mathbb{R}_{p \times n}[/tex] (1)
Where each element of the resulting matrix is equal to the following expression:
[tex]c_{(i, j)} = b_{(i, p)} \,\bullet\, a_{(p, j)}[/tex] (2)
Where the operator "[tex]\bullet[/tex]" represents a dot product.
Now we proceed to calculate each element of the matrix:
[tex]c_{(1, 1)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]
5 · 1 + 7 · 5 + 3 · (- 1)
37
[tex]c_{(1, 2)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]
5 · 7 + 7 · 2 + 3 · 2
55
[tex]c_{(1, 3)} = \left[\begin{array}{ccc}5&7&3\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]
5 · (- 3) + 7 · 1 + 3 · (- 4)
- 20
[tex]c_{(2, 1)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]
(- 3) · 1 + 7 · 5 + 9 · (- 1)
23
[tex]c_{(2, 2)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]
(- 3) · 7 + 7 · 2 + 9 · 2
11
[tex]c_{(2, 3)} = \left[\begin{array}{ccc}- 3&7&9\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]
(- 3) · (- 3) + 7 · 1 + 9 · (- 4)
- 20
[tex]c_{(3, 1)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}1\\5\\- 1\end{array}\right][/tex]
2 · 1 + 5 · 5 + 2 · (- 1)
25
[tex]c_{(3, 2)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}7\\2\\2\end{array}\right][/tex]
2 · 7 + 5 · 2 + 2 · 2
28
[tex]c_{(3, 3)} = \left[\begin{array}{ccc}2&5&2\end{array}\right] \,\bullet\,\left[\begin{array}{c}- 3\\1\\- 4\end{array}\right][/tex]
2 · (- 3) + 5 · 1 + 2 · (- 4)
- 9
The matrix [tex]\vec C[/tex] resulting from the multiplication between matrices [tex]\vec B[/tex] and [tex]\vec A[/tex] is equal to the matrix [tex]\left[\begin{array}{ccc}37&55&- 20\\23&11&- 20\\25&28&-9\end{array}\right][/tex]. (Correct choice: C)
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The graph shows f(x)and its transformation(x).
Enter the equation for g(x) in the box.
g(x) =
Answers
Using translation concepts, the equation for function g(x) given in the graph is:
[tex]g(x) = 2^{x + 2}[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The parent function for this problem is given as follows:
[tex]f(x) = 2^x[/tex]
From the graph, function g(x) was shifted 2 units left, hence x -> x + 2 and the definition is:
[tex]g(x) = 2^{x + 2}[/tex]
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5x6-3x²+7-2x6-3x6+4x² for x = -10
Answers
Answer:
Hope you like it. I have just wrote answers
please give detailed answer of the question.
Answers
The resulting coordinates for each row are (-2, 2), (0, 4),()2, 6), (6, 10) and (8,12) respectively
Functions and valuesGiven the linear function expressed as;
y = x + 4
where
x are the input values and y are the output values
If x = -2
y = -2+4
y = 2
The coordinate (x, y) will be (-2, 2)
If x = 0
y = 0+4
y = 4
The coordinate (x, y) will be (0,4)
If x = 2
y = 2+4
y = 6
The coordinate (x, y) will be (2, 6)
If x = 6
y = 6+4
y = 10
The coordinate (x, y) will be (6,10)
If x = 8
y = 8+4
y = 12
The coordinate (x, y) will be (8, 12)
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Will give brainliest
Answers
Answer:
Step-by-step explanation:
will give brainiest wrrwrwvrwvr
Which number line represents the solutions to |x + 4| = 2?
Answers
Answer: Option 1
Step-by-step explanation:
[tex]|x+4|=2\\\\x+4=\pm 2\\\\x=-4\pm 2\\\\x=-6, -2[/tex]
Solve Absolute Value.
| x + 4 | = 2
We know either x + 4 = 2 or x + 4 = −2
x + 4 = 2 (Possibility 1)
x + 4 - 4 = 2 - 4 (Subtract 4 from both sides)
x = -2
x + 4 = −2 (Possibility 2)
x + 4 - 4 = - 2 - 4 (Subtract 4 from both sides)
x = -6
Answer: x = - 2 or x = -6
Therefore we conclude that the solution of the exercise | x + 4 | = 2, is the first number line, since both results are negative.
Find the critical value needed to construct a confidence interval of the given level with the given sample size. Round the answer to at least three decimal places. Level 99%, sample size 10.
Answers
Answer:
1.894
3.169
2.064
3.690
Step-by-step explanation: 90% ; sample size = 8
Degree of freedom, df = n - 1
t(1 - α/2, 7) = t0.05, 7 = 1.894
The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1.
x –3 –2 0 1 2
h(x) 0 –23 –12 0 0
If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function?
h(x) = x3 + 6x2 + 11x – 6
h(x) = x3 – 7x + 6
h(x) = x3 – 7x – 6
h(x) = x4 + 2x3 – 7x2 – 8x + 12
Answers
The equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6
How to find the equation of a Polynomial?
From the given table, we see that the x-intercepts are;
(-3, 0), (1, 0) and (2, 0)
Now, we are told the the x-intercepts have a multiplicity of one which means they occur as roots only once. Thus, we can say that the roots in factor form are;
(x + 3), (x - 1), (x - 2)
Then, the polynomial will be;
h(x) = (x + 3) * (x - 1) * (x - 2)
h(x) = (x + 3)(x² - 3x + 2)
h(x) = x³ + 3x² - 3x² - 9x + 2x + 6
h(x) = x³ - 7x + 6
Thus, the equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6
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Which of the following sets shows all the numbers from the set {1, 2.5, 3, 4.5, 5} that make the inequality 3a + 4 ≥ 13 true?
{2.5, 3, 4.5}
{1, 2.5}
{3, 4.5, 5}
{4.5, 5}
Answers
3(3) + 4 ≥ 13
9 + 4 ≥ 13
13 ≥ 13
true
3(4.5) + 4 ≥ 13
13.5 + 4 ≥ 13
17.5 ≥ 13
true
3(5) + 4 ≥ 13
19 ≥ 13
true
What is the angle of rotation of the following figure?
Answers
This snow flake-like figure can be generated by rotating an end 60° five times around the center of the hexagon. There are two forms: (i) clockwise, (ii) counterclockwise.
What is the angle of rotation of a snow flake?
Geometrically speaking, snow flakes represent regular hexagons. Regular hexagons can divided into six concentric regular triangles, whose central angles have a measure of 60°. This fractal figure can be generated by rotating 60° five times around the center.
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the sum of two numbers is 55 and the difference is 15 what are the numbers
Answers
[tex]x + y = 55 \\ x - y = 15 \\ \\ 2x = 70 \: \: \: \: \: \: x = 35 \\ y = 55 - x = 55 - 35 = 20[/tex]
If HK and GJ are congruent, what is the measure of GOJ?
125 ° 80°
Answers
Answer:
80°
Step-by-step explanation:
Congruent means the same size, so we know that the angle of the shapes made by the lines HK and GJ are the same, meaning that the angle of GOJ is simply 80°.
Consider the probability that fewer than 26 out of 107 cell phone calls will not be disconnected. Assume the probability that a given cell phone call will not be disconnected is 25%.
Specify whether the normal curve can be used as an approximation to the binomial probability by verifying the necessary conditions.
Yes or no
please explain in detail how to do these
Answers
Since both np > 5 and n(1 - p) > 5, the normal curve can be used as an approximation to the binomial distribution.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The normal approximation can be used if:
np > 5.n(1 - p) > 5.In this problem, the parameters are:
n = 107, p = 0.25.
Hence:
np = 107 x 0.25 = 26.75.n(1 - p) = 107 x 0.75 = 80.25.More can be learned about the binomial distribution at https://brainly.com/question/24863377
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Trail A is 6 3/4 miles long. Trail B is 8 1/2 miles long. How many miles longer is Trail B than Trail A
Answers
Given the length of both trail, Trail B is 7/4 miles longer than Trail B.
How many miles longer is Trail B than Trail A?
Given that;
Length of Trail A = 6 3/4 = [ (6×4 + 3 )/4 = 27/4 miles Length of Trail B = 8 1/2 = [ (8×2 + 1 )/4 = 17/2 milesTo determine how many miles longer is Trail B more than Trail A, we subtract the length of tail A from Tail B.
Trail B - Trail A
17/2 - 27/4
17/2 is the same as; 34/4
34/4 - 27/4
We combine the numerators over common denominator
(34 - 27 )/4
7/4 miles
Given the length of both trail, Trail B is 7/4 miles longer than Trail B.
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Seven more than twice a number is six less than three times the same number
Answers
Answer:
13
Step-by-step explanation:
7+2x=3x-6
knowing this then you solve it
Step-by-step explanation:
7 more = + 7
twice a number = 2*x = 2x
6 less = -6
3 times the same number = 3 * x = 3x
Putting this together we get:
2x + 7 = 3x - 6
subtract two from both sides to isolate x
(-2x) + 2x + 7 = 3x - 6 (-2x)
7 = x - 6
add 6 to both sides to get your answer
7 (+6) = x - 6 (+6)
13 = x
or
x = 13
evaluate the sin, cos and tan for 120deg without using a calculator
Answers
Using equivalent angles, we have that the measures are given as follows:
[tex]\sin{120^\circ} = \frac{\sqrt{3}}{2}[/tex][tex]\cos{120^\circ} = -\frac{1}{2}[/tex][tex]\tan{120^\circ} = -\sqrt{3}[/tex]What are equivalent angles?Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
120º is in the second quadrant, hence the equivalent on the first quadrant is:
180º - 120º = 60º.
The sine on the second quadrant is positive, hence:
[tex]\sin{120^\circ} = \sin{60^{\circ}} = \frac{\sqrt{3}}{2}[/tex]
The cosine on the second quadrant is negative, hence:
[tex]\cos{120^\circ} = \cos{60^{\circ}} = -\frac{1}{2}[/tex]
The tangent is given by the sine divided by the cosine, hence:
[tex]\tan{120^\circ} = \frac{\sin{120^\circ}}{\cos{120^\circ}} = -\sqrt{3}[/tex]
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a 300-acre farm produced 20,000 bushels of corn last year. what is the minimum rate of production, in bushels per acre, that is needed this year, so the farm's two-year production total will be at least 49,100 bushels of corn?
Answers
The minimum production rate of bushels per acre of corn needed this year is 97 for two year's production to reach the goal of 49,100.
How to calculate the minimum production rate?To calculate the minimum production rate for this year, we must subtract the production rate of the previous year, with what is expected to be obtained this year.
49,100 - 20,000 = 29,100Then we must divide the minimum that must be obtained by the total area, by the 300 acres that we have, to know how much corresponds to each acre.
29,100 ÷ 300 = 97According to the above, each acre must produce 97 bushels of corn to reach the goal of 49,100 for both years.
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please help me with the question
Answers
Answer: [tex]\cos^{-1} \left(\frac{-22}{\sqrt{754}} \right)[/tex]
Step-by-step explanation:
[tex]a \cdot b=(3)(0)+(-4)(5)+(-1)(2)=-22\\\\|a| |b|=\sqrt{3^2 +4^2 +1^2} \sqrt{5^2 +2^2}=\sqrt{754}\\\\\therefore \cos \theta=\frac{-22}[\sqrt{754}}\\\\\theta=\cos^{-1} \left(\frac{-22}{\sqrt{754}} \right)[/tex]
Which of the following systems of linear inequalities is represented by the
solution graphed below?
A. y>2 and ysx
B. y 22 and y
C. x>2 and y2x
D. x22 and y> x
Answers
Answer: B
Step-by-step explanation:
The line y=2 is solid and shaded above, so it represents [tex]y \geq 2[/tex].
This allows us to eliminate all the options except for B.
Cycles travel at an the average speed of 20km/h for 1.5 Hours
calculate the distance she travels in 1.5
Answers
Answer:
30 km
Step-by-step explanation:
Distance = rate x time
Distance = 20 x 1.5
Distance = 30
[tex]20*1.5=30[/tex] [tex]km[/tex]
Correct answer:-
Avg. speed = [tex]20km/h[/tex]
Time = [tex]1.5 hour[/tex]
Distance traveled in 1.5 hours is Distance = Speed x Time
So,
[tex]D = 20 * 1.5 = 30.[/tex]
reference link-
a cyclist travels at a speed of 20 km per hour how far will he ...https://brainly.in › Math ›
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solve this pleas i need urgent answer
Answers
Answer:
f(n)={n/2 = if n is even= n={2/2
{3n+1 {3(2)+1 =7
Step-by-step explanation:
if n is even u can put any even no in that place and u can get odd no or even no.(i think)
Which equation could possibly represent the graphed function?
Answers
Answer: A
Step-by-step explanation:
The polynomial has roots at [tex]x=-4, -2, 4[/tex].
So, the equation should have factors of [tex](x+4), (x-2), (x-4)[/tex].
This eliminates everything except for A.
the sum of a number increased by three and the number decreased by seven
Answers
Answer is (n + 3) + (n - 7)
Simplified to 2n - 4
Using “n” for number