Find csc 0, sin 0, and cot 0, where is the angle shown in the figure.
Give exact values, not decimal approximations.
PLZ HELP I BEEN STUCK FOR AN HOUR I WILL MARK BRAINLIEST!!!
Answers
Answers:
[tex]\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]
=============================================
Explanation:
Before we can find the trig ratios, we need to determine the length of the missing side. Apply the pythagorean theorem
[tex]a^2+b^2 = c^2\\\\4^2+b^2 = 7^2\\\\16+b^2 = 49\\\\b^2 = 49-16\\\\b^2 = 33\\\\b = \sqrt{33}[/tex]
The vertical side is [tex]\sqrt{33}[/tex] units long.
------------------------------------
The side we just found is the opposite side to angle [tex]\theta[/tex] (greek letter theta)
The hypotenuse is 7 units long. The hypotenuse is always opposite the right angle.
Divide the hypotenuse over opposite to get the cosecant.
[tex]\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{7}{\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33*33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33^2}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\[/tex]
Note: In the third step, I multiplied top and bottom by sqrt(33) to rationalize the denominator.
------------------------------------
Recall that sine is the reciprocal of cosecant, and vice versa.
So we'll use the same idea as before, but flip the original fraction.
[tex]\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\[/tex]
The denominator is already a rational number, so there's not much else to do here.
--------------------------------------
Cotangent is the ratio of adjacent over opposite
[tex]\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}}\\\\\cot(\theta) = \frac{4}{\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33*33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33^2}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]
The steps are pretty much nearly identical as the section involving csc, except we're using the adjacent in place of the hypotenuse (so that means we use 4 in place of 7).
Related Questions
A square prism has a height of 16 centimeters and a volume of 784 cubic centimeters. What is the length in centimeters of each side of the square base
Answers
Answer:
7cm
Step-by-step explanation:
Volume of a prism = base area x height
base area = area of a square = length²
784 = length² x 16
divide both sides of the equation by 16
length² = 784/16
length² = 49
find the square root of both sides
length = 7
What is 16.99 times 0.80
Answers
Answer:
Hi, there your answer is 13.592
Step-by-step explanation:
Please help me quick…
Answers
20- +3
21- -7
22- +4
23- 8
24- 4
ask your teacher for further guidance because explaining negatives is difficult for me
Answer:
20) - 2+5
= 3
21) 8+(-15)
=8 - 15
= - 7
22) - 10 +14
= 4
23) 6-(-2)
=6 +2
= 8
24) - 16-(-20)
= - 16 +20
= 4
Step-by-step explanation:
This is step by step explanation
Please Mark me brainlist
guys please help me i cant solve this logarithmic equation
Answers
Answer:
Step-by-step explanation:
I'll just write log for log base 10. The important rules about logarithms we need to know are:
[tex] a \log b = \log( b^a) [/tex]
[tex] \log a + \log b = \log( ab) [/tex]
and at the end we'll need something like
[tex]\log a = \log b \implies a=b[/tex]
Suitably armed we can begin,
[tex] \left( 1 + \dfrac{1}{2x} \right) \log 3 + \log 2 = \log (27 - 3^{1/x}) [/tex]
First rule,
[tex] \log 3^{ 1 + 1/2x} + \log 2 = \log (27 - 3^{1/x}) [/tex]
Second rule,
[tex] \log 2(3^{ 1 + 1/2x}) = \log (27 - 3^{1/x}) [/tex]
Third rule,
[tex] 2(3^{ 1 + 1/2x}) = 27 - 3^{1/x} [/tex]
We can rewrite this to be a quadratic equation in [tex]y=3^{1/2x}[/tex].
[tex] 6 (3^{1/2x}) = 27 - (3^{1/2x})^2 [/tex]
[tex]y^2 +6y - 27 =0[/tex]
[tex](y - 3)(y+9)=0[/tex]
[tex]y=3 \textrm{ or } y=-9[/tex]
First solution:
[tex]3^{1/2x} = 3 = 3^{1}[/tex]
[tex]1/2x = 1[/tex]
[tex]1=2x[/tex]
[tex]x = 1/2[/tex]
Second solution,
[tex]3^{1/2x} = -9[/tex]
No real powers of 3 will be negative, no solution here.
Answer: x=1/2
Check:
1 + 1/2x = 2 so the left side is log 2(3²) = log 18
Right side, log(27-3^2) = log 18 √
Which of the following number patterns uses the rule below
Each number in the pattern is four times the previous number
A.6,24,48,72
B.7,21,63,189
C.5,20,80,320
D.4,20,100,500
DO NOT ANSWER IF YOUR NOT AT ACE LEVEL
Answers
The answer to the question is C. 5,20,80,320
Step-by-step explanation:
5*4=20
20*4=80
80*4=320
A bag contains red and blue marbles, such that the probability of drawing a blue marble is 1/8 An experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome.
Answers
Answer:
Find the volume of this prism.
Answer:
24% or d
Step-by-step explanation:
WILL GIVE BRAINLIST
WRITE THE PHRASE AS A VARIABLE EXPRESSION. USE X TO REPRESENT “a number”
THE PRODUCT OF 4 AND A NUMBER
Answers
Answer:
x+14.
Sum of a number and 14 is x+14.
Solve this equation
2 . B - 19 = -11
Answers
Answer:
B=8
Step-by-step explanation:
you add 19 to both sides of the equation to get B by itself.
[tex]B=-11+19\\B=8[/tex]
answer:
8,
reason
11+8=19
alalalalalalalaalalalalal
20character minimum^
Please help find volume of cone
Answers
Answer:
5275.2 m³
Step-by-step explanation:
We need the radius first:
[tex]\sqrt{l^2- h^2}[/tex] = 12
Formula for volume = πr²*h/3
Volume = 3.14 * 144 * 35/3
Volume = 5275.2
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
A soccer field is 120 yards long and 60 yards wide. How long is the diagonal of the field?
Answers
Answer:
134.16 yards or 134.2 if you round to the nearest tenth
Step-by-step explanation:
Using the formula a^2+b^2=c^2
120^2+60^2=c^2
18000=c^2
the square root of 18000 is around 134.16.
Find the solution(s) to the system of equations represented in the graph.
A. (0, 3) and (3, 0)
B. (0, 3) and (−3, 0)
C. (0, −3) and (3, 0)
D. (0, −3) and (−3, 0)
Answers
Answer:
(-3,0) and (0,3)
Step-by-step explanation:
The solution to the system of equation is where the two graphs intersect
The intersect at two points
(-3,0) and (0,3)
i need help with this plz
Answers
Answer:
-4 is the correct answer
Answer:
y=18
Step-by-step explanation:
equation:y=3x -7
x=7 then y =?
substitute the vale of x in the equation
y=3x-7
y=3*7-7
y=21-7
y=18
therefore the value of y corresponds to 7 is 18.
A caterer charges a setup fee of $50, plus $20 per person How much will the caterer charge if 35 people attend the party, and the customer has a coupon for $100 discount off the total?
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20x35= 700
700+50 = 750
750-100= 650
Round 187.890 to the nearest 10 000
Answers
Answer:
190,000
190,000
190,000
Step-by-step explanation:
190,000
190,000
Calculate the area of triangle ABC with altitude CD, given A (−3, −4), B (−6, 2), C (0, 0), and D (−4, −2). (5 points)
Question 8 options:
1)
14 square units
2)
15 square units
3)
18 square units
4)
20 square units
Answers
Answer: 2) 15 square units
Step-by-step explanation:
The area of the triangle is 15 square units if the triangle ABC with altitude CD, given A (-3, -4), B (-6, 2), C (0, 0), and D (-4, -2) which is correct option (2)
What is the distance between two points?The distance between two points is defined as the length of the line segment between two places represents their distance. Most significantly, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.
The formula of distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by: d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².
Given that a triangle ABC with altitude CD.
The coordinates for the triangle are A (-3, -4), B (-6, 2), C (0, 0), and D (-4, -2)
Given that the distance between C and D will be the height of the triangle
Since, the distance between the points by using the distance formula:
= √ (x₂ – x₁)² + (y₂ – y₁) ².
height = √ (-4 – 0)² + (-2 – 0) ²
height = √20
base = √45
Area of triangle = (1/2)base x height
Area of triangle = (1/2)√20×√45
Area of triangle = (1/2)30
Area of triangle = 15 square units
Hence, the area of the triangle is 15 square units if the triangle ABC with altitude CD
Learn more about distance between two points here:
https://brainly.com/question/15958176
#SPJ2
A runs 25% faster than B and is able to give him a start of 7 metres to end a race in dead heat. What is the length of race?
Answers
Answer:
35 metres
Step-by-step explanation:
The question states that A runs 25% faster than B. This means that, for every 1 second that B runs, A runs 1.25 second
Assuming that the total length of the race, that we're looking for, is D. Then we can say that B made a total distance of D-7 meters, and A runs D.
time taken by A = [tex]\frac{D}{1.25}[/tex]
time taken by B = [tex]\frac{D-7}{1}[/tex]
equating both together, we have
[tex]\frac{D}{1.25}[/tex] = [tex]\frac{D-7}{1}[/tex]
1.25D - 8.75 = D
1.25D - D = 8.75
0.25D = 8.75
D = 8.75/0.25
D = 35
What do you get when you subtract-3xy from 5xy
Answers
Answer:
8xy
Step-by-step explanation:
(5xy)-(-3xy)= 5xy+3xy=8xy
Why:
Well if you have 5 of that something and get 3 more of that something you have 8 of that something.
Answer:
8xy
Step-by-step explanation:
5xy--3xy
a - and a - equal a +, so it's 5xy+3xy, which equels 8xy.
Can someone pleaseeee help and if you’re correct i’ll give brainliest
Answers
Answer:
70
Step-by-step explanation:
the figure shown is a parallelogram with a base length of 10 ft and a height of 7 ft
the area of a parallelogram can simply be calculated by multiplying the base length by the height
hence, area = 7 * 10 = 70
Answer: 10 times 7
Step-by-step explanation: 10 times 7
Select all of the following that are equivalent to 1 10,000 1 A. (10,000) B.(-10,000 D c. 100) ( O D. (10)
Answers
Answer:
A. 10,000
Step-by-step explanation:
A. is 10,000, so it is equivalent to 10,000
B. -10,000 No
C. 100 No.
D. 10 No.
On the number line below, length
AB = [?]
A
В
16
45
Answers
Answer:
29
Step-by-step explanation:
45 - 16 =
Recall what you know about similarity. If circle B is similar to circle A, what must exist?
Answers
The similarities of two circles is dependent on the radius of circle A and circle B. So the radius of both circles must exist for the circles to be similar.
Given that:
Circles A and B
To prove the similarities of the two circles, the radius of both circles must be known.
Assume the radius of circle A is [tex]r_A[/tex] and the radius of circle B is [tex]r_B[/tex].
The similarity of both circles is proved using:
[tex]r_A = k * r_B[/tex]
or
[tex]r_B = k * r_A[/tex]
where k represents the scale of dilation
Hence, the radius of both circles must exist for the circles to be similar.
Read more about circle similarities at:
https://brainly.com/question/403891
what is the average rate of change from x equals negative 1 to x equals 1
Answers
Answer:
This question is incomplete, so I can not give you an exact answer, but I can give you the answer for the general case.
If we have a function f(x), the average rate of change between the values:
x = a and x = b,
is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
So if we want to find the rate of change from:
x = -1 to x = 1
it is just:
[tex]r = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{f(1) - f(-1)}{2}[/tex]
So just to show an example, if:
f(x) = 3*x^2 - 5
the average rate of change in that interval will be:
[tex]r = \frac{f(1) - f(-1)}{2} = \frac{3*1^2 - 5 - (3*(-1)^2 - 5)}{2} = \frac{-2 - (-2)}{2} = 0[/tex]
What is the equation for a parabola if the vertex is at (5,4) and goes through the point (3,-8)
Answers
Answer:
[tex]y=-3(x-5)^2+4[/tex]
Step-by-step explanation:
Hi there!
Given the vertex of a parabola and a point, it's easiest to organize the equation in vertex form:
[tex]y=a(x-h)^2+k[/tex] where the vertex is located at [tex](h,k)[/tex] and a is a numerical value
1) Plug the vertex into the equation
[tex]y=a(x-h)^2+k[/tex]
Plug in the vertex (5,4)
[tex]y=a(x-5)^2+4[/tex]
2) Solve for a
[tex]y=a(x-5)^2+4[/tex]
Plug in the given point (3,-8) and solve for a
[tex]-8=a(3-5)^2+4\\-8=a(-2)^2+4\\-8=4a+4[/tex]
Subtract 4 from both sides
[tex]-8-4=4a+4-4\\-12=4a[/tex]
Divide both sides by 4
[tex]\frac{-12}{4} = \frac{4a}{4} \\-3=a[/tex]
Therefore, a=-3. Plug this back into [tex]y=a(x-5)^2+4[/tex]:
[tex]y=-3(x-5)^2+4[/tex]
I hope this helps!
Hey can someone help with this? It’s Khan Academy
Aka suffering.
Thanks.
-Tornado
Answers
3n+3 djjdjdj
Answer:
3n+3
hope it helps
please help me i am in need of serious help or ill flunk :(
Answers
co.op
interest = principle * rate * time in years
8000*0.09*1= 720$
total owed =
principle + interest
8000+720= 8720$
bank
interest = principle * rate * time in years
interest = principle * rate * time in years8000*0.06*1= 480$
principle + interest
8000+480= 8480$
......
6)
Bank A
interest = 1500*2*0.18= 540$
total owed = 1500+540= 2040$
Bank B
compound interest =
1500(1+0.12)^2
compound interest= 1881.6
total owed = 1500+1881.6= 3381.6$
she should choose Bank A less total owed
she'll have to pay the bank 2040$
determine the equation of the circle graphed below
( help please )
Answers
9514 1404 393
Answer:
(x +2)^2 +(y -5)^2 = 9
Step-by-step explanation:
The circle shown has a radius of r = 3 and a center at (h, k) = (-2, 5).
The equation of a circle is ...
(x -h)^2 +(y -k)^2 = r^2
For the given center and radius, the equation is ...
(x +2)^2 +(y -5)^2 = 9
Sierra says that she can simplify the side of the inequality shown by combining the terms within the parentheses but that she can't do the same thing on the side. Is Sierra correct? Explain.
Answers
Answer:
Yes, Sierra is correct
Step-by-step explanation:
Given
[tex]4(y + 7) > -3 (4 + 5)[/tex]
Required
Is she correct
The right parenthesis has 4 + 5.
This can be simplified as: [tex]4 + 5 = 9[/tex]
So, we have:
[tex]4(y + 7) > -3 (4 + 5)[/tex]
[tex]4(y + 7) > -3 *9[/tex]
The left parenthesis has y + 7.
This cannot be simplified because y is a variable and 7 is a number.
Hence, Sierra is correct.
the point slope equation of a line is
Answers
Step-by-step explanation:
Point-slope is the general form y-y₁=m(x-x₁) for linear equations. It emphasizes the slope of the line and a point on the line (that is not the y-intercept).
Two points from the line of best fit can be used to find the slope of the line, which can be used to find the equation of the line. True or false?
Answers
Answer:
The statement is true.
Step-by-step explanation:
Let the two points are (x', y') and (x'', y'').
The equation of line passing through the two points is
[tex](y - y')=\frac{y''-y'}{x''-x'}\times (x - x')[/tex]
So, it is true to find the equation of line when the two points is given.
Help please i forgot the options on the last one sorry
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
The x-intercept of the graph is -7. (or (-7, 0). )
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Finding the Slope for the line:}}\\\\m = \frac{8-0}{1-(-7)}\\\\m = \frac{8}{8}\\\\\boxed{m = 1}[/tex]
⸻⸻⸻⸻
Option B is a false statement.
⸻⸻⸻⸻
We can tell with the point (-7,0) that the 'x' intercept of the function is -7.
⸻⸻⸻⸻
The line does not pass (7,0), making option C a false statement.
⸻⸻⸻⸻
The line also does not pass (-1, -8), making option D a false statement.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.