Answer:
cos2θ = -0.7041
Cos θ = -0.3847
Step-by-step explanation:
Firstly, we should understand that since θ is in quadrant 2, the value of our cosine will be negative. Only the sine is positive in quadrant 2.
Now the sine of an angle refers to the ratio of the opposite to the adjacent. And since there are three sides to a triangle, we need to find the third side which is the adjacent so that we will be able to evaluate the cosine of the angle.
What to use here is the Pythagoras’ theorem which states that the square of the hypotenuse is equal to the sum of the squares of the adjacent and the opposite.
Since Sine = opposite/hypotenuse, this means that the opposite is 12 and the hypnotist 13
Thus the adjacent let’s say d can be calculated as follows
13^2 = 12^2 + d^2
169 = 144 + d^2
d^2 = 169-144
d^2 = 25
d = √25 = ±5
Since we are on the second quadrant, the value of our adjacent is -5 since the x-coordinate on the second quadrant is negative.(negative x - axis)
The value of cos θ = Adjacent/hypotenuse = -5/13
Cos θ = -5/13
Cos θ = -0.3846
Using trigonometric formulas;
Cos 2θ = cos (θ + θ) = cos θ cos θ - sin θ sin
θ = cos^2 θ - sin^2 θ
Cos 2θ = (-5/13)^2 - (12/13)^2
Cos 2θ = 25/169 - 144/169
Cos 2θ = (25-144)/169 = -119/169
Cos 2θ = -0.7041
There are four quadrants in a coordinate geometry.
The cosine values are [tex]\mathbf{ cos(\theta)=- \frac{5}{13}}[/tex] and [tex]\mathbf{ cos(2\theta) = -\frac{119}{169}}[/tex]
The given parameter is:
[tex]\mathbf{sin(\theta) = \frac{12}{13}}[/tex]
Using trigonometry ratio, we have:
[tex]\mathbf{sin^2(\theta) + cos^2(\theta)= 1}[/tex]
Substitute [tex]\mathbf{sin(\theta) = \frac{12}{13}}[/tex]
[tex]\mathbf{(\frac{12}{13})^2 + cos^2(\theta)= 1}[/tex]
Expand
[tex]\mathbf{\frac{144}{169} + cos^2(\theta)= 1}[/tex]
Collect like terms
[tex]\mathbf{ cos^2(\theta)= 1-\frac{144}{169}}[/tex]
Evaluate fraction
[tex]\mathbf{ cos^2(\theta)= \frac{25}{169}}[/tex]
Take square roots of both sides
[tex]\mathbf{ cos(\theta)= \pm \frac{5}{13}}[/tex]
The angle is in the second quadrant.
So, we have:
[tex]\mathbf{ cos(\theta)=- \frac{5}{13}}[/tex]
Also, we have:
[tex]\mathbf{ cos(2\theta) = cos^2(\theta) - sin^2(\theta)}[/tex]
So, the equation becomes
[tex]\mathbf{ cos(2\theta) = \frac{25}{169} - \frac{144}{169}}[/tex]
Take LCM
[tex]\mathbf{ cos(2\theta) = \frac{25-144}{169}}[/tex]
[tex]\mathbf{ cos(2\theta) = -\frac{119}{169}}[/tex]
Hence, the values are:
[tex]\mathbf{ cos(\theta)=- \frac{5}{13}}[/tex] and [tex]\mathbf{ cos(2\theta) = -\frac{119}{169}}[/tex]
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please help asap! its needed badly
Answer:
can u retake the photo
Step-by-step explanation:
If P(not yellow) = StartFraction 4 over 15 EndFraction, which best describes the probability of the complement of the event?
Answer:
The P(yellow) = 11/15
Step-by-step explanation:
Here, we have;
P(not yellow) = 4/15
Mathematically, the addition of the probability of an event and its complement adds up to be 1
The complement we have here is P(yellow)
Thus, mathematically we have;
P(not yellow) + P(yellow) = 1
P(yellow) = 1 - P(not yellow)
From the question P(not yellow) = 4/15
Plugging this value, we have;
P(yellow) = 1 - 4/15 = 11/15
Answer:
C. 11/15
Step-by-step explanation:
hope this helped!
The top of a ladder rest at a height of 15 feet against the side of a house. If the base of a ladder is 6 ft from the house what is the length of the ladder? round to the nearest foot.
Answer:
16 feet
Step-by-step explanation:
We use Pythagorean Theorem to find the height.
leg of triangle= height of ladder = 15 feet
The hypotenuse of the formed triangle = length of ladder = L
base = 6 feet
What is length of ladder?
L^2 = 15^2 + 6^2 = 225 + 36 = 261
L = root(261) = 16.155 feet
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Answer:
b =7
Step-by-step explanation:
8b+15=71
Subtract 15 from each side
8b+15-15 =71-15
8b = 56
Divide each side by 8
8b/8 = 56/8
b = 7
Answer:
I believe b equals 7.
Step-by-step explanation:
8b +15= 71
-15. -15
8b = 56
56/8
7
b=7
Solve the equation by completing the square. If necessary, round to the nearest hundredth. x2+10x=18
To solve the quadratic equation x² + 10x = 18 by completing the square, we rearrange the equation, complete the square, solve for x by taking the square root of both sides, and then isolate x. The two solutions are x = -5 + √43 and x = -5 - √43, which can be approximated if necessary.
To solve the equation x² + 10x = 18 by completing the square, we first need to move all terms to one side to get the equation in the form of ax² + bx + c = 0.
Subtracting 18 from both sides, we have x² + 10x - 18 = 0.
To complete the square, we take the coefficient of x, which is 10, divide it by 2 to get 5, and then square it to get 25. We add 25 to both sides of the equation and then subtract it right back to maintain the balance:
x² + 10x + 25 - 25 - 18 = 0
Now we group the perfect square trinomial and simplify:
(x + 5)² - 43 = 0
Next, we add 43 to both sides:
(x + 5)² = 43
Then we take the square root of both sides:
(x + 5) = √43
Subtract 5 from both sides to solve for x:
x = -5 ± √43
The solutions are x = -5 + √43 and x = -5 - √43.
Damian's famouse punch calls for 6 liters of mango juice. The only mango juice he can find is sold in 500-milliliter cartons. How many cartons of mango juice does Damian need to buy?
Answer:
12 cartons
Step-by-step explanation:
500 millilitres is equal to 0.5 liters, so with this you can divide 6 L by 0.5 L to find that you need 12 cartons in total
If y - 12 = 23, what would you do to solve for x? *
option 1 - add the 12 to both sides
option 2 - subtract the 12 from both sides
option 3 - subtract 23
Answer:
Option 1 - add the 12 to both sides.
Step-by-step explanation:
If you meant solve for the variable, y, then you should:
Option 1 - add the 12 to both sides.
y - 12 = 23
Isolate the variable, y. Add 12 to both sides:
y - 12 (+12) = 23 (+12)
y = 23 + 12
Simplify:
y = 23 + 12
y = 35
~
What are the zeros of the quadratic function f(x) = 2x2 + 8x – 3?
Answer:
A
Step-by-step explanation:
Chester used the regression equation of the weight loss plan to make a prediction within the given data range. Complete his work to calculate the number of weekly hours of aerobic activity needed for a monthly weight loss of 3 pounds. Round to the nearest hundredth.
1. Regression equation: y = 1.178 x + 0.71. 2. Substitute 3 for y: 3 = 1.178 x + 0.71. 3. Subtract 0.71 from both sides: 2.29 = 1.178 x. 4. Divided both sides by 1.178: StartFraction 2.29 Over 1.178 EndFraction = StartFraction 1.178 Over 1.178 EndFraction x.
About
hours of weekly aerobic activity will result in 3 pounds of monthly weight loss.
Answer: 1.94
Step-by-step explanation:
Answer:
1.94
Step-by-step explanation:
trust me
Whatgdhshshsh shsbshe ushe shebe isnsdn
Answer:
yes
Step-by-step explanation:
Answer: yes
Step-by-step explanation:
5rtb rsgfttbh
Recipe for a cake needs 1 1/2 cups of milk. You are making 1/2 of the recipe. How much milk do you need
Answer:
3/4
Step-by-step explanation:
Answer:
3/4s
Step-by-step explanation:
1 1/2 is equal to 6/4 or 1 and 2/4 so divided by 2 equals 3/4
-102.75 / -3
Round to nearest tenth
Answer: To approximate a number to the nearest tenth you have to look at the hundredths digit. If it is 5 or more you have to add 1 to the tenths digit, else if it is lower than 5 you leave the tenths digit unchanged.
Step-by-step explanation:
Answer:
34.3
Step-by-step explanation:
i used my brain
Which expression is equal to 2x7x6?
Answers:
(2x7) + (2x6)
(2+7) x (2+6)
7+2+6
7x2x6
what's the answer?
Answer:
Option D is correct.
Step-by-step explanation:
As commutative principle 2x7x6 = 7x2x6
Hope this helps!
:)
The required form of the given expression is obtained as 7 × 2 × 6. The correct option is (D).
What is the commutative property for multiplication?The commutative property for multiplication states that the order of multiplication is not a necessary condition to change the product,
For example the products obtained from both the expressions 2 × 3 and 3 × 2 are the same.
The given expression is 2 × 7 × 6.
As per the commutative property the order of multiplication does not change the product.
Thus, the given expression can be written as,
7 × 2 × 6
Hence, the given expression can be rewritten as 7 × 2 × 6.
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How many seconds are in 3 minutes
I need help can you please help me please I need it
PLEASE HELP I need explanation if you can’t provide it’s ok thanks anyways
Answer:
We have, volume of cone:
V = (1/3) x base area x height
= (1/3) x pi x radius^2 x height
= (1/3) x pi x 2^2 x 4
= 16.76 (mi3)
Option D is correct
Hope this helps!
:)
Answer:
16.76
Step-by-step explanation:
Volume= πr^2 h/3
so its π (2)^2 4/3
which equals 16.76 mi^3
3.
The two right triangular prisms are congruent. What is the area of their bases?
15 in.
V = 90 in.
The two cylinders are congruent What is the height of cylinder B?
Step-by-step explanation:
3. The prisms are congruent, so they have the same base, height, and volume.
Volume of a prism is:
V = Ah
Plugging in values and solving for A:
90 in³ = A (15 in)
A = 6 in²
4. The cylinders are congruent, so they have the same radius, height, and volume.
Volume of a cylinder is:
V = πr²h
Plugging in values and solving for h:
176π cm³ = π (4 cm)² h
h = 11 cm
Write the coordinates of one point that lies in the second quadrant of the coordinate plane.
Answer:
Examples are: (-1,1), (-2,1), and (-3,1).
Step-by-step explanation:
The second quadrant on a coordinate plane is located in the top left.
Which answer explains why the sum of 12+12 is an even number
A.Any number plus 12 is even.
B.Both addends are equal.
C.Any number greater than 12 is even.
D.12+12 is equal to an odd number
Answer:
Even + Even = even
odd + odd = even
Odd + even = odd
even + odd = odd
Rule of thumb in addition.
Answer is B
Step-by-step explanation:
Final answer:
The sum of 12+12 is an even number because both addends are even numbers, and adding two even numbers always results in an even sum.
Explanation:
The question you're asking is about why the sum of 12+12 is an even number. To answer this, we need to understand a property of even numbers. An even number is any integer that can be divided by 2 without leaving a remainder. Adding two even numbers together will always result in another even number because the sum of two multiples of any number is a multiple of that number. Since 12 is an even number (it can be divided by 2 to get 6), adding it to itself (another even number) must result in an even sum.
It's not correct to say that any number plus 12 is even (Option A) because if you add 12 to an odd number, the result is odd. Option B is the closest to a correct explanation because both addends are equal and are even numbers. Saying any number greater than 12 is even (Option C) is incorrect because odd numbers also exist above 12. Finally, 12+12 is not equal to an odd number (Option D), so that choice is incorrect as well.
Please help me I will mark BRAINLIEST!!! Find the value of x
Answer:
x = 2√3 ≈ 3.464
Step-by-step explanation:
The side marked x is opposite the given 30° angle. The side marked 6 is adjacent to that angle. The trig function relating opposite and adjacent sides of a right triangle is ...
Tan = Opposite/Adjacent
Filling in values, we have ...
tan(30°) = x/6
Multiplying by 6 gives ...
x = 6tan(30°) = 6(√3/3)
x = 2√3 ≈ 3.464
If a car can drive 62 miles on 3 gallons of gas, how many gallons of gas will it use to travel 231 miles?
Answer:
11 gallons of gas is needed to travel 231 miles.
Step-by-step explanation:
We can set up a proportion for this problem.
For every 62 miles, you use 3 gallons of gas.
[tex]\frac{62}{3}*\frac{231}{?}[/tex]
Now, let's cross multiply.
[tex]\frac{693}{62}[/tex] ≈ [tex]11[/tex]
So, you will need about 11 gallons of gas to travel 231 miles.
The caribou’s spring migration takes 2 weeks. The longest recorded migration was 838 miles. How far did the caribou travel per day?
Answer:
59.85714285714286 miles a day ≈ 60 miles a day
Step-by-step explanation:
To find this, we'd have to make the weeks into days.
2 weeks * 7 days = 14 days
Now we need to divide the miles traveled by the days:
838/14=59.85714285714286 miles a day or about 60 miles per day
Answer:
~ 60 days
Step-by-step explanation:
We have 2 weeks. Since there are 7 days a week, 2 weeks is 14 days.
To find the number of miles walked per day, we need to divide the total number of miles by the total number of days:
838 / 14 ≈ 59.9 ≈ 60 days
8 is 2/3 of what number?
Answer:
12
Step-by-step explanation:
the number = x
2/3 of x =8
2x/3 = 8
2x= 24
x=12
Answer:
12
Step-by-step explanation:
8 is 1/3 of 24
so it's 2/3 of 12
Which equations explain why Mya's claim must be true?
Answer:
(4) (M∠1 + m∠2) = 180 and (m∠3 + m∠4 + m∠2) = 180
Step-by-step explanation:
The correct equation which represent Mya's claim must be true is,
⇒ m ∠1 + m ∠2 = 180°
And, m ∠3 + m ∠4 + m ∠2 = 180°
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degree.
Given that;
Mya claims that,
⇒ m ∠3 + m ∠4 = m ∠1
We know that;
Sum of all interior angles in triangle are 180 degree.
And, Sum of opposite angles of a triangle is equal to its exterior angle.
Hence, We get;
The correct equation which represent Mya's claim must be true is,
⇒ m ∠1 + m ∠2 = 180°
And, m ∠3 + m ∠4 + m ∠2 = 180°
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1 5/6 times 2 3/4
it says give the answer as a mixed number in it simplest form
Answer:
5 1/24
Step-by-step explanation:
first you turn the mixed fraction to improper fraction
1 5/6=11/6
2 3/4= 11/4
11/6 times 11/4 = 121/24
121 divided by 24= 5 1/24
Answer is 5 1/24. You have to keep, change, flip
-Dhruva;)
find the reciprocal of 2 / -5 × 3 / -7
Answer:
[tex] \frac{35}{6} [/tex]
Step-by-step explanation:
[tex] \frac{2}{ - 5} \times \frac{3}{ - 7} \\ = \frac{6}{35} [/tex]
Now turn the answer upside down[tex] \frac{6}{35} = = > \frac{35}{6} [/tex]
The system of equations shown below is graphed on a coordinate grid:
3y + x = 4
2y − x = 6
Which statement is true about the coordinates of the point that is the solution to the system of equations?
It is (−2, 2) and lies on both lines.
It is (−5, 3) and lies on both lines.
It is (−5, 3) and does not lie on either line.
It is (−2, 2) and does not lie on either line.
Answer:
A) (-2,2) lies on both lines
Step-by-step explanation:
Your answer would be the first option, (-2, 2).
We can solve this system of equations by adding them together, as the +x and -x will cancel:
3y + x = 4
+2y - x = 6
5y = 10
y = 2
Now we can find the x value by substituting the y value into one of the equations:
3(2) + x = 4
6 + x = 4
x = -2
Therefore your answer is (-2, 2). We know that it is the first option and not the last option because the point (-2, 2) does lie on both lines as it satisfies both equations when substituted in.
I hope this helps!
Evaluate the expression
7^0
Answer:
1
Step-by-step explanation:
Any number put to the 0 power is equal to 1.
Does that help?
what is the proablity of rolling a 3 and landing on heads
Answer:
2/5
Step-by-step explanation:
is the equation y = –16x2 + 20x + 4 a function
Answer: yes
Step-by-step explanation: