Answer:
Step-by-step explanation:
Our interval is 180 to 270 so that's quadrant III. In quadrant 3, both x and y are negative. If we set up our right triangle in this quadrant and label it accordingly with the values given for tangent theta, we find that the missing length is the hypotenuse. Solve for that using Pythagorean's Theorem. Doing that gives us that the hypotenuse is [tex]\sqrt{61}[/tex]. Now we can solve for your other identities. First,
[tex]cos(2\theta)=2cos^2\theta-1[/tex] (There are 3 identities for cos(2θ) and regardless of which one you pick, the answer will be the same every time...promise!)
Filling in now:
[tex]cos(2\theta)=2(\frac{-5}{\sqrt{61} })^2-1[/tex] and simplified a bit:
[tex]cos(2\theta)=2(\frac{25}{61})-1[/tex] and a bit more:
[tex]cos(2\theta)=\frac{50}{61}-\frac{61}{61}[/tex] giving us, finally:
[tex]cos(2\theta)=-\frac{11}{61}[/tex]
Now for b. We have an identity for the half angle of sin:
[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1-cos\theta}{2} }[/tex] and filling in:
[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1-(-\frac{5}{\sqrt{61} } )}{2} }[/tex] which simplifies a bit to:
[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{1+\frac{5}{\sqrt{61} } }{2} }[/tex] and a bit more to:
[tex]sin(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{\sqrt{61}+5 }{2\sqrt{61} } }[/tex] I'm not sure if this is the form you need it in, but this is the answer, as convoluted and crazy as it may look.
As for the cosine half-angle, the identity is the same, except there's a + sign in the numerator of the identity instead of a -, giving us the solution:
[tex]cos(\frac{\theta}{2})=[/tex] ±[tex]\sqrt{\frac{\sqrt{61}-5 }{2\sqrt{61} } }[/tex]
Please help me ASAP help
Answer:
[tex]62 in^2[/tex]
Step-by-step explanation:
[tex]===========================================[/tex]
Formulas:
Area of a rectangle/square:
[tex]A=lw[/tex]
[tex]===========================================[/tex]
Big Rectangles (2):
7*3=21
Multiply by 2
21*2= 42 in
Long rectangles (2)
7*1=7
Multiply by 2
7*2= 14 in
Short rectangles (2):
3*1=3
Multiply by 2
3*2= 6 in
Total:
Add.
42+14+6= 62 in2
Please help me solve this!
Please help quickly!
==========================================================
Explanation:
Focus on triangle TUS. The inner angles here are:
T = yU = xS = 180-2xNote how the angle measure for S is the supplement of 2x, which is adjacent to the angle S we have.
Add up those three angles and set the sum equal to 180
T+U+S = 180
y+x+180-2x = 180
y-x = 180-180
y-x = 0
y = x
We'll use this later.
-----------------
The diagram shows that angle VTU = y+y = 2y.
Focus your attention on triangle TUV.
Since TU = UV, this means the base angles T and V (which are opposite the congruent sides) are congruent angles. We found that angle T was 2y earlier. This means angle V is also 2y.
-----------------
Now shift your focus to triangle TSV.
This triangle has the inner angles
S = 2xT = yV = 2yRecall earlier that we found y = x at the conclusion of the first section. Using that and the fact that the angles of triangle TSV add to 180, we get...
T+S+V = 180
2x+y+2y = 180
2x+3y = 180
2x+3x = 180 .... replace y with x, since y = x
5x = 180
x = 180/5
x = 36
This is the value of y as well.
There are nine different marbles in a bag. Supposed you reach in and draw one at a time. And do this three times. How many ways can you draw the three marbles if you do not replace the marble each time
Answer: 504 ways
Step-by-step explanation:
Given
There are nine different marbles in a bag
For the first time, there are 9 possible ways to draw a marble
After removal of first marble, there are 8 possible ways to draw a marble
for the third time, there are 7 possible ways
so, total ways to draw three marble are
[tex]\Rightarrow 9\times 8\times 7=504\ \text{ways}[/tex]
Combine and simplify the following radical expression
Answer:
[tex]2 \sqrt[3]{3} [/tex]Step-by-step explanation:
[tex] \sqrt[3]{6} . \sqrt[3]{4} [/tex]
[tex] = \sqrt[3]{6 \times 4} [/tex]
[tex] = \sqrt[3]{3 \times 2 \times 2 \times 2} [/tex]
[tex] = 2 \sqrt[3]{3} (ans)[/tex]
Now that you know the vertex, find the y-values that pair with a few x-values that are less than 2 and a few that are greater than 2.
Plsssss help!!!!!!!
Which is the graph of the linear inequality {x-2y> -6?
Answer:
7
Step-by-step explanation:
Answer:
I think it is d
Step-by-step explanation:
need the answer for this question
Answer:
m<2 + m<3
Step-by-step explanation:
Theorem:
In a triangle, the measure of an exterior angle is equal to the sum of the measures of its remote interior angles.
<4 is an exterior angle of the triangle.
Angles 2 and 3 are the remote interior angles of <4.
m<4 = m<2 + m<3
Answer: m<2 + m<3
Answer:
<4 = <2 + <3
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
<4 = <2 + <3
for what is values of x does 4(3x-2) = 12x - 5? select all that apply.
A.12
B.-8
C.3
D.-3
E.none of these
Answer:
‼️A) 12‼️
Step-by-step explanation:
Key skills needed: Interior Angle Measure Theorem, Equation Creation
Step 1) First, we need to classify this shape. It has 7 sides, which means that we can use the Interior angle Theorem to find out the sum of all the interior angle measures
The theorem is: S = (n - 2)180S=(n−2)180
S is the sum of all interior angle measures
n is the number of sides of the polygon
Step 2) With this, we can plug in 7 for "n" (Since the figure has 7 sides) and get:
---> S = (7-2)180S=(7−2)180
---> (7-2) is 5 since 7 - 2 = 5 so --> S = 5(180)S=5(180)
---> 5(180) is the same as 5 x 180 which is 900 so --> S = 900S=900
This means that the sum of all interior angles is 900 degrees.
Step 3) Now, we have to find out the sum of all the angles that they gave us so:
---> 10x + 10x + 9 + 133 + 9x + 14 + 12x - 9 + 10x + 5 + 136 = 90010x+10x+9+133+9x+14+12x−9+10x+5+136=900
The left side is the sum of all interior angles in the shape, and the right side is what the sum should be when expressed as a number.
Step 4) We have to combine all like terms on the left side:
---> 10x + 10x + 9x + 12x + 10x = 51x10x+10x+9x+12x+10x=51x
---> 9 + 133 + 14 -9+5+136 = 2889+133+14−9+5+136=288
Step 5) This means that ---> 51x + 288 = 90051x+288=900
Subtract 288 from both sides and get:
---> 51x = 61251x=612 (900-288 = 612)
Then divide by 51 from both sides and get:
---> x = 12x=12 (612 ÷ 51 = 12)
Therefore A) 12 is your answer.
I think it should be none of these.
The term on the left has to be even no matter what value of x and the right has to be odd no matter what value of x. Therefore, there shouldn't be an integer value of x that satisfies the equation, let alone the answer choices A-D.
hich math expression means "the product of 16 and 26"?
O 16 - 26
26-16
16 - 26
0 16 +26
Answer:
infjfkflflfmdbfufifldndndhfififkfnf
A batch of peanut butter cookies requires \dfrac34 4 3 start fraction, 3, divided by, 4, end fraction of a jar of peanut butter. You want to make 333 batches. How many jars of peanut butter do you need?
Answer: 3 Jars
Step-by-step explanation:
Given
A batch of peanut butter cookies requires [tex]\frac{3}{4}[/tex] of a jar
For 3 batches of Cookies, No of Jars required
[tex]\Rightarrow 3\times \dfrac{3}{4}=\dfrac{9}{4}\\\\\Rightarrow \dfrac{9}{4}=2+\dfrac{1}{4}[/tex]
That is 2 complete Jar and one-fourth of third. In totality, it would be 3
jars.
What is the best approximate for the input value when f(x)=g(x)?
Answer:
(1.5 ,1)
Step-by-step explanation:
f(x) = g(x) where the two graphs intersect
x=1.5 and y = 1
(1.5 ,1)
Please help:)))))))))))
Answer:
good evening good evening good evening good evening
If the base of a triangle is 3 and its height is 4, then its area is 6. This triangle has an area of 6, so its base is 3 and its height is 4
Valid or invalid
9514 1404 393
Answer:
invalid
Step-by-step explanation:
There is more than one set of dimensions that will give a triangle with an area of 6. The fact that the area is 6 implies nothing about the dimensions (except that their product is 12).
The converse is invalid.
Answer:
The first sentence is valid but the second one is invalid.
Step-by-step explanation:
You can't say just because the area of the triangle is 6, its base is 3 and its height is 4, it might have a base of 1 and a hight of 12 so there are more than one answers for the second one.
Feel free to message me if you still have questions :)
HELPPPP MEEEE OUTTTT!!!
Answer:
Solution given:
Relationship between base and hypotenuse is given by Cos angle
Cos Angle(?)=base/hypotenuse
Angle{?}=Cos-¹(40/58)
Angle{?}=46°
The indicated angle is 46°
HELP!
Solve by completing the square: 2x^(2)+x-21
Answer: 3,-7/2
Step-by-step explanation:
If sin0=3/5 then tan0=
Answer:
I believe it is 3/4
Step-by-step explanation:
write 2^60 as an exponent with a base of 16
Recall that 2⁴ = 16. So you have
2⁶⁰ = 2⁴ˣ¹⁵ = (2⁴)¹⁵ = 16¹⁵
please help
yuffytdgtutidrysryrdf
Answer:
19 + 1 + 9 + 1
put any of those in the slots
Answer:
19 + 1 + 9 + 1
peace
Joyce paid $39.00 for an item at the store that was 70 percent off the original price. What was the original price?
Answer:the answer is 10 because if u subctract it will work
Step-by-step explanation:
jack takes a job after school to earn money to buy a sport car.He knows that the more hours he works .the more money he will make
Answer: What's the question? I'll edit my answer to the question if you would give me the actual problem
Step-by-step explanation:
Can anyone help with this question? The population of a small industrial town was 12 910 in 2000. Each year, the population decreases by an average of 5%. Estimate the population in the year 2020. Round to the nearest whole number.
Answer:
Population of town in 2020 = 4626 (Approx.)
Step-by-step explanation:
Given:
Population of town in 2000 = 12,910
Decrease rate = 5% = 0.05 yearly
Find:
Population of town in 2020
Computation:
Number of year = 20 years
Population of town in 2020 = Population of town in 2000[1-r]ⁿ
Population of town in 2020 = 12,910[1-0.05]²⁰
Population of town in 2020 = 12,910[0.95]²⁰
Population of town in 2020 = 12,910[0.3584]
Population of town in 2020 = 4625.944
Population of town in 2020 = 4626 (Approx.)
Answer:
The population is 4628.
Step-by-step explanation:
Population in 2000 = 12910
Rate of decrease = 5 %
Time, t = 2020 - 2000 = 20 years
Let the population is P.
Use the formula
[tex]P = Po\left ( 1-\frac{r}{100} \right )^t\\\\P = 12910\left ( 1-0.05 \right )^2\\\\P = 4628[/tex]
Dividing with powers of 10
6. Which of the following equations has a slope of -2 and passes
through the point (3,-4).
O) y=-2x - 4
O) y=-2x + 2
O) y = -2x+3
O) y = -2x - 1
Answer:
y=-2x+2
Step-by-step explanation:
substitute either the x or y value into the equations, if you substitute x=3 and get back y=-4, the equation is correct
what is the common difference if t4 = -14 and t10 = -32?
Answer:
-3
Step-by-step explanation:
-32 - (-14) / 10 - 4
-18/6
= -3
double the sum of all prime numbers between 10and 30 then add thrice the product of all positive numbers less than 8 what is the quotient
hope so this might help
ans is above in the pic
WILL MARK BRAINLIEST ^^
picture included!! PLEASE and thx
Explanation:
Like with the previous problems, the answer comes fairly straight forward from the values of c and d.
c = 4 tells us we have a shift of 4 units to the left
d = 3 indicates we're shifting 3 units up.
Note: we shift left instead of right because x+c = x+4 means the xy axis has been shifted 4 units to the right, giving the illusion the cosine curve is shifted 4 units to the left.
Who know how to do this??
Answer:
Step-by-step explanation:
With some research I found that the medians (QK, RJ, and SI) are broken into 2:1 ratios.
So what this means is that QD is twice as long as DK.
QD = 2DK
QD = 2 * 6.5
QD = 13
how didi the temperature change if at it decreased by 60% then increased by 80%
Answer:
It decreased
Step-by-step explanation:
It decreased. Assuming that the temperature is 100 and it is now reduced by 60% then the temperature will be at 40 and if it increased by 80% then the final temp is 72. So it is 48% of the original temp.
A rectangle garden has a lenght which is longer than the width 30 cm. What is the area of that garden? Know that the perimeter of that garden is 65 cm.
Answer:
The area is 75cm
Step-by-step explanation:
Firstly, the perimeter is 65 cm and the width of the rectangle is 30 cm, so using this information we can figure out the length of the rectangular garden.
The formula for perimeter is L+L+W+W, you add all sides. The rectangle has 4 sides and 2 of those sides are 30 cm. 30+30= 60, so now we know what the width added up is. So we do this to find the length: 65-60=5, and then 5÷ 2 = 2.5. So now we use the formula for area: L × W: 30 × 2.5=75
help plsssssssssssssssssssss
Answer:
Question 10:
Answer: b.
[tex]{ \tt{f(x) = 5 {x}^{2} + 9x - 4}} \\ { \tt{g(x) = - {8x}^{2} - 3x - 4 }}[/tex]
(f + g)x, add f(x) and g(x):
[tex]{ \tt{(f + g)x = (5 - 8) {x}^{2} + (9 - 3)x - 4 - 4}} \\ { \tt{(f + g)x = - 3 {x}^{2} + 6x - 8}}[/tex]
Question 11:
Answer: a.
In relation with solution of question 10, same procedure:
[tex]{ \tt{(f - g)x = - 3 {x}^{3} + (1 - 2) {x}^{2} + ( - 3 - 4)x + 9 - ( - 9)}} \\ { \tt{(f - g)x = - 3 {x}^{3} - {x}^{2} - 7x + 18 }}[/tex]
