Answers
Answer:
[tex]\large\boxed{\sin2\theta=\dfrac{\sqrt3}{2},\ \cos2\theta=\dfrac{1}{2}}[/tex]
Step-by-step explanation:
We know:
[tex]\sin2\theta=2\sin\theta\cos\theta\\\\\cos2\theta=\cos^2\theta-\sin^2\thet[/tex]
We have
[tex]\sin\theta=\dfrac{1}{2}[/tex]
Use [tex]\sin^2\theta+\cos^2\theta=1[/tex]
[tex]\left(\dfrac{1}{2}\right)^2+\cos^2\theta=1\\\\\dfrac{1}{4}+\cos^2\theta=1\qquad\text{subtract}\ \dfrac{1}{4}\ \text{from both sides}\\\\\cos^2\theta=\dfrac{4}{4}-\dfrac{1}{4}\\\\\cos^2\theta=\dfrac{3}{4}\to\cos\theta=\pm\sqrt{\dfrac{3}{4}}\to\cos\theta=\pm\dfrac{\sqrt3}{\sqrt4}\to\cos\theta=\pm\dfrac{\sqrt3}{2}\\\\\theta\in[0^o,\ 90^o],\ \text{therefore all functions have positive values or equal 0.}\\\\\cos\theta=\dfrac{\sqrt3}{2}[/tex]
[tex]\sin2\theta=2\left(\dfrac{1}{2}\right)\left(\dfrac{\sqrt3}{2}\right)=\dfrac{\sqrt3}{2}\\\\\cos2\theta=\left(\dfrac{\sqrt3}{2}\right)^2-\left(\dfrac{1}{2}\right)^2=\dfrac{3}{4}-\dfrac{1}{4}=\dfrac{3-1}{4}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]
Related Questions
Rochelle bought 4 pieces of ribbon to finish a project. Each puece was 1 5/12 yards long. What is the combined length of the ribbon she bought?
Answers
Answer:
is it 15/12 or a mixed fraction
Given h(t)=-2((-8)+5)•2+4 find h(-8)
Answers
Answer:
36
Step-by-step explanation:
-2 ((-8) + 5) * 2+4
(16 - 10) * (2+4)
6 * 6
36
Alex belongs to a music club. Club membership entitles him to buy a discount card for 19.95. the card allows him to buy CDs for 3.95 each. After one year, Alex has spent 63.40. How many CDs did he buy?
Answers
Answer:
11
Step-by-step explanation:
63.40 - 19.95 = 43.45
43.45/3.95 = 11
Answer:
11 CDs
Step-by-step explanation:
took it on progress learning got it right :)
can someone please help me.
the answers to choose from are
A. 2
B. 30
C. 38
D. 45
Answers
The answer is c
If it was around 25.2 at 12
6 hour later it would have been 12 1/2 more or more
And 25+12=37 and u round it off to 38
And therefore your answer is 38
Someone please help me with this problem
Answers
Answer:
corresponding
Step-by-step explanation:
ANSWER
corresponding.
EXPLANATION
We can trace an F-pattern for <5 and <7.
These two angles are on corresponding sides of the F-pattern.
The two lines l and m are parallel lines.
F-pattern angles form on parallel lines are called corresponding angles.
The correct choice is the last option.
Which expression is equivalent to 4/9(2n-3)
Answers
Answer:
[tex]\large\boxed{\dfrac{8}{9}n-\dfrac{4}{3}}[/tex]
Step-by-step explanation:
[tex]\dfrac{4}{9}(2n-3)\qquad\text{use the distributive property}\\\\=\left(\dfrac{4}{9}\right)(2n)+\left(\dfrac{4}{9}\right)(-3)=\dfrac{8}{9}n-\dfrac{4}{3}[/tex]
Equivalent expression are the equation which have the same identical solution for the variable but the way of representation is different. The given expression in the problem is equivalent to the,
[tex]f(n)=\dfrac{8}{9}n -1\dfrac{1}{3}[/tex]
Thus the option 4 is the correct option.
Given Information-The given expression [tex]f(n)[/tex] is,
[tex]f(n)=\dfrac{4}{9} (2n-3)[/tex]
Equivalent expression-Equivalent expression are the equation which have the same identical solution for the variable but the way of representation is different.
Open the bracket of above equation by multiplying the fraction with the numbers inside the bracket.
[tex]f(n)=\dfrac{4\times 2n}{9} -\dfrac{4\times 3}{9}[/tex]
[tex]f(n)=\dfrac{8n}{9} -\dfrac{12}{9}[/tex]
[tex]f(n)=\dfrac{8n}{9} -\dfrac{4}{3}[/tex]
Fraction 4/c can be written as the mixed number. Thus,
[tex]f(n)=\dfrac{8}{9}n -1\dfrac{1}{3}[/tex]
Hence the given expression in the problem is equivalent to the,
[tex]f(n)=\dfrac{8}{9}n -1\dfrac{1}{3}[/tex]
Thus the option 4 is the correct option.
Learn more about the equivalent equation here;
https://brainly.com/question/14332869
8. If three students in Miss Pagan's class are
sharing a pizza equally, what fraction of the
pizza will each student get?
Answers
Answer:
i think you forgot to add how many pizzass they have sorry but without pizzas i cant do nothing
Step-by-step explanation:
What is the probability of landing on an odd number and then landing on a number greater than 5?
Answers
Answer:
For any question like this you take the number of ways an event can happen (odd number) and divide by the total number of possibilities (sides of a die). If you assume a six sided die there are 3 odd numbers, 1,3, 5. And 6 total sides, so 3/6 = 1/2 or 50%.
Step-by-step explanation:
Final answer:
The probability of rolling an odd number and then a number greater than 5 on a six-sided die in sequence is calculated by multiplying the two independent probabilities, resulting in a combined probability of 1/12.
Explanation:
The student wants to know the probability of landing on an odd number and then landing on a number greater than 5 when rolling a six-sided die. To solve this problem, we need to consider the two separate events independently and then calculate the combined probability.
First, let's consider the probability of landing on an odd number. There are three odd numbers on a die: 1, 3, and 5. Since each outcome is equally likely, the probability is the number of favorable outcomes over the number of possible outcomes, which is P(odd number) = 3/6 = 1/2.
Next, we calculate the probability of landing on a number greater than 5, which is only one number, 6. So, P(number > 5) = 1/6.
To find the probability of both events happening in sequence, we multiply the two probabilities: P(odd number) * P(number > 5) = (1/2) * (1/6) = 1/12. Therefore, the probability of rolling an odd number and then a number greater than 5 is 1/12.
Spencer is carrying out a survey of the bear population at Yellowstone National Park. He spots 2 bears - one has a light colored coat and the other has a dark coat.
1- Assume that there are equal numbers of male and female bears in the park. What is the probability that both bears are male?
2- If the lighter colored bear is a male, what are the odds that both are male?
Answers
Answer:
1. 1/4
2. 1/2
Step-by-step explanation:
If there are equal numbers of males and females, we can simplify that by saying there's one male and one female for each coat color.
1. What's the probability that both are males?
Well, there's a 1/2 chances the light-colored coat bear is a male and there's also a 1/2 chances the dark-colored coat bear is a male. So, we can make this reference table:
Light Dark
Male Male
Male Female
Female Male
Female Female
As you can see, the probability that both of the spotted bears are males is 1/4 (1/2 * 1/2).
2. If the light-colored bear, what are the odds both are males?
If we know for sure the light-one is male, then there's 1/2 chances the other is too, refer to the table above to verify.
Find the area of the shaded region in the figure below
Answers
Answer:
Area of 9 cm circle = PI*radius^2 = 254.47
Area of 9 cm sircle = PI*4*4 = 50.27
Are of shaded region = 254.47 -50.27 = 204 sq cm
Answer is the bottom one on the list.
Step-by-step explanation:
Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
Whose plant grew at a faster rate, and what was the rate?
Answers
Answer:
Therefore, the plant that grew at a faster rate would be Megan’s at 2.5 inches per week.
Step-by-step explanation:
Megan's rate = 12 - 4.5 / 4 -1 = 2.5 inches per week
Suzanne's rate = 11 - 5 / 4-1 = 0.5 inches per week
Without the actual growth measurements, we cannot make a comparison or identify which plant grew faster.
Using the examples:
Suzanne's plant grew at a faster rate (1.5 inches/week) compared to Megan's plant (1 inch/week).
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To determine whose plant grew at a faster rate and what was the rate, we need information about the growth of their plants over the four-week period.
Without this information, we cannot determine the rate of growth or compare the rates of growth of their plants.
Assuming that we have the required information about their plant growth, we can compare the rates of growth of their plants by calculating the average weekly growth rate of each plant.
The plant with a higher average weekly growth rate grew at a faster rate.
For example:
If Megan's plant grew by 4 inches over four weeks, its average weekly growth rate would be:
The average weekly growth rate of Megan's plant = (Total growth in 4 weeks) / (Number of weeks)
= 4 inches / 4 weeks
= 1 inch/week
Similarly,
If Suzanne's plant grew by 6 inches over four weeks, its average weekly growth rate would be:
The average weekly growth rate of Suzanne's plant = (Total growth in 4 weeks) / (Number of weeks)
= 6 inches / 4 weeks
= 1.5 inches/week
In this example:
Suzanne's plant grew at a faster rate (1.5 inches/week) compared to Megan's plant (1 inch/week).
Thus,
Without the actual growth measurements, we cannot make a comparison or identify which plant grew faster.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ8
In a circle with an 8-inch radius, a central angle has a measure of 60°. How long is the segment joining the endpoints of the arc cut off by the angle?
8
8√2
8√3
Answers
Answer:
8_/3
Step-by-step explanation:
tan60=arc/8
arc=8×_/3=8_/3 ans
Answer:
Its 8. I just did this lesson and got it right.
Step-by-step explanation:
Please do it for me if you can
Answers
Answer: 25868
Find area of circle, then add to are of rectangle
Answer:
23745 ft²
Step-by-step explanation:
Area of the Rectangle = LW = 146 x 119 = 17374 ft²
Area of 3/4 of a circle = 3/4r²π = 3/4 x 52² x π = 6371.14990148... ≈ 6371 ft²
Total area = 23745 ft²
Use the table to identify values of pand a that can be used to factor
x2 + x - 12 as (x + p)(x+q).
Answers
Answer:
D. -3 and 4
Step-by-step explanation:
-12 = -3 x 4
-3 + 4 = 1
so
x^2 + x - 12
= (x - 3)(x + 4)
Answer
D. -3 and 4
ANSWER
D. -3 and 4
EXPLANATION
The given quadratic trinomial is
[tex] {x}^{2} + x - 12[/tex]
To factor this we need to find two factors of -12 that sum up to 1, the coefficient of x.
We can see from the table that, when p=-3 and q=4, then p+q =1.
The trinomial can now be factored as:
[tex] {x}^{2} + x - 12 = (x - 3)(x + 4)[/tex]
The correct answer is D.
Using the graph, estimate the cost of 100 kilowatts-hours of electricity
A. About $8
B. About $9
C. About $6
D. About $7
Answers
Answer: A - About $8
Step-by-step explanation:
Maria put a $50,000 deposit on a house. What is the cost of the house if the deposit is 15% of the total price? Round to the nearest dollar.
Answers
Answer:
333,333$
Step-by-step explanation:
15% goes into 100% 6-2/3 times
50,000 x 6-2/3 = 333,333
To find the cost of the house, we can start by setting up an equation. Let \( D \) be the deposit and \( C \) be the cost of the house. We know that the deposit represents 15% of the total cost of the house. Therefore, we can write this relationship as:
\[ D = \frac{15}{100} \times C \]
Given that the deposit \( D \) is $50,000, the equation becomes:
\[ 50,000 = \frac{15}{100} \times C \]
To solve for \( C \), the cost of the house, we will isolate \( C \) on one side of the equation. We can do this by dividing both sides of the equation by 0.15 (which is the decimal representation of 15%):
\[ C = \frac{50,000}{0.15} \]
Now let's calculate this:
\[ C = \frac{50,000}{0.15} = 333,333.\overline{3} \]
The result is approximately $333,333.33. Since we are asked to round to the nearest dollar, we look at the hundredth's place, which is a 3, and since it is less than 5, we round down the dollar amount.
So, the cost of the house rounded to the nearest dollar is $333,333.
Find the length of each leg. Leave an answer in simplest radical form.
Answers
Answer:
[tex]x=8\sqrt{2}[/tex] units
Step-by-step explanation:
The given triangle is an isosceles right triangle.
This implies that, the second leg is also x units.
We use the Pythagoras Theorem to obtain:
[tex]x^2+x^2=16^2[/tex]
[tex]2x^2=256[/tex]
Divide both sides by 2; to get
[tex]x^2=128[/tex]
Take positive square root to get:
[tex]x=\sqrt{128}[/tex]
[tex]x=8\sqrt{2}[/tex]
What is the length of the unknown leg in the right triangle? 6 mm 8 mm mm mm
Answers
Answer: 10mm
Step-by-step explanation: You are going to use the "Pythagorean Theorem" method.
Step 1 :
Equation : a^2+b^2=c^2
plug in your data to the equation given. Then simplify and add.
6^2+8^2=C^2
simplify : 36 + 64 = C^2
simplify : 100 = C^2
Step 2 :
Find what goes into 100 evenly.
100 = 10^2 = (10)(10) = C^2
Step 3:
Find the square root of 10^2 = C^2
10 = c
Last Step :
The length of the unknown leg in the right triangle is 10mm
YAY!!!! you're finished! I hope I explained this so it was easy for you to understand.
Answer:
10mm
Step-by-step explanation:
what is 41/13 written as a decimal and is rounded to the nearest hundredths
Answers
Answer: 3.1538461538462
Rounded: 3.15
Step-by-step explanation:
Answer:
3.154
Step-by-step explanation:
A clock tower has a circular clock face with an circumference of 144 pi ft
*the top question for the picture btw
Answers
Circumference is found by multiplying the diameter by PI.
Since the circumference is given in terms of PI, the diameter is the number given.
The diameter is 144 feet.
Answer:
144
Step-by-step explanation:
when u find curcumference, u multiply the diameter by pi. so to simplify 144(pi), you divide by pi leaving u with 144
The graphs of y = x2 and y = x2 + c are shown below.
Answers
Where’s the question though :/
Urgent! Please heeeeeeeeeeeeelp
Answers
The formula for area of a triangle is: 1/2 x base x height.
You are given the height of 4 and the area of 4.
Replace those in the formula and solve for x ( base)
4 = 1/2 x base x 4
Divide both sides by 4:
1 = 1/2 x base
Multiply both sides by 2:
2 = base
x = 2
Answer:
2=X
Step-by-step explanation:
The area of a triangle is ..
A=1/2 (b×h)
b=base
h=height
Therefore you must plug in what you know and work backwards
4=1/2 (x×4)
×2=×2
___ _________
8=(x×4)
÷4= ÷4
____ _____
2=x
Which of the following best describes a square root?
A. A factor of a number that, when subtracted from itself, gives the
number
O
B. A factor of a number that, when multiplied by itself, gives the
number
O
C. A factor of a number that, when divided by itself, gives the number
D. A factor of a number that, when added to itself, gives the number
Answers
Answer: the answer is c
Answer:
B. A factor of a number that, when multiplied by itself, gives the number
Step-by-step explanation:
[tex]y^{2} =a[/tex]
in other words, a number y whose square (the result of multiplying the number by itself, or y * y) is a
What’s is the mean absolute deviation for 11 of the data set 11 10 9 12 10
Answers
Answer: 0.6
Step-by-step explanation:
First you must calculate the mean of the data
The average is:
[tex]{\displaystyle {\overline {x}}}=\frac{11 +10 +9 +12 +10}{5}\\\\{\displaystyle {\overline {x}}}=10.4[/tex]
Now you must calculate the difference between the value 11 and the average
[tex]d = |11-{\displaystyle {\overline {x}}}|\\\\d=|11-10.4|\\\\d=|0.6|\\\\d=0.6[/tex]
The mean absolute deviation is 0.6
What is the radius of a circle whose equation is x^2+y^2+8x-6y+21=0
Answers
Answer:
2
Step-by-step explanation:
Ni Hua is an adventurous traveler. He skydives twice in every island he visits and skydives thrice in every peninsula he visits.
In the last decade, Ni Hua went skydiving a total of 454545 times in the 191919 islands and peninsulas that he visited.
How many islands and peninsulas did Ni Hua visit?
Choose 1 answer:
A)Ni Hua visited 121212 islands and 777 peninsulas.
B)Ni Hua visited 777 islands and 121212 peninsulas.
C)There is not enough information to determine the exact number of islands and peninsula Ni Hua visited.
D)The given information describes an impossible situation.
Answers
Answer:
A) Ni Hua visited 12 islands and 7 peninsulas.
Step-by-step explanation:
If all visits had been to islands, Hua would have skydived 19·2 = 38 times. He actually skydived 45-38 = 7 times more than that. Each peninsula that replaces an island adds 1 skydive to his total, so he must have visited 7 peninsulas.
Hua visited 7 peninsulas and 12 islands.
Evaluate 6+4/a+b/3 a=4 b=3
Answers
Answer:
8
Step-by-step explanation:
6+4/4+3/3=8
For this case we have the following expression:
[tex]6+ \frac {4} {a} + \frac {b} {3}[/tex]
We must evaluate the expression when:
[tex]a = 4\\b = 3[/tex]
Substituting in the expression:
[tex]6+ \frac {4} {4} + \frac {3} {3} =\\6 + 1 + \frac {3} {3} =\\6 + 1 + 1 =\\7 + 1 =\\8[/tex]
ANswer:
The value of the expression when[tex]a = 4[/tex] and [tex]b = 3[/tex], is 8
The population of bobcats in northern Anzona since 2008 can be modeled using the function (t) = -0.32+ 2.7t +
253
Answers
Answer:
t=-148+1/1.5740740740741
Step-by-step explanation:
(t)=-0.32+2.7t+253
We move all terms to the left:
(t)-(-0.32+2.7t+253)=0
We add all the numbers together, and all the variables
t-(2.7t+252.68)=0
We get rid of parentheses
t-2.7t-252.68=0
We add all the numbers together, and all the variables
-1.7t-252.68=0
We move all terms containing t to the left, all other terms to the right
-1.7t=252.68
t=252.68/-1.7
t=-148+1/1.5740740740741
Answer: t=-148+1/1.5740740740741
Step-by-step explanation: (t)-(-0.32+2.7t+253)=0
t-(2.7t+252.68)=0
t-2.7t-252.68=0
-1.7t-252.68=0
-1.7t=252.68
t=252.68/-1.7
t=-148+1/1.5740740740741
Reduce -8 + b^2 by 5 + b^2
Answers
Answer:-13
Step-by-step explanation:
-8 + b^2 - 5 - b^2
=============
-13
Answer:
-13 __________________________
Step-by-step explanation:
24 quarts equals how many pints
Answers
Answer: 48 Pints
Step-by-step explanation: Quarts are always half the number of pints so say if we had 48 pints, half of 48 is 24 so that is our answer..