[tex]A=\frac{\pi}{8}+\frac{n\pi}{4}or\ A=\frac{\pi}{2}+n\pi[/tex]
Step-by-step explanation:Find angles[tex]cos3A+cos5A=0[/tex]
________________________________________________________
Transform the expression using the sum-to-product formula[tex]2cos(\frac{3A+5A}{2})cos(\frac{3A-5A}{2})=0[/tex]
________________________________________________________
Combine like terms[tex]2cos(\frac{8A}{2})cos(\frac{3A-5A}{2})=0\\\\ 2cos(\frac{8A}{2})cos(\frac{-2A}{2})=0[/tex]
________________________________________________________
Divide both sides of the equation by the coefficient of variable[tex]cos(\frac{8A}{2})cos(\frac{-2A}{2})=0[/tex]
________________________________________________________
Apply zero product property that at least one factor is zero[tex]cos(\frac{8A}{2})=0\ or\ cos(\frac{-2A}{2})=0[/tex]
________________________________________________________
Cos (8A/2) = 0:Cross out the common factor[tex]cos\ 4A=0[/tex]
________________________________________________________
Solve the trigonometric equation to find a particular solution[tex]4A=\frac{\pi}{2}or\ 4A=\frac{3\pi}{2}[/tex]
________________________________________________________
Solve the trigonometric equation to find a general solution[tex]4A=\frac{\pi}{2}+2n\pi \ or\\ \\ 4A=\frac{3 \pi}{2}+2n \pi\\ \\A=\frac{\pi}{8}+\frac{n \pi}{4\\}[/tex]
________________________________________________________
cos(-2A/2) = 0Reduce the fraction[tex]cos(-A)=0[/tex]
________________________________________________________
Simplify the expression using the symmetry of trigonometric function[tex]cosA=0[/tex]
________________________________________________________
Solve the trigonometric equation to find a particular solution[tex]A=\frac{\pi }{2}\ or\ A=\frac{3 \pi}{2}[/tex]
________________________________________________________
Solve the trigonometric equation to find a general solution[tex]A=\frac{\pi}{2}+2n\pi\ or\ A=\frac{3\pi}{2}+2n\pi,n\in\ Z[/tex]
________________________________________________________
Find the union of solution sets[tex]A=\frac{\pi}{2}+n\pi[/tex]
________________________________________________________
A = π/8 + nπ/4 or A = π/2 + nπ, n ∈ ZFind the union of solution sets[tex]A=\frac{\pi}{8}+\frac{n\pi}{4}\ or\ A=\frac{\pi}{2}+n\pi ,n\in Z[/tex]
I hope this helps you
:)
20 In a village,
if it rains on one day, the probability
that it will rain on the next day is 0.8
if it does not rain on one day, the probability that it will rain on the next day is 0.6
A weather forecaster says,
“There is a 70% chance that it will rain in the village on Monday.”
Work out an estimate for the probability that it will rain in the village on Wednesday.
lou must show all your working.
Using it's concept, it is found that there is a 0.643 = 64.3% probability that it will rain in the village on Wednesday.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, considering Monday - Tuesday - Wednesday, the possible outcomes are as follows:
R - R - R(0.7 x 0.7 x 0.7)
R - N - R(0.7 x 0.2 x 0.6)
N - R - R(0.3 x 0.6 x 0.8)
N - N - R(0.3 x 0.4 x 0.6)
Then, the probability is given by:
p = 0.7 x 0.7 x 0.7 + 0.7 x 0.2 x 0.6 + 0.3 x 0.6 x 0.8 + 0.3 x 0.4 x 0.6 = 0.643.
0.643 = 64.3% probability that it will rain in the village on Wednesday.
More can be learned about probabilities at https://brainly.com/question/14398287
#SPJ1
[20 points]
Write the polynomial in standard form. (Look at the Photo)
Answer:
[tex]5x^4+5x^3+3x^2-4[/tex]
1 +5x2 + (1 + 3) to the second power
Answer:
27
Step-by-step explanation:
1 + (5)(2) + (1 + 3)^2
1 + 10 + (1 + 3)^2
11 + (1+3)^2
11+4^2
11+16
27
Hope this helps! Have an amazing day!NEED DONE ASAP. what is 6x3
Answer:18
Step-by-step explanation: pretty much 6 plus 6 plus 6 you add six 3 times.
State if the three
numbers below can be
the measure of the sides
of a triangle.
3, 10, 7
What is the perimeter of kite obde? 17 units 23 units 27 units 60 units
All sides add up to the perimeter. The perimeter of the kite is 27 units then the correct option is C.
What is the definition of geometry?It is concerned with the geometry, region, and density of various 2D and 3D forms.
The Pythagoras theorem will determine the kite's length (x).
H² = P² + B²
H² = 15² + 8²
H² = 225 + 64
H² = 289
H = 17
Then
[tex]\rm x = \dfrac{H}{2} \\\\x = \dfrac{17}{2}\\\\x = 8.5[/tex]
And another length of the kite is 5 units.
Then the perimeter of the kite will be
Perimeter = 2(8.5 + 5)
Perimeter = 27
More about the geometry link is given below.
https://brainly.com/question/7558603
Answer:27 units
Step-by-step explanation:
trust
Multiply: (x−3)(x 4) simplify and write your answer in standard form. hint standard form: ax2 bx c
What type of triangle is defined by the following set of side lengths
10, 9, 5
Question 3 options:
Acute
Obtuse
Right
Not a triangle
Answer:
the answer is acute according to this triangle calculator
Math 8: One-step equations word problems (writing algebraic expressions)
Answer:
x puls four is equal to
Step-by-step explanation:
Scott received a score of 91, 85, and 89 on three tests. What score must Scott get on the fourth test to have an overall average score of 90
Answer:
95
Step-by-step explanation:
So if you wanted to figure the average of the 3 tests, you would add 91+85+89 to get 265 & then divide by 3 tests to get an average of 88.
So that means for four tests, 91+85+89+4th test = answer that divided by 4 tests will equal 90. 90 x 4 = 360. Then 360 -265 (sum for 1st 3 tests) = 95
Chloe looked at the data below and said, "The median is 37." Which answer points out Chloe's
mistake?
38, 42, 51, 55, 37, 57, 34, 44, 56
A. Chloe should have added the numbers and divided by 9.
The median is 46.
B. Chloe did not make a mistake; the median is 37.
C. Chloe forgot to arrange the numbers in ascending order. The median is 44.
D. The median is the number which appears the most; there is no median.
Answer:
C. Chloe forgot to arrange the numbers in ascending order. The median is 44.
Step-by-step explanation:
We arrange the 9 numbers of the data from the least to the greatest
Then we spot the middle number (5th number) which is 44:
34 < 37 < 38 < 42 < 44 < 51 < 55 < 56 < 57
what is 2/8 simplified
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
when the numerator and denominator are no longer divisible by the same number, that's when it is in simplest form:
[tex]\frac{2}{8}[/tex] divides by [tex]\frac{2}{2}[/tex] to give you [tex]\frac{1}{4}[/tex]
2÷2 = 1
8÷2 = 4
Which expressions are equivalent to 6m+5(n+m)?
7m + 5n
11m + 5n
12m + n
6m + 5n + 5m
6(m + 5n + 5m)
Answer:
it's 11m+5m
Step-by-step explanation:
Rearrange term
6m+5(n+m)
6m+5(m+n)
Distribute
6m+5m+5n
Combine like terms
6m+5m+5n
=11m+5n
Do number 7 pleaseeee
Answer:
it says percentage increase so you do...
Step-by-step explanation:
106 divide by 100=1.06
then the answer multiply by 1.50=1.59
A
tyler has a points card for a movie theater.
he receives 75 rewards points just for signing up.
• he earns 10.5 points for each visit to the movie theater.
he needs 180 points for a free movie ticket.
.
a
how many visits must tyler make to earn a free movie ticket?
Answer:
at least 10 visits
Step-by-step explanation:
Given:
75 rewards points for signing up
10.5 points for each visit
Total Number of Points are :
75 + 10.5 · number of visits he makes
How many visits must Tyler make to earn a free movie ticket?
75 + 10.5 · x ≥ 180 points for a free movie ticket
Where, x is how many visits must Tyler make to earn a free movie ticket
10.5 · x ≥ 180 -75
x ≥ 105/ 10.5
x ≥ 10
Since the number of visits to reach 180 points is 10 then Tyler has to visit the movie theater 10 times or more.
Check our answer:
75 + 10.5 · 10 = 180 will earn him a free movie ticket
Answer:
Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables are studied under the supposition or demand that they depend, by some law or rule, on the values of other variables.
Step-by-step explanation:
A
tyler has a points card for a movie theater.
he receives 75 rewards points just for signing up.
• he earns 10.5 points for each visit to the movie theater.
he needs 180 points for a free movie ticket.
.
a
how many visits must tyler make to earn a free movie ticket?
what is x > 7 j don't get it pls help me
Answer:
j < x/7
Step-by-step explanation:
What is the area of a parallelogram with a base of 26 m and a height of 18 m?
Answer:
468 m²
Step-by-step explanation:
Given:
→ Base = 26 m
→ Height = 18 m
Formula:
[tex]\text{Area of parallelogram: Base} \times \text{Height}[/tex]
To determine the area of the parallelogram, we need to substitute the base and the height in the formula.
Substitute the measures in the formula:
[tex]\implies \text{Area of parallelogram: Base} \times \text{Height}[/tex]
[tex]\implies \text{Area of parallelogram} = 26 \times 18[/tex]
Evaluate the area of the parallelogram:
[tex]\implies \text{Area of parallelogram} = 26 \times 18[/tex]
[tex]\implies \text{Area of parallelogram}= \bold{468 \ \text{m}^{2}}[/tex]
Answer:
468 m²
Step-by-step explanation:
Given,
Base ( b ) = 26 m
Height ( h ) = 18 m
To find : The area of parallelogram
Formula : -
Area of parallelogram = bh
Area of paralleogram
= 26 x 18
= 468 m²
Therefore,
the area of the parallelogram is 468 m².
Carlos says that 17.43 divided by 100 is the same as 174.3 times 0.01. Is he correct?
Answer:
that's not correct.
17.43/100= 0.1743
174.3×0.01=1.743
Fill in the table using this function rule.
y=3x+3
Answer:
9
24
27
30
Step-by-step explanation:
f(2) = 3(2) + 3 = 9
f(7) = 3(7) + 3 = 24
f(8) = 3(8) + 3 = 27
f(9) = 3(9) +3 = 30
Hope this helps!
Find the odds agasinst getting a number less than 4
Answer:
3 out of 4 I think
Step-by-step explanation:
because the total amount is 4 so there's a 3/4 chance youll get less than 4
Which equation represents the Temperture, t, at hour h?
The value of a company equipment is $25000 and decreases at a rate of 15% per year. What is the value of the equipment after 8 years.
Answer: $6812.3
Step-by-step explanation: Just solve decreasing 15% each year
A shipping box has a width of 6 inches, a length of 10 inches, and a height of 7 inches. What is the volume of the shipping box?
Answer:
V = 420 in^3
Step-by-step explanation:
Formula
The volume of a 3 dimensional box is V = L * w * h
Givens
L = 10 in
w = 6 in
h = 7 in
V = ?
Solution
Substitute the givens into the formula
V = 10 * 6 * 7 Combine
V = 420 in^3
Solve for y. y /4 + 15 = 17
Answer:
y = 2 x ± [tex]\sqrt{2}[/tex] =± 2.8284
Step-by-step explanation:
y*y/4+15-(17)=0
Answer:
[tex]4 + 15 \div y = 17 \\ \\ 4 + 15 = 17y \\ \\ 19 = 17y \\ \\ y = \frac{19}{17} [/tex]
4 . 7 p - 10 p =
Answer please !! Wrong answer will get you reported !
Hey there!
4 * 7p - 10p
= 4(7p - 10p)
= 4(7p) + 4(-10p)
= 28p - 40p
= -12p
Therefore, your answer is: -12p
Good luck on your assignment & enjoy day!
~Amphitrite1040:)
Help me please I don’t understand
Answer:
Area of composite shape = 36 square units
Step-by-step explanation:
Area of composite shape:
Rectangle I:
Length = 3 units
width = 6 - 4 = 2 units
Area of rectangle I = length *width
= 3* 2
= 6 square units
Rectangle II:
length = 6 units
width = 5 units
Area of rectangle II = 6 * 5
= 30 square units
Area of composite shape = area of rectangle I + area of rectangle II
= 6 + 30
= 36 square units
Given the spinner below in which all regions are equal, which of the following point scales would result in a favorable game? a spinner is divided into 4 equal sections. each section is a different color and is labeled 1 through 4. red is 1; 2 is blue; 3 is green; 4 is yellow. the odd numbered regions will add one point. the even numbered regions lose one point. red will add one point. any other color will lose one point. a number less than or equal to 3 will add one point. a 4 will lose two points. odds will add a point value equal to the number on the space. evens will lose a point value equal to the number on the space.
The correct option is C: A number less than or equal to 3 will add one point and A.4 will lose two points.
Given the spinner below in which all regions are equal, which of the following point scales would result in a favorable game
Therefore a spinner is divided into 4 equal sections.
What is the favorable game?
A favorable game is one in which, loosely speaking, there are opportunities for favorable bets.
each section is a different color and is labeled 1 through 4.
red is 1; 2 is blue; 3 is green; 4 is yellow.
The odd-numbered regions will add one point.
The even-numbered regions lose one point.
red will add one point.
any other color will lose one point. a number less than or equal to 3 will add one point.
Therefore the option a and c is correct
C: A number less than or equal to 3 will add one point.
A.4 will lose two points.
Edge
To learn more about the favorable game visit:
https://brainly.com/question/1393329
Answer:
A number less than or equal to 3 will add one point.
A 4 will lose two points.
Step-by-step explanation:
The answer above is correct.
please find the area of the shaded region
Answer:
Step-by-step explanation:
Remark
The way to solve the shaded region is to find the area of the square first and subtract the area of the circle from it.
Area of the square
Area = s^2
s = 12
Area of the square = 12 * 12
Area of the square = 144 yd^2
Area of the circle = pi * r^2
r = d/2
d is actually the same as the side length of the square
r = 12/2
r = 6
pi = 3.14
Area of the circle = pi * 6^2
Area of the circle = 3.14 * 36
Area of the circle = 113.04
Area of the shaded region
Area of shaded region = area of the square - area of circle
Area of shaded region = 144 - 113.04
Answer: Area of the shaded region 30.96
Lucy Garcia took out a loan for $40,000 at 10 percent interest for 10 years. Her monthly payments are $528. 60. She made payments for one year and has paid the principal down to $37,546. 36. She now wants to repay the loan early. The loan specifies a $300 prepayment penalty if she pays the loan now. How much will she save by paying the loan early (round final answer to nearest dollar)?
The amount saved due to early payment is $19,242
Data;
Monthly payment = 528.60Number of payment = 10 years * 12 = 120 Total payment if not prepaid = 528.60 * 120 = $63,432Total Payment for the whole termThe total payment for the whole term is the equal to the product of monthly payment and the number of payment as calculated above.
The total amount in cash in case of prepayment is
[tex]total amount in case of prepayment = monthly payment * number completed + balance + penalty[/tex]
The number of payment completed = 12
Balance = $37,546.36
Penalty for prepayment = 300
The amount of prepayment is
[tex]528.60 * 12 + 37546.36 + 300 = 44,189.56[/tex]
The amount saved due to early payment is
[tex]63432 - 44189.56 = 19,242[/tex]
The amount saved due to early payment is $19,242
Learn more on payment plans here;
https://brainly.com/question/251701
3) Solve 5(x + 3) - 3x = 55 for x. Use mathematical properties to justify each step in the process.
Step 1
Step 2
Step 3
Step 4
Step 5
solution
5(x+3)-3x=55
5x+15-3x=555x-3x+15=552x+15=552x=55-152x=402x/2=40/2x=20