Use addition to solve the linear system of equations. Include all of your work in your final answer.
x - y = 4
x+ 2y = 4
sin^{2} theta +cos theta = 2
Use the pythagorem identity sin^{2} theta +cos^{2} theta =1 to replace sin^{2} theta in the given equation
Applying Pythagorean Identity, the original equation sin² theta +cos theta = 2 can be altered by substituting sin² theta with 1 - cos² theta. This forms a quadratic equation: cos² theta - cos theta - 1 = 0, which can be solved using the quadratic formula to find the possible values of cos theta.
Explanation:To solve the equation sin² theta +cos theta = 2 by using the Pythagorean identity sin² theta +cos² theta =1, we can substitute sin² theta in the original equation with 1 - cos² theta.
Step-by-step solution:
We start by replacing sin² theta in the equation with 1 - cos² theta. So, the equation becomes 1 - cos² theta + cos theta - 2 = 0.This can be rearranged to form a quadratic equation as cos² theta - cos theta - 1 = 0.We can solve this quadratic equation using the quadratic formula cos theta = [- (-1) ± √{(-1)²-4(1)(-1)} ] /2(1).Computing the values, we get the two possible values of cos theta.Learn more about Pythagorean Identity here:https://brainly.com/question/24287773
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Ms.kellsons storage closet is 3ft long,3ft wide,and 7 ft high.can she fit 67 boxes that each have a volume of 1 cubic foot in her closet
Consider the arithmetic series:
1 + 9 + 17 + 25 + ...
Write a formula for the sum of the first n terms in this series.
A) 4n2 - 3n
B) 6n2 - 7n
C) 8n2 - 5n
simplify radical (1-cos0)(1+cos0)/ cos^2 0
HELP ME PLS!! ASAP
A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. If being in band is the row variable and playing sports is the column variable, fill in the labels in the table. tables Which of the following correctly represents the given data in the problem?
D) a = 24, c = 48, e = 22, i = 80
Ajuda eu !!!!!!!!!!!!!!!!
Henry has a defined benefit plan that promises a 2.5% annual retirement benefit based on the average of his last five years of salary. At retirement Henry has 21 years of service and an average salary over the last five years of $95,000. What will his annual benefit be?
Henry's annual retirement benefit will be $2,375.
We have,
To calculate Henry's annual retirement benefit, we need to find 2.5% of his average salary over the last five years.
First, let's calculate 2.5% of $95,000:
2.5% = 2.5/100 = 0.025
Annual benefit = 0.025 * $95,000
Annual benefit = $2,375
Therefore,
Henry's annual retirement benefit will be $2,375.
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QS is the perpendicular bisector of PR solve for x
2x - 20 = 70 - x
3x - 20 = 70
3x = 90
x = 30
match the following situation with one of the linear systems. Lewis wants to acquire at most 12 packages of baseball cards. Some packages have 4 rookie cards and some have only 3. In all, there are at most 38 rookie cards.
A.
B.
C.
D.
The correct linear system for the student's question is D. x + 3y \<= 38, x + y \<= 12, which matches the conditions of Lewis's situation for acquiring baseball cards.
The student is looking to match a situation with a linear system. The situation is that Lewis wants at most 12 packages of baseball cards, some containing 4 rookie cards and others 3 rookie cards, with a total of 38 rookie cards at most.
To match the situation with the correct linear system, we must set up two inequalities: one for the number of packages and another for the number of rookie cards.
Let x represent the number of packages with 4 rookie cards and y represent the number of packages with 3 rookie cards.
The first condition is that Lewis can have at most 12 packages, which gives us the inequality x + y \<= 12. The second condition is that the total number of rookie cards is at most 38, which gives us the inequality 4x + 3y \<= 38.
Considering these conditions, the correct answer is: D. x + 3y \<= 38, x + y \<= 12.
Vanessa is opening a clothing store. She plans to start by selling gym shorts. If it costs her $4 for each pair of shorts, $3 for the ink per pair of shorts, and $0.20 a bag, what is her unit cost per pair of shorts?
Answer:
its $7.20 on APEX
Step-by-step explanation:
trignometry help what's the answer?
How does the volume of an oblique cylinder change if the radius is reduced to 2/9 of its original size and the height is quadrupled?
A. V=2/81pir^2h
B. V=16/81pir^2h
C. V=4/9pir^2h
D. V=16/9pir^2h
Which additional information is needed to solve this problem?
John wants to buy a new game for his computer. He can save $12 a week if he mows his neighbor's lawn and $10 a week if he babysits his nephew. How many weeks will it take John to save enough money to buy the computer game?
A.
total amount John can save in 1 week
B.
the cost of the game
C.
amount John earns per hour babysitting
A trapezoid with an area of 166.75 in has bases that measure 21 in and 8 in find the height of the trapezoid
The required height of the trapezoid is 11.5 inches.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
Here,
The formula for the area of a trapezoid is:
A = (b₁ + b₂) * h / 2
where A is the area, b1 and b2 are the lengths of the two bases, and h is the height.
We are given that the area of the trapezoid is 166.75 in² and the lengths of the two bases are 21 in and 8 in. So we can plug these values into the formula and solve for h:
166.75 = (21 + 8) * h / 2
Simplifying the expression on the right side:
166.75 = 29 * h / 2
Multiplying both sides by 2:
333.5 = 29 * h
Dividing both sides by 29:
h = 11.5
So the height of the trapezoid is 11.5 inches.
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Final answer:
To find the height of a trapezoid given its area (166.75 sq in) and bases (21 in and 8 in), you use the formula-
[tex]A = \frac{1}{2} h(b_1 + b_2)[/tex]
By rearranging to solve for h, you find that the height is 11.5 inches.
Explanation:
The question asks to find the height of a trapezoid given its area and bases. The area of a trapezoid is calculated using the formula A = [tex]\(\frac{1}{2}\)h(b_1 + b_2)[/tex], where A represents the area, h the height, and [tex]b_1[/tex] and [tex]b_2[/tex] the lengths of the two bases. In this case, the area is 166.75 square inches, and the bases measure 21 inches and 8 inches.
To find the height, we can rearrange the formula to-
h = [tex]\(\frac{2A}{b1 + b2}\)[/tex]
Plugging in the given values gives us-
h = [tex]\(\frac{2 \times 166.75}{21 + 8}\)[/tex]
which simplifies to-
h = [tex]\(\frac{333.5}{29}\)[/tex]
Therefore, the height of the trapezoid is 11.5 inches.
Algebra question ( Matrices and Determinants ) 20 points
In a weekly lottery, ten ping-pong balls numbered 0 to 9 are placed in each of six containers, and one ping-pong ball is drawn from each container. To win the prize, a participant must correctly identify the ping-pong ball that is drawn from each of the six containers. If Juan played the lottery last week and didn’t win, what is the probability that he will win this week?
The probability that he will win this week is 0.0001%.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Ten ping-pong balls numbered 0 to 9 are placed in each of six containers.
It will not effect the outcome if Juan didn't win last week.
So, the probability that he will win this week
= [tex](1/10)^6[/tex]
= 1/1,000,000
= 0.000001
= 0.0001%
Hence, the probability that he will win this week is 0.0001%.
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This is a question about inverse/transcendental functions. Can anyone confirm that the answer is D? The question is asking which statement is FALSE, and I'm bouncing back and forth a bit.
Cans of juice cost 25p each to produce
There are 6 cans in a pack.
12 packs are sold at £3.60 each.
What is the profit?
A poll was conducted in states A, B, and C to determine which candidate voters would most likely vote for. The results are displayed in the table below:
What is P(conservative | State B)?
State A State B State C Total
Liberal 17 20 12 49
Conservative 23 15 13 51
Total 40 35 25 100
Answer:
15/35 = 3/7 = 0.428571
Explanation:
We are asked to find the probability that a given voter is conservative given they are in State B.
Going to the State B column, we see that there are 15 conservatives. This is out of a total of 35 voters in state B; this makes the probability 15/35.
Probability helps us to know the chances of an event occurring. The probability that a voter from State B is supporting Conservative is 0.4285.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
We're supposed to figure out how likely it is that a specific voter in State B is a conservative.
There are 15 conservatives in State B, according to the column. This is based on a total of 35 voters in state B, resulting in a 15/35 probability. Therefore,
P(conservative | State B) = 15/35 = 3/7 = 0.4285
Hence, the probability that a voter from State B is supporting Conservative is 0.4285.
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|-x-2y| for x =-3 and y=3
Hexagon DEFGHI is translated 6 units down and 6 units to the right. If the coordinates of the pre-image of the point F are (-9,2) what are the coordinates of F
Answer:
-6,-6
Step-by-step explanation:
(-9,2) + (-8,3) = (-6,-6)
correct on the test :)
Which expression is equivalent to 4 sqrt 16x^11y^8/81x^7y^6
The given expression 4 sqrt(16x^11y^8/81x^7y^6) simplifies to (4/9) * x^2 * y by taking the square root of each term separately and then simplifying the powers of x and y.
Explanation:The expression given is 4 sqrt(16x^11y^8/81x^7y^6). To simplify this expression, we need to apply the square root to both the numerator and the denominator separately and simplify any like terms, as well as using the property of exponents to simplify the powers of x and y.
We start by simplifying the square root of each component:
Square root of 16 is 4.x^11 under the square root becomes x^(11/2).Similarly, y^8 under the square root becomes y^(8/2), which is y^4.The square root of 81 is 9.x^7 under the square root becomes x^(7/2).y^6 under the square root becomes y^(6/2), which is y^3.Now, divide and simplify:
(4 * x^(11/2) * y^4) / (9 * x^(7/2) * y^3) = (4/9) * x^((11/2) - (7/2)) * y^(4 - 3)
Therefore, we get:
(4/9) * x^2 * y
Tell whether each set of ordered pairs representd a function. Justify your answers.
a. (0,0), (1,1), (2,2), (3,3), (4,4)
b. (0,8), (1,6), (2,4), (3,2), (4,0)
c. (3,0), (3,1), (3,2), (3,3), (3,4)
You draw a single card from a standard deck of cards. what is the probability of drawing a diamond?
what is the solution of the equation?
please help!!
The line plot represents the heights of students in a second-grade classroom. Which statement is true?
A. The median is less than the mode.
B. The median height is 42 inches, and the mode height is 36 inches.
C. Most of the students in the class are shorter in height.
D. The mode is less than the median.
Answer:
B. The median is less than the mode
Step-by-step explanation:
The perimeter of the base of a pentagonal prism is 25 inches and one of its lateral edges is 4 inches. The lateral area of the prism is ________ square inches.
Answer:
Lateral area=100 square inches
Step-by-step explanation:
It is given that the perimeter of the base of a pentagonal prism is 25 inches, therefore each sides of the pentagon will be of 5 inches.
Also, one of its lateral edge is 4 inches, therefore each lateral face has area which will be equal to=[tex]5{\times}4[/tex]=[tex]20[/tex]square inches.
Since, there are 5 lateral faces of the pentagonal prism, therefore the lateral area of the prism will be: [tex]5{\times}20[/tex]
= [tex]100[/tex]square inches.
Need help with math thank u
During a family vacation, Ms. Walker drove 918 miles on 3 tanks of gasoline. Her daughter, Amani, wants to create an equation in the form em equals square tee, to represent the total number of miles, m, her mom can drive on t tanks of gasoline. What number should Amani put in the square to complete her equation?