Value of cosθ will be cosθ = (√2)/2 after using Pythagorean Identity.
The Pythagorean Identity states that sin²θ + cos²θ = 1. We can use this identity to find cosθ given that sinθ = (√2)/2 and θ terminates in Quadrant I.
Since sinθ = (√2)/2 and θ terminates in Quadrant I, we can draw a right triangle with angle θ in Quadrant I, opposite side equal to √2, adjacent side equal to 1, and hypotenuse equal to √3.
Using the Pythagorean Theorem, we can find the length of the hypotenuse as:
h² = a² + b²
√3² = 1² + (√2)²
3 = 1 + 2
3 = 3
So, the length of the hypotenuse is √3.
Now, we can use the Pythagorean Identity to find cosθ:
sin²θ + cos²θ = 1
Substituting sinθ = (√2)/2:
(√2/2)² + cos²θ = 1
Simplifying:
2/4 + cos²θ = 1
1/2 + cos²θ = 1
cos²θ = 1 - 1/2
cos²θ = 1/2
Since θ terminates in Quadrant I and sinθ is positive, we know that cosθ is also positive. Therefore, taking the positive square root of both sides, we get:
cosθ = √(1/2) = (√2)/2
So, cosθ = (√2)/2.
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what is the slope of the line that contains the points (-2,-20) and (3,30)?
The slope of the line that contains the points (-2,-20) and (3,30) is 10
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We have to find the slope of the line that contains the points (-2,-20) and (3,30)
Slope= 30-(-20)/3-(-2)
=30+20/3+2
=50/5
=10
Hence, the slope of the line that contains the points (-2,-20) and (3,30) is 10
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State the coordinates of the point after the reflection across each axis.
1. (5,2)
2. (-6, 12)
3. (2,-7)
4. (-4,-2)
5. (0,-2)
Reflect across
the x-axis
Reflect across
the y-axis
Answer:
Step-by-step explanation:
Reflecting a point across the x-axis results in changing the sign of the y-coordinate, but keeping the x-coordinate the same. Reflecting a point across the y-axis results in changing the sign of the x-coordinate, but keeping the y-coordinate the same.
Reflecting (5,2) across the x-axis gives (5,-2), and reflecting it across the y-axis gives (-5,2).
Reflecting (-6,12) across the x-axis gives (-6,-12), and reflecting it across the y-axis gives (6,12).
Reflecting (2,-7) across the x-axis gives (2,7), and reflecting it across the y-axis gives (-2,-7).
Reflecting (-4,-2) across the x-axis gives (-4,2), and reflecting it across the y-axis gives (4,-2).
Reflecting (0,-2) across the x-axis gives (0,2), and reflecting it across the y-axis gives (0,-2).
1. Which of the following is equivalent to 6/10? 5/9 9/15 8/12 36/100
A fair coin is tossed 8 times. Find the probability it comes up heads at least TWICE. Use nCr!
The probability of getting at least two heads is 0.965
Given that
Number of times fair coin tossed = 8
Since we know
The probability of getting head in single toss = 1/2
And probability of getting tail in single toss = 1/2
Now, there are 247 combinations to get least two heads (256—1–8=247).
Therefore,
The probability of getting at least two heads
= 247/256 or 0.965…
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Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
The statement that could be true for function g b) g(-13) = 20.
Since g has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45, it is possible that g(-13) = 20. The fact that g(0) = -2 and g(-9) = 6 does not provide enough information to determine the value of g at x = -13.
Statement (a) is not possible since g(7) is outside the domain of g. Statement (c) is not possible since g(0) was given as -2. Statement (d) is not possible since -11 is outside the range of g.
Correct Question :
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.
a) g(7) = -1
b) g(-13) = 20
c) g(0) = 2
d) g(-4) = -11
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Which of the following functions has a diagonal asymptote?
O
○ y = x + = 1/3
x+1
x-8
O y=
O y=
(x+4)(x-1)
x(x-7)
1
y ====
O y=
x-5
y = x(x − 3)
x + 2
y= x+1/x-8 has a diagonal asymptote. Therefore, the correct option is option A among all the given options.
A line that, in analytical geometry, is an asymptote either a curve is one where, when either or both of the x and y coordinates go to infinity, the distance among the curve as well as the line approaches zero. An asymptote on a curve appears a line that is tangential with the curve at an angle at infinity in projection geometry and similar contexts. y= x+1/x-8 has a diagonal asymptote.
Therefore, the correct option is option A.
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What’s the integral of 1/2
Solve for the missing side length. Round to the nearest tenth.
5.8
5.2
5.4
5.6
Answer:
C) 5.4-------------------------
Given two legs of a right triangle and we need to find the hypotenuse.
Use Pythagorean theorem:
[tex]PQ = \sqrt{QR^2+PR^2}[/tex][tex]PQ = \sqrt{2^2+5^2} =\sqrt{29} =5.385 = 5.4\ (rounded)[/tex]The matching choice is C.
Helppp pleaseeeeeeee
The values of the matrices operations are [tex]4G + 2F = \left[\begin{array}{ccccc}34&-4&-42&-18&48\\-42&-8&16&30&8\\24&32&4&34&34&-12&-32&-12&-42&-20\end{array}\right][/tex] and [tex]4D - 3B= \left[\begin{array}{ccccc}31&6&34&-14&-57\\-19&-27&-18&18&27\\47&14&-1&-40&9&10&12&-19&-15&-58&-14&-23&10&-8&10\end{array}\right][/tex]
Evaluating the matrices operationsFrom the question, we have the following parameters that can be used in our computation:
[tex]G = \left[\begin{array}{ccccc}8&-5&-7&-1&10\\-6&-7&1&9&2\\4&6&3&7&5&-4&-3&0&-10&-9\end{array}\right][/tex]
Also, we have
[tex]F = \left[\begin{array}{ccccc}1&8&-2&-5&9\\-9&10&6&-3&0\\4&5&-4&3&7&2&-10&-6&-1&-8\end{array}\right][/tex]
Using the above as a guide, we have
[tex]4G + 2F = 4\left[\begin{array}{ccccc}8&-5&-7&-1&10\\-6&-7&1&9&2\\4&6&3&7&5&-4&-3&0&-10&-9\end{array}\right] + 2 \left[\begin{array}{ccccc}1&8&-2&-5&9\\-9&10&6&-3&0\\4&5&-4&3&7&2&-10&-6&-1&-8\end{array}\right][/tex]
Evaluate the sum
[tex]4G + 2F = \left[\begin{array}{ccccc}34&-4&-42&-18&48\\-42&-8&16&30&8\\24&32&4&34&34&-12&-32&-12&-42&-20\end{array}\right][/tex]
Next, we have
[tex]D = \left[\begin{array}{ccccc}7&-6&3&-8&-9\\2&-9&-6&6&9\\8&2&5&-10&-3&10&-3&-4&3&-7&1&-2&4&-5&-2\end{array}\right][/tex]
Also, we have
[tex]B = \left[\begin{array}{ccccc}-1&-10&-8&-6&7\\9&-3&-2&2&3\\-5&-2&7&0&-7&10&-8&1&9&10&6&5&2&-4&-9\end{array}\right][/tex]
The matrix expression is then represented as
[tex]4D - 3B= 4\left[\begin{array}{ccccc}7&-6&3&-8&-9\\2&-9&-6&6&9\\8&2&5&-10&-3&10&-3&-4&3&-7&1&-2&4&-5&-2\end{array}\right] - 3\left[\begin{array}{ccccc}-1&-10&-8&-6&7\\9&-3&-2&2&3\\-5&-2&7&0&-7&10&-8&1&9&10&6&5&2&-4&-9\end{array}\right][/tex]
Evaluate
[tex]4D - 3B= \left[\begin{array}{ccccc}31&6&34&-14&-57\\-19&-27&-18&18&27\\47&14&-1&-40&9&10&12&-19&-15&-58&-14&-23&10&-8&10\end{array}\right][/tex]
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can some please help with 11 !!!!
Find the difference quotient f(x+h) -f(x)/h , where h does not equal 0, for the function below.
f(x)=-3x^2+6x-6
The difference quotient for the function f(x)=-3x²+6x-6 is -3h+6.
Now, let's move on to finding the difference quotient for the function f(x)=-3x²+6x-6. The difference quotient is a formula used to find the average rate of change of a function between two points.
The formula for the difference quotient is:
f(x+h) - f(x)
So, to find the difference quotient for the function f(x)=-3x²+6x-6, we first need to find f(x+h) and f(x):
f(x+h) = -3(x+h)² + 6(x+h) - 6
= -3(x² + 2xh + h²) + 6x + 6h - 6
= -3x² - 6xh - 3h² + 6x + 6h - 6
f(x) = -3x² + 6x - 6
Now we can plug these values into the difference quotient formula:
f(x+h) - f(x)
= [-3x² - 6xh - 3h² + 6x + 6h - 6] - [-3x² + 6x - 6]
= [-3x² - 6xh - 3h² + 6x + 6h - 6 + 3x² - 6x + 6] / h
= [-3h² + 6h] / h
= -3h + 6
This tells us the average rate of change of the function between x and x+h is -3h+6.
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To which linear equations is the coordinate a solution? Select two options. y = 2x + 13 y = –x – 2 y = 3x – 5 y = negative one-half x + 6 y = –2x – 2
The equation y = -x - 2 and y = 2x + 13 has the coordinate a solution (-5, 3).
From the given coordinate plane, the solution is (-5, 3).
A linear equation is in the form: y = mx + b
where y, x are variables, m is the rate of change and b is the y intercept.
When (x, y)=(-5, 3)
The linear equation y = -x - 2 satisfies this this equation because 3 = -(-5) -2
Also, the linear equation y = 2x + 13 satisfies this this equation because 3 = 2(-5) + 13
Therefore, the equation y = -x - 2 and y = 2x + 13 has the coordinate a solution (-5, 3).
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GIVE BRAINLIST PLEASE HELP
Answer:
P = π(11^2)/(22^2) = π/4 = .79 (about 79%)
25. Which statement about the following set
is true?
{60, 5, 18, 20, 37, 37, 11, 90, 72}
A) The median and the mean are equal.
B) The mean is less than the mode.
C) The mode is greater than the median.
D) The median is less than the mean.
E) The mode and the mean are equal.
The correct statement is,
D) The median is less than the mean.
E) The mode and the mean are equal.
Given that;
Data set is,
⇒ {60, 5, 18, 20, 37, 37, 11, 90, 72}
Hence, We can formulate;
Mean = {60 + 5 + 18 + 20 + 37 + 37 + 11 + 90 + 72} / 9
Mean = 38.89
Arrange data set into ascending order,
⇒ 5, 11, 18, 20, 37, 37, 60, 72, 90
Hence,
Median = (9 + 1)/2
= 5th term
= 37
Mode = 37
Thus, The correct statement is,
D) The median is less than the mean.
E) The mode and the mean are equal.
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Help on any of these pls
You start at (-1, -2). You move down 3 units. Where do you end?
You will end up at the point (-1, -5).
We have,
Starting at the point (-1,-2), moving down 3 units means moving 3 units in the negative y-direction.
Now,
The endpoint will have the same x-coordinate as the starting point but a y-coordinate that is 3 less than the starting y-coordinate.
This means,
The endpoint is (-1, -5).
Thus,
You will end up at the point (-1, -5).
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I will give brainliest and ratings if you get this correct
Answer:
the equilibrium output (Y) is (gA-b(10))Mo + 2520/25 = 1076 and the equilibrium interest rate (i) is -176.
Step-by-step explanation:
(a) Writing the IS-LM system in matrix form:
IS equation: Y = 1 - b(10) + gA
LM equation: Y = (Mo/k) - (/k)i
We can rewrite the equations in matrix form as:
| 1 - b(10) -gA | | Y | | 0 |
| 1/k /k | | i | = | Mo/k |
(b) Solving for Y and i by matrix inversion:
| Y | | (1/k) (gA-b(10))/k | | 0 |
| i | = | (1/k) (-1/k) | | Mo/k |
Multiplying the inverse matrix by the right-hand side:
| Y | | (1/k) (gA-b(10))/k | | 0 | | (gA-b(10))Mo/k |
| i | = | (1/k) (-1/k) | | Mo/k | = | -Mo/k |
Solving for Y and i:
Y = (gA-b(10))Mo + 2520
25
i = -176
Therefore, the equilibrium output (Y) is (gA-b(10))Mo + 2520/25 = 1076 and the equilibrium interest rate (i) is -176.
5x-8x+3 simplify the filling expression
Answer:
5x - 8x + 3 can be simplified as follows:
5x - 8x = -3x (subtract the coefficients of x)
Therefore, the simplified expression is:
-3x + 3
(Hi there, do you like stories? if so, go into my profile for my questions. Read the excerpt and give me feedback if you can)
Solve by completing the square.
j² + 14j + 5 = 0
Write your answers as integers, proper or improper fractions in simplest form, or decimals
rounded to the nearest hundredth.
Submit
or j =
=
Answer:
[tex]j = 7 \pm \sqrt{44}[/tex]
Step-by-step explanation:
First, move the constant term to the other side of the equation.
[tex]j\² + 14j + 5 = 0[/tex]
[tex]j\² + 14j = -5[/tex]
Next, add the coefficient of the first degree j term divided by 2, then squared to both sides.
[tex]j^2 + 14j + (14/2)^2 = -5 + (14/2)^2[/tex]
[tex]j^2 + 14j + (7)^2 = -5 + (7)^2[/tex]
[tex]j^2 + 14j + 49 = -5 + 49[/tex]
[tex]j^2 + 14j + 49 = 44[/tex]
Now, we can factor the left side as a square.
[tex](j+7)(j+7) = 44[/tex]
[tex](j+7)^2 = 44[/tex]
Finally, we can take the square root of both sides to solve for j.
[tex]\sqrt{(j+7)^2} = \sqrt{44[/tex]
[tex]j+7=\pm\sqrt{44}[/tex]
[tex]\boxed{j = 7 \pm \sqrt{44}}[/tex]
Note that there are two solutions, as [tex]\sqrt{44[/tex] could be positive OR negative because of the even root property:
if [tex]x^2 = a^2[/tex],
then [tex]x = \pm a[/tex]
because both [tex](+a)^2[/tex] and [tex](-a)^2[/tex] equal [tex]a^2[/tex].
A ladder is leaning against a brick chimney as shown in the picture below. The ladder is 25 feet long and is placed 15 fee up on the chimney. In order for the ladder to be stable, its base must be 15 feet or less away from the base of the chimney. Is the current position of the ladder stable?
Yes, the height of the ladder and the distance from the base of the chimney are both 15 feet.
No, the distance of the ladder from the base of the chimney is 20 feet.
Yes, the distance of the ladder from the base of the chimney is 10 feet.
No, the distance of the ladder from the base of the chimney is 40 feet.
Answer:
No, the distance of the ladder from the base of the chimney is 20 feet.
Step-by-step explanation:
PLS HELP NO TROLLING PLS
The probability that a randomly selected points falls within the red-shaded square is given as follows:
p = 9/16.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The area of the red-shaded square is given as follows:
3² = 9 units².
The total area is given as follows:
4² = 16 units².
Hence the probability that a randomly selected points falls within the red-shaded square is given as follows:
p = 9/16.
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Sasha Rudy and Mario each have 1 3/4 cups of flour. Can they make a recipe for bread that needs 5 cups of flour?
Answer:
Yes
Step-by-step explanation:
1 3/4 x 3 = 7/4 x 3 = 21/4 = 5 1/4 cups
find all solutions of x^2-6x+10=0 express in form a+bi
the solutions of the equation [tex]x^{2} -6x+10=0[/tex] in terms of a+ib are given by x=3-i and x=3+i.
The given equation is [tex]x^{2} -6x+10=0[/tex]. To find the solution to the equation, we use the quadratic formula.
The expression [tex]ax^{2} +bx+c=0[/tex] is the quadratic equation of the second degree, where a, b, and c are coefficients, then the quadratic formula is given by, [tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex].
Here, [tex]a=1[/tex], [tex]b=-6[/tex], and [tex]c=10[/tex]. Substitute all the values in the above formula, and we get
[tex]$x=\frac{-6\pm\sqrt{(-6)^2-4(1)(10)}}{2(1)}$[/tex]
[tex]$x=\frac{-6\pm\sqrt{36-40}}{2}$[/tex]
[tex]$x=\frac{-6\pm\sqrt{-4}}{2}$[/tex]
The squares of the negative real number give an imaginary unit 'i'.
So, the value of [tex]\sqrt{-4}[/tex] is [tex]2i[/tex]. Then,
[tex]x=\frac{-6\pm2i}{2}[/tex]
[tex]x=\frac{2(3\pm i)}{2}}[/tex]
[tex]x=3\pm i[/tex]
Therefore, the solutions of the equation [tex]x^{2} -6x+10=0[/tex] in terms of a+ib are given by [tex]x=3-i[/tex] and [tex]x=3+i[/tex].
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What are the x-intercepts of the quadratic function shown?
Answer:
if you are asking for an angle it's either 180° or 0°
Answer:
your answer is D. 1,0 & -3,0
Step-by-step explanation:
have a nice day.
There are 3 red jelly beans, 5 blue jelly beans, 2 orange jelly beans, and and 5 yellow jelly beans in a bag. Another bag has 1 pink jelly bean, 7 purple jelly beans, and 2 green jelly beans. What is the probability of randomly selecting a blue jelly bean from the first bag and then randomly selecting a green jelly bean from the second bag?
1/15
3/10
7/25
1/4
The probability of randomly selecting a blue jelly bean from the first bag and then randomly selecting a green jelly bean from the second bag is 1/15 (option a).
Firstly, we need to determine the total number of jelly beans in both bags.
The first bag contains 15 jelly beans (3+5+2+5) and the second bag contains 10 jelly beans (1+7+2).
Therefore, the total number of jelly beans in both bags is 25.
Next, we need to determine the probability of randomly selecting a blue jelly bean from the first bag.
Since there are 5 blue jelly beans out of a total of 15 jelly beans in the first bag, the probability of selecting a blue jelly bean is 5/15 or 1/3.
After selecting a blue jelly bean from the first bag, we move on to the second bag to select a green jelly bean.
Since there are 2 green jelly beans out of a total of 10 jelly beans in the second bag, the probability of selecting a green jelly bean is 2/10 or 1/5.
To determine the probability of both events occurring, we use the multiplication rule of probability.
Therefore, the probability of randomly selecting a blue jelly bean from the first bag and then randomly selecting a green jelly bean from the second bag is (1/3) x (1/5) = 1/15.
Hence, the answer is option (a) 1/15.
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tan=11/60, cos=60/11, sin=
[tex]{\boxed{\sf tan\Theta=\dfrac{sin\Theta}{cos\Theta}}}[/tex]
[tex]\\ \sf\longmapsto \dfrac{11}{60}=\dfrac{sin\Theta}{\dfrac{60}{11}}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{11}{60}\times \dfrac{60}{11}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{121}{3600}[/tex]
A 40% off sale begins today at Wandas women’s warehouse what is the sale price of women’s wool coats normally priced at $250
Answer: $150
Step-by-step explanation:
250 x 0.60
=$150
Please help !!!!!!!!!!! 25 points
When Cassie Pennicuik says "celebrate the effort," she likely means that it's important to acknowledge and recognize the hard work and dedication that goes into achieving a goal, regardless of whether the outcome is successful or not.
Understanding the statement of Cassie PennicuikBy celebrating the effort, she's encouraging people to appreciate the journey and process of working towards a goal, and not just focus solely on the end result.
Celebrating the effort can take many forms. Here are some of them:
acknowledging milestones: the progress made towards the goal,recognizing individual: team contributions and efforts of individual,taking time to reflect: reflect on what has been learned and achieved throughout the process.It's a way to show appreciation and support for the hard work and dedication that goes into pursuing a goal, and to foster a positive and motivating work culture.
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Find the perimeter of the figure below. Show all work for each step. Work should include explanations in words detailing how you simplify each specific radical. Take your time and be thorough. Include units in final answer.
The perimeter of the rectangle is 22√3 ft
Given that a rectangle with dimension 5√3 ft and 3√12 ft we need to find its perimeter,
So, the perimeter of a rectangle = 2(length + width)
= 2(5√3 + 3√12)
= 2(5√3 + 3√(4×3)
= 2(5√3 + 3×2√3)
= 2(5√3 + 6√3)
= 2(11√3)
= 22√3
Hence the perimeter of the rectangle is 22√3 ft
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please helppppppppppppppppppppppppppp
Answer: its the first one
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Volume = 27.2
⅓ × base area × height = 27. 2
Base area × height = 81.6
Base area = ½ bh = 1/2 × 3.2 × 8.5 = 13.6
13.6 × height = 81.6
Height = 81.6 ÷ 13.6 = 6 inches
