Use the Pythagorean Identity to find cosθ if sinθ=(√2)/2 and θ terminates in Quadrant I.

Answer:

Yes

Step-by-step explanation:

1  3/4    x 3   =   7/4 x 3 = 21/4 = 5 1/4 cups

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].

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).

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]

From 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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Answer:

No, the distance of the ladder from the base of the chimney is 20 feet.

Step-by-step explanation:

Answer:

-------------------------

Given two legs of a right triangle and we need to find the hypotenuse.

Use Pythagorean theorem:

The matching choice is C.

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)

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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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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[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]

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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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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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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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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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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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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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.

By 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:

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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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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Answer: $150

Step-by-step explanation:

250 x 0.60

=$150

Answer:

P = π(11^2)/(22^2) = π/4 = .79 (about 79%)

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.

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.

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

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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The probability that a randomly selected points falls within the red-shaded square is given as follows:

p = 9/16.

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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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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