Complete the equation of the line whose slope is -2
and y-intercept is (0,3)(

The transofrmation applied was a Clockwise rotation of 90°about the origin.

Answer: Option C

I attached to pictures, one of me solving the equation for you step by step and then what the graph should look like when i put it in my calculator!!

Answer:

To find two numbers that add up to +29 and multiply to +100, you can use algebra. Let's call the two numbers "x" and "y". We know that:

x + y = 29

xy = 100

We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for "y" in terms of "x" by subtracting "x" from both sides:

y = 29 - x

Now we can substitute this expression for "y" into the second equation:

x(29 - x) = 100

Expanding the left-hand side of the equation gives:

29x - x^2 = 100

Rearranging and simplifying gives a quadratic equation:

x^2 - 29x + 100 = 0

This quadratic can be factored as:

(x - 4)(x - 25) = 0

So the two numbers that add up to +29 and multiply to +100 are +4 and +25.

Lisa was exerting the force at an angle of 41.41 degrees.

The formula given to calculate the work done, W = Fd cosθ, involves the force F, the displacement d, and the angle θ between the force and the displacement. We are given that Lisa does 1500 joules of work (W), exerts a force of 100 newtons (F), and moves the object through a displacement of 20 meters (d). We need to find the angle θ.

Rearranging the formula, we have:

W = Fd cosθ

Substituting the known values, we get:

1500 = 100 * 20 * cosθ

Simplifying, we have:

1500 = 2000 * cosθ

Dividing both sides by 2000, we find:

0.75 = cosθ

To find the angle θ, we need to take the inverse cosine (cos⁻¹) of 0.75. Using a calculator or a trigonometric table, we find that the angle whose cosine is 0.75 is approximately 41.41 degrees.

Therefore, Lisa was exerting the force at an angle of approximately 41.41 degrees.

This means that the force she exerted was not directly aligned with the displacement, but rather at an angle of 41.41 degrees to it. The cosine of the angle determines the component of the force in the direction of the displacement. In this case, the cosine of 41.41 degrees is 0.75, indicating that 75% of the force was aligned with the displacement, resulting in the given amount of work.

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(a)The polynomial p(x) = 2x^3 - 3x^2 + qx +56 has a factor x-2 . Therefore, q = -30. (b)  Therefore, the solutions of p(x) = 0 are x = 2, x = -1/2, and  x = 2.

a) To show that q = -30, we can use the factor theorem. According to the factor theorem, if a polynomial p(x) has a factor (x - c), then p(c) = 0.

In this case, the given polynomial p(x) has a factor (x - 2), so we substitute x = 2 into p(x) and set it equal to 0.

p(2) = 2(2)^3 - 3(2)^2 + q(2) + 56 = 2(8) - 3(4) + 2q + 56 = 16 - 12 + 2q + 56 = 4 + 2q + 56 = 2q + 60

Setting this equal to 0, we have: 2q + 60 = 0 Now, solving for q: 2q = -60 q = -30

Therefore, q = -30.

b) To factorize p(x) completely, we can use synthetic division to divide p(x) by (x - 2).

Using synthetic division, we get: The remainder is 2q + 56.

Since we know q = -30, we can substitute it in: 2q + 56 = 2(-30) + 56 = -60 + 56 = -4

So, the remainder is -4. Now, we can write the factored form of p(x): p(x) = (x - 2)(2x^2 - 7x - 4)

To find the solutions of p(x) = 0, we can set each factor equal to zero and solve for x: x - 2 = 0

=> x = 2 2x^2 - 7x - 4 = 0

Using factoring or the quadratic formula, we find the solutions of the quadratic equation to be: x = 2, x = -1/2, x = 4/2

Therefore, the solutions of p(x) = 0 are x = 2, x = -1/2, and x = 2.

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Answer:

B

Step-by-step explanation:

I have no step by step explanation because I did this in my head but I'm required to put 20 characters soo

Answer:

-114

Step-by-step explanation:

f(6) it means f(x=6) so substituting x=6 in your equation gives us

f(6)= -4*(6)²+5*(6)

= -4*36+30

= -144+30

= -114

Answer:

1. Tan θ = √11/5

2. Cosec θ = 6√11 /11

3. Cos θ = 5/6

Step-by-step explanation:

Let the side opposite to angle θ be y.

The value of y can be obtained by using the pythagoras theory as follow:

b² = 6² – 5²

b² = 36 – 25

b² = 11

Take the square root of both side.

b = √11

1. Determination of Tan θ

Tan θ =?

Opposite = √11

Adjacent = 5

Tan θ = Opposite /Adjacent

Tan θ = √11/5

2. Determination of Cosec θ.

We'll begin by calculating the Sine θ. This is illustrated below:

Sine θ =?

Opposite = √11

Hypothenus = 6

Sine θ = Opposite /Hypothenus

Sine θ = √11/6

Now, we shall determine Cosec θ as follow:

Cosec θ = 1/Sine θ

Sine θ = √11/6

Cosec θ = 1 ÷ √11/6

Cosec θ = 1 × 6/√11

Cosec θ = 6/√11

Rationalise the denominator

Cosec θ = 6/√11 × √11/√11

Cosec θ = 6√11 /11

3. Determination of Cos θ.

Cos θ =?

Adjacent = 5

Hypothenus = 6

Cos θ = Adjacent / Hypothenus

Cos θ = 5/6

The correct answer is (b) all real numbers except odd multiples of π/2. The domain of validity for cscθ (cosecant) is restricted because cosecant is undefined when the sine of an angle is zero.

In the trigonometric identity cscθ = 1/sinθ, the denominator sinθ becomes zero at odd multiples of π/2 (such as π/2, 3π/2, 5π/2, etc.), resulting in a division by zero error. Therefore, the cosecant function is not defined for these values of θ.

For all other real numbers θ, the sine function is non-zero and well-defined, allowing us to calculate the reciprocal of the sine and determine the value of the cosecant. Hence, the domain of validity for cscθ is all real numbers except odd multiples of π/2, as stated in option (b).

It's important to note that in trigonometry, the domain of validity is determined by avoiding any values that would lead to undefined expressions or division by zero errors.

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The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π, because at these points the sine function equals zero, and division by zero is undefined.

In mathematics, the cosecant function (csc), is defined as the reciprocal of the sine function, or 1/sinθ. The domain of a function are all the possible input values that will yield real numbers (output). For the csc function, its domain includes all real numbers except where the denominator is zero because division by zero is undefined.

In the unit circle context, sine equals zero at 0, π, 2π, ..., and the negative counterparts. Basically, these are the multiples of π. Thus, for the csc function, the domain is all real numbers except multiples of π, which matches option d in your choices.

The domain of validity for csc θ = 1/sin θ is all real numbers except multiples of π.

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Answer:

I think that is the fist one.

6m/s

calculate the number of balloon that can be filled up.

Step-by-step explanation:

speed =wavelength ×Frequency

=6×2 =12m/d

C.8 is the answer.

Step-by-step explanation:

Mode: The number that occurs the highest number of times.

Answer:

The Answer is C). 8

Step-by-step explanation:

bcause there are more 8's then all the other number if that makes sense

Hope this helps!!!

Answer:Answer:The equation that could be used to determine the length of each of the four pieces of wood he cut is 3.5 = 0.6 + 4x and the solution is x = 0.725

Part A: Write an equation that could be used to determine the length of each of the four pieces of wood he cut.

Represent the length of the four pieces with x

So, the given parameters are:

Initial length = 3.5 feet

Remaining length = 0.6 feet

Number of pieces = 4

The equation that could be used to determine the length of each of the four pieces of wood he cut is represented as:

Initial length = Remaining length + Number of pieces * x

This gives

3.5 = 0.6 + 4x

Hence, the equation that could be used to determine the length of each of the four pieces of wood he cut is 3.5 = 0.6 + 4x

Part B: Explain how you know the equation from Part A is correct.

The equation in part (A) is correct because it can be used to determine the length of each of the four pieces of wood he cut

Part C: Solve the equation from Part A.

In part A, we have:

3.5 = 0.6 + 4x

Subtract 0.6 from both sides

2.9 = 4x

Divide both sides by 4

x = 0.725

Hence, the solution is x = 0.725

Step-by-step explanation:

Hope I helped ;)

a) The transition matrix from C to B is [1 0 0], [0 1 0], [0 0 1] b) The transition matrix from C to B is [1 0 0], [0 1 0], [0 0 1] c) p(x) = a + bx + cx² as a linear combination of the polynomials in C can be defined as p(x) = a + b + c(x - 1)²

(a) Finding the transition matrix from C to B

To find the transition matrix from C to B, we need to express the vectors in the basis C as linear combinations of the vectors in basis B.

Let's express each vector in basis C in terms of basis B

1 = 1(1) + 0(x) + 0(x²)

(2 - 1) = 0(1) + 1(x) + 0(x²)

(x - 1)² = 0(1) + 0(x) + 1(x²)

The coefficients of the linear combinations are the entries of the transition matrix from C to B. Thus, the transition matrix is

[1 0 0]

[0 1 0]

[0 0 1]

(b) Finding the transition matrix from B to C:

To find the transition matrix from B to C, we need to express the vectors in the basis B as linear combinations of the vectors in basis C.

Let's express each vector in basis B in terms of basis C

1 = 1(1) + 0(2 - 1) + 0((x - 1)²)

x = 0(1) + 1(2 - 1) + 0((x - 1)²)

x² = 0(1) + 0(2 - 1) + 1((x - 1)²)

The coefficients of the linear combinations are the entries of the transition matrix from B to C. Thus, the transition matrix is

[1 0 0]

[0 1 0]

[0 0 1]

(c) Writing p(x) = a + bx + cx² as a linear combination of the polynomials in C

To write p(x) = a + bx + cx² as a linear combination of the polynomials in C, we need to express the polynomial p(x) in terms of the basis C.

We have the basis C = {1, (2 - 1), (x - 1)²}

p(x) = a + bx + cx² = a(1) + b(2 - 1) + c((x - 1)²) = a + b(2 - 1) + c((x - 1)²)

Thus, the polynomial p(x) = a + bx + cx² can be written as a linear combination of the polynomials in C as

p(x) = a + b(2 - 1) + c((x - 1)²)

Simplifying further

p(x) = a + b + c(x - 1)²

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Answer:

a. let x be the number of apples and let y be the number of oranges

x + y = 60

x = y + 12

b. Apples: 24 Oranges: 36

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just don’t want to waste my time in case you don’t want me to :)

The probability to get a full house with 3 kings in poker is 0.0000058179 (approximately) or 1/171230.

How to get probbability?

The probability to get a full house with 3 kings in poker can be calculated using the formula below:

Probability = (Number of ways to get a full house with 3 kings) / (Total number of possible hands)Total number of possible hands

= C(52,5) = 2,598,960

2) To calculate the number of ways to get a full house with 3 kings, we need to choose 2 cards out of the remaining 48 (since there are only 4 kings) and multiply it by the number of ways to choose the remaining 2 cards.

This can be written as:

Number of ways to get a full house with 3 kings = C(4,3) x C(48,2)C(4,3) is the number of ways to choose 3 kings out of 4C(48,2) is the number of ways to choose 2 cards out of the remaining 48 cards

Therefore, the probability to get a full house with 3 kings in poker is:

Probability = C(4,3) x C(48,2) / C(52,5)

= (4 x 1128) / 2598960

= 4512 / 2598960= 1 / 171230

Therefore, the probability to get a full house with 3 kings in poker is 0.0000058179 (approximately) or 1/171230.

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Answer:

I believe it's 2(x-5)=3

The minimum number of multiplications required are 1800 .

Given,

P = 10×20

Q = 20×30

R = 30×40

Now,

Firstly,

First multiply  P with Q:

PQ = 10 × 20 × 30 = 6000

Now,

PQ *R = 10 × 30× 40 = 12000

Total multiplication = 12000 + 6000

Total multiplication = 18000

Hence the minimum number of multiplications require to multiply three matrices are 18000 .

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Answer:

60 millimeters

Step-by-step explanation:

1 centimeter is 10 milimeters. So, 6 centimeters is 60 millimeters.

*please mark brainliest*

Answer:nth term = 0 + ((n-1) mod 2) * (2/3)

Explanation:

Given : 0, 2/3, 0, 2/3

   we can use the following formula:

nth term = a + (n-1)d

where a = first term of the sequence, d =common difference between consecutive terms.

In this case, a = 0 and d = 2/3 - 0 = 2/3. Since the sequence has a period of 2, we can write:

nth term = 0 + ((n-1) mod 2) * (2/3)

where (n-1) mod 2 is the remainder when (n-1) is divided by 2. This expression gives us 0 for even values of (n-1) and 2/3 for odd values of (n-1), which matches the given sequence.

Therefore, a formula for the nth term of the sequence is:

nth term = 0 + ((n-1) mod 2) * (2/3)

option b is correct - covariance

The correlation coefficient (r ) is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables.

Covariance

A numerical measure of linear association between two variables.

Covariance is a measure of how changes in one variable are associated with changes in a second variable. Specifically, covariance measures the degree to which two variables are linearly associated. However, it is also often used informally as a general measure of how monotonically related two variables are.  It is similar to variance, but where variance tells you how a single variable varies, covariance tells you how two variables vary together.

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Answer:

I was wondering the same thing! like what was Johnny using that much soap for....? btw I loI that video

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Explanation:

The largest rectangle (composed of the green and yellow sections combined) has area of 11*12 = 132 cm^2.

The yellow region takes up 112 of those 132 sq cm. This must mean the green region takes up 132-112 = 20 cm^2.

The horizontal portion of the green rectangle is 12-x cm. The vertical portion is 11-x cm. We can form the area of the green rectangle as an algebraic expression like so

area = length*width

area = (11-x)*(12-x)

area = 132 - 11x - 12x + x^2 .... apply the FOIL rule

area = x^2 - 23x + 132

Set this equal to the 20 cm^2 we found earlier.

x^2 - 23x + 132 = 20

x^2 - 23x + 132-20 = 0

x^2 - 23x + 112 = 0

We could factor or we could use the quadratic formula. I'll go with the second option.

We'll plug in a = 1, b =  -23, c = 112

\(x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-23)\pm\sqrt{(-23)^2-4(1)(112)}}{2(1)}\\\\x = \frac{23\pm\sqrt{81}}{2}\\\\x = \frac{23\pm9}{2}\\\\x = \frac{23+9}{2}\ \text{ or } \ x = \frac{23-9}{2}\\\\x = \frac{32}{2}\ \text{ or } \ x = \frac{14}{2}\\\\x = 16\ \text{ or } \ x = 7\\\\\)

One of these solutions isn't feasible. Note how if x = 16, then this exceeds both the 11 cm and 12 cm sides. So this x value is not possible.

However, x = 7 is possible.

If x = 7, then the horizontal portion of the green rectangle is 12-x = 12-7 = 5 cm. Also, the vertical portion of the green rectangle would be 11-x = 11-7 = 4 cm. The area then is length*width = 5*4 = 20 cm^2 which matches up with what we got earlier. So the answer is confirmed.

The base case in the given pseudocode is factor(0).

The pseudocode is using recursion to find the factorial of a number. In each recursive call, the function is subtracting 1 from the given number (n - 1) and then multiplies it with the result of the recursive call for n - 1. The base case is the condition that stops the recursion and provides a result.

In this case, the base case is a factor(0). When the input number reaches 0, the recursion stops, and the function returns 1. This is because the factorial of 0 is defined as 1.

So, when the base case is reached, the recursion unwinds, and the factorial value is calculated by multiplying the current number (n) with the result of the previous recursive call (factor(n - 1)).

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To multiply a square root by a square root and a whole number, you can use the distributive property of multiplication

Given data ,

Let the numbers be represented by the expression A

Now , the value of A is

A = √2 × 3√5

First, you can simplify each square root:

√2 = 1.4142 (rounded to 4 decimal places)

3√5 = 5.1962 (rounded to 4 decimal places)

Next, you can multiply the two simplified square roots and the whole number:

√2 × 3√5 = 1.4142 × 5.1962 × 3

= 22.3607 × 3

= 67.0821

Hence , the expression is A = √2 × 3√5 = 67.0821

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Answer:

Look at attached.

Step-by-step explanation:

A full circle is 360 degrees. So 180 represents half of the circle and 90 represents a quarter.

Answer:

chocolate 180°

Step-by-step explanation:

chocolate=180°

vanilla=90°

othere flavor=90°

the total degrees of the pie chart 360 °