Solve each matrix equation. [2 -6 8] + [-1 -2 4] = X

Answer:

65 cm squared

Step-by-step explanation:

Answer:

x>4

Step-by-step explanation:

3x - 2 >10  add 2 to both sides

3x > 12  Divide both sides by 3

x >4

Answer:

\(x > \bf 4\)

Step-by-step explanation:

To find a solution to this inequality, we have to rearrange this equation to make \(x\) its subject:

\(3x - 2 > 10\)

⇒ \(3x - 2 + 2 > 10 + 2\)      [Add 2 to both sides]

⇒ \(3x > 12\)

⇒ \(\frac{3x}{3} > \frac{12}{3}\)                         [Divide both sides by 3]

⇒ \(x > \bf 4\)

Answer:

56a+40b

Step-by-step explanation:

43a plus 13a is 56a, -12b + 52b is 40b, together it's 56a+40b

The angles that can be used to make ΔABC are 71°, 41° and 68°

In this question, we have been given some angles.

A 71°71°

B 36°36°

C 41°41°

D 88°88°

E 68°

We need to find angles that can be used to make ΔABC.

We know that the sum of all angles of triangle is 180°

We need to find three angles whose sum is 180°

71° + 41° + 68° = 180°

Since the sum of angles 71°, 41° and 68° is 180°, we can use these angles to make ΔABC

Therefore, the angles that can be used to make ΔABC are 71°, 41° and 68°

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You have 4 replications for each treatment combination.

In this scenario, you have two factors: frequency (low and high) and liquid (distilled water and salt water). Each factor has two levels, making a total of four treatment combinations (low frequency with distilled water, low frequency with salt water, high frequency with distilled water, high frequency with salt water).

Since you have a total of 16 runs, the number of replications for each treatment combination can be determined by dividing the total number of runs by the number of treatment combinations. In this case, 16 runs divided by 4 treatment combinations gives you 4 replications per treatment combination.

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Answer:

-2x^2+4x+4= -4x+ 4x+4= 4

so the answer is 4

done

Explanation

Step1

let

Step 2

equation

I hope this helps you

Answer:

\(\mathrm{43ft,\ 76ft\ and\ 68ft}\)

Step-by-step explanation:

\(\mathrm{Let\ the\ shortest\ side\ of\ the\ triangle\ be\ x.\ Then,\ the\ longest\ side\ of\ the\ triangle}\\\mathrm{will\ be\ 2x-10.}\\\mathrm{Let\ the\ length\ of\ remaining\ side\ of\ the\ triangle\ be \ y.}\\\mathrm{Given,}\\\mathrm{Sum\ of\ two\ shorter\ sides=35+longest\ side}\\\mathrm{or,\ x+y=35+(2x-10)}\\\mathrm{or,\ y=25+x........(1)}\\\mathrm{Also\ we\ have}\\\mathrm{Perimeter\ of\ triangle=187ft}\\\mathrm{or,\ x+(2x-10)+y=187}\\\mathrm{or,\ 3x+y=197}\\\mathrm{or,\ y=197-3x...........(2)}\)

\(\mathrm{Equating\ equations\ 1\ and\ 2,}\\\mathrm{25+x=197-3x}\\\mathrm{or,\ 4x=172}\\\mathrm{or,\ x=43ft}\\\mathrm{i.e.\ length\ of\ shortest\ side=43ft}\\\mathrm{Now,\ length\ of\ longest\ side=2x-10=2(43)-10=76ft}\\\mathrm{Finally,\ length\ of\ third\ side=y=25+x=68ft}\)

\(\mathrm{So,\ the\ required\ lengths\ of\ triangle\ are\ 43ft,\ 76ft\ and\ 68ft.}\)

To solve the linear programming problem using the simplex method, we first convert the problem into standard form.

The original problem: Maximize z = -x₁ + 3x₂; subject to: x₁ + 3x₂ ≤ 5; -x₁ + x₂ ≤ 1 ; x₁ + x₂ ≤ 4; x₁, x₂ ≥ 0. The problem in standard form: Maximize z = -x₁ + 3x₂, subject to: x₁ + 3x₂ + x₃ = 5; -x₁ + x₂ + x₄ = 1; x₁ + x₂ + x₅ = 4; x₁, x₂, x₃, x₄, x₅ ≥ 0. Using the simplex method, we perform the iterations to find the optimal solution. Starting with the initial basic feasible solution, we pivot until we reach an optimal solution. The optimal solution is found when all coefficients in the objective row are non-negative. The final optimal solution obtained by the simplex method is: x₁ = 0; x₂ = 1; z = 3. To construct the dual linear programming problem, we use the coefficients from the constraints of the primal problem as the objective coefficients in the dual problem.

The variables in the primal problem become the constraints in the dual problem, and the constraints in the primal problem become the variables in the dual problem. The dual problem for the given primal problem is: Minimize w = 5y₁ + y₂ + 4y₃, subject to: y₁ - y₂ + y₃ ≥ -1; 3y₁ + y₂ + y₃ ≥ 3. Using the optimal simplex tableau of the primal problem, we can determine the solution of the dual problem. The optimal tableau will provide us with the values of the primal variables and the dual variables. In this case, the primal variables are x₁ and x₂, and the dual variables are y₁, y₂, and y₃. From the optimal simplex tableau, we find that x₁ = 0, x₂ = 1, y₁ = 1, y₂ = 0, and y₃ = 0. These values give the solution to the dual problem. The minimum value of the dual objective function w is obtained as w = 5(1) + 0 + 4(0) = 5.

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Answer:

12

Step-by-step explanation:

2007 - 1995

Explanation:

We simplify the square root of 64 to get 8

\(\sqrt{64} = \sqrt{8^2} = 8\)

Then we'll have the plus minus out front to say

\(x = \pm \sqrt{64} = \pm 8\)

That breaks down into x = 8 or x = -8

As a check

x^2 = (8)^2 = 8*8 = 64

x^2 = (-8)^2 = (-8)*(-8) = 64

Both values lead to 64 when squaring.

The graph of y=3x^4-16x^3+24x^2+48 is concave down for x values greater than or equal to 0.

The graph of y=3x^4-16x^3+24x^2+48 is an example of a polynomial function. To determine the concavity of a polynomial function, we must first identify the intervals where the function is increasing and decreasing. In this case, the function is increasing for all x values greater than or equal to 0.

Next, we must find the second derivative and determine the intervals where the second derivative is negative. If the second derivative is negative, then the graph is concave down. For this polynomial, the second derivative is y'' = -48x + 48, which is negative for all x values greater than or equal to 0. This means that the graph of y=3x^4-16x^3+24x^2+48 is concave down for all x values greater than or equal to 0.

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Answer:

Below

Step-by-step explanation:

Answer 10.1: 15

Explanation:

(-4)^2 is 16 and (-1)^3 is -1, so (-4)^2 + (-1)^3 = 16 - 1 = 15.

Answer 10.3: -23

Explanation:

(-2)^2 is 4 and -27 minus 4 is -23.

Answer 10.5: None

Explanation:

The expression is incomplete as there is no number or operation after the "^3".

Answer 10.7: 0.7

Explanation:

√0.04 is 0.2 and (0.5)^2 is 0.25, so 0.2 + 0.25 = 0.45. The square root of 0.45 is approximately 0.671.

Answer 10.9: 0.02788

Explanation:

(0.2)^3 is 0.008 and 0.027 plus 0.008 is 0.035. Raising 0.035 to the power of 1/3 gives approximately 0.315. Therefore, the final answer is approximately 0.02788.

Answer 10.2: -2018

Explanation:

Using the order of operations, we start with 62 divided by 3 which is approximately 20.67, then multiply that by -33 to get approximately -682.44.

Answer 10.4: -2

Explanation:

Empty brackets imply multiplication. Therefore, ()^2 is 0, and (-1)^3 is -1. Thus, 0 - 1 = -1.

Answer 10.6: 0.11

Explanation:

(0.1)^2 is 0.01 and (0.1)^3 is 0.001, so 0.01 + 0.001 = 0.011.

Answer 10.8: 0.38

Explanation:

0.0144 + 0.04 = 0.0544, and the square root of 0.0544 is approximately 0.2336. Subtracting (-0.2)^2 (which is 0.04) from 0.0544 gives 0.0144. Taking the square root of 0.0144 gives approximately 0.12. Finally, 0.2336 minus 0.12 is approximately 0.38.

The value of the expression \((1/6)^0\) is 1.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

\((1/6)^0\)

Anything to the power zero is always 1.

Thus,

The value is 1.

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Answer:

Step-by-step explanation:

Dont do it. Just take the detention

Answer:

1

by looking only 1 is missing

C I think not 100 percent sure

Answer:

7.35

Step-by-step explanation:

To find the elements α and β such that ∣α∣=2, ∣β∣=2, and ∣αβ∣=3 in S₃, we can consider the elements of the symmetric group S₃ which consists of the permutations of three elements. Let's denote the elements of S₃ as (1 2), (1 3), and (2 3), where (a b) represents the permutation that swaps a and b.

To satisfy the given conditions, we need to find two permutations α and β such that the absolute values of their cycles are equal to 2 and the absolute value of the cycle resulting from their product is equal to 3.

One possible solution is α = (1 2) and β = (1 3).

For α = (1 2), the absolute value of its cycle is 2 since it swaps 1 and 2. Similarly, for β = (1 3), the absolute value of its cycle is also 2 as it swaps 1 and 3.

Now, let's calculate the product αβ. (1 2)(1 3) = (1 3 2), which has a cycle length of 3, satisfying ∣αβ∣=3.

Therefore, one possible solution is α = (1 2) and β = (1 3) in S₃.

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Answer:

Step-by-step explanation:

56n+24 = 24 + 7n

49n + 24 = 24

49n = 0

n = 0

solution

Answer:

n = 0

Step-by-step explanation:

8(7n + 3) = 24 +7n

1. distribute the 8 inside the paranthesis

56n + 24 = 24 + 7n

2. subtract 24 from both sides

56n = 7n

3. subtract 7n from both sides

49n = 0

n = 0

Answer:

if it is a square, then it is a quadrilateral

Step-by-step explanation:

The general term of the Taylor series for f(x) = xe^(x^3) centered at x = 0 is (x^(3n+1)) / n!

The first four non-zero terms of the Taylor series for the function f(x) = xe^(x^3) centered at x = 0, along with the general term, are as follows:

f(0) = 0

f'(x) = e^(x^3) + 3x^3 e^(x^3)

f'(0) = 1

f''(x) = (6x^6 + 9x^2 + 1) e^(x^3)

f''(0) = 1

f'''(x) = (54x^9 + 81x^5 + 27x) e^(x^3)

f'''(0) = 0

The general term of the Taylor series for f(x) can be written as:

f^(n)(0) / n! * x^n

where f^(n) denotes the nth derivative of f. Therefore, the general term of the Taylor series for f(x) = xe^(x^3) centered at x = 0 is:

(x^(3n+1)) / n!

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Answer:

1 8/15

Step-by-step explanation:

We need to equal the denominators. We have 1/3 and 4/5, and we need to make the bottom numbers equal to each other. The closest common factor is 15 (which we got from 3 x 5). With the denominators solved, we now need to equal out the top numbers, or the numerators. 1 x 5 gives us 5/15, and 4 x 3 gives us 12/15. Then, we need to apply these to each variable. This gives us Jill's 2 12/15th cups of flour, and the recipe's call for 4 5/15 cups. We then subtract these from each other, giving us 1 8/15 cups of flour is needed from Jill.

The output energy spectral density ψy(f) is  \(sinc^2\)(f) * rect(f/(a+2)).

To determine the output energy spectral density ψy(f), we need to find the Fourier transform of the autocorrelation function Rx(τ) and multiply it by the magnitude squared of the Fourier transform of the impulse response H(f).

Given:

Rx(τ) = \(sinc^2\)((a+2)τ)

h(t) = rect(t-(a+1))

First, let's find the Fourier transform of Rx(τ):

Rx(f) = F{Rx(τ)} = F{\(sinc^2\)((a+2)τ)}

Using the property of the Fourier transform, the squared sinc function transforms to a rectangular function:

Rx(f) = rect(f/(a+2))

Next, let's find the Fourier transform of the impulse response h(t):

H(f) = F{h(t)} = F{rect(t-(a+1))}

Using the shifting property of the Fourier transform, we get:

H(f) = \(e^{-j2\pi f(a+1)\)sinc(f)

Now, we can calculate the output energy spectral density ψy(f) by multiplying the Fourier transforms of Rx(τ) and h(t):

ψy(f) = \(|H(f)|^2\) * Rx(f)

ψy(f) = \(|e^{-j2\pi f(a+1)}sinc(f)|^2\) * rect(f/(a+2))

Simplifying, we have:

ψy(f) = \(sinc^2\)(f) * rect(f/(a+2))

Therefore, the output energy spectral density ψy(f) is \(sinc^2\)(f) multiplied by a rectangular function centered at f/(a+2).

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Answer:

V = 144π mm³

Step-by-step explanation:

the volume (V) of a cone is calculated as

V = \(\frac{1}{3}\) πr²h ( r is the radius of the base and h the height of the cone )

here diameter of base = 12 , then r = 12 ÷ 2 = 6 and h = 12 , then

V = \(\frac{1}{3}\) π × 6² × 12

  = \(\frac{1}{3}\) π × 36 × 12

  = π × 12 × 12

  = 144π mm³

The Volume of Cone is 144π mm³.

We have,

Diameter of Base= 12 mm

Radius of Base = 6 mm

Height of Cone = 12 mm

So, the formula for Volume of Cone

= 1/3 πr²h

= 1/3 π (6)² 12

= 4 x 36π

= 144π mm³

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Answer:

  y = 64√3

Step-by-step explanation:

Step(i):-

Given that the 'y' varies directly as √x

    ⇒ y∝ √x

    ⇒  y = k√x

Put y=3 and x=3

       3 = k ×√3

   √3  k = √3×√3

After cancellation '√3' on both sides, we get

      k = √3

Step(ii):-

   Given that x=64 and k = √3

We have a function   y = k√x ..(i)

substitute x =64 and k = √3 in equation (i)

               y = √3 × 64

             y = 64√3

Answer:

2x=18

x=9

Step-by-step explanation:

So, to start you subtract 12 from 30 to get 18.

then 18 divided by x gives you 9

so X=9

Answer:

2x = 18 and x = 9

Step-by-step explanation:

i've done it before so i know its right

Answer:

r= 12.4m (3 s.f.)

Step-by-step explanation:

Area of circle= πr², where r is the radius

154π= πr²

Divide both sides by π:

154= r²

r²= 154

Square root both sides:

\(r = \sqrt{154} \)

r= 12.4m (3 s.f.)

Answer:

The radius of circular pond is 12.4 m.

Step-by-step explanation:

Given :

To Find :

Using Formula :

\(\star\small{\underline{\boxed{\sf{\red{Area_{(Circle)} = \pi{r}^{2}}}}}}\)

Solution :

Finding the radius of circular pond by substituting the values in the formula :

\({\dashrightarrow{\sf{Area_{(Circle)} = \pi{r}^{2}}}}\)

\({\dashrightarrow{\sf{154 \pi = \pi{r}^{2}}}}\)

\({\dashrightarrow{\sf{154 \times \dfrac{22}{7} = \dfrac{22}{7} \times {r}^{2}}}}\)

\({\dashrightarrow{\sf{154 \times \cancel{\dfrac{22}{7}} = \cancel{\dfrac{22}{7}} \times {r}^{2}}}}\)

\({\dashrightarrow{\sf{154 = {r}^{2}}}}\)

\({\dashrightarrow{\sf{r = \sqrt{154} }}}\)

\({\dashrightarrow{\sf{r \approx 12.4 }}}\)

\(\star{\underline{\boxed{\sf{\purple{r \approx 12.4 \: m }}}}}\)

Hence, the radius of circular pond is 12.4 m.

\(\rule{300}{1.5}\)

Answer:

84 grams and 5 ounces

Step-by-step explanation:

because one ounce equals 28 grams, that means 3 ounces = 3 * 28 = 84

because 28 grams equals 1 ounce, 140 grams = 140 / 28 = 5 ounces