Solve by using Cramer's Rule: \[ \begin{array}{l} -3 x-4 y-4 z=-8 \\ x-3 y-3 z=-19 \\ -x+y-2 z=3 \end{array} \]

Step-by-step explanation:

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Answer:

12 blocks will made from the 3 pound block

Step-by-step explanation:

The maximum value of the function is 6.9159 and the minimum value is -6.9159, accurate to 4 decimal places. The answers should be provided as a list separated by commas, so the final answer is:

max = 6.9159, min = -6.9159

The first step in solving 5sin(x)−2cos(x)=3 is to rearrange the equation to isolate the sin(x) term. We can do this by adding 2cos(x) to both sides of the equation:

5sin(x) = 3 + 2cos(x)

Next, we can divide both sides of the equation by 5 to isolate the sin(x) term:

sin(x) = (3 + 2cos(x))/5

Now, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to substitute for cos(x) and solve for sin(x):

sin^2(x) = (3 + 2√(1 - sin^2(x)))/5

Multiplying both sides of the equation by 5 and rearranging gives us:

5sin^2(x) - 2√(1 - sin^2(x)) - 3 = 0

We can use the quadratic formula to solve for sin(x):

sin(x) = (-(-2) ± √((-2)^2 - 4(5)(-3)))/(2(5))

Simplifying gives us:

sin(x) = (2 ± √(28))/10

Using a calculator, we can find the first 2 positive solutions for x:

x = sin^-1((2 + √(28))/10) ≈ 0.72, 2.42

Therefore, the first 2 positive solutions for x are 0.72 and 2.42, accurate to at least 2 decimal places.

To find the maximum and minimum values of f(x)=5.7sin(x)−3.9cos(x), we can use the formula:

max = √(a^2 + b^2)

where a and b are the coefficients of the sin(x) and cos(x) terms, respectively. Substituting in the values for a and b gives us:

max = √((5.7)^2 + (-3.9)^2) ≈ 6.9159

The minimum value of the function is the negative of the maximum value:

min = -6.9159

Therefore, the maximum value of the function is 6.9159 and the minimum value is -6.9159, accurate to 4 decimal places. The answers should be provided as a list separated by commas, so the final answer is:

max = 6.9159, min = -6.9159

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The list that gives the sample space for pulling two slips of paper out of the hat with replacement is list 4 ( optionD)

A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. A sample space may contain a number of outcomes that depends on the experiment.

For example if a fair die is thrown, the probability of getting an even number. This means that the sample space of even number in a fair die is 3 i.e, 2,4 and 6

Similarly, There are three names with slip, Analise, Benjamin and cora, the sample space to bring 2 slips out with replacement has this results

The slips can be;

1. Benjamin, cora

2. Analise, cora

3. Benjamine, Analise

4. Analise , Benjamin

5. cora, Analise

6. cora, Benjamin

7. cora, cora

8. Benjamin, Benjamin

9. Analise, Analise

The list that shows these result or sample space is list 4

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Answer:

The list that gives the sample space for pulling two slips of paper out of the hat with replacement is list 4 ( optionD)

Step-by-step explanation:

The equation that can be used to determine the weight of the textbooks is  t = 0.7(t + 4 + 2) = t

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given that, the notebooks weigh a total of 4 pounds, and the backpack itself weighs 2 pounds. If the backpack contains only textbooks and notebooks, seventy percent of the total weight is textbooks,

Let the weight of the textbooks= t

The backpack of the book= 2 pounds

The weight notebook in total = 4 pounds

But remember that 70% of total weight is the textbooks.

Therefore, the equation can be computed as

70%(t + 4 + 2) = t

0.7(t + 4 + 2) = t

Hence, the equation that can be used to determine the weight of the textbooks is  t = 0.7(t + 4 + 2) = t

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Answer:

0.95 and 95%

Step-by-step explanation:

19/20 as a decimal is 19÷20=0.95

as it's 0.95 as a decimal it's 95% as a percentage

Answer:

A) 0.95

B) 95%

I hope you mark me as a brainliest pls

If the diameter of a cone is 19 yd and the height is 13 yd, the volume of this cone is equal to 1,228 cubic yard.

Mathematically, the volume of a cone can be calculated by using this formula:

V = 1/3 × πr²h

Where:

Radius = diameter/2 = 19/2 = 9.5 cm.

Substituting the given parameters into the volume of a cone formula, we have the following;

V = 1/3 × πr²h

V = 1/3 × 3.14 × 9.5² × 13

Volume, V = 1,228 cubic yard.

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The equation 5r2 - 5r + 2 = 0 has two real solutions.

The two real solutions of the equation are:
x = (5 + 3i) / 10 and x = (5 - 3i) / 10

To solve this equation, you can use the Quadratic Formula:

x = (-b ± √(b2 - 4ac)) / (2a)

In this case, a = 5, b = -5, c = 2, so:

x = (-(-5) ± √((-5)2 - 4*5*2)) / (2*5)
x = (5 ± √(25 - 40)) / 10
x = (5 ± √(-15)) / 10
x = (5 ± 3i) / 10

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(A) The equation relating fare to number of miles traveled, m, is y = 0.50 + 0.80m

(B) The equation for earnings, E, in terms of sales volume, V, is E = 50 + 0.10V. The slope of this line is called marginal revenue.

A) The taxi fare starts at 50 cents and increases by 20 cents for every quarter mile traveled. This means that for every mile traveled (4 quarters), the additional cost will be 80 cents per mile traveled. The equation that will relate the fare, y, to the number of miles traveled, m, is y = 0.50 + 0.80m.

B) The equation E = 50 + 0.10V shows that the weekly earning of a salesman starts at $50 and increases by 10 percent of the retail value of the goods he sells. The slope of this line is 0.10, which represents the rate of change in earnings with respect to sales volume. This slope is called the marginal revenue, as it represents the additional revenue earned for each additional unit of sales volume.

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The expression will be 5 + 11x.

What is an expression?

An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

It is possible to compare expressions to phrases. In English, a phrase by itself may contain an action, but it does not constitute a whole sentence.

Explanation: 3 + 7

Let the number to be "x"

Step 1 : the number is multiplied by - 8

           So, -8 x

Step 2 : subtracted from the sum of 5 and 3 times the number

       So,  (5 +3x) - (-8x)

           = 5+3x + 8x

           = 5 + 11x

Hence, The final expression will be 5 + 11x.

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Answer:

see explanation

Step-by-step explanation:

the diagonals of a rhombus are perpendicular to each other, then

∠ 1 = 90°

AB and CD are parallel ( opposite sides of a rhombus are parallel )

∠ 2 and 51° are alternate angles and are congruent , then

∠ 2 = 51°

the diagonals bisect the angles , then

∠ 3 = ∠ 2 = 51°

the sum of the 3 angles , in the triangle with ∠ 4 sum to 180°

∠ 1 + ∠ 3 + ∠ 4 = 180°

90° + 51° + ∠ 4 = 180°

141° + ∠ 4 = 180° ( subtract 141° from both sides )

∠ 4 = 39°

then

∠ 1 = 90° , ∠ 2 = 51° , ∠ 3 = 51° , ∠ 4 = 39°

Answer:

Rectangle, yes yes or no rectangle

Step-by-step explanation:

Using the equatiοns, we fοund that the maximum amοunt οf spοrts drinks yοu can purchase fοr $75 is 86.

A mathematical equatiοn is a fοrmula that uses the equals symbοl (=) tο cοnnect twο expressiοns and express their equality. The definitiοn οf an equatiοn in algebra is a mathematical statement that prοves twο mathematical expressiοns are equal. LHS = RHS (left-hand side = right-hand side) appears in all mathematical equatiοns. Yοu can sοlve equatiοns tο determine an unknοwn variable's value, which cοrrespοnds tο an unknοwn quantity. It is nοt an equatiοn if there is nο "equal tο" sign in the statement. That shall be taken intο accοunt as an expressiοn.

Let,

the number οf drinks = x

the tοtal cοst οf the x drinks = y

Then we can write equatiοns using the given infοrmatiοn.

When the οrder cοntains 50 οr fewer spοrts drinks, the equatiοn is:

y = 0.8x + 10

When the οrder cοntains mοre than 50 spοrts drinks, the equatiοn is:

y = 0.7x + 15

Since we have tο find the number οf drinks fοr $75, we can write that:

y = 75

Substituting in the equatiοns,

75 = 0.8x +10

65 = 0.8x

x= 81.25 = 81

75 = 0.7x +15

60 = 0.7x

x = 85.7 = 86

Nοw, 86 > 81

Therefοre using the equatiοns, we fοund that the maximum amοunt οf spοrts drinks yοu can purchase fοr $75 is 86.

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Hypothesis 1: There is a positive correlation between gender and GPA.
Hypothesis 2: There is a positive correlation between age and midterm score.
Hypothesis 3: There is a negative correlation between nationality and income.
Hypothesis 4: There is a negative correlation between expenditure and no. of credits.
Hypothesis 5: There is a positive correlation between no. of absences and learning preference.
Hypothesis 6: There is a positive correlation between online device usage and income.

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Answer:

11.35

or 11 7/20

Step-by-step explanation:

Simplifying x^7/x^3 we get x^4.

We have the numerator of the given fraction x^7/x^3 as x^7, that is x raised to the power 7. We can rewrite x^7 equals to (x^4)(x^3) , that is x raised to the power 4 multiplied by x raised to the power 3 (by exponential method).

Similary, the denominator of the given fraction x^7/x^3 is x^3, that is x raised to the power 3.

Rewritting the fraction x^7/x^3 as,

(x^4)(x^3) / x^3  { using division rule}

= x^4  (that is, x raised to the power 4)

Thus after simplifying x^7/x^3 (using division rule) we get x^4.

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-3, -1, 3

X-intercepts are also known as the roots or zeros of a function.

Finding Intercepts From Graphs

In the problem, we are given a basic polynomial graph. The x-intercepts are where the graphs intersect with the x-axis. Remember that the x-axis is the horizontal axis. Finding x-intercepts when given a graph is as simple as just looking to see where the line crosses over. We can see that the graph crosses the axis in three points. The x-intercepts are x = -3, -1, and 3.

Finding Intercepts From Equations

In this question, we are not given an equation, but if we were there is another possible way to solve it. The x-intercepts occur when y = 0. So, to find x-intercepts from an equation, all you need to do is plug 0 in for y and solve.

To solve this problem, we'll start by finding the polar coordinates r and θ in terms of x1 and x2. We have r^2 = x1^2 + x2^2, tan(θ) = x2/x1.

Taking the derivative of x1 with respect to time t, we have: dx1/dt = dx2/dt - 2x1(dx1^2 + x2^2 - 1) - x1^2(2x1dx1 + 2x2dx2)

Similarly, the derivative of x2 with respect to t is: dx2/dt = -dx1/dt -2x2(dx1^2 +x2^2 -1) - x2^2(2x1dx1 + 2x2dx2) Using the chain rule, we can write: dr/dt = (x1dx1 + x2dx2)/r dθ/dt = (1/r^2)(x2dx1 - x1dx2)

Substituting dx1/dt and dx2/dt in these equations and simplifying, we get: dr/dt = -r(r^2 -1) dθ/dt = -1 Now, to prove that r=1 is a stable limit cycle, we can use the method of linearization.

This involves finding the Jacobian matrix at the equilibrium point r=1, θ=0: Jacobian = [[-3 -1], [-1 -3]] Taking the eigenvalues of this matrix, we get -4 and -2.

Since both eigenvalues are negative, we conclude that the equilibrium point corresponds to a stable limit cycle at r=1, θ=0. In summary, we have shown that the differential equations for dr/dt and dθ/dt are -r(r^2 -1) and -1, respectively. We have also demonstrated that r=1 is a stable limit cycle.

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The function combinations and their respective domains are as follows:

(a) (f+g)(x) = f(x) + g(x) = x^2 - 11x + x + 9 = x^2 - 10x + 9
The domain of (f+g)(x) is all real numbers, since there are no restrictions on the values of x.

(b) (f-g)(x) = f(x) - g(x) = x^2 - 11x - (x + 9) = x^2 - 12x - 9
The domain of (f-g)(x) is also all real numbers, since there are no restrictions on the values of x.

(c) (fg)(x) = f(x) * g(x) = (x^2 - 11x)(x + 9) = x^3 - 2x^2 - 99x
The domain of (fg)(x) is all real numbers, since there are no restrictions on the values of x.

(d) (gf)(x) = g(x) * f(x) = (x + 9)(x^2 - 11x) = x^3 - 2x^2 - 99x
The domain of (gf)(x) is all real numbers, since there are no restrictions on the values of x.

In conclusion, the domain of all the function combinations is all real numbers, since there are no restrictions on the values of x.

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Answer:

Perimeter=33

Step-by-step explanation:

2x+3=4x-3

0=2x-8

2x=8

x=4

Input 4 as Variable

2x+3=2(4)+3

=8+3

=11

P=3x11

P=33

The solutions to the quadratic equation (u-3)^(2)-20=0 are u=3+2√5 and u=3-2√5.

To solve the quadratic equation (u-3)^(2)-20=0, we will use the following steps:

1. Add 20 to both sides of the equation to isolate the squared term: (u-3)^(2)=20

2. Take the square root of both sides of the equation: u-3=±√20

3. Simplify the radical on the right side of the equation: u-3=±2√5

4. Add 3 to both sides of the equation to isolate the variable: u=3±2√5

5. Write the two solutions separately: u=3+2√5 or u=3-2√5

Therefore, the solutions to the quadratic equation (u-3)^(2)-20=0 are u=3+2√5 and u=3-2√5.

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The number of minutes that could have passed if the pool now has less than 74 gallons of water left is greater than 9 minutes.

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The amount of water remaining in the pool after x minutes is given by:

110 - 4x

We want to find the number of minutes, x, such that the pool now has less than 74 gallons of water left.

110 - 4x < 74

To solve for x, we can first subtract 110 from both sides of the inequality:

-4x < 74 - 110

Simplifying, we get:

-4x < -36

Divide both sides of the inequality by -4,

x > 9

Therefore, the number of minutes that could have passed if the pool now has less than 74 gallons of water left is greater than 9 minutes.

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Factorization of expression 16t³ + 10t is 2t (8t² + 5) .

Factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is a factorization of the integer 15

Given expression

16t³ + 10t

It can be written as

2 × 8 (t . t . t ) + 2 × 5 (t)

Factoring out common factors

2t (8t² + 5)

Hence, 2t (8t² + 5) is factorization of expression 16t³ + 10t

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The series n=1∑[infinity]​(−1)n−13n+4ln(5n+2)​ is conditionally convergent.

To determine the convergence of a series, we can use the Alternating Series Test. This test states that if the absolute value of the terms in the series decrease to zero, then the series is convergent.

First, we need to find the absolute value of the terms in the series:

| (−1)n−13n+4ln(5n+2)​ | = | 3n+4ln(5n+2)​ |

Next, we need to determine if the absolute value of the terms decrease to zero. To do this, we can use the Limit Comparison Test. We will compare the series to the series 1/n:

lim n→∞ | 3n+4ln(5n+2)​ | / (1/n) = lim n→∞ | 3n^2+4nln(5n+2)​ |

Since the limit of the series is infinity, the series is divergent. However, since the series alternates between positive and negative terms, it is conditionally convergent.

Therefore, the series n=1∑[infinity]​(−1)n−13n+4ln(5n+2)​ is conditionally convergent.

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A floor cannot be tiled using only regular pentagons.

A floor cannot be tiled using only regular pentagons. For a regular hexagon, the measure of each vertex angle is 120°, which means that 3 regular hexagons fit to form 360°, and the plane can be filled. However, for a regular pentagon, the measure of each vertex angle is 108°, so regular pentagons cannot be placed together to fill the plane because the measure of the plane, 360°, is not divisible by the measure of each vertex angle. Therefore, a floor cannot be tiled using only regular pentagons.

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We can deduce that 3pi/4<5pi/3<2pi

The angle is in the 4th quadrant. To find the angle you just do:

[tex]2\pi -\frac{5\pi }{3}=\frac{\pi }{3}[/tex]

The answer to your question is B. I hope that this is the answer that you were looking for and it has helped you.

For none of the option the linear equation x+4=c have solution.

The equation x + 4 - c = 0 can be rearranged to isolate the variable c on one side of the equation. This gives us:

c = x + 4

Now, we can see that the value of c depends on the value of x. In other words, there are infinitely many values of c that make the equation true, as long as they are equal to x + 4.

So the answer to the question is that there are infinitely many values of c that make the equation x + 4 - c = 0 true. None of the given options (A) c = -4, (B) c = 0, or (C) 0 are correct.

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The uncertainity for the meter stick and weights in this experiment are σₓ =  σₓ₀ = 1 × 10⁻³ (m) and σₙ = 0.05 × m (kg), respectively.

This means that the uncertainty in the measurement of the meter stick is 1 × 10⁻³ meters and the uncertainty in the measurement of the weights is 0.05 kg. To calculate the uncertainity of the results, one must use the appropriate formulae, taking into account the uncertainities of each measurement.

For example, if you are measuring the mass of an object, you must use the uncertainty in the measurement of the weight and the uncertainty in the measurement of the meter stick to calculate the uncertainty in the mass.

The uncertainty in the mass is then equal to the square root of the sum of the squares of the uncertainties of the measurements.

By taking into account the uncertainties in each measurement, one can accurately calculate the uncertainty of the results.

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Complete question:

In this experiment you can use  σₓ =  σₓ₀ = 1 × 10⁻³ (m) and σₙ = 0.05 × m (kg)  as the uncertainity for the meter stick and weights, respec.

Three radians, or 45 degrees, are the greater angle between each pair of measurements.

An angle is a figure created in geometry by two rays or line segments that meet at the vertex of the angle. The edges of the angle are the rays or line segments. Angles are used to describe the amount of rotation or turn between two lines or objects. For instance, a 90-degree angle is equivalent to a quarter turn, while a 180-degree angle is equivalent to a half turn or a straight line. A full turn plus a smaller angle is equivalent to an angle that is larger than 180 degrees but less than 360 degrees.

given

In degrees, express each radian number.

• 3 radians equals 60 degrees (multiply the radian measurement by 180/ to transform radians to degrees).

• 225 degrees = 5/4 radians

Use radians to determine each degree.

• 30° Equals /6 radians (multiply the degree measurement by /180 to convert degrees to radians)

• 120° equals 2.3 radians

Circle the larger angle between each set of measurements.

• Radians or degrees: 200 degrees (to measure, 180 degrees are equal to one radian).

• 200 degrees or 32 radians: 200 degrees

• One radian is equal to 90 degrees.

Three radians, or 45 degrees, are the greater angle between each pair of measurements.

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