What number is the opposite of 913?

The final expression is

sqrt (39y9) = y4 • sqrt(39y) assuming y as positive.

Rewrite

39 y ^9 as ((y^2)^2)^2 . 39 y

Factor out y^8.

√39(y^8 . y).

Rewrite   \(y^8 as (y^4)^2\)

 √39(y^4)^2 . y).

Rules for simplifying variables which may be raised to a power:

  (1) variables with no exponent stay inside the radical

  (2) variables raised to power 1 or (-1) stay inside the radical

  (3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:

    sqrt(x8)=x4

    sqrt(x-6)=x-3

  (4) variables raised to an odd exponent which is  >2  or  <(-2) , examples:

     sqrt(x5)=x2•sqrt(x)

     sqrt(x-7)=x-3•sqrt(x-1)

Applying these rules to our case we find out that

SQRT(y9) = y4 • SQRT(y)

Therefore, sqrt (39y9) = y4 • sqrt(39y)

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Answer:

3/7

And then you added 1 to the numerator and denominator which would give you 4/8

Step-by-step explanation:

Answer:

  x = 17 1/3

Step-by-step explanation:

Corresponding segments are proportional.

  (3x)/(4x) = (3x +7)/(5x -8)

  3(5x -8) = 4(3x +7) . . . . . . . . multiply by 4(5x-8)

  15x -24 = 12x +28 . . . . . . eliminate parentheses

  3x = 52 . . . . . . . . . . add 24-12x

  x = 17 1/3 . . . . . . . . . divide by 3

The range of the rational function:

y = 1/(x + 2) - 1

is R: (-∞, 0) U (0, ∞)

Remember that for a function y = f(x), we define the range as the set of the possible inputs of the function (the possible values of y).

In this case we have the rational function:

y = 1/(x + 2) - 1

Notice that when x approaches at -2, the function tends to positive or negative infinity (deppending if it comes from the left or right).

And then as x goes affar from -2, the absolute value decreases.

But the function never reaches the value 0, as tends to infinity or negative infintiy the functio approaches zero, but it will never be equal to zero, then the range is:

R: (-∞, 0) U (0, ∞)

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9514 1404 393

Answer:

  (-1, 3)

Step-by-step explanation:

The midpoint is the average of the end points.

  M = (H +K)/2

  M = ((-4, 10) +(2, -4))/2 = (-4+2, 10-4)/2 = (-2, 6)/2

  M = (-1, 3)

The coordinates of the midpoint are (-1, 3).

Answer:

Good luck mate with that

Step-by-step explanation:

Claude would have to rotate the wheel 54 times to complete a 100m unicycle race. And the unicycle moves 1.884 meters when the wheel turns once.

How to solve the question?

A) To determine how far the unicycle moves when the wheel turns once, we need to find the circumference of the wheel.

The formula for the circumference of a circle is:

C = πd

where C is the circumference, π (pi) is a mathematical constant equal to approximately 3.14, and d is the diameter of the circle.

So, in this case, the circumference of the unicycle wheel is:

C = πd = 3.14 x 60cm = 188.4cm

To convert centimeters to meters, we need to divide by 100:

188.4cm ÷ 100 = 1.884m

Therefore, the unicycle moves 1.884 meters when the wheel turns once.

B) To determine how many times the wheel must rotate to travel 100m, we need to divide the distance by the distance covered in one revolution of the wheel, which is the circumference.

Using the circumference we calculated above, we can divide the total distance by the distance covered in one revolution:

100m ÷ 1.884m/revolution ≈ 53 revolutions

Therefore, Claude must rotate the wheel approximately 53 times to travel 100m. Since he cannot rotate the wheel partially, we must round up the number of revolutions to the nearest whole number, which is 54.

In conclusion, Claude would have to rotate the wheel 54 times to complete a 100m unicycle race.

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The linear equation best estimate of the difference between the number of yellow and blue paper clips is option(b).

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables.

Number of yellow paper clips found in one box = 27955

Number of blue paper clips found in another box = 9427

We are asked to find the best estimate of the difference in the number of yellow and blue paper clips that Kimberly found.

The actual difference between the number of yellow and blue paper clips = 27955 - 9427 = 18528

An estimate of a number means the closest number that the actual number can be rounded off for simplifying calculations or understanding.

In this case, from the given options the closest number of 18528 is 19000.

Therefore option(b) is the best estimate of the difference between yellow and blue paper clips.

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Answer:

Step-by-step explanation:

x+y = 9

x-y = 60

-----------

2x = 69

x = 34.5

y = 9-x = -25.5

smaller number: -25.5

larger number: 34.5

If Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

To show that x is also an eigenvector of QT, we need to demonstrate that QT * x is a scalar multiple of x.

Given that Q is an orthogonal matrix, we know that QT * Q = I, where I is the identity matrix. This implies that Q * QT = I as well.

Let's denote x as the eigenvector corresponding to the eigenvalue λ1 This means that Q * x = λ1 * x.

Now, let's consider QT * x. We can multiply both sides of the equation Q * x = λ1 * x by QT:

QT * (Q * x) = QT * (λ1 * x)

Applying the associative property of matrix multiplication, we have:

(QT * Q) * x = λ1 * (QT * x)

Using the fact that Q * QT = I, we can simplify further:

I * x = λ1 * (QT * x)

Since I * x equals x, we have:

x = λ1 * (QT * x)

Now, notice that λ1 * (QT * x) is a scalar multiple of x, where the scalar is λ1. Therefore, we can rewrite the equation as:

x = λ2 * x

where λ2 = λ1 * (QT * x).

This shows that x is indeed an eigenvector of QT, with the eigenvalue λ2 = λ1 * (QT * x).

In conclusion, if Q is an orthogonal matrix with an eigenvalue λ1 = 1, then x, the eigenvector corresponding to λ1, is also an eigenvector of QT with an eigenvalue λ2 = λ1 * (QT * x).

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Answer:

97.8

Step-by-step explanation:

All you need to do is times the percentage with the number(make sure to change the percent to a decimal)

104 x 0.94 = 97.76

97.8

Answer:

$3.24

Step-by-step explanation:

0.87 x 7 = 6.09

9.33 - 6.09 = 3.24

Answer:

ching chong

Step-by-step explanation:

The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.

the greatest common divisor of 5! and 7! is 120.

To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.

First, let's calculate the values of 5! and 7!:

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, let's factorize both numbers:

Factorizing 120:

120 = 2^3 * 3 * 5

Factorizing 5,040:

5,040 = 2^4 * 3^2 * 5 * 7

To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).

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The balloon on the right is 137.3 meters higher than the balloon on the left.

Trigonometry is a topic in mathematics which require the application of some function to determine the value of an unknown side or measure of internal angle of a right angled triangle. The basic functions are: sine, cosine and tangent.

In the given question, let the vertical height of the balloon on the left be represented by x, and that of the balloon on the right by y.

So that,

i. for the balloon to the left, applying the appropriate trigonometric function we have;

Cos θ = adjacent/ hypotenuse

Cos 19 = x/ 810

x = Cos 19 * 810

  = 765.87

x = 765.87 meters

ii. for the balloon to the right, we have;

Cos θ = adjacent/ hypotenuse

Cos 15 = y/ 935

y = Cos 15*935

  = 903.141

y = 903.141 meters

The distance between the two balloons = y - x

                                             = 903.141 - 765.87

                                             = 137.271

The distance between the two balloons is 137.3 meters.

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Answer:

3 units

Step-by-step explanation:

Answer: 105 dollars

Step-by-step explanation:

Let's say that the original price x dollars, we can use the equation to find the original price.

80%x = 84

x = 105

Answer:

$105

Step-by-step explanation:

The multiplier is 0.8

To get the price after the discount,the original price was multiplied by 0.8(100 - 20 = 80% = 0.8

Therefore to obtain the original price from the price after the discount, we use reverse percentage:

$84 ÷ 0.8 = $105

Step-by-step explanation:

The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.

Let u = sin(x), then du = cos(x)dx

The integral becomes:

∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)

= (u^6)/6 evaluated at sin(π/2) and 0

= (sin^6(π/2))/6 - 0

= (1^6)/6

= 1/6

So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.

Answer:

1300

Step-by-step explanation:

453 trees left + 773 new ones = 1226    approx 1300

Answer:

No slope.

Step-by-step explanation:

There is no such thing as a vertical slope, meaning that there is no slope. I hope this helps! :)

Answer:

No slope

Step-by-step explanation:

The line is going straight up :)

Brainliest pls?

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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Answer:

1. z=4

2. z=2/3

3. x=1

4. x=3

Step-by-step explanation:

I can't explain just trust me I went through algebra class.

Hope this helps

6z+3=8z-5

6z+3-3=8z-5-3

6z-8z=8z-8z-8

-2z/-2=-8/-2

z=4

3-4z=-5+8z

subtract three from both sides

-4z-8z=-8+8z-8z

-12z/-12=-8/-12

z=2/3

3x-5=x-3

add 5 to both sides

3x-x=x-x+2

2x/2=2/2

x=1

3x+14=11+4x

subtract 14 from both sides

3x-4x=-3+4x-4x

-x/-1=-3/-1

x=3

Answer:

1. z=42. z=2/33. x=14. x=3Step-by-step explanation:I can't explain just trust me I went through algebra class.Hope this helps6z+3=8z-56z+3-3=8z-5-36z-8z=8z-8z-8-2z/-2=-8/-2z=43-4z=-5+8zsubtract three from both sides-4z-8z=-8+8z-8z-12z/-12=-8/-12z=2/33x-5=x-3add 5 to both sides3x-x=x-x+22x/2=2/2x=13x+14=11+4xsubtract 14 from both sides3x-4x=-3+4x-4x-x/-1=-3/-1x=3

Step-by-step explanation:

Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

Let's assume the number of miles driven is represented by 'm'. The cost of renting a moving truck for one day at Rentals Plus can be calculated using the equation:

Cost at Rentals Plus = $5.24 + $4.46 * m

Similarly, the cost of renting a moving truck for one day at Speedy Move can be calculated using the equation:

Cost at Speedy Move = $85.24 + $0.46 * m

To find the number of miles that makes the costs equal, we can set up the equation:

$5.24 + $4.46 * m = $85.24 + $0.46 * m

By rearranging the equation, we can solve for 'm':

$4.46 * m - $0.46 * m = $85.24 - $5.24

$4 * m = $80

m = $80 / $4

m = 20

Therefore, Jessica would have to drive 20 miles for the cost to rent a moving truck for one day to be the same at Rentals Plus and Speedy Move.

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Answer:

The answer is below

Step-by-step explanation:

The equation of a linear function is given as:

y = mx + b;

where y, x are variables, m is the rate of change and b is the initial value of variable y.

A) Since there is B bacteria in the Petri dish at 12:00 midnight and the number of bacteria increases after midnight by 25 every hour. Let h represent the time in hours and T represent the total number of bacteria, therefore the equation is:

T = 25h + B

B) Given that B = 5, h = 6, hence:

T = 25(6) + 5 = 150 + 5 = 155 bacteria

C) The equation of the graph is:

T = 25h + 5

The graph was plotted using geogebra online graphing.

The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.

The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.

Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).

The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.

The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.

The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).

Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.

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The simplified forms are;

1) 2x\(y^2\)

2) \(x^2y^3\)

3) \(2xy^3z^5\)

4)\(5p^2q\)

5) \(5a^3b^5c^3/2\)

6)\(4x^4y^5/3z^3\)

7)\(7a^3b^3/2\)

8) \(x^2y^3z^6\)

9)-4a

10) \(3xy^5z^13/2\)

To simplify a surd, you need to find the largest perfect square factor that divides the number under the square root symbol.

We can see that the surds here can be reduced to the simplest forms when we apply the basics of the rules of exponent which have been used to show the simplified forms as shown here.

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The coordinate of the point after transformation is: (3, -4)

The coordinate initially is given as (0, -4).

Moving one unit to the left means a deduction of 1 unit from the x coordinate to get:

(0 - 1, -4)

= (-1, -4)

Moving by 4 units to the right means an addition of 4 units to x coordinate to get:

(-1 + 4, -4)

= (3, -4)

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Answer:

y=25x

Step-by-step explanation:

It is a linear equation with a slope of 25