the sum of two numbers is 51 and the difference is 13. what are the numbers

Answer:

x<4

Step-by-step explanation:

3x < 12

Divide with 3 on each side

x< 4

In words x has all the real numbers that are less than 4 or x belongs to any number from -ve infinity to 4.

The graph of the inequality 3x < 12 on a number line would consist of an open circle at 4, followed by a shaded region to the left of 4 and extending indefinitely in that direction.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

To graph the inequality 3x < 12 on a number line, we can follow these steps:

- Start by isolating x by dividing both sides of the inequality by 3, which gives us x < 4.

- Draw a number line and mark a point at 4, which is the boundary between the values of x that satisfy the inequality and those that don't.

- Since the inequality is strict (i.e., "less than" and not "less than or equal to"), we need to indicate that the point x = 4 is not included in the solution set.

We can do this by making an open circle (or "unfilled dot") at 4 on the number line.

- Shade the portion of the number line to the left of the point x = 4, since these are the values of x that satisfy the inequality 3x < 12.

We can use an arrow pointing to the left to indicate that the shaded region extends indefinitely in that direction.

Thus,

The graph of the inequality 3x < 12 on a number line would consist of an open circle at 4, followed by a shaded region to the left of 4 and extending indefinitely in that direction.

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The probability that a mouse leaves first and then a bat is given as follows:

14/55.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

As the animal is not replaced, the probabilities for this problem are given as follows:

Hence the probability is given as follows:

4/11 x 7/10 = 2/11 x 7/5 = 14/55.

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Answer: \(r(s(5))=-26\)

Step-by-step explanation:

\(s(5)=5^2 +2=27\\\\r(s(5))=r(27)=-27+1=-26\)

Answer:

The answer to the question is 2

Correct expression which represents the final sale price, in dollars, of the bicycle is,

⇒ p - 0.15p

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

We have to given that;

A bicycle is on sale at a store for 15% off it’s original price.

And, The original price, in dollars, of the bicycle is represented by the variable p.

Hence, We can formulate;

The final sale price, in dollars, of the bicycle is,

⇒ p - 15% of p

⇒ p - 0.15 x p

⇒ p - 0.15p

Thus, Correct expression which represents the final sale price of the bicycle is,

⇒ p - 0.15p

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The area of the enclosed region is  16√2 - 8 squared units

We have,

The region enclosed between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = 0.9π consists of two parts, one above the x-axis and one below the x-axis. We can find the area of each part separately and then add them to get the total area.

First, let's find the x-coordinates of the points where the curves intersect. These are the points where 4 sin(x) = 4 cos(x), or sin(x) = cos(x), which occurs when x = π/4 + kπ/2 for any integer k. Since we are only interested in the intersection points between x = 0 and x = 0.9π, we only need to consider the case k = 0. So the intersection point is x = π/4.

Now, let's consider the part of the region above the x-axis. We need to find the area between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = π/4. This is given by the integral:

A1 = ∫[0, π/4] (4 sin(x) - 4 cos(x)) dx

Using the identities sin(x) = cos(x - π/2) and cos(x) = sin(x + π/2), we can rewrite this as:

A1 = ∫[0, π/4] (4 sin(x) - 4 sin(x + π/2)) dx

 = ∫[0, π/4] (4 sin(x) + 4 sin(x)) dx   (since sin(x + π/2) = sin(x))

 = 8 ∫[0, π/4] sin(x) dx

 = 8 [-cos(x)] [0, π/4]

 = 8 (1 - 1/√2)

 = 8√2 - 8

Next, let's consider the part of the region below the x-axis. We need to find the area between the curves y = 4 cos(x) and y = 4 sin(x) from x = π/4 to x = 0.9π. This is given by the integral:

A2 = ∫[π/4, 0.9π] (4 cos(x) - 4 sin(x)) dx

Using the identities sin(x) = cos(x - π/2) and cos(x) = sin(x + π/2), we can rewrite this as:

A2 = ∫[π/4, 0.9π] (4 cos(x) - 4 cos(x - π/2)) dx

 = ∫[π/4, 0.9π] (4 cos(x) + 4 sin(x)) dx   (since cos(x - π/2) = sin(x))

 = 4 ∫[π/4, 0.9π] (2 cos(x) + 2 sin(x)) dx

 = 4 [2 sin(x) - 2 cos(x)] [π/4, 0.9π]

 = 4 (2/√2 + 2) - 4 (1 - 1/√2)

 = 8√2

So the total area of the region enclosed between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = 0.9π is:

A = A1 + A2

A = 8√2 - 8 + 8√2

A = 16√2 - 8 squared units

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Answer:

It is 63

Step-by-step explanation:

Answer:20%

Step-by-step explanation:

1500/75=20(%)

Answer:

First time=7hours

First speed=990km/hour

First distance=first time×first speedD=(

S×T)

D=990km/hr×7hrs

D=6930km.

Second time=6&14min.

Second speed=920km/hr

Second distance=second speed×second time (D=s×t)

D=920km/hr×6&14min.

D=1500

Total distance=6930+1500

=8430

Answer:

y=1/4x-5

Hope this helps!

The value of x in the triangle is determined as 45.

The value of x in the triangle is calculated by applying the following formula,.

The measure of angle ABD = 0.2x + 52

The measure of angle CBD = 0.2x + 42

From the diagram, we can set-up the following equations;

x + 16 = 0.2x + 52

Simplify the equation above, by collecting similar terms;

x - 0.2x = 52 - 16

0.8x = 36

Divide both sides of the equation by " 0.8 "

0.8x / 0.8 = 36/0.8

x = 45

Thus, the value of x in the triangle is calculated by equating the appropriate values to each other.

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The fraction represented by point A, it is crucial to have information about the scale, intervals, and the relative position of point A on the number line.

With these details, you can calculate the fraction accurately.

Point A on the number line represents a fraction that requires additional information to determine its precise value.

I can provide you with a general approach to finding the fraction corresponding to a given point on the number line.

A number line represents a range of values, typically with a specific scale or interval.

The scale can be divided into equal parts, such as units or fractions.

To determine the fraction represented by point A, we need to know the scale and the position of point A relative to that scale.

Let's consider a number line that ranges from 0 to 1, with evenly spaced tick marks representing tenths.

If point A is located halfway between the tick marks representing 0.4 and 0.5, then it represents the fraction 0.45 (or 9/20 in simplified form).

If the number line has a different scale or is divided into different intervals, the fraction represented by point A will be different.

Without specific details about the number line and the position of point A, it is impossible to determine the fraction precisely.

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Answer:

In the equation y = 2 cos(5x + 3) - 6, we can ignore the coefficients 2 and -6 for the purposes of calculating the period because they do not change the period. They only change the amplitude (2) and vertical shift (-6) of the function.

The coefficient 5 in front of x inside the cosine function affects the period of the function. It is a horizontal compression/stretch of the graph of the function.

The period of the basic cosine function, y = cos(x), is 2π. When there is a coefficient (let's call it b) in front of x, such as y = cos(bx), the period becomes 2π/b.

So, in your case, b = 5, so the period T of the function y = 2 cos(5x + 3) - 6 is:

T = 2π / 5

This is the simplest form for the period of the given function.

Answer:

10 my fault

Step-by-step explanation:

please trust

Answer:

4.80

Step-by-step explanation:

To find the solution to this problem we will use the Pythagoras theorem.

\( {c}^{2} = {a}^{2} - {b}^{2} \)

\( = \sqrt{ {12}^{2} - {11}^{2}} \\ = 4.7958... \\ = 4.8\)

Answer: Let X = the smaller of the two consecutive odd integers. Therefore (X + 2) = the larger of the two consecutive odd integers.

The values of the coordinates x and y is P ( 6 , 3 )

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( x , y )

Let the second point be Q ( 0 , 0 )

Now , the slope of the line is m₁ = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m₁ = y / x

m₁ = 1/2

So , y/x = 1/2

And , x = 2y

Now , the third point is R ( 7 , 5 )

m₂ = ( 5 - y ) / ( 7 - x )

m₂ = 2

On simplifying , we get

( 5 - y ) / ( 7 - x ) = 2

Multiply by ( 7 - x ) , we get

5 - y = 14 - 2x

Adding 2x and subtracting 5 on both sides , we get

2x - y = 9

Substitute the value of x from m₁ , we get

2 ( 2y ) - y = 0

3y = 9

Divide by 3 on both sides , we get

y = 3

And , the value of x = 6

Hence , the coordinate of the point P is P ( 6 , 3 )

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The critical values for a 99% confidence interval using the chi-square distribution with 10 degrees of freedom are 18.3278 and 28.3092.

The chi-square distribution is a continuous probability distribution that is used to determine the probability of a statistic being greater than or less than a certain value. The chi-square distribution with 10 degrees of freedom is used to calculate critical values for a 99% confidence interval.

To find the critical values, we need to use the chi-square distribution calculator. In the calculator, we should enter the degrees of freedom, which is 10 in this case, and the confidence level, which is 99% in this case. The calculator will then return the critical values for the 99% confidence interval for a chi-square distribution with 10 degrees of freedom, which are 18.3278 and 28.3092.

Step 1: Go to the chi-square distribution calculator.

Step 2: Enter the degrees of freedom, which is 10 in this case.

Step 3: Enter the confidence level, which is 99% in this case.

Step 4: Click the “Calculate” button.

Step 5: The calculator will return the critical values for a 99% confidence interval for a chi-square distribution with 10 degrees of freedom, which are 18.3278 and 28.3092.

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Answer:

Barts total cost is (c)213.36

Step-by-step explanation:

First, you subtract 6% from $219

=204.92

add shipping,

+7.50

=213.36

Hope this helps <3

Answer:

C. $213.36

Step-by-step explanation:

The original price is $219 and the discount is 6% which is equal to $13.14

$219 - $13.14 + $7.50 (shipping cost) = $213.36

Answer:

11

Step-by-step explanation:

3-(-8) = 3+8

= 11

Answer:

The answer is 32.50

Step-by-step explanation:

You would just keep counting up by fives and then you would also have to add tax because it is food -- I am happy to help! :)

We can conclude that budget software can help you: identify places to reduce spending.

Budget software is a computer software or program that helps you to plan and allocate how you spend your money.

Budget software makes it easy for you to track what you've spent as money comes in and what you are owed.

Therefore, we can conclude that budget software can help you: identify places to reduce spending.

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The line of best fit for the given data is represented by equation C, which is y= 0.95x + 12.

To find the line of best fit, the data points are plotted on a graph, and the line is drawn so that the distance between each data point and the line is minimized.

This is done using various statistical methods, such as the least squares method, to determine the equation of the line that best represents the data.
The equation of the line of best fit can then be used to make predictions or estimations about future values of the dependent variable based on the independent variable.

In this case, the line of best fit represents the relationship between x and y, and can be used to predict the value of y for a given value of x.
In conclusion, the line of best fit for the data is represented by equation C, y= 0.95x + 12.

This line provides the closest approximation to the data points and can be used to make predictions about future values of the dependent variable based on the independent variable.

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Answer:

\(a=4, b=-8, c=-12\)

Step-by-step explanation:

Compare the given equation with the general form \(y=ax^2 + bx+c\).

The simplified form of these solution is x = -2 ± √6.

What is the solution of an equation?

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given that the solution to 2x² + 8x - 4 =0 are x = (-8 ± √96)/4.

First we will find simplest form of √96.

96 = 4 × 4 × 6

Therefore √96 = √(4 × 4 × 6) = 4√6.

Putting √96 = 4√6 in  x = (-8 ± √96)/4

x = (-8 ± 4√6)/4

Divide the denominator and numerator by 4:

x = -2 ± √6

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the difference of elevation between a and b.Let AB = x, tan 36 = x/111.356 ,x = 111.356 tan 36= 64.39 m and Difference in elevation = 64.39m

We are given that two ridges B and C form a valley with a point A at the bottom part with an elevation difference of 111.356m between the ridges and and angle of elevation of 36 degrees at point A. To find the difference of elevation between A and B, we use the formula of tangent which is tan θ = Opposite/Adjacent. We substitute the values and solve for x, which is the elevation difference between A and B. So the difference in elevation between A and B is 64.39m.

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The given differential equation has characteristic equation

\(r^5 - 4r^4 + 4r^3 - r^2 + 4r - 4 = 0\)

Solve for the roots \(r\).

\(r^3 (r^2 - 4r + 4) - (r^2 - 4r + 4) = 0\)

\((r^3 - 1) (r^2 - 4r + 4) = 0\)

\((r^3 - 1) (r - 2)^2 = 0\)

\(r^3 - 1 = 0 \text{ or } (r-2)^2=0\)

The first case has the three cubic roots of 1 as its roots,

\(r^3 = 1 = 1e^{i0} \implies r = 1^{1/3} e^{i(0+2\pi k)/3} \text{ for } k\in\{0,1,2\} \\\\ \implies r = 1e^{i0} = 1 \text{ or } r = 1e^{i2\pi/3} = -\dfrac{1+i\sqrt3}2 \text{ or } r = 1e^{i4\pi/3} = -\dfrac{1-i\sqrt3}2\)

while the other case has a repeated root of

\((r-2)^2 = 0 \implies r = 2\)

Hence the characteristic solution to the ODE is

\(y_c = C_1 e^x + C_2 e^{-(1+i\sqrt3)/2\,x} + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}\)

Using Euler's identity

\(e^{ix} = \cos(x) + i \sin(x)\)

we can reduce the complex exponential terms to

\(e^{-(1\pm i\sqrt3)/2\,x} = e^{-x/2} \left(\cos\left(\dfrac{\sqrt3}2x\right) \pm i \sin\left(\dfrac{\sqrt3}2x\right)\right)\)

and thus simplify \(y_c\) to

\(y_c = C_1 e^x + C_2 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_3 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right) \\ ~~~~~~~~ + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}\)

For the non-homogeneous ODE, consider the constant particular solution

\(y_p = A\)

whose derivatives all vanish. Substituting this into the ODE gives

\(-4A = 69 \implies A = -\dfrac{69}4\)

and so the general solution to the ODE is

\(y = -\dfrac{69}4 + C_1 e^x + C_2 e^{-x/2} \cos\left(\dfrac{\sqrt3}2x\right) + C_3 e^{-x/2} \sin\left(\dfrac{\sqrt3}2x\right) \\ ~~~~~~~~ + C_3 e^{-(1-i\sqrt3)/2\,x} + C_4e^{2x} + C_5xe^{2x}\)

Answer:

7:11

Step-by-step explanation:

Hope this helps! God bless.