an object that weighs 200 pounfs is on an invline planethat makes an angle of 10 degrees with the horizontal

The inverse of the function in slope-intercept form is f⁻(x) = -x/2 - 2

What is the inverse function?

A function that can change into another function is referred to as inverse. In other words, the inverse of any function "f" will take y to x if it takes x to y in the first place. If a function is written as "f" or "F," the inverse function is written as "f⁻" or "F⁻."

What is slope-intercept form?

The slope-intercept form of a straight line is used to find the equation of a line.

Here,

A function is given to us and we need to find the inverse of the function in slope-intercept form. The given function is,

f(x)= −2x−4

Let assume that y = f(x), then

y = -2x - 4

Now interchange the positions of x and y, and we get

x = -2y - 4

Solve this equation for y in terms of x,

Adding 4 on both sides, we get

x + 4 = -2y

After, dividing both sides by 2, we get

x/2 + 2 = -y

-x/2 - 2 = y

Now replace y with f⁻(x)

f⁻(x) = -x/2 - 2

Hence, the inverse of the function in slope-intercept form is f⁻(x) = -x/2 - 2

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Answer:

x + 1.5y = 25

Step-by-step explanation:

Given that Mr. Guy spends a total of $25, we can set the equation equal to 25. Since x is used to represent the number of pencils, we put 1x into the left side of the equation. We also know that it cost $1.50 for each y pens, therefore 1.5y. If we put together what we have, the equation will be x + 1.5y = 25.

3q+30q+12q = 45q

Hope that helped :)

Answer:

35q+8qq

Step-by-step explanation:

i know is ryt

but y did u separate de first 4's other q like dat?

Answer:

17

Step-by-step explanation:

3 + 7 * 6 / 3

PEMDAS says we multiply and add before adding and subtracting so we multiply first (going from left to right)

3 + 42 / 3

Then we divide

3 + 14 = 17

Answer:

the answer should be B, 1/12 > 0.083

The solution set of the equation -x² + 2x + 15 = 0 is options (G) -3, 15 and (I) -3, 5.

Based on the table of ordered pairs that satisfy the equation y = -x² + 2x + 15, we need to find the solution set of the equation -x² + 2x + 15 = 0.

To do this, we need to find the x-values that make the equation equal to zero.

Let's substitute each x-value into the equation and check if it satisfies the equation.

For option (F):
If we substitute x = 0 into the equation, we get -0² + 2(0) + 15 = 0 + 0 + 15 = 15. This does not satisfy the equation.

For option (G):
If we substitute x = -3 into the equation, we get -(-3)² + 2(-3) + 15 = -9 - 6 + 15 = 0. This satisfies the equation.

For option (H):
If we substitute x = 5 into the equation, we get -(5)² + 2(5) + 15 = -25 + 10 + 15 = 0. This satisfies the equation.

For option (I):
If we substitute x = -3 into the equation, we get -(-3)² + 2(-3) + 15 = -9 - 6 + 15 = 0. This satisfies the equation.

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The probability of getting one marble of each color will be 0.044.

The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place. A random event's recurrence is the subject of this area of mathematics. The range of the number is 0 to 1. The degree to which something is likely to happen is essentially what probability means. You will discover the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

In this question,

Total number of balls=4+5+6=15

probability of red ball= 4/15

probability of white ball = 5/14  (Since the number of balls are decreasing

probability of blue ball= 6/13

probability of getting one marble of each color= 4/15×5/14×6/13    

                                                                              = 0.044

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Answer:

4.3 hours

Step-by-step explanation:

Add all of the fractions to get

7.7

and then simply do

12 - 7.7

Answer:

4.3 hours

Step-by-step explanation:

The proportion of the variation in the values of a response y that is explained by the least-squares regression of y on x is: square of correlation coefficient.

What is square of correlation coefficient?

A helpful number in linear regression is the square of the correlation coefficient, or r2.

The percentage of the variance in one variable that can be partially explained by another variable is represented by this value.

The summary table in the Regression output contains the "R" value, which is the coefficient of correlation.

Coefficient of determination is another name for R square. To calculate R squared, multiply R by R.

The square of the correlation coefficient is what is meant by the term "coefficient of determination."

Hence, the proportion of the variation in the values of a response y that is explained by the least-squares regression of y on x is: square of correlation coefficient.

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Answer:

30 gallons,in the industry but it also depends on your water pressure

Answer:

Part A: \(\frac{3}{5}\)

Part B: \(\frac{1}{2}\)

Step-by-step explanation:

We know that Alinn flipped a coin 20 times, and that 12 of those times resulted in heads. The other 8 times resulted in tails.

Part A wants us to find the experimental probability of the coin landing on heads. Experimental probability is the probability determined based on the experiments performed.

Part B wants us to find the theoretical probability of the coin landing on heads. Theoretical probability is determined based on the number of favorable outcomes over the number of possible outcomes.

Experimental probability is determined as # of times something occurred experimentally / total number of times.  

Since 12 of the 20 times that Alinn flipped the coin resulted in heads, this means that the experimental probability of Alinn flipping heads is \(\frac{12}{20}\), which simplifies down to \(\frac{3}{5}\).

Theoretical probability, as stated above, is the number of favorable outcomes / possible outcomes.

Our favorable outcome is flipping heads, and on a coin, there are two sides that a coin can land on: heads and tails. This means that there are two possible outcomes, and only one of them is favorable.

This means that our theoretical probability is \(\frac{1}{2}\).

Answer:

-2

Hope you could understand.

If you have any query, feel free to ask.

Step-by-step explanation:

\(4x + 14 =- 3x\)

\(4x + 3x = - 14\)

7\(x = - 14\)

x=-2

Answer:

x+5 is the right answer because it says 5 more than a number

In a game of chance, the probability of winning 50 is 40 percent and the probability of having to pay 50 is 60 percent. Therefore, the expected value of this game is -10. The correct answer is option A.

To find out what the expected value of this game is, we will need to use the formula:

Expected value (E) = (probability of winning x amount won) - (probability of losing x amount lost)

Let's substitute the values given in the question:

Probability of winning = 0.4

Amount won = 50

Probability of losing = 0.6

Amount lost = 50

Expected value (E) = (0.4 x 50) - (0.6 x 50)

                               = 20 - 30

                               = -10

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Answer:

Stephen gets £147

Step-by-step explanation:

Given

Let

\(S = Stephen; B = Bridget; R = Richard\)

So:

\(S + B + R = 490\)

\(R = 2S\)

\(S = 3B\)

Required

Find S

Make B the subject in \(S = 3B\)

\(B = \frac{S}{3}\)

Substitute: \(R = 2S\) and \(B = \frac{S}{3}\) in \(S + B + R = 490\)

\(S + \frac{S}{3} + 2S = 490\)

Take LCM

\(\frac{3S + S + 6S}{3}= 490\)

\(\frac{10S}{3}= 490\)

Solve for S

\(S = \frac{490 * 3}{10}\)

\(S = 49 * 3\)

\(S = 147\)

Stephen gets £147

Answer:

Hello!!

The correct answer is false. The exposition begins with conclusions that introduce the characters and the conflict they face

Hope this helps!!

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Step-by-step explanation:

Area of rectangle is length x breadth.

Area = (x + 7)(x + 5)

= (x² + 5x + 7x + 35)

= (x² + 12x + 35)

Answer:

10

Step-by-step explanation:

a^2 +b^2=c^2

6^2 +8^2 = c^2

6×6 is 36

8×8 is 64

36+64 = 100

So 100=c^

Now you need to square root 100

Which is 10

:) I hope that helps

This is Pythagoras theorum

A and b are the shorter sides and make an L shape

The longer side is always c

If you are able to rearrange formulas, I think that would help you a ton x

The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The complementary solution to the homogeneous equation y'' - 2y' + 2y = 0 can be found by solving the characteristic equation\(r^2 - 2r + 2 = 0.\)The roots of this equation are complex conjugates, r = 1 ± i.

Assuming a particular solution in the form y_p = u(x)*v(x), we find u(x) and v(x) by substituting y_p into the original equation and solving for u'(x) and v'(x). This leads to u(x) = \(e^x*csc(x) and v(x) = e^(-x).\)

To determine the variation of parameters, we let y = u(x)*y_1 + v(x)*y_2, where y_1 and y_2 are the linearly independent solutions of the homogeneous equation. Using the Wronskian, we can find the variation of parameters u(x) and v(x).

Finally, the general solution is given by y(x) = y_c + y_p, where y_c is the complementary solution and y_p is the particular solution obtained using the variation of parameters.

Note: The detailed calculations and algebraic steps involved in finding the complementary solution, particular solution, and variation of parameters have been omitted for brevity.

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Answer:

-3/3

Step-by-step explanation: rise over run the red line the rise goes up by three and the blue the run goes over by three but the line in going like this \ so the slope is negative

To find the coordinates of p(x) = -10 + 24x + 7x^2 relative to the basis B = {1 - x + 2x^2, 2 - 4x - 2x^2, 2 - 8x - x^2}, we need to express p(x) as a linear combination of the basis vectors.

Let p(x) = a(1 - x + 2x^2) + b(2 - 4x - 2x^2) + c(2 - 8x - x^2), where a, b, and c are the coordinates we want to find.

By equating the coefficients of the powers of x, we get the following system of linear equations:

a + 2b + 2c = -10
-a - 4b - 8c = 24
2a - 2b - c = 7

Solving this system, we find a = -1, b = -2, and c = 3. Therefore, the coordinates of p(x) relative to this basis are [p(x)]_B = [-1, -2, 3].

To find the coordinates of p(x) relative to the basis b, we need to express p(x) as a linear combination of the basis vectors. We can set up the equation:

p(x) = c1(1 - x^2) + c2(2 - 4x - 2x^2) + c3(2 - 8x - x^2)

where c1, c2, and c3 are the coordinates of p(x) relative to the basis b.

We can simplify this equation by expanding the basis vectors:

p(x) = (c1 + 2c2 + 2c3) - (c1 + 4c2 + 8c3)x + (-c1 - 2c2 - c3)x^2

Now we can see that the coefficients of the terms 1, x, and x^2 in the expression for p(x) give us the coordinates c1, c2, and c3, respectively. So we can solve the system of equations:

c1 + 2c2 + 2c3 = -10
-c1 - 4c2 - 8c3 = 24
-c1 - 2c2 - c3 = 7

There are different methods to solve this system of equations, but one possible way is to use elimination. For example, we can subtract the second equation from the third to eliminate c1, and then subtract twice the first equation from the second to eliminate c2:

c1 + 2c2 + 2c3 = -10
-2c1 - 2c2 - 7c3 = -17
2c2 + 6c3 = -44

Now we can solve for c3 by dividing the last equation by 2:

c3 = -22 - c2

Substituting this expression for c3 into the second equation gives:

c1 = -12 - 2c2

Substituting these expressions for c1 and c3 into the first equation gives:

-12 - 2c2 + 4c2 - 44 - 44 + 2c2 = -10

Simplifying and solving for c2 gives:

c2 = -7

Then we can substitute this value for c2 into the expressions for c1 and c3 to get:

c1 = 2
c3 = -15

Therefore, the coordinates of p(x) relative to the basis b are:
[p(x)]b = [2, -7, -15]

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The linear interpolation spline between points (0,1) and (1,0) for x=1/2 is y=1/2. The quadratic interpolation spline using (0,1), (1,0), and (5/2,0) is y=-8/5x^2 + 9/5x + 1 for x in [1/2,5/2].

To find the linear interpolation spline and quadratic interpolation spline, we can use the following formulas

For linear interpolation, the spline between data points (x1,y1) and (x2,y2) is given by

y = y1 + (y2-y1)/(x2-x1)*(x-x1)

For quadratic interpolation, the spline between data points (x1,y1), (x2,y2) and (x3,y3) is given by

y = y1*((x-x2)(x-x3))/((x1-x2)(x1-x3)) + y2*((x-x1)(x-x3))/((x2-x1)(x2-x3)) + y3*((x-x1)(x-x2))/((x3-x1)(x3-x2))

To find the linear interpolation spline, we can use the points (0,1) and (1,0) since they are the nearest neighbors to x = 1/2:

y = 1 + (0-1)/(1-0)*(1/2-0) = 1/2

Therefore, the linear interpolation spline is y = 1/2 for x in [1/2,1].

To find the quadratic interpolation spline, we need to use three neighboring points. We can use (0,1), (1,0), and (5/2,0) since they are the three nearest neighbors to x = 1/2. Substituting these values into the formula, we get

y = 1*((x-1)(x-5/2))/((0-1)(0-5/2)) + 0*((x-0)(x-5/2))/((1-0)(1-5/2)) + 0*((x-0)(x-1))/((5/2-0)(5/2-1))

Simplifying, we get:

y = -8/5x^2 + 9/5x + 1

Therefore, the quadratic interpolation spline is y = -8/5x^2 + 9/5x + 1 for x in [1/2,5/2].

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Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45