Find the coordinates of the y-intercept for the graph with equation: y=x2+x−1

Answer:

  3 -√7

Step-by-step explanation:

You want to rationalize the denominator of 2/(3 +√7).

The denominator of such an expression is turned to an integer by multiplying numerator and denominator by the conjugate of the denominator.

  \(\dfrac{2}{3+\sqrt{7}}=\dfrac{2}{3+\sqrt{7}}\cdot\dfrac{3-\sqrt{7}}{3-\sqrt{7}}=\dfrac{2(3-\sqrt{7})}{3^2-7}=\boxed{3-\sqrt{7}}\)

__

Additional comment

This process takes advantage of the factorization of the difference of squares:

  a² -b² = (a +b)(a -b)

If 'b' is a value that can be made a rational real number by squaring it, then this multiplication by the conjugate can achieve that end. The conjugate of a sum is the corresponding difference.

This process is also used with complex numbers, since i² = -1, a real number.

Answer:

1,002,014

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

Step 1: Define

h(x) = 3x + 1

h(x) = 4

Step 2: Substitute and Evaluate

4 = 3x + 1

3 = 3x

x = 1

Answer:

3/4 divided by 9 (break it down) = 1/12

Answer:

Question 1: A - 5,400sqft

Question 2: 11 bags of fertilizer

Step-by-step explanation:

Question 1: You need the areas of the white squares added together and then subtracted from the total area of the park.

Question 2: To find the number of bags needed to fertilize the grass we simply divide the area one bag can fertilize by the shaded area. We could use a basic equation such as:

In this equation x represents the number of bags needed to fertilize the shaded area. The answer is 10.8, but logically speaking you cannot buy .8 of a bag so you just round up to 11.

The estimated probability that the machine is still operating after 1300 hours is approximately 0.034.

To estimate the probability that the machine is still operating after 1300 hours, we can use the exponential distribution.

Given that the mean of the battery life is 25 hours, we can use the formula for exponential distribution:
\(P(X > t) = e^{-t/\mu}\)

Where X is the random variable representing the battery life, t is the time, and μ is the mean battery life.

we need to find the parameter λ, which is the rate parameter and is equal to 1/μ. In this case, λ = 1/25.
we want to find the probability that the machine is still operating after 1300 hours.
P(X > 1300) = \(e^{-1300/25}\)

To estimate this probability, we can substitute the value of λ and calculate it using a calculator or software.
P(X > 1300) ≈ 0.034

Rounded to three decimal places, the estimated probability that the machine is still operating after 1300 hours is approximately 0.034.

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Complete question:

Suppose a machine requires a specific type of battery that lasts an exponential amount of time with mean 25 hours. As soon as the battery fails, you replace it immediately. If you have 50 such batteries, estimate the probability that the machine is still operating after 1300 hours. Round your answer to three decimal places. Save your answer as p4 . Prompt 1: Suppose 30 numbers are selected at random from the interval [0, 1]. That is, X; -U[0, 1] for i = 1, 2,...30. Given X = (1/30) L. X; estimate P(0.5 < X <0.6). (Round your answer to three decimal places.)

Step-by-step explanation:

a)

(a)255+350 <455

ans...605-455

..150

.........profit per week is 60 +45

105.

105 x 150

weekly profit is..$15750

Answer:

See below.

Step-by-step explanation:

Let's first define our variables. Let's let:

x denote the amount of software programs made and

y denote the amount of video games made.

Part A)

Now, let's write our equations and constraints.

The company can produce at most 225 software programs. So:

\(x\leq225\)

And the company can produce at most 350 video games. So:

\(y\leq 350\)

Total product (the sum of software programs and video games) cannot exceed 455 items per week. In other words:

\(x+y\leq455\)

Part B)

Refer to the first graph:

We have four corner points: A, B, C, and D.

The darkest portion represents the feasible portion. Any combination of software programs and video games within this portion can be produced.

Part C)

Refer to the second graph.

To find what to produce to find the maximum profit, let's write an equation. Let P equal to maximum profit. So, it would be the sum of the total profit from the software programs and video games. We can write the following equation:

\(P=60x+45y\)

Let's solve for y in order to graph it. Subtract 60x from both sides:

\(45y=-60x+P\)

Divide both sides by 45:

\(y=-\frac{4}{3}x+\frac{P}{45}\)

In order produce the maximum profit, P must be the greatest while simultaneously touching our corner points.

Note: The P, Q, R, and S are just rough estimates.

I've graphed four versions of our equation using different variables (for P). We can see that the equation with the highest profit P is the one the crosses point C with P equaling approximately $24,000.

Therefore, in order to maximize profits, the company should produce (Remember that C is at (225, 230)) 225 software programs and 230 video games.

And we're done!

The solution of the given recurrence relation `T(n) = 2T(n/2) + 23n` using all three methods are:`T(n) = Θ(nlog2n)`

Given recursive relation is `T(n) = 2T(n/2) + 23n`.

We have to solve the above recursion using all three methods in any order we choose and label each solution as recursion tree, substitution, or Master Theorem.

Now, let's solve the above recursion using all three methods one by one:

1. Recursion Tree method:

To solve the above relation using recursion tree method, we will create a tree and the value of each level will be the sum of the values of all nodes present in that level or the sum of all previous levels + current level.

The tree will look like:

Therefore, the answer of the given recurrence relation `T(n) = 2T(n/2) + 23n` using the recursion tree method is:

`T(n) = Θ(nlog2n)`

2. Substitution method:

To solve the above recurrence relation using the substitution method, we can assume a solution and prove it by the Mathematical induction method.

Let `T(n) = 2T(n/2) + 23n`

Then, `T(n/2) = 2T(n/4) + 23n/2`

Also, `T(n/4) = 2T(n/8) + 23n/4`

Therefore, `T(n) = 2(2T(n/4) + 23n/2) + 23n`Or, `T(n) = 2²T(n/2²) + 23n(1 + 2)`

In general, we have `T(n) = 2kT(n/2k) + 23n(1 + 2 + ... + 2k-1)`

When `n/2k = 1`Or, `k = log2n`

Therefore, `T(n) = 2log2nT(1) + 23n(1 + 2 + ... + 2log2n-1)`Or, `T(n) = 2log2nT(1) + 23n(2log2n - 1)`

As `T(1) = 1`

Therefore, `T(n) = Θ(nlog2n)`

Hence, the answer of the given recurrence relation `T(n) = 2T(n/2) + 23n` using the substitution method is:

`T(n) = Θ(nlog2n)`

3. Master Theorem method:

To solve the above recurrence relation using the Master theorem, we have to compare the function `nlogba` with the function `f(n)`.

Here, `a = 2`, `b = 2`, and `f(n) = 23n`.

As per the Master theorem:

`If f(n) = Θ(nlogba),

then T(n) = Θ(nlogba log2n)` `

               = Θ(nlog2n)` if

`f(n) = 23n

      = Θ(nlog2n)`

Therefore, the solution of the given recurrence relation `T(n) = 2T(n/2) + 23n` using the Master theorem is:

`T(n) = Θ(nlog2n)`

Hence, the solution of the given recurrence relation `T(n) = 2T(n/2) + 23n` using all three methods are:`T(n) = Θ(nlog2n)`

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A one-sample t-test is the appropriate test to compare the average satisfaction rating of Riverside community hospital to the population average.

To determine what test should be used in this scenario, we need to consider the nature of the data and the objective of the analysis.

Based on the given information, we have two sets of data: the average satisfaction rating for all hospitals (population) and the average satisfaction rating for Riverside community hospital (sample).

If our objective is to compare the average satisfaction rating of Riverside community hospital to the population average, we can use a hypothesis test. Specifically, we can perform a one-sample t-test.

The one-sample t-test allows us to compare a sample mean to a known population mean when the population standard deviation is unknown. In this case, we know the population mean (7.8) and the population standard deviation (0.5), which makes the one-sample t-test appropriate.

By comparing the average satisfaction rating of Riverside community hospital (8.1) to the population mean (7.8), along with the sample standard deviation (1.5) and the known population standard deviation (0.5), we can conduct a one-sample t-test to determine if the difference is statistically significant.

Therefore, a one-sample t-test is the appropriate test to compare the average satisfaction rating of Riverside community hospital to the population average.

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The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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Answer:

(64.7, 67.9)

Step-by-step explanation:

(66.3-2*08, 66.3+2*0.8)

(66.3-1.6, 66.3+1.6)

(64.7, 67.9)

Answer:

x = -1

Step-by-step explanation:

Isolate x.

First, subtract 3 from both sides.

3 + (2/x) - 3 = 1 - 3

2/x = -2

Then, multiply by x on both sides.

2/x * x = -2 * x

2 = -2x

Lastly, divide by -2 on both sides.

2 / -2 = -2x / -2

-1 = x

Answer:

x=2 and x=-2

Step-by-step explanation:

Original Equation:

\(x^2-6x=-6x+4\\\)

Add 6x to both sides

\(x^2=4\)

Subtract 4 from both sides

\(x^2-4=0\)

Use difference of squares: \(a^2-b^2=(a-b)(a+b)\)

\((x-2)(x+2)=0\)

Since the factors are being multiplied by each other, if one of the factors is equal to zero, then the entire thing becomes zero, since 0 * anything = 0

So to find the values of x that satisfy this equation, set each factor equal to zero

\(x-2=0\)

Add 2 to both sides

\(x=2\)

\(x+2=0\)

subtract 2 from both sides

\(x=-2\)

We have both values that satisfy this equation, x=2 and x=-2

The inscribed angles are  3°, 5°, and 2.5°.

It is the angle inscribed on the arc of a circle.

The measure of the angle is half of the intercepted arc.

We have,

From the figure,

We are assuming that the intercepted arc length:

1)

Intercepted arc length = 6

Inscribed angle.

= 1/2 x 6

= 3°

2)

Intercepted arc length = 10

Inscribed angle.

= 1/2 x 10

= 5°

3)

Intercepted arc length = 5

Inscribed angle.
= 1/2 x 5

= 2.5°

Thus,

The inscribed angles are  3°, 5°, and 2.5°.

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Jack's average speed in meters per second is 350m / 314.2s = 1.11 meters/second.

Jack swims seven lengths of the pool in a time of 5 minutes and 14.2 seconds. To find his average speed, we need to convert the time into seconds only. To convert 5 minutes and 14.2 seconds to seconds, we multiply 5 minutes by 60 seconds (since there are 60 seconds in a minute) and add 14.2 seconds.

This gives us a total of 314.2 seconds. Now, we can calculate Jack's average speed by dividing the distance he covered (7 lengths of the pool, which is 7 * 50.0m = 350m) by the time it took (314.2 seconds). In conclusion, on this day,

Jack's average speed in the 50.0-meter-long Olympic-size swimming pool was 1.11 meters per second.

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Answer: It grew by 13,640 people

Step-by-step explanation:

First, turn 6.2% into 0.062.

Next, multiply 0.062x220,000.

You get 13,640.

The rest of the information is unnecessary.

Answer:

Your Balance Would Be $1400.

How I Found The Answer:

$1000 Is 100%

$1000 ÷ 100 = $10

$10 Is 1%

$10 × 8 = $80

$80 × 5 = $400

$1000 + $400 = $1400

Your Balance Would Be $1400.

Answer:

Step-by-step explanation:

The confidence interval (0.14, 0.26) and a sample size of 50 trees, it can be estimated that anywhere from 7 to 13 trees were dead but still standing in the large forest the correct answer is option A.

To determine the number of trees that were dead but still standing, we need to analyze the confidence interval provided. The confidence interval (0.14, 0.26) represents a range of values within which the true proportion of dead but still standing trees in the large forest is likely to fall.

The lower bound of the confidence interval is 0.14, which means that at least 14% of the trees in the forest are estimated to be dead but still standing. The upper bound of the confidence interval is 0.26, indicating that at most 26% of the trees are estimated to be dead but still standing.

To estimate the number of trees within this range, we multiply the lower and upper bounds of the confidence interval by the sample size of 50 trees. This gives us a range of 7 to 13 trees.

Therefore, based on the given information, we can conclude that anywhere from 7 to 13 trees were estimated to be dead but still standing in the large forest. The correct answer is option a: anywhere from 7 to 13.

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The critical numbers of the function h(x) = sin2 x cos x on the interval 0 < x < 2 are: 0.955, 1.186

To find the critical numbers follow these steps:

1. Find the derivative of h(x) with respect to x, which is h'(x).
Using the product rule and the chain rule:
h'(x) = (d(sin^2(x))/dx)cos(x) + sin^2(x)(d(cos(x))/dx)

The derivative of sin^2(x) is:
2sin(x)cos(x)

The derivative of cos(x) is:
-sin(x)

So,
h'(x) = (2sin(x)cos(x))cos(x) + sin^2(x)(-sin(x))
h'(x) = 2sin(x)cos^2(x) - sin^3(x)

2. Find the critical points by setting h'(x) equal to zero and solving for x:
0 = 2sin(x)cos^2(x) - sin^3(x)

Factor out sin(x):
0 = sin(x)(2cos^2(x) - sin^2(x))

3. Solve for x within the given interval 0 < x < 2:
sin(x) = 0:
There are no solutions for sin(x) = 0 in the interval 0 < x < 2.

2cos^2(x) - sin^2(x) = 0:
Using the identity sin^2(x) + cos^2(x) = 1, rewrite the equation:
2cos^2(x) - (1 - cos^2(x)) = 0
3cos^2(x) = 1
cos^2(x) = 1/3
cos(x) = ±sqrt(1/3)

The solutions within the given interval are:
x = arccos(±sqrt(1/3))
x ≈ 0.955, 1.186

So, the critical numbers of the function h(x) = sin^2(x)cos(x) for 0 < x < 2 are approximately x = 0.955 and x = 1.186.

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Answer:

hope this helps

Answer:

1

Step-by-step explanation:

Please attach the diagram with your question

Answer:

y = -x + 9.5

this is the answer to the line parallel to y=-x that passes through (7, 2.5)

Answer:

y - 5 = 1.5x

Step-by-step explanation:

First to find the equation we have to find the slope:

15/10 = 1.5 is the slope ( 56.3 degrees )

Then find the correct equation:

y - 5 = 1.5x

There can be others like:

y = 1.5x + 5 etc.

Answer: y= x^2/16-6x/16+41/16

Step-by-step explanation:

The equation of a parabola will be; y = x^2/16 - 6x/16 + 41/16

If a quadratic equation is written in the form

y=a(x-h)^2 + k

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

Otherwise, we had to use calculus to get critical points, then second derivative of functions to find the character of critical points as minima or maxima or saddle etc to get the location of vertex point.

This point (h,k) is called the vertex of the parabola that quadratic equation represents.

WE need to find the equation of a parabola that has a vertical axis, passes through the point (–1, 3), and has its vertex at (3, 2)

Thus, the equation of a parabola will be;

y = x^2/16 - 6x/16 + 41/16

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The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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Answer:

Deepika Deepika use 32% of his salary ^ housed and which is the amount of this is Monica is in driving on the monthly on the this is profit or loss we know don't don't know that we are what we do if x x is value of you don't know why I don't know it's your mistake I don't care

Answer:

x = 15

Step-by-step explanation:

Using the Altitude- on- Hypotenuse theorem

( leg of large Δ )² = ( part of hypotenuse below it ) × ( whole hypotenuse )

x² = 9 × 25 = 225 ( take the square root of both sides )

x = \(\sqrt{225}\) = 15

Answer:

6

Step-by-step explanation:

The average rate of change is the same as the slope. Since the slope is the same no matter what interval you choose, the answer is 6.

Answer:

6

Step-by-step explanation:

The average rate of change is the same as the slope. Since the slope is the same no matter what interval you choose, the answer is 6.

95 kg is equal to 0.45359237 lbs. A kilogram (kg) is said to weigh 2.2 times more than a pound (represented as lbs). As a result, 2.26 pounds equal one kilo of mass.

The kilogram (kg) is the SI's (International System of Units) definition of a unit of mass. It is a measurement scale that is widely used in science, engineering, and business all around the world. "1,000 grams" is what it means. The International System of Units' unit of mass is the kilogram, which is represented by the unit sign kg. It is a measurement scale that is widely used in science, engineering, and business all around the world. Its meaning is "1,000 grams." The abbreviation for a kilogram is kg or kilo. A kilogram weighs 0.4535 pounds. 2.2046 pounds are equal to one kilogram.

95 kg= 0.45359237 lbs

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