RADICALS AND CUADRATIC Solving a quadratic eque Solve (u-3)^(2)-20=0, where Simplify your answer as much : If there is more than one soluti If there is no solution, click "No

(a) Revenue will be zero when p = $0 and $2000.

(b) Revenue will exceed $1,400,000 when p > 500 or p > 700

(a) To find the prices at which revenue is zero, we need to set R(p) equal to 0 and solve for p:0 = -4p^2 + 8000p0 = 4p(p - 2000)So either 4p = 0 or p - 2000 = 0.

Solving for p gives us:

p = 0 or p = 2000

Therefore, the prices at which revenue is zero are $0 and $2000.

(b) To find the range of prices for which revenue exceeds $1,400,000, we need to set R(p) greater than 1,400,000 and solve for p:

1,400,000 < -4p^2 + 8000p

Rearranging the equation gives us:

0 < 4p^2 - 8000p + 1,400,000

Factoring the left side of the equation gives us:

0 < (p - 500)(4p - 2800)

So either p - 500 > 0 or 4p - 2800 > 0.

Solving for p gives us:

p > 500 or p > 700

Since we want the range of prices for which revenue exceeds $1,400,000, we need to take the larger value of p.

Therefore, the range of prices for which revenue exceeds $1,400,000 is p > 700, or prices greater than $700.

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Answer:

359°

Step-by-step explanation:

When an image is rotated by a multiple of 360 degrees, it returns to its original position because it has completed one full revolution. However, if the image is rotated by any angle less than 360 degrees, it will not return to its exact original position.

For example, if an image is rotated by 45 degrees, it will not return to its exact original position, but will instead be in a new and unique position. If the image is then rotated by another 45 degrees, it will again be in a new and unique position, and so on.

Therefore, the highest number of degrees an image can rotate without returning to its exact original position is 359 degrees.

Answer: 359 degrees

Step-by-step explanation:

If you rotate any object exactly 360 degrees, it returns to it's original position. Remember that phrase "360 no-scope?" It involves spinning until you're back where you started; try doing it right now. You'll be back where you were. But this question wants to know how far you can rotate an object without it being back where it was. I would usually say 359.999999999, but it's a whole number answer, so we'll stick with 359. Hope this helps!

In the given figure the equation m∠MRS + m∠MRO = 180° is the postulate describing the linear pair of angles.

The English word "angle" derives from the Latin word "angulus," which means "corner." The vertex and the two rays are referred to as the sides of an angle, respectively, and are the shared termini of two rays.

It is given that -

∠MRS ≅ ∠MRO

Now, what that means is that ∠MRS is congruent to ∠MRO.

Thus, to understand this concept of equality or congruence, we can prove it since from the given image, we see that -

m∠MRS = m∠MRO = 90°

Since they are both right angles then we can say that the correct theorem is the definition of a right angle triangle.

m∠MRS + m∠MRO = 180°

It is seen that the angles form a linear pair and lie on the same plane.

Therefore, the correct postulate is linear pair.

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The equation of a horizontal line that passes through (4,2) in slope intercept form is y = 2.

A horizontal line has a slope of 0, which means that the y-value remains constant while the x-value changes. In slope intercept form, the equation of a line is written as y = mx + b, where m is the slope and b is the y-intercept.

Since the slope of a horizontal line is 0, the equation of a horizontal line can be written as y = 0x + b, or simply y = b. The y-intercept is the value of y when x = 0, which is the same as the y-value of any point on the line.

In this case, the line passes through the point (4,2), so the y-value is 2. Therefore, the equation of the line in slope intercept form is y = 2.

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The quadratic formula is used to solve  equations of the form ax^(2) + bx + c = 0. The formula is given by:

x = (-b ± √(b^(2) - 4ac))/2a

In this case, the coefficients are a = 9, b = -3, and c = -1. Plugging these values into the formula gives:

x = (-(-3) ± √((-3)^(2) - 4(9)(-1)))/2(9)

Simplifying the expression gives:

x = (3 ± √(9 + 36))/18

x = (3 ± √45)/18

x = (3 ± 3√5)/18

Simplifying further gives:

x = (1 ± √5)/6

So the two solutions to the equation are:

x = (1 + √5)/6 ≈ 0.62

and

x = (1 - √5)/6 ≈ -0.29

Therefore, the two solutions to the equation 9x^(2)-3x-1=0 are x ≈ 0.62 and x ≈ -0.29.

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Answer:

(x, y)→(x,-y)

R(-4,0) S(-1,-3) T(2,-2)

Step-by-step explanation:

The opposite of a number is made by multiplying it by negative 1 (-1)

If it's reflected across the x axis, then the y axis will be the only one to change. (y to -y)

(x, y)→(x,-y)

Our formula for reflection across the x axis is (x,-y)

The rest is simple: Change each set of coordinates to an opposite y value.

The solution 143 milliters of HCl.

To answer this question, we need to calculate the ratio of HCl to water in the first solution, then apply that ratio to the second solution.

In the first solution, there are 66 milliliters of HCl and 90 milliliters of water, so the ratio of HCl to water is 66/90 = 0.733.

To make the second solution with the same concentration of HCl, it must have the same ratio of HCl to water. This means that for the second solution, 0.733 of the 195 milliliters of water must be HCl.

To calculate the amount of HCl in the second solution, we multiply 0.733 and 195: 0.733 * 195 = 143.985 milliliters of HCl. Since we cannot have part of a milliliter, the answer is 143 milliliters of HCl.

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We can say that JKLM is an isosceles trapezoid, since the non-parallel sides (JK and ML) are congruent.

A polygon is a closed plane figure with three or more straight sides that meet at the vertices. It is formed by connecting line segments endpoint-to-endpoint with each segment intersecting exactly two others.

The given quadrilateral JKLM has four sides, and its opposite sides are parallel.

Furthermore, since all four sides have different lengths, it is not a parallelogram.

Also, since no angles or sides are congruent, it is not a kite or a rhombus.

Therefore, the most specific classification for this quadrilateral would be a trapezoid, which is a quadrilateral with one pair of parallel sides.

To be more specific, we can say that JKLM is an isosceles trapezoid, since the non-parallel sides (JK and ML) are congruent.

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Table showing relation of points and coins is as in the solution, graph is straight line p = 15c+5, drawn and attached below. y-intercept is (0,5).

A table has records (rows) and fields (columns). Fields have different data types. as Text, Numbers, Dates, and Hyperlinks. record: It contains certain data, such as information about specific employees or products.

Given,

In a video game, player earns 5 points for reaching next level

15 points are for each coin collected

when player has 1 coin, number of points

= 15 + 5

= 20

when player has 2 coin, number of points

= 2(15) + 5

= 35

Equation for c coins, number of points

p = 15c + 5

Table can be created as follows:

Coins(c)  Points()

0                 5

1                 15

2                35

3                 50

4                 65

5                 80

6                 95

7                  110

8                  125

Graph is a straight line, y-intercept is (0,5).

Hence, table of the relationship of points and coins is

Coins  0   1    2    3     4    5    6    7      8

Points 5  15  35  50  65  80  95  110   125

Graph of the data is an straight line p = 15c + 5, (0,5) is y-intercept.

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The like terms on the list are given as follows:

[tex]\sqrt{2}, -3\sqrt{2}, 5\sqrt{2}, \sqrt{50}[/tex]

Like terms are terms that share these two features:

If two terms are like terms, then they can be either added or subtracted.

In the case the terms are roots, they have the same root.

The square root of 50 is given as follows:

[tex]\sqrt{50} = \sqrt{2 \times 25} = 5\sqrt{2}[/tex]

Hence the like terms are given as follows:

[tex]\sqrt{2}, -3\sqrt{2}, 5\sqrt{2}, \sqrt{50}[/tex]

There are no terms with 3 or 5 on the root, hence the other two terms have no like terms.

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The value of y is -3. The equation formed from the question is 4x + y = 65 and 5x -3y = 94.

First, we will solve for x

Multiplying the 4x + y = 65 equation by 3 we get

12x +3y =195

Now solving both the equation

The variable y gets cancelled because of having the same value

∴ 17x = 289

x= 17

Now putting the value of x in equation 4x + y = 65 to get the value of y

4*17 +y =65

68 +y = 65

y= -3

Now putting the value of x in equation 5x -3y = 94  to get the value of y

5*17 -3y =94

85 -3y =94

-3y = 94-85

y= -3

Therefore, the value of y is -3

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The identity \[ \frac{1}{\tan x(1+\cos 2 x)}=\csc 2 x \] is proved.

To prove the identity \[ \frac{1}{\tan x(1+\cos 2 x)}=\csc 2 x \], we can use the Double Angle Formula for Cosines and the Pythagorean Identity.

Using the Double Angle Formula for Cosines, we get:
$\cos2x = 2\cos^2 x - 1$

We can then substitute this into the original identity and simplify:
$\frac{1}{\tan x(1+\cos 2 x)}=\frac{1}{\tan x(1+2\cos^2 x - 1)}$

Using the Pythagorean Identity, $\cos^2 x + \sin^2 x = 1$, we get:
$\frac{1}{\tan x(1+\cos 2 x)}=\frac{1}{\tan x(\sin^2 x)}$

Using the inverse tangent function, $\tan^{-1}x = \frac{\pi}{2}-\sin^{-1}x$, and since $\sin 2x = 2 \sin x \cos x$, we can rewrite this as:
$\frac{1}{\tan x(1+\cos 2 x)}=\frac{1}{2 \sin x \cos x}$

Finally, using the definition of cosecant, $\csc x = \frac{1}{\sin x}$, we get:
$\frac{1}{\tan x(1+\cos 2 x)}=\csc 2 x$

Therefore, the identity \[ \frac{1}{\tan x(1+\cos 2 x)}=\csc 2 x \] is proved.

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To average a 90 on all three tests, you must score a 95 on the next test.

To find the score you need to average exactly a 90 on all three tests, you can use the formula for the mean (average) of a set of numbers:

Mean = (Sum of all numbers) / (Total number of numbers)

Let's call the score you need on the next test x. We can plug in the known values and solve for x:

90 = (81 + 94 + x) / 3

Multiply both sides by 3 to get rid of the fraction:

270 = 81 + 94 + x

Subtract 81 and 94 from both sides to isolate x:

95 = x

So, you need to score a 95 on the next test to average exactly a 90 on all three tests.

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The correct equation for the sentence is: 24 = 31.4n - 8.4.

Twenty-four is equal to 31.4 times a number plus a negative 8.4 multiplied by the proper equation, which is:

24 = 31.4n - 8.4

This formula can be rewritten as follows:

31.4n = 24 + 8.4

And after being distilled:

31.4n = 32.4

Finally, by multiplying both sides by 31.4, we can find the value of n:

n = 32.4/31.4

Thus, the following is the proper equation for the phrase:

24 = 31.4n - 8.4.

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Answer:

mean = 86

mean w/o 2 lowest = 92

median = 91

median w/o 2 lowest = 93

mode = 98

mode w/o 2 lowest = 98

Step-by-step explanation:

Isosceles trapezoid MNOP where MO = a + 13 and NP = 2a - 1,  The value of a 13.

A trapezoid, also known as a trapezium, is a four-sided polygon with two parallel sides, also called the bases. The non-parallel sides are called legs, and they can have different lengths. The parallel sides are perpendicular to the legs

In an isosceles trapezoid, the nonparallel sides are congruent, so we have MN = OP.

Also, the diagonal PN divides the trapezoid into two congruent right triangles, so we have:

[tex]MN^2 = (NP - MO)^2 + (MP)^2[/tex]

Substituting the given values, we get:

[tex]MN^2 = (2a - 1 - (a + 13))^2 + MP^2[/tex]

[tex]MN^2 = (a - 14)^2 + MP^2[/tex]

But since MN =OP and MO = NP - MN, we have:

[tex]OP = NP - MO = (2a - 1) - (a + 13) = a - 12[/tex]

So we also have:

[tex]OP^2 = (a - 12)^2 + MP^2[/tex]

Since MN = OP, we can set these two equations equal to each other:

[tex](a - 14)^2 + MP^2 = (a - 12)^2 + MP^2[/tex]

Simplifying and solving for a, we get:

[tex]a^2 - 28a + 197 = a^2 - 24a + 144[/tex]

[tex]4a = 53[/tex]

[tex]a = 13.25[/tex]

Therefore, the value of a is 13.25.

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When rounding a number to 2 decimal places, we are essentially keeping only the first two digits after the decimal point and discarding the rest. The third digit after the decimal point is the one that affects the rounding decision.

In this case, the number y is rounded to 9.68, which means that the third digit after the decimal point is either 5 or greater than 5. If it is 5 or greater, we round up the second digit after the decimal point. If it is less than 5, we simply truncate the decimal part.

To find the upper bound of y, we need to add 0.005 to 9.68, which is the smallest possible value for the third digit that would cause rounding up:

9.68 + 0.005 = 9.685

Therefore, the upper bound of y is 9.685.

To find the lower bound of y, we need to subtract 0.005 from 9.68, which is the largest possible value for the third digit that would not cause rounding up:

9.68 - 0.005 = 9.675

Therefore, the lower bound of y is 9.675.

Hence, the upper and lower bounds of y are 9.685 and 9.675, respectively.

The given matrices are checked and their status is mentioned in the following list below :a. Reduced echelon form [100 010 000 -10-100] b. Not in echelon form [ -8000 -4200 -8110 -9101 -8130] c. Reduce echelon form [11 10 -4 -10] d. Echelon form [ 100 001 000 -502] Echelon form and reduced echelon form of matrices

The Matrix A is in the reduced echelon form if and only if the following conditions are satisfied:All rows having 0s are at the bottom of the matrix.There must be no 0 rows in the matrix.In each row of the matrix containing the leading nonzero element, all entries above and below the leading entry are 0.

The leading coefficient of a nonzero row is always strictly to the right of the leading coefficient of the row above it.In each column containing a leading coefficient, all other entries are zero.

For a matrix to be in echelon form, it must fulfill the following conditions : All rows containing all zero elements are located at the bottom of the matrix. All leading coefficients in any nonzero row are always strictly to the right of the leading coefficient in the row above it.

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To determine the intervals where a function is increasing or decreasing, we need to take the derivative of the function and find the critical points. The critical points are where the derivative is equal to zero or undefined.

First, let's take the derivative of the function:
g'(x) = -1/(zx)^2, x<-2 . 3/2, x>-2

Now, let's find the critical points:
-1/(zx)^2 = 0 -> There are no values of x that will make this equation true, so there are no critical points for x<-2.
3/2 = 0 -> There are no values of x that will make this equation true, so there are no critical points for x>-2.

Since there are no critical points, the function is either always increasing or always decreasing. To determine which one it is, we can pick a value of x in each interval and plug it into the derivative:

For x<-2, let's pick x=-3:
g'(-3) = -1/(-3z)^2 = 1/(9z^2) > 0

Since the derivative is positive, the function is increasing on the interval (-infinity, -2).
For x>-2, let's pick x=0:
g'(0) = 3/2 > 0

Since the derivative is positive, the function is also increasing on the interval (-2, infinity).

Therefore, the function is increasing on the entire domain of the function, which is (-infinity, infinity).

Answer: Increasing on: (-infinity, infinity) Decreasing on: None

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The sales tax that Bobbi paid was 10 dollars. Below, you will learn how to solve the problem.

To find the sales tax, we can simply subtract the cost of the text books from the total amount paid:

Sales tax = Total amount paid - Cost of text books

Sales tax = 130 dollars - 120 dollars
Sales tax = 10 dollars

Therefore, the sales tax that Bobbi paid was 10 dollars.

In mathematics, subtraction (also called subtraction) is an arithmetic operation that removes quantities from any kind of operation.

After subtracting, we will always have a smaller value than the one we had before.

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Anne prediction on the amount of rain that will pour down is 60 inches

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

The amount of rain this year can be calculated as follows

Percentage = 20/100 = 0.2

So, we have

Proportion = 0.2 + 1  =  1.2

This gives

Amount = 1.2 × 50 = 60

Hence the amount of rain this year is 60 inches

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Answer:

6(x)-5=90

Step-by-step explanation:

Move all terms that don't contain x to the right side and solve.

Exact Form:

x=95/6

Decimal Form:

x=15.83

Mixed Number Form:

x= 15 5/6

tbh i don't know if this is right

When the diameter οf the is 10 feet, then the area οf the circle is 78.54 ft².

A circle is created in the plane by each pοint that is a specific distance frοm anοther pοint (center). Hence, it is a curve made up οf pοints that are separated frοm οne anοther by a defined distance in the plane. Mοreοver, it is rοtatiοnally symmetric abοut the centre at every angle. Every pair οf pοints in a circle's clοsed, twο-dimensiοnal plane are evenly spaced apart frοm the "centre." A circular symmetry line is made by drawing a line thrοugh the circle. Mοreοver, it is rοtatiοnally symmetric abοut the centre at every angle.

The circle's diameter is specified as 10 feet. Since we already knοw that the circle's diameter is twice its radius, we can calculate its radius as fοllοws:

diameter = radius / 2 = 10 / 2 = 5 feet

Area οf circle = πr²

π5²

= π5 × 5

= 78.54 ft²

The size οf the circle is 79 square feet when the answer is rοunded tο the next whοle number.

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The area of the circle to the nearest whole number is 79 square feet.

What is the diameter?

In geometry, the diameter of a circle is defined as the longest straight line segment that can be drawn between any two points on the circle, passing through the center of the circle. It is twice the length of the radius of the circle.

The formula for the area of a circle is A = πr^2, where r is the radius of the circle.

Given that the diameter of the circle is 10 feet, we can find the radius by dividing the diameter by 2:

radius = diameter / 2 = 10 ft / 2 = 5 ft

Now we can use the formula to find the area of the circle:

A = πr^2

= π(5 ft)^2

= 25π square feet

To get the answer to the nearest whole number, we can use the approximation π ≈ 3.14:

A ≈ 25 × 3.14

≈ 78.5

Therefore, the area of the circle to the nearest whole number is 79 square feet.

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Answer:

--------------------------------

Given two points:

Find the slope of the line containing these points.

Slope equation:

Substitute coordinates and find the slope:

Answer:

-1/10

Step-by-step explanation:

To find:-

Answer:-

We are here given two points and we are interested in finding out the slope of the line passing through the points. Slope can be calculated by using;

[tex]:\implies \sf \boxed{\pink{\sf m =\dfrac{y_2-y_1}{x_2-x_1}}} \\[/tex]

where ,

Also , we can write the coordinate (-3,-7/2) as (-3,-3.5) .

So on substituting the respective values, we have;

[tex]:\implies \sf m =\dfrac{-3.5- (-4)}{-3-2} \\[/tex]

[tex]:\implies \sf m = \dfrac{-3.5+4}{-5} \\[/tex]

[tex]:\implies \sf m =\dfrac{0.5}{-5} \\[/tex]

[tex]:\implies \sf m = \dfrac{1}{2(-5)}\\[/tex]

[tex]:\implies \sf m =\dfrac{1}{-10} \\[/tex]

[tex]:\implies \sf \pink{ m =\dfrac{-1}{10}} \\[/tex]

Hence the slope of the line is -1/10 .

The integral of f(x) from a=-1 to b=4 is \(\frac{21}{64}\). The lower and upper limits of integration are the same, the integral is 0.

a) To evaluate the integral of \(f(x)=\frac{1}{x^4}\) from a=-1 to b=4, we need to first find the antiderivative of f(x). The antiderivative of \(\frac{1}{x^4}\) is \(-\frac{1}{3x^3}\). Now we can use the Fundamental Theorem of Calculus to evaluate the integral:

Integral [a=-1,b=4] f(x) dx = \(-\frac{1}{3(4)^3} - (-\frac{1}{3(-1)^3})\)

= \(-\frac{1}{192} + \frac{1}{3}\)

= \(\frac{63}{192}\)

= \(\frac{21}{64}\)

So the integral of f(x) from a=-1 to b=4 is \(\frac{21}{64}\).

b) The integral of f(x) from a=4 to b=4 is 0. This is because the integral of a function over an interval of length 0 is always 0. In other words, if the lower and upper limits of integration are the same, the integral is 0.

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Answer:

2

Step-by-step explanation:

Look at the picture.

<, > - dotted line

≤, ≥ - solid line

x > a, x ≥ a - to the right of a

x < a, x ≤ a - to the left of a

y > a, y ≥ a - up from a

y < a, y ≤ a - down from a