.....................

cos^-1(x) represents the inverse of cos(x).

The equivalent equation is (4x² + 9)(4x² - 9) and the zero's are x =± 3 / 2 and x = ± 3 / 2i

The equivalent equation can be found by factoring. Factoring of a polynomial is the method of breaking the polynomial into a product of its factors.

Therefore,

f(x) = 16x⁴ - 81 = 0

Hence,

9 × 9 = 81

4x² × 4x² = 16x⁴

Therefore,

16x⁴ - 81  = (4x² + 9)(4x² - 9)

Hence,

The zeros of a function, also referred to as roots or x-intercepts, occur at x-values where the value of the function is 0 (f(x) = 0).

The zero's of the function are as follows:

4x²  = 9

x² = 9 / 4

x =± 3 / 2

4x² = -9

x² = - 9 / 4

x =√-9 / 2

x = ± 3 / 2i

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The equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².

Based on the calculations, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5²

The equation of a circle.

Mathematically, the standard form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

Where:

h and k represent the coordinates at the center.

r is the radius of a circle.

The midpoint of the given points represents the center of this circle:

h = (4 + 4)/2 = 4

k = (5.5 + 10.5)/2 = 8

Next, we would determine the radius by using the distance formula for coordinates:

r = √[(x₂ - x₁)² + (y₂ - y₁)²]

r = √[(4 - 4)² + (10.5 - 5.5)²]

r = √[0² + 5²]

r = √25

r = 5 units.

Therefore, the equation of this circle in standard form is equal to (x - 4)² + (y - 8)² = 5².

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Answer:

17) 3

18) -5/4

19) 4/2 or 2

20) 1

21) 2/4 or 1/2

22) 4/7

23) -2/2 or -1

24) -1/3

Step-by-step explanation:

the easiest thing to do is go by rise over run and count the number of units, hope this helped!

[tex]\frac{7}{30}[/tex] units of time is left.

To find how much time is left:

Given - Tony is given [tex]\frac{9}{10}[/tex] hour to mow a lawn. he only uses [tex]\frac{2}{3}[/tex]  the given time to mow the lawn.

Simplify subtract   [tex]\frac{9}{10}[/tex]  by  [tex]\frac{2}{3}[/tex]  as follows:

[tex]\frac{9}{10}-\frac{2}{3} =\frac{27-20}{30} =\frac{7}{30}[/tex]

Therefore, [tex]\frac{7}{30}[/tex] units of time is left.

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The profit he would make in one week is  $30.

Profit is the total revenue less total cost.

Total revenue = price of one hot dog x number of hotdogs sold

$10.25 x 100 = $1025

Total cost = 950 +( 0.45 x 100)

950 + 45 = 995

Profit = 1025 - 995 = $30

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Answer:

The file contains the solution to the above question

Answer:

  ₹168 per hour

Step-by-step explanation:

The hourly rate at which Tamara is paid can be found by dividing her ₹1050 pay by the 6:15 hours that she worked.

We know there are 60 minutes in an hour, so the fraction of an hour represented by 15 minutes is ...

  (15 min)/(60 min/h) = (15/60) h = 1/4 h = 0.25 h

Added to the 6 whole hours Tamara worked, her pay is for 6.25 hours.

The pay per hour is found by dividing pay by hours.

  ₹1050/(6.25 h) = ₹168/h

Tamara's hourly rate of pay is ₹168 per hour.

Answer:

See below.

Step-by-step explanation:

The $2 charge is independent of the miles driven.  It cost $2 regardless of mileage.  The $0.20.half mile is the dependent variable.  The cost changes as a function of 1/2 miles driven.

The number of unique combinations that can be formed by picking one object from each set is =960. That is option C.

Number combination is a mathematical technique that shows the number of possible arrangements in a collection of items.

The first set of objects = 4. There are a total of 4 possibilities.

The second set of objects = 5. There are a total of 5 possibilities

Therefore from first and second set, the total number of possibilities = 4×5 = 20

For the whole set, the total possibilities;

= 4×5×6×8

= 960

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Answer: Yes

Step-by-step explanation:

Since ABCD is a rectangle, [tex]\angle AXY[/tex], [tex]\angle YBZ[/tex], [tex]\angle WCZ[/tex], and [tex]\angle WDX[/tex] are all right angles, and are thus all congruent because all right angles are congruent. Furthermore, because ABCD is a rectangle, we know that [tex]\overline{AB} \cong \overline{CD}[/tex] and [tex]\overline{AD} \cong \overline{BC}[/tex]. Because we are given that X, Y, Z, and W are midpoints, using the fact that halves of congruent segments are congruent, we can conclude that [tex]\overline{AY} \cong \overline{YB} \cong \overline{CW} \cong \overline{WD}[/tex] and that [tex]\overline{AX} \cong \overline{XD} \cong \overline{BZ} \cong \overline{ZC}[/tex]. As a result, we can conclude that [tex]\triangle AYX \cong \triangle DXW \cong \triangle CWZ \cong \triangle BYZ[/tex] by SAS, and thus by CPCTC, [tex]\overline{AY} \cong \overline{XW} \cong \overline{ZW} \cong \overline{YZ}[/tex]. Therefore, since the quadrilateral formed by the midpoints has four congruent sides, it must be a rhombus.

The median of an equilateral triangle are equal has been proved.

The medians are given as AD, BE, and CF.

Let AB = AC = BC = x unit.

In triangles, BFC and CEB, we've

BF = CE.

ABC = ACB since they're both 60°

BC = BC

By SAS congruence,

BFC = CEB = BE = CF.

Similarly, we've AB = BE

Therefore, AD = BE = CF

median of an equilateral triangle are equal has been proved.

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There are 404 numbers between 1 and 2020 inclusive that can be the side of the hypotenuse given that three sides of the right triangle have integral lengths which form an arithmetic sequence. This can be obtained by forming the arithmetic sequence, equating by Pythagoras theorem and finding numbers divisible by the integral.

Let the arithmetic sequence be (a - d), a, (a+d)

Using Pythagoras theorem,

(a - d)² + a² = (a+d)²

a² -2ad + d² + a² = a² + 2ad + d²

2a² - 2ad + d² = a² + 2ad + d²

2a² - a² + d² - d² = 2ad + 2ad

a² = 4ad

a = 4d

Thus hypotenuse will be (a + d) = 4d + d = 5d

Since the value of hypotenuse is 5d, the total numbers divisible by 5 between 1 and 2020 will be the number of possible sides of the hypotenuse.

There are 2020 numbers between 1 and 2020 inclusive

The numbers divisible by 5 = 2020/5 = 404

Hence there are 404 numbers between 1 and 2020 inclusive that can be the side of the hypotenuse given that three sides of the right triangle have integral lengths which form an arithmetic sequence.

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Answer:

y<x

Step-by-step explanation:

Alright so you do know that the y=x has got the equal amount for both y and x right and it also is a bisector for the first and third area, that's that

the graph is show the same thing but with some blue area and the area show x values which less than y values sooo you answer is y<x

Answer:

Use the slope and one of the points to solve for the y-intercept (b). One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.

Step-by-step explanation:

Answer:

27 cm³

Step-by-step explanation:

To find the volume, multiply the length, the width, and the depth together.

3*3*3=27

The volume of the cube is 27 cm³

Hope this helps!

Answer:

Step-by-step explanation:

Our equation will be 3x+8=20.6

3x=12.6

x=4.2

Answer:

[tex]-\frac{345}{37}[/tex]

Step-by-step explanation:

Just follow the order of operations

210÷[5+16÷2{6−18÷(7+2)}]−15  

= 210÷[5+16÷2{6−18÷9}]−15   (calculate 7+2)

= 210÷[5+16÷2{6−2}]−15 (calculate 18÷9)

= 210÷[5+16÷2{4}]−15  (calculate 6-4)

= 210÷[5+16÷2×4]−15

= 210÷[5+8×4]−15  (calculate 16÷2)

= 210÷[5+32]−15  (calculate 8×4)

= 210÷[37]−15  (calculate 5+32)

= 210÷37−15

= 210÷37−(15×37)÷37  (put on the same denominator)

= 210÷37−555÷37  (calculate 15×37)

= (210−555)÷37

=-345÷37   (calculate 210-555)

If the test gives positive results for 95% of those having disease and correctly gives negative results for 90% of those who don't have disease and the incidence of the disease is 1% then the chance of having disease is 0.0105.

Given that a test for a disease correctly gives positive results for 95% of those having the disease and correctly gives negative results for 90% of those who don't have the disease.

We have to calculate the chance of having disease.

Probability that test is correct in determining the disease when person is suffering from it is 0.95.

Probability that test is not correct in determining the disease when person is suffering from it is 1-0.95=0.05.

Probability that test is correct in determining that the person is not suffering from disease  when person is not suffering from it is 0.90.

Probability that test is not correct in determining that the person is not suffering from disease  when person is not suffering from it is 1-0.9=0.10.

The chance of having disease is equal to incidence of disease multiplied by probabilities that the test has corectly determined disease when personis suffering from it and when test is not able to determine the disease when person is suffering from it.

Chance=0.01*0.95+0.01*0.10

=0.0095+0.001

=0.0105.

Hence the chance of having disease is 0.0105.

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The answer is 8300.

Divide 91300 by 11 you will get the answer.

Problem-solving is the act of defining trouble; figuring out the cause of the problem; figuring out, prioritizing, and choosing alternatives for an answer; and enforcing a solution.

Problem-fixing starts with identifying the difficulty. For instance, a teacher might want to discern the way to improve student performance on a writing talent test. To do that, the trainer will assess the writing checks looking for areas of development.

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The number from the grid that fulfills all the given clues is; 12

The grid is shown in the attached image.

Now, we are told that Manju and Arif are thinking of a number on the grid and the clues are;

It is a multiple of 3.

It is even.

It is in the third row.

Now, looking at the third row, we see the numbers as;

11, 12, 13, 14, 15

Now, the only number that fulfills all the given clues is 12.

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The calculated probabilities are

Probability = 60/110

= 0.5455

probability = 65/110

= 0.5909

Probability = 30/65

= 0.4615

25/45

= 0.5556

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The function g(x) is a translation of 3 units to the right and a vertical dilation by scale factor k = 2 of f(x), the graphs of both functions can be seen in the image at the end.

We know that g(x) is a transformation of the parent function f(x) = √x, such that:

g(x) = 2*f(x - 3)

g(x) = 2*√(x - 3)

Then we can see that g(x) is a translation of 3 units to the right followed by a vertical dilation of scale factor 2 of the parent function f(x).

So to graph g(x) you first need to move the whole graph of f(x) 3 units to the right, and then apply a dilation vertically.

The graph of g(x) and f(x) can be seen in the image below:

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The Ratio would be 43:100.

Lets simplify the problem,

Expected increase of nurses = 711900

Expected increase of physicians = 168300

Ratio = Expected increase of nurses / Expected increase of physicians

Ratio = 711900 / 168300

= 43/100

Ratio = 43:100

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The amplitude is 6 and vertical translation is 2. Therefore Option C is correct

For the transformation of y=f(x) to f(x)+k, for k>0, f(x) is moved k upwards and for transformation of f(x) to f(ax) it depends upon the value of a If |a|>1 then f(ax) is f(x) squashed horizontally by a factor of a and If 0<|a|<1 then f(x) is stretched horizontally by a factor of a.

So by the graph it is clearly visible that amplitude of the graph is 6 as the distance from the centre line (or the still position) to the top of a crest or to the bottom of a trough is 6 and the vertical translation is 2 as distance moved by the graph upwards is 2.

Thus the amplitude is 6 and vertical translation is 2.

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Answer:

500x - 300xp.

Step-by-step explanation:

100x(5 - 3p)

First distribute the 100x over the parentheses:

= 100x*5 - 100x * 3p

Now simplify:

= 500x - 300xp.

Answer:

875

Step-by-step explanation:

1-0.32=0.68 so its 0.68 of its original price.

x*0.68=595 x is the original price

x=595/0.68

x=875

Answer:

================

The exponential growth function has:

When the function is reflected across the y-axis, we'll have no change to domain or range from what is described above.

Alissa is correct, the input values change to opposite, however the domain stays same - all real numbers.

It means Simon is correct with his statement.

The matching answer choice is C.

Answer:

Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input.

Step-by-step explanation:

Exponential Function

General form of an exponential function:  [tex]f(x)=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Reflection in the y-axis

[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]

As the exponential function is a growth function, b > 1.

If the exponential growth function has been reflected in the y-axis, the x variable is negative:

[tex]\implies f(x)=ab^{-x}[/tex]

Regardless whether the initial value [tex]a[/tex] (y-intercept) is positive or negative, the domain of an exponential function is (-∞, ∞) so it is unrestricted.

Therefore, if the function is reflected across the y-axis, the output value for each input value will change, but the domain itself will not change and will still be all real numbers.

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Answer:

(-4,-4)

Step-by-step explanation:

If the point is moved 2 units to the rights then we add 2 to the x value: -6+2 = -4

(-4,-4)

For an exponential function  [tex]f(x) = 3^{-x}2[/tex] as x goes to infinity, f(x) goes to zero.

We have been given an exponential function [tex]f(x) = 3^{-x}2[/tex]

We need to check the end behavior of f(x) as x goes to infinity.

Consider,

[tex]\lim_{x \to \infty} f(x)\\\\= \lim_{x \to \infty} 3^{-x}2\\\\=2\times \lim_{x \to \infty} 3^{-x}\\\\=2\times 3^{-\infty}\\\\=2\times 0\\\\=0[/tex]

This means, x [tex]\rightarrow[/tex] infinity, f(x) goes to 0

As x goes to infinity, f(x) goes to zero.

Therefore, for an exponential function  [tex]f(x) = 3^{-x}2[/tex] as x goes to infinity, f(x) goes to zero.

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