What is the solution of the inequality x^2-9x+18 less then or equal to zero? Graph solution.

Answer:

The graph is symmetric about the x-axis only

Step-by-step explanation:

* Lets study the limacon curve

- Equations of the form:

# r = a + b sin θ

# r = a – b sin θ

# r = a + b cos θ

# r = a – b cos θ  

All will produce limacons.    

* Lets examine what happens for various values of a and b.  

- When the value of a is less than the value of b, the graph is  

 a limacon with and inner loop.

- When the value of a is greater than the value of b, the graph is

 a dimpled limacon.

- When the value of a is greater than or equal to the value of 2b,  

 the graph is a convex limacon.

- When the value of a equals the value of b, the graph is a special  

 case of the limacon.  It is called a cardioid.

* Notice that, in each of the graphs of the liamcons, changing

 from sine to cosine does not affect the shape of the graph just its  

 orientation.  

- Equations using sine will be symmetric to the vertical axis  

- Equations using cosine are symmetric to the horizontal axis.  

∵ r = -2 + 3 cos Ф

- from the notes up the equation of cosine is symmetric to

 the horizontal axis

∴ The graph is symmetric about the x-axis only

Answer: [tex]128cm^2[/tex]

Step-by-step explanation:

You need to find the ratio of the area.

Knowing that the larger base of smaller trapezoid is 15 centimeters and the larger base of the larger trapezoid is 20 centimeters, you can find the ratio of the area:

[tex]r_{A}=(\frac{20cm}{15cm})^2\\\\r_{A}=\frac{16}{9}[/tex]

Then, to calculate the area of the larger trapezoid, you need to multiply the area of the smaller trapezoid by the ratio of the area.

Therefore you get that the area of the larger trapezoid is:

[tex]A_l=(r_{A})(A_s)\\\\A_l=(\frac{16}{9})(72cm^2)\\A_l=128cm^2[/tex]

Answer:

The sum of the first 53 terms of the sequence is 3286

Step-by-step explanation:

* Lets talk about the arithmetic sequence

- There is a constant difference between each two consecutive numbers

Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic Progression:

- U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

- Un = a + (n – 1)d, where a is the first term , d is the difference

  between each two consecutive terms and n is the position of

  the term in the sequence

* Sum of an Arithmetic Progression:

  is calculate from  Sn = n/2[2a + (n - 1)d]

* Lets solve the problem

- The sequence is 140 , 137 , 134 , 131 , .........

∵ 137 - 140 = -3 and 134 - 137 = -3

∴ The sequence is arithmetic

- The first term a = 140

- The common difference d = -3

- n = 53

∵ Sn = n/2[2a + (n - 1)d]

∴ S53 = 53/2[2 × 140 + (53 - 1)(-3)]

∴ S53 = 53/2[280 + 52(-3) = 53/2[280 + -156] = 53/2[124]

∴ S53 = 3286

* The sum of the first 53 terms of the sequence is 3286

Answer:

S =3,286

Step-by-step explanation:

We are given the following sequence and we are to find the sum of the first 53 terms of this sequence:

[tex]140, 137, 134, 131, ...[/tex]

Finding the common difference [tex]d[/tex] = [tex]137-140[/tex] = [tex]-3[/tex]

[tex]a_1=140[/tex]

[tex]a_n=?[/tex]

[tex]a_n=a_1+(n-1)d[/tex]

[tex] a_n = 140 + (53 - 1 ) -3 [/tex]

[tex] a _ n = -16 [/tex]

Finding the sum using the formula [tex]S_n = \frac{n}{2}(a_1+a_n)[/tex].

[tex]S_n = \frac{53}{2}(140+(-16))[/tex]

S = 3,286

Answer:

  12 cents

Step-by-step explanation:

(200 yd)·(3 ft/yd)·(0.02 ¢/ft) = 12 ¢

Answer: It is shopping around for the best prices and saves money.

Step-by-step explanation: Bargain has the word "gain" in it. That's the best way I would look at it. Therefor I would cross out any other option that has to do with no benefit or the loss of something. Because we you bargain, you're getting multiple of something for a good price or maybe getting something that's on sale for a good price. For example: Buy 1 get 1 free items.

Answer:

Angle 8.

Step-by-step explanation:

It is equal to angle 8. These are called vertical angles in the States and opposite angles in the UK.

∠2 is equal to ∠8.

We need to find ∠2 is to which angle in the given figure.

Vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines. Vertically opposite angles are equal to each other.

Here the vertically opposite angles are as follows:

∠2=∠8, ∠1=∠7, ∠3=∠5 and ∠6=∠4.

Therefore, ∠2 is equal to ∠8.

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about 19 percent (~19%)

Answer:

50%

Step-by-step explanation:

Answer:

x = [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Using the rules of logarithms

• log[tex]x^{n}[/tex] ⇔ n logx

• logx - logy = log([tex]\frac{x}{y}[/tex])

• logx = logy ⇔ x = y

Given

2log2 - 3log2 = log2x

log2² - log2³ = log2x

log4 - log8 = log2x

log[tex]\frac{4}{8}[/tex] = log2x, hence

2x = [tex]\frac{1}{2}[/tex]

x = [tex]\frac{1}{4}[/tex]

The answer is -- 29,524

Answer:

29,524

Step-by-step explanation:

This is a geometric sequence; notice how each new term is 3 times the previous term.  Thus, a(n) = 1 · 3^(n-1).  The 10th term is a(10) = 3^(9) = 19683.

a(4) = 27 (given)

a(5) = 81 (calculated)

a(6) = 243

a(7) = 729

a(8) = 2107

a(9) = 6561

a(10) = 19683 (previously calculated)

So the sum of the first 10 terms is 29,524.

1 + 3 + 9 + 27 + 81 + ... + 6561 + 19683 =

Answer:  B) 3 out of 20

Step-by-step explanation:

[tex]\text{3 out of 30: }\dfrac{3}{30}=10\%\\\\\text{3 out of 20: }\dfrac{3}{20}=15\%\\\\\text{3 out of 15: }\dfrac{3}{15}=20\%\\\\\text{3 out of 12: }\dfrac{3}{12}=25\%[/tex]

The only option that results in 15% rotten apples is (B) 3 out of 20

Answer:

B. E. D. A. C

Step-by-step explanation:

The correct order of steps to determine the significance of results is:

B) Randomly separate the employees’ individual results into two groups.

E) Calculate the mean of each group.

D )Calculate the difference of the means.

A) Run the experiment many times.

C) Calculate the probability of a difference of 10.

Answer:

option c

amplitude 1 ; period 2π/3

Step-by-step explanation:

Given in the question a function,

f(t)=-cos3t

Standard form of cosine function is

f(t)=acos(bt)

Amplitude is given by = |a|

Period of function is given by = 2π/b

So the amplitude is |-1| = 1

    the period is 2π/3 = 2π/3

Answer:

c. The amplitude is 1.

The period is [tex]\frac{2\pi}{3}[/tex]

Step-by-step explanation:

The given cosine function is ;

[tex]f(t)=-\cos 3t[/tex]

This function is of the form;

[tex]f(t)=a\cos bt[/tex]

The amplitude is given by |a|

|-1|=1

The period of this function is given by;

[tex]T=\frac{2\pi}{|b|}[/tex]

[tex]T=\frac{2\pi}{|3|}=\frac{2\pi}{3}[/tex]

The amplitude is 1.

The period is [tex]\frac{2\pi}{3}[/tex]

Answer:

two solutions x = 1 and x = - 8/3 x

Step-by-step explanation:

These are two questions and two answers:

Question 1:

A quadratic equation is shown below: 3x^2 − 15x + 20 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work.

Answer: The negative value of the radicand means that the equation does not have real solutions.

Explanation:

1) With radicand the statement means the disciminant of the quadratic function.

2) The discriminant is: b² - 4ac, where a, b, and c are the coefficients of the quadratic equation: ax² + bx + c

3) Then, for 3x² - 15x + 20, a = 3, b = - 15, and c = 20

and the discriminant (radicand) is: (-15)² - 4(3)(20) = 225 - 240 = - 15.

4) The negative value of the radicand means that the equation does not have real solutions.

Question 2:

Part B: Solve 3x^2 + 5x − 8 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used.

Answer: two solutions x = 1 and x = - 8/3x

Explanation:

1) I choose factoring (you may use the quadratic formula if you prefer)

2) Factoring

Given: 3x² + 5x − 8 = 0

Make 5x = 8x - 3x: 3x² + 8x - 3x - 8 = 0

Group: (3x² - 3x) + (8x - 8) = 0

Common factors for each group: 3x(x -1) + 8(x - 1) = 0

Coomon factor x - 1: (x - 1) (3x + 8) = 0

The two solutions are for each factor equal to zero:

x - 1 = 0 ⇒ x = 1

3x + 8 = 0 ⇒ x = -8/3

Those are the two solutions. x = 1 and x = - 8/3

Answer:

the answer is 21

Step-by-step explanation:

its 21 because 10+11=21

Answer:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

y = tan(2x - π)

y = tan (2*(x-π/2))

We can compare it to its parent function

g(x) = tan(x)

The answer is

Option a.

Horizontal shrink by 1/2 and horizontal shift of π/2 to the right

Answer:

Step-by-step explanation:

The answer is D. I just did it.

Answer:

Option D.

Step-by-step explanation:

We have to solve the trigonometric expression give below.

[tex]tan(x+\frac{\pi }{3})[/tex]

[tex]=\frac{tanx+tan\frac{\pi }{3}}{1-tanx.tan\frac{\pi }{3}}[/tex]

[Since [tex]tan(a+b)=\frac{tana+tanb}{1-tana.tanb}[/tex]]

Now we place the value of [tex]tan\frac{\pi }{3}=\sqrt{3}[/tex]

[tex]=\frac{tanx+\sqrt{3}}{1-tanx\sqrt{3}}[/tex]

Therefore, option D. is the answer.

The probability that the die will land with a value less than 3 and on a red square, given an equal number of black and red squares, is 1/6.

The subject of this question is probability, a branch of Mathematics. In the given scenario, Gabrielle is tossing a die onto a black-and-red checkerboard. There are two separate events here - the roll of the die and the colour of the square where the die lands.

Firstly, the probability that the die will land with a value less than 3 is 2/6, or 1/3, as there are two sides of a six-sided die that have values less than 3 (1 and 2).

Secondly, assuming the checkerboard has an equal number of red and black squares, the probability that the die will land on a red square is 1/2.

Since these are separate events, we can calculate the combined probability by multiplying the probabilities of the individual events: (1/3) * (1/2) = 1/6. So, the answer is 1/6.

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Answer:

[tex]9.42\ ft^{2}[/tex]

Step-by-step explanation:

step 1

Find the surface area of one hanging lantern

we know that

The surface area of a cone (hanging lantern) is equal to

[tex]SA=\pi r^{2} +\pi rl[/tex]

we have

[tex]r=0.5\ ft[/tex]

[tex]l=1.5\ ft[/tex]

assume

[tex]\pi=3.14[/tex]

substitute the values

[tex]SA=(3.14)(0.5)^{2} +(3.14)(0.5)(1.5)[/tex]

[tex]SA=3.14\ ft^{2}[/tex]

step 2

Find the surface area of the three hanging lanterns

[tex]SA=(3)*3.14=9.42\ ft^{2}[/tex]

Answer:

9.42

Step-by-step explanation:

Answer:

2. distributive property

4. addition property of equality

5. addition property of equality

Hope this helps! :)

Answer:

a

Step-by-step explanation:

The volume of a cube with a side length of 1 foot is 1 cubic foot, or 1728 cubic inches. So, 1 cubic foot is equal to 1728 cubic inches. The ratios of 1 cubic inch to 1/1728 cubic foot and 1 cubic foot to 1728 cubic inches can be used to convert between cubic inches and cubic feet.

When dealing with volumes, it's crucial to understand the relationship between cubic feet and cubic inches. Since 1 foot is equivalent to 12 inches, 1 cubic foot contains 12 × 12 × 12 = 1728 cubic inches. This conversion factor arises because volume is a measure of three-dimensional space, so each dimension is multiplied by itself three times.

To convert between cubic feet and cubic inches, you can use the conversion factor: 1 cubic foot = 1728 cubic inches. This means that to convert cubic feet to cubic inches, you multiply the volume in cubic feet by 1728, and to convert cubic inches to cubic feet, you divide the volume in cubic inches by 1728.

Understanding this relationship allows for easy conversion between the two units, whether you're dealing with measurements in feet or inches.

The probable question may be:

The volume of a cube with a side length of 1 foot is __ cubic foot, or __ cubic inches. So, 1 cubic foot is equal to __ cubic inches. The ratios of __ cubic inches to __ cublc foot and __ cubic foot to __ cubic inches can be used to convert between cubic inches and cubic feet.

The compass was used to make the crossing arcs at point E and point B is labeled, so the next step would be :

A. Use a straight edge to draw a line through points B and E.

Option: A is the correct answer.

A.   Use a straightedge to draw a line through points B and E.

Perpendicular bisector--

It is a line that is perpendicular to the given line and the point where it intersects the given line segment is the mid-point of the line i.e. the perpendicular line bisects the line segment into  two equal parts.

Answer:

Choice C: approximately 121 green beans will be 13 centimeters or shorter.

Step-by-step explanation:

What's the probability that a green bean from this sale is shorter than 13 centimeters?

Let the length of a green bean be [tex]X[/tex] centimeters.

[tex]X[/tex] follows a normal distribution with

In other words,

[tex]X\sim \text{N}(11.2, 2.1^{2})[/tex],

and the probability in question is [tex]X \le 13[/tex].

Z-score table approach:

Find the z-score of this measurement:

[tex]\displaystyle z= \frac{x-\mu}{\sigma} = \frac{13-11.2}{2.1} = 0.857143[/tex]. Closest to 0.86.

Look up the z-score in a table. Keep in mind that entries on a typical z-score table gives the probability of the left tail, which is the chance that [tex]Z[/tex] will be less than or equal to the z-score in question. (In case the question is asking for the probability that [tex]Z[/tex] is greater than the z-score, subtract the value from table from 1.)

[tex]P(X\le 13) = P(Z \le 0.857143) \approx 0.8051[/tex].

"Technology" Approach

Depending on the manufacturer, the steps generally include:

For example, on a Texas Instruments TI-84, evaluating [tex]\text{normalcdf})(-1\text{E}99,\;13,\;11.2,\;2.1 )[/tex] gives [tex]0.804317[/tex].

As a result,

[tex]P(X\le 13) = 0.804317[/tex].

Number of green beans that are shorter than 13 centimeters:

Assume that the length of green beans for sale are independent of each other. The probability that each green bean is shorter than 13 centimeters is constant. As a result, the number of green beans out of 150 that are shorter than 13 centimeters follow a binomial distribution.

Let [tex]Y[/tex] be the number of green beans out of this 150 that are shorter than 13 centimeters. [tex]Y\sim\text{B}(150,0.804317)[/tex].

The expected value of a binomial random variable is the product of the number of trials and the probability of success on each trial. In other words,

[tex]E(Y) = n\cdot p = 150 \times 0.804317 = 120.648\approx 121[/tex]

The expected number of green beans out of this 150 that are shorter than 13 centimeters will thus be approximately 121.

Answer:

according to the equation it is 158.330917...

Step-by-step explanation:

put w as 64 and solve for t

Answer: 158.331 minutes.

Step-by-step explanation: To solve this problem we need to replace the given level of water (64 cups) in the equation, and isolate and calculate the time (t):

W=-0.414t+129.549

isolating t:

W-129.549=-0.414t

t=(W-129.549)/-0.414

replacing W=64

t=(64-129.549)/-0.414

t=-65.549/-0.414

t=158.331 minutes.

Answer:

It is A.

Step-by-step explanation:

In function A we see that there are 2 ordered pairs with value 2 in the first position with y values 6 and 2. So this is not a function.

A function is a relation in which each input pairs with exactly one output. In the given relations, option A is not a function because the input 2 pairs with both 6 and 2, contradicting the definition of a function.

In mathematics, a function is a relation in which every input, also known as the domain, corresponds to exactly one output, called the range. Looking at the following relations, we determine if a relation is not a function by seeing if any input values are paired with more than one output.

Option A: {(2, 6), (- 4, 0), (2, 2), (3, 5)} is NOT a function because the input 2 corresponds to both 6 and 2, which violates the definition of a function.

Options B, C, and D each pair every input with exactly one output, thus they are all functions. In conclusion, the relation provided in option A is the only one that is not a function.

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Answer:

B. cylinder

Step-by-step explanation:

Answer:

Option D) multiply y by 4 in the first equation and subtract the second equation

Step-by-step explanation:

we have

2x+y=-10 ----> first equation

3x+4y=-20 ---> second equation

Verify each case

case A) multiply the first equation by 4 and subtract the second equation

so

(2x+y)*4=-10*4 ------> 8x+4y=-40

[8x+4y=-40]-[3x+4y=-20] -----> 5x=-20 -----> x=-4

This step is correct

case B) multiply the first equation by -4 and add the second equation

so

(2x+y)*-4=-10*-4 ------> -8x-4y=40

[-8x-4y=40]+[3x+4y=-20] ----->-5x=20 -----> x=-4

This step is correct

case C)  add 8 times the first equation and −2 times the second equation

so

(2x+y)*8=-10*8 ------> 16x+8y=-80

(3x+4y)*-2=-20*-2 ----> -6x-8y=40

[16x+8y=-80]+[-6x-8y=40] ----->10x=-40 -----> x=-4

This step is correct

case D) multiply y by 4 in the first equation and subtract the second equation

so

2x+4y=-10

[2x+4y=-10]-[3x+4y=-20] -----> -x=-10+20 -----> x=-10

This step is incorrect

NOT produce a system with the same solution

Answer:

$129.04

Step-by-step explanation:

Gross pay:  $815.70

The following will be deducted as

 (0.062 · $815.70 + 0.0145 · $815.70 + 0.19 · $56  +  $56,  or:

         $50.57         +         11. 83            +     $10.64 + $56, or

$129.04

His pay will be reduced by $129.04.

Next time, please share ALL of the possible answer choices.  Thx.

The amount that Chuck's gross pay will reduce by as a result of the items withheld is d. 273.38

The items withheld from Chuck's pay are:

= Federal tax + Social security tax + Medicare tax + State tax

Solving gives:

= 56 + (6.2% x 815.70) + (1.45% x 815.70) + (19% x 815.70)

= 56 + 50.57 + 11.83 + 154.98

= $273.38

In conclusion, the total reduction will be $273.38

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Answer:

144 (Answer B)

Step-by-step explanation:

We must do exponentiation first.  Next comes multiplication and division.  Last comes addition and subtraction.

the proper evaluation (not solution)  of  100 ÷ 5 × 4 + 4³ is as follows:

Evaluate 4³ first; it is 64.

Next, do the division:  20 · 4 + 64 = 80 + 64 = 144 (Answer B)

Answer:

15 yards

Step-by-step explanation:

1 balloon = 2.5 feet

18 balloons = 2.5 x 18 = 45 feet

1 yard = 3 feet

[tex]\frac{3 feet}{1 yard}=\frac{45 feet}{x yard}[/tex]

45 = 3x

x = 15 yards