Write the equation for a circle centered at the origin with x-intercepts of (-9,0) and (9,0).use ^2 for squared, ^3 for cubed,

Answer:

x^2-3/3x

Step-by-step explanation:

=x*x-1*3/3*x

=x^2-3/3x

a. The rocket splashes down after 63.94 seconds.

b. The rocket peaks at 7386.68 m

Since the height of the rocket is h(t) = -4.9t² + 370t + 402, the rocket splashes down when h(t) = 0.

So, h(t) = 0

-4.9t² + 370t + 402 = 0

Using the quadratic formula, we find t.

[tex]t = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]

where a = -4.9, b = 370 and c = 402

So, [tex]t = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}\\= \frac{-307 +/- \sqrt{(307)^{2} - 4(-4.9)(402)} }{2(-4.9)}\\= \frac{-307 +/- \sqrt{94249 + 7879.2} }{-9.8)}\\= \frac{-307 +/- \sqrt{102128.2} }{-9.8)}\\= \frac{-307 +/- 319.58}{-9.8)}\\= \frac{-307 + 319.58}{-9.8)} or \frac{-307 - 319.58}{-9.8)}\\= \frac{12.58}{-9.8)} or \frac{-626.58}{-9.8}\\= -1.28 or 63.94[/tex]

Since t cannot be negative t = 63.94 s

So, the rocket splashes down after 63.94 seconds.

Since h(t) = -4.9t² + 370t + 402, to find the time the rocket reaches it peak, we differentiate h(t) with respect to t and equate to zero.

Soi, dh(t)/dt = d(-4.9t² + 370t + 402)/dt

= -9.8t + 370

dh(t)/dt = 0

-9.8t + 370 = 0

-9.8t = -370

t = -370/-9.8

t = 37.76 s

Substitung t = 37.76 into h(t), we have

h(t) = -4.9t² + 370t + 402

h(37.76) = -4.9(37.76)² + 370(37.76) + 402

h(37.76) = -4.9(1425.82) + 370(37.76) + 402

h(37.76) = -6986.518 + 13971.2 + 402

h(37.76) = 7386.682 m

h(37.76) ≅ 7386.68 m

So, the rocket peaks at 7386.68 m

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Answer:100

Step-by-step explanation: The question asks us to round the given numbers to the nearest hundred. 295 rounded to the nearest hundred is 300 and 198 rounded to the nearest hundred is 200. 300-200 is 100, so they need to sell 100 more tickets for the show to be houseful.

The form of deductive reasoning used in the given argument is; Law of Syllogism

The argument we are given is;

If a number ends in 0, then it is divisible by 10.

If a number is divisible by 10, then it is divisible by 5.

If a number ends in 0, then it is divisible by 5.

The law used for the deductive reasoning in the given argument is called Law of Syllogism. This is because this law of mathematical logic states that;

If the following two statements are true:

(1) If p , then q .

(2) If q , then r .

Then we can derive a third true statement:

(3) If p , then r .

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Measures of central tendency are called such because they all find approximately the same "center" of a data set (option B).

A measure of central tendency attempts to describe a data set by determining the central value of the data set. Measures of central tendency are mean, median and mode

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number.

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order.

Mode refers to a value that appears most frequently in a data set.

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The lowest grade he could earn is 120% of the grade at the end of the semester.

The following statement is given:

I have 90% after about 75% of the semester.

We are asked to find the lowest grade by the end of this semester.

A percentage is a number expressed as a fraction of 100.

- 50% = 50/100 = 1/2

- 25% = 25/100 = 1/4

- 20% = 20/100 = 1/5.

We can write this statement "I have a 90% grade after about 75% of the semester" as:

90% grade  =  75% semester.............(1)

By the end of the semester means at 100% semester.

Multiplying equation (1) by 100/ 75 on both sides of the equation.

We get,

(100/75) x 90% grade = (100/75) x 75% semester

(100 x 90)/75 % grade = 100% semester

120% grade = 100%

Thus the lowest grade he could earn is 120% of the grade at the end of the semester.

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The measure of angle < APD = 98°. That is option D

Angle APB = 62°

Angle DPC = 102°

But length AD = BC

Therefore, angle APD = BPC

Also, the angle at a point = 360°

The sum of the angles given = 102 + 62 = 164°

The remaining angle = 360 - 164 = 196°

Therefore angle APD = 196/2 = 98°

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Recall the Pythagorean identity,

[tex]\sin^2(x) + \cos^2(x) = 1[/tex]

Use it to rewrite the equation in terms of cos only.

[tex]12 (1 - \cos^2(x)) + \cos(x) - 6 = 0[/tex]

[tex]-12 \cos^2(x) + \cos(x) + 6 = 0[/tex]

Factorize the left side.

[tex]-(3\cos(x) + 2) (4\cos(x) - 3) = 0[/tex]

Solve the two cases for [tex]\cos(x)[/tex].

[tex]3 \cos(x) + 2 = 0 \text{ or } 4\cos(x) - 3 = 0[/tex]

[tex]\cos(x) = -\dfrac23 \text{ or } \cos(x) = \dfrac34[/tex]

From the first equation, we get one family of solutions:

[tex]\cos(x) = -\dfrac23[/tex]

[tex]x = \cos^{-1}\left(-\dfrac23\right) + 2n\pi \text{ or } x = -\cos^{-1}\left(-\dfrac23\right) + 2n\pi[/tex]

From the second equation, we get another family:

[tex]\cos(x) = \dfrac34[/tex]

[tex]x = \cos^{-1}\left(\dfrac34\right) + 2n\pi \text{ or } x = -\cos^{-1}\left(\dfrac34\right) + 2n\pi[/tex]

where [tex]n[/tex] is an integer.

We get solutions in the given domain for

[tex]n = 0 \implies \boxed{x = \cos^{-1}\left(-\dfrac23\right)} \text{ or } \boxed{x = \cos^{-1}\left(\dfrac34\right)}[/tex]

[tex]n=1 \implies \boxed{x = 2\pi - \cos^{-1}\left(-\dfrac23\right)} \text{ or } \boxed{x = 2\pi - \cos^{-1}\left(\dfrac34\right)}[/tex]

Apply the exponent rule (x^a)^b= x^ab.

(b^9)^3= b^9*3= b^27

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

A mean is also referred to as an arithmetic average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the distance between the means of both classes A and B is given by:

Distance = Mean of class A - Mean of class B

Distance = 12 - 4

Distance = 8.

The mean absolute deviation (MAD) for class A is given by:

MAD A = 1/9[2(9 - 12) + (10 - 12) + (11 - 12) + (12 - 12) + (13 - 12) + (14 - 12) + 2(15 - 12)]

MAD A = 1/9[2(3) + (2) + (1) + 0 + (1) + (2) + (1) + 2(3)]

MAD A = 1/9[6 + 2 + 1 + 1 + 2 + 1 + 6]

MAD A = 1/9 × [18]

MAD A = 18/9

MAD A = 2.

Also, the mean absolute deviation (MAD) for class B is given by:

MAD B = 1/9[2(1 - 4) + (2 - 4) + (3 - 4) + (4 - 4) + (5 - 4) + (6 - 4) + 2(7 - 4)]

MAD B = 1/9[2(3) + 2(2) + (1) + (0) + (1) + (2) + 2(3)]

MAD B = 1/9[6 + 4 + 1 + 0 + 1 + 2 + 6]

MAD B = 1/9 × [18]

MAD B = 18/9

MAD B = 2.

Therefore, distance between the means = four (4) times the MAD.

Distance = Means × MAD

8 = 4 × 2.

In conclusion, we can infer and logically deduce that there is no overlap and the distance between the means of both players A and B is between one (1) times the MAD and five (5) times the MAD.

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By algebraic handling, the value of k of the system of equations is equal to 2.

Herein we find a system formed by two equations, a linear function and a quadratic equation with the following characteristics:

y = x² + b · x + 5        (1)

y = 2 · x + b               (2)

If we eliminate y in (1) and (2), then we have this expression:

x² + b · 3 + 5  = 2 · x + b

3² + b · x + 5 = 2 · 3 + b

3 · b + 14 = 6 + b

14 = 6 - 2 · b

8 = - 2 · b

b = - 4

By (2), y = k, x = 3 and b = - 4, we find the value of k:

k = 2 · 3 - 4

k = 6 - 4

k = 2

By algebraic handling, the value of k of the system of equations is equal to 2.

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The completed equations are:

2x + 3y = 80 equation 1

x + y = 37 equation 2

In order to determine the number of each type of shots made, two equations would be derived based on the information provided in the question. These equations would be solved simultaneously in order to determine the required values.

[(type of basket made)x ]+ [(type of baskets made)y] = total number of points

2x + 3y = 80

x + y = total number of baskets

x + y = 37

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Answer:

12a^3b^2+18a^2b

Step-by-step explanation:

12 3b2+182b

Answer:

Please make the question clearer, but I would say B

Step-by-step explanation:

I am not sure what you mean, to me the question is unclear

Answer: 17

Step-by-step explanation:

substitute -3 for a and -5 for b. the equation will be[tex]\frac{(-3)^{2}+(-5)^{2} }{-3-(-5)}[/tex]. then when you simplify, you will get [tex]\frac{9+25}{-3+5}[/tex]. finally, add and you will get [tex]\frac{34}{2}[/tex] which is 17.

Based on the samples that the scientists picked, and the weight of these samples, the various sample means are:

The range of the sample means is 0.4 pounds.

The true statements on the mean weights to be used by the scientists are:

First, find the sample means of each sample.

Sample 1:

= (3 + 2 + 6 + 4 + 2) / 5

= 3.4 pounds

Sample 2:

= (2 + 2 + 3 + 7 + 3) / 5

= 3.4 pounds

Sample 3:

= (6 + 4 + 2 + 2 + 4) / 5

= 3.6 pounds

Sample 4:

= (5 + 3 + 2 + 5 + 4) / 5

= 3.8 pounds

The range is;

= 3.8 - 3.4

= 0.4

The closer the range of the mean is to 0, the better the sample because it shows that in general, the sample means are the same. This is good for the research because it points to the uniformity of fish weights.

Using all the sample means as an average captures the data better than if a single sample mean is used.

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The interpretation of the slope is that (b) the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute

Linear equations are equations that have constant average rates of change, slope or gradient

From the table of values, we have the following points

(x, y) = (5, 5.5) and (10, 5)

The slope of the table of values is calculated as:

m = (y2 - y1)/(x2 - x1)

Substitute the known values in the above equation

m = (5 - 5.5)/(10 -5)

Evaluate the difference

m = -0.5/5

Evaluate the quotient

m = -0.1

This means that the slope is -0.1

From the table of values, we have

x represents the elapsed time and y represents the volume of helium

So, the interpretation of the slope is that (b) the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute

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Answer:

29, 21, 84

Step-by-step explanation:

Let the first number be x.

The second number is x - 8.

The third number is 4(x - 8).

Their sum is 134.

x + (x - 8) + 4(x - 8) = 134

x + 5(x - 8) = 134

x + 5x - 40 = 134

6x = 174

x = 29

x - 8 = 29 - 8 = 21

4(x - 8) = 4(29 - 8) = 4(21) = 84

Adam says that the number 4 has four factors. The above statement is incorrect as 4 only three factors 1,2, and 4.

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The solution to this problem is (s2+1)Y(s)−2s−1=2s2+4 .

We let  L[y(t)]=Y(s) . With that, tabular Laplace-transform laws entail

L[y′]=sY(s)−y(0)=sY(s)−2

L[y′′]=s2Y(s)−sy(0)−y′(0)=s2Y(s)−2s−1

∴L[y′′+y]=(s2+1)Y(s)−2s−1 .

Since the Laplace transform of  sin(kt)  is  ks2+k2 , we have

(s2+1)Y(s)−2s−1=2s2+4 .

This equation readily solves to  Y(s)=2s3+s2+8s+6(s2+1)(s2+4) . We compute its partial fraction decomposition as  Y(s)=2s+53s2+1+−23s2+4 .

Our final step is to use tabular Laplace-transform laws ( sin(kt)↦ks2+k2 , and  cos(kt)↦ss2+k2 ) to get  y(t)=2cost+53sint−13sin(2t) . One can check that this indeed satisfies the initial value problem.

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The surface area of the rectangular prism is 2(lw + wh + lh). A rectangular prism has six rectangular faces.

The area of a rectangle with length and width is

Area = length × width

I.e., A = l × w sq. units

A rectangular prism has six rectangular faces and the length 'l', width 'w', and height 'h'.

So, the areas of each face are as follows:

A(R1) = l × w

A(R2) = l × h

A(R3) = w × h

A(R4) = l × w

A(R5) = l × h

A(R6) = w × h

Thus, the area of the prism = sum of areas of all the faces

⇒ Area of the prism = lw + lh + wh + lw + lh + wh

⇒ A = 2lw + 2lh + 2wh

⇒ A = 2(lw + lh + wh)

Therefore, the area of the rectangular prism is A = 2(lw + lh + wh).

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In the  expression written below. the value of equation x  is known to be x=10/c.

From the question, we were given: 3(cx-7)=9

Therefore, we have to simply it to  make x the subject of the formula (to look for x)

Hence: 3(cx-7)=9

=(cx-7)=3

=cx=10  

x=10/c

Therefore, In the  expression written below. the value of equation x  is known to be x=10/c.

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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. Solve the following equation for x, and express its value in terms of c. 3(cx-7)=9

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Answer:

  (a)  h^-1(x) = (x+6)/6

Step-by-step explanation:

The inverse relation can be found by solving for y: x = h(y).

  x = h(y) . . . . . the inverse relation

  x = 6y -6 . . . . . use the function definition

  x +6 = 6y . . . . add 6

  (x +6)/6 = y . . . . divide by 6

The inverse function is ...

  [tex]\boxed{h^{-1}(x)=\dfrac{x+6}{6}}[/tex]

Answer:

y=[-4]x+[10]

Step-by-step explanation:

For a line to be perpendicular to another it must have the reverse reciprocal of the opposite line, to find the reverse reciprocal you take your slope, flip the numerator and denominator, and multiply it by -1.

The slope [tex]\frac{1}{4}[/tex] turns into [tex]\frac{4}{1}[/tex] and is then multiplied by -1 to become [tex]\frac{-4}{1}[/tex] which can be simplified down to: [tex]-4[/tex]

Now that we know the slope we need the line to pass through a point, so we will use point slope form:

[tex]y-y1=m(x-x1)[/tex]
Substitute in our slope and point values:

[tex]y-2=-4(x-2)[/tex]

Now solve for y:

[tex]y-2=-4(x-2)\\y-2=-4x+8\\y=-4x+10[/tex]

Then you will find that line [tex]y=-4x+10[/tex] runs perpendicular to [tex]y=\frac{1}{4}x-8[/tex] and intersects point (2,2).

Answer:

1) c = 25m + 90

2) c = 17m; $85

3) c = 10m + 15; $135

Step-by-step explanation:

Let m = number of months

1)

c = 25m + 90

2)

c = 17m

For 5 months, m = 5.

c = 17m = 17 × 5 = 85

$85

3)

c = 10m + 15

1 year = 12 months, so m = 12

c = 10m + 15 = 10 × 12 + 15 = 120 + 15 = 135

$135

Answer:

-0.5, either ⅙ or ⅓

Step-by-step explanation:

slope = rise / run

3) slope = (6 - 7) / (3 - 1)

slope = -1 / 2

slope = -0.5

ur mouse is blocking 4 (I'll do 2 scenarios):

4) slope = (-4 - -5) / (2 - -4)

slope = 1 / 6

I will leave it in fractional form

4) slope = (-4 - -6) / (2 - -4)

slope = 2 / 6

slope = 1/3

slope = 0.33

Answer:

A plastic board