Divide. Reduce the answer to lowest terms.

Answer:A or C

Step-by-step explanation: i guessed plus 19 hours ago

The volume of the oblique cylinder is 6867.18 cubic units

The given parameters are:

Height = 27

Radius = 9

The volume is calculated as:

[tex]V = \pi r^2 h[/tex]

So, we have:

[tex]V = 3.14 * 9^2 * 27[/tex]

Evaluate

V = 6867.18

Hence, the volume of the oblique cylinder is 6867.18 cubic units

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Subsets with bit strings:

To find the subsets with bit strings:

We need to express a) b) and c) into bit strings.

Firstly, a number of elements in the universal set represent the number of bits in the bit string.

Secondly, 1 = yes element is present in both universal sets as well as in subset.

0 = No, the element is not present in the subset but present in the universal set.

Hence, we have:

a) Subset {3,4,5} = 0011100000  (As there are 3 1's which means only 3,4,5 are present in both universal set and subset.

Similarly,

b) Subset {1, 3, 6, 10} = 1010010001

c) Subset {2, 3, 4, 7, 8, 9} = 0111001110

Therefore, Subsets with bit strings:

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Complete question:

Suppose that the universal set is U={1,2,3,4,5,6,7,8,9,10}. Express each of the following subsets with bit strings (of length 10) where the ith bit (from left to right) is 1 if i is in the subset and zero otherwise.

a) {3, 4, 5}

b) {1, 3, 6, 10}

c) {2, 3, 4, 7, 8, 9}.

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: (1.6 \times 10 {}^{5} ) \sdot(2 .3 \times {10}^{1} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: (1.6 \times 2.3) \sdot(10 {}^{5} \times 10 {}^{1} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3.68 \times 10 {}^{6} [/tex]

Answer:

The maximum amount of people that can go to the amusement park is 15.

Step-by-step explanation:

First you create an equation to represent the question

8.75+25.75x≤420

You put the less than or equal to sign because 420 is the maximum amount of money.

Now you just solve the equation.

25.75x≤420-8.75

25.75x≤411.25

x≤411.25/25.75

x≤15.9708738

Then you have to round down because you cant have .9 of a person.

So x≤15

Then, Check your solution

8.75+(25.75 x 15)≤420

8.75+386.25≤420

395≤420

That is true. But to make sure that is the maximum add another 25.75

395+25.75≤420

420.75≤420

This is equation is false so, our answer is correct.

The maximum amount of people that can go to the amusement park is 15.

Considering the area of the rectangle, we have that the length is of 8 units and the width is of 10 units.

The area of a rectangle of length l and width w is given as follows:

A = lw.

In this problem, the area is of 80 square units, while the length and the width are consecutive even integers, hence:

Then:

l(l + 2) = 80

l² + 2l - 80 = 0

(l + 10)(l - 8) = 0.

We need the positive measure, hence:

l -  8= 0 -> l = 8 units.

w = l + 2 = 10 units.

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Answer:

  D.  completing the square

Step-by-step explanation:

The process shown rearranges the standard-form quadratic equation to vertex form. It involves factoring out the leading coefficient and distributing the constant so that the variable terms can be written as a perfect square.

A perfect square trinomial is the square of a binomial. It has the form ...

  (x +b)² = x² +2bx +b²

Given two variable terms, x² and 2bx, the perfect square trinomial can be formed by adding b², which is the square of half the x-term coefficient.

When b² is added to the sum (x² +2bx), the square is complete. The sum (x² +2bx +b²) can be written as the square (x +b)².

This process of adding b² to the sum (x² +2bx) will change the polynomial unless a similar quantity is subtracted. That is why the 3rd line of the problem statement show 4 being added and subtracted inside parentheses:

  y = 5(x² +4x +4 -4) -17

When we're applying this transformation, we do not want to change the equation. We simply want to rearrange it.

In the next step, the subtracted term is brought outside the parentheses. This lets us write the quantity in parentheses as a perfect square.

  y = 5(x² +4x +4) +5(-4) -17

  y = 5(x² +4x +4) -20 -17

This process of adding and subtracting a suitable quantity and rearranging the equation so the variable terms make a perfect square is called ...

  "completing the square."

__

Additional comment

The equation in this form is said to be in "vertex form."

  y = a(x -h)² +k

In this form, the constant 'a' is a vertical scale factor; the ordered pair (h, k) identifies the vertex of the quadratic on a graph.

Answer:

[tex]\huge\boxed{\sf \{(-2,1)\}}[/tex]

Step-by-step explanation:

Given equations:

y = x + 3

y = -x - 1

By comparing the above equations, we get:

x + 3 = -x - 1

Add x to both sides

Subtract 3 to both sides

2x = -1 - 3

2x = -4

Divide 2 to both sides

x = -4/2

Substitute x = -2 in first equation.

y = x + 3

y = -2 + 3

So,

[tex]\rule[225]{225}{2}[/tex]

Answer:

[tex]x = - 2 \\ y = 1[/tex]

Step-by-step explanation:

The above are Simultaneous equations.

Simultaneous equations are two or more algebraic equations which share same variables like X,Y or X,Y and Z.

They are called simultaneous equations because they can be solved the same time.

From the question,

[tex]y = x + 3 - - - - - - (1) \\ y = - x - 1 - - - - - - (2) \\ Substitute \: equation \: (2)into \: (1) \\ - x - 1 = x + 3 \\ Collect \: liketerms \\ - x - x = 3 + 1 \\ - 2x = 4 \\ Divide \: bothsides \: by \: - 2 \\ \frac{ - 2x}{ - 2} = \frac{4}{ - 2} \\ x = - 2 \\ Substitute \: the \: value \: of \: x \: into \: equation \: (1) \\ y = x + 3 \\ y = - 2 + 3 \\ y = 1 \\ Therefore \: x = - 2 \: \: and \: y = 1[/tex]

The coordinates of the vertex that A maps to after Daniel's reflections are (3, 4) and the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)

From the given figure, the coordinate of the vertex A is represented as:

A = (-5, 2)

The coordinates of the vertex that A maps to after Daniel's reflections

The rule of reflection across the line x = -1 is

(x, y) ⇒ (-x - 2, y)

So, we have:

A' = (5 - 2, 2)

Evaluate the difference

A' = (3, 2)

The rule of reflection across the line y = 2 is

(x, y) ⇒ (x, -y + 4)

So, we have:

A'' = (3, -2 + 4)

Evaluate the difference

A'' = (3, 4)

Hence, the coordinates of the vertex that A maps to after Daniel's reflections are (3, 4)

The coordinates of the vertex that A maps to after Zachary's reflections

The rule of reflection across the line y = 2 is

(x, y) ⇒ (x, -y + 4)

So, we have:

A' = (-5, -2 + 4)

Evaluate the difference

A' = (-5, 2)

The rule of reflection across the line x = -1 is

(x, y) ⇒ (-x - 2, y)

So, we have:

A'' = (5 - 2, 2)

Evaluate the difference

A'' = (3, 2)

Hence, the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)

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We use the chi-square distribution when making inferences about a single population variance.

Short Description of Chi-Square Distribution

The continuous probability distribution known as the chi-square distribution. The number of degrees of freedom (k) a chi-square distribution has determines its shape. This type of sampling distribution has a variance of 2k and a mean equal to its number of degrees of freedom (k). The range is of a chi-square distribution is from 0 to ∞.

Variance plays a key role in the analysis of risk and uncertainty. The sample variance, an unbiased estimator of population variance, is expressed by the following formula of core statistic for a sample size 'n' and Y' as the sample mean:

S² = ∑(Yₓ - Y') / (n-1)

The formula, (n-1)S² / σ² has the central chi-square distribution as χ²ₙ₋₁. Here (n-1) represents the degrees of freedom.

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Answer:

[tex]\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]

Step-by-step explanation:

NOTE :

[tex]x^2+ax=\left( x+\frac{a}{2} \right)^{2} -\left( \frac{a}{2} \right)^{2}[/tex]

………………………………………

f(x) = x² + x +1

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

     [tex]=\left( x+\frac{1}{2} \right)^{2} -\left( \frac{1}{2} \right)^{2} +1[/tex]

     [tex]=\left( x+\frac{1}{2} \right)^{2} - \frac{1}{4}+1[/tex]

     [tex]=\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]

Answer:

Step-by-step explanation:

Elasticity Demand

(Q1 - Q2)/(Q1 + Q2)

(P1 - P2)/(P1 + P2)

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Since the geometric series has 6 terms, increases by a factor of 4, and has a sum of 1365, the value of the first term is 1.

The sum of a geometric series is given by

Sₙ = a(rⁿ - 1)/(r - 1) with r > 1 where

Now, since our Geometric Series has 6 terms, n = 6. Also, it increases by a factor of 4, so, r = 4 and has a sum of 1365, so Sₙ = 1356. So,we have that

Since we require the first term, a , making a subject of the formula, we have

a = Sₙ(r - 1)/(rⁿ - 1)

Substituting the values of the variables into the equation, we have

a = Sₙ(r - 1)/(rⁿ - 1)

a = S₆(r - 1)/(r⁶ - 1)

a = 1365(4 - 1)/(4⁶ - 1)

a = 1365(3)/(4096 - 1)

a = 4095/4095

a = 1

So, the value of the first term is 1.

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The equation of the line in explicit form is y = - 2 · x + 5, whose implicit form is 2 · x + y = 5. (Correct choice: D)

In this question we must find the equation of the line perpendicular to the segment BC and that goes through the point A(x, y) = (1, 3). First, the slope of the line segment BC is:

m = [1 - (- 3)]/[5 - (- 3)]

m = 4/8

m = 1/2

And the slope of the line is:

m' = - 1/(1/2) = - 2

The intercept of the line is found by using the explicit form of equation of the line, m' = - 2 and (x, y) = (1, 3):

3 = - 2 · 1 + b

b = 5

The equation of the line in explicit form is y = - 2 · x + 5, whose implicit form is 2 · x + y = 5. (Correct choice: D)

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Answer:

If you divide it out and it comes out a whole number unless the original set of numbers is a fraction

The equation of a parabola whose vertex is (0, 0) and focus is (1 / 8, 0) is equal to x = 2 · y².

Herein we have the case of a parabola whose axis of symmetry is parallel to the x-axis. The standard form of the equation of this parabola is shown below:

(x - h) = [1 / (4 · p)] · (y - k)²     (1)

Where:

The distance from the vertex to the focus is 1 / 8. If we know that the location of the vertex is (0, 0), then the standard form of the equation of the parabola is:

x = 2 · y²     (1)

The equation of a parabola whose vertex is (0, 0) and focus is (1 / 8, 0) is equal to x = 2 · y².

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The statements that are true about the domain and range of the functions f(x), g(x), and h(x) include:

It should be noted that a function simply means a relation between a set of inputs to a set of possible outputs.

In this case, f(x) has a domain of all real numbers as well as g(x) which also has a domain of all real numbers.

In conclusion, the correct options are A and D.

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Answer:

A and D

Step-by-step explanation:

Edge 2022

Answer:

y = -3x + 9

Step-by-step explanation:

The slope is

[tex] \frac{6 - 0}{1 - 3} = - 3[/tex]

Substituting into point-slope form, we get

y = -3(x-3)

y = -3x + 9

The general form of the equation for the given circle centered at O(0, 0) is x^2 + y^2 = 41

The given parameters are

Center = (0, 0)

Point = (4, 5)

Rewrite the given parameters are

(a, b)= (0, 0)

(x, y) = (4, 5)

The general form of the equation for the given circle is represented as:

(x - a)^2 + (y - b)^2 = r^2

Substitute the known values in the above equation to calculate the radius r

(4 - 0)^2 + (5 - 0)^2 = r^2

Evaluate the difference

4^2 + 5^2 = r^2

Evaluate the exponent

16 + 25 = r^2

Evaluate the sum

41= r^2

Rewrite as

r^2 = 41

Substitute r^2 = 41 in (x - a)^2 + (y - b)^2 = r^2

(x - a)^2 + (y - b)^2 = 41

Substitute (a, b)= (0, 0) in (x - a)^2 + (y - b)^2 = 41

(x - 0)^2 + (y - 0)^2 = 41

Evaluate the difference

x^2 + y^2 = 41

Hence, the general form of the equation for the given circle centered at O(0, 0) is x^2 + y^2 = 41

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Answer:

  $70,300

Step-by-step explanation:

The amount Kaydence saved is the value of an arithmetic series with first term 100 and common difference 100. The number of terms in the sum is 37. The formula for the sum can be used.

The formula for the sum of n terms of an arithmetic series is ...

  Sn = (2a1 +d(n -1))(n/2) . . . . . . first term a1, common difference d

The number of terms being added is ...

  2050 -2014 +1 = 37 . . . . . . years Kaydence made deposits

The formula with a1=100, d=100, and n=37 is ...

  [tex]S_{37}=(2\cdot100+100(37-1))\dfrac{37}{2}=\dfrac{(200+3600)\cdot37}{2}\\\\S_{37}=70,\!300[/tex]

Kaydence would have saved $70,300 by the end of Jan 1, 2050.

Using it's concepts, the domain and the range of the graph are given as follows:

In this graph, have that the function is defined for all values of x except x = -1, and assumes all real values, hence the domain and the range of the graph are given as follows:

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation a.}[/tex]

[tex]\rm{2x^2 - 162 = 0}[/tex]

[tex]\huge\textbf{Solving for:}[/tex]

[tex]\rm{2x^2 - 162 = 0}[/tex]

[tex]\huge\textbf{Add \boxed{\bf 162} to both sides:}[/tex]

[tex]\rm{2x^2 - 162 + 162 = 0 + 162}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{2x^2 = 0 + 162}[/tex]

[tex]\rm{2x^2 = 162}[/tex]

[tex]\huge\textbf{Divide \boxed{\bf 2} to both sides:}[/tex]

[tex]\rm{\dfrac{2x^2}{2} = \dfrac{162}{2}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{x^2 = \dfrac{182}{2}}[/tex]

[tex]\rm{x^2 = 81}[/tex]

[tex]\huge\textbf{Take the square root of \boxed{\bf 81}}[/tex]

[tex]\rm{x = \pm \sqrt{81}}[/tex]

[tex]\rm{x = 9\ or\ x = -9}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\textsf{x = } \frak{9\ or } \ \textsf{x = }\frak{-9}}\huge\checkmark[/tex]

[tex]\huge\textbf{Equation b.}[/tex]

[tex]\rm{-\dfrac{1}{2}(x - 3)^2 = -2}[/tex]

[tex]\huge\textbf{Solving for:}[/tex]

[tex]\rm{-\dfrac{1}{2}(x - 3)^2 = -2}[/tex]

[tex]\huge\textbf{Simplify both sides of your equation:}[/tex]

[tex]\rm{-\dfrac{1}{2}x^2 + 3x - \dfrac{9}{2} = -2}[/tex]

[tex]\huge\textbf{Subtract \boxed{\bf -2} to both sides:}[/tex]

[tex]\rm{-\dfrac{1}{2}x^2 + 3x - \dfrac{9}{2} - (-2) = -2 - (-2)}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{- \dfrac{1}{2}x^2 + 3x - \dfrac{5}{2} = 0}[/tex]

[tex]\huge\textbf{Now, we can convert the equation to:}[/tex]

[tex]\rm{-0.5x^2 + 3x - 2.5 = 0}[/tex]

[tex]\large\text{When we changed the equation entirely, we made it easier to solve}\uparrow[/tex]

[tex]\huge\textbf{Use the quadratic formula to solve.}[/tex]

[tex]\large\textsf{The quadratic formula:}[/tex]

[tex]\mathsf{x= \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

[tex]\huge\textbf{Here are your labels:}[/tex]

[tex]\text{a = }\rm{-0.5}\\\\\text{b = }\rm{ 3}\\\\\rm{c = }\rm{\ -2.5}[/tex]

[tex]\huge\textbf{Your new equation:}[/tex]

[tex]\rm{x = \dfrac{-(3) \pm \sqrt{3^2 - 4(-0.5)(-2.5)}}{2(-0.5)}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\rm{x = \dfrac{-3 \pm \sqrt{4}}{-1}}[/tex]

[tex]\rm{x = 1\ or \ x = 5}[/tex]

[tex]\huge\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\textsf{x = }\frak{1}\ \textsf{or x = }\frak{5}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

[tex]a)\ x_1=-9,\ x_2=9\\\\b)\ x_1=1,\ x_2=5[/tex]

Given equations:

[tex]a)\ 2x^2 - 162 = 0\\\\b) -\dfrac{1}{2}(x-3)^2=-2[/tex]

A) 2x² - 162 = 0

Step 1: Divide both sides by 2.

Step 2: Take the square root of both sides (using both the positive and negative roots).

[tex]\\\implies \sqrt{x^2}=\sqrt{81}\\\\\implies x=\pm\ 9[/tex]

Step 3: Separate into two cases.

[tex]\implies x_1 = -9,\ x_2 =-9[/tex]

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

B) -1/2(x - 3)² = -2

Step 1: Multiply both sides by -2.

[tex]\\\implies -2\left(-\dfrac{1}{2}(x-3)^2\right)=-2(-2)\\\\\implies (x-3)^2=4[/tex]

Step 2: Take the square root of both sides (using both the positive and negative roots).

[tex]\\\implies\sqrt{(x-3)^2}=\sqrt{4}\\\\\implies x-3=\pm\ 2[/tex]

Step 3: Separate into two cases and solve each one.[tex]1)\ x-3=-2\implies x=-2+3\implies \boxed{x=1}\\\\2)\ x-3=2\implies x=2+3\implies \boxed{x=5}[/tex]

Using the unit circle, the correct answer regarding the comparison of angles w and t is given by:

a. t > w.

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

From this, we get that the sine is represented by the vertical axis. As we advance into the second quadrant, as the angle increases, sine decreases. Hence, since sin w > sin t, we have that t > w and option a is correct.

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Answer:

x ≤ 135/2

Step-by-step explanation:

x is the cost per night. You have to pay for 2 nights, and you do not want to spend more than $135 total. Another way to say that, is you want to spend less than or equal to $135.

x = cost per night

2 = number of nights

2x = total cost

Total cost must be less than or equal to $135.

2x ≤ 135

Divide each side by 2.

x ≤ 135/2

The proportion cranberry juice should be mixed with 84 ounces of apple juice 1:5 that is 1 parts of cranberry juice and 5 parts of lemon juice.

According to the question,

A punch recipe calls for mixing 2 parts of cranberry juice with 5 parts of apple juice.

84/2 = 42

5*42=210

Hence, the proportion cranberry juice should be mixed with 84 ounces of apple juice 1:5 that is 1 part of cranberry juice and 5 parts of lemon juice.

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OPTION A is the correct answer

Considerando la expresión de una ecuación lineal, la ecuación de la recta que pasa por el punto (5, –8) con pendiente 5 es y= 5x - 33.

Una ecuación lineal o línea se puede expresar en la forma y = mx + b

donde

La ecuación lineal se puede expresar también mediante la ecuación punto-pendiente de la recta, que se plantea si se conoce la pendiente de la recta y cualquiera de sus puntos. Con ello queda determinada la recta, conociendo la pendiente  “m” y un punto  (x1, y1) dado:

y - y1= m(x -x1)

En este caso, la recta que pasa por el punto (5, –8) con pendiente 5.

Reemplazando en la ecuación punto-pendiente de la recta:

y - (-8)= 5(x -5)

Resolviendo:

y + 8= 5(x -5)

Aplicando propiedad distributiva:

y + 8= 5x - 5×5

y + 8= 5x - 25

Aislando la variable "y":

y= 5x - 25 - 8

y= 5x - 33

Finalmente, la ecuación de la recta que pasa por el punto (5, –8) con pendiente 5 es y= 5x - 33.

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