Surface area of prisms and cylinders

Answer:

[tex]x=3[/tex]

Step-by-step explanation:

we know that

The vertical asymptote occur when the denominator of the function f(x) is equal to zero.

we have

[tex]f(x)=\frac{6}{x-3}[/tex]

so

[tex]x-3=0[/tex]

[tex]x=3[/tex]-----> is the vertical asymptote

Answer: 3

Step-by-step explanation:

The red line goes through it

Answer:

the domain of g(x) ÷ f(x) is :D = ]-∞ ; 4[U] 4 ; +∞[

Step-by-step explanation:

g(x) ÷ f(x) exist for : 2-x^1/2 ≠ 0

 2-x^1/2 = 0

  x^1/2 = 2

  (x^1/2)² = 2²

x = 4

the domain of g(x) ÷ f(x) is :D = ]-∞ ; 4[U] 4 ; +∞[

ANSWER

[0,4) U (4,+∞)

EXPLANATION

The given functions are:

[tex]f(x)=2- \sqrt{x} [/tex]

and

[tex]g(x) = {x}^{2} - 9[/tex]

We want to find the domain of:

[tex] g(x) \div f(x) = \frac{ {x}^{2} - 9}{2 - \sqrt{x} } [/tex]

This function is defined for:

[tex]2 - \sqrt{x} \ne0[/tex]

[tex]2 \ne \: \sqrt{x} [/tex]

Square both sides,

[tex] {2}^{2} \ne \: ({\sqrt{x}})^{2} [/tex]

[tex]4 \ne \: x[/tex]

Also [tex] x\:\ge0[/tex]

Therefore the domain is

[0,4) U (4,+∞)

Answer:

168

Step-by-step explanation:

you would times 3.75 by 82 and subtract the answer from 2071.50 and get 1764 then divide 1764 by 10.50 and get 168

Answer:

168 adult adult ticket were sold

Step-by-step explanation:

Hello

The tickets cost for adults is     $10.50

The tickets cost for students is $3.75

number of adult ticket sold:       A

number of student  ticket sold:  B

10.50A+3.75B=2071.50     Equation 1

B=82                                   Equation 2

replacing equation 2 in equation 1

10.50A+3.75(82)=2071.50

10.50A=2071.50-307.50

[tex]A=\frac{1764}{10.50} \\\\A=168\\\\\\[/tex]

168 adult adult ticket were sold

Have a great day.

For this case, we must subtract the given matrices, for this we subtract term to term.

So, we have:

Equal signs are added and the same sign equals:

[tex]\left[\begin{array}{ccc}-2-2\\-2-1\\1-1\end{array}\right][/tex]=

[tex]\left[\begin{array}{ccc}-4\\-3\\0\end{array}\right][/tex]

ANswer:

[tex]\left[\begin{array}{ccc}-4\\-3\\0\end{array}\right][/tex]

Answer:

[tex]\left[\begin{array}{ccc}-4\\-3\\0\end{array}\right][/tex]

Step-by-step explanation:

Given in the question two matrix, a matrix can only be added to (or subtracted from) another matrix if the two matrices have the same dimensions.

Here the dimensions are 3x1 and 3x1 .

[tex]\left[\begin{array}{ccc}-2\\-2\\1\end{array}\right][/tex]-[tex]\left[\begin{array}{ccc}-2\\1\\1\end{array}\right][/tex]

To subtract two matrices, just subtract the corresponding entries

=[tex]\left[\begin{array}{ccc}-2-2\\-2-1\\1-1\end{array}\right][/tex]

=[tex]\left[\begin{array}{ccc}-4\\-3\\0\end{array}\right][/tex]

9 games equals 36 percent of x number of total games.

9=(36/100)x

Multiply both sides by (100/36) to isolate x.

9*(100/36)=x

x=25 total games

Answer:

.074 I believe

Step-by-step explanation:

1 meter = 1000 millimeters, so set an equal proportion. x / 72.74mm = 1m / 1000mm. Cross multiply to get 1000x = 72.74; divide both sides by 1000 to get x = 0.07274 m or if you're rounding, 0.07m

The equation [tex]\(525=25(x-2)\)[/tex] helps answer option (C): How many members are in the band when no one is absent?

let's break it down step by step:

1. Define variables: Let [tex]\(x\)[/tex] represent the total number of members in the band.

2. Calculate members present: Since 2 members were absent, the number of members present is [tex]\(x - 2\).[/tex]

3. Programs folded by each member: We know that each present member folded 25 programs.

4. Total programs folded: To find the total number of programs folded, we multiply the number of present members by the number of programs each member folded. So, the total programs folded is \(25(x-2)\).

5. Set up equation: We are given that the total number of programs folded is 525. So, we set up the equation:

[tex]\[ 25(x-2) = 525 \][/tex]

6. Solve for [tex]\(x\):[/tex] By solving this equation, we can find the value of [tex]\(x\),[/tex]which represents the total number of members in the band when no one is absent.

So, the equation [tex]\(525=25(x-2)\)[/tex] helps us determine how many members are in the band when no one is absent. This aligns with option (C).

Complete Question:

Answer:

246.61 feet (rounded to 2 decimal places)

Step-by-step explanation:

We multiply 3/4 with previous minute traveling.

Minute #1: travels 75 feet

Minute #2: travels (3/4)*75 = 56.25 ft

Minute #3: travels (3/4)(56.25) = 42.19 ft

Minute #4: travels (3/4)(42.1875) = 31.64 ft

Minute #5: travels (3/4)(31.64) = 23.73 ft

Minute #6: travels (3/4)(23.73) = 17.80 ft

So, in 6 minutes, the car travels  75 + 56.25 + 42.19 + 31.64 +23.73 + 17.80 = 246.61 feet.

The next term in the given sequence is 4

Given the sequence of values

93 27 14

The product of the two digits of each term will give the subsequent term. From the sequence given for instance;

93 = 9 * 3  = 27 (next term)

27 = 2 * 7 = 14 (3rd term)

For the next term;

14 = 1 * 4 = 4 (This will given the next term in the sequence)

Hence the next term in the sequence is 4

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Without additional context or a defined pattern, it's not possible to definitively determine the next number in the sequence 93, 27, 14. The sequence could potentially be arithmetic, geometric, quadratic, or even something more complex, but with only three terms provided, it's not possible to identify a clear pattern.

The given sequence in the question is 93, 27, 14. The solution to this sequence isn't immediately clear, as a standard mathematical pattern - such as addition, subtraction, multiplication, or division - doesn't seem to apply across all elements. Unfortunately, without additional context or a defined pattern to follow, it's not possible to definitively determine the next number in the sequence. Sequences can follow a vast array of potential patterns, including (but not limited to) geometric sequences, arithmetic sequences, quadratic sequences, or even patterns that incorporate elements of probability, set theory, or number theory.

For example, if we were looking for a simple arithmetic pattern in the given sequence, an initial glance might suggest that we are subtracting 66 and then 13 to find the second and third terms respectively. However, continuing this pattern does not result in a logical (-1) for the 'fourth' term in the sequence.

The sequence could also potentially be following a more intricate pattern - it could be geometric (each term multiplied or divided by a consistent number), quadratic (based on square or cube numbers), or even something more complex. However, with only three terms provided, it's not possible to identify a clear pattern of this nature.

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We can solve for an acute angle in a right triangle if we know the other two angles. In the given hypothetical example, we assumed one angle was 30 degrees and the other was 90 (a right angle). We then subtracted these angles from 180 (the sum of all angles in a triangle) to find the acute angle NPO.

To solve for the acute angle NPO, we would typically need more specific information about the properties of the figure in question. However, let's suppose that triangle NPO is a right triangle and one of the given angles is 30 degrees. In this case, we can use the knowledge that the sum of all angles in a triangle equals 180 degrees.

Therefore, we set up an equation: 30 (degree of the given angle) + 90 (degree of the right angle) + X (angle NPO to be found) = 180. Solving for X gives us that NPO = 180 - 30 - 90 = 60 degrees.

Please remember that solving for an acute angle typically requires specific information about the figure and not all problems are as simple as this example demonstrates.

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A linear pair involves adjacent angles formed when two lines intersect. In this context, <NPO is 40°, and <SPR is 50°, adhering to the linear pair property.

A linear pair is formed when two lines intersect at a single point, creating two adjacent angles. If these angles align in a straight line, they constitute a linear pair, and the sum of their measures is always 180°. These angles are often termed supplementary or additional angles.

In the given scenario, angle <QPO is provided as 140°. According to the linear pair property, the angle <NPO supplementary to <QPO forms a straight line, and their sum equals 180°. Therefore, <NPO is calculated as 180° - 140°, resulting in <NPO being 40 degrees.

Moving on to the second part, three angles <SPN, <SPR, and <RPQ are considered. Applying the linear pair property, the sum of these angles is 180°. Given that <SPN is 90° and <RPQ is already known as 140°, the calculation involves finding <SPR. Thus, 90° + <SPR + 40° equals 180°. Solving for <SPR, it is determined to be 50 degrees.

In summary, for the provided angles:

a) <NPO is found to be 40 degrees.

b) <SPR is determined as 50 degrees through the linear pair property.

The question probable may be:

7.What is the measure of Angle NPO?

8.What is the measure of Angle SPR if the measure of Angle RPQ is 40°?

Answer:

B) x^2 – 1

Step-by-step explanation:

x(x – 1)(y + 1)

FOIL (x-1)(y+1)

firsy: xy

outer 1x

inner -1y

last (1)(-1) =-1

Add them together  xy +x-y-1

x( xy +x-y-1)

Replace xy with 1

x( 1+x-y-1)

x(+x-y)

Distribute

x^2-xy

But xy=1

x^2 -1

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

area of rectangle is 5800.

Answer:

12y-8

Step-by-step explanation:

so what you do is to distribute the 2 to both 6y and -4 so 2 times 6y is 12y and 2 times -4 equals -8

The equivalent expression for the given expression is 12y-8.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 2(6y-4)

= 12y-8

Therefore, the expression is equivalent to 2(6y-4)​ is 12y-8.

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Kyle was 1 minute and 47 seconds faster in a 3-mile race yesterday compared to his normal running time.

Kyle's normal time is 23 minutes and 25 seconds, which is (23 * 60) + 25 = 1405 seconds. Yesterday, Kyle's time was 21 minutes and 38 seconds, which is (21 * 60) + 38 = 1298 seconds.

Now, we subtract the faster time from the normal time: 1405 seconds - 1298 seconds = 107 seconds.

Thus, Kyle was 107 seconds faster yesterday than his normal time. To put it back into minutes and seconds, we divide by 60:  107  \ 60 = 1 minute and 47 seconds.

So, Kyle was 1 minute and 47 seconds faster yesterday.

Answer:

Step-by-step explanation:

The general equation is y = a*b^x

The specific equation is

100000 = 78918 * 1.06^x

y is the goal (100000 people)

a is the beginning number of people at the time the prize is offered.

a = 78918

b = the base increase per year. (1.06 in this case)

x is the number of years. Just for fun, let's solve for x even though you are not asked for it.

100000 = 78918 * 1.06^x  Divide both sides by 78918

100000/78918 = 1.06^x

1.26713 = 1.06^x                Take the log of both sides.

log(1.26713) = x * log(1.06) Divide both sides by log(1.06)

log(1.26713)/log(1.06) = x

x = 4.06 years.

Answer:

B

Step-by-step explanation:

A sum of cubes has the form

a³ + b³

8x³ = (2x)³ and 125 = 5³

Hence

8x³ + 125 = (2x)³ + 5³ ← a sum of cubes

The answer is 6

Explaination:

Step-by-step explanation:

(-)(-) = (+)(+) = (+)

(-)(+) = (+)(-) = (-)

13 + (-12) - (-5) = 13 - 12 + 5 = 1 + 5 = 6

ANSWER

[tex]x = \frac{\pi}{6} \: or \: x = \frac{5\pi}{6} [/tex]

EXPLANATION

The given trigonometric equation is

[tex]4 \sin ^{2} x - 4 \sin(x) + 1 = 0[/tex]

This is a quadratic equation in sinx.

We split the middle term to obtain,

[tex]4 \sin ^{2} x - 2 \sin(x) - 2 \sin(x) + 1 = 0[/tex]

Factor by grouping to get,

[tex]2 \sin(x) (2 \sin(x) - 1) - 1(2 \sin(x) - 1) = 0[/tex]

This implies that,

[tex](2 \sin(x) - 1)(2 \sin(x) - 1) = 0[/tex]

[tex] \sin(x) = 0.5[/tex]

This gives us,

[tex]x = \frac{\pi}{6} [/tex]

in the first quadrant.

Or

[tex]x = \pi - \frac{\pi}{6} [/tex]

[tex]x = \frac{5\pi}{6} [/tex]

in the second quadrant.

Answer:

x = [tex]\frac{\pi}{6}[/tex], [tex]\frac{7\pi}{6}[/tex],  [tex]\frac{11\pi}{6}[/tex].

Step-by-step explanation:

The given equation is 4 sin²x - 4 sin x + 1 = 0

(2sinx)² - 2(2sinx) + 1 = 0

(2sinx - 1 )² = 0

Sinx = [tex]\frac{1}{2}[/tex] ⇒ x = sin⁻¹ ( [tex]\frac{1}{2}[/tex])

So between the interval [0, 2π] value of x will be  [tex]\frac{\pi}{6}[/tex],  [tex]\frac{7\pi}{6}[/tex],  [tex]\frac{11\pi}{6}[/tex]

[Since sine is positive in 1st 3rd and 4th quadrant]

So value of x will be x =  [tex]\frac{\pi}{6}[/tex], [tex]\frac{7\pi}{6}[/tex],  [tex]\frac{11\pi}{6}[/tex].

Answer:

x=9

Step-by-step explanation:

x – 2 = 7

Isolate the variable, x.

x-2+2=7+2

x=9

x=9

Answer: [tex]x=9[/tex]

Step-by-step explanation:

Given the equation [tex]x-2=7[/tex], you need solve for the variable "x", to do this, you need to remember the Addition property of equality, which states that:

[tex]If\ a=b,\ then\ a+c=b+c[/tex]

Therefore, add 2 to both sides of the equation to calculate the value of the variable "x", then you get the following result:

[tex]x-2+(2)=7+(2)[/tex]

[tex]x=9[/tex]

Answer:

There are 5 1/2 oranges altogether.

Step-by-step explanation:

The 2 and 3 in front of each fraction indicate that there are a total of 5 whole oranges altogether. Now we have to settle these fractions. the 1/4 and the 1/4 both have a common denominator so there is no need to find one. When the common denominator is found, we simply have to add the numberators on the top of the fraction. 1+1 is 2, and, since the denominator stays the same, we should get a total of 2/4. I am unsure as to whether you were asked to simplify your answer (if you weren't you could keep your answer like this), but if you were to simplify the answer, both the numerator and denominator of our total can be divided by 2, so when that is done, we have a simplified total of 1/2. Take that 1/2 of an orange and add it to our 5 whole oranges, and we should get our answer of 5 1/2 oranges in total.

Answer:

Translation and a rotation 90 degrees

Step-by-step explanation:

if this is some kind of riddle then i think its 5

A quadrilateral with one pair of parallel sides is a trapezoid

A quadrilateral with only one pair of parallel sides can be classified as a trapezoid, which is a distinct type of four-sided figure unlike rectangles or squares.

The quadrilateral Lily designed, with only one pair of parallel sides, can be classified as a trapezoid. In geometry, this kind of shape is distinct from others we learn about in elementary levels, such as squares and triangles. A trapezoid is a four-sided figure, which makes it a type of quadrilateral but not all sides are parallel like in a rectangle or a square.

The defining feature of a trapezoid is that it has at least one set of parallel sides, known as the bases, while the other sides, which are not parallel, are referred to as the legs. Because it only has one pair of parallel sides, it differs from other quadrilaterals like rectangles, squares, and parallelograms, which have two pairs of parallel sides. The non-parallel sides of a trapezoid can be of different lengths and angles to each other, which can make trapezoids quite diverse in shape and size.

ANSWER

[tex]( - \infty , - 7) \cup( - 7 , 0) \cup(0 , 7 )\cup(7 , + \infty )[/tex]

EXPLANATION

The given function is

[tex]h(x) = \frac{9x}{x( {x}^{2} - 49) } [/tex]

This function is defined for values where the denominator is not equal to zero.

[tex]x( {x}^{2} - 49) \ne0[/tex]

[tex]x(x - 7)(x + 7) = 0[/tex]

The domain is

[tex] x \ne - 7, x \ne0, \: and \: x \ne 7,[/tex]

Or

[tex]( - \infty , - 7) \cup( - 7 , 0) \cup(0 , 7 )\cup(7 , + \infty )[/tex]

The domain of the function h=9x/x(x^2-49) is x = -7, x = 7.

The domain of the function h = 9x/(x(x^{2}-49)) can be determined by considering the values of x that make the denominator non-zero. Since division by zero is undefined, we need to find the values that would make the denominator equal to zero. In this case, the denominator is x(x^{2}-49), which factorizes to x(x+7)(x-7). So, the values of x that make the denominator equal to zero are x=0, x=-7, and x=7.

However, we also need to consider that the function is undefined when cancelling out those values of x that would also make the numerator zero. In this case, x=0 would make the numerator zero, so it cannot be a part of the domain.

Therefore, the domain of the function h = 9x/(x(x^{2}-49)) is given by x = -7, x = 7.

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It is would last for 6 hours.

1.892a is the correct answer

The expanded form of the expression 2.15a+0.03∙(3.4a−12a) is 2.252a - 0.36

Given the following expression

2.15a+0.03∙(3.4a−12a)

Open the parenthesis

2.15a+0.03∙(3.4a) −0.03(12a)

2.15a+ 0.102a - 0.36

Simplify

2.252a - 0.36

Hence the expanded form of the expression 2.15a+0.03∙(3.4a−12a) is 2.252a - 0.36

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I believe it is C, there is a geometric law that states that the opposite angles across a line with both going into parallel lines will be the same angle. Rather confusing but a video online would likely explain it better than anyone could here.

Answer:

Option C. 0.5

Step-by-step explanation:

In the given diagram, AB is parallel to DE, and line AE is the transverse.

So ∠DEF ≅ ∠FAB [ Alternate angles ]

and ∠EFD ≅ AFB ≅ 90° [ Vertically opposite angles ]

So, Third angle of the triangles will also be equal.

Since angles DEF and FAB are equal so their sine values will also be equal.

Therefore, sinA = sinE = 0.5

Option C). 0.5 will be the answer.

Answer:

[tex]\large\boxed{\left(3x^2y\right)^3=27x^6y^3}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\\left(3x^2y\right)^3=3^3(x^2)^3y^3=27x^6y^3[/tex]

Answer:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10

. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

5×106 this is for 5,000,000

Step-by-step explanation:

The answer is:

The equation of the line in slope-intercept form:

[tex]y=\frac{5}{6}x+\frac{7}{3}[/tex]

To find the equation in slope-intercept form, we need to follow the next steps:

Find the slope of the line:

Using the slope formula, we have:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

We are given the points:

[tex](2,4)\\(-4,-1)[/tex]

So, substituting we have:

[tex]m=\frac{(-1)-(4)}{-4-2}[/tex]

[tex]m=\frac{-5}{-6}[/tex]

[tex]m=\frac{5}{6}[/tex]

Find the "b" value:

Now that we know the value of the slope, we can write the equation of the line:

[tex]y=\frac{5}{6}x+b[/tex]

In order to find "b" we need to substituite any of the given points, we know that line is thru both of the given points, so, substituting (2,4) we have:

[tex]4=\frac{5}{6}*2+b\\\\4=\frac{10}{6}+b\\\\4=\frac{5}{3}+b\\\\b=4-\frac{5}{3}=\frac{(3*4)-5}3}=\frac{12-5}{3}=\frac{7}{3}[/tex]

Now that we know the slope and "b", we can write the equation of the line in slope-intercept form:

[tex]y=\frac{5}{6}x+\frac{7}{3}[/tex]

Have a nice day!