Please help it would be amazing if you knew this

The fifth term in the sequence would be C.

Answer:

1196cm³

Step-by-step explanation:

Step 1

Find the volume of the Rectangular Prism = Length × Width × Height

Length = 12 cm

Width = 20 cm

Height = 5 cm

Volume of a Rectangular prism = 12 × 20 × 5

= 1200cm³

Step 2

Volume of the Eraser

The Eraser has the shape of a box.

Volume = Length × Width × Height

Length = 0.5 cm

Width = 2 cm

Height = 4 cm

Volume = 4cm³

Step 3

Find the volume of the art box not taken up by the eraser

Volume of the art box not taken up by the eraser = Volume of the Art box - Volume of the Eraser

= 1200cm³ - 4cm³

= 1196cm³

Therefore, volume of the art box not taken up by the eraser is 1196cm³

A. The equation of the line through C(-6,5) and perpendicular to CD is y = (8/3)x + 31/3;     B. The equation of the line through D(2,2) and perpendicular to CD is y = (8/3)x - 10/3.

A. To find the equation of the line through point C(-6,5) and perpendicular to CD, we need to determine the slope of CD and then find the negative reciprocal of that slope.

First, let's calculate the slope of CD using the coordinates of points C(-6,5) and D(2,2):

slope_CD = (y2 - y1) / (x2 - x1) = (2 - 5) / (2 - (-6)) = -3 / 8

The negative reciprocal of -3/8 is 8/3.

Now, using the point-slope form of a linear equation, we can write the equation of the line passing through C(-6,5) with a perpendicular slope of 8/3:

y - y1 = m(x - x1)

y - 5 = (8/3)(x - (-6))

y - 5 = (8/3)x + 16/3

Simplifying further:

y = (8/3)x + 31/3

B. To find the equation of the line through point D(2,2) and perpendicular to CD, we follow a similar process. The slope of CD is still -3/8, so the negative reciprocal is 8/3.

Using the point-slope form with D(2,2) and a perpendicular slope of 8/3:

y - y1 = m(x - x1)

y - 2 = (8/3)(x - 2)

y - 2 = (8/3)x - 16/3

y = (8/3)x - 16/3 + 6/3

y = (8/3)x - 10/3

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A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The value of f(x) when the value of x is 9 is 38.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,

y =mx + c

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is the y-intercept.

The given data points are in a linear relation, therefore, if we find the slope of the line on which these data points will be located. Then the slope will be,

m = (17-5)/(2+2) = 3

Now, equate any point and the slope in the general equation of line, therefore, the equation will be,

y = 3x + c

17 = 3(2) + c

17 - 6 = c

c = 11

Further, the value of f(x) when the value of x is 9 will be,

f(x) = 3x + 11

f(9) = 3(9) + 11

f(9) = 38

Hence, the value of f(x) when the value of x is 9 is 38.

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Answer:

the answer is answer is 14

Step-by-step explanation:

doesnt need to be rounded

Line A'B' is three times longer and three times further from the origin than line AB when line AB is dilated with a scale factor of 3 and a center of dilatation at the origin. The line's slope and direction are unaltered.

A geometric alteration called a dilation alters the size of a shape. A dilation increases each point's distance from the shape's fixed centre point by a predetermined scale factor. The form is "stretched" or made larger if the scale factor is more than 1, and "shrunk" if the scale factor is less than 1. The centre of dilation is the location where the dilation begins and ends. A dilatation keeps a figure's form but not always its orientation or location.

Line A'B' is three times longer and three times further from the origin than line AB when line AB is dilated with a scale factor of 3 and a center of dilatation at the origin. The line's slope and direction are unaltered.

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For this problem, we are given the dimensions of a garden and the cost of planting seeds per square meter in this garden. We need to determine the total cost of planting the seeds.

The first step is to calculate the area of the garden, for which we need to multiply the length and width:

Now we need to multiply the area by the cost of the seeds per square meter. We have:

The total cost is 21.5x² + 40.85x -32.25

The set of strings that are in both languages, which is {bba, bbab}.

The intersection of the languages specified by (L₁;L₂;) and L₃ is the set of strings that are in both languages.

The language (L₁;L₂;) is formed by concatenating a string from L₁ with a string from L₂. Since L₁ only contains the string "bb", every string in (L₁;L₂;) starts with "bb" and is followed by a string from L₂. Thus, (L₁;L₂;) contains the strings "bba" and "bbab".

The language L₃ contains all strings of length 3 or less over the alphabet {a,b}. Thus, L₃ contains the strings "a", "b", "aa", "ab", "ba", "bb", "aaa", "aab", "aba", "abb", "baa", "bab", "bba", and "bbb".

The intersection of (L₁;L₂;) and L₃ is the set of strings that are in both languages, which is {bba, bbab}.

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a Given:-

A image.

To find the total area of the given image.

So the given image is splitted into three images they are a triangle at the top and a rectangle at the middle and parallelogram at the bottom.

So the formula for triangle is,

So the formula for rectangle is,

So the formula for parallogram is,

So from the given image we have the values as,

Triangle has,

Rectangle has,

Paralleogram has,

So now we substitute the following values. so we get,

For Triangle,

For Rectangle,

For paralleogram,

So the total area is,

So the total area is 46 in.sq.

The correct statement is Most of the songs were between 3 minutes and 3.8 minutes long.

Based on the given information from the graph, we can determine the following:

The graph shows an upward trend from 2.8 to 3.4 on the horizontal axis.

Then, there is a downward trend from 3.4 to 4 on the horizontal axis.

From this, we can conclude that most of the songs played during the one-hour interval were between 3 minutes and 3.8 minutes long. This is because the upward trend indicates an increase in length from 2.8 to 3.4, and the subsequent downward trend suggests a decrease in length from 3.4 to 4.

Therefore, the correct statement is:

Most of the songs were between 3 minutes and 3.8 minutes long.

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Answer:

A

Step-by-step explanation:

Answer:  She observed older fossils that contained many of the same minerals as the newer ones

Step-by-step explanation:

Answer:

chaupapi

\\

Step-by-step explanation:

The simplified form is \(6x^{3}\).

What are indices in maths?

The equation is -

\(\sqrt{\frac{2160x^{3} }{60x^{2} } }\)

We can rewrite this using property of multiplication to obtain

\(\sqrt{\frac{2160}{60} * \frac{x^{8} }{x^{2} } }\)

We simplify variable expression in the radicand using

\(\frac{a^{m} }{a^{n} } = a^{m - n}\)

\(\sqrt{36 * x^{8 - 2} }\)

\(\sqrt{36 * x^{6} }\)

\(\sqrt{36 * (x^{3})^{2} }\)

\(\sqrt{36} * \sqrt{(x^{3})^{2} }\)

\(6 * x^{3}\)

Therefore,  the simplified form is \(6x^{3}\)

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The fifth roots of the complex number 3 + j3 can be expressed in polar form and exponential form. In polar form, the fifth roots are given by r^(1/5) * cis(theta/5),

To find the fifth roots of 3 + j3, we first convert the complex number into polar form. The magnitude r is calculated as the square root of the sum of the squares of the real and imaginary parts, which in this case is sqrt(3^2 + 3^2) = sqrt(18) = 3sqrt(2). The angle theta can be determined using the arctan function, giving us theta = arctan(3/3) = pi/4.

Next, we express the fifth roots in polar form. Each root can be represented as r^(1/5) * cis(theta/5), where cis denotes the cosine + j sine function. Since we are finding the fifth roots, we divide the angle theta by 5.

In exponential form, the fifth roots are given by r^(1/5) * exp(j(theta/5)), where exp denotes the exponential function.

Calculating the values, we have the fifth roots in polar form as 3sqrt(2)^(1/5) * cis(pi/20), 3sqrt(2)^(1/5) * cis(9pi/20), 3sqrt(2)^(1/5) * cis(17pi/20), 3sqrt(2)^(1/5) * cis(25pi/20), and 3sqrt(2)^(1/5) * cis(33pi/20).

In exponential form, the fifth roots are 3sqrt(2)^(1/5) * exp(j(pi/20)), 3sqrt(2)^(1/5) * exp(j(9pi/20)), 3sqrt(2)^(1/5) * exp(j(17pi/20)), 3sqrt(2)^(1/5) * exp(j(25pi/20)), and 3sqrt(2)^(1/5) * exp(j(33pi/20))

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Answer: 60

Step-by-step explanation:10 x 6 = 60 ( Also, 6x6x6x6x6x6x6x6x6x6 = 60

Answer:

its the 2nd one

Step-by-step explanation:

y=mx+b

M=slope

B=y-intercept

Answer:

Slope: 5x    Y-Intercept: -7

Step-by-step explanation:

The slope is the rate at which it increases, the y-intercept is the point in the graph that crosses the y-axis

y=mx+b  

mx = slope

b = y-intercept

Answer:

9 people per 32 square ft

(or 9:32)

Step-by-step explanation:

First find the area:

8*8=64 sqr ft

Next create a ratio

18 people to 64'sqr

Now we try reducing

18/2 = 9

64/2 = 32

So the final ratio is 9 people per 32 square ft

9:32

Hope this helps! :)

Answer:

13

Step-by-step explanation:

Using the pytago We have

edge to find = apartment (5^2 + 12^2) = 13

The point-slope equation of the line for the given slope and coordinates is found as : y = -3x - 16.

For the stated question.

The slope of the line m = -3.

Coordinates = (5,-7)

The general point-slope equation is given as:

y - y1 = m (x - x1)

y - 5 = -3(x + 7)

y - 5 = -3x - 21

y = -3x - 16

Thus, the point-slope equation of line for the given slope and coordinates is found as : y = -3x - 16.

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Question 3: True

Question 4: False

Question 5: True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.

This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.

True

When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.

Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.

False

A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.

Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.

True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

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Answer:

y = \(\frac{24}{x}\)

Step-by-step explanation:

Given that y varies inversely with x then the equation relating them is

y = \(\frac{k}{x}\) ← k is the constant of variation

To find k use the condition y = 4 when x = 6 , then

4 = \(\frac{k}{6}\) ( multiply both sides by 6 )

24 = k

y = \(\frac{24}{x}\) ← equation of variation

Answer:

3(x + 2) = 3x + 6

Step-by-step explanation:

3(x + 2) = 3x + 6

Distribute --> 3x + 6 = 3x + 6

The pair which shows equivalent expressions are 3(x + 2) = 3x + 6.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given are four equations.

A) 3(x + 2) = 3x + 6

This is equivalent, since,

3(x + 2) = 3x + (3 × 2) = 3x + 6

B) 3x + 2x= x² (3 + 2)

This is incorrect since, 3x + 2x = x(3 + 2)

C) 3x + 2 = 3(x + 2)

This is also not equivalent since we cannot take 3 outside since it is not common.

D) -3(2 + x) = -6x - 3

This is also not true since,

-3(2 + x) = (-3 × 2) + (-3x) = -6 - 3x.

Hence the equivalent expression is 3(x + 2) = 3x + 6.

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Answer:

red marbles

Step-by-step explanation:

Since the formula is;

Probability = number of required outcome

_______________________

number of possible outcome

3/8. = x/56

8x. = 168

x. 21 ( number of blue marbles)

Therefore if the total marbles = 56 and 21 of the marbles are blue then to get the red marbles

= 56 - 21

= 35

Answer:

3.42

Step-by-step explanation:

The two triangles ΔRST and ΔUVW are similar to each other by the SAS property.

Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.

Given that there are two triangles ΔRST and ΔUVW. ΔRST has the angle ∠T = 59° and the sides RT = 15 units and ST = 13 units. The other triangle ΔWVU has the angle ∠W = 59° and the sides WV= 52 units and WU= 60 units.

Firstly the two angles are the same,

∠T= ∠W = 59°

The two sides are dilated by a scale factor of 4,

WV /  ST = 52 / 13 = 4

WU /  RT = 60 / 15 = 4

So these sides are similar.

Hence, from the SAS property, the two triangles are similar.

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The minimum value of the function f(x) =0. 9x2+3. 4x-2. 4 is -3.77 and its parabolic curve is upward because of its minimum value.

Let's consider the equation of a function.

f(x) = \(0.9x^{2} + 3.4x -2.4\)

Now, divide each and every element and assume that a, b, and c are coefficients of the function given.

a: 0.9

b: 3.4

c: -2.4

The sign of the coefficient of a determines the exposure of the parabola. Since a >  0, the parabola is open upwards and has a minimum value.

We can find the "x" of the vertex using the following expression.

x(v) = -b/2a = -3.4/(0.9)

x(v) = -3.77

We can find the "y" of the vertex by replacing this x in the equation

y(v) = 0.9(-3.77)² + 3.4(-3.77) -2.4

y(v)  = -2.42

The minimum value of the function is -3.77

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Reason 1: Distributive Property

The 1/4 x was distributed to each term in the parentheses.

Reason 2: Commutative Property

The individual factors were moved around to put numbers next to numbers and variables next to variables.  (Technically the associative property was also used, to break down the previous parentheses, but I don't think your teacher is thinking about that.)

Reason 3: Associate Property

The similar factors were then regrouped.

Reason 4: Simplify

This is just simplifying.

Reason 1: Distributive property

Reason 2: Commutative property

Reason 3: Associative property

Reason 4: Simplify

What is the property of commutativity?

The rule governing the ordering of variables is the commutative property. It states that the order of the variables does not influence the final answer when they are added or multiplied.

What is the property of associativity?

The associative feature of real numbers relates to grouping variables. It states that altering the grouping of variables added to or multiplied by one another has no effect on the output.

In mathematics, what is a distributive property?

This property states that multiplying the sum of two or more addends by a number yields the same result as multiplying each addend separately by the number and then putting the resulting products together.

First Argument: Distributive Property

\(\frac{1}{4x}\)was allocated to each phrase between the parenthesis.

Reason 2: Property of Commutation

The individual elements were rearranged in order to place numbers alongside numbers and variables alongside variables. (Technically, the associative property was also utilized to separate the preceding parenthesis, although I doubt your teacher is aware of this.)

Reason 3: Associative Property

Similar elements were subsequently gathered.

Fourthly: simplify

This is just simplifying.

Reason 1: Distributive property

Reason 2: Commutative property

Reason 3: Associative property

Reason 4: Simplify

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Check the picture below.

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below

\((\stackrel{x_1}{15}~,~\stackrel{y_1}{200})\qquad (\stackrel{x_2}{40}~,~\stackrel{y_2}{125}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{125}-\stackrel{y1}{200}}}{\underset{\textit{\large run}} {\underset{x_2}{40}-\underset{x_1}{15}}} \implies \cfrac{ -75 }{ 25 } \implies - 3\)