Which of the following situations could be represented with the following system of equations?

The volume of the pyramid is 2496 cu.m.

A pyramid is a three dimensional structure which has a polygon base and  in general triangular faces which join at the top .

It is given that

A pyramid [tex]\rm frustum[/tex] has a 4 m by 4 m square top

Height = 12 m

Base = 20 m

The volume of a square pyramid with a  [tex]\rm frustum[/tex] is given by

V = (1/2) * ( Area of base + Area of  [tex]\rm frustum[/tex] ) * height of the  [tex]\rm frustum[/tex] from the base

V = 0.5 * ( 20 *20 + 4*4 ) * 12

V = 2496 cu.m

The volume of the pyramid is 2496 cu.m.

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Answer: y = f(x) = a + bx y = f(x) = a + bx y = f(x) =

explanation: The following is the formula for a linear function. y = f(x) = a + bx y = f(x) = a + bx y = f(x) = One independent variable and one dependent variable make up a linear function.

Answer:

I don't knowwwwwwwwwwwwwwww

Answer:

x = -2

Step-by-step explanation:

2x^3 +16 = 0

We are solving for x

Subtract 16 from each side

2x^3 +16- 16 = 0-16

2x^3 = -16

Divide each side by 2

(2x^3 ) /2 = -16/2

x^3 = -8

Take the cube root of each side

[tex]\sqrt[3]{x^3} = \sqrt[3]{-8}[/tex]

x = -2

Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

Given equation:

[tex]2x^3+16=0[/tex]

To solve for the unknown variable x, apply arithmetic operations to isolate the variable.

Subtract 16 from both sides:

[tex]\implies 2x^3+16-16=0-16[/tex]

[tex]\implies 2x^3=-16[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{2x^3}{2}=\dfrac{-16}{2}[/tex]

[tex]\implies x^3=-8[/tex]

Take the cube root of both sides:

[tex]\implies \sqrt[3]{x^3}=\sqrt[3]{-8}[/tex]

[tex]\implies x=-2[/tex]

When taking the cube root of a negative number, the result will be negative.  To understand why, examine what happens when we cube a negative number.

When a number is cubed, it is multiplied by itself, then by itself again.

When multiplying a negative number by another negative number, the result is always positive.

When multiplying a positive number by a negative number, the result is always negative.

Therefore:

[tex]\begin{aligned}\implies (-2)^3 &= -2 \cdot -2 \cdot -2\\ & = 4 \cdot -2\\& = -8\end{aligned}[/tex]

So if -8 is cube rooted, the result is -2.

f(x) = 10x -5 and g(x) = (x+5)/10  are inverses of each other , Option D is the correct answer.

A function is a mathematical statement which relates two variables , a dependent and an independent variable.

The inverse of a function is found by replacing every y by x and vice versa , and then solve for y

The equation

f(x) = 4/x - 3

or

y= 4/x -3

Replacing y by x

x = 4/y -3

x +3 = 4/y

y = 4/(x+3)

Which do not correlate with the given inverse

f(x) = 10x -5

y = 10x -5

for finding inverse

10y -5 = x

10y = x+5

y = (x+5)/10

g(x) = (x+5)/10

Therefore , Option D is the correct answer.

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Answer:

I think it’s C

Step-by-step explanation:

I think

Answer:

a

Step-by-step explanation:

2^3 = 8; 4^3 = 64; 8/64 = 1/8

(g^5)^3 = g^15

(h^2)^3 = h^6

g^15/8h^6

Answer:

-28

Step-by-step explanation:

put 3 where is x

f(x) = −5(3)^2 − (3) + 20

exponents flrst

(−5*9) − (3) + 20

-45 -3 +20

-48 + 20

-28

The table of values for the comparison of a function and its inverse function is shown in the image attached below.

An inverse function refers to a type of function that is obtained by reversing the operation of a given function (f(x)).

In Mathematics, a given function (f(x)) and its inverse function has the following property f⁻¹(f(x)) = x. By applying this property to the table (see attachment), we have:

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Using the normal distribution, it is found that:

a) The pilot is at the 72th percentile.

b) 19.13% of pilots are unable to fly.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 72.6, \sigma = 2.7[/tex].

Item a:

The percentile is the p-value of Z when X = 74.2, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{74.2 - 72.6}{2.7}[/tex]

Z = 0.59

Z = 0.59 has a p-value of 0.7224.

72th percentile.

Item b:

The proportion that is able to fly is the p-value of Z when X = 78 subtracted by the p-value of Z when X = 70, hence:

X = 78:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{78 - 72.6}{2.7}[/tex]

Z = 2

Z = 2 has a p-value of 0.9772.

X = 70:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{70 - 72.6}{2.7}[/tex]

Z = -0.96

Z = -0.96 has a p-value of 0.1685.

0.9772 - 0.1685 = 0.8087 = 80.87%.

Hence the percentage that is unable to fly is:

100 - 80.87 = 19.13%.

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Answer:

y = -3x + 1

Step-by-step explanation:

The line crosses the y-axis at 1. This is called the y-intercept. This is the number you fill in for c in the form of the equation given.

You can pick any two points on the line to calculate the slope. But you can actually SEE the slope without having to calculate it when you have the graph to look at. See the line crossing the y-axis at 1. Look for another point (that has nice whole number coordinates) there is one DOWN3 and OVER1. If you notice, the next point is also DOWN3 and OVER1.

DOWN3 and OVER1 is the slope -3/1, which is equal to -3.

Fill in -3 in place of the m in the equation.

y = -3x + 1

Done!

Answer:

y = -3x + 1

Step-by-step explanation:

The equation of a line in slope/intercept form is y = mx + c where m is the slope and c the y-intercept(ie the value of y when x =0)

The slope can be found by taking any two points on the line,  (x1, y1) and (x2,y2) and computing (y2-y1)/(x2-x1)

If you look at the line 2 points on the line are P(2,-5) and (0,1)

Slope = (-5-1)/(2-0) = -3

The y-intercept is the y-value at which the line intersects the y-axis ie at x = 0 and you can see that this is 1

Therefore equation is
y = -3x + 1

You can check to see if this is correct by plugging in some other value of x and seeing if the correct y value corresponds to the equation y-value

For example, in the graph we see that at x = 1, y = -2

Indeed -3(1) + 1 = -3 + 1 = -2 also

In a regular polygon, all interior angles have equal measures because the polygon has congruent sides and angles. The sum of all interior angles in a polygon can be found using the formula:

(n-2) * 180°,

where n represents the number of sides of the polygon.

Based on this, we can determine which angles cannot be interior angles in a regular polygon.

24°: This angle can be an interior angle in a regular polygon because it is smaller than the interior angles of any polygon with more than 6 sides.

72°: This angle can be an interior angle in a regular pentagon (5 sides) or any polygon with more sides, as it satisfies the requirement for interior angles.

135°: This angle cannot be an interior angle in a regular polygon because it is larger than the interior angles of any polygon with less than 8 sides.

164°: This angle cannot be an interior angle in a regular polygon because it is larger than the interior angles of any polygon with less than 9 sides.

179°: This angle cannot be an interior angle in any regular polygon because it is larger than the maximum measure of interior angles in any polygon.

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Answer:

$10

Please mark me as brainliest

The synthetic division of the polynomial, (2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2) =  2x³ + 2x + 4.

The division of the polynomial is determined as follows;

(2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2)

                     2x³ + 2x + 4

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

     x + 2   √(2x⁴ + 4x³ + 2x² + 8x + 8)

                - (2x⁴ + 4x³)

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

                                        2x² + 8x + 8

                                     - (2x² + 4x)

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

                                                  4x + 8

                                               - (4x + 8)

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

                                                       0

Thus, the synthetic division of the polynomial, (2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2) =  2x³ + 2x + 4.

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a straight line make an angle of 180° ,

so 115+y=180

y=65°

for the top part of the triangle it makes an angle of 360° , so 304+y=360

y=56

sum measure of interior angles of triangle is 180° , According to this rule (n-2)180 ; where n is the no. of sides .

so

65+56+y= 180

121+y=180

y=59( the angle next to X)

X+59=180( together they make an angle of 180)

x=121°

Hope it helps

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Answer: -24

Step-by-step explanation:

See attached image.

The vertex of this angle is point S.

The process capability index for the process is 0.1754.

The first sided specification limit will be:

= (Upper specification limit - mean)/(3 × standard deviation)

= (23.1 - 22.9)/(3 × 0.19)

= 0.2/0.57

= 0.3508

The second sided specification limit will be:

= (22.9 - 22.8)/(3 × 0.19)

= 0.1/0.57

= 0.1754

The process capability index for the process is 0.1754 wine it's the lower value.

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Answer:

Volume = 7WH - (1/2)W^2H

Step-by-step explanation:

The base consists of the length (L) and the width (W).  It is rectangular, so the perimeter would be the sum of all four sides:

Perimeter = L + W + L +W,

or      Perimeter = 2L + 2W

We are told that 2L + 2W = 28cm     [The perimeter is 28 cm]

------

The volume of the box is given by:  

Volume = L*W*H     [Length x Width x Height]

=====

Let's rearrange the first equation and use it in the second:

2L + 2W = 28cm

2L = 28cm - 2W

L = (28cm - 2W)/2

L = (14 - W)

Now use this definition of L (14 - W) in the second equation:

Volume = L*W*H

Volume = (14 - W)/2)*W*H

Volume = (7-(1/2)W)*W*H

Volume = 7WH - (1/2)W^2H

This can also be written as:  Volume = WH(7 - (1/2)W)

Answer: The first graph

Step-by-step explanation: A graph’s inverse will have all of their roots inverted as well. If you put the graph f(x)= 3x+3 into a graphing calculator, you’ll be able to see all the roots. From there, just invert (switch) the roots. Since on the original graph the most prominent roots are {(0,3), (-1,0),(-2,-3)}, you just need to invert those roots and find them ALL on one of the graphs, then you have your answer. So, the inverted roots will be {(3,0),(0,-1),(-3,-2)}.

Still, I find the simplest thing is to put them into a graphing calc like GeoGebra.

Coordinates are numerical lengths or angles that uniquely identify locations on two-dimension. The missing coordinates are coordinates 3 and 4.

A Cartesian coordinate plane is a two-dimensional plane with infinite dimensions. On an endless 2d plane, any two-dimensional figure may be drawn. A location is assigned to each point on a Cartesian plane.

It is the perpendicular distance between that point and the horizontal and vertical axes, which are commonly referred to as the x-axis and y-axis.

Location is then written as (a,b), where 'a' is the point's shortest distance from the y-axis, 'b' is the point's shortest distance from the x-axis, and 'c' is the point's shortest distance from the x-axis.

Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ).

Mathematics, scientists, and engineers frequently employ a variety of coordinate systems.

Hence the missing coordinates are coordinates 3 and 4.

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Answer:

C. (-2.2, -3)

Answer:

No

Step-by-step explanation

because 5+2=7 so I don't have a piece of cake left over

Answer:

  b, c e

Step-by-step explanation:

A congruence statement lists corresponding parts in the same order. CPCTC says corresponding parts are congruent.

__

To see if any particular statement is consistent with CPCTC, identify the locations of the referenced parts in the congruence statement. If they match, the congruence is true

  a. l = r ... jkl = rst . . . . not in the same place

  b. jk = rs ... jkl = rst . . . . a match; true

  c. k = s ... jkl = rst . . . . a match; true

  d. j = s ... inconsistent with (c)

  e. kl = st ... jkl = rst . . . . a match; true

  f. jl = rs ... inconsistent with (b)

Statements b, c, e are consistent with the congruence statement, and are true by CPCTC.

Answer:

Step-by-step explanation:

Let the base camp is point A and boats' locations after two hours are points B and C.

By connecting the three points together we get a triangle ABC with sides:

The angle between AB and AC is:

We are looking for the distance BC, which can be found by using the law of cosines:

The distance between the boats is 197.93 km.

Answer: See Attachment

Step-by-step explanation: I wasn’t sure if you meant -2 < x, but that’s the work I did to get the answer. If you can, send a picture of the question itself in case you didn’t mean -2 < x.

Answer:

With monthly compounding, the bank will calculate interest on your account just once per month. It will not update your balance on a daily basis when it calculates how much interest it owes you. Assuming that the APR is the same, accounts with monthly compounding offer a lower APY than accounts with daily compounding.

Answer:

F (3)=-1

Step-by-step explanation:

The domain consists of the pre-images and the range has the images. We have the f (3)=-1 since -1 is the image of 3. When we are looking for the function of a number and we are given a diagram of such, we just need to take the value of the number it is pointing to.