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A rectangular pyramid is sliced parallel to its base as shown in the figure.

What is the shape of the resulting two-dimensional cross section?

Select from the drop-down menu to correctly complete the statement.

The shape of the resulting two-dimensional cross section is a
Choose...
.

Answer:

A. y = 1/4x - 2

Step-by-step explanation:

The y- coordinate is placed at -2, on the y-axis

Then the line rises up 1 unit, and runs 4 units, landing on a point and forming the line.

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Answer:

7.8 for 1 cake so add that to your total

Step-by-step explanation:

Answer:

1 and 8,  4 and 5

Step-by-step explanation:

There are two pairs, 1 and 8,  4 and 5

The angles in each pair must be on opposite sides of the transversal k, and on the outsides of the parallel lines l and m.

Answer:

Option B

Step-by-step explanation:

Given the piecewise function, we see that there are two vertical asymptotes at lines x=-3 and x=3. Around the vertical asymptote x=-3, the limit of the function f(x) as x approaches -3 from the left side is ∞, and the limit of the function as x approaches -3 from the right side is -∞. The behavior of the function around the vertical asymptote x=3 is exactly the same. Therefore, option B is correct.

The statement which describes the behaviour of the function round the vertical asymptotes is b which is around x=-3+ limit of f(x)-=infinity and for limit f(x)+ is -x. Around x=3 the function behaves within the same manner as around x=-3.

Limit of a function describes the behaviour of a function as when the function behaves at a specific point.

We can see that there are two vertical asymptotes at lines x=-3 and x=3. round the vertical asymptote x=-3 the limit of the function as x approaches -3 from the left side is infinity and also the limit of the function as x approaches -3 from the proper side is -infinity.

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Algebra

Since the numbers are the same, you are allowed to add the exponents.

[tex] {7}^{7} \times {7}^{3} = {7}^{10} [/tex]

Answer:

[tex]7^{10}[/tex]

Step-by-step explanation:

The laws of exponents state that if two terms share a base they can be simplified. Specifically, the product exponent law says that if 2 like bases are being multiplied then the exponents can be added together. So, because the two bases are like and 7+3=10, the final answer is [tex]7^{10}[/tex].

Answer:

27

Step-by-step explanation:

The measure of segment YX is 27 units, the correct option is C.

Trigonometric Ratios are ratios of the side of a right angled triangle. These are used to find the missing sides and angles of a right angled triangle.

A right angled triangle is a triangle with measure of one of the angle as 90 degree.

The triangle  XYW is a right triangle, with right angle at W.

The measure of angle X is f degrees and the measure of angle Y is d degrees.

The value of the trigonometric ratio sin f = 8/9

The measure of segment YW is 24 units,

The sin of an angle is the ratio of Perpendicular to the angle and the hypotenuse of the triangle.

sin f = YW / XY

8/9 = 24 / XY

XY = 24 * 9/8

XY = 27 °

The value of YX has been determined.

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Answers:

=========================================================

Explanations:

Step-by-step explanation:

in a parallelogram, opposite angles are equal..

so C is 4a + 22. and B is 6a - 12.

sum of interior angles in a quadrilateral = 360

4a + 22. + 6a - 12. + 4a + 22. + 6a - 12 = 360

20a + 20 = 360

20a = 340

a = 17

sum of angles on a straight line = 180

B + x = 180

6 ( 17) - 12 + x = 180

102 + × = 180

× = 180 - 102

× = 78

9514 1404 393

Answer:

  m∠RPQ = 20°

Step-by-step explanation:

Exterior angle QRS is equal to the sum of interior angles RPQ and PQR.

  7x +8 = (x +12) +(3x +20)

  3x = 24 . . . . . . . . . . . . . . . . . . subtract 4x+8

  x = 8

  m∠RPQ = (x+12)° = (8+12)°

  m∠RPQ = 20°

Answer:

10=x

Step-by-step explanation:

Intersecting Chords Formula:(segment piece) x (segment piece) =

       (segment piece) x (segment piece)

6*5 = 3*x

30 = 3x

Divide by 3

30/3 = 3x/3

10 =x

Answer:

12702

Step-by-step explanation:

Since there are 2 digits after the decimal in 14.60, add a decimal to the 870 and put two 0s after it (So it looks like this 870.00)

Then put the two numbers on top of each other, make sure to line up the decimals and multiply normally. When you're done, you should come out with the number 127020000. Since there is 2 digits behind the first number and 2 digits behind the second number, resulting in 4 digits, you're gonna count 4 numbers from the back of your answer and put a decimal there (so it is now 12702.0000) but you don't really need those 0s there so you can just remove them. (Answer 12702)

Hope this helped. If not, search up "Multiply a Whole Number by a Decimal | Math with Mr. J"  it might explain better

Answer:

slope = -0.5

Step-by-step explanation:

There is a drop from 3 to 0. ∆y = -3

The run goes from  -2 to 4. ∆x = 6

slope = ∆y / ∆x

slope  = -3/6 = -1/2

slope = -0.5

Answer:

slope=-0.5

Step-by-step explanation:

(y2-y1)/(x2-x1)

(0-3)/(4-(-2))=-0.5

Answer:

3015.9

Step-by-step explanation:

its 3015.9 to nearest 10th because formula of volume of cylinder is

v = pi x radius squared x height

so pi x 8 squared = 201.06192983...

REMEMBER - dont round until the end so scientific calculator is best for this

then you do (answer) x height = 3015.9

                                        (15)

hope this helped :D

Step-by-step explanation:

everything can be found in the picture

10/3 = k/9

10 x 9 = 3 x k

90 = 3 k

k = 90/3

k = 30

Answer:

option B

Step-by-step explanation:

Given :

[tex]y = \frac{2}{3}x + 3\\\\y = \frac{5}{2}x + \frac{7}{2}\\\\[/tex]

Step 1 : simplify the equation :

[tex]3y = 2x + 9\\\\2y = 5x + 7\\[/tex]

Step 2: Arrange the terms :

[tex]2x - 3y = - 9\\\\5x -2 y = -7[/tex]

Step 3 : Solve for x and y :

                                2x - 3y = - 9 ------ ( 1 )

                                5x - 2y = - 7 --------- ( 2 )

                              _____________________

              ( 1 ) x 5 => 10x - 15y = - 45    ---------- (3 )

              ( 2) x 2 => 10x - 4y = - 14    ----------- (4 )

                             _______________________              

           ( 3 ) - ( 4 ) =>  0x - 11y = - 31

                                    - 11 y = - 31

                                        [tex]y = \frac{31}{11}[/tex]

              Substitute y in ( 1 ) :

                     2x - 3y = - 9

                     [tex]2x - 3 (\frac{31}{11}) = - 9\\\\2x = -9 + 3(\frac{31}{11})\\\\2x = - 9 + \frac{93}{11}\\\\2x = \frac{-99 + 93}{11} \\\\2x = \frac{-6}{11} \\\\x = \frac{-6}{2 \times 11} = -\frac{3}{11}[/tex]

Therefore the solution to the sytem is [tex]( - \frac{3}{11} , \frac{31}{11})[/tex]

The solution of the system of equation is a point which lies

on the both the lines.

Option A : False ,  It says the solution lies above one of the given line.

               But the solution of the system of equation always lies on

                both the line.

Option B : True , says the solution is a point on the coordinate plane.

Option C : False, because if the solution is on the x-axis , then

                  the y coordinate in the solution would be zero.

                   But it  is not zero.

Option D : False , the solution is the point where both the lines intersect.

Answer:

$20 - $1.75N

Step-by-step explanation:

the amount of change she receives is equal to the amount she paid less the total value of cards

total value of cards = price per card x total quantity of cards bought

$1.75 x N =  $1.75N

Amount of change = $20 - $1.75N

If she buys 10 cards, the amount of change she receives would be

$20 - $1.75(10) =

20 - 17.5 = 2.5

Answer:6

Step-by-step explanation:

Which graph represents the function f(x) = 5x + 3?

6

5

A++

4

34

2

1

o

-6 -5 -4 -3 -2 -14

1

2

3

4

5

х

2

3

The graph of the linear equation can be seen below.

Here we have the linear function:

y = 5x + 3

To graph this, we need to find two points on the equation and then connect them with a line.

By evaluating in 0 we get:

y = 5*0 + 3 = 3

So the point (0, 3) is on the line.

By evaluating on 1 we get:

y = 5*1 + 3 = 8

So we have the point (1, 8).

Now we just plot them and connect them with a line, the graph is the one below.

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Answer:

6

Step-by-step explanation:

Let the first number be x

Let the second number be y

x + 2y= 4............equation 1

2x +y= 11............equation 2

From equation 1

x + 2y= 4

x = 4-2y

Substitute 4-2y for x in equation 2

2x + y= 11

2(4-2y) + y= 11

8-4y+y= 11

8-3y= 11

-3y= 11-8

-3y= 3

y= -1

Substitute -1 for y in equation 1

x + 2y= 4

x + 2(-1) = 4

x-2= 4

x = 4+2

x = 6

Hence the first number is 6

Step-by-step explanation:

[tex] {(3a - \frac{1}{6} b)}^{2} = 9 {a}^{2} - \frac{1}{2} ab - \frac{1}{2} ab + \frac{1}{36} {b}^{2} [/tex]

[tex]= 9 {a}^{2} - ab + \frac{1}{36} {b}^{2} [/tex]

Answer:

x = 50.8°

Step-by-step explanation:

We are given:

1.) Angle x

2.) Side opposite to angle x

3.) Hypotenuse

Therefore to find the angle x, we will use the sin inverse:

Sin(x) = Opposite / Hypotenuse

Sin(x) = 6.2/8

x = Sin⁻¹(6.2/8)

x = 50.8°

Hope this helps!

Answer:

x = 10

Step-by-step explanation:

x - 3 + 5 = 12

x + 2 = 12

x + 2 - 2 = 12 - 2

x = 10

Answer:

x = 10

Step-by-step explanation:

x−3+5=12

Combine like terms

x +2 = 12

Subtract 2 from each side

x+2-2 = 12-2

x = 10