The sum of 3 consecutive odd numbers is 51. What is the second number in this sequence?

PLEASE SOMEONE HELP ILL GIVE BRAINLIEST!

grin007 [14]

Answer:

Part A

The rotation of the point (x, y) 180° about the origin gives the point (-x, -y)

Therefore, we have the points, ΔLMN, L(1, 1), and M(2, 2), and N(3, 3)

The coordinates of the vertices of the image, ΔL'M'N' are L'(-1, -1), and M'(-2, -2), and N'(-3, -3)

Please find attached the graph of triangle ΔLMN and ΔL'M'N'

Part B

The lines drawn through L and L' and through M and M' are colinear

Part C

A line is defined by two points, such as L and M. Rotation of a line through 180° about the origin will give an image location on the same path as the extension of the original line.

The third point, N, however, defines a plane, and the rotation of a plane by 180° will give an image which is turned upside down with regards to the preimage

Therefore, a trough in the preimage becomes a peak in the image and the lines drawn through N and N' crosses the colinear lines drawn throgh M and M' and L and L'

Step-by-step explanation:

5 0

3 years ago

draw a strip diagram to Model 5 hours 8 minutes minus 3 hours 12 minutes write an equation to find the difference

attashe74 [19]

You can convert everything in minutes once you've solved it you turn it back to hours and minutes....5hrs and 8min= 308min....3hrs 12min=192min....308-192=116.....116 is 1hr and 56min

8 0

3 years ago

Postulate: If two lines intersect, then they intersect in exactly one point. true or false

ololo11 [35]

Answer:

Step-by-step explanation:

The given postulate If two lines intersect, then they intersect in exactly one point is true because whenever the two lines intersect they intersect at one point only and we know that a postulate is a statement that we accept without proof.

The given theorem If two distinct planes intersect, then they intersect in exactly one line is true as theorem is a statement that has been proved and it has been proved that if two distinct planes intersect, then they intersect in exactly one line.

The figures are drawn to prove them.

7 0

3 years ago

You’ve been asked to order cake for your school dance. Here’s a formula for the scenario: z=xa/y

olga nikolaevna [1]

Answer:

The number of cake for order is 15 cakes .

Step-by-step explanation:

Given as :

Total number of people to attend the dance = x = 60

The number of slices each person will eat = A = 2 slices

The number of slices per cake = y = 8 slices

Let The number of cake for order = z

Now, According to question

Total slices of cake required for 60 people when each people eat 2 slices = total number of people × number of slices each person will eat

i.e Total slices of cake required for 60 people when each people eat 2 slices = x × A

Or, Total slices of cake required for 60 people when each people eat 2 slices = 60 × 2 slices

Or,Total slices of cake required for 60 people when each people eat 2 slices = 120 slices

Again

∵ number of slices per cake = 8

∴ The number of cake for order = $\dfrac{\textrm Total slices of cake required for 60 people when each people eat 2 slices}{\textrm number of slices per cake }$

Or, z = $\frac{x\times A}{y}$

i.e z = $\frac{120}{8}$

∴ z = 15 cakes

So,The number of cake for order = z = 15 cakes

Hence,The number of cake for order is 15 cakes . Answer

7 0

3 years ago

A parabola can be drawn given a focus of (-11, -2) and a directrix of x= -3

fgiga [73]

Check the picture below, so the parabola looks more or less like that.

now, the vertex is half-way between the focus point and the directrix, so that puts it where you see it in the picture, and the horizontal parabola is opening to the left-hand-side, meaning that the distance "P" is negative.

$\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\begin{cases} h=-7\\ k=-2\\ p=-4 \end{cases}\implies 4(-4)[x-(-7)]~~ = ~~[y-(-2)]^2 \\\\\\ -16(x+7)=(y+2)^2\implies x+7=-\cfrac{(y+2)^2}{16}\implies x=-\cfrac{1}{16}(y+2)^2-7$

8 0

2 years ago