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Mrrafil [7]
3 years ago
7

Please help!! Due really soon!

Mathematics
1 answer:
Alisiya [41]3 years ago
4 0

9514 1404 393

Answer:

  f(x) = 6x +1

Step-by-step explanation:

Differences in x-values (first row) are 1, 1, 1.

Differences in y-values (second row) are 6, 6, 6.

The constant ratio of differences (6/1) tells you the function is linear, and has a slope of m = 6/1 = 6.

Using the first point in the form ...

  y = mx + b

we have ...

  y = 6x + b

  7 = 6·1 + b . . . . (x, y) = (1, 7)

  1 = b . . . . . . subtract 6

Then the equation can be written ...

  y = 6x +1

In functional form, this is ...

  f(x) = 6x +1

You might be interested in
Help me Please....................
MakcuM [25]

9514 1404 393

Answer:

  1.3363

Step-by-step explanation:

The basic idea here is to find an expression for the direction vector between a point on L1 and a point on L2. Then, solve for the points on L1 and L2 that make that vector perpendicular to both lines L1 and L2. (The dot product of direction vectors is zero.) The distance between the points found is the shortest distance between the lines.

__

Let P be a point on L1. Then the parametric equation for P is ...

  P = (6t, 0, -t) . . . . . . origin + t × direction vector

Let Q be a point on L2. The direction vector for L2 is given by the difference between the given points. It is (4-1, 1-(-1), 6-1) = (3, 2, 5). Then the parametric equation for Q is ...

  Q = (3s+1, 2s-1, 5s+1) . . . . (1, -1, 1) + s × direction vector

The direction vector for PQ is ...

  Q -P = (3s+1-6t, 2s-1, 5s+1+t)

The dot product of this and the two lines' direction vectors will be zero:

  (3s+1-6t, 2s-1, 5s+1+t)·(6, 0, -1) = 0 = 13s -37t +5 . . . perpendicular to L1

  (3s+1-6t, 2s-1, 5s+1+t)·(3, 2, 5) = 0 = 38s -13t +6 . . . perpendicular to L2

The solution to these equations is ...

  s = -157/1237

  t = 112/1237

Then (Q-P) becomes (94, -1551, 564)/1237, and its length is ...

  |PQ| = √(94² +1551² +564²)/1237 ≈ 1.3363

The distance between the two lines is about 1.3363 units.

8 0
3 years ago
What is 73×28 in multiply with regrouping
klio [65]
First, u multiply 8x3. Only the 4 can go in the ones place so put the four beneath the line and put the 2 over the 7.
Multiply 8x7 and add 2.
Move to the tens place, do 2x3 then 2x7.
Add the products and put the comma. Then ur done

4 0
3 years ago
Ted has a shelf that is 75/4 inches wide. How many books can Ted arrange on the shelf if each book is 5/4 inches thick?
Paladinen [302]
(75/4) / (5/4) = 
75/4 * 4/5 = 
300/20 =
15 books

6 0
3 years ago
Help me out please???
xenn [34]

Answer:

(x,y) => (x+3, y+4)

Step-by-step explanation:

Given a triangle DEF, D(4,2), E(3,3), F(2,1).

Centroid of the area (and the vertices) equals the mean of the coordinates, namely ( (4+3+2)/3, (2+3+1)/3 ) = (3,2)

To translate (3,2) to (6,6), we need the rule

(x,y) => x+(6-3), y+(6-2), or

(x,y) => (x+3, y+4)

5 0
3 years ago
Suppose you invested $10,000 part at 6% annual interest and the rest at 9% annual interest. If you received $684 in interest aft
victus00 [196]
Assuming simple interest (i.e. no compounding within first year), then
At 6%, interest = 10000*0.06=$600
At 9% interest = 10000*0.09 = $900

Two ways to find the ratio
method A. let x=proportion at 6%
then
600x+900(1-x)=684
Expand and solve
300x=900-684=216
x=216/300=0.72 or 72%
So 10000*0.72=7200 were invested at 6%
10000-7200=2800 were invested at 9%

method B: by proportions
Ratio of investments at 6% and 9%
= 900-684 : 684-600
=216 : 84
= 18 : 7
Amount invested at 6% = 18/(18+7) * 10000 = 0.72*10000 = 7200
Amount invested at 8% = 7/(18+7)*10000=0.28*10000=2800
5 0
3 years ago
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