The sum of the angle measures of a polygon with s sides is 2520 find s

Determine the equation of the line that goes through points (1.1) and (3.7).

ValentinkaMS [17]

Answer:

The equation of the line that goes through points (1,1) and (3,7) is $\mathbf{y=3x-2}$

Step-by-step explanation:

Determine the equation of the line that goes through points (1,1) and (3,7)

We can write the equation of line in slope-intercept form $y=mx+b$ where m is slope and b is y-intercept.

We need to find slope and y-intercept.

Finding Slope

Slope can be found using formula: $Slope=\frac{y_2-y_1}{x_2-x_1}$

We have $x_1=1, y_1=1, x_2=3, y_2=7$

Putting values and finding slope

$Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{7-1}{3-1}\\Slope=\frac{6}{2}\\Slope=3$

We get Slope = 3

Finding y-intercept

y-intercept can be found using point (1,1) and slope m = 3

$y=mx+b\\1=3(1)+b\\1=3+b\\b=1-3\\b=-2$

We get y-intercept b = -2

So, equation of line having slope m=3 and y-intercept b = -2 is:

$y=mx+b\\y=3x-2$

The equation of the line that goes through points (1,1) and (3,7) is $\mathbf{y=3x-2}$

4 0

2 years ago

How much do you need to subtract from 41/6 to get 6

Svetllana [295]

Well 41 divided by 6 is 6.8333333333333 so you just need to subtract .833333333333

I hope this answered your question

3 0

3 years ago

13. 11 = 2b +17 14. 5 = 4a -7

dedylja [7]

$13.\ 2b+17=11\qquad|-17\\\\2b=-6\qquad|:2\\\\\boxed{b=-3}\\\\14.\ 4a-7=5\qquad|+7\\\\4a=12\qquad|:4\\\\\boxed{a=3}\\\\16.\ 2g-3=-19\qquad|+3\\\\2g=-16\qquad|:2\\\\\boxed{g=-8}\\\\17.\ 5x-9=16\qquad|+9\\\\5x=25\qquad|:5\\\\\boxed{x=5}\\\\19.\ 5+\dfrac{y}{8}=-3\qquad|-5\\\\\dfrac{y}{8}=-8\qquad|\cdot8\\\\\boxed{y=-64}$

3 0

3 years ago

If the cubic function P(x) includes the points (−1, 0), (−2, 0), (3, 0), and (0, −12) which of the following represents this fun

zhannawk [14.2K]

I think the answer would be <span>2(x + 1)(x + 2)(x - 3).
Hope this helped! :) </span>

3 0

2 years ago

Choose 5 cards from a full deck of 52 cards with 13values (2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A) and 4 kinds(spade, diamond, h

Delvig [45]

Answer:

a) 182 possible ways.

b) 5148 possible ways.

c) 1378 possible ways.

d) 2899 possible ways.

Step-by-step explanation:

The order in which the cards are chosen is not important, which means that we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In this question, we have that:

There are 52 total cards, of which:

13 are spades.

13 are diamonds.

13 are hearts.

13 are clubs.

(a)Two-pairs: Two pairs plus another card of a different value, for example:

2 pairs of 2 from sets os 13.

1 other card, from a set of 26(whichever two cards were not chosen above). So

$T = 2C_{13,2} + C_{26,1} = 2*\frac{13!}{2!11!} + \frac{26!}{1!25!} = 182$

So 182 possible ways.

(b)Flush: five cards of the same suit but different values, for example:

4 combinations of 5 from a set of 13(can be all spades, all diamonds, and hearts or all clubs). So

$T = 4*C_{13,5} = 4*\frac{13!}{5!8!} = 5148$

So 5148 possible ways.

(c)Full house: A three of a kind and a pair, for example:

4 combinations of 3 from a set of 13(three of a kind ,c an be all possible kinds).

3 combinations of 2 from a set of 13(the pair, cant be the kind chosen for the trio, so 3 combinations). So

$T = 4*C_{13,3} + 3*C_{13.2} = 4*\frac{13!}{3!10!} + 3*\frac{13!}{2!11!} = 1378$

So 1378 possible ways.

(d)Four of a kind: Four cards of the same value, for example:

4 combinations of 4 from a set of 13(four of a kind, can be all spades, all diamonds, and hearts or all clubs).

1 from the remaining 39(do not involve the kind chosen above). So

$T = 4*C_{13,4} + C_{39,1} = 4*\frac{13!}{4!9!} + \frac{39!}{1!38!} = 2899$

So 2899 possible ways.

4 0

2 years ago