All categories

2 years ago

Find the equation of a line with slope 1/2 through the point (10,12)

Mathematics

1 answer:

mihalych1998 [28]2 years ago

5 0

Answer:

$x-2y+14=0$

Step-by-step explanation:

$Slope \:( m) =\frac{1}{2}$

$(x_1 \:y_1) =(10, \:12)$

Equation of line in point slope form is given as:

$y-y_1 =m(x-x_1)$

Plugging the values of m and $(x_1 \:y_1)$ , we find:

$y-12=\frac{1}{2} (x-10)$

$2y-24=x-10$

$0=x-10-2y+24$

$x-2y+14=0$

This is the required equation of line.

You might be interested in

Let C(n, k) = the number of k-membered subsets of an n-membered set. Find (a) C(6, k) for k = 0,1,2,...,6 (b) C(7, k) for k = 0,

vladimir1956 [14]

Answer:

(a) $C(6,0) = 1$ , $C(6,1) = 6$ , $C(6,2) = 15$ , $C(6,3) = 20$ , $C(6,4) = 15$ , $C(6,5) = 6$ , $C(6,6) = 1$ .

(b) $C(7,0) = 1$ , $C(7,1) = 7$ , $C(7,2) = 21$ , $C(7,3) = 35$ , $C(7,4) = 35$ , $C(7,5) = 21$ , $C(7,6) = 7$ , $C(7,7)=1$ .

Step-by-step explanation:

In this exercise we only need to recall the formula for C(n,k):

$C(n,k) = \frac{n!}{k!(n-k)!}$

where the symbol $n!$ is the factorial and means

$n! = 1\cdot 2\cdot 3\cdot 4\cdtos (n-1)\cdot n$ .

By convention 0!=1. The most important property of the factorial is $n!=(n-1)!\cdot n$ , for example 3!=1*2*3=6.

(a) The explanations to the solutions is just the calculations.

$C(6,0) = \frac{6!}{0!(6-0)!} = \frac{6!}{6!} = 1$

$C(6,1) = \frac{6!}{1!(6-1)!} = \frac{6!}{5!} = \frac{5!\cdot 6}{5!} = 6$

$C(6,2) = \frac{6!}{2!(6-2)!} = \frac{6!}{2\cdot 4!} = \frac{5!\cdot 6}{2\cdot 4!} = \frac{4!\cdot 5\cdot 6}{2\cdot 4!} = \frac{5\cdot 6}{2} = 15$

$C(6,3) = \frac{6!}{3!(6-3)!} = \frac{6!}{3!\cdot 3!} = \frac{5!\cdot 6}{6\cdot 6} = \frac{5!}{6} = \frac{120}{6} = 20$

$C(6,4) = \frac{6!}{4!(6-4)!} = \frac{6!}{4!\cdot 2!} = frac{5!\cdot 6}{2\cdot 4!} = \frac{4!\cdot 5\cdot 6}{2\cdot 4!} = \frac{5\cdot 6}{2} = 15$

$C(6,5) = \frac{6!}{5!(6-5)!} = \frac{6!}{5!} = \frac{5!\cdot 6}{5!} = 6$

$C(6,6) = \frac{6!}{6!(6-6)!} = \frac{6!}{6!} = 1$ .

(b) The explanations to the solutions is just the calculations.

$C(7,0) = \frac{7!}{0!(7-0)!} = \frac{7!}{7!} = 1$

$C(7,1) = \frac{7!}{1!(7-1)!} = \frac{7!}{6!} = \frac{6!\cdot 7}{6!} = 7$

$C(7,2) = \frac{7!}{2!(7-2)!} = \frac{7!}{2\cdot 5!} = \frac{6!\cdot 7}{2\cdot 5!} = \frac{5!\cdot 6\cdot 7}{2\cdot 5!} = \frac{6\cdot 7}{2} = 21$

$C(7,3) = \frac{7!}{3!(7-3)!} = \frac{7!}{3!\cdot 4!} = \frac{6!\cdot 7}{6\cdot 4!} = \frac{5!\cdot 6\cdot 7}{6\cdot 4!} = \frac{120\cdot 7}{24} = 35$

$C(7,4) = \frac{7!}{4!(7-4)!} = \frac{6!\cdot 7}{4!\cdot 3!} = frac{5!\cdot 6\cdot 7}{4!\cdot 6} = \frac{120\cdot 7}{24} = 35$

$C(7,5) = \frac{7!}{5!(7-2)!} = \frac{7!}{5!\cdot 2!} = 21$

$C(7,6) = \frac{7!}{6!(7-6)!} = \frac{7!}{6!} = \frac{6!\cdot 7}{6!} = 7$

$C(7,7) = \frac{7!}{7!(7-7)!} = \frac{7!}{7!} = 1$

For all the calculations just recall that 4! =24 and 5!=120.

6 0

2 years ago

Which names are correct for FM−→− ?

fiasKO [112]

Answer with explanation:

⇒A segment , $\Bar {AB}$ is equivalent to $\Bar {BA}$ .

⇒We can assert this by this way, if Distance between Two points A and B is 6 unit, then Distance between B and A will be 6 unit also.

So,

$\bar{FM}=\bar{MF}$

FM−→−⇒MF−→−

Option A

6 0

3 years ago

Read 2 more answers

Alyssa is 1/4 Tammy's height . If Alyssa is 1 1/2 feet tall how tall is Tammy?

denpristay [2]

Your answer would be 6 ft

you already know that Alyssa is 1 1/2 feet tall which is 1/4 of tammy's height.
so you will take 1 1/2 x 4 (the number of 1/4's needed to get a whole number) = 6 feet

3 0

2 years ago

Which symbol creates a true sentence when x equals 3?

kondaur [170]

Answer:

Step-by-step explanation:

8×3-4×2=16

7(10-3)=14

so 16 is greater

7 0

3 years ago

Mary can either take her lunch or buy it at school. It cost 1.95 to buy lunch. If she wants to spend no more than $30 on lunch p

yaroslaw [1]

Answer:

She can buy 15 lunches.

Step-by-step explanation:

1.95x15=29.25

3 0

2 years ago