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2 years ago

8

What is an equation of the line that passes through the points (4,-6) and has a slope of -3

1 answer:

Akimi4 [234]2 years ago

7 0

Answer:

1) y = -3x + 6

Step-by-step explanation:

1) First, write the equation of the line in point-slope form with the given information. Use the point-slope formula $y-y_1 = m (x-x_1)$ and substitute values for $m$ , $x_1$ , and $y_1$ .

Since $m$ represents the slope, substitute -3 in its place. Since $x_1$ and $y_1$ represent the x and y values of the point the line intersects, substitute the x and y values of (4,-6) into the formula as well. This gives the following equation:

$y+6 = -3(x-4)$

2) Now, isolate the y in the equation to put it in slope-intercept form and find the answer.

$y + 6 = -3(x-4)\\y + 6 = -3x+12\\y = -3x+6$

So, the first option is correct.

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Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.

frutty [35]

<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

$2^n\leq 2^{n+1}-2^{n-1}-1$

where n is a positive integer.

Let us take n=1

then we have:

$2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2$

Hence, the result is true for n=1.

Let us assume that the result is true for n=k

i.e.

$2^k\leq 2^{k+1}-2^{k-1}-1$

Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u> $2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Let us take n=k+1

Hence, we have:

$2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)$

( Since, the result was true for n=k )

Hence, we have:

$2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2$

Also, we know that:

$-2$

(

Since, for n=k+1 being a positive integer we have:

$2^{(k+1)+1}-2^{(k+1)-1}>0$ )

Hence, we have finally,

$2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

$2^n\leq 2^{n+1}-2^{n-1}-1$ where n is a positive integer.

6 0

3 years ago

In order for a field trip to be scheduled, at least 30 students

Stella [2.4K]

Answer:

7 more students need to sign up.

Step-by-step explanation:

if you subtract the number of students needed by the number of students you have, you get 7 (30-23)

5 0

2 years ago

Read 2 more answers

UNO [17]

T - Shirts = $10
SweatShirts = 15$

24 *15 =360$

105 - 24 = 81

81 * 10 = 810$

810 + 360 = 1170$

T shirts = 81
Sweat= 24. /A\is the correct Answer

8 0

2 years ago

Vera owns 17 pairs of socks how many sock does she have in all

madam [21]

Answer:

Step-by-step explanation:

The total number of socks = 17 × 2 = 34

Since there are 2 socks in one pair

So in 17 pairs there are 34 socks

Plz mark it as brainliest

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2 years ago

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Keira rented a car for 3 days. She paid $118 rent

Stells [14]

Answer:

389

Step-by-step explanation:

3*118 + 35

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2 years ago