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3 years ago

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

Mathematics

1 answer:

mihalych1998 [28]3 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.

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Mohamed decided to track the number of leaves on the tree in his backyard each year The first year there were 500 leaves Each ye

svetlana [45]

Answer:

The required recursive formula is

$f(n)= 500\times(1.4)^{n-1}\\$

Step-by-step explanation:

Mohamed decided to track the number of leaves on the tree in his backyard each year.

The first year there were 500 leaves

$Year \: 1 = 500$

Each year thereafter the number of leaves was 40% more than the year before so that means

$Year \: 2 = 500(1+0.40) = 500\times 1.4\\$

For the third year the number of leaves increase 40% than the year before so that means

$Year \: 3 = 500\times 1.4(1+0.40) = 500 \times 1.4^{2}\\$

Similarly for fourth year,

$Year \: 4 = 500\times 1.4^{2}(1+0.40) = 500\times 1.4^{3}\\$

So we can clearly see the pattern here

Let f(n) be the number of leaves on the tree in Mohameds back yard in the nth year since he started tracking it then general recursive formula is

$f(n)= 500\times(1.4)^{n-1}\\$

This is the required recursive formula to find the number of leaves for the nth year.

Bonus:

Lets find out the number of leaves in the 10th year,

$f(10)= 500\times(1.4)^{10-1}\\\\f(10)= 500\times(1.4)^{9}\\\\f(10)= 500\times20.66\\\\f(10)= 10330$

So there will be 10330 leaves in the 10th year.

3 0

2 years ago

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marysya [2.9K]

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3 years ago

4x - (-6) what’s the answer

OlgaM077 [116]

Answer:

4x + 6

Step-by-step explanation:

If i remember correctly, two minuses make a positive, so -(-6) would turn into +6. I dont think that you can add a number with a variable to a regualar number so the answer is as simplified as it can get. If that one is wrong, try 10x. Hope this helps!

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2 years ago

What’s the correct answer for this question?

xxMikexx [17]

Answer:

12.22

Step-by-step explanation:

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