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Anit [1.1K]
3 years ago
7

What is the orthocenter of the triangle with two altitudes given by the lines x = -1 and y = x+1

Mathematics
1 answer:
zysi [14]3 years ago
3 0
Answer: (-1,0)

------------------------------------------------

Explanation:

A quick method is to simply look at the graph and notice the two altitudes cross at (-1,0)

----------

A longer method involves a bit of algebra but its not too bad

y = x+1
y = -1+1 ... plug in x = -1 (ie replace x with -1)
y = 0
So when x = -1, the value of y is y = 0
They pair up to get (x,y) = (-1,0) which confirms what the graph is showing

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30 POINTS!! WILL VOTE BRAINIEST
Alex787 [66]
Part A:

Consider from x = -5 to x = -4, they are 1 unit apart and the difference of their outputs is given by:

-3 - (-11) = -3 + 11 = 8.

Thus, the value of the output increases by 8 units for each one unit increase in the input.



Part B:

Consider from x = -3 to x = -1, they are 2 units apart and the difference of their outputs is given by:

21 - 5 = 16.

Thus, the value of the output increases by 16 units for each two units increase in the input.



Part C:

Consider from x = 0 to x = 3, they are 3 units apart and the difference of their outputs is given by:

53 - 29 = 24.

Thus, the value of the output increases by 24 units for each three units increase in the input.



Part D:

It can be noticed that the ratio difference in the outputs to the input intervals are equal for all the given input intervals.

i.e 8 / 1 = 16 / 2 = 24 / 3.
7 0
3 years ago
A geometric sequence has an initial value of 2 and a common ratio of 3. Which formula would be more practical to use if you were
Makovka662 [10]

Answer:

19th term = ar^18

19th term = 774,840,978

Step-by-step explanation:

First term, a = 2

Common ratio, r = 3

nth term of a geometric sequence = ar^(n-1)

19th term = ar^(19-1)

19th term = ar^18

= 2 × 3^18

= 2 × 387,420,489

= 774,840,978

19th term = 774,840,978

8 0
3 years ago
I NEED MEGA HELP WITH THIS QUESTION
katrin2010 [14]

Answer:

C. y =  -  \frac{1}{4} x - 2

Step-by-step explanation:

To find slope using coordinates, use the formula above.

(4, - 3) \: (0, - 2)→ \frac{ - 2 - ( - 3)}{0 - 4}→ \frac{ - 2 + 3}{ - 4} → -  \frac{1}{4}

Now, using the y = mx + b formula, plug in -  \frac{1}{4} as m (slope) and either coordinate as the x and y values. It looks like this:

- 3 =   - \frac{1}{4}(4)  + b

To solve for b, continue to use PEMDAS.

- 3 =   - \frac{1}{4}(4)  + b→ - 3 =  - 1 + b→ - 2 = b

Now use m and b to solve for your equation:

y =  -  \frac{1}{4} x - 2

The answer is C.

4 0
3 years ago
How much money does the dessert store make from selling three muffins and four cakes?
Lapatulllka [165]

Answer:

If everything is a dollar then the store will make $7 from selling all of those treats.

Step-by-step explanation:

:D

8 0
3 years ago
Literal Equations: 8c + 6j = 5p, for c
bixtya [17]
8c + 6j = 5p         Subtract 6j from both sides
       8c = 5p - 6j   Divide both sides by 8
         c = \frac{5p - 6j}{8}
3 0
3 years ago
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