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Leviafan [203]
3 years ago
8

Not sure how to graph this

Mathematics
1 answer:
pychu [463]3 years ago
5 0
<h3>Answer: Graph a straight line through (0,-4) and (1,-8)</h3><h3>See diagram below</h3>

============================================================

Explanation:

Pick any number you want for x. I find x = 0 to be easiest. Plug this into the equation to get...

y = -4x-4

y = -4(0) - 4

y = 0-4

y = -4

This is the y intercept. The graph crosses the y axis at -4. So one point on this line is (0,-4) since x = 0 and y = -4 pair up together

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

Repeat for another x value, say x = 1

y = -4x-4

y = -4(1)-4

y = -4-4

y = -8

We have x = 1 and y = -8 pair up now. Therefore another point on this line is (1,-8)

We could repeat for other x values, but we have enough info to graph this straight line. We only need two points minimum to graph a straight line.

So from here all you need to do is plot (0,-4) and (1,-8). Then draw a straight line through the two points. The line extends infinitely out in both directions.

You could use any other two points you wanted. For me I just find it easiest to work with 0 and anything close to it.

-------

Note how starting at (0,-4) we have moved 4 units down and 1 unit to the right to arrive at (1,-8). The "4 units down, 1 unit to the right" comes exactly from the slope of -4 = -4/1

slope = rise/run = -4/1

rise = -4 means we move down 4

run = 1 means we move 1 to the right

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The answer is 1
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A 2-column table has 4 rows. The first column is labeled x with entries negative 1, 0, 1, 2. The second column is labeled f (x)
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The decay factor of the exponential function given in the table is of \frac{2}{3}.

<h3>What is an exponential function?</h3>

A decaying exponential function is modeled by:

A(t) = A(0)(1 - r)^t

In which:

  • A(0) is the initial value.
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In this problem, we have that when x increases by 1, y decreases by a factor of 3, hence the decay rate r is found as follows:

1 - r = \frac{1}{3}

r = 1 - \frac{1}{3}

r = \frac{2}{3}

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6 0
2 years ago
A dog runs 100 yards from one corner of a rectangular park to the opposite corner. If the length of the park is 28 yards, what i
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9514 1404 393

Answer:

  96 yards

Step-by-step explanation:

The diagonal through the park cuts the rectangle into two right triangles. The Pythagorean theorem tells you the relationship between the sides of a right triangle and its hypotenuse: the sum of the squares of the sides is equal to the square of the hypotenuse.

The diagonal is the hypotenuse, so we have ...

  100² = 28² + w²

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The width of the park is 96 yards.

_____

<em>Additional comment</em>

The integer side lengths of a right triangle form what is called a "Pythagorean triple." One of the most often seen of these is (3, 4, 5). Other commonly seen Pythagorean triples are (5, 12, 13), (7, 24, 25), (8, 15, 17).

You may notice that the numbers here are those of the (7, 24, 25) Pythagorean triple, multiplied by 4. If you recognize the given lengths as having the ratio 28:100 = 7:25, you have the clue you need to determine the answer simply from your knowledge of Pythagorean triples.

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3 years ago
The students in the Go Green dub started a whool recling program. In
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Answer:

Students collected

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Step-by-step explanation:

In September, the students collected 85 pounds of paper and 18 pounds of cans to recycle.

In October, their goal is to collect three times the amount of paper and five times the amount of cans they collected in September.

Hence, in October they collected

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In total, they collected

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