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2 years ago

Graph the line with slope 1/2 that passes through the point (-1,2).

Mathematics

1 answer:

enyata [817]2 years ago

8 0

9514 1404 393

Answer:

see the attachment for a graph

Step-by-step explanation:

With the given point and slope, the equation of the line can be written in point-slope form:

y -k = m(x -h) . . . . . line with slope m through point (h, k)

y -2 = 1/2(x +1) . . . . line with slope 1/2 through point (-1, 2)

Slope is the ratio of rise to run, so a slope of 1/2 means the line will rise 1 unit for each 2 units of run (to the right). If you're plotting this by hand, you can identify a second point that is 2 right and 1 up from the given point:

(-1 +2, 2 +1) = (1, 3).

You can draw your line through those two points.

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Andrew is hiking in a mountainous area of a state park. Use the given key features to sketch a graph.

Molodets [167]

Using the features, a piece-wise function is defined, and the graph is sketched at the end of this answer.

A piece-wise function is a function that has multiple definitions, depending on the value of the input.

He starts at 0 feet, and reaches a maximum elevation of 800 feet in 30 minutes, with a steady(linear) increase thus, for the first 30 minutes, the definition is:

$h(t) = \frac{800}{30}t, 0 \leq t < 30$

For the next 5 minutes, he stops to rest, at the maximum elevation of 800 feet, thus, the definition is:

$h(t) = 800, 30 \leq t < 35$

For the final 20 minutes, he descends 800 meters, at a linear rate, thus:

$h(t) = 800 -\frac{800(t-35)}{20} = 800 - 40(t - 35), 35 \leq t \leq 55$

Using these definitions, the graph is sketched at the end of this answer.

A similar problem is given at brainly.com/question/13205719

7 0

2 years ago

Graphing exponential functions and then State the domain, range and asymptote

Luda [366]

9514 1404 393

Answer:

D: all real numbers

R: f(x) > 0

A: f(x) = 0

(-∞, 0), (+∞, +∞)

vertical stretch by a factor of 2; left shift 2 units

Step-by-step explanation:

The transformation ...

g(x) = a·f(b(x -c)) +d

does the following:

vertical stretch by a factor of 'a'
horizontal compression by a factor of 'b'
translation right by 'c' units
translation up by 'd' units

For many functions, horizontal coordinate changes are indistinguishable from vertical coordinate changes. Exponential functions tend to be one of those.

Using the above notation, you seem to have f(x) = 3^x, and g(x) = 2f(x+2). The transformation is a vertical stretch by a factor of 2, and a translation left 2 units.

As with all exponential functions, ...

the domain is "all real numbers"
the range is all numbers above the asymptote: f(x) > 0
the horizontal asymptote is f(x) = 0

The function is a growth function, so ...

x → -∞, f(x) → 0
x → ∞, f(x) → ∞

_____

Additional comment

The left shift is equivalent to an additional vertical stretch. The function could be rewritten as ...

f(x) = 18(3^x)

with no left shift and a vertical stretch by a factor of 18 instead of 2.

6 0

2 years ago

Suppose a room is 5.2 m long by 4.3m wide and 2.9 m high and has an air conditioner that exchanges air at a rate of 1200 L/min.

Readme [11.4K]

Answer:

54 minutes

Step-by-step explanation:

From the question, we are given;

A room with dimensions 5.2 m by 4.3 m by 2.9 m
The exchange air rate is 1200 L/min

We are required to determine the time taken to exchange the air in the room;

First we are going to determine the volume of the room;

Volume of the room = length × width × height

= 5.2 m × 4.3 m × 2.9 m

= 64.844 m³

Then we should know, that 1 m³ = 1000 L

Therefore, we can convert the volume of the room into L

= 64.844 m³ × 1000 L

= 64,844 L

But, the rate is 1200 L/min

Thus, time = Volume ÷ rate

= 64,844 L ÷ 1200 L/min

= 54.0367 minutes

= 54 minutes

Therefore, it would take approximately 54 minutes

4 0

2 years ago

Add the two expressions. 8.9x−5 and −6.8x+8 Enter your answer, in simplified form, in the box.

Verizon [17]

Let's simplify step-by-step.8.9x−5−6.8x+8=8.9x+−5+−6.8x+8

Combine Like Terms:=8.9x+−5+−6.8x+8=(8.9x+−6.8x)+(−5+8)=2.1x+3

The simplified answer is 2.1x+3

8 0

2 years ago

bob's deep sea fishing charges customers a flat fee of $75 plus $25 per hour spent at sea. complete the table and graph to show

Gemiola [76]

Answer:

I think the relationship is proportional.

Step-by-step explanation:

6 0

1 year ago