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Angelina_Jolie [31]
3 years ago
12

Consider the line -x+3y=1

Mathematics
1 answer:
deff fn [24]3 years ago
6 0
The line
<span>-x+3y=1 can be moved into slope intercept form to get slope.
slope is what matters for questions that asks about perpendicular/parallel...

isolate y to get slope intercept form

</span>
<span>-x+3y=1
add x to both sides
3y = x + 1
divide both sides by 3
y = (x+1)/3
y = x/3 + 1/3

the slope is 1/3 because x/3 is the same as 1/3 * x.

the line that is perpendicular to this line has a slope that is the negative recirpocal of the original slope like.

perpendicular line slope: -3. (reciprocal of 1/3 is 3; then make that negative).

Told that this perp line passes through (7,-5), using slope intercept form y = mx + b with unknown y-intercept b value:

y = -3x + b

since (7,-5) means at x = 7, y = -5, plug those numbers in to solve for b

-5 = -3(7) + b
-5 = -21 + b
b = -5 + 21
b = 16

perpendicular line:
y = -3x + 16

for the parallel line has the same slope as the original
slope of parallel line: 1/3

we are told that parpall line goes through (7,-5) so using the unfinished slope-intercept form y = mx + b with unfinishe dinfo: we have

y = 1/3 x + b

since at x = 7 we have y = -5, plug it in

-5 = (1/3)(7) + b
-5 = 7/3 + b
b = -5 - 7/3
b = -15/3 - 7/3 .... same denominator for fraction add/subtract
b = -22/3

parallel line equation:
y = 1/3x - 22/3
</span>
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The ball followed a path modelled by the equation h = −0.001! + 0.5 + 2.5 where h is the height of the ball in feet and is the h
Mama L [17]

The heights the balls hit a fence at 350 ft distance are 65 feet, 38 feet and 30 feet, respectively

<h3>Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph. </h3>

<u>Juan</u>

Juan's equation is given as:

h = -0.001d^2 + 0.5d + 2.5

h =

Set d to multiples of 50 from 0 to 400.

So, the table of values of Juan's function is:

d (ft)                   h(ft)

0                          2.5

50                        25

100                      42.5

150                        55

200                      62.5

250                        65

300                      62.5

350                        65

400                      42.5

See attachment for the graph of Juan's function

<u>Mark</u>

A quadratic function is represented as:

h = ad^2 + bd + c

Using the values on the table of values, we have:

c = 3 -- the constant value

So, the equation becomes

h = ad^2 + bd + 3

Using the two other values on the table of values, we have:

23 = a(50)^2 + b(50) + 3

38 = a(100)^2 + b(100) + 3

Using a graphing tool, we have:

a = -0.001

b = 0.45

So, Mark's equation is h(d) = -0.001d^2 + 0.45d + 3

See attachment for Mark's graph.

<u>Barry</u>

From the graph, we have the table of values of Barry's function to be:

d (ft)                   h(ft)

0                          2.5

50                        21

100                      35

150                       44

200                      48

250                       46

300                      41

350                       30

400                      14

450                      0

Using a graphing tool, we have the quadratic function to be:

y = -0.001x^2 +0.4x +2.5

<h3><u>The shortest and the greatest distance before hitting the ground</u></h3>

From the graphs, equations and tables, the distance travelled by the balls are:

Juan = 505 feet

Mark = 457 feet

Barry = 450 feet

This means that Juan's ball would travel the greatest distance while Barry's ball would travel the shortest.

<h3>The height the balls hit a fence at 350 ft distance</h3>

To do this, we set d = 350

From the graphs, equations and tables, the height at 350 ft by the balls are:

Juan = 65 feet

Mark = 38 feet

Barry = 30 feet

The above represents the height the balls hit the fence

Read more about quadratic functions at:

brainly.com/question/12446886

#SPJ1

4 0
2 years ago
Which inequality represents all possible solutions of −6n&lt;−12?
muminat

Answer:

B n>2

Step-by-step explanation:

−6n<−12

Divide each side by -6, remembering to flip the inequality

-6n/-6 > -12/-6

n >2

5 0
3 years ago
Which point is an x-intercept Og the quadratic function f(x) = (x-4)(x+2)?
user100 [1]
<span>(-6,0) would be correct </span>
8 0
3 years ago
Read 2 more answers
...........................
cupoosta [38]

Answer:

3/5 or 0.6

Step-by-step explanation:

Here, given the value of tan theta , we want to find the value of sine theta

Mathematically;

tan theta = 0pposite/adjacent

Sine theta = opposite/hypotenuse

Firstly we need the length of the hypotenuse

This can be obtained using the Pythagoras’ theorem which states that the square of the hypotenuse equals sum of the squares of the two other sides.

Let’s call the hypotenuse h

h^2 = 3^2 + 4^2

h^2 = 9 + 16

h^2 = 25

h = √(25)

h = 5

Now from the tan theta, we know that the opposite is 3

Thus, the value of the sine theta = 3/5 or simply 0.6

5 0
3 years ago
6. Jay has a rope that is 31 ft long. He
SCORPION-xisa [38]

Answer:

No, he does not have enough rope. 0.26 ft short.

Step-by-step explanation:

3 x 10.42 = 31.26

31.26 - 31 = 0.26

3 0
3 years ago
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