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Scilla [17]
2 years ago
10

Match each system to the correct choice.

Mathematics
1 answer:
pogonyaev2 years ago
8 0

Answer:

Option A - Neither. Lines intersect but are not perpendicular. One Solution.

Option B - Lines are equivalent. Infinitely many solutions

Option C - Lines are perpendicular. Only one solution

Option D - Lines are parallel. No solution

Step-by-step explanation:

The slope equation is known as;

y = mx + c

Where m is slope and c is intercept.

Now, two lines are parallel if their slopes are equal.

Looking at the options;

Option D with y = 12x + 6 and y = 12x - 7 have the same slope of 12.

Thus,the lines are parrallel, no solution.

Two lines are perpendicular if the product of their slopes is -1. Option C is the one that falls into this category because -2/5 × 5/2 = - 1. Thus, lines here are perpendicular and have one solution.

Two lines are said to intersect but not perpendicular if they have different slopes but their products are not -1.

Option A falls into this category because - 9 ≠ 3/2 and their product is not -1.

Two lines are said to be equivalent with infinitely many solutions when their slopes and y-intercept are equal.

Option B falls into this category.

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Arlecino [84]
There’s no circle :/ sorry
6 0
3 years ago
1. The mechanics at Lincoln Automotive are reborning a 6 in deep cylinder to fit a new piston. The machine they are using increa
Firdavs [7]

Answer:

0.0239\frac{in^{3}}{min}

Step-by-step explanation:

In order to solve this problem, we must start by drawing a diagram of the cylinder. (See attached picture)

This diagram will help us visualize the problem better.

So we start by determining what data we already know:

Height=6in

Diameter=3.8in

Radius = 1.9 in (because the radius is half the length of the diameter)

The problem also states that the radius will increase on thousandth of an inch every 3 minutes. We can find the velocity at which the radius is increasing with this data:

r'=\frac{1/1000in}{3min}

which yields:

r'=\frac{1}{3000}\frac{in}{min}

with this information we can start solving the problem.

First, the problem wants us to know how fast the volume is increasing, so in order to find that we need to start with the volume formula for a cylinder, which is:

V=\pi r^{2}h

where V is the volumen, r is the radius, h is the height and π is a mathematical constant equal approximately to 3.1416.

Now, the height of the cylinder will not change at any time during the reborning, so we can directly substitute the provided height, so we get:

V=\pi r^{2}(6)

or

V=6 \pi r^{2}

We can now take the derivative to this formula so we get:

\frac{dV}{dt}=2(6)\pi r \frac{dr}{dt}

Which simplifies to:

\frac{dV}{dt}=12\pi r \frac{dr}{dt}

We can now substitute the data provided by the problem to get:

\frac{dV}{dt}=12\pi (1.9) (\frac{1}{3000})

which yields:

\frac{dV}{dt}=0.0239\frac{in^{3}}{min}

3 0
3 years ago
Will give brainliest Question on the picture
raketka [301]

Answer:

12

Step-by-step explanation:

since i helped can i have brainlist please :D

3 0
3 years ago
Write an equation of the line below.
katrin [286]
Hello!

The equation would be y= -2/6x + (-3). Since, the y-intercept is -3 and the slope/growth is -2/6 (it's decreasing).

To find the slope just make a growth triangle. We go down twice (then to the right 6 times).
8 0
3 years ago
the pie chart shows the information about the favourite ice cream flavour of each student in a school there are 720 students in
kirill115 [55]

Answer:

chocolate= 180 students

vanilla= 120

strawberry= 210

mango= 210

Step-by-step explanation:

The chocolate section of the pie chart is at a right angle (90 degrees), which means a quarter of the students prefer chocolate

720/4= 180

The vanilla section is 60 degrees which is 2/3 of 90

180/3=60

60x2=120

the mango and strawberry sections represent whats left which is 420 students. The sections are equal to each other so they're each 210 students

7 0
3 years ago
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