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guajiro [1.7K]
3 years ago
14

A math teacher instructed students to graph the following equations on a coordinate plane. y=2.5x+2 and y=2x+4. If graphed corre

ctly at what points will the two lines intersect on the coordinate plane?
Mathematics
1 answer:
algol [13]3 years ago
8 0

Both the graphical lines will intersect at (4,12)

Step-by-step explanation:

Step 1; We must find the point in the graph where the lines of y=2.5x+2 and y=2x+4 intersect. To find out the intersecting point we must substitute values of x in both equations and see in which co-ordinate they are the same.

Step 2; We plot various values of x on the line governed by the equation y=2.5x+2

For a value of x=1 , y=2.5(1) + 2 = 4.5

For a value of x=2 , y=2.5(2) + 2 = 7

For a value of x= 3, y=2.5(3) + 2 = 9.5

For a value of x= 4, y=2.5(4) + 2 = 12

For a value of x= 5, y=2.5(5) + 2 = 14.5

Step 3; Now we also plot the values of x on the other line governed by y=2x+4

For a value of x= 1, y=2(1) + 4 = 6

For a value of x= 2, y=2(2) + 4 = 8

For a value of x= 3, y=2(3) + 4 = 10

For a value of x= 4, y=2(4) + 4 = 12

For a value of x= 5, y=2(5) + 4 = 14

Step 4; For both lines we must see if any of the values repeat at a particular point. In this case at the point (4,12) repeats for both so that becomes the point of intersection.

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Which graph shows the solution to the system of linear inequalities?
tangare [24]

Answer:

  • See below

Step-by-step explanation:

<u>Given system:</u>

  • y ≥ 2x + 1
  • y ≤ 2x – 2

The solution is the common area shaded by the inequalities.

The lines are parallel because of same slope.

Both lines are solid because of equal sign in both inequalities.

The first inequality has a y-intercept of 1 and shaded area is to the left of the line since the value of y is greater as x increases.

The second inequality has a y-intercept of -2 and shaded area is to the right of the line since the value of y is greater as x increases.

The matching graph is the second picture (or attached below) and there is no solution.

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2 years ago
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181 is 22% of what number?
baherus [9]

Answer:

Step-by-step explanation:822.73

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6 0
3 years ago
The fox population in a certain region has a continuous growth rate of 6 percent per year. It is estimated that the population i
Ksivusya [100]

Answer:

P(t) = 9800(1.06)^t

P(8) = 15620

Step-by-step explanation:

For growth the equation is

y = ab^x  where a is the initial value, b = 1 plus the growth percentage, and x is the number of years

P(t) = 9800 (1+.06) ^t

P(t) = 9800(1.06)^t

from 2000 to 2008 is 8 years

P(8) = 9800(1.06)^8

15619.71113040224768

We can only have whole foxes

P(8) = 15620

3 0
3 years ago
An unfair coin with​ Pr[H] = 0.2 is flipped. If the flip results in a​ head, a marble is selected at random from a urn containin
satela [25.4K]
Normally when dealing with coins the probability of getting heads or tails is 0.5 each. However in this case since its an unfair coin, the probability of getting heads is 0.2. 
H - head 
T - tails
R - red marble
pr (H) = 0.2
urn
6 red and 4 blue
pr (T)   = 0.8
urn
3 red and 5 blue

when heads is obtained 
red - 6/10 -0.6
blue - 4/10 - 0.4
therefore when multiplying with 0.2 probability of getting heads
pr (R ∩ H) red - 0.6*0.2 = 0.12

when tails is obtained 
red - 3/8 - 0.375
blue - 5/8 - 0.625
when multiplying with 0.8 probability of getting tails
pr (R ∩ T) red - 0.375 * 0.8 = 0.3

using bayes rule the answer can be found out, 
the following equation is used;
pr (H | R) = pr (R ∩ H) / {pr (R ∩ H) + pr (R ∩ T)}
               = 0.12 / (0.12 + 0.3)
               = 0.12 / 0.42
               = 0.286
the final answer is 0.286
6 0
3 years ago
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