Is (4,3) a solution to 2x-y <4?

2 answers:

3 0

Sub the point into the inequality
2(4)-3<4
8-3<4
5<4
Therefore, no, it is not a solution because 5 is not less than 4
Hope this helps!

Alika [10]2 years ago

3 0

Well to know, just plug in the numbers!
(2) (4) - 3 < 4
8 - 3 < 4
5 < 4
4 is not greater than 5 so (4,3) can NOT be your solution

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Step-by-step explanation:

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“a railroad bridge spans a gorge 40 feet wide and connects two cliffs at heights of 98 and 158 feet above the bottom of the gorg

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Answer:

Height above the bottom gorge is 113 feet

Step-by-step explanation:

The width of the gorge = 40 feet

The height of the higher cliff = 158 feet

The height of the lower cliff = 98 feet

The length of the bridge = √((158-98)² + 40²) = 72.11 feet

The slope of the bridge = (158-98)/40 = 1.5

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The height above the bottom at 3/4 from the higher cliff = The height above the bottom at 1/4 from the lower cliff = 98+ 18.03×sin(56.31 ) = 113 feet

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2 years ago

Given the equation y=2x+3, write a second equation that would create an independent consistent linear system

STALIN [3.7K]

Two equations will be called independent if their graphs touch only on one point (they have one solution for the x-value and one solution for the y-value), and two equations will be dependent if they touch at every point (there is an infinite number of solutions).

This definition of independent and dependent equations is shown in the following diagram. Consider that there are two lines, one red line and one blue line:

They are independent if they touch only on one point and dependent if they touch at every point (they are the same line).

In our case, we are asked to write an equation in order to create an independent consistent linear system.

Note: Consistent means that the system has a solution.

First, we graph the given equation:

$y=2x+3$

There are many different equations that will form an independent consistent linear system with this equation.

We are going to choose the following line equation:

$y=-x+1$

Because when we graph this equation next to the previous line:

We can see that they touch at one point, thus there is a solution and the system is independent --> we have created an independent consistent linear system.

Answer:

$y=-x+1$