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2 years ago

Find a linear inequality with the following solution set. Each grid line represents one unit.

Mathematics

1 answer:

ikadub [295]2 years ago

5 0

The linear inequality in standard form is: x + y < -2 or x + y + 2 < 0

<h3>How to Write a Linear Inequality?</h3>

To determine what sign to use, follow these rules:

Use "<" or ">" when the boundary line is dotted or dashed.
Use "<" or "≤" when the shaded area is under the boundary line (dotted or dashed).
Use "≤" or "≥" when the boundary line is not dotted or dashed.
Use ">" or "≥" when the shaded area is above the boundary line (dotted or dashed).

The graph given has the following features:

It has a boundary line that is dotted/dashed.
It has a shaded area that is under the boundary line.
Thus, the inequality sign we would use is, "<".

Find the slope:

Slope (m)= rise/run = -(2 units) / (2 units).

Slope (m) = -1.

The y-intercept (b) = -2.

Substitute m = -1 and b = -2 into y < mx + b:

y < (-1)x + (-2)

y < -x - 2

Rewrite

x + y < -2

x + y + 2 < 0

Learn more about inequality on:

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3 years ago

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Topic: The Quadratic Formula

Finger [1]

Answer:

Step-by-step explanation:

The quadratic formula for a equation of form

ax²+bx + c = 0 is

$x= \frac{-b +- \sqrt{b^2-4ac} }{2a}$

For the first equation,

x²+3x-4=0,

we can match that up with the form

ax²+bx + c = 0

to get that

ax² = x²

divide both sides by x²

a=1

3x = bx

divide both sides by x

3 = b

-4 = c

. We can match this up because no constant multiplied by x could equal x² and no constant multiplied by another constant could equal x, so corresponding terms must match up.

Plugging our values into the equation, we get

$x= \frac{-3 +- \sqrt{3^2-4(1)(-4)} }{2(1)} \\= \frac{-3+-\sqrt{25} }{2} \\ = \frac{-3+-5}{2} \\= -8/2 or 2/2\\= -4 or 1$

as our possible solutions

Plugging our values back into the equation, x²+3x-4=0, we see that both f(-4) and f(1) are equal to 0. Therefore, this has 2 real solutions.

Next, we have

x²+3x+4=0

Matching coefficients up, we can see that a = 1, b=3, and c=4. The quadratic equation is thus

$x= \frac{-3 +- \sqrt{3^2-4(1)(4)} }{2(1)}\\= \frac{-3 +- \sqrt{9-16} }{2}\\= \frac{-3 +- \sqrt{-7} }{2}\\$

Because √-7 is not a real number, this has no real solutions. However,

(-3 + √-7)/2 and (-3 - √-7)/2 are both possible complex solutions, so this has two complex solutions

Finally, for

4x² + 1= 4x,

we can start by subtracting 4x from both sides to maintain the desired form, resulting in

4x²-4x+1=0

Then, a=4, b=-4, and c=1, making our equation

$x=\frac{-(-4) +- \sqrt{(-4)^2-4(4)(1)} }{2(4)} \\= \frac{4+-\sqrt{16-16} }{8} \\= \frac{4+-0}{8} \\= 1/2$

Plugging 1/2 into 4x²+1=4x, this works as the only solution. This equation has one real solution

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3 years ago

What is the volume of a rectangular prism with a length of 5 cm, width of 4cm, and height of

Zepler [3.9K]

Answer:

180cm^3

Step-by-step explanation:

All you have to do is multiply everything together to get the volume. l x w x h

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I need this problem to be simplified

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The correct answer would be 2y^5

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What are the coordinates of the point on the directedline segment from K(-5,-4) to L(5,1) that partitionsthe segment into a rati

Diano4ka-milaya [45]

You can solve this either just plain algebra or with the use of trigonometry.
In this case, we'll just use algebra.

So, if we let M be the the point that partitions the segment into a ratio of 3:2, we have this relation:
KM/ML = 3/2
KM = 1.5 ML

We also have this:
KL = KM + ML
Substituting KM,
KL = (3/2) ML + ML
KL = 2.5 ML

Using the distance formula and the given coordinates of the K and L, we get the length of KL
KL = sqrt ( (5-(-5)^2 + (1-(-4))^2 ) = 5 sqrt(5)

Since,
KL = 2.5 ML

Substituting KL,
ML = (1/2.5) KL = (1/2.5) 5 sqrt(5) = 2 sqrt(5)

Using again the distance formula from M to L and letting (x,y) as the coordinates of the point M
ML = 2 sqrt(5) = sqrt ( (5-x)^2 + (1-y)^2 ) [let this be equation 1]

In order to solve this, we need to find an expression of y in terms of x. We can use the equation of the line KL.
The slope m is:
m = (1-(-4))/(5-(-5) = 0.5

Using the general form of the linear equation:
y = mx +b
We substitue m and the coordinate of K or L. We'll just use K.
-5 = (0.5)(-4) + b
b = -1.5

So equation of the line is
y = 0.5x - 1.5 [let this be equation 2]

Substitute equation 2 to equation 1 and solving for x, we get 2 values of x,
x=1, x=9

Since 9 does not make sense (it does not lie on the line), we choose x=1.
Using the equation of the line, we get y which is -1.

So, we get the coordinates of point M which is (1,-1)

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3 years ago