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Vesna [10]
3 years ago
7

Solve the Linear-Quadratic System of Inequalities. Shade the solution on the graph provided.

Mathematics
1 answer:
Pachacha [2.7K]3 years ago
3 0

Answer:

We have the system:

y > x^2 - 1

y < (-1/2)*x + 3

To find the solutions of this set we need to graph the solutions range of both sets, and see the intersection between these solution ranges.

How we do it?

Start with the first one.

First, we graph the equation:

y = x^2 - 1

Now because we are using the symbol ">" means that y is smaller than the thing at the right, then the graph of the equation will be with a dashed line (which means that the points on the line are not solutions) and we will shade all the region above the line

For the other inequality we do the same:

First we graph:

y = (-1/2)*x + 3

And because we have the symbol "<" we again use a dashed line, but this time we will shade all the region below the line.

Once we shaded both regions, the region where we have both shades will be the region of solutions for the system of inequalities.

You can see the graph below.

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What’s the class width
aksik [14]

Answer:

4

Step-by-step explanation:

Class width is said to be the difference between the upper class limit and the lower class limit consecutive classes of a grouped data. To calculate class width, this formula can be used:

CW = UCL - LCL

Where,

CW= Class width

UCL= Upper class limit

LCL= Lower class limit

From the table above:

For class 1, CW = 64 - 60 = 4

For class 2, CW = 69 - 65 = 4

For class 3, CW = 74 - 70 = 4

For class 4, CW = 79 - 75 = 4

For class 5, CW = 84 - 80 = 4

Therefore, the class width of the grouped data = 4

6 0
3 years ago
Find all the zeros of the equation
lapo4ka [179]

Divide both sides by -3, and replace x^2 with y. Then

-3x^4+27x^2+1200=0\iff y^2-9y-400=0

Factorize the quadratic in y to get

y^2-9y-400=(y+16)(y-25)=0\implies y=-16,y=25

which in turn means

x^2=-16,x^2=25

But x^2\ge0 for all real x, so we can ignore the first solution. This leaves us with

x^2=25\implies x=\pm\sqrt{25}=\pm5

If we allow for any complex solution, then we can continue with the solution we ignored:

x^2=-16\implies x=\pm\sqrt{-16}=\pm i\sqrt{16}=\pm4i

6 0
3 years ago
What is the scale factor of ABC to A DEF?
vampirchik [111]

Answer:

6

Step-by-step explanation:

All sides of triangle EFD have x6 of BAC.

E.g.: BA = 2. ED = 2 x 6 = 12

8 0
3 years ago
A regular pentagon with a perimeter of 21 inches is dilated by a scale factor of
levacccp [35]
<h3>Answer: 35 inches</h3>

Each side of the pentagon is multiplied by 5/3 to get the length of each new side, so the perimeter is multiplied by 5/3 to get the new perimeter.

New perimeter = (scale factor)*(old perimeter)

New perimeter = (5/3)*(old perimeter)

New Perimeter = (5/3)*(21)

New Perimeter = (5/3)*(21/1)

New Perimeter = (5*21)/(3*1)

New Perimeter = 105/3

New Perimeter = 35 inches

5 0
3 years ago
Read 2 more answers
&lt;A and &lt;J are complementary angles. Find the value of x m&lt;A = 5x + 30 m&lt;J = 4x +15
uranmaximum [27]

Sum of complementary angles always equal to 90°.

Given, <A and <J are complementary angles. So, we can set up an equation as following:

m<A+ M<J= 90

Next step is to plug in m<A = 5x + 30 and m<J = 4x +15 in the above equation. So we will get,

5x+30+4x+15=90

(5x+4x)+(30+15)=90 Group the like terms.

9x+45=90 Combine the like terms.

9x+45-45=90-45 Subtract 45 from each sides.

9x=45 By simplifying.

\frac{9x}{9}=\frac{45}{9} Divide each sides by 9.

x=5.

So, x=5.

8 0
3 years ago
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