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4 years ago

Solve a combined inequality that is a conjunction of two linear equalities.

Mathematics

1 answer:

deff fn [24]4 years ago

8 0

Answer:

-10 < n < 8
5/4 < x ≤ 6

Step-by-step explanation:

1. Subtract 9:

-10 < n < 8

2. Add 12, then divide by 8:

10 < 8x ≤ 48

10/8 < x ≤ 6

5/4 < x ≤ 6 . . . . . with the fraction reduced

_____

The rules of equality allow us the do these operations, provided that we do them to all parts of the compound inequality. That is, when we say "subtract 9", we mean ...

-1 -9 < 9 +n -9 < 17 -9

This simplifies to the inequality we show above:

-10 < n < 8

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"Complete the square" to convert the equation of each circle to graphing form. Identify the center and the radius.

Reil [10]

Answer:

The center is (-3,2) and the radius is r=2

Step-by-step explanation:

The general equation of the given circle is

$x^2+6x+y^2-4y=-9$

Add the square of half the coefficient of the linear terms to both sides of the equation to obtain;

$x^2+6x+3^2+y^2-4y+(-2)^2=-9+3^2+(-2)^2$

$x^2+6x+9+y^2-4y+4=-9+9+4$

$x^2+6x+9+y^2-4y+4=4$

The quadratic trinomials in x and y on the left side of the equations are perfect squares.

We factor to obtain;

$(x+3)^2+(y-2)^2=4$

$(x--3)^2+(y-2)^2=2^2$

Comparing to:

$(x-h)^2+(y-k)^2=r^2$

The center is (-3,2) and the radius is r=2

8 0

3 years ago

The display of a student's calculator shows: 1.2731568

8_murik_8 [283]

Answer:

rational

Step-by-step explanation: because the decimal terminates, it is necessarily rational - specifically, rational with a denominator that is a power of 10. Thus 1.3 = 13/10, 0.5761 = 5761/10000, and

1.2731568 = 12731568/10000000.

6 0

4 years ago

Read 2 more answers

7(1 - y) = -3(y-2) What is the answer

Fynjy0 [20]

Answer:

$\huge y = \frac{1}{4}$

Step-by-step explanation:

$7(1 - y) = -3(y-2)$

Expand the terms in the bracket

That's

$7 - 7y = - 3y + 6$

Add 3y to both sides of the equation

$7 - 7y + 3y = 3y - 3y + 6 \\ 7 - 4y = 6$

Subtract 7 from both sides by the equation

$7 - 7 - 4y = 6 - 7 \\ - 4y = - 1$

Divide both sides by - 4

$\frac{ - 4y}{ - 4} = \frac{ - 1}{ - 4} \\$

We have the final answer as

$y = \frac{1}{4} \\$

Hope this helps you

4 0

3 years ago

A girl throws a 2 kg rock with a net force of 6 N. What is the acceleration of the rock?

krek1111 [17]

Answer:
acceleration = 3 m/s²

Explanation:
From Newton's second law:
Force = mass * acceleration
We are given that:
Force = 6 Newton
mass = 2 kg

Substitute with the givens in the above equation to get the acceleration as follows:
Force = mass * acceleration
6 = 2 * acceleration
acceleration = 6 / 2 = 3 m/s²

Hope this helps :)

8 0

3 years ago

What is the slope intercept of (1,20)(2,40)(4,80)?

AleksandrR [38]

They all have the same slope do it with the equation (y2-y1)/(x2-x1) so if you do it for all of them for example (80-40)/(4-2)=20 and the same answer goes to every single combination.

Hope this helps!

6 0

3 years ago