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3 years ago

Solve each compound inequality. Graph your solutions. 5 + m > 4 or 7m< -35

Mathematics

1 answer:

Yuliya22 [10]3 years ago

5 0

Answer:

Solving the inequality $5 + m > 4\: or\: 7m< -35$ we get $\mathbf{m>-1\:or\: \:m$

The graph of the inequality is shown in figure attached.

Step-by-step explanation:

We need to Solve each compound inequality $5 + m > 4\: or\: 7m< -35$

Solving the inequalities

For solving compound inequalities we solve both inequalities simultaneously and find the value of m.

For solving 5+m > 4, we subtract 5 from both sides.

While solving 7m < -35, we divide both sides by 7 to get value of m

Applying these functions we get:

$5 + m > 4\: or\: 7m< -35\\m>4-5\:or\:m-1\:or\:m$

So, solving the inequality $5 + m > 4\: or\: 7m< -35$ we get $\mathbf{m>-1\:or\: \:m$

The graph of the inequality is shown in figure attached.

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Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

What are the coordinates of the circumcenter of this triangle?

Oduvanchick [21]

Answer:

The coordinates of the circumcenter of this triangle are (3,2)

Step-by-step explanation:

we know that

The circumcenter is the point where the perpendicular bisectors of a triangle intersect

we have the coordinates

$A(-2,5),B(-2,-1),C(8,-1)$

step 1

Find the midpoint AB

The formula to calculate the midpoint between two points is equal to

$M=(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M=(\frac{-2-2}{2},\frac{5-1}{2})$

$M_A_B=(-2,2)$

step 2

Find the equation of the line perpendicular to the segment AB that passes through the point (-2,2)

Is a horizontal line (parallel to the x-axis)

$y=2$ -----> equation A

step 3

Find the midpoint BC

The formula to calculate the midpoint between two points is equal to

$M=(\frac{x1+x2}{2},\frac{y1+y2}{2})$

substitute the values

$M=(\frac{-2+8}{2},\frac{-1-1}{2})$

$M_B_C=(3,-1)$

step 4

Find the equation of the line perpendicular to the segment BC that passes through the point (3,-1)

Is a vertical line (parallel to the y-axis)

$x=3$ -----> equation B

step 5

Find the circumcenter

The circumcenter is the intersection point between the equation A and equation B

$y=2$ -----> equation A

$x=3$ -----> equation B

The intersection point is (3,2)

therefore

The coordinates of the circumcenter of this triangle are (3,2)

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3 years ago

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Aleonysh [2.5K]

Step-by-step explanation:

do like the picture I sent

3 0

3 years ago

Solve the system and enter the smallest x-coordinate first

ankoles [38]

Answer:
(2,-3)(6,5)
Step-by-step explanation:
We can use substitution to get the equation: x^2-6x+5 = 2x-7
Solve:
x^2-6x+5 = 2x-7
x^2 = 8x-12
x^2-8x+12 = 0 (we now have a polynomial)
(x-6)(x-2) = 0 (set each equation to equal 0 and solve)
x-6 = 0 --> x=6
x-2 = 0 --> x=2
To get the Y coordinates:
y=2(2)-7 --> y = -3
y = 2(6)-7 --> y = 5

Check work:
5 = 6^2-6(6)+5 --> 5 = 36-36 +5 --> 5=5
-3 = 2^2-6(2)+5 --> -3 = 4-12+5 --> -3=-3

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2 years ago

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miss Akunina [59]

Answer:

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