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Dmitriy789 [7]
1 year ago
15

Solve the inequity for x and identify the graph of its solution.|x+2|<2

Mathematics
1 answer:
sladkih [1.3K]1 year ago
3 0

Given:

|x + 2| < 2

Let's solve for x.

Given the absolute value, we have 2 conditions. They are:

x + 2 < 2 and x + 2 > -2

Let's find x for both conditions.

Condition 1:

x + 2 < 2

Subtract 2 from both sides:

x + 2 - 2 < 2 - 2

x < 0

Condition 2:

x + 2 > -2

Subtract 2 from both sides:

x + 2 - 2 > -2 - 2

x > -4

Therefore,

x < 0 and x > -4

In interval notation, we have the solution as:

(-4, 0)

The graph of the inequality is below:

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A quadratic function passes through the points ( − 5 , − 8 ) and ( 8 , − 8 ) . Find the equation for the line (axis) of symmetry
ra1l [238]

Answer:

The equation for the axis of symmetry is x=1.5.

Step-by-step explanation:

It is given that a quadratic function passes through the points ( − 5 , − 8 ) and ( 8 , − 8 ) .

In the given points y-coordinates are same, i.e., -8. It means both the points lie on the horizontal line y=-8.

If a quadratic function passes through two points (a,c) and (b,c), then the equation for the axis of symmetry is

x=\frac{a+b}{2}

According to the given points a=-5, b=8 and c=-8. Put these value in the above formula.

x=\frac{-5+8}{2}

x=\frac{3}{2}

x=1.5

Therefore the equation for the axis of symmetry is x=1.5.

8 0
3 years ago
A car travels 120 miles in 3 hours how far will it take to travel. 200 miles
docker41 [41]
Find mph
120/3 = 40 mph
200/40 = 5 hours to travel 200 miles
4 0
3 years ago
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Write the slope-intercept form of the equation of the line given the
svetoff [14.1K]

Answer:

y= -4x-7 or 4x+y= -7

Step-by-step explanation:

we know y=mx+c

given,

m=-4 c=-7

the equation y= -4x-7 or 4x+y= -7

thank u

5 0
3 years ago
Please help with problem and show work
luda_lava [24]

Answer:

x = 7

Step-by-step explanation:

The image below shows the relationship between secants chords and tangents.

Imagine that the letters in the image represent the numbers in the actually problem

E would equal 9

C would equal 12

and A would equal x

We would then use the same formula C² = E * ( E + A ) to solve for x , but once again instead of using letters we use the numbers in the problem

We would have 12² = 9( 9 + x )

we now solve for x

Step 1 simplify and distribute

12²=144

9 * 9 = 81

9 * x = 9x

we would then have 144 = 81 + 9x

step 2 subtract 81 from each side

144 - 81 = 63

81 - 81 cancels out

we now have 63 = 9x

step 3 divide each side by 9

63 / 9 = 7

9x / 9 = x

we're left with x = 7

7 0
3 years ago
9. The surface area, S, of a right rectangular prism with length l, width w, and height h can be found using the formula below.
iren [92.7K]

Answer:

Surface area is 300 in Squared

Step-by-step explanation:

2(lw + wh + hl) = rectangular Prism Formula

Length- 12

Width- 9

Height- 2

So just Substitute the values.

2( 12 x 9+ 9 x2 + 12 x 2) = ?

2(108 +18+ 24)

2 x 150

= 300

6 0
3 years ago
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