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2 years ago

Solve for |4x+3| < 9

1 answer:

7 0

Under the absolute value could be positive or negative number, but absolute value make them both positive.
For positive number we can write is (4x+3) and for negative -(4x+3)
4x+3<9
4x< 6
x< 3/2 (-∞, 3/2)

-(4x+3)<9
-4x-12<9
-4x<21
x>-21/4 (-21/4, +∞)

(-∞, 3/2)∩ (-21/4, +∞) =(-21/4, 3/2) it could be written as (-5.25, 1.5)

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How many pounds of bananas cost $3.75?

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2 years ago

Four points partition the directed line segment from A to B. • Point P partitions the directed line segment from A to B into a 3

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Answer:

S is closest to B.

Step-by-step explanation:

Given a directed line segment from point A to B.

Point P divides the line A to B in a ratio 3:4.

Point Q divides the line A to B in a ratio 4:3.

Point R divides the line A to B in a ratio 2:5.

Point S divides the line A to B in a ratio 5:2.

To find:

The point which is closest to the point B.

Solution:

Here, to find the point closest to B we need to find the distances PB, QB, RB and SB.

We can see the sum of ratio 3:4, 4:3, 2:5 and 5:2 is 7.

Let the distance between A and B be 7 units.

Now, the distances can be found easily.

$PB = \dfrac{4}{7}\times 7 = 4\ units$

$QB = \dfrac{3}{7}\times 7 = 3\ units$

$RB = \dfrac{5}{7}\times 7 = 5\ units$

$SB = \dfrac{2}{7}\times 7 = 2\ units$

The point which has the minimum distance from point B, will be nearest to B.

We can clearly observe that SB is the minimum distance.

Therefore, <em>S is closest to B</em>.

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2 years ago

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How to solve a one step equation of R+3= -6 1/2 <br> please show all the work

IgorC [24]

Solve for R:
R + 3 = -(1/2 + 6)
Put 1/2 + 6 over the common denominator 2. 1/2 + 6 = (2×6)/2 + 1/2:
R + 3 = -(2×6)/2 + 1/2
2×6 = 12:
R + 3 = -(12/2 + 1/2)
12/2 + 1/2 = (12 + 1)/2:
R + 3 = -(12 + 1)/2
12 + 1 = 13:
R + 3 = -13/2
Subtract 3 from both sides:
R + (3 - 3) = -13/2 - 3
3 - 3 = 0:
R = -13/2 - 3
Put -13/2 - 3 over the common denominator 2. -13/2 - 3 = (-13)/2 + (2 (-3))/2:
R = (-13)/2 - (3×2)/2
2 (-3) = -6:
R = (-6)/2 - 13/2
(-13)/2 - 6/2 = (-13 - 6)/2:
R = (-13 - 6)/2
-13 - 6 = -19:
Answer: R = (-19)/2

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3 years ago