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ivann1987 [24]
3 years ago
14

Solve and graph the absolute value inequality: |4x + 1| ≤ 5.

Mathematics
2 answers:
Montano1993 [528]3 years ago
8 0
Here is how you would graph it --


Andrews [41]3 years ago
7 0
You would have to do it two times, one being negative and one being positive.
4x + 1 < 5
     -1     -1
4x < 4
x < 1

4x - 1 < 5
    +1    +1
4x < 6
x < 1.5

So the answer would be x<1 and x<1.5

I hope this helps!
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A scientist needs 10 liters of a 20% acid solution for an experiment, but she has only a 5% solution and a 40% solution. To the
tamaranim1 [39]

Answer:

The volume of 40% solution= 4.3L

The volume of 5% solution= 10L - 4.3L= 5.7L

Step-by-step explanation:

From the given information:

Let consider  x to be the of volume 40% solution

therefore the volume of 5% is said to be:

10 L= 40% solution volume + 5% solution volume

10 L= (x + 5%) solution volume

making 5% solution volume the subject; we have

5% solution volume= 10 L - x

To estimate the value of the volume, we now have:

Volume  of 20% × Concentration of  20%= (Volume of 40%  × concentration40%) + (Volume of 5% × Concentration of 5% )

∴

10L  ×  20%= (x) L × 35% + 10 L × 5%

(x) L × 35 = 10L × 20 - 10 L × 5 = 10 L × 15

x L = 10L \times \dfrac{15}{35}

x = 4.28 L

x \simeq 4.3L

∴

The volume of 40% solution= 4.3L

The volume of 5% solution= 10L - 4.3L= 5.7L

8 0
4 years ago
Solve for x and round to the nearest tenth
ANEK [815]

Answer:

x = 6.0

Step-by-step explanation:

Given:

Line AB is the hypotenuse

50.1 degrees is an angle

90 degrees is a right angle

Line CB is x and is opposite to the 50.1 degree angle

Line AC is 5 and is adjacent to the 50.1 degree angle

We know we have angles of 50.1 degrees and 90 degrees

We could find the third angle by doing 180 = 50.1 + 90 + a; a = 39.9 degrees

Sin(angle) = Opp/Hyp, Cosine(angle) = Adj/Hyp, Tan(angle) = Opp/Adj

We know the adjacent length, degree of angle, and are looking for the opposite side; therefore, we can use tan(angle) = opp/adj

tan(50.1) = x/5

x = 5.9979

or

tan(angle) = opp/adj

tan(39.9) = 5/x

x = 5.9979

Round to the nearest tenth:

x = 6.0

6 0
3 years ago
Which expression is eqivalent to 10c - 6c + 3 + 7d + 12 + 4d?
vesna_86 [32]

Answer:

d. 4c + 11d + 15

Step-by-step explanation:

This is a pretty simple combining like terms problem.

10c - 6c = 4c

3 + 12 = 15

7d + 4d = 11d

Therefore, our expression will be 4c + 11d + 15.

6 0
3 years ago
Read 2 more answers
If QRST is a rectangle with QT = 30 and RS = 4x + 10, find x.
ArbitrLikvidat [17]
The opposite side pairs in a rectangle are congruent, so basically QT would be congruent to RS when you draw the rectangle and label the points.
4x+10=30
4x=20
x=5
4 0
3 years ago
Use the slope formula to find the slope of the line that passes through the points (4, -1) and (3, -1) *
GenaCL600 [577]

Answer:

slope = 0

Step-by-step explanation:

Calculate m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (4, - 1 ) and (x₂, y₂ ) = (3, - 1 )

m = \frac{-1-(-1)}{3-4} = \frac{-1+1}{-1} = \frac{0}{-1} = 0

7 0
3 years ago
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