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hammer [34]
3 years ago
12

Solve the following inequality algebraically. ∣x−5∣≤11

Mathematics
1 answer:
Igoryamba3 years ago
4 0

Answer:

-6\leq x\leq 16

Step-by-step explanation:

So we have the inequality:

|x-5|\leq 11

Definition of Absolute Value:

x-5\leq 11\text{ or } x-5\geq -11

Note that the sign is flipped in the second case because we multiplied by a negative.

Add 5 to both sides to both equations:

x\leq 16\text{ or } x\geq -6

Merge:

-6\leq x\leq 16

And we're done!

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It would be less because when you multiply something by 1/2 you are basically dividing it by 2, finding half. So when you multiply 9 8/9 by 1/2 your product would be less than 9 8/9
5 0
3 years ago
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In a 4 day period, a delivery person delivered the following number of
Westkost [7]

Answer: 1400 packages

Step-by-step explanation:

1150+1200+1900+1350 divided by the 4 day interval means and average of:

1400 packages per day

6 0
2 years ago
XY is a diameter of a circle and Z is a point on the circle such that ZY=6. If the area of the triangle XYZ is 18 square root 3
nataly862011 [7]
<h2>Answer:</h2>

4π

<h2>Step-by-step explanation:</h2>

As shown in the diagram, triangle XYZ is a right triangle. Therefore, its area (A) is given by:

A = \frac{1}{2} x b x h      -------------(i)

Where;

A = 18\sqrt{3}

b = XZ = base of the triangle

h = YZ = height of the triangle = 6

<em>Substitute these values into equation(i) and solve as follows:</em>

18\sqrt{3} =  \frac{1}{2} x b x 6

18\sqrt{3} =  3b

<em>Divide through by 3</em>

6\sqrt{3} =  b

Therefore, b = XZ = 6\sqrt{3}

<em>Now, assume that the circle is centered at O;</em>

Triangle XOZ is isosceles, therefore the following are true;

(i) |OZ| = |OX|

(ii) XZO = ZXO = 30°

(iii) XOZ + XZO + ZXO = 180°   [sum of angles in a triangle]

=>  XOZ + 30° + 30° = 180°

=>  XOZ + 60° = 180°

=>  XOZ = 180° - 60°

=>  XOZ = 120°

Therefore we can calculate the radius |OZ| of the circle using sine rule as follows;

\frac{sin|XOZ|}{XZ} = \frac{sin|ZXO|}{OZ}

\frac{sin120}{6\sqrt{3} } = \frac{sin 30}{OZ}

\frac{\sqrt{3} /2}{6\sqrt{3} } = \frac{1/2}{|OZ|}

\frac{1}{12}  = \frac{1}{2|OZ|}

\frac{1}{6} = \frac{1}{|OZ|}

|OZ| = 6

The radius of the circle is therefore 6.

<em>Now, let's calculate the length of the arc XZ</em>

The length(L) of an arc is given by;

L = θ / 360 x 2 π r          ------------------(ii)

Where;

θ = angle subtended by the arc at the center.

r = radius of the circle.

In our case,

θ = ZOX = 120°

r = |OZ| = 6

Substitute these values into equation (ii) as follows;

L = 120/360 x 2π x 6

L = 4π

Therefore the length of the arc XZ is 4π

5 0
3 years ago
Eric practiced piano and guitar for a total of 8 hours this week. He practiced the piano for 1/4 of that time. How many hours di
Oduvanchick [21]

Answer:

I don’t know

Step-by-step explanation:

I said idk

5 0
3 years ago
Graph the function f(x) = -3x - 2.
Elza [17]

Answer: slope is -3 and y-intercept is -2

Step-by-step explanation:

when x= 0, y=-2

when x=1, y=-5

i believe you have just to change the value of the letter x in the equation to find the value of y

5 0
3 years ago
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