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Vlada [557]
3 years ago
12

Simplify negative 2 and 1 over 9 – negative 4 and 1 over 3.

Mathematics
1 answer:
Ugo [173]3 years ago
4 0

Answer:

The correct answer is

2\frac{2}{9}

Step-by-step explanation:

Method 1

We want to simplify,

-2\frac{1}{9} -(-4\frac{1}{3})


The double negatives becomes positive,


=-2\frac{1}{9} +4\frac{1}{3}


We now add the whole number parts and the fractions separately


=-2+4-\frac{1}{9} +\frac{1}{3}


This will give us,

=2-\frac{1}{9} +\frac{1}{3}


The least common denominator for the fractional parts is 9.

=2+\frac{-1+3\times1}{9}


=2+\frac{-1+3}{9}


=2+\frac{2}{9}


=2\frac{2}{9}


Method 2

We want to simplify,

-2\frac{1}{9} -(-4\frac{1}{3})


The double negatives becomes positive,


=-2\frac{1}{9} +4\frac{1}{3}


We first convert the mixed numbers to improper fractions to obtain,


=-\frac{2\times9+1}{9} +\frac{4\times3+1}{3}


We carry out the multiplication in the numerator to get,


=-\frac{18+1}{9} +\frac{12+1}{3}


We add in the numerator to get,

=-\frac{19}{9} +\frac{13}{3}

The least common denominator is 9.

=\frac{-19+13\times3}{9}


=\frac{-19+39}{9}

=\frac{20}{9}

We convert back to mixed numbers to get,

=2\frac{2}{9}









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The answer is the number 1.
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3 years ago
In the figure below, points M, P, H, J, and K lie in plane Z.
marishachu [46]

Answers:

  • (a) LN
  • (b) PHJ
  • (c) K
  • (d) HK

===================================================

Explanation:

Part (a)

Lines LN and PN have the point N in common. This is the intersection point.

-----------------

Part (b)

To name a plane, pick any three non-collinear points that are inside it. We cannot pick points H, J, K together because infinitely many planes pass through it. Imagine the piece of flat paper able to rotate around this axis (like a propeller). Having the points not all on the same line guarantees we form exactly one unique plane.

I'll pick the non-collinear points P, H and J to get the name Plane PHJ. Other answers are possible.

------------------

Part (c)

Points H, J and K are collinear as they are on the same line. Pick either H or K to fill out the answer box. I'll go with point K

------------------

Part (d)

Point P and line HK are coplanar. They exist in the same flat plane, or on the same sheet of flat paper together.

We can think of that flat plane as the ground level while something like point N is underground somewhere. So point N and anything on that ground plane wouldn't be coplanar.

Note: there are other possible names for line HK such as line JH or line JK. The order doesn't matter when it comes to naming lines.

4 0
3 years ago
Noah tried to prove that cos(θ)=sin(θ) using the following diagram. His proof is not correct.
alukav5142 [94]

Answer:

The first statement is incorrect. They have to be complementary.

Step-by-step explanation:

You can't say the measure of angle B is congruent to theta because it is possible for angles in a right triangle to be different.

You can only say that what he said is true if the angle was 45 degrees, but based on the information provided it is not possible to figure that out.

The other two angles other than the right angle in a right triangle have to add up to 90 degrees, which is the definition of what it means for two angles to be complementary. A is the correct answer.

3 0
3 years ago
Read 2 more answers
What is the volume of a cylinder with a height of 2 feet and a radius of 6 feet?
melamori03 [73]
V≈226.19ft³
Hope this helped :) please mark brainlist

6 0
3 years ago
A cylinder has a base radius of 4m and a height of 6m. What is its volume in cubic m, to the nearest tenths place?
Ronch [10]
<h3>Answer:</h3>

301.6 cubic meters

<h3>Step-by-step explanation:</h3>

A cylinder is a shape with straight sides with circular or oval cross-sections. We know that the cylinder in the question must be a circular cylinder due to its radius description. 

Volume Formula

A circular cylinder has a volume of V=\pi r^2h. In this equation, V is the volume, r is the radius, and h is the height. The question tells us that r=4m and h=6m. So, we can plug these values into the formula.

Solving for Volume

To solve plug the values into the formula and rewrite the equation.

  • V=\pi *4^2*6

Next, apply the exponents.

  • V=\pi *16*6

Then, multiply the constants.

  • V=\pi *96

Finally, multiply the remaining terms. Remember to use the pi button on the calculator and not an estimation to get a more exact value.

  • V=301.6

Make sure your answer is rounded to the correct digit. This means that the volume must be 301.6 cubic meters.

6 0
2 years ago
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