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ivolga24 [154]
3 years ago
7

Verify that (a+b)+c = a+ (b+c) by taking a = -8 , b = (-8/11) , c = (-8/12)

Mathematics
2 answers:
gogolik [260]3 years ago
6 0

Answer:

Step-by-step explanation:

(-8+-\frac{8}{11} ) + (-\frac{8}{12}) = -\frac{96}{11} + (-\frac{2}{3}) = -\frac{288 + 22}{33}) = -\frac{310}{33}\\ (-8) + (-\frac{8}{11} + (-\frac{2}{3})) = (-8) + (-\frac{46}{33})= -\frac{310}{33}

Levart [38]3 years ago
3 0

Answer:

The expression is true

Step-by-step explanation:

The expression (a+b)+c = a+ (b+c) is an associative law. Given a = -8 , b = (-8/11) , c = (-8/12), we need to verify that the expression is true. To do that we need to substitute the values given into the right hand side and the also left hand side of the expression and the values gotten for both sides must be equal.

Given the left hand side to be (a+b)+c, substituting the values of a,b and c into the expression, we have:

{-8+(-8/11)}+(-8/12)

= (-8-(8/11))-8/12

= (-88-8)/11-8/12

= -96/11-8/12

= (-1152-88)/132

= -1240/132

= -620/-66

= -310/33

Similarly for the right hand side of the expression a+(b+c)

= -8+(-8/11+(-8/12))

= -8+(-8/11-8/12)

= -8+{(-96-88)/132}

= -8+(-184/132)

= (-1056-184)/132

= -1240/132

= -310/33

Since both expression are equal to -310/33, then the associative law given above is true.

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Which of the following statements is NOT true about the graph of a system of
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Answer:

The lines will have one positive y-intercept and one negative y-intercept is NOT true.

Step-by-step explanation:

If a graphed system has infinitely many solutions, that means that the two equations are the exact same. This means that they'll have the same slope, y-intercept, and will share all of the same points. Answer b is the only choice left.

5 0
3 years ago
Geometry problem help!<br><br> Please refer to the image below...
Vinil7 [7]

Answer:

A. 1/3

B. √10

C. -1, 1

D. √8, 6

E. congruent and opposite pairs parallel

F. perpendicular, not congruent

G. rhombus, explanation below

Step-by-step explanation:

Hey there! I'm happy to help!

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

A.

Slope is the rise over the run. Let's look at F to G.

We are going from -1 to 2 on our x-axis (run), so our run is 3 units.

Our rise is 1 unit as we go from 2 to 3 on the y-axis.

slope=\frac{rise}{run} =\frac{1}{3}

This slope is the same for all of the sides.

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

B.

We will use the distance formula (which is basically just the Pythagorean Theorem) to calculate the length of each side. Let's go between F and G again, but this distance is the same for all the sides.

\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-1,2)\\\\(x_2,y_2)=(2,3)\\\\\\\sqrt{(2+1)^2+(3-2)^2 } \\\\\sqrt{(3)^2+(1)^2 }\\\\\sqrt{9+1 }\\\\\sqrt{10}

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

C.

The diagonals are the lines that connect the non-adjacent vertices.

Our two diagonals are FH and GE.

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

<u>FH</u>

We go from x-value -1 to 1 from F to H, so our run is 2.

We go from y-value 2 to 0. so our rise is -2.

slope=\frac{rise}{run} =-\frac{2}{2} =-1

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

<u>GE</u>

We go from x-value -2 to 2 from E to G, so our run is 4.

We go from y-value -1 to 3. so our rise is 4.

slope=\frac{rise}{run} =\frac{4}{4} =1

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

D.

Let's use the distance formula on each of our diagonals.

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

<u>FH</u>

<u />\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-1,2)\\\\(x_2,y_2)=(1,0)\\\\\\\sqrt{(1+1)^2+(0-2)^2 } \\\\\sqrt{(2)^2+(-2)^2 }\\\\\sqrt{4+4 }\\\\\sqrt{8}<u />

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

<u>GE</u>

\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-2,-1)\\\\(x_2,y_2)=(2,3)\\\\\\\sqrt{(2+2)^2+(3+1)^2 } \\\\\sqrt{(4)^2+(4)^2 }\\\\\sqrt{16+16 }\\\\\sqrt{36}\\\\6

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

E.

They are congruent as they all have the same length (√10) and the opposite sides are parallel as they have the same slope (1/3)

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

F.

They are perpendicular diagonals as their slopes are negative reciprocals (1 and -1), and they are not congruent as they have different lengths (√8 and 6).

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

G.

<u>Parallelogram-</u> quadrilateral with opposite pairs of parallel sides.

<u>Rhombus-</u> a parallelogram with four equal sides

<u>Square-</u> a rhombus with four right angles

We can see that this is a parallelogram as we saw that the opposite sides are parallel due to having the same slope, and the perpendicular diagonals show that as well. This is also a rhombus because if we use that distance formula on all the sides, it will be the same. It is not a square though because it does not have four right angles, so this is a rhombus.

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

Have a wonderful day and keep on learning!

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Ugh, more algebra pretending to be geometry.  Why?

This is a pretty awful instance of the genre, with no units on the constant 16, assumed to be degrees.

The total arc measure in a circle is 360 degrees.  Geometry part over.

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8m = 344

m = 344/8 = 43

Arc measures:

Arc 3m+16 = 3(43)+16 = 145°.  The angle subtended by that arc is half that, 145/2=72.5°

Arc 2m=2(43)=86°.  The angle subtended is half that, 43°

Arc 3m=3(43)=129°.  The angle subtended is half that, 64.5°

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A couple has 2 children. what is the probability that both are girls if the older of the two is a girl?
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This question comes from the 'boy or girl paradox', a.k.a. the Mrs Smith Problem.
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Find the means of these numbers 3,7,2,9,4,7,3,7,5,2
Sholpan [36]

The "mean" of a group of numbers is also called their "average".

To calculate the mean, add up all the numbers, then
divide the sum by the number of items on the list.

Step #1:  Addum up:  3+7+2+9+4+7+3+7+5+2 = 49

Step #2:  Count the number of items on the list:  I count 10 .

Step #3:  Divide the sum by the number of items on the list.

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