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Anarel [89]
3 years ago
11

C-0.6=7.1 show work and check

Mathematics
1 answer:
alexira [117]3 years ago
7 0
7.1-0.6=6.5 is the answer
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Using the following information = Universal set = {2,3,4,5,6,7,8,9,12,13,14,16,20,22,56). Subset A = {9,12,13,20,22,56); Subset
Cloud [144]

\dfrac{2}{5},\dfrac{13}{15},\dfrac{3}{5},\dfrac{1}{5},\dfrac{1}{5}

step-by-step explanation:

The intersection of two sets A and B, denoted by A ∩ B, is the set containing all elements of A that also belong to B.

The union (denoted by ∪) of a collection of sets is the set of all elements in the collection.

P(s) of a set s is defined as ratio of number of elements in s to the number of elements in universal set

given Universalset=\{\text{2,3,4,5,6,7,8,9,12,13,14,16,20,22,56}\}

given A=\{9,12,13,20,22,56\} and H=\{4,5,8,9,16,22\}

and C=\{1,4,20,22,56\}

For Question A:

A∩H=\{9,12,13,20,22,56\} ∩ \{4,5,8,9,16,22\}

=\{9,22}\}

(A∩H)∪C=\{9,22}\} ∪ C=\{1,4,20,22,56\}=\{1,4,9,20,22,56\}

p((A∩H)∪C)=\frac{6}{15}=\frac{2}{5}

For Question B:

H∩C=\{4,22\}

p(H∩C)'=\frac{15-2}{15}=\frac{13}{15}

For Question C:

p(H)'=\frac{15-6}{15}=\frac{3}{5}

For Question D:

C\H=\{1,20,56\}

p(C\H)=\frac{3}{15}=\frac{1}{5}

For Question E:

A\C=\{9,12,13\}

p(A\C)=\frac{3}{15}=\frac{1}{5}

7 0
3 years ago
Decide if the following statement is valid or invalid. If two sides of a triangle are congruent then the triangle is isosceles.
Naya [18.7K]

Answer:

Step-by-step explanation:

Properties of an Isosceles Triangle

(Most of this can be found in Chapter 1 of B&B.)

Definition: A triangle is isosceles if two if its sides are equal.

We want to prove the following properties of isosceles triangles.

Theorem: Let ABC be an isosceles triangle with AB = AC.  Let M denote the midpoint of BC (i.e., M is the point on BC for which MB = MC).  Then

a)      Triangle ABM is congruent to triangle ACM.

b)      Angle ABC = Angle ACB (base angles are equal)

c)      Angle AMB = Angle AMC = right angle.

d)      Angle BAM = angle CAM

Corollary: Consequently, from these facts and the definitions:

Ray AM is the angle bisector of angle BAC.

Line AM is the altitude of triangle ABC through A.

Line AM is the perpendicular bisector of B

Segment AM is the median of triangle ABC through A.

Proof #1 of Theorem (after B&B)

Let the angle bisector of BAC intersect segment BC at point D.  

Since ray AD is the angle bisector, angle BAD = angle CAD.  

The segment AD = AD = itself.

Also, AB = AC since the triangle is isosceles.

Thus, triangle BAD is congruent to CAD by SAS (side-angle-side).

This means that triangle BAD = triangle CAD, and corresponding sides and angles are equal, namely:

DB = DC,

angle ABD = angle ACD,

angle ADB = angle ADC.

(Proof of a).  Since DB = DC, this means D = M by definition of the midpoint.  Thus triangle ABM = triangle ACM.

(Proof of b) Since angle ABD = angle ABC (same angle) and also angle ACD = angle ACB, this implies angle ABC = angle ACB.

(Proof of c) From congruence of triangles, angle AMB = angle AMC.  But by addition of angles, angle AMB + angle AMC = straight angle = 180 degrees.  Thus 2 angle AMB = straight angle and angle AMB = right angle.

(Proof of d) Since D = M, the congruence angle BAM = angle CAM follows from the definition of D.  (These are also corresponding angles in congruent triangles ABM and ACM.)

QED*

*Note:  There is one point of this proof that needs a more careful “protractor axiom”.  When we constructed the angle bisector of BAC, we assumed that this ray intersects segment BC.  This can’t be quite deduced from the B&B form of the axioms.  One of the axioms needs a little strengthening.

The other statements are immediate consequence of these relations and the definitions of angle bisector, altitude, perpendicular bisector, and median.  (Look them up!)

Definition:  We will call the special line AM the line of symmetry of the isosceles triangle.  Thus we can construct AM as the line through A and the midpoint, or the angle bisector, or altitude or perpendicular bisector of BC. Shortly we will give a general definition of line of symmetry that applies to many kinds of figure.

Proof #2 (This is a slick use of SAS, not presented Monday.  We may discuss in class Wednesday.)

The hypothesis of the theorem is that AB = AC.  Also, AC = AB (!) and angle BAC = angle CAB (same angle).  Thus triangle BAC is congruent to triangle BAC by SAS.

The corresponding angles and sides are equal, so the base angle ABC = angle ACB.

Let M be the midpoint of BC.  By definition of midpoint, MB = MC. Also the equality of base angles gives angle ABM = angle ABC = angle ACB = angle ACM.  Since we already are given BA = CA, this means that triangle ABM = triangle ACM by SAS.

From these congruent triangles then we conclude as before:

Angle BAM = angle CAM (so ray AM is the bisector of angle BAC)

Angle AMB = angle AMC = right angle (so line MA is the perpendicular bisector of  BC and also the altitude of ABC through A)

QED

Faulty Proof #3.  Can you find the hole in this proof?)

In triangle ABC, AB = AC.  Let M be the midpoint and MA be the perpendicular bisector of BC.

Then angle BMA = angle CMA = right angle, since MA is perpendicular bisector.  

MB = MC by definition of midpoint. (M is midpoint since MA is perpendicular bisector.)

AM = AM (self).

So triangle AMB = triangle AMC by SAS.

Then the other equal angles ABC = ACB and angle BAM = angle CAM follow from corresponding parts of congruent triangles.  And the rest is as before.

QED??

8 0
2 years ago
Write and evaluate the expression. Then, select the correct answer.
FromTheMoon [43]

                            zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz                                                          

4 0
2 years ago
Point p’ (1,5) is the image of p (-3,1) under a translation<br><br> khan academy
GarryVolchara [31]

Answer:

<h2>X = \frac{-x}{3}</h2><h2>Y = 5y.</h2>

Step-by-step explanation:

We need to find the translation for which, (-3, 1) becomes (1, 5).

-3 will become 1, if it is divided by -3.

Hence, the translation for x axis is X = \frac{-x}{3}.

1 will become 5, when it is multiplied by 5.

Hence, The translation for y axis is Y = 5y.

6 0
3 years ago
Read 2 more answers
Which expression and diagram represent “three times a number”?
kozerog [31]

Answer:

You've picked the right one! It's the one you've marked in the picture!

Step-by-step explanation:

Multiplication is just like addition; you're just doing it multiple times instead of once. 3<em>x</em> is equal to <em>x</em> + <em>x</em> + <em>x</em>. That's exactly what the option you chose in the image shows. Great job! You've got this!

6 0
3 years ago
Read 2 more answers
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