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AlladinOne [14]
2 years ago
9

Write the equation of the line that passes through the points (1,-7)(1,−7) and (-6,-9)(−6,−9). Put your answer in fully reduced

point-slope form, unless it is a vertical or horizontal line.
Mathematics
2 answers:
BlackZzzverrR [31]2 years ago
7 0

Answer:

6x+6)(6+4)

Step-by-st(ep explanation:

nbpbf wefqlbwpoi

ruslelena [56]2 years ago
5 0

Answer:

y+7=2/7x-2/7

Step-by-step explanation:

So we first want to find the slope. It's calculated by taking the difference in y values and dividing it by the difference in x values.

-9-(-7)/-6-1

=-9+7/-7

=-2/-7

=2/7.

This is the m in the point-slope equation.

Next, we just plug in the points. We only need 1 point so I will use the (1,-7)

y-y1=m(x-x1)

y-(-7)=2/7(x-1)

y-(-7)=2/7x-2/7

y+7=2/7x-2/7

I've never really seen fully reduced point-slope form, but I'm assuming the above is it because if I keep simplifying it's going to turn into slope-intercept form.

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Complete question :

According to the National Association of Realtors, it took an average of three weeks to sell a home in 2017. Suppose data for the sale of 39 randomly selected homes sold in Greene County, Ohio, in 2017 showed a sample mean of 3.6 weeks with a sample standard deviation of 2 weeks. Conduct a hypothesis test to determine whether the number of weeks until a house sold in Greene County differed from the national average in 2017. Useα = 0.05for the level of significance, and state your conclusion

Answer:

H0 : μ = 3

H1 : μ ≠ 3

Test statistic = 1.897

Pvalue = 0.0653

fail to reject the Null ; Hence, we conclude that their is no significant to accept the claim that number I weeks taken to sell a house differs.

Step-by-step explanation:

Given :

Sample size, n = 40

Sample mean, x = 3.6

Population mean, μ = 3

Standard deviation, s = 2

The hypothesis :

H0 : μ = 3

H1 : μ ≠ 3

The test statistic :

(xbar - μ) ÷ (s/√n)

(3.6 - 3) / (2/√40)

0.6 / 0.3162277

Test statistic = 1.897

Using T test, we can obtain the Pvalue from the Test statistic value obtained :

df = n - 1; 40 - 1 = 39

Pvalue(1.897, 39) = 0.0653

Decison region :

If Pvalue ≤ α ; Reject the null, if otherwise fail to reject the Null.

α = 0.05

Pvalue > α ; We fail to reject the Null ; Hence, we conclude that their is no significant to accept the claim that number I weeks taken to sell a house differs.

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Answer:

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Step-by-step explanation:

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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
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