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Anna007 [38]
3 years ago
13

The possible value of x?

Mathematics
2 answers:
sukhopar [10]3 years ago
7 0
X= 7 thank you hope that helped
yulyashka [42]3 years ago
3 0

Answer:

x = 7 and x = 5

Step-by-step explanation:

12x - 35 = x²

x² - 12x + 35 = 0

(x - 7)(x - 5) = 0

x = 7 and x = 5

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The most common Native American language used in 2010 is Navajo, with about 169,000 people speaking the language nationally. If
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169,000/308,700,000 which can be simplified to 169/308,700 and decimal form just divide 169,000 by 308,700,000 and you get .0005474571, and percentage multiply the decimal by 100 so you get .055% (rounded)
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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??

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If Tom runs 3.5 miles in 29.4 minutes, how many hours would it take him to run 26 miles? Show your work.
Thepotemich [5.8K]

Answer:

Step-by-step explanation:

3.5 miles/(29.4 minutes)

26 miles × (29.4 minutes)/(3.5 miles) = 218.4 minutes

218.4 minutes × (1 hour)/(60 minutes) = 3.64 hours

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Austin walks 1/3 of the way to school and stopped to rest. Devyn walks 2/6 of the way to the school and stops to rest who travel
r-ruslan [8.4K]

Answer:

Austin and Devyn.

Step-by-step explanation:

1/3 and 2/6 are equal fractions.

7 0
3 years ago
HELPPP RIGHT NOW PLEASEEEEE
Nadusha1986 [10]

The value of the variable x will be 37°. Then the measure of the angle ∠QNP will be 105°.

<h3>What is an angle?</h3>

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

The measure of angles ∠MNQ = (2x + 1)° and ∠QNP = (3x - 6)°.

Then the value of x will be

We know that the angles ∠MNQ and ∠QNP are supplementary angles. Then the value of the variable x will be

∠MNQ + ∠QNP = 180°

(2x + 1)° + (3x - 6)° = 180°

5x - 5° = 180°

5x = 185°

x = 37°

Then the measure of the angle ∠QNP will be

∠QNP = [3(37) - 6]°

∠QNP = 111° - 6°

∠QNP = 105°

The value of the variable x will be 37°. Then the measure of the angle ∠QNP will be 105°.

More about the angled link is given below.

brainly.com/question/15767203

#SPJ1

4 0
2 years ago
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