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Mama L [17]
3 years ago
13

5. Are the slidutu pun - Complete: 1 = = = 8 It’s asking me to complete 1/2=

Mathematics
1 answer:
meriva3 years ago
5 0

Answer:1/2=2/4=4/8

Step-by-step explanation:It's quite simple if you do 1/2 times 2 you would get 2/4 1*2=2  2*2=4 2/4 same with 2/4 time 2 2*2=4 4*2=8 4/8.

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The base of a ladder is 2.8m placed away from a tree that is 4.5m tall. The end of the ladder touches the top of the tree. Calcu
horrorfan [7]

Step-by-step explanation:

Hello all beautiful your day

4 0
2 years ago
Your family is going on a road trip to Disney World! On Day 1, you traveled x miles. On Day 2, you drove 58 miles more than 3 ti
ladessa [460]
First we write the expressions of each day separately:
 Day 1:
 you traveled x miles:
 x
 Day 2:
 you drove 58 miles more than 3 times the thousands on Day 1:
 3x + 58
 Day 3: 
 your family went 25 fewer thousands than Day 1
 x-25
 Then, we have:
 Day 1 + Day 2 + Day 3:
 x + (3x + 58) + (x-25)
 Rewriting:
 x + 3x + x + 58 - 25
 5x + 33
 Then, for x = 100
 5 * (100) + 33 = 533 miles.
 answer:
 5x + 33
 Total miles that family traveled from home to Disney World is
 533 miles
5 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
Solve for x in the equation x 2 - 4 x - 9 = 29.
Marizza181 [45]

Answer:

x= -19

Step-by-step explanation:

2x-4x-9=29

-2x=29+9

x=38/-2

= -19

5 0
3 years ago
Read 2 more answers
Please i need to know if im correct with these questions
telo118 [61]

Answer: No Solution

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

ln x - ln (x + 2) = 4             restrictions: x > 0  and  x + 2 > 0   →    x > 0

ln (\frac{x}{x + 2}) = 4

(\frac{x}{x + 2}) = e⁴

x = e⁴ (x + 2)

x = 54.5982 (x + 2)

x = 54.5982x + 109.1964

- 53.5982x = 109.1964

x = \frac{109.1964}{-53.5982}

x = -2.0373

-2.0373 is not greater than 0 so is not valid

**************************************************************************

Answer: 2.1972

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

eˣ = 9

ln eˣ = ln 9

   x = ln 9

   x ≈ 2.1972

**************************************************************************

Answer: \frac{3}{2}

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

log₂ (3x - 4) = -1

        3x - 4 = 2⁻¹

         3x - 4 = \frac{1}{2}

       <u>       +4 </u>   <u>+4 </u>

          3x     = 4\frac{1}{2}

          3x     = \frac{9}{2}

          \frac{3x}{3} = \frac{9}{2} * \frac{1}{3}

            x = \frac{3}{2}

**************************************************************************

Answer: 1.117519

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

in the calculator, type in 1 ÷ 9.

Then hit the eˣ button.

 e¹⁾⁹

= e°¹¹¹¹¹¹

= 1.117519

rounded to 6 decimal places: 1.117519

6 0
2 years ago
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