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3 years ago

A student solved 6x+4=2(x−8) in four steps as shown:

1 answer:

7 0

The first thing you should do is solve the equation yourself.

1) Distribute the 2.
6x + 4 = 2x – 16

2) Next, you'll want to get the x's on one side. So add -2x to both sides.
6x + 4 + -2x = 2x + -2x - 16
4x + 4 = -16

3) Now subtract 4 from both sides
4x + 4 – 4 = -16 – 4
4x = -12

4) Finally, divide both sides by 4
4x/4 = -12/4
x = –3

To solve this problem all you need to do is look back out you work, and figure out the correct solution. The answer the question is The student made an error in Step 1.

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State whether the triangles could be proven congruent, if possible, by SSS or SAS.

Helen [10]

Answer:

1. SSS

2. SAS

3. SAS

4. SSS

5. SAS

6. SAS

Step-by-step explanation:

1) Side FY ≅ Side CW Given

Side FP ≅ Side CM Given

Side YP ≅ Side MW Given

∴ΔMCW ≅ ΔFPY by the Side-Side-Side (SSS) rule of congruency

2) ∠CBD ≅ ∠BCA given that both are alternate interior angles

Side EB ≅ Side EC and Side DB ≅ Side CA Given

ΔBED ≅ ΔAEC by Side-Angle-Side (SAS) rule of congruency

3. ∠SVU ≅ ∠SVT Given

Side SV ≅ Side SV by reflexive property

Side VT ≅ Side VU Given

∴ ΔVSU ≅ ΔVST by Side-Angle-Side (SAS) rule of congruency

4. Side MN ≅ Side QP Given

Side MQ ≅ Side NP Given

Side NQ ≅ Side NQ by reflexive property

∴ΔQNM ≅ ΔQNP by the Side-Side-Side (SSS) rule of congruency

5. Indirect proof

Side GL ≅ Side HL Given

Side GJ ≅ Side HK Given

∠JLG ≅ ∠HLK vertically opposite angles

By sine rule

GJ/sin(∠JLG) = GL/n(∠GJL)

Similarly

HK/sin(∠HLK) = HL/n(∠HKL)

∴ ∠GJL ≅ ∠HKL

∴ ∠LGJ ≅ ∠LHK third angle of two triangles given the other two angles are congruent

∴ΔQNM ≅ ΔQNP by the Side-Angle-Side (SAS) rule of congruency

6. ∠XZY ≅ ∠XZW Supplementary ∠s with ∠XZY = 90°

Side XZ ≅ Side XZ by reflexive property

Side ZW ≅ Side ZY Given

∴ ΔXYZ ≅ ΔXWZ by Side-Angle-Side (SAS) rule of congruency.

3 0

2 years ago

Solve the equation using square roots. x^2-15=34

matrenka [14]

x^2-15=34
x^2 = 34 + 15
x^2 = 19
x = + 7 and x = -7

answer is

x = + 7 and x = -7

3 0

3 years ago

A plane flies 35 km in the direction n 30° w, then flies 60 km in the direction n 60° e. how far is the plane from its original

Kipish [7]

The distance of plane from the starting point is 69.46 km.

Given that the plane first flies 35 km in the direction N30W and then 60 km in the direction N60E.

We have to find the distance of plane from starting point.

We have to use pythagoras theorem in this which says that the square of hypotenuse is equal to sum of squares of the base and perpendicular.

$H^{2} =P^{2} +B^{2}$