In the right ∆ABC, BL is an angle bisector. If LB = 1.2 in and LC = 0.6 in. Find the distance from L to AB
AND find the measurement of

= 0.6 inch

m∠ABC = 60°

Step-by-step explanation:

The given parameters are;

The given triangle ΔABC = A right triangle

The angle bisector of ∠CBA = BL

The length of BL = LB = 1.2 in.

The length of LC = 0.6 in.

We have;

≅ reflexive property

∠ABC = ∠CBL + ∠DBL and ∠CBL ≅ ∠DBL definition of bisected angle

∠CBL = ∠DBL by definition of congruency

∠CLB + ∠CBL = ∠CLB + ∠DBL = 90°, opposite angles of a the right angle triangle are supplementary

∴ ∠CLB = ∠CLB by addition property of equality

ΔLDB ≅ ΔLBC are congruent by the Angle-Side-Angle rule of congruency

∴ ≅ Congruent Parts of Congruent Triangles are Congruent (CPCTC)

= = 0.6 in. by definition of congruency

= 0.6 in.

sin(m∠CBL) = Opposite side/(Hypotenuse side) = / = 0.6/1.6 = 1/2

m∠CBL = sin⁻¹(1/2) = 30°

m∠CBL = m∠DBL = 30°

m∠ABC = m∠CBL + m∠DBL = 30° + 30° = 60°

m∠ABC = 60°

Simple....

Which value is a solution of the equation 2 – 8x = –6?(1 point)• 1• –1• 8
You have: 2-8x=-6

plug n chug...

2-8(1)=-6

2-8=-6

-6=-6 (Yes)  (<<---Answer)

2-8(-1)=-6

2+8=-6

10=-6 (No)

2-8(8)=-6

2-64=-6

-62=-6 (No)

3. Which ordered pair is a solution of the equation y = x – 4?(1 point)• (2, 6)• (6, 2)• (–2, 6)• (–6, 2)
Plug n chug.....

you have:y=x-4

(2,6)

6=2-4

6=-2 (No)

(6,2)

2=6-4

2=2 (Yes) (<<<---Answer)

(-2,6)

6=-2-4

6=-6 (No)

(-6,2)

2=-6-4

2=-10 (No)

4. Which ordered pair is a solution of the equation y = 4x?(1 point)• (1, 3)• (–1, –4)• (–4, –1)• (1, –4)
You have: y=4x

(1,3)

3=4(1)

3=4 (No)

(-1,-4)

-4=4(-1)

-4=-4 (Yes) (<<<----Answer)

(-4,-1)

-1=4(-4)

-1=-16 (No)

(1,-4)

-4=4(1)

-4=4 (No)

5. Which ordered pair is a solution of the equation y = –9x + 4?(1 point)• (10, –86)• (–4, –58)• (6, –41)• (–6, 57)

You have: y=-9x+4

(10,-86)

-86=-9(10)+4

-86=-90+4

-86=-86 (Yes) (<<<---Answer)

(-4,-58)

-58=-9(-4)+4

-58=36+4

-58=40 (No)

(6,-41)

-41=-9(6)+4

-41=-54+4

-41=-50 (No)

(-6,57)

57=-9(-6)+4

57=54+4

57=58 (No)

6. Mike and his best friend Dan have the same birthday, but Mike is three years older than Dan. Let the variable x represent Mike’s age and y represent Dan’s age. Which graph represents the relationship between Dan’s age and Mike’s age?(1 point)

There is no graph.

7. Solve the following equation.
–4 = g + 1(1 point)• g = –4• g = 4• g = –5• g = –3
You have: -4=g+1

-4=g+1
-1     -1

-5=g (Answer/C)

8. Solve the following equation. 
x – 3 = –5(1 point)• x = • x = –2• x = –8• x = 15
You have: x-3=-5

x-3=-5
  +3  +3

x=-2 (Answer)
9. Solve the following equation.
2.8 = 2y(1 point)• y = 1.4• y = • y = 2.8• y = 0.6

You have: 2.8=2y

2.8=2y



1.4=y (Answer)

10. 
Solve the following equation. 

–8 = 
(1 point)
• z = –
• z = –5
• z = –24
• z = 
11. 
Solve the following equation.

–9 = 
(1 point)
• n = 
• n = 
• n = 
• n = 

NUMBER 10 AND 11..THERE IS NOTHING I CAN WORK WITH,THEREFORE I CAN NOT GIVE AN ANSWER....

12. 
Which equation is an identity?
(1 point)
• 11 – (2v + 3) = –2v – 8
• 5w + 8 – w = 6w – 2(w – 4)
• 7m – 2 = 8m + 4 – m
• 8y + 9 = 8y – 3

You have:

11-(2v+3)=-2v-8

11-2v-3=-2v-8

-2v+8=-2v-8 (No)

5w+8-w=6w-2(w-4)

4w+8=6w-2w+8

4w+8=4w+8 (Yes) (<<<<--Answer)

7m-2=8m+4-m

7m-2=7m+4 (No)

8y+9=8y-3 (No)

13. 
Which equation has no solution?
(1 point)
• 8 – (5v + 3) = 5v – 5
• 3m – 6 = 5m + 7 – m
• 3w + 4 – w = 5w – 2(w – 2)
• 7y + 9 = 7y – 6

You have:

8-(5v+3)=5v-5

8-5v-3=5v-5

-5v+5=5v-5
      +5         +5
-5v+10=5v
+5v      +5v

10=10v

1=v

3m-6=5m+7-m

3m-6=4m+7
-3m    -3m

-6=m+7
-7      -7 

-13=m

3w+4-w=5w-2(w-2)

2w+4=5w-2w+4

2w+4=3w+4
-2w    -2w

4=w+4
-4    -4

0=w

7y+9=7y-6
-7y     -7y

NO SOLUTION  (ANSWER)

Thus, your answer.