Answer:
Δ JKL is similar to Δ ABC ⇒ D
Step-by-step explanation:
Similar triangles have equal angles in measures
In ΔABC
∵ m∠A = 15°
∵ m∠B = 120
∵ The sum of the measures of the interior angles of a Δ is 180°
∴ m∠A + m∠B + m∠C = 180°
→ Substitute the measures of ∠A and ∠B
∵ 15 + 120 + m∠C = 180
→ Add the like terms in the left side
∴ 135 + m∠C = 180
→ Subtract 135 from both sides
∴ 135 - 135 + m∠C = 180 - 135
∴ m∠C = 45°
The similar Δ to ΔABC must have the same measures of angles
If triangles ABC and JKL are similar, then
m∠A must equal m∠J
m∠B must equal m∠K
m∠C must equal m∠L
∵ m∠J = 15°
∴ m∠A = m∠J
∵ m∠L = 45°
∴ m∠C = m∠L
∵ m∠J + m∠K + m∠L = 180°
→ Substitute the measures of ∠J and ∠L
∵ 15 + m∠K + 45 = 180
→ Add the like terms in the left side
∴ 60 + m∠K = 180
→ Subtract 60 from both sides
∴ 60 - 60 + m∠K = 180 - 60
∴ m∠K = 120°
∴ m∠B = m∠K
∴ Δ JKL is similar to Δ ABC
Answer:
B. 1.55 x 106
Step-by-step explanation:
This is an example of the distributive property. In order to turn it back to the regular form, you need to do this:
3.40
-
1.85
--------
1.55
Don't forget to put the 106!
3.40
-
1.85
--------
1.55 x 106
You can do it in both forms and get the same answer. It depends on what the question asks for or whichever form you like best/you think is the easiest.
Answer:
-20, probably.
Step-by-step explanation:
This is worded weirdly I assume it means there is a slope of one. Also, I hate that you got the points for this question by putting nonsense "answers" on questions, but you seemed like a halfway decent person.
X = 5/6.
The square of 3x+1 is written as (3x+1)². The square of x-2 is (x-2)². Using the information given to us, we want to solve the equation
(3x+1)²=9(x-2)²
(3x+1)(3x+1)=9(x-2)(x-2)
Multiplying the first two binomials, we have:
3x*3x + 1*3x + 1*3x + 1*1 = 9(x-2)(x-2)
9x²+3x+3x+1 = 9(x-2)(x-2)
9x²+6x+1 = 9(x-2)(x-2)
Multiplying the second two binomials, we have:
9x²+6x+1 = 9(x*x-2*x-2*x-2(-2))
9x²+6x+1 = 9(x²-2x-2x+4)
9x²+6x+1 = 9(x²-4x+4)
Using the distributive property gives us
9x²+6x+1 = 9*x²-9*4x+9*4
9x²+6x+1 = 9x²-36x+36
Subtracting 9x² from both sides leaves us
6x+1 = -36x + 36
Adding 36x to both sides we get
42x+1 = 36
Subtracting 1 from both sides we have
42x = 35
Divide both sides by 42:
42x/42 = 35/42
x = 35/42 = 5/6
