Answer:
Proved that GB ≅ AH.
Step-by-step explanation:
See the attached diagram.
Statement 1: ∠ GBH ≅ ∠ AHB
Reason 1: This is given.
Statement 2: ∠ GHB ≅ ∠ ABH
Reason 2: This is also given.
Statement 3: BH ≅ HB.
Reason 3: From the diagram. Reflexive property of congruence.
Statement 4: Δ GBH ≅ Δ AHB
Reason 4: By Angle-Side-Angle or ASA criteria of congruency.
Statement 5: GB ≅ AH
Reason 5: Corresponding sides of two congruent triangles. (Proved)
Answer:
x = 20
Step-by-step explanation:
angle m<3 + angle m<5 = 180° because these angles are supplementary
5x + 10 + 3x + 10 = 180° add like terms
8x + 20 = 180
8x = 160 divide both sides by 8
x = 20
Answer:
23, 69 and 123
Step-by-step explanation:
let the first number be x then the second number is 3x ( 3 times the first) and the third number is x + 100 ( 100 more than the first number)
The sum of the three numbers is
x + 3x + x + 100 = 215
5x + 100 = 215 ( subtract 100 from both sides )
5x = 115 ( divide both sides by 5 )
x = 23
The 3 numbers are
x = 23, 3x = 3 × 23 = 69 and x + 100 = 23 + 100 = 123
Answer:
1.4650 (the first option in the list of possible answers)
Step-by-step explanation:
Start by isolating the exponential expression on one side of the equal sign, thus subtracting 2 from both sides:
Now, in order to solve for "x", we need to lower the exponent, and for that purpose we use logarithm base "3":
In order to find this logarithm, we use the change of base formula:
which rounded to four decimals gives: 1.4650
