Please help due Monday

1. 43, 45, and 47

2. 50, 52, and 54

3. 47 years old

4. 106 degrees

5. 66 degrees

Step-by-step explanation:

1. Let's assume that the first number in the three consecutive odd numbers is x.

We can write an equation to express this now. .

Combining like terms, we get . Subtracting by (x+2) on each side, we get . Since the smallest number is 43, we can find the two larger numbers as well, since they are 2 more than one another. Therefore, the numbers are 43, 45, and 47.

2. Let's assume that the first number in the three consecutive even integers is x.

We can write an equation to express this now.

Combining like terms, we get . Subtracting by (x+2) on each side, we get . Since the smallest number is 50, we can find the two larger numbers as well, since they are 2 more than one another. Therefore, the numbers are 50, 52, and 54

3. We can write his current age in years as x. Next year, his age will be x+1. We know that the sum of his current age and his age next year is 73, so we can write an equation to express this.

. Therefore, 2x + 1 = 73, or 2x = 72. This means that x = 36, or his current age is 36. In 11 years, his age will be 36 + 11 = 47 years old.

4. . Combining like terms, we get Subtracting by 5 on both sides, we get This means that . Now, we can find the degree measures of both angles and find the larger one. The degree measure of the angle on the left is 21(5) + 1 = 106 degrees, and the degree measure of the angle on the right is 14(5) + 4 = 74 degrees. Therefore, the degree measure of the larger angle is 106 degrees.

5. We know that the sum of the angles in a triangle is 180 degrees. Therefore, we can sum the angles up and equate them to 180 degrees.

(x-24) + (2x-108) + (1/3x+12) = 10/3x - 120 = 180. Adding 120 to both sides, we get 10/3x = 300. Multiplying both sides by 3/10, we get x = 900/10 = 90. Therefore, plugging in x = 90, we get 66 degrees.

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.