Answer:
Answer choice C. 
.
Step-by-step explanation:
The entire question is present in the attached figure.
It is established that
The function f(x) is represented by
,
indicating a parabola that opens upward.
The vertex is situated at the point (0,0).
The function g(x) shares the same parabolic shape.
The vertex of g(x) is located at (-3,1).
Therefore,
The transformation from f(x) to g(x) can be described as:
(0,0) transforms to (-3,1).
(x,y) transforms to (x-3,y+1).
This indicates a shift of 3 units to the left and 1 unit upward.
Thus,
The equation for g(x) in vertex form can be expressed as
.
The expression indicates that the total earnings of Mike over the two weeks amount to 2.05x dollars
Solution:
It is given that Mike earned x dollars during the first week at his new job,
While in the second week, he earned 5% more than the earnings of the first week.
To determine: Total earnings over the two weeks
From the information provided,
Earnings in the first week = "x" dollars
Earnings in the second week = 5% more than first week earnings
Thus,
Earnings in the second week = x + 5% of x
Therefore, earnings in the second week equal to 1.05x dollars
The total earnings over the two weeks:
Total earnings = Earnings from first week + Earnings from second week
Thus, the expression for the total earnings of Mike for both weeks is 2.05x dollars
All prime numbers are odd with the exception of two. Hence, if we consider the sum of the first million primes, it consists of one even number combined with 999,999 odd numbers. Since the product of an odd number multiplied by another odd number results in an odd number, we conclude that the sum must be an odd number, being even + odd = odd.
It's clear that an odd number ends with an odd digit, so the only digit that can be eliminated is b (an even digit).
Answer:
Step-by-step explanation:
Given:
KL ║ NM,
LM = 45
m∠M = 50°
KN ⊥ NM
NL ⊥ LM
To determine: KN and KL
1. Analyzing triangle NLM, we see it is a right triangle due to NL ⊥ LM. In this context,
LM = 45
m∠M = 50°
Consequently,
It is also true that
(angles LNM and M are complementary).
2. Now considering triangle NKL, it also forms a right triangle as KN ⊥ NM. Within this triangle,
(alternate interior angles)
(angles KNL and KLN are complementary).
Thus,
and
Apply the Pythagorean theorem
x^2 + x^2 = 2x^2
sqrt(2x^2)=x sqrt(2)
