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
.
Answer:
Area= 247 feet²
Volume= 1235 feet³
Step-by-step explanation:
The storage pod features a rectangular base measuring 19 feet by 13 feet, with a flat ceiling height of 5 feet above.
Calculating the area of the floor yields: length multiplied by width
Length = 19 feet
Width = 13 feet
Area = 19*13
Area = 247 feet²
The volume of the pod can be found by multiplying the area by the height
Height of the pod = 5 feet
Area = 247 feet²
Volume = 247*5
Volume = 1235 feet³
Question:
Which statement is accurate concerning the function’s discontinuities 
A) There are gaps at x = 7 and.
B) Asymptotes exist at x = 7 and.
C) Asymptotes exist at x = –7 and.
D) Gaps are present at (–7, 0) and.
Answer:
B) Asymptotes exist at x = 7 and 
Step-by-step explanation:
Given:
Goal:
Identify the correct statement
We need to factor the denominator first.
To express x in terms of (3x+4) and (x-7):
3x + 4 =
3x = -4
Divide both sides by 3:
x - 7
x = 7
Next, evaluate the limit when and at (x = 7)
lim f(x) as = ±∞
lim f(x) as (x=7) = ±∞
Since both scenarios result in the denominator approaching zero, they represent asymptotes.
Thus, asymptotes are found at and x=7
Option B is determined to be correct
Response: The following comparison is made.
Detailed explanation:
At the playground, a climbing structure is 6 feet high and stretches 4 feet horizontally.
The slope can be calculated as vertical height divided by horizontal length.
= 6/4 = 3/2 = 1.5
In contrast, a climbing structure in the gym stands 10 feet tall, extending 6 feet horizontally.
Therefore, slope, 
= 10/6 = 5/3 = 1.67 (approximately)
As such, <
Thus, the slope of the first climbing structure is less than that of the second.
To tackle the problem, the general approach is to convert all measurements into the smallest unit possible.
a. 3 km 9 hm 9 dam 19 m + 7 km 7 dam
3,000 m 900 m 90 m 19 m + 7,000 m 70 m = 4,009 + 7,070 = 11,079 m
b. 5 sq.km 95 ha 8,994 sq.m + 11 sq. km. 11 ha 9,010 sq. m.
5,000,000 sq m 95,0000 sq m 8,994 sq m + 11,000,000 sq m 110,000 sq
9,010 sq m
5,103,994 sq m + 11,119,010 sq m = 16,223,004 sq m
c. 44 m - 5 dm
44 m - 0.5 m = 43.5 m
d. 73 km 47 hm 2 dam - 11 km 55 hm
73,000 m 4,700 m 20 m - 11,000 m 5,500 m
77,720 m - 16,500 m = 61,220 m
