30 people liked Brand X. This is 20% of the people in a survey.
1 answer:
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Slope-intercept form of a line is y=mx+b where m= slope and b=y-intercept.
First step is to compare this line with the given line y=5x+2 to get the value of m.
After comparing we will get m=5.
Now slope of all parallel lines are equal which means if slope of this line is 5 then slope of the line which is parallel to this line will also be 5.
Point- slope form of a line is:
Given the line passes through (-6,-1). So, plug in x1=-6, y1=-1 and m=5 in the above equation. So,
y-(-1)=5(x-(-6))
y+1=5(x+6)
y+1=5x+30
y=5x+30-1
y=5x+29.
Answer:
y = negative (2) Superscript x Baseline + 3
Step-by-step explanation:
An exponential function has a range of y > 0. In order for it to have a range of y < 3, it must be reflected across the x-axis (given a negative multiplier) and must be translated upward 3 units.
That is, for some exponential function y = b^x, you must have something of the form ...
y = -a·b^x +3
Only one answer choice has this form:
Answer:
98(1 + 2√2) in² ≈ 375 in²
Step-by-step explanation:
Assuming the shaded region is outside of the square and inside of the octagon, we can find the area by subtracting the area of the square from the area of the octagon.
The area of a regular octagon is 2 (1 + √2) s². We can show this by finding the area of the square outside of the octagon, and subtracting the triangles in the corners:
(s + √2 s)² − 4 (½ (½√2 s)²)
(1 + √2)² s² − 4 (½ (s²/2))
(1 + 2√2 + 2) s² − s²
2 (1 +√2) s²
The diagonal of the inner square is equal to the width of the octagon, (1+√2) s. So the side length of the square is:
½√2 (1+√2) s
½(2+√2) s
The area of the square is therefore:
(½(2+√2) s)²
¼(2+√2)² s²
¼(4+4√2+2) s²
¼(6+4√2) s²
½(3+2√2) s²
The area of the shaded region is therefore:
2 (1 +√2) s² − ½(3+2√2) s²
½ s² (4 (1 +√2) − (3+2√2))
½ s² (4 + 4√2 − 3 − 2√2)
½ s² (1 + 2√2)
The side length of the octagon is s = 14 in, so the area is:
½ (14 in)² (1 + 2√2)
= 98(1 + 2√2) in²
≈ 375 in²
