Answer:
= 10 
Step-by-step explanation:
The n th term of a geometric sequence is
= a 
where a is the first term and r the common ratio
Here a = 10 and r = 30 ÷ 10 = 3, thus
= 10
Answer: y = 2/3x + 41/3
Step-by-step explanation:
First convert the equation into slope-intercept
3x + 6y = 4y - 4
-4y -4y
3x + 2y = -4
-3x -3x
2y = -3x - 4
y = -3/2x - 2
Perpendicular lines have a negative reciprocal for their slopes.
The negative reciprocal of -3/2 is 2/3
Now using the slope 2/3 you will use the formula y =mx +b and input the slope, and the x and y coordinates of the given point, (-10,7), to solve for the y-intercept.
7 = 2/3(-10) + b
7 = -20/ 3 + b
+ 20/3 + 20/3
b = 20/3 + 21/3 = 41/3
Since the the y-intercept is 41/3 then the equation will be , y = 2/3x + 41/3
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Answer:
42.6cm
Step-by-step explanation:
The sum total of all the sides of the shape is the perimeter of the shape. Hence;
Perimeter = x+3 + 4 + x+9 + 2x+5
Perimeter = 4x + 21
Given
Area of the figure = 75cm^2
Area = (x+3)(2x+5) + (2x+1)(6)
75 = 2x²+5x+6x+15+12x+6
75 = 2x²+23x+21
2x²+23x+21-75 = 0
2x²+23x-54 = 0
x = -23±√23²-4(2)(-75)/4
x = -23±√529+600/4
x = -12±√1129/4
x = -12+33.6/4
x = 21.6/4
x = 5.4
Recall that;
Perimeter = 4x+21
Perimeter = 4(5.4) + 21
Perimeter = 21.6+21
Perimeter = 42.6cm
Hence the perimeter is 42.6cm
“Four times the difference of a number and 7 is 32”
Translation-
4(x-7)=32
