Function rule: a = 20w + 115
Slope: 20
Initial value: 115
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We start with $115 in the account. This is the initial value. Each week we add on $20.
So we add $20 for 1 week
We add 2*20 = $40 for 2 weeks
We add 3*20 = $60 for 3 weeks
etc etc
In general, we add 20*w dollars for w weeks onto 115 to get a = 20w+115
The slope is 20 because this is the rate of change, ie how fast the account grows. It grows 20 dollars per week.
If you compare it to the parent function x^(1/3):
g(x) is just shifted 4 down and 2 to the right.
Therefore:
h = 2
k = -4
Answer:
Length = 9units
Width = 7units
Step-by-step explanation:
It is said that the length is 2units more than the width
Assume that the width is x, then the length will be 2 + x
ie
Width = x
Length = 2 + x
Area of the rectangle = 63units
Area of rectangle = l * b
l - length of the rectangle
b - width of the rectangle
A = l * b
63 = (2 + x) * x
63 = ( 2 + x) x
63 = 2x + x^2
Let's rearrange it
x^2 + 2x - 63 = 0
Let's find the factor of 63
A factor that can be multiplied to give -63 and that can be added to give +2
Let's use -7 and +9
x^2 - 7x + 9x - 63 = 0
Separate with brackets
( x^2 - 7x) + ( 9x - 63) = 0
x( x - 7) + 9(x - 7) = 0
( x + 9)(x - 7) = 0
( x + 9) = 0
( x - 7) = 0
x + 9 = 0
x = -9
x - 7 = 0
x = 7
Note: the length of a rectangle can not be negative
So therefore,
x = 7
Length = 2 + x
= 2 + 7
= 9units
Width = x
= 7units
Answer:
89 degrees
Step-by-step explanation:
The angle 1 is the same as angle 3.
Angle 2 is the same as angle 4.
The sum of these four angles is 360 degrees.
We have that:
Angle 2 = Angle 4 = 7x - 14
Angle 3 = Angle 1 = 5x + 14
Finding x:
Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360
2*(5x + 14) + 2*(7x - 14) = 360
10x + 28 + 14x - 28 = 360
24x = 360
x = 15
Angle 1:
5x + 14 = 5*15 + 14 = 89 degrees
M/_XYZ is 50°, if you need to copy and paste the degrees symbol, here it is: °
