The solution to the questions are:
- x = 2 in 6(6-4x) + 16x = 8x + 4
- |-3d - 6| + |-5 - d^2| = 29 when d = 3
- The formula for t is t = S/5r^2
- The equation y = 3x + 7 is steeper than y = 1/2x + 9
How to solve the equation?
The equation is given as:
6(6-4x) + 16x = 8x + 4
Open the brackets in the above equation
36 - 24x + 16x = 8x + 4
Collect the like terms
-24x + 16x - 8x = 4 - 36
Evaluate the like terms
-16x = -32
Divide both sides by -16
x = 2
How to evaluate the expression
The expression is given as:
|-3d - 6| + |-5 - d^2|
And the value of d is
d = 3
Substitute d = 3 in |-3d - 6| + |-5 - d^2|
|-3(3) - 6| + |-5 - 3^2|
Evaluate the exponent and expand the bracket
|-9 - 6| + |-5 - 9|
Evaluate the difference
|-15| + |-14|
Remove the absolute bracket
15 + 14
Evaluate the sum
29
How to solve the formula for t?
The formula is given as:
S=5r^2t
Divide both sides of the equation by 5r^2
t = S/5r^2
How to determine which equation’s line is steeper
The equations are given as:
y = 3x + 7
y = 1/2x + 9
The slopes of the above equations are
Slope 1 = 3
Slope 2 = 1/2
The higher the slope, the steeper the line.
This means that, the equation with the higher slope is steeper
Hence, the equation y = 3x + 7 is steeper than y = 1/2x + 9
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