Step-by-step explanation:
By Remainder Theorem, f(5) = 91.
=> (5)³ - 4(5) + k = 91
=> 125 - 20 + k = 91
=> 105 + k = 91
=> k = -14.
F(x)= 2x²+4x-6 and g(x)=2x-2, find each function
1. (f/g) (x) = f(x)÷g(x) = (2x²+4x-6)÷(2x-2)
First factor both top and bottom:
(2x-2)(x+3)÷(2x-2) = x+3
2. f(a + 2) = plug (a+2) in anywhere there is an x in f(x)=2x²+4x-6 -->
2(a+2)^2 +4(a+2)-6 = 2(a^2+4a+4)+4a+8-6, now distribute:
2a^2+8a+8+4a+2, combine like terms
2a^2+12a+10
3. g(a/2) = plug (a/2) in anywhere there's an x in g(x)=2x-2:
2(a/2)-2 = a-2
Answer: t = 3seconds
Step-by-step explanation:
To find the zero means we will equate the function to zero and then solve, that is
+ 32t + 48 = 0
by factorizing , we have
(t+1)(-16t+48) = 0
Therefore:
t = -1 or t = 3
since time can not be negative , then , t = 3 seconds
The - number has to t o be more then 6 in order to get -10. Answer= -16
The equation of the line through the point (8,−9) and perpendicular to 3x+8y=4 is given by 8x - 3y = 91.
We are aware that any straight line's equation can be expressed as
y = mx + c,
where m denotes the slope and c denotes a constant.
Also, two perpendicular lines' slopes are the negative reciprocals of one another.
Here, the equation of the given straight line is
3x+8y=4
i.e. 8y = 4 -3x
i.e. y = (4/8) - (3/8)x
Now the negative reciprocal of - 3/8 is 8/3.
Then we can write the equation of the perpendicular line is
y = (8/3)x + c ...(1)
Since (1) passes through the point (8, -9), so we can put x = 8 and y = -9 in (1) to get the value of c.
So, -9 = (8/3)*8 + c
i.e. -9 = 64/3 + c
i.e. c = -9 -64/3 = - (27 + 64)/3 = - 91/3
(1) can be written as
y = (8/3)x - (91/3)
i.e. 3y = 8x - 91
i.e. 8x - 3y = 91
Therefore the equation of the line through the point (8,−9) and perpendicular to 3x+8y=4 is given by 8x - 3y = 91.
Learn more about perpendicular lines here -
brainly.com/question/12209021
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