How do you solve 7+3t over 4 =-t over 8?

This is: ?
(7+3t)/4 = -t/8
If it was the equation above do the following..
multiply both sides with 8 which gives you:
2(7+3t) = -t (get 2 due to (8/4 = 2))
14 + 6t = -t
6t + t = -14
t = -2

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Describe the effect of each number on the graph of f(x) =7 (-1x + 1)^3 +4.?

Describe the effect of each number on the graph of f(x) =7 (-1x + 1)^3 +4.
Match:
7
1
4
-1
3
Match with:
a. shifts the graph up
b. identifies the common graph to be used
c. shifts the graph to the left
d. stretch
e. reflects the graph over the y axis

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differentiation of exponential functions?

you have fraction, note that
[a/b]' = (a'b-b'a)/b^2
in your case a=x
b=e^x
as you know
x'=1
(e^x)' = e^x
so we get
(1*e^x - xe^x)/e^(2x)

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Find all the zeros of each equation.?

1. x^5 – 3x^4 – 15x^3 + 45x^2 – 16x + 48 = 0
A. 3, 4, i
B. 4, –4, i,–i
C, 3, 4, –4, i, –i
D. 3, –4, –i
2. x^3 – x^2 + 5x – 5 = 0
A. i, –i, 1
B. i, –i, –1
C. , –, –1
D. i, 1
3. 7x^2 – 144 = –x^4
A. 3, –3, 4i, 0
B. 3, 4i
C. 3, –3, 4i, –4i
D. –3, –4i

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Given that x²+y²=14x+6y+6,find the largest possible value of the expression E=3x+4y?

x^2-14x +y^2-6y=6
(x-7)^2 +(y-3)^2 = 6+49+9 = 64 = 8^2
this is a circle centre (7,3) radius 8
y = 3 + 8 sin[theta]
x= 7+ 8 cos[theta]
E= 3(7+8cos( theta)) +4 (3 +8 sin[theta])
= 21 +24 cos (theta) + 12 +32 sin (theta)
= 33 +24 cos (theta)+ 32 sin(theta)
dE/ d (theta)= -24sin(theta) +32cos (theta)=0
32cos theta=24sin (theta)
tan (theta) = 32/24 = 4/3
theta = arctan(4/3)
E= 33 +24 cos (arctan(4/3)) + 32 sin(arctan(4/3)
=73

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For a cubic graph, how do you know if it goes below the x axis or above the x axis?

every cubic (or in general, every polynomial of odd order) crosses x-axis.
to find where that happens, you solve for y=0.
for example if you have cubic, it would be ax^3+bx^2+cx+d=0

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Quick! Do arithmetic sequences have to be addition and subtraction?

I am learning about arithmetic sequences, and my book only shows addition and subtraction. Are multipication patterns arithmetic sequences too?
Examples:
I know 2, 4, 6, 8, 10 is an arithmetic sequence. +2
But is 1, 3, 9, 27 an arithmetic sequence too? x3

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