If f(x)=e^x-1 +5 and g(x) is a transformation or, the same thing just moved, and its y-intercept is -3 then its equation would be:
D) g(x)=e^x-1 -3
For properties of logarithm we have the following:
loga (x ^ b) = b * loga (x)
Therefore, following this property we have for this case:
log3 (x ^ 9) = 9log3 (x)
Answer:
the power property to rewrite log3x9 is:
B) 9log3x
Hey, I'm assuming you mean five refrigerators every eight hours. So . . .
1250 divide by 5. Which gives you 250.
Then take that 250 and multiply it by 8, and you have 2000.
So it would take 2000 hrs for a factory, that can produce 5 refrigerators every eight hours to, produce 1250 refrigerators.
ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work
EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same
For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y
For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4
Therefore, for the two expressions to be conjugates, we must satisfy the two conditions.
Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the
x²y = -4 ... (I)
Condition 2: Real parts are the same
x² + y = -3 ... (II)
We have a system of equations since both conditions must be satisfied
x²y = -4 ... (I)
x² + y = -3 ... (II)
We can rearrange equation (II) so that we have
y = -3 - x² ... (II)
Substituting into equation (I)
x²y = -4 ... (I)
x²(-3 - x²) = -4
-3x² - x⁴ = -4
x⁴ + 3x² - 4 = 0
(x² + 4)(x² - 1) = 0
(x² + 4)(x-1)(x+1) = 0
Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.
Solve for y:
y = -3 - x² ... (II)
y = -3 - (±1)²
y = -3 - 1
y = -4
So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:
-3 + ix²y
= -3 + i(±1)²(-4)
= -3 - 4i
x² + y + 4i
= (±1)² - 4 + 4i
= 1 - 4 + 4i
= -3 + 4i
They result in conjugates
Answer:
y=3x
Step-by-step explanation:
To put this in slope intercept form, let’s first find the slope
To find slope, use the equation Y2-Y1/X2-X1
When we do this, we get 0-6/0-2
This simplifies out into -6/-2 which is 3
So our slope is 3. Our equation becomes y=3x+b
Now, we find our b
We don’t have to do any solving for this, since we have the point 0,0 listed for us, it goes through the origin and that is our y-intercept or b
So our final equation is y=3x
Hope this helps and have a good day!
