Answer:
g(x) = (-1/25)x + (203/25)
Step-by-step explanation:
The general equation for a line is slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept.
We know that perpendicular lines have opposite-signed, reciprocal slopes of the original line. Therefore, if the slope of f(x) is m = 25, the slope of g(x) must be m = (-1/25).
To find the y-intercept, we can use the newfound slope and the values from the given point to isolate "b".
g(x) = mx + b <----- General equation
g(x) = (-1/25)x + b <----- Plug (-1/25) in "m"
8 = (-1/25)(3) + b <----- Plug in "x" and "y" from point
8 = (-3/25) + b <----- Multiply (1/25) and 3
200/25 = (-3/25) + b <----- Covert 8 to a fraction
203/25 = b <----- Add (3/25) to both sides
Now that we know both the values of the slope and y-intercept, we can construct the equation of g(x).
g(x) = (-1/25)x + (203/25)
1/sin^2x-1/tan^2x=
1/sin^2x-1/ (sin^2x/cos^2x)<<sin tan= sin/cos>>
= 1/sin^2x- cos^2x / sin^2x
= (1- cos^2x) / sin^2x <<combining into a single fraction>>
sin^2 x / sin^2x <<since 1- cos^2 x sin^2 x
=1
this simplifies to 1.
Let us start with assuming the amount of coffee worth $20 a pound to be "x" pounds.
Now she wants to mix "x" pounds of $20 coffee with 70 pounds of $90 coffee.
So the mixture would be (x + 70) pounds.
And the value of mixture would be = 20·x + (90)·(70) = (20x + 6300) dollars.
She want to sell this mixture at rate of $30 a pound. Her earning would be = 30·(x + 70) = (30x + 2100) dollars.
We know that the value of mixture would be equal to her earnings.
30x + 2100 = 20x + 6300
30x - 20x = 6300 - 2100
10x = 4200
x = 420
So, 420 pounds of $20 coffee would be used.
Answer: 8.76%
Step-by-step explanation:
The formula to find the simple interest is given by :-
, where P is the principal amount, r is rate of interest () in decimal and t is the time ( in years). (1)
Given : Justin deposited $2,000 into an account 5 years ago.
i.e. P = $2,000 , t= 5 years
He has just withdrawn $2,876. i.e. Future value = $2,876
Interest (I)=$2,876-$2,000=$876 [Subtract Principal value from Future value]
Substitute all the above values of P , t , and I in the formula (1) , we get
In percent , 
Hence, the rate of interest = 8.76%
Answer:
5
Step-by-step explanation:
4.5*10^-8/ 9*10^-9
1) Reduce the fraction, express 9 as a product of multiplying 4.5*2
4.5*10^-8/4.5*2*10^-9
2) Then notice the common factor of numerator and denominator( 4.5) , get rid of it in both numerator and dnominator
3) 10^-8/ 2*10^-9= 1/2*(10^-8/10^-9)= 0.5* (10^-8/10^-9)
10^-8/10^-9= 10^(-8-(-9))= 10^1=10.
so 0.5*10=5 (it is the answer written in scientific form)
