Answer:
Step-by-step explanation:
[1] 2x + y = -1
[2] x - 2y = -8 <------- given linear equations
Graphic Representation of the Equations : ----> given in attatchment
y + 2x = -1 -2y + x = -8 < ----- point where they connect is shown in graph
Solve by Substitution :
// Solve equation [2] for the variable x
[2] x = 2y - 8
// Plug this in for variable x in equation [1]
[1] 2•(2y-8) + y = -1
[1] 5y = 15
// Solve equation [1] for the variable y
[1] 5y = 15
[1] y = 3
// By now we know this much :
x = 2y-8
y = 3
// Use the y value to solve for x
x = 2(3)-8 = -2
Solution :
{x,y} = {-2,3}
Answer:
1. $67.72
2. It's correct.
Step-by-step explanation:
1.
bill: $68.89
discount: $10
tip: 15%
Calculate the total with the discount.
68.89-10=58.89
Now calculate 15% of that.
Convert 15% to decimal by dividing by 100
Multiply
Add this to the original amount.
----------------------------------------------------------------------------
Calculate 20% of 148.25
Convert 20% to decimals by dividing by 100
Multiply
This is how much they will tip.
Add this to the original bill;
Answer:
Step-by-step explanation:
f * g = (x^2 + 3x - 4) (x+4)
open bracket
x((x^2 + 3x - 4) + 4 (x^2 + 3x - 4)
x³ +3x²-4x+x²+12x-16
x³+3x²+x²-4x+12x-16
x³+4x²+8x-16 (domain is all real numbers.
f/g = (x^2 + 3x - 4)/(x+4)
factorising (x^2 + 3x - 4)
x²+4x-x_4
x(x+4) -1 (x+4)
(x+4)(x-1)
f/g = (x^2 + 3x - 4)/(x+4) =(x+4)(x-1)/(x+4) = (x-1)
Before factorisation, this was a rational function so the domain is all real numbers excluding any value that would make the denominator equal zero.
Hence I got x - 1, and x cannot equal -4
So the domain is just all real numbers without -4
<span>204
First, lookup a standard normal table and see what the z-score is for 0.025 (one half of 100% - 95%) to allow for equal sized tails. You should find that the z-score is 1.96. That means that 95% of the time, the value should be within 1.96 standard deviations of the mean. Now let's calculate the standard deviation.
800 is 800 - 1200 = -400 to the left of the mean of 1200.
1600 is 1600 - 1200 = 400 to the right of the mean of 1200.
So we are an equal distance of 400 on both sides of the mean. And we know from the z-score of 1.96, that we're 1.96 standard deviations from the mean. So a little division will give us the standard deviation. Which is:
400 / 1.96 = 204.0816327
So the standard deviation of the light bulbs is 204</span>
Answer:
x= 8/9
Step-by-step explanation:
Open everything up to get 5x+2x-6=-2x+2. Move numbers with an x to the left side and without to the right to have 5x+2x+2x=2+6. Simplify to have 9x=8. Divide by 9 which leaves you with x= 8/9
