Answer:
2/4
Step-by-step explanation:
Answer:
78
Step-by-step explanation:
The tricky part of this is figuring out how to assign the unknowns. We are told that we are working with two consecutive even integers. Consecutive means "next to" or "in order" and sum means to add. If we use 2 and 4 as examples of our 2 consecutive even integers and assign x to 2, then in order to get from 2 to 4 we have to add 2. So the lesser of the 2 integers is x, and the next one in order will be x + 2. (2 and 4 are just used as examples; they mean nothing to the solving of this particular problem. You could pick any 2 even consecutive integers and find the same rule applies. All we are doing here with the example numbers is finding a rule for our integers.) Now we have the 2 expressions for the integers, we will add them together and set the sum equal to 158:
x + (x + 2) = 158
The parenthesis are unnecessary since we are adding, so when we combine like terms we get
2x + 2 = 158 and
2x = 156 and
x = 78
That means that the lesser of the 2 integers in 78, and the next one in order would be 80, and 78 + 80 = 158
Given:Price of one taco = x; price of 2 tacos = 2xPrice of salad = $2.50Sales tax = 8% of the combined price of two tacos and a salad, namely .08(2x + 2.50)Tip = constant fee = $3.00Total bill = $13.80 Therefore the equation becomes
2x + 2.50 + .08(2x + 2.50) + 3 = 13.80 Solutions: 2x + 2.50 + .16x + .20 + 3 = 13.80 (using the distributive property to multiply 2x and 2.5 by .08).2.16x + 2.70 + 3 = 13.80 (combining like terms)2.16x + 5.70 = 13.80 (combining like terms)2.16x + 5.70 = 13.80 - 5.70 (subtraction property of equality)2.16x = 8.10x = 8.10/2.16 = 3.75 (division property of equality)
The cost of a single taco is $3.75
comparing the relation given
thus y= -2x +1 to the general equation of a line
where y= mx + c
where m is the gradient and c is the intercept on the y-axis.
from the question, the gradient is -2 and since the line is perpendicular, the gradient is given as
so substituting the value of m in to the equation
=
as the gradient
equation of line is given by
y - y1 = m( x-x1)
from the question y1= -2 and x1=1
substitute them
y-(-2) = 1/2 (x -1)
y+2 =1/2 (x-1)
multiplying through by 2
2 (y+2) = x-1
2y +4 = x-1
2y =x-1-4
2y =x-5
x -2y -5 = 0
therefore the equation for the line is x-2y -5=0
