Given:
Seven times the smaller of two consecutive even integers is the same as -300 minus 4 times the larger integer.
To find:
The integers
.
Solution:
Let the smaller even integer be x.
So, larger even integer is x+2 because they are consecutive even integers.
Seven times the smaller integer = 7x
-300 minus 4 times the larger integer = -300-4(x+2)
Now,
Divide both sides by 11.
So, the smaller even integer is -28.
So, the larger even integer is -26.
G(-4) = 4^2 + 3(-4) - 2
16 - 12 - 2
4 - 2
answer: 2
9514 1404 393
Answer:
11.5 m
Step-by-step explanation:
The fact that the figures are similar means the side lengths are proportional:
RS/QT = BC/AD
RS/(7 m) = (2.3 m)/(1.4 m)
RS = (7 m)(2.3/1.4) . . . . . . multiply by 7 m
RS = 11.5 m
Here are the steps required for Simplifying Radicals:
Step 1: Find the prime factorization of the number inside the radical. Start by dividing the number by the first prime number 2 and continue dividing by 2 until you get a decimal or remainder. Then divide by 3, 5, 7, etc. until the only numbers left are prime numbers. Also factor any variables inside the radical.
Step 2: Determine the index of the radical. The index tells you how many of a kind you need to put together to be able to move that number or variable from inside the radical to outside the radical. For example, if the index is 2 (a square root), then you need two of a kind to move from inside the radical to outside the radical. If the index is 3 (a cube root), then you need three of a kind to move from inside the radical to outside the radical.
Step 3: Move each group of numbers or variables from inside the radical to outside the radical. If there are nor enough numbers or variables to make a group of two, three, or whatever is needed, then leave those numbers or variables inside the radical. Notice that each group of numbers or variables gets written once when they move outside the radical because they are now one group.
Step 4: Simplify the expressions both inside and outside the radical by multiplying. Multiply all numbers and variables inside the radical together. Multiply all numbers and variables outside the radical together.
Shorter version:
Step 1: Find the prime factorization of the number inside the radical.
Step 2: Determine the index of the radical. In this case, the index is two because it is a square root, which means we need two of a kind.
Step 3: Move each group of numbers or variables from inside the radical to outside the radical. In this case, the pair of 2’s and 3’s moved outside the radical.
Step 4: Simplify the expressions both inside and outside the radical by multiplying.
Answer: y=-1/3x+1
Step-by-step explanation:
To find an equation that contains the given point and has the same slope, we can plug it into slope-intercept form to find the y-intercept.
3=-1/3(-6)+b [multiply]
3=2+b [subtract both sides by 2]
b=1
Now that we know the y-intercept, we know that the equation is y=-1/3x+1.
