Find two consecutive positive integers such that the square of the smaller integer added to seven times the larger integer is equal to 85

6 and 7 are the consecutive numbers.

Step-by-step explanation:

5 and 6 are consecutive integers because 6 is right after 5.

Let me revise the way I say that:

5 and 5+1 are consecutive integers.

So and are consecutive integers.

If they are both positive, then clearly is more than .

We are given the square of the smaller, , is added to seven times the larger, , is equal to 85.

This means:

Let's solve.

First we should use the distributive property:

Now I would like the right hand side to be 0 so I can factor and then put both factors equal to 0 and solve for .

Subtract 85 on both sides:

Simplify:

Now we want to find two numbers that multiply to be -78 and add to be 7.

Let's think of some numbers that multiply to be -78:

-78=-2(39); this wouldn't work because -2+39 isn't 7

-78=2(-39); this wouldn't work because 2+(-39) isn't 7.

-78=-6(13); this would work because -7+13 is 7.

So the factored form is:

This implies or .

We are going to solve the first equation by adding 6 on both sides giving us: .

We are going to solve the second equation by subtracting 13 on both sides giving us: .

Now we are looking for positive integers, so .

This implies the value of .

The numbers are 6 and 7.

Let's check.

<-This is the square of the smaller.

<-This is the square of the smaller added to seven times the larger. We got 85 so the check is good.

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: