We can use elimination for these set of systems.
First, we need to set up our variables.
Belts=b
Hats=h
Now, the situation is 6 belts and 8 hats for $140. The situation after is 9 belts and 6 hats for $132.
Let’s set up our system of equations.
6b+8h=140
9b+6h=132
We need to eliminate a variable. Since b has coefficients of 6 and 9, we can easily eliminate b by multiplying the top equation by 3 and the bottom by -2.
18b+24h=420
-18b-12h=-264
Now let’s add.
12h=156
Let’s divide to get h by itself.
156/12=13=h
So a hat costs $13. We need to put in 13 for one of the equations so we can find the cost of a belt.
9b+6(13)=132
9b+78=132
We need b by itself.
9b=54
54/9=6
Belts are $6
We can also use the first equation to check our answers.
6(6)+8(13)
36+104
140.
So, the price of a belt is $6 while the price of a hat is $13.
Answer:
x=-3
Step-by-step explanation:
we know that
The slope of a vertical line is undefined
The formula to calculate the slope between two points is equal to
we have
A(x+14, 5) and B(2−3x, 8)
substitute
so
If the slope is undefined
then
The denominator must be equal to zero
solve for x
Answer:
Wednesday (9 weeks later) = 10th October.
Step-by-step explanation:
We label the days with the initials of the names.
M= 4
D = 7
B = 6
LCM of 6 +7 = 42
LCM of 6+7 + 4 = 84
We find 84 is the amount of days we need to add on to july 18th
We first find the weeks 84/7 = 9 weeks.
As Wednesday July 18th is exclusive it would be 84 days after this event.
18+ 84 = 102 days.
31 days in july = 31
31 days in Aug = 31
30 days in Sept = 30
= 92
102-92 = 10
We now know date is Wednesday 10th October
We can check 84 days = 9 weeks
13 days in July makes 31st july
31 days in Aug makes 31st Aug
30 days in Sept makes 30th Sept
= 74 days + 10 days = 84
10th October is the checked date and we know it is also a Wednesday as Wednesday had stayed exclusive and prove that there are 7 days in the week to account x 9, to account for an exact 9 weeks later duration.
Answer:
13,254
hope this helps :)
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