Answer:
2t + n + 3d = 65
3t + 2n + 5d = 85
t + n + td = 40
Step-by-step explanation:
tubs of popcorn = t
plates of nachos = n
drinks = d
The Smiths: 2t + n + 3d = 65
The Langes: 3t + 2n + 5d = 85
The Radfords: t + n + td = 40
So, the correct answer would be the one including all 3 of these equations. :)
Answers:
- C) x = plus/minus 11
- B) No real solutions
- C) Two solutions
- A) One solution
- The value <u> 18 </u> goes in the first blank. The value <u> 17 </u> goes in the second blank.
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Explanations:
- Note how (11)^2 = (11)*(11) = 121 and also (-11)^2 = (-11)*(-11) = 121. The two negatives multiply to a positive. So that's why the solution is x = plus/minus 11. The plus minus breaks down into the two equations x = 11 or x = -11.
- There are no real solutions here because the left hand side can never be negative, no matter what real number you pick for x. As mentioned in problem 1, squaring -11 leads to a positive number 121. The same idea applies here as well.
- The two solutions are x = 0 and x = -2. We set each factor equal to zero through the zero product property. Then we solve each equation for x. The x+2 = 0 leads to x = -2.
- We use the zero product property here as well. We have a repeated factor, so we're only solving one equation and that is x-3 = 0 which leads to x = 3. The only root is x = 3.
- Apply the FOIL rule on (x+1)(x+17) to end up with x^2+17x+1x+17 which simplifies fully to x^2+18x+17. The middle x coefficient is 18, while the constant term is 17.
Answer:
<em>Cathy was born in 1980 and she was 18 years old in 1998</em>
Step-by-step explanation:
<u>Equations</u>
This is a special type of equations where all the unknowns must be integers and limited to a range [0,9] because they are the digits of a number.
Let's say Cathy was born in the year x formed by the ordered digits abcd. A number expressed by its digits can be calculated as
In 1998, Cathy's age was
And it must be equal to the sum of the four digits
Rearranging
We are sure a=1, b=9 because Cathy's age is limited to having been born in the same century and millennium. Thus
Operating
If now we try some values for c we notice there is only one possible valid combination, since c and d must be integers in the range [0,9]
c=8, d=0
Thus, Cathy was born in 1980 and she was 18 years old in 1998. Note that 1+9+8+0=18
Answer:
y - 5 = -7(x - 8)
Step-by-step explanation:
We can immediately adapt y - k = m(x - h) as follows: replace m with -7, h with 8 and k with 5, obtaining:
y - 5 = -7(x - 8)
This is the desired equation in point-slope form.
Answer:
Option C. (-x,y)
Step-by-step explanation:
we know that
A point reflected across the y-axis has the following rule
(a,b)------> (-a,b)
so
If the center of the original circle was located at (x, y)
then
the center of the new circle after the transformation will be (-x,y)
