1 answer:
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9514 1404 393
Answer:
- 7 forks
- 20 spoons
Step-by-step explanation:
Let x and y represent the numbers of forks and spoons made, respectively.
The cost of materials is ...
1.70x + 1.30y = 37.90
The revenue from sales is ...
5.60x + 5.40y = 147.20
You can solve these by any of your favorite methods. A graph is attached. It shows the solution is (x, y) = (7, 20).
They made 7 forks and 20 spoons.
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<em>Additional working out</em>
The equation coefficients are not "nice" multiples of each other, so elimination and substitution will require multiplying both equations by some numbers. If we're going to that trouble, we may as well use Cramer's Rule or a variation of the "cross multiplication method". The latter is relatively straightforward and can be easy to remember. It tells you the solution to ...
ax +by +c = 0
dx +ey +g = 0
is ...
1/(ae-db) = x/(bg-ey) = y/(cd-ga)
Here, that becomes ...
1/(1.70·5.40-5.60·1.30) = x/(1.30·(-147.20)-5.40·(-37.90))
= y/(-37.90·5.60-(-147.20·1.70))
1/1.9 = x/13.3 = y/38
x = 13.3/1.9 = 7 . . . number of forks
y = 38/1.9 = 20 . . . number of spoons
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The above solution formula may be more easily remembered in terms of the cross-multiplication pattern that gives the method its name. When the coefficients are written in two rows of four, with the last being a repeat of the first:
- a b c a
- d e g d
each of the three denominators (of 1, x, and y) is the difference of products in adjacent columns, formed in an X fashion: ae-db, bg-ec, cd-ga. Note that the equations are written in "general" form, which is similar to "standard" form, but with all of the non-zero terms on the left of the equal sign. (This has the effect of changing the sign of the constants: 1.7x+1.3y=37.9 ⇒ 1.7x+1.3y-37.9=0)
Answer:
The explicit rule is:
Step-by-step explanation:
The explicit rule is given by:
The given sequence is 25,21,17,13
d=21-25
d=-4
We plug in the values into the formula to get;
Answer:
. hole or removable discontinuity at x=2
Step-by-step explanation:
Well generally if you want the simplest form, you factor each the denominator and numerator and then see if you can cancel any of the factors out (because they're in the denominator and numerator)
So let's start by factoring the first equation:
Now let's find what ac is (it's just c since a=1...)
List factors of -6
.
Now we have to look for two numbers that add up to -5. It's a bit obvious here since there isn't many factors, but it's -2 and -3, and they're both negative since 6 is positive, and -5 is negative...
So using these two factors we get
Ok now let's factor the second equation:
Multiply a and c
List factors of 12:
.
Factors that add up to -7 and multiply to 12:
Rewrite equation:
Group terms:
Factor out GCF:
Rewrite:
Now let's write out the equation using these factors:
.
Here we can factor out the x-2 and the simplified form is:
So we can "technically" define f(2) using the most simplified form, but it's removable discontinuity, so it has a hole as x=2. since it makes (x-2) equal to 0 (2-2) = 0.