Answer:
<em>a:b:c=8:12:15</em>
Step-by-step explanation:
<u>Combined Ratio</u>
We are given the ratios:
a:b=2:3
b:c=4:5
The combined ratio a:b:c will include all three variables in one single expression.
Before finding it, we must have a common number for the common variable (b). Since b is 3 in the first ratio and 4 in the second ratio, we must equate both by finding the LCM of 3 and 4=12, thus both ratios will be amplified as follows:
a:b=2:3=(2*4):(3*4)=8:12
b:c=4:5=(4*3):(5*3)=12:15
Now there is a common factor in both ratios, we can combine them removing the common factor:
a:b:c=8:12:15
To solve with Elimination:
Write the equations under one another, like this:
2x - y = -1
+ 3x + 4y = 26
Ideally, we would like for one of the variables to be eliminated when we add vertically (straight down). But if we add them as they are this does not happen. We must manipulate one of the equations so that it will happen. Again, you can try to eliminate either x or y. I always look for a term that has a coefficient of 1 (or negative 1). So, let's use that y from the first equation again.
If the coefficient of the y in the other equation is POSITIVE 4, then I need the coefficient from the first equation to be its opposite, NEGATIVE 4. To do this, simply multiply the first equation by 4, this will create MAGIC!
4( 2x - y = -1)
+ 3x + 4y = 26
Be certain to Distribute across the entire first equation, so multiply all three terms by 4.
8x - 4y = -4
+ 3x + 4y = 26
Now add straight down (vertically). The y term will be eliminated.
11x = 22
Divide both sides of the equation by 11.
x = 2
Almost there! Now, substitute the 2 in for x in either of the original equations. Either one will work. I'm gonna use the second equation.
3x + 4y = 26
3(2) + 4y = 26
6 + 4y = 26
Subtract 6 from both sides of the equation.
4y = 20
Divide both sides of the equation by 4.
y = 5
That's it! There it is again. Put it all together. If x = 2 and y = 5, then the solution is the ordered pair, (2,5).
Answer:
Make Width = 'x'
Length = 4 + 2x
Perimeter = 2 x Width + 2 x Length
86 = 2(x) + 2(4 + 2x)
86 = 2x + 8 + 4x
Collect like terms:
2x + 4x = 86 - 8
6x = 78
x = 13
Width = 13 cm
Length = 30 cm
Step-by-step explanation:
Sorry for the confusion, redoing my answer for you!
Using the points (9/2,1), (-7/2,7)
m=y2−y1 over x2−x1
Substitute in the values of x and y into the equation to find the slope.
m=7−(1) over −72−(92)
simplify
m=−3/4
Use the slope −3/4 and a given point (9/2,1) to substitute for x1 and y1 in the point-slope form y−y1=m(x−x1)
y−(1)=−3/4⋅(x−(9/2))
Rewrite in y=mx+b
solve for y
y=−3x/4+35/8
ill use desmos to graph (y=−3x/4+35/8)
Call the number of days 'd' and the number of miles 'm'.
(Original, eh ?)
Then the equation for Gamma's price is
Price-G = 30.39d + 0.55m
and the equation for Delta's price is
Price-D = 50.31d + 0.43m .
We're going to set the prices equal, and find out
what the number of miles is:
Price-G = Price-D.
30.39d + 0.55m = 50.31d + 0.43m .
Before we go any farther, I'm going to assume that both cases would be
one-day rentals. My reasons: ==> the solution for the number of miles
depends on how many days each car was rented for; ==> even if both
cars are rented for the same number of days, the solution for the number
of miles depends on what that number of days is.
For 1-day rentals, d=1, and
30.39 + 0.55m = 50.31 + 0.43m .
Beautiful. Here we go.
Subtract 0.43m
from each side: 30.39 + 0.12m = 50.31
Subtract 30.39
from each side: 0.12m = 19.92
Divide each side by 0.12 : m = 166 .
There it is ! If a car is rented from Gamma for a day, and another car
is rented from Delta for a day, and both cars are driven 166 miles, then
the rental prices for both cars will be the same ... (namely $121.69)
