Answer:
x = 5.4
Step-by-step explanation:
(This question has already been answered, but both of the incorrect ones were deleted, so for future reference...)
Fig A is a scale image of Fig D. These two quadrilaterals are similar, and thus, the side lengths of corresponding sides are proportional. Set the proportion x/3 = 7.2/4 (you could alternatively write it as x/7.2 = 3/4 but for the simplicity's sake, and assuming anyone who has this problem would already know how to solve proportions like these...)
7.2/4 = 1.8
so
x/3 = 1.8
now multiply both sides by 3 to get x = 5.4
18 kg of 15% copper and 72 kg of 60% copper should be combined by the metalworker to create 90 kg of 51% copper alloy.
<u>Step-by-step explanation:</u>
Let x = kg of 15% copper alloy
Let y = kg of 60% copper alloy
Since we need to create 90 kg of alloy we know:
x + y = 90
51% of 90 kg = 45.9 kg of copper
So we're interested in creating 45.9 kg of copper
We need some amount of 15% copper and some amount of 60% copper to create 45.9 kg of copper:
0.15x + 0.60y = 45.9
but
x + y = 90
x= 90 - y
substituting that value in for x
0.15(90 - y) + 0.60y = 45.9
13.5 - 0.15y + 0.60y = 45.9
0.45y = 32.4
y = 72
Substituting this y value to solve for x gives:
x + y = 90
x= 90-72
x=18
Therefore, in order to create 90kg of 51% alloy, we'd need 18 kg of 15% copper and 72 kg of 60% copper.
f(9) is the x value, find where the line is in the y direction at x = 9
The line crosses y = 3 at x = 9
Answer:
f(9) = 3
Answer:
Step-by-step explanation:
Given that prices for a pair of shoes lie in the interval
[80,180] dollars.
Delivery fee 20% of price.
i.e. delivery fee will be in the interval [4, 9]
(1/20th of price)
Total cost= price of shoedelivery cost
Hence f(c) = c+c/20 = 21c/20
The domain of this function would be c lying between 80 to 180
So domain =[80,180]
---------------------------------
Amount to be repaid = 42 dollars
Once he received this amount, the price would be
105+42 =147
But since price range is only [21*80/20, 21*180/20]
=[84, 189]
Since now Albert has 147 dollars, he can afford is
[80,147]
the discriminant b^2 - 4ac when the equation is in the form of ax^2 +bx+c=0
13x^2-16x = x^2 -x
we need to get in it the standard form
subtract x^2 from each side
12x^2 -16x = -x
add x to each side
12x^2 -15x = 0
12x^2 -15x -0 =0
a=12 b=-15 c=0
b^2 -4ac
the discriminant = b^2
b^2 = (-15)2 = 225