Answer:
P= $2.75
Step-by-step explanation:
So first we need to create our system of equations
since each popcorn is 0.40 less than each drink we can make the equation:
D - 0.40 = P we can rewrite that as P + 0.40 = D so that we have D by its self.
Next, we create the overall equation:
$24.00 = 3P + 5D
Now plug in D from the first equation into the second equation:
$24.00 = 3P + 5( P + 0.40)
Distribute the five and solve for P:
$24.00 = 3P + 5P + 2
$22.00 = 8P
P = $2.75
Now add 0.40 which would be $3.15 and plug it into the first equation just to make sure that the answer is correct.
The converse would be If x² = 100 then x = -10
So essentially if the conditional statement is p → q then the converse is q → p (In essence, the converse of a conditional statement is formed by interchanging the hypothesis and the conclusion.)
Answer: Nearly all thermal energy on Earth originates from the sun and radiates to the surface of our planet, traveling in the form of electromagnetic waves, such as visible light. Materials on Earth then absorb these waves to be used for energy or reflect them back into space. In an energy transformation, energy changes form.
Step-by-step explanation:
This is the concept of application of quadratic equations; To get the number of dimes and quarters we proceed as follows;
suppose there are x dimes and y quarters;
x+y=95.......i
but we know;
$0.1=1 dimes
$0.25=1 quarters
thus
0.1x+0.25y=23.45.....ii
solving equation i and ii by substitution we shall have:
from i;
x=95-y
thus substituting the value of x in equation ii we get
0.1(95-y)+0.25y=23.45
9.5-0.1y+0.25y=23.45
collecting like terms we get:
0.15y=13.95
dividing both sides by 0.15 we get;
y=13.95/0.15=93
x=95-93=2
therefore we conclude that there were 2 dimes and 93 quarters
