I. 1250 + 20x = the cost of the party, x = the number of people attending.
II. If there are 300 people attending, the cost would be $7,250.
III. (attached) I'm not sure what kind of graph you're looking for, but I created a table. A represents the number of people attending. B represents the total cost.
IV. Daryl is incorrect. If there are 750 people attending, the total cost would be $16,250 because 750 multiplied by $20 (the cost per person) is $15,000. That plus $1,250 (the cost of the mansion) equals $16,250.
$16,250 does not equal $16,500.
Both vehicles will never have the same amount of fuel in their tanks
<h3>In how many miles will both vehicles have the same amount of fuel in their tanks?</h3>
The given parameters are:
Vehicle A
Initial = 22-gallon
Rate = 20 miles per gallon
Vehicle B
Initial = 16.7-gallon
Rate = 30 miles per gallon
The equation of each vehicle is represented as;
Fuel = Initial - Rate * Number of miles
So, we have
y = 22 - 20x --- A
y = 16.7 - 30x --- B
Substitute y = 16.7 - 30x in y = 22 - 20x
16.7 - 30x = 22 - 20x
Collect the like terms
30x - 20x = 16.7 - 22
Evaluate the difference
10x = -5.3
Divide by 10
x = -0.53
Distance cannot be negative
Hence, both vehicles will never have the same amount of fuel in their tanks
Read more about linear equations at:
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Set f(x) = x³ - 2x² + 10x + 136.
Use Descartes' rule of signs.
f(x) has 2 change in sign, so there are
(1) 2 real roots, or
(ii) a pair of conjugate imaginary roots.
f(-x) = -x³ - 2x² - 10x + 136
f(-x) has 1 sign change so there is 1 real root.
Scan the function for the first zero crossing, using negative values of x.
x f(x)
--- ---------
-1 123
-2 100
-3 61
-4 0
x = -4 is a root, so (x+4) is a factor.
Perform synthetic division (or long division if you do not know synthetic division).
-4 | 1 -2 10 136
-4 24 -136
---------------------
1 -6 34 0
Therefore
f(x) = (x+4)(x²- 6x + 34) = 0
Before factoring x² - 6x + 34, test the discriminant.
D = (-6)² - 4*34 = -100 => we have a pair of imaginary roots.
Use the quadratic formula.
x = (1/2)[6 +/- √-100]
= 3 +/- 5i
Answer: C
The roots are -4, 3 +/- 5i
30/54 in simplest form is 5/9
Answer:
-2
Step-by-step explanation:
