86. D. -10
87. H. -6, -3, 0, 2
88. Quadrant 1
Answer:
Equations:
y + 10x = 23
y + 15x = 33
cost of basket with 25 apples = $53
Step-by-step explanation:
A basket with 10 apples cost $23 and a basket with 15 apples cost $33. Note that these costs also include the cost of the basket, which is same in both case. Let the cost of empty basket with "y" and cost of each apple be "x"
Cost of basket and 10 apples is $23. We can transform this statement into an equation as:
y + 10x = 23 Equation 1
Similarly,
Cost of basket and 15 apples is $33. This gives us another equation:
y + 15x = 33 Equation 2
Subtracting Equation 1 from Equation 2 , we get:
y + 15x - (y +10x) = 33 - 23
5x = 10
x = 2
Using the value of x in equation 1, we get:
y + 10(2)= 23
y = 23 - 20
y = 3
This means, cost of basket is $3 and cost of each apple is $2.
Now we can calculate the cost of basket with 25 apples, which will be:
Cost of basket + Cost of 25 apples = Total Cost
3 + 25(2) = 3 + 50 = $53
Rational numbers are numbers that can be written as a fraction....positive and negative, just like -1/2. It is not a whole number, natural number, or an integer.
Answer:
5^4
Step-by-step explanation:
5^7/5^3
When we divided exponents with the same base
a^b / a^c = a^(b-c)
5^7/5^3 = 5^(7-3) = 5^4
p(x) = 90 / (9 + 50 * e^(-x))
e = 2.718, so we can use e = 2.7 as a quick substitute
p(3) =>
90 / (9 + 50 * e^(-3)) =>
90 / (9 + 50 * 2.7^(-3)) =>
90 / (9 + 50 / 2.7^3) =>
90 / ((9 * 2.7^3 + 50) / 2.7^3) =>
90 * 2.7^3 / (9 * 2.7^3 + 50)
2.7^3 =>
(27/10)^3 =>
27^3 / 1000 =>
729 * 27 / 1000 =>
2187 * 9 / 1000 =>
6561 * 3 / 1000 =>
19683 / 1000 =>
19.683
90 * 2.7^3 / (9 * 2.7^3 + 50) =>
90 * 19.683 / (9 * 19.683 + 50)
9 * 19.683 =>
9 * (20 - 0.317) =>
180 - 9 * 0.317 =>
180 - 9 * 0.3 - 9 * 0.017 =>
180 - 2.7 - 9 * 0.01 - 9 * 0.007 =>
177.3 - 0.09 - 0.063 =>
177.3 - 0.153 =>
177.15 - 0.003 =>
177.147
90 * 19.683 / (9 * 19.683 + 50) =>
10 * 177.147 / (177.147 + 50) =>
1771.47 / 227.147 =>
1771470 / 227147 =>
1770000 / 225000 =>
1770/225 =>
4 * 1770 / 900 =>
4 * 177 / 90 =>
708/90 =>
70.8 / 9 =>
23.6 / 3 =>
(21 + 2.6) / 3 =>
7 + 0.866666.... =>
7.8666666...
Actual value: 7.8333389811057471507345888320992.....
Not bad for some estimates, is it?
