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Fernandez Harris
10/19/2021 · Middle School
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of \( 35 \) liters per minute. There are \( 500 \) liters in the pond to start.
Let \( W \) represent the amount of water in the pond (in liters), and let \( T \) represent the number of minutes that water has been added. Write an equation relating \( W \) to \( T \) , and then graph your equation using the axes below.
Equation: \( \square \)
\(W= 35T+ 500\)
Tickets to a basketball game can be ordered online for a set price per ticket plus a\(\$ 5.50\)service fee. The total cost in dollars for ordering\(5\)tickets is\(\$ 108.00\). Which linear function represents\(c\), the total cost, when\(x\)tickets are ordered?
\(c ( x ) = 5.50 + 20.50 x\)
\(c ( x ) = 5.50 x + 20.50\)
\(c ( x ) = 5.50 + 21.60 x\)
\(c ( x ) = 5.50 x + 21.60\)
The third\(( 3^ { rd} ) \)and seventh\(( 7^ { th} ) \)terms of an arithmetic sequence are seven\(( 7 ) \)and fifteen\(( 15 ) \)respectively. i. Write two linear equations showing the relationships between the terms and the first term\(a\)and the common difference\(d\). [\(2\)marks ] ii. Solve the equations ( part i) for the first term\(a\)and the common difference\(d\). iii. Using the values derived for\(a a d\)determine the sum of the first one hundred\(( 100 ) \)terms of the sequence.
Let\(U = \{ \text { all sode pops} \} ; A = \{ \text { all diet sode pops} \} ; B = \{ \text { all cola soda pops} \} ; C = \{ \text { all sode pops in cans} \} ; \text { and } D = \{ \text { all caffeine- free soda pops} \} .\)Describe the given set in words. A'\(\cap \)C Select one: a. All non-diet soda pops and all soda pops in cans b. All non-diet soda pops in cans c. All diet soda pops in cans d. All diet soda pops and all soda pops in cans Let\(U = \{ \)all soda pops\(\} ; A = \{ \)all diet soda pops\(\} ; B = \{ \)all cola soda pops\(\} ; C = \{ \)all soda pops in cans\(\} \); and\(D = \{ \)all caffeine-free soda pops\(\} \). Describe the given set in words.
\(A ^ { \prime } \cap C\)
Select one:
a. All non-diet soda pops and all soda pops in cans
b. All non-diet soda pops in cans
c. All diet soda pops in cans
d. All diet soda pops and all soda pops in cans
Solve the system. Use any method you wish.
\(x + y + 2 = 0 \) (1)
\(x^ 2 + y^ 2 + 4y - 3x = - 4\) (2)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is\(\{ \} \).
(Simplify your answer. Type an ordered pair. Type exact answers, using radicals as needed. Use a comma to separate answer as needed.)
B. There is no solution.
9.5 Solve Applications of Quadratic Equations
Question\(13\)
An rock is thrown downward from a platform that is\(158\)feet above ground at\(75\)feet per second. Use the projectile formula\(h = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 } \)to determine when the rock hit the ground. [Recall that\(v _ { 0 } \)is the initial velocity of the object and\(h _ { 0 } \)is the inital height of the object.]
Answer: The rock will hit the ground after\(\square \)
Note: Round any numerical responses to two decimal places. If there are multiple answers, separate them with commas.
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