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1. In the system of equations above, k is a constant. If the system has no solution, what is the value of k?
2. Two moonflower vines are growing on a trellis in Mallory's backyard. She bought thefirst vine when it was 11 inches long and found that it grows at a rate of 0.25 inchesper day. Exactly 20 days later, Mallory bought the second vine, which started at 24inches long and has a growth rate of 0.125 inches per day. How many days will Malloryhave had the first vine when the lengths of the two vines are the same?
3. If, then what is one possible value of x – y?
4. Margo can peel and slice at least 10 dozen apples per hour and at most 15 dozen applesper hour. Based on this information, what is a possible amount of time, in hours,that it could take Margo to peel and slice 60 dozen apples?
5. The variables x and y represent numbers for which the statementsandare true. What is the smallest integer that x can equal?
6. A subway car passes 3 stations every 10 minutes. At this rate, how many stations willit pass in 1 hour?
7. Comix Fanatix has 250 customers who subscribe to its newsletter, 68% of whom are male.After some female customers cancel their subscriptions, the total number of subscribersbecomes 1.3 times the number of male subscribers. How many female customers canceledtheir subscriptions?
8. In preparation for buying a house, Sergey and Juanita draft a budget to see how muchthey can afford. Their monthly spending and income are shown in the table. Numbersin parentheses indicate expenses (money being spent); numbers without parenthesesindicate income (money being earned). Sergey and Juanita will not buy a house unlessthey can save at least $400 a month after all expenses, including the new mortgagepayment and property taxes, are paid.
The couple would like to buy a house that costs $230,400, for which the monthly mortgagepayment would be $730, and the annual property taxes would be 2.5% of the purchaseprice. By what percent could Sergey and Juanita cut their monthly food spending inorder to buy this particular house and meet their criteria for purchasing a house?(Ignore the percent sign and grid in your answer as a whole number.)
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