Write the decimal as a fraction or mixed number in lowest terms.0.5
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Answer: C
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Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.The manager of a coffee shop has one type of coffee that sells for $9 per pound and another type that sells for $15 per pound. The manager wishes to mix 80 pounds of the $15 coffee to get a mixture that will sell for $11 per pound. How many pounds of the $9 coffee should be used?
A. 240 pounds B. 160 pounds C. 120 pounds D. 80 pounds
Provide an appropriate response.
(i) List the sequence of pentagonal numbers that corresponds to the sequence of dot patterns above and find two in addition to these. (ii) Complete the following list of equations suggested by the sequence of dot patterns and the pentagonal numbers you find in part (i). 1 = 1 1 + 4 = 5 1 + 4 + 7 = 12 1 + 4 + 7 + 10 = 22 _________________ = ___ _________________ = ___Observe that each pentagonal number is the sum of an arithmetic progression.(iii) Compute the eleventh term in the arithmetic progression 1, 4, 7, 10, ... .(iv) Compute the eleventh pentagonal number.(v) Determine a
formula for nth term in the arithmetic progression 1, 4, 7, 10, ... .(vi) Determine a formula for the nth pentagonal number pn. A. 1, 5, 7, 9, 11, 13, ... (ii) 1 + 3 + 5 + 7 + 9 = 25 1 + 3 + 5 + 7 + 9 + 11 = 36 (iii) Eleventh term: 1 + 3(11) = 34 (iv) Eleventh pentagonal number: 182 (v) nth term: 1 + 3(n) or 3n + 1 (vi) pn = 3n(n)/2 B. 1, 6, 18, 40, 76, 128, ... (ii) 1 + 4 + 7 + 10 + 13 = 35 1 + 4 + 7 + 10 + 13 + 16 = 51 (iii) Eleventh term: 3(10)- 1= 29 (iv) Eleventh pentagonal number: 220 (v) nth term: 1 + 3(n - 2) or 3n - 1 (vi) pn = 2n(n - 1) C. (i) 1, 5, 12, 22, 35, 51, ... (ii) 1 + 4 + 7 + 10 + 13 = 35 1 + 4 + 7 + 10 + 13 + 16 = 51 (iii) Eleventh term: 1 + 3(10) = 31 (iv) Eleventh pentagonal number: 176 (v) nth term: 1 + 3(n - 1) or 3n - 2 (vi) pn = n(3n - 1)/2 D. 1, 5, 13, 23, 36, 52, ... (ii) 1 + 4 + 7 + 10 + 13 = 35 1 + 4 + 7 + 10 + 13 + 16 = 51 (iii) Eleventh term: 1 + 3(12) = 37 (iv) Eleventh pentagonal number: 187 (v) nth term: 1 + 3(n + 1) or 3n + 4 (vi) pn = n(3n + 1)/2
Perform the indicated division and express your answer in simplest form.
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Answer the question.If the trinomial ax2 + bx + c is a perfect square, what can we conclude about the solutions of the equation ax2 + bx + c = 0?
A. The equation has exactly one irrational solution. B. The equation has no real number solutions. C. The equation has two different rational solutions. D. The equation has exactly one rational solution.