Two positive, consecutive, odd integers have a product of 143. what is the equation and the greater integer?

1 answer:

5 0

The product of two consecutive odd numbers is 143. Find the numbers. (Hint: if the first odd number is x, what is the next odd number?) ... Ad: You enter your algebra equationor inequality - Algebrator solves it step-by-step while ... We need two numbers that add up to 2. ... The next consecutive odd integer is , so

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The numbers 2/1/3,h,k,7/7/8 firm a geometric progression. find the value of h and of k

taurus [48]

$\text{We have }\ 2\dfrac{1}{3},\ h,\ k,\ 7\dfrac{7}{8}.\\\\\text{Convert the mixed numbers to the improper fractions}\\\\2\dfrac{1}{3}=\dfrac{2\cdot3+1}{3}=\dfrac{7}{3}\\\\7\dfrac{7}{8}=\dfrac{7\cdot8+7}{8}=\dfrac{63}{8}\\\\\text{If}\ a_1,\ a_2,\ a_3,\ a_4\ \text{is a geometric seqence, then:}\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=r\\\\a_2=a_1r\\\\\text{and}\ \dfrac{a_4}{a_1}=r^3\\\\\text{Substitute:}$

$r^3=\dfrac{\frac{63}{8}}{\frac{7}{3}}\\\\r^3=\dfrac{63}{8}\cdot\dfrac{3}{7}\\\\r^3=\dfrac{9\cdot3}{8\cdot1}\\\\r^3=\dfrac{27}{8}\to r=\sqrt[3]{\dfrac{27}{8}}\\\\r=\dfrac{3}{2}\\\\h=2\dfrac{1}{3}\cdot\dfrac{3}{2}=\dfrac{7}{3}\cdot\dfrac{3}{2}=\dfrac{7}{2}\\\\k=\dfrac{7}{2}\cdot\dfrac{3}{2}=\dfrac{21}{4}\\\\Answer:\ \boxed{h=\dfrac{7}{2}=3\dfrac{1}{2}\ and\ k=\dfrac{21}{4}=5\dfrac{1}{4}}$

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A river is flowing at the speed of 2 miles per hour. A kayaker moves 528 feet upstream in 20 minutes. At this rate, how fast wou

CaHeK987 [17]

D=rt
r=(boatrate+riverrate)=(x+2)mph

d=528ft=528/5280mi=1/10mi
t=1/3hr
remember to keep the same units
so

1/10=(x+2)(1/3)
times both sides by 3
3/10=x+2
minus 2 or 20/10
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adelina 88 [10]

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so we can easily use the concept of ratios to find x
in other words: x÷2=6÷5
so x=6×2÷5=12/5=2.4
x=2.4

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