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3 years ago

14

there are 15 oranges available to be cut up for a hockey team. Each member of the team will get two third of an orange. Using op

eration with fractions, you need to calculate how many team members will get two third of an oranges.

1 answer:

Yuki888 [10]3 years ago

3 0

Each member of the team will get two thirds of an orange.

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Evaluate the expression. [(8 x 7) – 2): 9

frozen [14]

Answer:

☑ Answer is 6

Step-by-step explanation:

${ \tt{ \{(8 \times 7) - 2 \} : 9}} \\ = { \tt{(56 - 2) :9 }} \\ = { \tt{54 :9 }}$

» But this is a ratio, so it can be expressed in terms of fractions:

$= { \tt{ \frac{54}{9} }} \\$

» Divide both the denominator and numerator by 9:

${ \tt{ = \frac{54 \div 9}{9 \div 9} }} \\ \\ = { \tt{ \frac{6}{1} }} \\ \\ = 6$

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Step-by-step explanation:

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3 years ago

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3 years ago

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Show that 2x +1 is a factor of 2x3 +5x2+4x+1 and factories completely

larisa [96]

$\text{According to the factor theorem, if f(b) = 0, then x-b is a factor of f(x).}\\\\\text{Given that,}\\\\f(x) = 2x^3 +5x^2 +4x +1 \\\\f\left(-\dfrac 12 \right) = 2\left( - \dfrac 12 \right)^3 +5 \left( - \dfrac 12 \right)^2 +4 \left( - \dfrac 12 \right) +1 \\\\\\~~~~~~~~~~~~=-2 \cdot \dfrac 18 + 5 \cdot \dfrac 14 -2 +1 \\\\\\~~~~~~~~~~~=\dfrac 54 -\dfrac14 -1\\\\\\~~~~~~~~~~~=\dfrac 44 -1 \\\\\\~~~~~~~~~~~=1-1\\\\\\~~~~~~~~~~~=0\\\\\text{So,}~ 2x +1 ~ \text{is a factor of f(x).}$

$\text{Now,}\\\\f(x) = 2x^3 +5x^2 +4x +1 \\\\~~~~~~=2x^3+x^2 +2x^2 +2x +2x+1\\\\~~~~~~=x^2(2x+1) +2x(2x+1) + (2x+1)\\\\~~~~~~=(2x+1)(x^2 +2x +1)\\\\~~~~~~=(2x+1)(x+1)^2$

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2 years ago