Which expression is the factorization of x2 10x 21? (x 3)(x 7) (x 4)(x 6) (x 6)(x 15) (x 7)(x 14)

Mathematics

1 answer:

Leona [35]2 years ago

6 0

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$\sf{↪ {x}^{2} + 10x + 21} \\ \\ \sf{↪by \: splitting \: middle \: term} \\ \\ \sf{↪ {x}^{2} + 7x + 3x + 21} \\ \\ \sf{↪taking \: common} \\ \\ \sf{↪x(x + 7) + 3(x + 7)} \\ \\ \sf{↪(x + 3)(x + 7) \: is \: yr \: answer}$

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Daniel uses \large \frac{2}{3}cup of orange juice for every \large \frac{1}{4}cup of carrot juice to make his drink. Enter the n

USPshnik [31]

Answer:

$\dfrac{8}{3}\ \text{cups of orange juice}$ or $2\dfrac{2}{3}\ \text{cups of orange juice}$ is used

Step-by-step explanation:

Daniel uses the proportions of $\dfrac{2}{3}$ cups of orange juice and $\dfrac{1}{4}$ cups of carrot juice to make a mixed juice.

Now, in the question 1 cup of carrot juice is used. So 4 times of the proportion of the carrot juice is used. Accordingly 4 times of the cups of orange juice will be used.

$\dfrac{2}{3}\ \text{cups of orange juice}=\dfrac{1}{4}\ \text{cups of carrot juice}\\\Rightarrow 4\times \dfrac{2}{3}\ \text{cups of orange juice}=4\times \dfrac{1}{4}\ \text{cups of carrot juice}\\\Rightarrow \dfrac{8}{3}\ \text{cups of orange juice}=1\ \text{cup of carrot juice}$