X is called the _ When using scientific notation the _ is 10.

Mathematics

1 answer:

Bumek [7]2 years ago

7 0

Answer:

X is called the power of

1 is 10

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Randi and her sister make balloon animals and sold them for $.50 each. They made $48.00. If rando made twice as many animals as

nydimaria [60]

Randy made 64 ballon animals and her sister made 32 ballon animals

Solution:

Let the number of ballon animals sold by Randi be "x"

Let the number of ballon animals sold by her sister be "y"

Cost of 1 ballon animal = $ 0.50

Rando made twice as many animals as her sister

Number of ballon animals sold by Randi = twice the number of ballon animals sold by her sister

x = 2y ---- eqn 1

Together, they earned $ 48

Therefore, we can frame a equation as:

Number of ballon animals sold by Randi x Cost of 1 ballon animal + number of ballon animals sold by her sister x Cost of 1 ballon animal = 48

$2y \times 0.50 + y \times 0.50 = 48$

$1y + 0.5y = 48\\\\1.5y = 48\\\\y = \frac{48}{1.5}\\\\y = 32$

Therefore, from eqn 1

x = 2y

x = 2(32)

x = 64

Thus Randy made 64 ballon animals and her sister made 32 ballon animals

6 0

2 years ago

Rationalize the numerator. <img src="https://tex.z-dn.net/?f=%20%20%5Cfrac%7B%20%5Csqrt%5B3%5D%7B144x%20%7D%20%7D%7B%20%5Csq

Simora [160]

rationalizing the numerator, or namely, "getting rid of that pesky radical at the top".

we simply multiply top and bottom by a value that will take out the radicand in the numerator.

$\bf \cfrac{\sqrt[3]{144x}}{\sqrt[3]{y}}~~
\begin{cases}
144=2\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3\\
\qquad 2^3\cdot 18
\end{cases}\implies \cfrac{\sqrt[3]{2^3\cdot 18x}}{\sqrt[3]{y}}\implies \cfrac{2\sqrt[3]{ 18x}}{\sqrt[3]{y}}
\\\\\\
\cfrac{2\sqrt[3]{ 18x}}{\sqrt[3]{y}}\cdot \cfrac{\sqrt[3]{(18x)^2}}{\sqrt[3]{(18x)^2}}\implies \cfrac{2\sqrt[3]{(18x)(18x)^2}}{\sqrt[3]{(y)(18x)^2}}\implies \cfrac{2\sqrt[3]{(18x)^3}}{\sqrt[3]{18^2x^2y}}$

$\bf \cfrac{2(18x)}{\sqrt[3]{324x^2y}}~~
\begin{cases}
324=2\cdot 2\cdot 3\cdot 3\cdot 3\cdot 3\\
\qquad 12\cdot 3^3
\end{cases}\implies \cfrac{36x}{\sqrt[3]{12\cdot 3^3x^2y}}
\\\\\\
\cfrac{36x}{3\sqrt[3]{12x^2y}}\implies \cfrac{12x}{\sqrt[3]{12x^2y}}$