Answer:
Mrs. Wright's paycheck is $630
Step-by-step explanation:
Let x = Mrs. Wright's paycheck.
Mrs. Wright spent 2/9 of her paycheck on food. This means that the amount of money spent on food is 2/9 × x = 2x/9
She spent 1/3 on rent. This means that the amount spent on rent is
1/3 ×x x = x/3
Amount she spent on food and rent is x/3 + 2x/9 =3x + 2x /9
= 5x/9
The remainder is her pay check - the amount that she spent on food and rent. It becomes
x - 5x/9 = (9x- 5x)/9 = 4x/9
She spent 1/4 of the remainder on transportation. It means that she spent 1/4 × 4x/9 = x /9 on transportation.
Amount left = 4x /9 - x/9= 3x/9
She had $210 left. Therefore,
210 = 3x/9
3x = 9×210 = 1890
x = 1890/3
x = $630
One square can be a 3 by 3 square, meaning each side is 3 units.The area for this would be 9.
Another one is the square can be a 9 by 9 square, meaning each side is 9 units. The area for this would be 81.
Answer:
![(\sqrt[7]{3} )^{4}](https://tex.z-dn.net/?f=%28%5Csqrt%5B7%5D%7B3%7D%20%29%5E%7B4%7D)
Step-by-step explanation:
The only radical that matches the equivalent answer is the fifth one down. We can easily eliminate the radicals without exponents on the outside, since we know they won't create leftover fractions. So that leaves us with the second, fourth and fifth answers to contemplate.
Let's look at ![(\sqrt[4]{3} )^{7}](https://tex.z-dn.net/?f=%28%5Csqrt%5B4%5D%7B3%7D%20%29%5E%7B7%7D)
and ![\sqrt[4]{3^{7} }](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B3%5E%7B7%7D%20%7D)
first. It's good to know that these are equivalent radicals. The numbers are the same, and they will produce the same answers.
When you do the math, the exponent rule gives us fractions of 
for exponents, and eventually, a 
for both answers. So these are eliminated.
Now, for ![(\sqrt[4]{3}^{7}](https://tex.z-dn.net/?f=%28%5Csqrt%5B4%5D%7B3%7D%5E%7B7%7D)
, we can easiy simplify by changing the 7th root to a fraction in our exponent. Use the rule: ![\sqrt[n]{x} = x^{\frac{1}{n} }](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7Bn%7D%20%7D)
- <em>Multiply the exponents:</em>
- <em>Insert the product into the exponent: </em> <u>
</u>
And we can see the answer we're looking for! If you use this method to look at the other problems, you'll see that this is the only radical that simplifies to the required answer.
76,500/100,000 divide by 100
765/1,000. divide by 5
153/500
<em>54</em>
- Step-by-step explanation:
<em>- 2n(5 + n - 8 - 3n) =</em>
<em>replace n = 3</em>
<em>- 2(3)(5 + 3 - 8 - 3×3)</em>
<em>= - 6(8 - 8 - 9)</em>
<em>= - 6(0 - 9)</em>
<em>= - 6 × - 9</em>
<em>= 54</em>
<em>(-)(-) = +</em>
