<h3>a)
![\frac{2}{5} \div ( - \frac{3}{4} )](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B5%7D%20%20%5Cdiv%20%28%20%20-%20%5Cfrac%7B3%7D%7B4%7D%20%29)
</h3><h3>■Dividing a positive and a negative equals a negative: (+)÷(-)=(-)</h3>
<h2>
![- \frac{2}{5} \div \frac{3}{4}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B2%7D%7B5%7D%20%20%5Cdiv%20%20%5Cfrac%7B3%7D%7B4%7D%20)
</h2><h3>■To divide by a fraction, multiply by the reciprocal of that fraction</h3>
<h2>
![- \frac{2}{5} \times \frac{4}{3}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B2%7D%7B5%7D%20%20%5Ctimes%20%20%5Cfrac%7B4%7D%7B3%7D%20)
</h2><h3>■Multiply the fractions</h3>
<h2>
![- \frac{8}{15}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B8%7D%7B15%7D%20)
</h2>
<h3>Hence, Quotient =
![- \frac{8}{15}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B8%7D%7B15%7D%20)
</h3>
<h3>b)
![0.4 \div ( - 0.75)](https://tex.z-dn.net/?f=0.4%20%5Cdiv%20%20%28%20-%200.75%29)
</h3><h3>■Convert the decimals into a fractions</h3>
<h2>
![\frac{2}{5} \div ( - \frac{3}{4} )](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B5%7D%20%20%5Cdiv%20%28%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20%29)
</h2><h3>■Dividing a positive and a negative equals a negative: (+)÷(-)=(-)</h3>
<h2>
![- \frac{2}{5} \div \frac{3}{4}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B2%7D%7B5%7D%20%20%5Cdiv%20%20%5Cfrac%7B3%7D%7B4%7D%20)
</h2><h3>■To divide by a fraction, multiply by the reciprocal of that fraction</h3>
<h2>
![- \frac{2}{5} \times \frac{4}{3}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B2%7D%7B5%7D%20%20%5Ctimes%20%20%5Cfrac%7B4%7D%7B3%7D%20)
</h2><h3>■Multiply the fractions</h3>
<h2>
![- \frac{8}{15}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B8%7D%7B15%7D%20)
</h2><h3>Hence, Quotient is
![- \frac{8}{15}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B8%7D%7B15%7D%20)
</h3>
<h3>c)
![- \frac{2}{5} \div \frac{3}{4}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B2%7D%7B5%7D%20%20%5Cdiv%20%20%5Cfrac%7B3%7D%7B4%7D%20)
</h3><h3>■To divide by a fraction, multiply by the reciprocal of that fraction</h3>
<h2>
![- \frac{2}{5} \times \frac{4}{3}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B2%7D%7B5%7D%20%20%5Ctimes%20%20%5Cfrac%7B4%7D%7B3%7D%20)
</h2><h3>■Multiply the fractions</h3>
<h2>
![- \frac{8}{15}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B8%7D%7B15%7D%20)
</h2><h3>Hence, The Quotient is
![- \frac{8}{15}](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B8%7D%7B15%7D%20)
</h3>
Answer:
6.6%
Step-by-step explanation:
Given:
Jeffery babysits for 4 dollars per hour and works as a math tutor for 7 dollars per hour.
He is only allowed to work 13 hours total per week.
He wants to make at least 65 dollars.
To find:
The system of inequalities to represent this situation.
Solution:
Let x be the number of hours he babysits per week and y be the number of hours h works as a math tutor.
He is only allowed to work 13 hours total per week. It means sum of x and y must be less than or equal to 13.
![x+y\leq 13](https://tex.z-dn.net/?f=x%2By%5Cleq%2013)
He wants to make at least 65 dollars. It means total earnings must be greater than or equal to 65.
![4x+7y\geq 65](https://tex.z-dn.net/?f=4x%2B7y%5Cgeq%2065)
Number of hours can not be negative.
.
Therefore, the required system of inequalities contains some equations,
and
.
<span><span>13−<span>6x</span></span>=<span><span><span>(<span><span>2x</span>−5</span>)</span>2</span>+3</span></span>Step 1: Simplify both sides of the equation.<span><span><span>−<span>6x</span></span>+13</span>=<span><span><span>4<span>x2</span></span>−<span>20x</span></span>+28</span></span>Step 2: Subtract 4x^2-20x+28 from both sides.<span><span><span><span>−<span>6x</span></span>+13</span>−<span>(<span><span><span>4<span>x2</span></span>−<span>20x</span></span>+28</span>)</span></span>=<span><span><span><span>4<span>x2</span></span>−<span>20x</span></span>+28</span>−<span>(<span><span><span>4<span>x2</span></span>−<span>20x</span></span>+28</span>)</span></span></span><span><span><span><span>−<span>4<span>x2</span></span></span>+<span>14x</span></span>−15</span>=0</span>Step 3: Use quadratic formula with a=-4, b=14, c=-15.<span>x=<span><span><span>−b</span>±<span>√<span><span>b2</span>−<span><span>4a</span>c</span></span></span></span><span>2a</span></span></span><span>x=<span><span><span>−<span>(14)</span></span>±<span>√<span><span><span>(14)</span>2</span>−<span><span>4<span>(<span>−4</span>)</span></span><span>(<span>−15</span>)</span></span></span></span></span><span>2<span>(<span>−4</span>)</span></span></span></span><span>x=<span><span><span>−14</span>±<span>√<span>−44</span></span></span><span>−<span>8</span></span></span></span>
Given :
The number is given as 90.
Explanation :
To find the product of prime factors in expanded form
![90=2\times3\times3\times5](https://tex.z-dn.net/?f=90%3D2%5Ctimes3%5Ctimes3%5Ctimes5)
Answer :
Hence the answer is