Answer:
temperature on the 5th days was -3 degree Celsius
Step-by-step explanation:
Mean is the average of the numbers
As per the statement:
The mean temperature for the first 4 days in January was 7°C.
Sum of the first 4 days temperature = ![4 \cdot 7 = 28^{\circ} C](https://tex.z-dn.net/?f=4%20%5Ccdot%207%20%3D%2028%5E%7B%5Ccirc%7D%20C)
It is also given that:
the mean temperature for the first 5 days in January was 5°C.
then;
Sum of the first 5 days temperature = ![5 \cdot 5 = 25^{\circ} C](https://tex.z-dn.net/?f=5%20%5Ccdot%205%20%3D%2025%5E%7B%5Ccirc%7D%20C)
We have to find the temperature on the 5th days.
![\text{Temperature on 5th days}=\text{Sum of first 5 days temperature}-\text{Sum of first 4 days temperature}](https://tex.z-dn.net/?f=%5Ctext%7BTemperature%20on%205th%20days%7D%3D%5Ctext%7BSum%20of%20first%205%20days%20temperature%7D-%5Ctext%7BSum%20of%20first%204%20days%20temperature%7D)
Substitute the given values we have;
![\text{Temperature on 5th days} = 25-28 =- 3^{\circ} C](https://tex.z-dn.net/?f=%5Ctext%7BTemperature%20on%205th%20days%7D%20%3D%2025-28%20%3D-%203%5E%7B%5Ccirc%7D%20C)
Therefore, the temperature on the 5th days was -3 degree Celsius
![\boxed{D(x)= (x-2)(x+2)(x-3)(x+3)}](https://tex.z-dn.net/?f=%5Cboxed%7BD%28x%29%3D%20%28x-2%29%28x%2B2%29%28x-3%29%28x%2B3%29%7D)
<h2>Explanation:</h2>
We have the following expression:
![D(x)=x^4-13x^2+36](https://tex.z-dn.net/?f=D%28x%29%3Dx%5E4-13x%5E2%2B36)
So we need to rewrite this equation as the product of linear factors. Linear factors are given of the form:
![ax+b \\ \\ \\ Where: \\ \\ a \ and \ b \ are \ real \ constants](https://tex.z-dn.net/?f=ax%2Bb%20%5C%5C%20%5C%5C%20%5C%5C%20Where%3A%20%5C%5C%20%5C%5C%20a%20%5C%20and%20%5C%20b%20%5C%20are%20%5C%20real%20%5C%20constants)
Since the degree of the polynomial function is 4, the greatest number of linear factors is also 4. Therefore:
Let's change:
![Let's \ change: \ u\mathrm{=}x^2 \\ \\ So: \\ \\ x^4-13x^2+36 \ changes \ to \ u^2-13u+36 \\ \\ \\ Factor \ out: \\ \\ u^2-9u-4u+36 \\ \\ u(u-9)-4(u-9) \\ \\ (u-4)(u-9) \\ \\ \\ But \ u=x^2 \\ \\ D(x)=(x^2-4)(x^2-9) \\ \\ \\ Applying \ difference \ of \ squares: \ a^2-b^2=(a-b)(a+b) \\ \\ \boxed{D(x)= (x-2)(x+2)(x-3)(x+3)}](https://tex.z-dn.net/?f=Let%27s%20%5C%20change%3A%20%5C%20u%5Cmathrm%7B%3D%7Dx%5E2%20%5C%5C%20%5C%5C%20So%3A%20%5C%5C%20%5C%5C%20x%5E4-13x%5E2%2B36%20%5C%20changes%20%5C%20to%20%5C%20u%5E2-13u%2B36%20%5C%5C%20%5C%5C%20%5C%5C%20Factor%20%5C%20out%3A%20%5C%5C%20%5C%5C%20u%5E2-9u-4u%2B36%20%5C%5C%20%5C%5C%20u%28u-9%29-4%28u-9%29%20%5C%5C%20%5C%5C%20%28u-4%29%28u-9%29%20%5C%5C%20%5C%5C%20%5C%5C%20But%20%5C%20u%3Dx%5E2%20%5C%5C%20%5C%5C%20D%28x%29%3D%28x%5E2-4%29%28x%5E2-9%29%20%5C%5C%20%5C%5C%20%5C%5C%20Applying%20%5C%20difference%20%5C%20of%20%5C%20squares%3A%20%5C%20a%5E2-b%5E2%3D%28a-b%29%28a%2Bb%29%20%5C%5C%20%5C%5C%20%5Cboxed%7BD%28x%29%3D%20%28x-2%29%28x%2B2%29%28x-3%29%28x%2B3%29%7D)
<h2>Learn more:</h2>
Factor expressions: brainly.com/question/11962748
#LearnWithBrainly
Answer:
yes because you multiplying the sides
Step-by-step explanation:
To find this, you'd just add 13 to -2. So -2 + 13 = 11. So the starting temperature was 11 degrees.
Answer:
A discount of 15% off the regular price
Step-by-step explanation:
Given
![Regular = \$285](https://tex.z-dn.net/?f=Regular%20%3D%20%5C%24285)
Required
The best deal
See attachment for complete question.
For (a):
![Discount = 5\%](https://tex.z-dn.net/?f=Discount%20%3D%205%5C%25)
![Coupon = \$10](https://tex.z-dn.net/?f=Coupon%20%3D%20%5C%2410)
First, apply discount.
![New\ price = Regular * (100\% - Discount)](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20Regular%20%2A%20%28100%5C%25%20-%20Discount%29)
![New\ price = Regular * (100\% - 5\%)](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20Regular%20%2A%20%28100%5C%25%20-%205%5C%25%29)
![New\ price = Regular * 95\%](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20Regular%20%2A%2095%5C%25)
![New\ price = \$285 * 95\%](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20%5C%24285%20%2A%2095%5C%25)
![New\ price = \$270.75](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20%5C%24270.75)
Remove coupon of $10
![New\ price = \$270.75 -\$10](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20%5C%24270.75%20-%5C%2410)
![New\ price = \$260.75](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20%5C%24260.75)
For (b):
![Discount = 15\%](https://tex.z-dn.net/?f=Discount%20%3D%2015%5C%25)
Apply discount
![New\ price = Regular * (100\% - Discount)](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20Regular%20%2A%20%28100%5C%25%20-%20Discount%29)
![New\ price = Regular * (100\% - 15\%)](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20Regular%20%2A%20%28100%5C%25%20-%2015%5C%25%29)
![New\ price = Regular * 85\%](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20Regular%20%2A%2085%5C%25)
![New\ price = \$285 * 85\%](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20%5C%24285%20%2A%2085%5C%25)
![New\ price = \$242.25](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20%5C%24242.25)
For (c):
![New\ price = \$245](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20%5C%24245)
For (d):
![Coupon = \$10](https://tex.z-dn.net/?f=Coupon%20%3D%20%5C%2410)
![Rebate = \$15](https://tex.z-dn.net/?f=Rebate%20%3D%20%5C%2415)
The new price is calculated as:
![New\ price = Regular - Coupon -Rebate](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20Regular%20-%20Coupon%20-Rebate)
![New\ price = \$285 - \$10 - \$15](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20%5C%24285%20-%20%5C%2410%20-%20%5C%2415)
![New\ price = \$260](https://tex.z-dn.net/?f=New%5C%20price%20%3D%20%5C%24260)
<em>From the list of options, (b) is the best deal because it is the cheapest</em>