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zlopas [31]
3 years ago
12

Factor 7(x − 3)2 − 4(x − 3) − 3 completely.

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
7 0
7(x-3)^2-4(x-3)-3\\\\substitute\ t=x-3,\ then\ we\ have\\\\7t^2-4t-3\\\\a=7;\ b=-4;\ c=-3\\\\\Delta=b^2-4ac\\\\\Delta=(-4)^2-4\cdot7\cdot(-3)=16+84=100\\\\t_1=\dfrac{-b-\sqrt\Delta}{2a};\ t_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{100}=10\\\\t_1=\dfrac{-(-4)-10}{2\cdot7}=\dfrac{4-10}{14}=\dfrac{-6}{14}=-\dfrac{3}{7}\\\\t_2=\dfrac{-(-4)+10}{2\cdot7}=\dfrac{4+10}{14}=\dfrac{14}{14}=1\\\\7t^2-4t-3=7\left(t+\dfrac{3}{7}\right)(t-1)=(7t+3)(t-1)\\\\=(7(x-3)+3)(x-3-1)=(7x-21+3)(x-4)\\\\=\boxed{(7x-18)(x-4)}
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4. Find the solution to the equation below.<br> please finish<br> this<br> problem
velikii [3]

Answer:

w = 12

Step-by-step explanation:

We are given the equation:

\displaystyle{\dfrac{w-2}{4} = \dfrac{2w+1}{10}}

First, clear out the denominators by multiplying both sides by LCM. In this scenario, our LCM is 40. Thus, multiply both sides by 40:

\displaystyle{\dfrac{w-2}{4} \cdot 40= \dfrac{2w+1}{10} \cdot 40}

Simplify the expressions/equations:

\displaystyle{(w-2)\cdot 10= (2w+1)\cdot 4}\\\\\displaystyle{10w-20= 8w+4}

Isolate w-variable:

\displaystyle{10w-20= 8w+4}\\\\\displaystyle{10w-8w=4+20}\\\\\displaystyle{2w=24}\\\\\displaystyle{w=12}

Hence, the solution is w = 12

If you have any questions regarding my answer or explanation, do not hesitate to ask away in comment!

4 0
1 year ago
Four more then the product of 3 and x is less than 40
dedylja [7]

3x + 4 < 40

Hope this helps! ;)

5 0
3 years ago
5. A function is given below.<br> f(x) = 3x2 - x + 6<br> What is f(2)?<br> 2
goldenfox [79]

Answer:   10

Step-by-step explanation:

f(x)= 3 (2) - x + 6

f(x)= 6 - 2 + 6

f(x)=  4 + 6

f(x) = 10

7 0
3 years ago
Read 2 more answers
What is an isometry that maps all points of a figure the same distance in the same direction.
stira [4]
 A translation
(I'm assuming that this isn't multiple choice since you didn't include the answer choices.)
4 0
3 years ago
Use the formula s=32, 512(1.10)^t to calculate your salary after 2 years. Round your answer to the nearest dollar.
Amiraneli [1.4K]

<em><u>Answer:</u></em>

s = $39,340

<em><u>Explanation:</u></em>

Note: I will use the symbol "n" instead of "t" in the solution.

<u>The given formula is:</u>

s = 32,512 * (1.1)ⁿ where "n" is the number of years.

We want to get the salary after 2 years. This means that we will substitute with n = 2 in the above equation and get the value of s.

<u>This is shown as follows:</u>

s = 32,512 * (1.1)²

s = $39,339.52 which is approximately $39,340

Hope this helps :)

8 0
3 years ago
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