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3 years ago

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Max found a pair of jeans on sale for 40 percent off. He used a coupon for an additional 20 percent off. If the original price o

f the pair of jeans was $68, what is the final price of the pair of jeans before taxes?

1 answer:

Novay_Z [31]3 years ago

3 0

Answer:

$27.2

Step-by-step explanation:

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Log(x-2)+log2=2logy<br>log(x-3y+3)=0

In-s [12.5K]

Answer:

<h2>x = 4 and y = 2 or x = 10 and y = 4</h2>

Step-by-step explanation:

$\left\{\begin{array}{ccc}\log(x-2)+\log2=2\log y&(1)\\\log(x-3y+3)=0&(2)\end{array}\right$

$===========================\\\text{DOMAIN:}\\\\x-2>0\to x>2\\y>0\\x-3y+3>0\to x-3y>-3\\=====================\\\\\text{We know:}\ \log_ab=c\iff a^c=b,\\\\\text{therefore}\ \log_ab=0\iff a^0=b\to b=1\\\\\text{From this we have}\\\\\log(x-3y+3)=0\iff x-3y+3=1\qquad\text{add}\ 3y\ \text{to both sides}\\\\x+3=3y+1\qquad\text{subtract 3 from both isdes}\\\\\boxed{x=3y-2}\qquad(*)\\\\\text{Substitute it to (1)}$

$\log(3y-2-2)+\log2=2\log(y)\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log(3y-4)+\log2=\log(y^2)\qquad\text{subtract}\ \log(y^2)\ \text{from both sides}\\\\\log(3y-4)+\log2-\log(y^2)=0\\\\\text{Use}\ \log_ab+\log_ac=\log_a(bc)\ \text{and}\ \log_ab-\log_ac=\log_a\dfrac{b}{c}\\\\\log\dfrac{(3y-4)(2)}{y^2}=0\qquad\text{use}\ \log_ab=0\Rightarrow b=1\\\\\dfrac{(3y-4)(2)}{y^2}=1\iff y^2=(3y-4)(2)\\\\\text{Use the distributive property}\ a(b+c)=ab+ac$

$y^2=(3y)(2)+(-4)(2)\\\\y^2=6y-8\qquad\text{subtract}\ 6y\ \text{from both sides}\\\\y^2-6y=-8\qquad\text{add 8 to both sides}\\\\y^2-6y+8=0\\\\y^2-2y-4y+8=0\\\\y(y-2)-4(y-2)=0\\\\(y-2)(y-4)=0\iff y-2=0\ \vee\ y-4=0\\\\\boxed{y=2\ \vee\ y=4}\in D$

$\text{Put the values of}\ y\ \text{to }\ (*):\\\\\text{for}\ y=2:\\\\x=3(2)-2\\\\x=6-2\\\\\boxed{x=4}\in D\\\\\text{for}\ y=4:\\\\x=3(4)-2\\\\x=12-2\\\\\boxed{x=10}\in D$

4 0

3 years ago

A hemisphere has a diameter of 26 centimeters. What is the volume of a sphere with the same radius?

salantis [7]

$r= \frac{d}{2}= \frac{26}{2} \;\Rightarrow r=13\,cm \\ \\ 
V= \frac{4}{3} \pi r^3 \\ \\ 
V= \frac{4}{3} \pi \,(13)^3 \\ \\ 
V= \dfrac{4\cdot 2197}{3} \pi \\ \\ 
V= \frac{8788}{3} \pi\approx 9202,77\,cm^3$

4 0

3 years ago

If my grade is an 72 and I get a 100 on a test, how will that affect my grade? (What will my grade be after?)

pychu [463]

Answer: It depends on what categories your teacher has and what percent of your grade it is worth. I would recommend an online grade calculator

4 0

2 years ago

Read 2 more answers

Alexander is riding his bicycle to school. After one mile, he is a third of the way there. How much farther does he have to ride

Alekssandra [29.7K]

Alexander has to miles to go because if one mile is a third you can simply maltiply by three, then subtract the mile he already went. you maltiply by three because it was a third of the way there

4 0

3 years ago

A triangle has perimeter 59 cm. The lengths of the sides are 2x – 5 cm, 3x + 2 cm and 2x – 1 cm.

Dennis_Churaev [7]

Answer:2x - 5cm + 3x +2cm + 2x - 1cm=59cm

2x + 3x + 2x + 2cm + 1cm - 5cm=59cm

7x - 2cm=59cm

7x - 2cm + 2cm=59cm + 2cm

7x=61cm

X=8 5/7cm

Step-by-step explanation:

4 0

3 years ago