Hey guys I really need help on this one!

In-s [12.5K]

Answer:

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

Find the angle of elevation of a kite on a 50m<br> string flying 40m vertically above the ground.

Lera25 [3.4K]

Sin(x)=40/50
x= sin^-1(40/50)
x= 53.1301023542—>53.1 rounded to the nearest tenth
angle of elevation is 53.1

6 0

2 years ago

HELP ME PLEASE!!!!!!! ASAP!!!

Svet_ta [14]

x2+5x+3x-24

x(x+5)+3(x-8)

(x+3)(x+5)

x+3=0orx+5=0

x=-3orx=-5

6 0

3 years ago

An expression is given (3^2)^3•3^6/3^4 the rest of the question is in the picture

timama [110]

Answer:

3⁷

Step-by-step explanation:

it's kinda messy but my step by step is in the picture. practically when you "multiply" an exponent (as long as they have the same base number) with another like 3⁴×3⁵ or (3⁴)⁵ you add the exponents together so you'd get 3⁴×3⁵=3⁹

when dividing an exponent by another exponent (with again, the same base number) you subtract the exponents like this: 3⁶÷3² or 3⁶/3² would equal 3⁴

6 0

3 years ago

Twenty-seven minus 1.5 of a number (x) is not more than 36. What is the number?

alexandr1967 [171]

Translate this into symbols: 27 - 1.5x is equal to or less than 36. Find x.

Add 1.5x to both sides, so as to make the coefficient of x positive:

27 = 36 + 1.5x, or -9 = 1.5x, or x = -6 but also
x > -6

Check: let x = -6. Is the given equation then true?

27 = 36 + 1.5(-6) => -9 = -9? Yes.

Check: let x > -6. Is <span>Twenty-seven minus 1.5 of a number (x) not more than 36? 27 - 1.5(0) not more than 36? True.

Thus, x is equal to or greater than -6.</span>

5 0

3 years ago