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2 years ago

Which expression give the prime factorization of 80?

Mathematics

2 answers:

liq [111]2 years ago

7 0

Answer:

Prime factorization: 80 = 2 x 2 x 2 x 2 x 5 which can also be written 80 = 2⁴ x 5.

Step-by-step explanation:

hope this helped <3

lana [24]2 years ago

7 0

Answer:

2 x 2 x 2 x 2 x 5

Step-by-step explanation:

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

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

2 years ago

Given that 1/f = 1/u + 1/v , express u in terms of v and f

JulijaS [17]

Answer:

u = fv/(v - f)

Step-by-step explanation:

1/f = 1/u + 1/v

1/u = 1/f - 1/v = v/fv - f/fv = (v-f)/fv

1/u = (v-f)/fv

u = fv/(v - f)

5 0

3 years ago

Help me please I don’t understand this question so please help?

Luba_88 [7]

Answer:

11- All 0's are on the x and y planes

12- All positive points/numbers are where the x and y axis are both positive (Quadrant 1, 2, and 4)

13- All negative points/numbers would be wherever the x and y axis are negative (Quadrants 2, 3, and 4)

3 0

2 years ago

What is the equation of the trend line in the scatter plot ?

ryzh [129]

Answer:

Equation: -3x + 18

Hope this helps!

6 0

2 years ago

PLS HELP WILL MARK BRAINLIEST, NO FAKE ANSWERS OR WILL BE REPORTED.

Travka [436]

False

Like terms have the same literal coefficients but can have different Numerical Coefficients

Hope this helped you- have a good day bro cya)

3 0

2 years ago

Read 2 more answers