MATHEMATICS HIGH SCHOOL

Solve for x
log(x–4)+log(x+3)=2logx

Answers

Answer 1
Answer: D:x-4>0 \wedge x+3>0 \wedge x>0\nD:x>4 \wedge x>-3 \wedge x>0\nD:x>4\n\n\log(x-4)+\log(x+3)=2\log x\n\log(x-4)(x+3)=\log x^2\n(x-4)(x+3)=x^2\nx^2+3x-4x-12=x^2\n-x=12\nx=-12\n-12\not\in D\n\Downarrow\n\boxed{x\in\emptyset}

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2x plus 4 in vertex form

Answers

Vertex form only applies to quadratics. A quadratic is a polynomial with 2 being the largest exponent. I don't see any x^2 term here. Please check the problem to make sure that it's typed correctly. 

Convert the following to a fraction:

0.363636

Answers

0.363636 = 90909
250000
as a fraction
To convert the decimal 0.363636 to a fraction, just follow these steps:
Step 1: Write down the number as a fraction of one:
0.363636 = 0.363636
1
Step 2: Multiply both top and bottom by 10 for every number after the decimal point:
As we have 6 numbers after the decimal point, we multiply both numerator and denominator by 1000000. So,
0.363636
1
= (0.363636 × 1000000)
(1 × 1000000)
= 363636
1000000
.
Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(363636,1000000) = 4. So,
(363636÷4)
(1000000÷4)
= 90909
250000
when reduced to the simplest form.

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Hope it works!

Given the equation 4x + 7 = 3(2x − 5), solve for the variable. Explain each step and justify your process.B.Sam solved a similar equation below. Is Sam's solution correct? Explain why or why not.
5x − 1 = 2(x + 4)
5x − 1 = 2x + 8
7x − 1 = 8
7x = 7
x = 1

Answers

Part 1: 4x + 7 = 3(2x - 5) 

4x+7=6x-15 

7=6x-15-4x 

7=2x-15 

7+15=2x 

22=2x 

22=2x / 2 

x=11 

Part 2: Sam is not correct because he messed up the second step. He added 2x on both sides to get 7x, instead he should have subtracted. 

A quantity h varies directly with w and inversely with p. If h = 2, w = 4, and p = 6. What is the constant of variation?A. 1/2
B. 4/3
C. 3
D. 12

Answers

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

h varies directly with w and inversely with p.

so, Mathematically, it is expressed as

h=(kw)/(p)

Here, h = 2

w = 4

p = 6.

So, it becomes,

2=(4k)/(6)\n\n2* 6=4k\n\n12=4k\n\n(12)/(4)=k\n\nk=3

Hence, Option 'C' is correct.
answer is (C).

let's take the constant as K.

h= K. (w/p)

so; K= (hp ÷w)
K= (2x6) ÷ 4
K = 12÷4
K= 3

When 5 is added to 2 times a number the result is 45

Answers

I'm going to assume that you want us to figure out what the number is for you.

You said:  2x + 5 = 45

Subtract 5 from each side:

2x = 40

Divide each side by 2 :

x = 20
the answer is 20 which I calculated from the equation of 2x+5=45

The water level in Noah's water tank is 72 inches high. Noah begins to drain a water tank by opening a valve. The water drains at a speed up 5 inches per minute.

Answers

So, Noah would most likely have - wait hold up what's the main question?is it how much Noah has? if it is I will be able to solve it. Or is it how much water will fill it or something?
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