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2 years ago

Given logx 2=p and logx 7=q , express log7 4x² in terms of p and q

Mathematics

1 answer:

kodGreya [7K]2 years ago

5 0

Answer:

[2(p + 1)]/q

Step-by-step explanation:

logx 2 = p

logx 7 = q

log7 4x² = log7 (2x)²

= (logx (2x)²)/(logx 7)

= (2 logx 2x)/(logx 7)

= (2 logx 2 + 2 logx x)/(logx 7)

= (2p + 2)/q

= [2(p + 1)]/q

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Fill in the missing expression

padilas [110]

Answer:

The complete table is:

[ 5a ] + [ a + 3 ] + [ 4a ] = [ 10a + 3 ]

+ + + +

[ 2b ] + [ 4 + a ] + [ -a ] = [ 2b + 4 ]

+ + + +

[ 2a ] + [ a + 1 ] + [ -3a ] = [ 1 ]

= = = =

[ 7a + 2b ] + [ 3a + 8 ] + [ 0 ] = [10a + 2b + 8 ]

Explanation:

You can determine the content of each box by subtraction, running the rows and the columns.

The expressions are:

[ 5a ] + [ ] + [ 4a ] = [ 10a + 3 ]

+ + + +

[ 2b ] + [ 4 + a ] + [ ] = [ ]

+ + + +

[ ] + [ ] + [ -3a ] = [ 1 ]

= = = =

[ ] + [ 3a + 8 ] + [ ] = [10a + 2b + 8 ]

1. First row:

[ 5a ] + [ ] + [ 4a ] = [ 10a + 3 ]

[ ] = [10a+ 3] - [ 4a ] - [ 5a ] = 10a - 4a - 5a + 3 = a + 3

2. Second colum:

[ a + 3 ] + [ 4 + a ] + [ ] = [ 3a + 8 ]

[ ] = [ 3a + 8 ] - [ a + 3 ] - [ 4 + a ] = 3a - a + a + 8 - 4 - 3 = a + 1

So far, you have completed this:

[ 5a ] + [ a + 3 ] + [ 4a ] = [ 10a + 3 ]

+ + + +

[ 2b ] + [ 4 + a ] + [ ] = [ ]

+ + + +

[ ] + [ a + 1 ] + [ -3a ] = [ 1 ]

= = = =

[ ] + [ 3a + 8 ] + [ ] = [10a + 2b + 8 ]

3. Complete the row 3:

[ ] + [ a + 1 ] + [ -3a ] = [ 1 ]

[ ] = [ 1 ] - [ a + 1 ] - [ -3a ] = - a + 3a + 1 - 1 = 2a

So far, you have completed this:

[ 5a ] + [ a + 3 ] + [ 4a ] = [ 10a + 3 ]

+ + + +

[ 2b ] + [ 4 + a ] + [ ] = [ ]

+ + + +

[ 2a ] + [ a + 1 ] + [ -3a ] = [ 1 ]

= = = =

[ ] + [ 3a + 8 ] + [ ] = [10a + 2b + 8 ]

4. Complete the fourth column:

[ 10a + 3 ] + [ ] + [ 1 ] = [10a + 2b + 8 ]

[ ] = 10a + 2b + 8 - 10a - 3 - 1 = 2b + 4

So far, this is the results:

[ 5a ] + [ a + 3 ] + [ 4a ] = [ 10a + 3 ]

+ + + +

[ 2b ] + [ 4 + a ] + [ ] = [ 2b + 4 ]

+ + + +

[ 2a ] + [ a + 1 ] + [ -3a ] = [ 1 ]

= = = =

[ ] + [ 3a + 8 ] + [ ] = [10a + 2b + 8 ]

5. Complete the second row:

[ 2b ] + [ 4 + a ] + [ ] = [ 2b + 4 ]

[ ] = [ 2b + 4 ] - [ 2b ] - [ 4 + a ] = 2b - 2b + 4 - 4 - a = - a

So far:

[ 5a ] + [ a + 3 ] + [ 4a ] = [ 10a + 3 ]

+ + + +

[ 2b ] + [ 4 + a ] + [ -a ] = [ 2b + 4 ]

+ + + +

[ 2a ] + [ a + 1 ] + [ -3a ] = [ 1 ]

= = = =

[ ] + [ 3a + 8 ] + [ ] = [10a + 2b + 8 ]

6. Complete the first colum:

[ 5a ] + [ 2b ] + [2a ] = [ ]

[ ] = [ 7a + 2b ]

So far:

[ 5a ] + [ a + 3 ] + [ 4a ] = [ 10a + 3 ]

+ + + +

[ 2b ] + [ 4 + a ] + [ -a ] = [ 2b + 4 ]

+ + + +

[ 2a ] + [ a + 1 ] + [ -3a ] = [ 1 ]

= = = =

[ 7a + 2b ] + [ 3a + 8 ] + [ ] = [10a + 2b + 8 ]

7. Complete the last row:

[ 7a + 2b ] + [ 3a + 8 ] + [ ] = [10a + 2b + 8 ]

[ ] = [10a + 2b + 8 ] - [ 7a + 2b ] - [ 3a + 8 ] = 0

The complete table is:

[ 5a ] + [ a + 3 ] + [ 4a ] = [ 10a + 3 ]

+ + + +

[ 2b ] + [ 4 + a ] + [ -a ] = [ 2b + 4 ]

+ + + +

[ 2a ] + [ a + 1 ] + [ -3a ] = [ 1 ]

= = = =

[ 7a + 2b ] + [ 3a + 8 ] + [ 0 ] = [10a + 2b + 8 ]

5 0

3 years ago

The mean monthly car payment for 123 residents of the local apartment complex is $624. What is the best point estimate for the m

Natali [406]

Answer:

The best point estimate for the mean monthly car payment for all residents of the local apartment complex is $624.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

In this question:

We apply the inverse Central Limit Theorem.

The mean monthy car payment for 123 residents of the local apartment complex is $624.

So, for all residents of the local apartment complex, the best point estimate for the mean monthly car payment is $624.

3 0

3 years ago

PLSSS HELP PANICKING

devlian [24]

Answer:

Step-by-step explanation:

a systems of equations can be made from the information on the problem

x+y=48

x=2y+3

since x= 2y+3 substitute 2y+3 in the firat equation to get:

(2y+3)+y=48 -> 3y+3=48 -> 3y=45 -> y=15

plug in 15 for y in the second equation to solve for x

x+15 =48 --> x=33

8 0

2 years ago

Convert 0.6 shuttle orbits per hour to orbits per year

Hoochie [10]

Answer:

5256 orbits

Step-by-step explanation:

There are 8760 hours in a year, and at a rate of 0.6 orbits per hour you can find how many orbits there are per year by multiplying the rate and time like this

8760 x 0.6

This gives us an answer of 5256 which is the number of orbits per year

4 0

3 years ago

PART1

Mice21 [21]

Part 1: $\frac{5x^{3} + 10x^{2} + 15x}{5x} = \frac{5x^{3}}{5x} + \frac{10x^{2}}{5x} + \frac{15x}{5x} = x^{2} + 2x + 3$
The answer is C.

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The answer is A.

8 0

3 years ago

Given logx 2=p and logx 7=q , express log7 4x² in terms of p and q​

Given logx 2=p and logx 7=q , express log7 4x² in terms of p and q