Solve. Please show your work

Answer:

Proof below

Step-by-step explanation:

Irrational and Rational Numbers

We need to use the basic property of logarithms:

[tex]log_b\ a=x\ \ \Rightarrow b^x=a[/tex]

We are given:

[tex]log_3\ 7[/tex]

And we will prove it's an irrational number, i.e., it's not a rational number.

Recall a rational number can always be expressed as a fraction a/b, where a and b are integer numbers. Thus, if the expression was a rational number, then:

[tex]\displaystyle log_3\ 7=\frac{a}{b}[/tex]

Applying the property:

[tex]\displaystyle 3^{\frac{a}{b}}=7[/tex]

Raising to the power of b:

[tex]3^a=7^b[/tex]

It's not possible to find two integers a and b that satisfy the condition above. That contradiction comes from the assumption that [tex]log_3\ 7[/tex] is rational, thus, it's proven [tex]log_3\ 7[/tex] is irrational.

Answer:

hi im zachary Grace im a male please wait while i type your awsner ;) So, m = 180 - 110 or 70°. interior angles, so they have the same measure so i think its A or B i tried hope this helps

Answer:

choice b

Step-by-step explanation:

Answer:

x= 1/25

Step-by-step explanation:

Answer:

0.1

Step-by-step explanation:

divide the length value by 1000

Answer:

exponential decay

Step-by-step explanation:

anything less than 1 in the parenthesis is decay

Not exactly correct.

y=mx+b Slope is m and y intercept is b.

So, here count the units for the slope. it goes barley to the 7th box. Now, count the units for the y intercept. It goes to the fourth box.

Thus, your equation is y=7x+4

[tex]\underline{Hope\;it\;helps\;out!}[/tex]

Answer:

Step-by-step explanation:

1. is 10

4. is 6

6. is $3.19

7. is $6

Answer:

Step-by-step explanation:

She has 80% of the total amount she had before she sold any. Can't solve any further for you, unless you provide me the number sold or the amount she had before she sold them.

Answer:

no

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

i just divided 448 and 16 and got that, om on that same question

here is how to divide that so you know on  your own

Step 1:

Start by setting it up with the divisor 16 on the left side and the dividend 448 on the right side like this:

 1 6 ⟌ 4 4 8

Step 2:

The divisor (16) goes into the first digit of the dividend (4), 0 time(s). Therefore, put 0 on top:

       0    

 1 6 ⟌ 4 4 8

Step 3:

Multiply the divisor by the result in the previous step (16 x 0 = 0) and write that answer below the dividend.

       0    

 1 6 ⟌ 4 4 8

      0    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (4 - 0 = 4) and write the answer below.

       0    

 1 6 ⟌ 4 4 8

     - 0    

       4    

Step 5:

Move down the 2nd digit of the dividend (4) like this:

       0    

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

Step 6:

The divisor (16) goes into the bottom number (44), 2 time(s). Therefore, put 2 on top:

       0 2  

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

Step 7:

Multiply the divisor by the result in the previous step (16 x 2 = 32) and write that answer at the bottom:

       0 2  

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

       3 2  

Step 8:

Subtract the result in the previous step from the number written above it. (44 - 32 = 12) and write the answer at the bottom.

       0 2  

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

     - 3 2  

       1 2  

Step 9:

Move down the last digit of the dividend (8) like this:

       0 2  

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

     - 3 2  

       1 2 8

Step 10:

The divisor (16) goes into the bottom number (128), 8 time(s). Therefore put 8 on top:

       0 2 8

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

     - 3 2  

       1 2 8

Step 11:

Multiply the divisor by the result in the previous step (16 x 8 = 128) and write the answer at the bottom:

       0 2 8

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

     - 3 2  

       1 2 8

       1 2 8

Step 12:

Subtract the result in the previous step from the number written above it. (128 - 128 = 0) and write the answer at the bottom.

       0 2 8

 1 6 ⟌ 4 4 8

     - 0    

       4 4  

     - 3 2  

       1 2 8

     - 1 2 8

           0

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 448 divided by 16 calculated using Long Division is:

28

0 Remaind

Answer:

option A 9/15

im srry i suck at math

Answer:

she drive 65 miles Per hour

Answer:

if she drive for two more hours that means she drove 4 hours and plus 130 plus 130 and that will equal 260. so the answeris 260.

Step-by-step explanation:

Given:

The number is -6.

To find:

The inverse with respect to addition of the given number.

Solution:

We need to find the additive inverse of -6, to get the inverse with respect to addition of -6.

We know that, the sum of a number and its additive inverse is 0.

Let the additive inverse of -6 be x. Then,

[tex]-6+x=0[/tex]

Adding 6 on both sides, we get

[tex]-6+x+6=0+6[/tex]

[tex]x=6[/tex]

Therefore, the inverse with respect to addition of -6 is 6.

Answer:

Length = 12

Width = 8

Height = 4

Step-by-step explanation:

Let length of box = l

Width = 2/3 * l

Height = 1/3 * l

Volume of the box = 384 ft³

Volume = Length * width * height

Volume of box = l * 2/3 l * 1/3 l

384 = 2l³ / 9

384 * 9 = 2l³

3456 = 2l³

l³ = 3456 / 2

l³ = 1728

Take the Cube root of 1728

l = 12

Length = 12

Width = 2/3 * 12 = 8

Height = 1/3 * 12 = 4

Answer:

-x.(3x^2+4)

Step-by-step explanation:

Brain-list?

Answer:

-3(-1)^3-4(-1)= 27+4=31

Step-by-step explanation:-3 and -1 when you multiply both minus will change into plus. same for -4 and -1 when you multiply will change the signs. so you will get 27+4=31

Answer:

m < 1 = 72

Step-by-step explanation:

Since we know that line l and line m are parallel and that p is one of their transversals, it sets up a situation where we can identify which angles are congruent (equal) to one another according to their positions.

In this case, we can see that < 3 and < 1 are in the same matching corners created by the transversal. When angles are in the same matching corners they are called corresponding angles - and according to the Corresponding Angles Postulate, corresponding angles are congruent.

Therefore, m < 3 = m < 1, and since it's given that  m < 3 = 72, we know that m < 1 = 72 too.

The given expression is :

2xx+3-5(x-2)

We know that, [tex]x{\cdot}x=x^2[/tex]

[tex]=2x^2+3-5(x-2)\\\\=2x^2+3+(-5)(x)+(-5)(-2)\\\\=2x^2+3-5x+10[/tex]

Aleena expands 2xx+3-5(x-2) as 2x²+3-5x-10. She is mistaken because the sign before 10 should be +10 instead of -10. Hence, the correct expanded form is 2x²+3-5x+10. Hence, this is the required solution.

Answer: 47?

Step-by-step explanation:

Answer:

We conclude that after 6 drops how much liquid the scientist has added 0.84 mL.

Step-by-step explanation:

Given that the scientist adds drops of liquid to a test tube.

In order to determine the amount of liquid after 6 drops, all we need is to multiply 0.14 mL by 6.

i.e.

The amount of liquid in 6 drops = 0.14 × 6

                                                     = 0.84 mL

Therefore, we conclude that after 6 drops how much liquid the scientist has added 0.84 mL.

Answer: A

Step-by-step explanation:

1000 = 500e^(2x)

2 = e^(2x)

ln2 = 2x

Step-by-step explanation:

1000 = 500e^(2x)

2 = e^(2x)

ln2 = 2x

x = ln2 / 2. (A)

Answer:

9 cm.

Step-by-step explanation:

First, let's form an equation. We'll represent the final depth of snow on Cherry Street with the variable d. We'll represent the hours with the variable h.

10 - 1/3h = d

Now, you already know what h equals so you can replace h with 3 for 3 hours.

10 - 1/3(3) = d

1/3 * 3 = 1.

10 - 1 = d

10 - 1 = 9

Now, we know what d equals.

10 - 1/3(3) = 9.

Do NOT forget the unit of measurement in your final answer, cm. In the photo, it looks as though it has already been provided.

The final answer is 9 cm.

Answer:

Double root / x = -3

Step-by-step explanation:

Answer:

CI  = ( 36,6  ;  41,4 )

Step-by-step explanation:

CI = 99,9  %       α = 0,1 %      α = 0,001

We find z scre for α = 0,001 in z -table

z(s) = - 3,08

CI =  μ₀  ±  MOE          where    μ₀  = 39 min  and   MOE = z(s) * σ/√n

CI = 39  ±   3,08 * 4,8 / √37

CI = 39  ±   2,4315

CI  = ( 36,6  ;  41,4 )

Answer:

Step-by-step explanation:

Y la pregunta?

Answer:

x=8

y=138

Step-by-step explanation:

5x+2+6x=90

11x+2=90

11x=88

x=8

y+5x+2=180

y+40+2=180

y+42=180

y= 138

Answer:

.56

Step-by-step explanation:

Answer:

7:45 AM I believe:)

Step-by-step explanation:

Answer:

Given - Twice a no. is 42 less than 5 times a no.

To find - The no.

Solution -

According to the question the equation made is -

2x = 5x - 42

2x - 5x = (-42)

(-3x) = (-42)

x= (-42)/(-3)

x = 14

The no. is 14

Answer:

We accept with 99 % of confidence that p₁ ( the proportion in the group aged 18 - 34 ) is bigger than p₂ (the proportion in the group aged 35-44)

Step-by-step explanation:

Group aged  18 - 34

Sample size n₁  =  655  sample size enough to apply a normal distribution aproximation for the test

p₁ = 0,45      and   q₁ =  1 - p₁      q₁ = 0,55

p₁*n₁  =  0,45*655 = 294     q₁*n₁  = 0,55*655 = 360

both bigger than 5

p₁  = 45 %     or     p₁  = 0,45          then  q₁  = 1 - 0,45    q₁ = 0,55

Group aged 35 - 44

Sample size  n₂  =  420 sample size enough to apply a normal distribution aproximation for the test

p₂  =  37%   p₂ = 0,37     and    q₂  = 0,63

p₂*n₂  =  0, 37*420 =  155     q₁*n₁  = 0,63*420 = 264

Test Hypothesis

Null Hypothesis        H₀                                             p₁  =  p₂

Alternative Hypothesis Hₐ                                        p₁  >  p₂

Significance level    α  =  1%   α  = 0,01

Confidence Interval     CI = 99 %

Then   from z table  we find   critical z   z (c )  = 3,1

Calculating   z(s)

z(s)  =  (  p₁ - p₂ )/ √[ ( p₁*q₁)/n₁ ] + [ (p₂*q₂)/n₂ ]

z(s ) = (0,45 - 0,37 ) /  √ 0,45*0,55)/655  +  0,37*0,63 /420

z(s)  = 0,08  /0,03

z(s) = 2,66

Comparing  z(s)  and z(c)

z(s) < z(c)

Then z (s) is inside the acceptance region for H₀