Rearrange x = 3g + 2 to make g the subject.

The value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.

We are given the logarithmic functions:

log₄3 = 0.792 ,,, (i), and log₄21 = 2.196 ... (ii),

and we are asked to find the value of the logarithmic function log₄7.

On subtracting (i) from (ii), we get:

log₄21 - log₄3 = 2.196 - 0.792.

Using the quotient law of logarithms, according to which:

logₓa - logₓb = logₓ(a/b), we can write the above equation as:

log₄(21/3) = 1.404,

or, log₄7 = 1.404.

Therefore, the value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.

Learn more about logarithms at

https://brainly.com/question/11707281

#SPJ4

Answer:

A.

1.404

Step-by-step explanation:

Answer:

18.1cm

Step-by-step explanation:

Please refer to the attached photo for a better understanding. Apologies for the terrible drawing.

First we will find the length of BE by using pythagoras' Theorem.

[tex]c^{2} =a^{2} +b^{2} \\AB^{2} =BE^{2} +EA^{2} \\16^{2} =BE^{2} +7^{2} \\256=BE^{2} +49\\BE^{2} =256-49\\BE=\sqrt{207} cm[/tex]

We will leave BE as it is as it is not the final answer.

Since we know CD = BE,

CD = [tex]\sqrt{207} cm[/tex]

Now from the photo, draw a line from C to A or A to C, you will see another triangle.

Now we will use Pythagora's Theorem again to find AC.

[tex]AC^{2} =AD^{2} +DC^{2} \\AC^{2} =11^{2} +(\sqrt{207}) ^{2} \\AC^{2} = 121+207\\AC^{2} =328\\AC=\sqrt{328} \\=18.1cm (1dp)[/tex]

Step-by-step explanation:

calculated the cost of numbers of units usex

Answer: 6.71

Step-by-step explanation:

[tex]AB=\sqrt{(-1-5)^{2}+(6-3)^{2}} \approx \boxed{6.71}[/tex]

Answer:

Area of a triangle = 1/2 * base * height

here ,

base = 120 ft

height = 25 ft

Area = 1/2* 120*25

= 60 * 25

= 1500 ft²

Answer 2

Answer:

1/2 * base * height

so 1/2 * 25 * 120

= 1500

The table that could be used to model his climb will consist of 125 ft/h for the first two hours and 87.5 ft/h for the next 4 hours.

The equation that can be used to model the motion of the climber is calculated as follows;

(1, 150)

(2, 275)

(4, 525)

(6, 700)

m = (275 - 150)/(2 - 1) = 125 ft per hour

m = (700 - 525)/(4 - 2) = 87.5 ft/hr

Thus, the table that could be used to model his climb will consist of 125 ft/h for the first two hours and 87.5 ft/h for the next 4 hours.

Learn more about slope here: https://brainly.com/question/3493733

#SPJ1

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:f < 0 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 33 + 6f < 33[/tex]

[ subtract 33 on both sides ]

[tex]\qquad \tt \rightarrow \: 33 - 33+ 6f < 33 - 33[/tex]

[tex]\qquad \tt \rightarrow \: 6f < 0[/tex]

[tex]\qquad \tt \rightarrow \: f < 0[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

Answer:

x = 7

Step-by-step explanation:

[tex](\sqrt{4x-3} )^{2} =5^{2}[/tex]

[tex]4x-3=25[/tex]

[tex]4x=25+3[/tex]

[tex]x=\frac{28}{4}[/tex]

[tex]x=7[/tex]

Hope this helps

Answer:

7

Step-by-step explanation:

5x-3 = 3x+1

2x=4

x=2

plug in

5(2)-3

10-3

7

answer: 7

In terms of l?

TSA

LSA

Answer:

[tex]\sf SA=54\pi\:\:\:cm^2[/tex]

Step-by-step explanation:

Surface Area of a Cone

[tex]\sf SA=\pi r l+\pi r^2[/tex]

where:

Given:

Substitute the given values into the formula and solve for SA:

[tex]\implies \sf SA=\pi (3)(15)+\pi (3)^2[/tex]

[tex]\implies \sf SA=45\pi+ 9 \pi[/tex]

[tex]\implies \sf SA=54\pi\:\:cm^2[/tex]

Therefore, the surface area of the cone in terms of pi is:

[tex]\sf SA=54 \pi\:\:\:cm^2[/tex]

Answer:

[tex]28{cm}^{2} [/tex]

Step-by-step explanation:

we know

area of rectangle=l*b=(7*4)sq cm=28sq cm

Delete the commas if necessary.

============================================================

Explanation:

There are 6 freshmen total and we want to pick 2 of them, where order doesn't matter. The reason it doesn't matter is because each seat on the committee is the same. No member outranks any other. If the positions were labeled "president", "vice president", "secretary", etc, then the order would matter.

Plug n = 6 and r = 2 into the nCr combination formula below

[tex]n C r = \frac{n!}{r!(n-r)!}\\\\6 C 2 = \frac{6!}{2!*(6-2)!}\\\\6 C 2 = \frac{6!}{2!*4!}\\\\6 C 2 = \frac{6*5*4!}{2!*4!}\\\\ 6 C 2 = \frac{6*5}{2!}\\\\ 6 C 2 = \frac{6*5}{2*1}\\\\ 6 C 2 = \frac{30}{2}\\\\ 6 C 2 = 15\\\\[/tex]

This tells us there are 15 ways to pick the 2 freshmen from a pool of 6 total.

Repeat those steps for the other grade levels.

n = 13 sophomores, r = 5 selections leads to nCr = 13C5 = 1287. This is the number of ways to pick the sophomores.

You would follow the same type of steps shown above to get 1287. Let me know if you need to see these steps.

Similarly, 8C4 = 70 is the number of ways to pick the juniors.

Lastly, 14C3 = 364 is the number of ways to pick the seniors.

-----------------------------

To recap, we have...

Multiply out those values to get to the final answer.

15*1287*70*364 = 491,891,400

This massive number is a little under 492 million.

Answer:

Shirts are 6

Hats are 5

Step-by-step explanation:

This is a system of equations. Set up the equations first.

7s + h = 47

5s + h = 35    

-----------------------      Subtract the equations to eliminate the h variable

2s = 12                      Divide by 2 to solve

s = 6                          Each hat is 6

Plug the 6 in for s in either of the original equations

7(6) + h = 47

42 + h = 47          Subtract 42 from both sides

h = 5

Answer:

b

Step-by-step explanation:

Answer:

Group A, because seven children have a forearm length longer than 10 inches

Step-by-step explanation:

Create the dot plots based on the given information (please see attached images).

Group A = blue dots

Group B = red dots

From inspection of the attached dot plots, we can see that Group A appears to have the longer average forearm length.  This is because 7 children have a forearm length of longer than 10 inches.

To calculate the average forearm length, sum all data values and divide by the total number of data values.

[tex]\textsf{Average of Group A}=\dfrac{ 3 \times 10 + 4 \times 11 + 3 \times 12}{10}=11[/tex]

[tex]\textsf{Average of Group B}=\dfrac{ 3 \times 9 + 5\times 10+ 2\times 11}{10}=9.9[/tex]

Thus proving that Group A has the longer average former length.

According to given text data

Average of both groups

A:-

B:-

Group A has bigger average

Answer:

O 8 ^x/3

Step-by-step explanation:

Remember that :

[tex]\sqrt[n]{x} = x^\frac{1}{n}[/tex]

………………………………

Then

[tex]\sqrt[n]{8^x} = (8^{x})^{\frac{1}{3}}[/tex]

      [tex]= 8^{x\times\frac{1}{3}[/tex]

      [tex]=8^{\frac{x}{3}[/tex]

Answer:

A = -12

Step-by-step explanation:

A   put in -2 for 'x' in the equation to find value

       2(-2)  - y = 8       add 4 to both sides

              -y = 12

               y = -12              

        I think YOU can now find B and C  with this method !

Answer:

√72

Decimal Form:

1.32287565…

Step-by-step explanation:

To subtract fractions, find the LCD and then combine.

Answer:

BODMAS

[tex] {6}^{3 } + 5(4 - 2) = 216 + 5(2) \\ = 216 + 10 \\ = 226[/tex]

Answer: Answer is 226

Step-by-step explanation: Do math

Answer:

282.743 yd²

Step-by-step explanation:

Surface Area of the Cylinder: Top Base + Bottom Base + Side

Area of Top Base (Circle): πr² = π(5 yd)² = 25π yd²

Area of Bottom Base (Circle): same as top base = 25π yd²

Area of Side (Rectangle): Circumference*Height = (2πr)*(4 yd) =

2π(5 yd)*(4 yd) = 40π yd²

Total Surface Area = 25π yd² + 25π yd² + 40π yd² = 90π yd² = 282.743 yd²

The input value that produces the same output value in both charts is 2. so the correct answer is option D.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

You are given two functions  f (x) = -0.5X +2 and g(x) = 2x - 3

x      f(x)

-3     3.5

-2     3

-1     2.5

0     2

1      1.5

2     1

3     0.5

The second table is given below:-

x      g(x)

-3      

-2      

-1      

0    

1      

2      

3      

We will put the points and will find the value of functions:-

g(-3) = 2(-3) - 3 = -6 -3 = -9

g(-2) = 2 -(-2) -3 = -7

g(-1) = 2( -1) -3 = -3

g(0) = 2 - 0  - 3 = -3

g(1) = 2.1 - 3 = -1

g(2) = 2.2 -3 = 1

g(3) = 2.3 -3 = 3

Hence the second table will be

x      g(x)

-3      -9

-2      -7

-1       -5

0       -3

1        -1

2       1

3       3

The input value that produces the same output value in both charts is 2.

To know more about function follow

https://brainly.com/question/25638609

#SPJ1

Answer:

1/7 + r = 1/3

Step-by-step explanation:

Rocco takes 7 hours to do the job.
In 1 hour, Rocco does 1/7 of the job.

Rocco's rate is 1/7 job per hour.

It takes Giulia x hours to do the job.

In 1 hour, Giulia does 1/x of the job.

Let r = 1/x. Giulia's rate is r part of the job per hour.

Together, Rocco and Giulia take 3 hours to do the job.

In 1 hour, Rocco and Giulia do 1/3 of the job.

Together, their rate is 1/3 of the job per hour.

1/7 + r = 1/3

Answer:

9,000 minutes (150 hours)

Step-by-step explanation:

You have 3,600 points total; you need to divide it by 2 points.
3,600 ÷ 2 = 1,800

So, now you need to multiply the 1,800 points by 5 minutes.

1,800 × 5 = 9,000

Another way:

You can figure out how long it takes to get 1 point. If 2 points takes 5 minutes, divide 5 by 2.

5 ÷ 2 = 2.5

Now you need to figure out how long it would take to get 3,600 points. If each point takes 2.5 minutes, just multiply.

3,600 × 2.5 = 9,000

It would take 9,000 minutes (which is equivalent to 150 hours) to get to 3,600 points.

The square for the  equation:  [tex]y=2x^{2} + 12x +1[/tex] is [tex]y=2(x+3)x^{2} -17[/tex]

The square for the  equation:  [tex]y=4x^{2} +48x-10[/tex] is [tex]y=4(x+6)x^{2} -154[/tex]

a)

[tex]y=2x^{2} +12x +1[/tex]

[tex]y = 2[(x^{2} + 6x)] + 1[/tex] ( taking common)

[tex]y = 2[(x+3)^{2} - 9] + 1[/tex] ( adding and subtracting 9 to make a square term

[tex]y = 2(x+3)^{2} - 18 + 1[/tex] ( multiplying by 2)

[tex]y=2(x+3)x^{2} -17[/tex]

b)

[tex]y=4x^{2} +48x-10[/tex]

[tex]y = 4[(x^{2} + 12x)] - 10[/tex]  (taking 4 common)

[tex]y = 4[(x+6)^{2} - 36)] - 10[/tex] (adding and subtracting 36)

[tex]y = 4(x+6)^{2} - 144 - 10[/tex](multiplying by 4)

[tex]y=4(x+6)x^{2} -154[/tex]

For more information about quadratic equations, visit https://brainly.com/question/1596209

#SPJ10

Answer:

People surveyed: 79

a) p(s) = 46/79

b) p(snv) = 13/79

c) p(suv) = 96/79

hope this helps, and tell me if you get it right! It's prob wrong though, im bad at venn diagrams (×_×)⌒☆

Answer:

  4/3

Step-by-step explanation:

The tangent of any angle (θ) in standard position that has point (x, y) on its terminal ray is ...

  tan(θ) = y/x

__

For the given point on the terminal side, the tangent is ...

  tan(θ) = (-4)/(-3) = 4/3

_____

Additional comment

There are several ways this can be explained. One of them makes use of the relation between rectangular and polar coordinates:

  (x, y) = (r·cos(θ), r·sin(θ))

Then the ratio y/x is ...

  y/x = (r·sin(θ))/(r·cos(θ)) = sin(θ)/cos(θ) = tan(θ)

If the function is vertically stretched by a factor of 3, the resulting function will be g(x) = [tex]3(5^{x-2})[/tex]

Given the parent function f(x) = x, if the function is vertically stretched by k units, the resulting function will be g(x) = kx

Given the parent function

f(x) = [tex]5^{x-2}[/tex]

If the function is vertically stretched by a factor of 3, the resulting function will be g(x) = [tex]3(5^{x-2})[/tex]

Learn more on vertical stretch here: https://brainly.com/question/14325265

#SPJ1