What is the value of x in the figure shown below?
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The logarithmic function f(x) = a·log₃(x - 4), passing through the points (13, 7), has the values;

5 a. The value of a is 3.5

b. Please find attached the graph of the function, f(x) = 3.5·log₃(x - 4), created with MS Excel

A logarithmic function is a function that contain and involves logarithm operation and it is the inverse of an exponential  function

The function is f(x) = a·log₃(x - 4),

x > 4 and a > 0

The coordinates of a point on the graph of the function, f is A(13, 7)

5 a. The value of a can be found by plugging in the value of (13, 7) = (x, f(x)), as follows

f(13) = 7 = a·log₃(13 - 4) = a·log₃9 = a·log₃3²

7 = a·log₃3²

7 = 2·a·log₃3 = 2·a·1 = 2·a

2·a = 7

a = 7 ÷ 2 = 3.5

a = 3.5

5 b. The coordinates of the x-intercept of the graph = (5, 0)

The equation of the function is;

f(x) = 3.5·log₃(x - 4)

A third point on the graph is given when f(x) = 14 as follows;

f(x) = 14 = 3.5·log₃(x - 4)

log₃(x - 4) = 14 ÷ 3.5 = 4

3⁴ = x - 4

x = 3⁴ + 4 = 85

Which gives the point, (85, 14)

Similarly, we have the point (31, 10.5), (7, 3.5)

Please find attached the graph of f(x) created with MS Excel

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Answer:

46 or even 42 could be the answer

Step-by-step explanation:

i could be incorrect

Answer:

y=-.5x-7

Step-by-step explanation:

Yes, Jalen is correct because the rectangle has a perimeter of 20 inches with the smaller side measuring 3 inches and the longer side of the rectangle had to be 7 inches.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(3 + 7)

20 = 2(10)

20 = 20 (True).

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Answer:736

Step-by-step explanation:

The equation that represent the gross pay is y = 0.12x + 1760. The commission was $10896 and gross pay was $12656

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Let y represent the gross pay for x total sales.

Donald Simmons a $1760 monthly salary plus a 12% commission on merchandise he sells each month, hence:

y = 1760 + 12% of x

y = 0.12x + 1760

Donald's sales were $90,800 for last month. Hence:

a) Commission = 0.12 * $90800 = $10896

b) Gross pay:

y = 10896 + 1760 = $12656

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The linear function that relates y to x is given as follows:

y = -0.5x + 57.

The slope indicates that the height decays 0.5 feet per minute. The y-intercept indicates that the descent starts at a cruising altitude of 57 feet.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

From the table, when x = 0, y = 57, hence the intercept b is given as follows:

b = 57.

When x increases by 10, y decays by 5, hence the slope m is given as follows:

m = -5/10

m = -0.5.

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Answer:

300 dollars

Step-by-step explanation:

each month you get paid 100 and march is the 3rd month and 100x3 is 300

Answer: Driving Speed

Step-by-step explanation:

The Independent variable is the one that is being experimented on to see the effect it will have on the dependent variable.

The Independent variable is adjusted to different levels to see if a relationship exists between these adjustments and a change in the dependent variable.

In this scenario the independent variable would be the speed you drive your car whilst time taken to completely stop is the dependent variable because the speed is the variable being adjusted to see the time taken to completely stop the car.

Answer:

809.4cm²

Step-by-step explanation:

Given the following :

Systematic error = 3.8cm (The measured length is always more than the actual length.)

Most probable dimension :

Width = 85.7 cm

Length = 123.5 cm

Hence most probable area of Rectangle :

Area = Length × Width

Area = 85.7cm × 123.5cm = 10583.95 cm²

Dimension due to Systematic error :

Length = (85.7cm + 3.8cm) = 89.5cm

Width = (123.5cm + 3.8cm) = 127.3cm

Area = Length × width

Area = ( 89.5cm × 127.3) = 11393.35cm²

Systematic error of the area :

value of area with Systematic error - Probable value of area :

11393.35cm² - 10583.95 cm² = 809.4cm²

Answer:

d = 5 is a solution to the equation 13 - d = 8

Step-by-step explanation:

We have to solve 13 - d = 8

Now,

13 - d = 8,

We add d on both sides,

13 - d + d = 8 + d

13 = 8 + d

we subtract 8 from both sides,

13 - 8 = 8 - 8 + d

5 = d

d = 5

Hence the answer is 5

Answer: 52,416,000 km

Step-by-step explanation:

If a comet travels 273,000 km/hr

1) Multiply 273,000 km by 24 hours to find how far the comet travels in one day

2) multiply the answer from 1 by 8 to determine how far it travels in 8 days

1) \(\frac{273,000 km}{hr}\)*\(\frac{24 hr}{1 day}\) = \(\frac{6,552,000km}{day}\) (hours cancel out)

2)\(\frac{6,552,000km}{day}\)*8 day= 52,416,000 km in 8 days

The comet approximately travelled 52,416,000km from when it began to travel to when it reached Earth. Hope this helped :)

Answer:

2.5 & 3.5

Step-by-step explanation:

152 = 12+96t- 16t²

140+96t- 16t²=0

152 = 12+96t- 16t²

4t²-24t+35=0

(2t-7)(2t-5)=0

t = 2.5 & 3.5

The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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Answer:

z = 20

Step-by-step explanation:

subtract 19z from 20z, and add 8 to 12. you will be left with 20 = 1z. Divide 1 by 20 and you will have Xz =20.

I hope this helps!

Answer:

Step-by-step explanation:

A= 2(5*2) + 2(1*4) + (3*5) + 2(2*3) + (1*3) + (4*3) + (6*3) = 88 cm^2

Answer:

-3

Step-by-step explanation:

Answer:

$3498.11 at the end of 10 years.

Step-by-step explanation:

2000 + 0.0575*2000*10 = 3150 dollars at the end of 10 years.

The sampling distribution of the sample mean height and the sampling distribution of the sample range of height are 71.5 inches and 7 inches.

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

Heights: 68, 71, 72, and 75 inches

Now,

Mean height.

= (68 + 71 + 72 + 75) / 4  

= 286/4

= 71.5 inches

Sample range.

= Highest height - Lowest height

= 75 - 68

= 7 inches

Thus,

The mean height is 71.5 inches.

The sample range of height is 7 inches.

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The equivalent ratios are 8: 6 and 12:9.    

Two ratios are equivalent if they represent the same proportion or relative size. To find an equivalent ratio, we can multiply both terms of the ratio by the same non-zero number. This doesn't change the condition between the two terms.  

Here we have 4:3

To find equivalent ratios, we can multiply both terms by the same number.

Multiplying by 2

=> 4 × 2 : 3 × 2

=> 8 : 6

Multiplying by 3

=> 4 × 3 : 3 × 3

=> 12: 9

Therefore,

The equivalent ratios are 8: 6 and 12:9.    

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Complete Question

What is the equivalent ratio for 4: 3

how many were there? well, really there were "x", which oddly enough is the 100%, we also know that 40% of "x" is 80, so

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 80& 40 \end{array} \implies \cfrac{x}{80}~~=~~\cfrac{100}{40} \\\\\\ \cfrac{ x }{ 80 } ~~=~~ \cfrac{ 5 }{ 2 }\implies 2x=400\implies x=\cfrac{400}{2}\implies x=200\)

In calculating the factor A variation, there are two degrees of freedom. In determining the variation of factor B, there are two degrees of freedom.

A two-factor factorial design is an experiment that collects data for all potential values of the two factors of the study. The design is a balanced two-factor factorial design if equivalent sample sizes are used for every of the possible factor combinations.

Suppose we have two components, A and B, each of which has a high number of levels of interest. We will select a random level of component A and a random level of factor B, and n observations will be taken for each experimental combination.

From the data given:

a.

In calculating the factor A variation, there are two degrees of freedom.

In determining the variation of factor B, there are two degrees of freedom.

b.

Finding the degree of freedom using the interaction variation, there are four degrees of freedom.

c.

In finding the random variable, there are 9(4-1) = 27 degrees of freedom.

d.

In calculating the total variable, there are 9*4-1 =35 degrees of freedom.

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Answer:

Its 2.4, glad to help ya out!

Step-by-step explanation:

Remember v/pi times r squared

Check the picture below.

Answer:

175,208 square units

Step-by-step explanation:

Lets calculate the width first:

464 + 26 - 6 = 484

The area is equal to the length times the width, so

362 x 484 = the area

= 175,208 square units

The search results are unrelated to the question of finding the reflection image of (5, -3) across the y-axis. To find the reflection image of a point across the y-axis, we need to change the sign of the x-coordinate of the point. Therefore, the reflection image of (5, -3) across the y-axis is (-5, -3).

Answer:

p ∨ q

Step-by-step explanation:

I took the test and got a 100

The correct statement for the shape being a rectangle is p ∨ q

Any figure bounded by 3 sides and sum of all the internal angles is 180° is called a triangle.

Any figure bounded by four sides, where the opposite sides are equal and all the internal angles are 90° is called a rectangle

As we know a triangle cannot have four sides, so p cannot imply q and vice versa.

According to the problem,

This is a contradiction.

So for the shape being a rectangle the correct option will be p v q(p intersection q)

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Answer: 1 22/100 (1 11/50 simplified)