Solve for x if log(x - 1) + log(x + 1) = log21​

Tthe length of PQ and QR.​ is 6 and 8 m

Area of rectangular field ABCD is = 4m x 6m = 24m2

Area of rectangular field PQRS (ABCD with uniform path) = (4 + x)(6 + x)

= 24 + 4x + 6x + x²

48 = 24 + 10x + x²

x² + 10x - 24 = 0

x² + 12x - 2x - 24

x(x + 12) - 2(x + 12)

(x - 2)(x + 12) = 0

x - 2 = 0

x = 2

PQ = 4 + 2 = 6

QR = 6 + 2 = 8

Therefore,  the length of PQ and QR.​ is 6 and 8 m

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Answer:

Step-by-step explanation:

Answer:(1)  y-intercept exists 490 and the slope is -2/3x.

(2) First, I observe the point (0,490) and plot a point there. Then utilize our slope -2/3 to compute the direction and angle the line moves by measuring 2 down and 3 to the right.

(3) The equation of the function is

The diagram illustrates how many wraps could've been sold for each number of sandwich sales to maintain the identical earnings of $1,470.

(4) The graph of the equation is shown below.

(5) The profits exist the same (slope) but the y-intercept is more increased than the actual diagram.

(6) The equation is

Step-by-step explanation:

(1)

slope-intercept form of a linear equation is where one side includes only "y".

⇒

⇒

Therefore,

.

Hence, the y-intercept exists at 490 and the slope is -2/3x.

(2)  

I would graph this line using the slope-intercept method First, I observe the point (0,490) and plot a point there. Then utilize our slope -2/3 to compute the direction and angle the line moves by measuring 2 down and 3 to the right.

(3)

The equation of the function is. The diagram illustrates how many wraps could've been sold for each number of sandwich sales to maintain the identical earnings of $1,470.

(4)

The graph of the function is shown below,

(5)

Therefore,

The profits exist the same (slope) but the y-intercept is more increased than the actual diagram.

(6)

y intercept= 300

The equation will be,

Answer: 119

Step-by-step explanation:

(4^2+1)(3*4-5)

=(16+1)(12-5)

=17*7

=119

Answer:

g(4) = 119

Step-by-step explanation:

g(x) = (x² + 1) (3x - 5)

Substitute x for 4 in the equation

g(4) = (4² + 1) (3(4) - 5)

g(4) = (16 + 1) (12 - 5)

g(4) = (17) (7)

g(4) = 119

Hence, the value of g(4) is 119

Answer:

b = 5

Step-by-step explanation:

Add 8b to both sides :

2+6b = 5b+7

Subtract 5b from both sides :

2+b = 7

Subtract 2 from both sides :

b = 5

Let's check :

-8(5) + 2 +6(5) = -3(5) + 7

-40 + 2 + 30 = -15 + 7

-38 + 30 = -8

-8 = -8

Correct

Hope this helped and have a good day

Answer:

b = 5

Step-by-step explanation:

to solve this you must first combine like terms

-8b + 2 + 6b = -3b + 7

combine (add) -8b and 6b

that makes -2b

-2b + 2 = -3b + 7

now add 3b to both sides to put b on one side

-2b + 2 + 3b = -3b + 3b + 7

b + 2 = 7

now subtract 2 to both side

b + 2 - 2 = 7 - 2

b = 5

that is your answer

Answer: See coordinate graph below.

Step-by-step explanation: The black point is the original point and the red point is the reflected point.

Ordered pair of the reflected point:

A': (1, -4)

Let me know if this is right! :)

Option D. The sample space when one marble is to be chosen is given as S =  {green, blue, yellow, orange, purple, red}

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.

The sample space here have been listed based on the colors of the marbles that was presented in the question that we have here.

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Answer:

OPTION D is not correct I took the test and its B

Step-by-step explanation:

also here is a picture

Answer:

Step-by-step explanation:

1. First multiply to get the number of hours for 5 painters.

5*21= 105 minutes for 5 painters.

2. Divide by 7 for hours taken for the 7 painters!

105/7=15

3. Answer=15 hours

The graph of the linear function w(x) = 3/5x + 2 is coordinates or points   (0,2), (1,2.6) (2,3.2) (3,3.8)

What is a linear function?

A linear function is a straight line on an x-y coordinate.

Formula

w(x) = 3/5x +2 in each coordinate I have a x so for example 3.

I would rewrite this as 3/5(3) + 2

w(x) = 3/5x +2

w(3) = 3/5(3) + 2

y = 1.8 + 2

y = 3.8

Answer: 0.3278

PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!!

If Tater and Pepper incurred $14.4 million in depreciation expense and paid $30.5 million in taxes on EBIT in 2021. The EBIT is $93.3 million.

First step is to find the operating cash flow

Operating cash flow =$47.1 million + $30.1 million

Operating cash flow = $77.1 million

Now let find the EBIT

EBIT = Operating cash flow + Depreciation expenses - taxes

EBIT = $77.1 million + ($30.5 million - $14.4 million)

EBIT = $93.3 million

Therefore the EBIT is $93.3 million.

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Answer:

Mark did 12 pull ups

Step-by-step explanation:

48 / 4 = 12

The statement that best describes the relationship between the two triangles is the option;

Two triangles are similar if they satisfy the following conditions.

The length of the sides of the triangles are;

First triangle, a₁ = 3, b₁ = 5. c₁ = 15

Second triangle. a₂ = 9, b₂ = 6, c₂ = 18

The ratio of the corresponding sides is therefore;

[tex]\dfrac{a_1}{a_2} = \dfrac{3}{9} =\dfrac{1}{3}[/tex]

[tex]\dfrac{b_1}{b_2} = \dfrac{5}{6}[/tex]

[tex]\dfrac{c_1}{c_2} = \dfrac{15}{18} =\dfrac{5}{6}[/tex]

The ratio of the three corresponding sides of the triangles are not the same such that the corresponding sides of the triangles are not constantly  proportional.

Therefore the two triangles are not similar because all the corresponding sides are not proportional.

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The linear function that could express the relationship between x and y is given as follows:

y = -0.4x + b, b > 0.

The slope-intercept representation of a linear function is given by the rule presented below as follows:

y = mx + b

The coefficients of the function, along with their meaning, are listed as follows:

In the relationship, we have that each time x decreases by 5 , y increases by 2, hence the slope is obtained as follows:

y = -2/5 = -0.4.

The y-intercept is positive, hence the definition of the function is given as follows:

y = -0.4x + b, b > 0.

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the answer to that question is 34cm² of the circumference

The probability that both bills are $20 if the first selected is a $20 bill is 1/16.

The probability formula is as defined as the possibility of any event to happen which comes to be equal to the ratio of the number of favourable outcomes and the total number of outcomes.

Probability of event to occur P (E) =

[tex]\frac{Number of favourable outcomes}{ Total number of outcomes }[/tex]

Hat contains four bills: a $1, a $5, a $10, and a $20 bill.

Probability(P1) of Getting $20 bill in 1st selection = 1/4 ;

After Replacement,

Probability(P2) of Getting $20 bill in 2nd selection = 1/4 ;

So, the probability that both bills are $20 if the first selected is

a $20 bill = 1/4 * 1/4 = 1/16,

Hence we get 1/16 as the probability of getting both bills of $20.

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The structure's length is 93 feet long and its width is 62 feet.

acc to our question -

Let W stand for the rectangle's flower garden's width and L for its length.

A rectangle flower garden with a width that is precisely two thirds of its length is created by an architect.

The following can be written:

W=2/3L

Given that the fence is 310 feet long, the rectangle's perimeter must also be 310 feet.

Perimeter = 2 (L + W)

The perimeter surrounding it)

2w + 2h = 310

2((2/3) * h) + 2h = 310

4h/3 + 2h = 310

10h/3 = 310

10h = 930

h = 93 feet

w = (2/3) * 93

w = 62 feet

Hence, The structure's length is 93 feet long and its width is 62 feet.

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By using the concept of function, it can be calculated that

[tex]f^{-1}(x) = \frac{3x - 4}{6}[/tex]

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here, the function is

[tex]f(x) = 2x + \frac{4}{3}\\[/tex]

Let f(x) = y

[tex]2x + \frac{4}{3} = y\\\frac{6x + 4}{3} = y\\[/tex]

6x + 4 = 3y

6x = 3y - 4

[tex]x = \frac{3y - 4}{6}[/tex]

[tex]f^{-1}(x) = \frac{3x - 4}{6}[/tex]

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Answer:

The y-intercept is the point where the graph ( line or curve ) intercepts the y-axis. The y-intercept is the y value of the point, ( x, y ).

Hope this helps!

Step-by-step explanation:

After 16.9 years the population will reach to 24300.

What do you mean by exponential growth and decay?

Quantities that fluctuate quickly are subject to exponential growth and decay. The idea of geometric progression has been used to infer exponential growth and decay. Exponential growth or exponential decay are terms used to describe quantities that vary exponentially rather than continuously. Studying bacterial growth, population expansion, and money growth schemes all use exponential growth.

It is given that a town has a population of 16000 and grows at 2.5% every year.

Now we need to  find the time period when the population will reach 24300

So, [tex]24300 = 16000(1+0.025)^{t}[/tex]

24300/16000 = [tex](1+0.025)^{t}[/tex]

24300/16000 = [tex]1.025^{t}[/tex]

1.51875 = [tex]1.025^{t}[/tex]

Taking log on both sides we get,

log(1.51875) = t log(1.025)

0.18148 = t (0.01072)

t = 0.18148/0.01072 = 16.9

Therefore, after 16.9 years the population will reach to 24300.

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If f(x) = x², the graph of g(x) = f(x) is x².

What is a Graph of a function?

The graph of a function f is the set of all points in the plane of the form (x, f(x)).

How to find the graph of a function:

You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.

We are given the function; f(x) = x²

Also, we want to find the graph of g(x) = f(x)

From the above, it means that we put x in place of x for function f(x) to get the function g(x).

so, g(x) = f(x)

     g(x) = (x)²

Hence the graph of g(x) = f(x) is x².

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Based on the equation, the minimum number of years an employee would have to stay to make a salary of over $40,000 per year is B. 12 years.

An equation is a mathematical statement that defines that two or more mathematical expressions are equal or equivalent.

Equations show equality using the equation symbol (=).

When one expression is more or less than, or not equal to another expression, it is an inequality.

If S = $33,113 + $600t

Where S = the salary before taxes

t = the time since the date of hire in years.

For S ≥ $40,000:

$33,113 + $600t ≥ $40,000

$600t ≥ $40,000 - $33,113

$600t ≥ $6,887

t ≥ 11.48

t = 12 years

Thus, using the given equation, an employee needs to stay at the work for 12 years to earn more than $40,000 a year.

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The solution of the system equation is C) There is no solution

What is system equation?

  A set of one or more equations comprising numerous variables is referred to as a system of equations. The variable mappings that satisfy all of the component equations in a system of equations, or the points where the components of this system of equations intersect, are the solutions to that system. A system of equations in algebra is made up of two or more equations that are solved together. the process of eliminating, substituting, and graphing solutions to a system of equations or inequalities in two variables

Here the given equations are ,

=> y+7=3x-------> 1

=> y = 3x-7 ------> 2

and 6x-2y =12------> 3

Now put value of 2 into 3 then,

=> 6x-2(3x-7)=12

=> 6x-6x+14=12

=>14=12

The statement is false for any real number.

Therefore the correct option for the given system equation  is C) There is no solution.

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The focus of parabola is (4 , -1) and directrix is 5

The general equation of a parabola is: y = a(x-h)²+ k or x = a(y-k)² +h, where (h ,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.

Focus: The point (a, 0) is the focus of the parabola

Directrix: The line drawn parallel to the y-axis and passing through the point (-a, 0) is the directrix of the parabola. The directrix is perpendicular to the axis of the parabola.

Given equation of parabola is :

y = - 1/12 (x - 4) - 2

Comparing it with standard equation,

h = 4

k = 2

a = -1/12

using Focus: (h, k+ (1/4a)) and Directrix: y = k - 1/4a)

=> focus = (4 , 2+(12/4×-1))

=> focus = (4 , 2-3)

=> focus = (4 , -1)

and directrix is : y = 2-(1/4×-1/12)

y = 2 + 12/4

y=2 + 3 => 5

So, the focus is (4,-1) and directrix is 5

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The tip of his shadow moving when he is 50 ft from the pole is 10ft/s

The practical approach of differentiation may be performed utilizing just algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.

The theory offers the following fundamental guidelines for differentiating the sum, product, or quotient of any two functions f(x) and g(x) whose derivatives are known (where a and b are constants) for functions constructed of combinations of these types of functions

I assume the man and pole are standing straight up, which means the 2 triangles are similar to each other.

(y-x)/y =6/15

15(y-x)=6y

9y=15x

y=(5/3)x

Differentiating both sides with respect to t,

dy/dt=(5/3)dx/dt

We know that, dx/dt= 6 ft/s

((5/3)*6=10 ft/s

Therefore, the tip of his shadow moving when he is 50 ft from the pole is 10ft/s

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Answer:

x = 3.2

Step-by-step explanation:

[tex] \sf \frac{x}{2} = \frac{8}{5} \\ [/tex]

Use cross multiplication.

[tex] \sf5x = 8 \times 2 \\ \sf 5x = 16[/tex]

Divide both sides by 5.

[tex] \sf \: x = 3.2[/tex]

The surface area of the largest size sphere that can fit in this box is 400π

What is the surface area of the sphere?

The surface area of a sphere is the space that the sphere's outer surface occupies. A sphere is a circle in three dimensions. A circle is a two-dimensional (2D) shape, whereas a sphere is a three-dimensional (3D) shape, which is the difference between the two.

Here, we have

The diameter of the biggest sphere will be equal to the side of the sphere.

radius = 20/2

​ = 10

The surface area of the sphere = 4πr²

=4π(10)²

= 400π

Hence, the surface area of the largest size sphere that can fit in this box is 400π.

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Answer:

Hope the picture will help you