Answer: [tex]x=\pm \sqrt{22}[/tex]
Step-by-step explanation:
[tex]\log(x-1)+\log(x+1)=\log 21\\\\\log((x-1)(x+1))=\log 21\\\\\log(x^2-1)=\log 21\\\\x^2-1=21\\\\x^2=22\\\\x=\pm \sqrt{22}[/tex]
Answer:
sqrt(22) = [tex]\sqrt{22}[/tex]
Step-by-step explanation:
we can use the logarithm rule, "log x + log y = log(xy)" to solve this problem
log(x-1) + log(x+1) = = [tex]log((x-1)(x+1))[/tex] = log(21)
this means that x^2 - 1 equals 21
xx-1 = 21
xx=22
x=sqrt(22)
how to solve this proportion
Answer:
Hope the picture will help you
Assume that a hat contains four bills: a $1, a $5, a $10,
and a $20 bill. Two bills are to be selected at random with
replacement. Find the probability that both bills are $20 if
the first selected is a $20 bill?
The probability that both bills are $20 if the first selected is
a $20 bill is
(Simplify your answer. Type an integer or a fraction.)
The probability that both bills are $20 if the first selected is a $20 bill is 1/16.
What is probability ?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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Find the focus and the directrix of the parabola with the equation y = - 1/12 (x - 4) 2. (A) Focus = (4, -1), directrix is y = -5 (B) Focus = (4,2), directrix is y = 5 (C) Focus = (4,1), directrix is y = -5 (D) Focus = (4, -1), directrix is y = 5
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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A street light is mounted at the top of a 15-ft-tall pole. a man 6 ft tall walks away from the pole with a speed of 6 ft/s along a straight path. How fast is the tip of his shadow moving when he is 50 ft from the pole?
The tip of his shadow moving when he is 50 ft from the pole is 10ft/s
What is meant by differentiation?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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6th grade problem i need help
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
5. The diagram shows a rectangular field ABCD has a path of uniform width around it. AB and BC are 6m and 4 m respectively. Given that area PQRS is twice the area of ABCD. Find the length of PQ and QR.
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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What is the equation of this line in slope intercept form?
2x+3y=−6
In your own words, describe the y-intercept.
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:
For every pull-up Mark completes, he does 4 push-ups. If he did 48 push-up, how many pull-ups did he do?
Answer:
Mark did 12 pull ups
Step-by-step explanation:
48 / 4 = 12
14.4.3 Quiz: Stretching and Compressing Functions
Question 2 of 10
Suppose f(x) = x². What is the graph of g(x)=f(x)?
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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Write 3.278 correct to 1 decimal place.
Answer: 0.3278
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!!
Two triangles are shown below. 3 5 15 9 6 18 Which statement best describes the relationship between the two triangles ? The triangles are not similar all corresponding angles are not equal . The triangles are not similar ; all corresponding sides are not proportional . The triangles are similar ; the similarity ratio is 1: 3. The triangles are similar ; the similarity ratio is 2 :3.
The statement that best describes the relationship between the two triangles is the option;
The triangles are not similar; all the corresponding sides are not proportionalWhat are the conditions for the similarity of two triangles?Two triangles are similar if they satisfy the following conditions.
Two angles of one triangle are congruent to two angles in the other triangle (AA, Angle-Angle similarity postulate)Two sides of one triangle are proportional to two sides of the other triangle and the included angle of the two sides in each triangle are congruent (SAS, Side-Angle-Side similarity postulate)The three sides of one triangle are proportional to the three sides of the other triangle (SSS, Side-Side-Side, similarity postulate)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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An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. if 420 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden. what is the length of the garden?
The structure's length is 93 feet long and its width is 62 feet.
What is rectangle?We also refer to a rectangle as an equiangular quadrilateral since all of its angles are equal. A closed 4-sided shape is called a quadrilateral.A rectangle can also be referred to as a right-angled parallelogram because its sides are parallel. A quadrilateral with equal and parallel opposite sides is referred to as a parallelogram. Paralleograms are a specific instance of rectangles.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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Tater and Pepper Corp. reported free cash flows for 2021 of $47.1 million and investment in operating capital of $30.1 million. Tater and Pepper incurred $14.4 million in depreciation expense and paid $30.5 million in taxes on EBIT in 2021.
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.
How to find EBIT?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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A paper bag has six colored marbles. The marbles are red, green, blue, purple, yellow, and orange. List the sample space when choosing one marble.
S = {1, 2, 3, 4, 5, 6}
S = {red, blue, green, orange, yellow}
S = {g, r, b, y, o}
S = {green, blue, yellow, orange, purple, red}
Option D. The sample space when one marble is to be chosen is given as S = {green, blue, yellow, orange, purple, red}
What is sample space in probability?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
Find the area and circumference of a circle with a diameter of 15 cm.
the answer to that question is 34cm² of the circumference
-8b+ 2 + 6b = -3b + 7
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
Graph the linear function w(x)=3/5x+2
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
A town has a population of 16000 and grows at 2.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 24300?
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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A company gives yearly raises to their employees. The salaries at the company are based on the equation below, where S is the salary before taxes and t is the time since the date of hire in years.
S = $33,113 + $600t
What is the minimum number of years an employee would have to stay to make a salary of over $40,000 per year?
A. 13 years
B. 12 years
C. 11 years
D. 1 year
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.
What is an equation?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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x/2=8/5
what is x???
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]
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper
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,
What is the correct 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! :)
Which of the following is the inverse of f(x) =
2x+4/3
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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What is the solution of the following system?
Use the substitution method.
y+7=3x
6x - 2y = 12
O The only solution is (14, 12).
O The only solution is (12, 14).
O There is no solution.
O There are an infinite number of solutions.
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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Can somebody please help me find a answer key for these
Answer:
Step-by-step explanation:
the variables x and y are related such that each time x decreases by 5 , y increases by 2 .if y is a positive value when x=0. which of the following equations could express the relationship between x and y
The linear function that could express the relationship between x and y is given as follows:
y = -0.4x + b, b > 0.
What is a linear function?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:
m is the slope of the function, being obtained by the division of the change in y by the change in x.b is the y-intercept of the function, representing the values of the output variable y when the input variable x assumes a value of zero.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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Add and simplify.
7/12 + 2/15
Question 6
The functions g is defined on the real numbers by g (x) = (x² + 1) (3x - 5). What is the value
of g(4) ?
-51
63
119
175
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
A cube box is 20 cm x 20 cm x 20 cm. What is the surface area of the largest size sphere that can fit in this box? Leave your answer in terms of pi.
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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