Using translation concepts, the equation for the transformed logarithm is given by:
[tex]f(x) = \log{(x + 3)} - 3.48[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The logarithm function is given by:
[tex]f(x) = \log{x}[/tex].
We have that:
It passes through (1,0), and in this problem it passes through (-2,0), that is, it was shifted left 3 units, hence x -> x + 3.Hence:
[tex]f(x) = \log{x + 3} + b[/tex]
To find the shift up/down, we consider that f(0) = -3, hence:
[tex]-3 = \log{0 + 3} + b[/tex]
[tex]b = -3 - \log{3}[/tex]
b = -3.48.
Hence the function is given by:
[tex]f(x) = \log{x + 3} - 3.48[/tex]
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Choose the system of inequalities that best match the graph below.
The system of the linear inequality that fulfill the condition of the graph will be y ≥ 2x – 1 and y ≤ 1/3 x + 1. Then the correct option is A.
The complete question is attached below.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The system of the linear inequality that fulfill the condition of the graph will be
y ≥ 2x – 1
y ≤ 1/3 x + 1
Then the correct option is A.
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which equation has the solution x=6
Answer:
need more info
Step-by-step explanation:
what I can tell you is that when you change all the x's in the equation to 6s, both sides of the equation will equal eachother.
What is the asymptote of the graph of f(x)=5x−1?
The asymptotes of the graph of [tex]f(x) = \frac{5}{x - 1}[/tex] are as follows:
Vertical: x = 1.Horizontal: y = 0.What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.In this problem, the function is:
[tex]f(x) = \frac{5}{x - 1}[/tex]
For the vertical asymptote, we have that:
[tex]x - 1 = 0 \rightarrow x = 1[/tex].
For the horizontal asymptote, we have that:
[tex]y = \lim_{x \rightarrow \infty} f(x) = \frac{5}{\infty - 1} = 0[/tex].
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Follow the steps to find the
area of the shaded region.
First, use the formula
below to find the area
of the whole sector.
=
angle of sector
360
¹) πr²
Sector Area = [?] cm²
Round to four decimal places.
Sector Area
14 cm
46°
14 cm
Enter
Based on the calculations, the area of the whole sector is equal to 4,508 cm².
Given the following data:
Angle of sector = 46°.Radius of circle = 14 cm.How to calculate the area of a sector?Mathematically, the area of a sector can be calculated by using this formula:
Area of sector = θr²/2
Where:
r is the radius.θ is the central angle.Substituting the given parameters into the formula, we have;
Area of sector = 46 × 14²/2
Area of sector = 46 × 196/2
Area of sector = 9016/2
Area of sector = 4,508 cm².
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The circle below is centered at the point (-1, 2) and has a radius of length 3.
What is its equation?
O A. (*+ 1)2 + (y- 2)2 = 9
O B. (x- 2)2 + (y + 1)? =
32
O c. (x- 1)2 + (y + 2)2 = 9
l
O D. (x+ 2)2 + (y- 1)2 =
32
Answer:
it should be option A
and in option there should be "x" instead of "*"
Equation of circle is,
⇒ (x + 1)² + (y - 2)² = 9
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The circle below is centered at the point (-1, 2) and has a radius of length 3.
Now, We get;
The equation of circle is,
⇒ (x - (- 1))² + (y- 2)² = 3²
⇒ (x + 1)² + (y - 2)² = 9
Thus, Equation of circle is,
⇒ (x + 1)² + (y - 2)² = 9
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The pH can be calculated using the equation pH = –log(H+), where H+ is the hydronium ion concentration. Find the hydronium ion concentration of a particular soda if the pH level is 2.3.
Answer:
Step-by-step explanationp :
ph =lo 4
)The width of a rectangle is shown below:
A coordinate plane with a point A at negative 3, 3 and C at negative 3, negative 2.
If the area of the rectangle to be drawn is 20 square units, where should points B and D be located if they lie to the right of points A and C?
B(1, 3) and D(1, −2)
B(3, 3) and D(3, −2)
B(2, 3) and D(2, −2)
B(1, 2) and D(1, −3)
Answer: B(1, 3) and D(1, −2)
Step-by-step explanation:
The distance from A to C is 5, meaning we need the length to be 4.
If they lie to the right, we need to add 4 to the x coordinates, so the x coordinates should be 1, and the y coordinates should be 3 and -2.
The locations of B and D are given by (A) B(1,3) and D(1,-2).
The area of rectangle is given by the product of the length and width of that rectangle.
Area = Length*Width
Distance between two points (a,b) and (c,d) is given by,
[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex]
Here in the given question it is mentioned that AC forms width of a rectangle and A is at (-3,3) and C is at (-3,-2)
Now the width is [tex]=\sqrt{(-3-(-3))^2+(-2-3)^2}=\sqrt{0^2+(-5)^2}=\sqrt{25}=5[/tex] unit.
Also it is given that, the area of the rectangle is 20 square units.
So the length is = 20/5 = 4 units
B and D lie to the right of points A and C respectively.
We have to go 4 units right to the A to find B and 4 units right to C to find D.
A is at (-3,3)
then B is at (-3+4,3) = (1,3)
C is at (-3,-2)
So D is at (-3+4,-2) = (1,-2)
Hence correct option is (A) B(1,3) and D(1,-2)
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Help me with this i need steps :c!
Answer:
The area of a triangle is 1/2 × base × height. 24 = 1/2 × 12 × height. Therefore height = 24/6 = 4 .
Answer:
8
Step-by-step explanation:
24=6*h/2
48=6*h
8=h
h is altitude
A survey of 600 randomly selected high school students determined that 290 play organized sports. what is the probability that a randomly selected high school student plays sports
Answer:
29/60
Step-by-step explanation:
probability of playing is 290/600 which when simplified is29/60
What 2 numbers add up to 37 and multiply to 210?
Answer: 30 and 7
Step-by-step explanation: 30 plus 7 is 37, 30 times 7 is 210
Select the solution(s) of the original equation.
0 x = √√√2
x = 1
X=1
x = -1
0 *=-√√2
X = -1
DONE ✔
0000
Answer:
the first,second,forth and fifth.
Step-by-step explanation:
I got it off of edg.
A line / passes through point (-2, 5) and has the same y-intercept as
the line y-3x-4. What is the equation for the line /?
I'm assuming you meant to write y = 3x-4
We know that the y-intercept of the given line is (0,-4), so we need to find the equation of the line passing through (-2,5) and (0,-4).
The slope is
[tex]\frac{-4-5}{0-(-2)}=-\frac{9}{2}[/tex]
So, this means the equation is [tex]\boxed{y=-\frac{9}{2}x-4}[/tex]
What is the midpoint of AB?
Answer: Point G.
Step-by-step explanation:
Count the number of spaces between points A and B. Then divide that number by 2 and count that many spaces from one point.
14/2=7
I hope this helps!! Pls mark brainliest :)
. It costs C(x) = [tex]\sqrt{x}[/tex] dollars to produce x golf balls. What is the marginal production cost to make a golf ball? What is the marginal production cost when x = 25? when x= 100? (Include
units.)
The marginal cost when x = 25 and when x = 100 are $0.1 and $0.05 respectively.
What is a Marginal Production Cost?A marginal production cost is a derivative of a cost function. From the information given, the total cost is:
C(x) = [tex]\mathbf{\sqrt{x}}[/tex]The marginal production cost can be expressed as:
[tex]\mathbf{C'(x) = \dfrac{d}{dx}(\sqrt{x})}[/tex]
[tex]\mathbf{C'(x) = \dfrac{1}{2\sqrt{x}}}[/tex]
However, when the cost is 25, the marginal production is:
[tex]\mathbf{C'(25) = \dfrac{1}{2\sqrt{25} }}[/tex]
[tex]\mathbf{C'(25) = \dfrac{1}{2\times5}}[/tex]
[tex]\mathbf{C'(25) = \dfrac{1}{10}}[/tex]
C' (25) = $0.1
Also, when the cost is 100, the marginal production is:
[tex]\mathbf{C'(100) = \dfrac{1}{2\sqrt{100} }}[/tex]
[tex]\mathbf{C'(100) = \dfrac{1}{2\times10}}[/tex]
[tex]\mathbf{C'(100) = \dfrac{1}{20}}[/tex]
C' (100) = $0.05
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PLSSS! Fast! I will give 5 stars! At noon, the temperatures in Portland, Maine and Phoenix, Arizona had opposite values. The temperature in Portland was lower than in Phoenix. What was the temperature in each city? Explain your reasoning.
Opposite values are those values which on the number line has the same distance between them and zero. The temperature in each city is PoT=-PhT and PhT =+PoT.
What are opposite values?Opposite values are those values which on the number line has the same distance between them and zero. Although the sign on the values may be difference. For example if the first value is 4, then its opposite value is -4.
In general, the temperature equation for Portland, Maine is stated mathematically as
PoT=-PhT
As it is given in the question that the Portland, Maine and Phoenix, Arizona had opposite values. Also, the temperature in Portland is lower than in Phoenix. Therefore, the temperature in each city can be written as,
PoT=-PhT
PhT =+PoT
Hence, the temperature in each city is PoT=-PhT and PhT =+PoT.
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The sum of a number and 3 is less than 10 if x denotes the number what would be the possible values of x
x>13
x<13
x>7
x<7
Answer:
x<7
Step-by-step explanation:
Consider the number x (as mentioned in the question). Now carefully pay attention to the given condition
⇒"The sum of a number and 3 is less than 10"
Remember the notation of the term "less than" in mathematical context is indicated by "<" sign. Hence our inequality is
⇒ x+3<10
adding or subtracting any number from the both sides of an inequality DOESN'T change its direction. Thus, if we cancel out 3 from both sides it won't swap the inequality. Therefore
⇒ x+3-3<10-3
⇒ [tex]x<7[/tex]
In terms of interval notation
[tex]\implies x\in( -\infty,7)[/tex]
In conclusion
The answer is D) [tex]x < 7[/tex]
Let the number be x
The sum of number and 3
x+3Is less than 10
x+3<10Lets solve it
x<10-3x<7Hence
Option D is correct
Use the calculator to graph the function y = 2x2 25x + 3. What are the coordinates of the turning point of the graph to the nearest hundredth?
Vertex = (
,
)
The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]In this problem, the function is given by:
y = 2x² + 25x + 3.
Hence the coefficients are a = 2, b = 25, c = 3, then the coordinates of the vertex are given as follows:
[tex]x_v = -\frac{25}{2(2)} = -6.25[/tex][tex]y_v = -\frac{25^2 - 4(2)(3)}{4(2)} = -75.13[/tex]The coordinates of the turning point of the graph of the quadratic equation is given by: (-6.25, -75.13).
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Answer:
6.25, -75.13
Step-by-step explanation:
it just is
Which equation describes the same line as y-5=-2(x+4)
Select the correct answer from each drop-down menu.
The function f is given by the table of values as shown below.
x 1 2 3 4 5
f(x) 13 19 37 91 253
Use the given table to complete the statements.
If function f was translated down 4 units, the _
values would be _
A point in the table for the transformed function would be _
Using translation concepts, the correct statement is given by:
If function f was translated down 4 units, the f(x) values would be subtracted by 4. A point in the table for the transformed function would be (1,9).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
A translation down 4 units means that the output values are subtracted by 4, hence the table would be given by:
x 1 2 3 4 5
f(x) 9 15 33 87 249
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Answer:
The CORRECT answer is:
1. f(x)
2. decreased by 4
3. (4, 87)
Step-by-step explanation:
Took the test
Suppose Jenny places 9500 in an account that pays 13% interest compounded each year. Assume that no withdrawals are made from the account.
tell me your the greatest but once you turn they hate us
What is the domain of the function
f(x) = [tex]\sqrt{1/3 x + 2}[/tex]
The domain of the function is:
D: {x ∈ R | x ≥ -6}
How to get the domain of the function?
Here we have:
[tex]f(x) = \sqrt{(1/3)*x + 2}[/tex]
Remember that the argument of a square root can be only numbers equal to or larger than zero, so the domain of that function is such that:
[tex](1/3)*x + 2 \geq 0[/tex]
Now we can solve that for x.
[tex](1/3)*x + 2 \geq 0\\(1/3)*x \geq -2\\\\x \geq -2*(3/1)\\\\x \geq -6[/tex]
So the domain of the function is:
D: {x ∈ R | x ≥ -6}
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Answer:
The domain of the function is:
D: {x ∈ R | x ≥ -6}
Simplify this equation 10 ^-8
Which equation is made true by the opposite angles theorem? A. 40 − 2x = 85 + y B. x − 8 = 40 − 2x C. x − 8 = 3y − 15 D. 3y − 15 = 85 + y
Option B. x-8 = 40-2x is the correct equation for the opposite angle theorem.
According to the Opposite angles theorem,
Vertical angles theorem or vertically opposite angles theorem states that two opposite vertical angles formed when two lines intersect each other are always equal (congruent) to each other.
[tex]= > x-8=40-2x[/tex] ( : Because opposite vertex angles are equal)
So option B is correct in the given question
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Answer:
D.) 3y-15 =85+
Step-by-step explanation:
simply put, opposite angles theorem is where the angles are on the opposite side so the parallelogram in the photo shows that 3y-15 is on the opposite angle as 85+y (I also got this one right lol)
Photo is attached, please help! Will give brainliest
Here you go! please make sure you read it all too understand it, and make sure you try work before asking for help :D Have a awesome day/night
Answer:735
Step-by-step explanation:I was hoping you’d have another. Dv/dt=d/dt((7+5t)^3)=3x5x((7+5t)^2)=15x49. Does this work?
Find the domain and range of the function graphed below. Write your answers in interval notation.
Answer:
Domain: [tex][-2, 3)[/tex]Range: [tex](-5, 4][/tex]Is the relation a function? - YesStep-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
A relation is a function if each value of x maps onto no more than one value of y.
Question 3 of 10
Mark all the statements that are true.
How do you classify the following polynomial?
-4x³ + 2x² - 5x+3x²
Answer:
-4 x³+2x²-5x+3x²
combine like terms
-4x³ +5x²-5x
common factors
-1(4x³-5x²+5x)
find one factors
Ans: -x (4x²-5x+5)
In the standard Normal distribution, which z-score represents the 99th percentile?
Find the z-table here.
–3.00
–2.33
2.33
3.00
Picture posted below
The Z- score representing the 99th percentile is given by 2.33
Problems of commonly distributed samples can be solved using the z-score formula.
For a set with a standard deviation, the z-score scale X is provided by:
Z = ( x- mean )/ standard deviation
Z-score measures how many standard deviations are derived from the description. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the scale is less than X, that is, the X percentage. Subtract 1 with p-value, we get the chance that the average value is greater than X.
To Find the z-result corresponding to P99, 99 percent of the normal distribution curve.
This is the Z value where X has a p-value of 0.99. This is between 2.32 and 2.33, so the answer is Z = 2.33
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What is the equation for a cosecant function with vertical asymptotes found at x equals pi over 3 plus pi over 3 times n comma such that n is an integer?
f (x) = 3csc4x
g(x) = 3csc2x
h(x) = 4cscx
j (x) = 4csc3x
Despite not being a part of the function graph, a vertical asymptote is a vertical line that serves as a guide f (x) = 3csc4x.
How do you find a vertical asymptote?The denominator of the function, n(x), is the place where vertical asymptotes can be located.
If the numerator, t(x), is not zero for the same value of x, then the vertical asymptotes can be determined by solving the equation n(x) = 0 where n(x) is the denominator.
f (x) = 3csc4x.
Periodicity of 3csc(4x) : π / 2
Domain of 3csc(4x) :
Solution : π / 2 n<x < π / 4 + π / 2 n or π /4 + π / 2 n< x < π /2 + π /2 n
Interval Notation : ( π / 2 n,π /4 + π /2)n) ∪ (π / 4 + π /2 n, π / 2 + π /2 n)
Range of 3csc(4x) :
Solution : f(x) ≤ -3 or f(x) ≥ 3
Interval notation : ( - ∝ , -3 ) ∪ (3,∝)
Axis interception points of 3csc(4x) : None
Asymptotes of 3csc(4x) : vertical: x = π / 2 n, x = π / 4 + π/2 n
extreme points of 3csc(4x) :
Minimum (π /8 + π / 2 n,3 ),
Maximum ( 3π / 8 + π/2n, -3).
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Despite not being a part of the function graph, a vertical asymptote is a vertical line that serves as a guide f (x) = 3csc4x.
How do you find a vertical asymptote?The denominator of the function, n(x), is the place where vertical asymptotes can be located.
If the numerator, t(x), is not zero for the same value of x, then the vertical asymptotes can be determined by solving the equation n(x) = 0 where n(x) is the denominator.
f (x) = 3csc4x.
Periodicity of 3csc(4x) : π / 2
Domain of 3csc(4x) :
Solution : π / 2 n<x < π / 4 + π / 2 n or π /4 + π / 2 n< x < π /2 + π /2 n
Interval Notation : ( π / 2 n,π /4 + π /2)n) ∪ (π / 4 + π /2 n, π / 2 + π /2 n)
Range of 3csc(4x) :
Solution : f(x) ≤ -3 or f(x) ≥ 3
Interval notation : ( - ∝ , -3 ) ∪ (3,∝)
Axis interception points of 3csc(4x) : None
Asymptotes of 3csc(4x) : vertical: x = π / 2 n, x = π / 4 + π/2 n
extreme points of 3csc(4x) :
Minimum (π /8 + π / 2 n,3 ),
Maximum ( 3π / 8 + π/2n, -3).
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Two trains leave station 416 miles apart. One train is traveling 90 miles per hour while the other is traveling 70 miles per hour. How long will it take the two trains to meet
Answer:
2.6 hours
Step-by-step explanation:
Let t be the time that the trains meet.
[tex]90t = 416 - 70t[/tex]
[tex]160t = 416[/tex]
[tex]t = 2.6[/tex]
