For Vertical asymptotes at x=0 and x=3 , horizontal asymptote at y=0 , a zero at -4, the rational function will be - (x+4) / (x)(x-3)
What are asymptotes?Asymptote, a line or curve that serves as the boundary of another line or curve in mathematics. An example of an asymptotic curve is a descending curve that approaches but does not reach the horizontal axis, which is the asymptote of the curve.
Given,
Vertical asymptotes at x=0 and x=3 , it means that these both factors are included in the denominator.
horizontal asymptote at y=0, it means means highest degrees in both numerator and denominator is 0.
zero at -4, it means we have this as factor in numerator.
The required rational function will be -
(x+4) / (x)(x-3)
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Write a potential exponential function (y= ab^x) that has a y-intercept of (0,3) and passes through the point (2,48)
Please solve and explain so that I can try and do it on my own too, thank you
A potential exponential function (y = abˣ) that has a y-intercept of (0, 3) and passes through the point (2, 48) is equal to y = 3·4ˣ
What is an exponential function?An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function can be represented by this standard formula:
y = abˣ
Next, we would solve for the value of "a" using y-intercept (0, 3):
y = abˣ
3 = ab⁰
3 = a(1)
a = 3.
Also, we would determine the value of "b" from point (2, 48):
y = abˣ
48 = 3b²
16 = b²
b = √16
b = 4.
Substituting the parameters into the standard formula, we have;
y = 3·4ˣ
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HEY, guys I REALLY NEED HELP WITH THESE. I THINK I HAVE 5 QUESTIONS I NEED HELP WITH. HERE THEY ARE. I WILL AWARD BRAINIEST IF U CAN SOLVE THEM. THANK YOU, GUYS! I NEED THEM ASAP!!!!!!
Answer:
1. y = 0.5x – 0.5 or y = 1/2x -1/2
2. y = -1.5x – 2 or y= -3/2x- 2
3. y= -x -5
4. y=x+3
i dk how to do the last picture
Solve. Check for extraneous solutions. √3 x+7=x-1
x = 6 is the extraneous solution of the equation
The equation given is
[tex]\sqrt{3x + 7}[/tex] = x -1
To find the Extraneous solution we need to square on both sides of the equation
[tex](\sqrt{3x + 7} )^{2}[/tex] =[tex](x - 1)^{2}[/tex]
3x + 7 = [tex]x^{2}[/tex] --2x + 1
[tex]x^{2}[/tex] - 5x - 6 = 0
[tex]x^{2}[/tex] - 6x + x - 6 = 0
x(x - 6) +1(x -6) =0
(x-6)(x+1) = 0
x = -1, 6
Now we need to put the value of x in the equation
x = -1
[tex]\sqrt{(3 * -1) + 7}[/tex] = -1 -1
[tex]\sqrt{4}[/tex] = -2
2≠ -2
Now put
x = 6
[tex]\sqrt{3 * 6 + 7}[/tex] = 6 -1
[tex]\sqrt{25}[/tex] = 5
5=5
Therefore we get to know that x = -1 is the extraneous solution and x = 6 is the solution of the equation
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Joseph works in the soft-drink booth at every school baseball game. He earns ⅓ of the total soft drinks sales at each game. At Friday’s game,the total soft drink sales were $79.26. At Saturday’s game, the total soft drink sales were $95.70.How much did Joseph earn by working at the soft ball booth on Friday and Saturday?
Answer:
$58.32
Step-by-step explanation:
x = 1/3(79.26 + 95.70)
x = 1/3(147.96) Divide 147.96 by 3
x = 58.32
The mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by y = 3.50x + 6.00 explain how you can use this linear function to find out how many games you can bowl for $34.
If the mathematical relationship between the total cost for a person to bowl at the local bowling alley and the number of games played is represented by y = 3.50x + 6.00, then the number of games you can bowl for $34 is equal to 8.
A linear function can be described as an equation in which the highest power of the variables is not more than 1. As the linear function given is;
y = 3.50x + 6.00
Here y represents the total cost and x represents the number of games played.
We can find the number of games you can bowl for $34 as follows;
y = 3.50x + 6.00
34 = 3.50(x) + 6.00
34 - 6.00 = 3.50(x)
28 = 3.50(x)
x = 28 ÷ 3.50
x = 8
Hence, the number of games you can bowl for using the equation y = 3.50x + 6.00 is calculated to be 8.
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Please help me out please please please
Answer:
B. 2(5+3)
Step-by-step explanation:
PEMDAS
2(5+3)
5+3= 8
2 × 8 = 16
10 + 6 = 16
8. A car consumes 25.00 liters of fuel when driving a distance of 400.0 km. How many
gallons will it consume when driving 250.0 miles?
The amount of fuel required to drive 250 miles will be 25.14 liters.
What is an expression?Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that a car consumes 25.00 liters of fuel when driving a distance of 400.0 km. The amount of fuel required for 250 miles will be calculated as:-
1 km = 0.6213 miles
400 km = 400 x 0.6213 miles
400 km = 248.52 miles
248.52 miles = 25 litres
1 mile = 25 / 248.52 litres
250 miles = ( 250 x 25 ) / 248.52 litres
250 miles = 25.14 litres
Therefore, the amount of fuel required to drive 250 miles will be 25.14 liters.
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How do I solve these types of questions? Any hints or help will be appreciated
Step-by-step explanation:
ATTACHED ARE THE SOLUTIONS !!!!
Step-by-step explanation:
a)=
y = 70 + 41 (exterior angle is equal to sum of its opposite interior angles)
so, y = 111°
Now,
y = x + 58° ((exterior angle is equal to sum of its opposite interior angles)
or. 111° - 58° = x
so, x = 53°
b)=
x = 180° - 127° (linear pair of x is corresponding to 127)
so, x = 53°
Now,
y = 83° (y is vertically opposite to angle that is corresponding to 83)
c)= x = 47° (alternate angles)
y = 47 + 32 (exterior angle is equal to sum of its opposite interior angles)
so, y = 79°
d)= other angle = 180-45-45 = 90
Using the formula:-
sinA/a = sinB/b = sinC/c
or, sin45/3 = sin45/y
or, 1/√2/3 = 1/√2/y
or, y = 3
Now,
sinC/c = sinA/a
or, sin90/x sin45/3
or, 1/x = 1/√2/3
or, 1/x = 1/3√2
so, x = 3/√2
When x = 4, the value of 2x⁰ +x! is
Answer:
26
Step-by-step explanation:
[tex]2(4)^0+4! \\ \\ =2(1)+24 \\ \\ =26[/tex]
Simplify. ∛4 - 2∛4
The simplified value of the expression is [tex]-2^{2/3}[/tex].
The cube root of any given number is that number which we can multiply 3 times by itself to get the original number. It is denoted by ∛, for example- the cube root of x will be ∛x. It can also be written as (x)^1/3.
Here, we are given the expression ∛4 - 2∛4
We can also write this expression as follows-∛4 (1 - 2)= ∛4(-1)= - ∛4
Further, 4 can be written as: 2 × 2 = 2² = - (∛2)² = [tex]-2^{2/3}[/tex]
We cannot simplify this expression any further.
Thus, the value of the expression comes out to be [tex]-2^{2/3}[/tex].
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Find the measure of x. 15(x+1) 120°
Answer: x=7
Step-by-step explanation: 15x=120, x=8, 8-1= 7 brainliest?
Occupation
Median Annual Earnings (Dollars)
Postsecondary Education or Training Category
Sheet metal worker
37,360
Long-term on-the-job training
Massage therapist
33,400
Postsecondary vocational award
Religious worker
24,330
Bachelor’s degree
Mathematician
86,930
Doctor’s degree
Makeup artist
31,820
Postsecondary vocational award
Private detective
33,750
Work experience in a related occupation
U.S. Bureau of Labor Statistics, 2006.
Jasmine wants to enter a career with median earnings of at least $33,500, but she doesn’t want to go to college. Which of the following occupations fits her plan?
a.
Makeup artist
b.
Mathematician
c.
Private detective
d.
Massage therapist
Since Jasmine wants to enter a career with median earnings of at least $33,500, but she doesn’t want to go to college, the occupation that fits her will be C Private detective.
How to illustrate the information?It should be noted that from the information, Jasmine wants to enter a career with median earnings of at least $33,500, but she doesn’t want to go to college.
A Makeup artist earns $31,820.
A Mathematician earns $86,930.
A Private detective earns $33,750
A Massage therapist earns $33,400.
Therefore, the best occupation for her since she doesn't want to go to college and earns above $33500 is the private detective.
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Answer:
C. Private detective
Step-by-step explanation:
Draw the image of Quadrilateral ABCD translated -2 units horizontally and 5 units vertically. Label the image points using prime notation. (in other words Rule: (x, y) --> (x-2, y+5) )
The image of Quadrilateral ABCD after transformation is shown in graph with coordinates A' (0, 2), B' (2, 4), C' (5, 4) and D' (4, 3).
What is Transformation?
Transformation is the act or process of changing completely.
The rule of transformation is given as;
(x, y) --> (x-2, y+5)
Now, The coordinates of Quadrilateral ABCD are;
A (2, -3) , B (4, -1), C (7, -1) and D (6, -2)
Apply the rule of transformation to find the coordinates of the image of Quadrilateral ABCD as;
A' (2-2, -3+5) = (0, 2)
B' (4-2, -1+5) = (2, 4)
C' (7-2, -1+5) = (5, 4)
D' (6-2, -2+5) = (4, 3)
Hence, The coordinates of image of Quadrilateral ABCD are;
A' (0, 2), B' (2, 4), C' (5, 4) and D' (4, 3).
And, The image of Quadrilateral ABCD after transformation is shown in graph.
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Expand each logarithm.
log 4 √47/5²
The value of logarithmic expression log 4 √47/5² is log (47/25)^1/4.
By considering the given logarithmic expression
log 4 √47/5²
log 4 √47/25
log (47/25)^1/4
The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.
Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).
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Jordin worked 48 hours and 45 minutes. He's paid $13.00 an hour. He is paid time and a half for any time over 40 hours. How much will he get paid?
Change minutes to hours then multiply.
This is pay, so round all answers to the nearest cent if necessary. Two decimal places
Answer:
$690.63
Step-by-step explanation:
45 minutes = 0.75 hr, so he worked for 48.75 hrs.
This means he worked 8.75 hours of overtime, so his pay is
[tex]40(13)+(8.75)(13)(1.5) \approx \$690.63[/tex]
Diana and Joby wrote the following proofs to prove that vertical angles are congruent. Who is correct? Please explain why as well to get Brainly.
O Diana is correct, but Joby is not.
O Both Diana and Joby are correct.
O Neither Diana nor Joby is correct.
O Joby is correct, but Diana is not.
The proof that is correct about vertical angles being congruent is; Joby's proof
How to prove that vertical angles are congruent?Vertical angles are defined as the angles formed when two lines meet each other at a point. They are always equal to each other and as such they are congruent.
Now, from the given image, we see that four angles are formed which are; ∠1, ∠2, ∠3, ∠4
Now, according to vertical angle theorem, we can say that;
∠2 = ∠4 and ∠1 = ∠3
Thus, we can conclude that vertical angles are congruent by the vertical angle theorem
Thus, we conclude that Joby's proof is correct.
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let f(x)= 2x+4. Write a function g whose graph is a horizontal shrink of the graph of f by a factor of 1/2. g(x)=?
x + 2 is the graph of the function g, whose graph is a horizontal reduction of the graph of f by a factor of 1/2.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The translation is a way of changing the position of an object on a xy-plane.
The function that results from shrinking a function f(x) horizontally by a factor of 1/a is given as;
g(x) =1/a f(x)
Give the function f(x) = 2x + 4, which will result in the following function if the function is shortened horizontally:
g(x) = 1/2(2x+4)
g(x) = x + 2
Hence the function g whose graph is a horizontal shrink of the graph of f by a factor of 1/2 is x + 2.
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If triangle LMN has an obtuse angle at vertex M, which statements could be true? Check all that apply.
Triangle LMN is an obtuse triangle.
The angle at vertex L is acute.
The angle at vertex L is right.
The angle at vertex N is right.
The angle at vertex N is acute.
Triangle LMN is a right triangle.
The statement which are true for triangle LMN are :
1 ) The angle at vertex L is acute.
2) The angle at vertex N is acute.
What is obtuse angle ?
An obtuse angle is defined as an angle measuring less than 180 degrees and greater than 90 degrees. Examples of obtuse angle degrees include 165°, 135°, 110°, 179°, 91°, etc., which lie between 90° and 180°.
Here, it is given that triangle LMN has an obtuse angle at vertex M that is :
The angle formed by vertex L and N will be acute angle that is less then 90 degrees as to satisfy the triangle law of addition (all sum of all the angles of a triangle is 180 degree).
Therefore, option A and D are correct.
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Answer: 1, 2 and 5
Step-by-step explanation:
Analyzing Obtuse Triangles
see picture
please help me fast its worth 50 points
Yes, the claim is correct because √16 + π = 4 + π and 4 + π is an irrational number
What is the sum of rational and Irrational Numbers?Rational numbers are numbers that can be expressed as the ratio of two integers while Irrational numbers cannot be expressed as the ratio of two numbers.
The sum of a rational and an irrational number is always an irrational number.
Example:
Consider a rational number: 4 and an irrational number: 2.7582...
When we add these two numbers, we get,
4 + 2.7582... = 6.7582....
Thus, it is clear that this sum is also an irrational number as the numbers after decimal are non-terminating and non-recurring.
Thus, the correct option is that the claim is correct because √16 + π = 4 + π which is an irrational number
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this one is weird to me pls help
Use long division to convert 2/9 to a decimal. Your approximation should have one decimal place.
Answer:
0.2
Step-by-step explanation:
Divide 2 by 9. You’ll get 0.222222…
So, you have to round it down to 0.2
I hope this helps. Please mark me brainliest.
Aditi bought 20 apples at Rs 25 each and sold them at Rs 32 each. What is her total profit?
Answer: 140
Step-by-step explanation: 25x20=500
32x20=640
640-500= 140!!
help me please I need this done today and please tell me A, B, C, OR D and on question 8 try to give me a good answer and show work
The graph shows the high temperatures on July 4 over a 15 year. What is the. Approximate assessment probability that next year is temperature year 16 will be in the 90s
The Approximate assessment probability that next year is temperature year 16 will be in the 90s is 0.53
How to solve for the probabilityIn the image that we have, there are 8 years out of a total of 15 years that would be having the temperature in the 90s.
This can be written in the fraction as 8 / 15 = 0.53
The probability can be defined as the chances of having something happening.
Hence we would say that the Approximate assessment probability that next year is temperature year 16 will be in the 90s is 0.53
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2 ba
14. DIG DEEPER What is Descartes's
number?
46.29
• It is greater than 46.98.
●
It is less than 47.
• The thousandths digit is greater
than the hundredths digit.
00
Answer:
Step-by-step explanation:
the answer is 46.989
tenths, ones, decimal, hundredths, thousandths
the answer must be greater than 46.98 but less than 47.
PLEASE ANSWER THIS AS QUICK AS U CAN.VERY QUICK PLS!
6t ÷ 9
I hope this helps!
Answer: 6t
Step-by-step explanation:
there are 6 t's so yea it's the 6th work for me -_-
Graph the coordinates of the triangle in the coordinate plane. Multiply each coordinate by a scale factor of 3 (k=3). Then, graph the new triangle. How are the triangles related?
The two triangles are similar triangles and the graph of the triangles are attached
Graph the coordinates of the triangle in the coordinate plane.The complete question is added as an attachment
The coordinates of the triangle are given as
A (0, 3), B (3, 3) and C (3, -1)
So, we enter the above coordinates in a graphing calculator
See attachment for the graph of the triangle
Multiply each coordinate by a scale factor of 3 (k=3).
Here, we have
A' 3 * (0, 3), B' 3 * (3, 3) and C' 3 * (3, -1)
This gives
A' (0, 9), B' (9, 9) and C' (9, -3)
Next, we enter the above coordinates in a graphing calculator
See attachment for the graph of the triangle
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Write each equation in logarithmic form.
5⁻³ = 1/125
The logarithmic form of 5⁻³ = 1/125 is , [tex]log_5(\frac{1}{125} ) =-3[/tex]
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as [tex]log_{a}x[/tex] .
where, a is the base of function or equation
x define expression
Mathematically, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_aN = x[/tex].
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.
Some important formulas of logarithms :
[tex]log a + log b = log a.b[/tex][tex]log a - log b = log \frac{a}{b}[/tex][tex]log a^x = x loga[/tex][tex]log_aa=1[/tex][tex]log_a1=0[/tex]According to statement,
5⁻³ = 1/125
as, if [tex]a^x = N[/tex] is an exponential function then, this can be converted to logarithmic function as [tex]log_aN = x[/tex]
Here,
a= 5, x= -3, N = 1/125
therefore logarithmic form is : [tex]log_5(\frac{1}{125} ) =-3[/tex]
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Write an equation for the translation of y=2/x that has the given asymptotes. x=4 and y=-8
Equation that has the specified asymptotes for the translation of y=2/x. x=4 and y=-8 is :
y = 2 / x- 4 - 8
How to write an equation for the translation (given asymptotes)?The graph is shifted by that many units in the positive direction if you deduct a constant from your original function's x.
The original function's graph is shifted downward by that many units if a constant is subtracted from the y value.
CalculationYour first formula was y=2/x. The vertical asymptote is discovered when the denominator's root is solved for. It is x=0 in this instance, or the y-axis.
And when x changes to ∞, y=2/∞=0. This indicates that the y-axis, or your horizontal asymptote, is at y=0.
GRAPHSAfter seeing the first graph
Now, you can see the transformation of y=2/x below. As is evident, it has shifted 2 units to the right and 8 units down with vertical asymptote at x=4 and horizontal asymptote at y=−8.
you can see the second graph here...
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what is the name of a line drawn across two parallel lines?
Answer:transversal
Step-by-step explanation:
geometry help please!
Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.105ft2 is the area of given figure.
What is Area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
The given figure has rectangle and semi circle.
Area of rectangle=length * Breadth
=10*8
=80 ft2
Area of semicircle=1/2πr2 (r=4ft)
=1/2*3.14*(4)^2
=3.14*4*2=25.12ft2
Therefore area of figure is
=Area of rectangle+Area of semicircle
=80ft2+25.12ft2
=105ft2.
Therefore area of figure is 105ft2.
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