Answer: 6.30
Step-by-step explanation:
Write a rational function with the following characteristics.
b. Vertical asymptotes at x=0 and x=3 , horizontal asymptote at y=0 , a zero at -4
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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hellllllllllp hurrryyy pleaseee
The rate at which Riya is applying the mulch to the garden is 250000:1.
What is the rate?It should be noted that rate is simply used to show the relationship between two things. A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio expresses the corresponding rate of change in the dependent variable if the denominator of the ratio is written as a single unit of one of these quantities and it is assumed that this quantity may be modified systematically (i.e., is an independent variable).
Per unit of time is a frequent sort of rate, and examples include speed, heart rate, and flux. Exchange rates, literacy rates, and electric field ratios are examples of ratios with a non-time denominator (in volts per meter).
From the information, Riya is applying mulch to the garden and she applied at a rate of 250000cm³ for every m² of space.
Therefore, the rate at which Riya is applying the mulch to the garden is 250000:1.
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50 points!! Find the two consecutive asymptotes, the period (in radians), the phase shift (in radians) and the vertical shift of the function: y = 4csc(5θ - 3π/4)
Two consecutive asymptotes are θ = - π / 20 and θ = 3π / 20 and the period is π / 5.
How to determine two consecutive asymptotes from a trigonometric function
In this question we must look for two consecutive vertical asymptotes related to a trigonometric function. A function becomes undefined when its denominator is zero. Now we proceed to simplify the expression by trigonometric formulas:
y = 4 · csc (5θ - 3π / 4)
y = 4 / sin (5θ - 3π / 4)
y = 4 / (sin 5θ · cos 3π / 4 - cos 5θ · sin 3π / 4)
y = 4 / [(- √2 / 2) · sin 5θ - (√2 / 2) · cos 5θ]
The function is undefined for (- √2 / 2) · sin 5θ - (√2 / 2) · cos 5θ = 0:
(- √2 / 2) · sin 5θ - (√2 / 2) · cos 5θ = 0
(- √2 / 2) · sin 5θ = (√2 / 2) · cos 5θ
- sin 5θ = cos 5θ
tan 5θ = - 1
5θ = - π / 4 + i · π
θ = - π / 20 + i · π / 5
θ = (π / 5) · (- 1 / 4 + i)
There are two consecutive asymptotes:
i = 0
θ = - π / 20
i = 1
θ = 3π / 20
And the period is ΔT = 3π / 20 - (- π / 20) = π / 5.
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Consider the polynomial -y4+2y2+3y+8.
1) What is the constant term?
2) What is the exponent of the third term?
a. 1) The constant term is -y4.
2) The exponent of the third term is 3.
b. 1) The constant term is 8.
2) The exponent of the third term is 1.
c. 1) The constant term is 8.
2) The exponent of the third term is 3.
d. 1) The constant term is -y4.
2) The exponent of the third term is 1
1. The constant term of the polynomial is: 8.
2. The exponent of the third term is 1.
What is a Term of a Polynomial?A term of a polynomial can include any of the following:
An alphabet which is referred to as a variable, standing alone.The product of a variable and a number.A number that stands alone which is called a constant.The product of a variable that has an exponent and a number.A variable with an exponent.Any of the above is referred to as a term of a polynomial.
Given the polynomial, -y^4 + 2y² + 3y + 8, the polynomial has 4 terms, -y^4, 2y², 3y, and 8.
Thus:
1. The constant term of the polynomial is: 8.
2. The exponent of the third term is 1.
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If you add 17 to an even number, the answer will be even.
OA. True
OB. False
Answer:
the answer is false because it will always be a odd number
Answer:
Step-by-step explanation:
well, first you have to add the number to an even number 4+17=21
21 is not an even number 12+17=29 which is also an odd number
answer B is false.
1, 6, 15, 28, ...
find nth term
Find the inverse of each function. Determine whether each inverse is a function. f(x)=(2 x-3)²
The inverse of function f( x ) = ( 2x - 3)² is [tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex].
A function that can reverse into another function is known as an inverse function or anti-function. A function takes in values, applies specific operations to them, and produces an output. In order to find y when x is swapped with another variable, we must first determine the inverse function. On the other hand, the inverse function and the original function likewise have interchangeable domains and ranges.
We have the function,
f(x) = y = ( 2x - 3 )²
x = ( 2y - 3 )²
2y - 3 = ±√x
Adding 3 from each side.
2y - 3 + 3 = ±√x + 3
2y = ±√x + 3
Dividing each side of the equation by 2.
[tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex]
Hence, the inverse of function f( x ) = ( 2x - 3 )² is [tex]y=\frac{\pm\sqrt{x} +3}{2}[/tex].
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Find an equation of the line passing through the points (5, 2) with the slope m =5/6
Step-by-step explanation:
I guess, the equation is meant to be in slope-intercept form :
y = ax + b
"a" is the slope, "b" is the y intercept (the y value when x = 0).
in a situation like this, where we have the slope and one point of the line, we can start with the point-slope form
y - y1 = a(x - x1)
"a" is again the slope, and (x1, y1) is the given point.
and then we transform this over to the slope-intercept form.
so, in our case here
y - 2 = 5/6 × (x - 5) = 5x/6 - 25/6
let's simplify this by multiplying everything by 6 :
6y - 12 = 5x - 25
6y = 5x - 13
y = 5/6 x - 13/6
or
y = 1/6 × (5x - 13)
ABC is a right triangle with vertices at A (0,0), B (0, 2b) and C (2a, 0). Point D (a, b) is the
midpoint of BC. Which of the following statements could be used to show that the midpoint of the hypotenuse of any right triangle is equidistant from the vertices of the triangle?
Using the midpoint concept and the distance between two points, the correct statement is given by:
[tex]\sqrt{(0 - a)^2 + (2b - b)^2} = \sqrt{(2a - a)^2 + (0 - b)^2} = \sqrt{(a - 0)^2 + (b - 0)^2}[/tex]
What is the midpoint concept?The midpoint between two points is the halfway point between them, and is found using the mean of the coordinates.
Hence the coordinates of the midpoint of the hypotenuse are given as follows:
x: (2a + 0)/2 = a.y: (0 + 2b)/2 = b.What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence the distance from the midpoint of the hypotenuse to any vertex is given by:
[tex]\sqrt{(0 - a)^2 + (2b - b)^2} = \sqrt{(2a - a)^2 + (0 - b)^2} = \sqrt{(a - 0)^2 + (b - 0)^2}[/tex]
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A small business averages $5,500 per month in online revenue, plus another $300 per salesperson per month. Which graph shows all solutions for the number of salespeople who need to be working for the business to generate at least $7,300 in monthly revenue?
A.
A number line ranges from 0 through 10 from left to the right in increments of 1. A solid circular point is at 6. An arrow extends from the point toward the left.
B.
A number line ranges from 0 through 10 from left to the right in increments of 1. A hollow circular point is at 6. An arrow extends from the point toward the left.
C.
A number line ranges from 0 through 10 from left to the right in increments of 1. A hollow circular point is at 6. An arrow extends from the point toward the left.
D.
A number line ranges from 0 through 10 from left to the right in increments of 1. A hollow circular point is at 6. An arrow extends from the point toward the right.
Answer:
D.
Step-by-step explanation:
Hey there!
In order to find which description of the graph matches the problem, we must first create an equation or an inequality
So, we need to find how much more people the company needs to reach their goal to generate at least $7,300 in monthly revenue
We know that each person adds $300 to the already total of $5,500 per month
Now we can form the equation with this knowledge
[tex]300x + 5,500 \geq 7,300[/tex] where x is the number of people
Now we can simplify the equation
[tex]300x\geq 7500 - 5500\\ 300x\geq 2000\\x\geq 6.67[/tex]
Since we cannot have 6.67th of a person, we must round down because it means that we need more than 6 people
If we round up, it means that you need more 7 people in order to get $7,300 which isn't true
This means, you need more than 6 salespeople per month in order to meet the monthly quota of $7,300 in monthly revenue
Now that we know this, we can make a graph, or find the correct description of the graph
Since they need more than 6 people, the dot that sits on 6 in the number line will not be filled in, indicating that you need more than 6 salespeople
And since we need MORE, not LESS, the line will be pointing to the right
So, the correct answer would be D.
(b) Find the nth term of the geometric sequence 5 15 45 135
The nth term of this given G.P. is [tex]T_n =5\times[3]^{n-1}[/tex].
Given that
geometric sequence 5 15 45 135To find
nth term of this GP.So, according to the question
We have,
A GP5 15 45 135
From this G.P.
The first term a = 5,The common ratio r = [tex]\frac{15}{5}[/tex]So, we know that
The the nth term of the geometric sequence is:[tex]T_n =ar^{n-1}[/tex]
Where,
Tn = nth term of G.P. n = nth number.Now, putting the all given values
[tex]T_n =5\times[3]^{n-1}[/tex] -----------------(1)
The nth term of this given G.P. is [tex]T_n =5\times[3]^{n-1}[/tex], from it we will be calculate all terms till n.To learn more about Geometric Progression, please click on the link:
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Help. Its an emergenc
Answer:
Angle A is 20°
Step-by-step explanation:
The sum of the interior angles of a triangle is 180°.
90 + 10x + x +13 = 180 Combine like terms
103 + 11x + 180 Subtract 103 from both sides
11x = 77 Divide both sides by 11
x = 7
Angle A is 13 + x. X is 7, so 13 + 7 = 20
Please help me I need help
Answer:
2
Step-by-step explanation:
8+14 = 22
22-5 = 17
17-7 = 10
10+3 = 13
13-7 = 6
6-4 = 2
Answer:
d) 2
Step-by-step explanation:
PLS HELP 20 points!!1
1. What inequality does this graph represent?
2. Explain how you determined the inequality that is represented by the given graph. What was your thought process?
3. What is a real-world situation that can be modeled using this graph or part of the graph? In your answer, include how you would label for the axes. Describe one point in the solution set.
Please answer with the question number such as,
1.
2.
3.
Thank you!
Answer:
Step-by-step explanation:
1.
IF THE SHADED REGION IS THE WANTED AREA then the inequality is
y > 2x + 1
BUT IF THE SHADED REGION IS THE UNWANTED AREA then the in equality is
y < 2x + 1
2.
You have to figure out the equation of the dotted line.
Since the line is dotted, it means less than or greater than, it cant be less than equals to or greater than equal to
The gradient of the line is 2 as
rise / run = 14/7 = 2
and y intercept is 1
y > 2x + 1
3.
this is used in economics and for planning to maximize profits and minimize costs.
If you need to drive 30 miles, you have many options. For instance, you can drive 15 miles per hour for 2 hours, 30 miles per hour for 1 hour, or 60 miles per hour for half an hour. Notice that when you double your speed, it takes half as much time to get to your destination. Mathematicians describe this kind of relationship as an inverse variation. Why do you suppose they use the word inverse to describe it?
The word Inverse is used here because as the speed of traveled goes on increase, then the amount of time it takes to travel a particular distance will decrease .
What is inverse variation ?The inverse variation property states that , whenever the product of values of two quantities is a constant value then there is opposite variation between these two corresponding values. Or we can also say that if the productive nature of two corresponding values is constant, then one quantity is inversely varies with second quantity.
Let say if x and y are two values and k is a constant value, then
According to inverse variation
k = xy or y = k/x
In the question here, when we double your speed, it takes half as much time to reach the destination. The word Inverse is used here because as the speed of traveled goes on increase, then the amount of time it takes to travel a particular distance will decrease .
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3 - 4 ^ 2 + 6/2  simplify
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3 - 4^2 + \dfrac{6}{2}}[/tex]
[tex]\mathsf{= 3 - 4\times 4 + \dfrac{6}{2}}[/tex]
[tex]\mathsf{= 3 - 16 + \dfrac{6}{2}}[/tex]
[tex]\mathsf{= -13 + \dfrac{6}{2}}[/tex]
[tex]\mathsf{= -13 + 3}[/tex]
[tex]\mathsf{= -10}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{-10}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
write 0.243 as a repeating decimals, rounded to six digits
Answer:
[tex]0.243243[/tex]
Given: -2x-5=4x-29
Prove: x=4
Answer:
-2x-5=4x-29
-2x-4x=-29+5
-6x =-24
x=-24/-6
x=4
hence proved
Sarah buys a bag of candy to give out to Trick or Treaters. There are 120 pieces of candy in the bag, and she paid $26.40 for the whole bag. How much did she pay for each piece of candy?
Answer: 0.22
Step-by-step explanation:
26.40/120
0.22
0.22 x 120 = 26.40
The y-coordinate of the y-intercept is the _____ term
Answer:
constant
Step-by-step explanation:
Which graph represents the solution to this inequality?
A graph which represent the solution to this inequality is: graph B.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following arguments:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).Given the following inequality:
-1/4(12x + 8) ≤ -2x + 11
Opening the bracket, we have:
-3x - 2 ≤ -2x + 11
3x - 2x ≤ -11 - 2
x ≤ -13
Note: When the arrow points to the left and shaded, the inequality is either (≤).
In conclusion, a graph which represent the solution to this inequality is graph B.
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answer the problem below
............4
Can (x↑y)2/3 be simplified? yes or no
If yes show how with work if not explain why
Note show your work or ill delete your answer.
It depends on what you mean "simplify". Chances are the goal here is to resolve any exponents that are improper fractions, meaning we don't want exponents larger than 1, like 4/3, for instance, but smaller than 1, like 2/3, is okay.
Now, by the distributive property of exponentiation,
[tex]\left(x^4 y\right)^{2/3} = \left(x^4\right)^{2/3} y^{2/3}[/tex]
Since [tex](x^a)^b = x^{ab}[/tex], we have
[tex]\left(x^4 y\right)^{2/3} = x^{4\cdot2/3} y^{2/3} = x^{8/3} y^{2/3}[/tex]
Convert the improper fraction to a mixed number.
[tex]\dfrac83 = 3 + \dfrac23[/tex]
Then we can write
[tex]x^{8/3} = x^{3 + 2/3} = x^3 x^{2/3}[/tex]
since [tex]x^{a+b}=x^ax^b[/tex].
Finally, we group together the factors with the same power.
[tex]\left(x^4 y\right)^{2/3} = x^3 x^{2/3} y^{2/3} = \boxed{x^3 (xy)^{2/3}}[/tex]
Un tipo de tela cuesta $31.25 por 5 yardas cuadradas. Otro tipo de tela cuesta $71.50 por 11 yardas cuadradas. ¿La relación entre el número de yardas cuadradas y el costo es proporcional entre los dos tipos de tela?
Answer:
como proporción de dos tipos de tela es diferente.
por lo tanto, la relación entre el número de yardas cuadradas y el costo
no es proporcional entre los dos tipos de tejido
Explicación paso a paso:
Para que una relacion sea proporcional
a:b = c:d
en otra forma
a/b = c/d
______________________________________________
Proporción para el primer tipo de tejido
costo de tela/ área de tela = 31.25/5 = 6.25
Ratio para otro tipo de tejido
costo de tela/ área de tela = 71.50/11 = 6.5
como proporción de dos tipos de tela es diferente.
por lo tanto, la relación entre el número de yardas cuadradas y el costo
no es proporcional entre los dos tipos de tejido
Step-by-step explanation:
add 4 to 6, then subtract y from the result
Answer:
10
4 plus 6 is equal to 10 there you go
16 Brett was given the problem: "Evaluate 2x¹ +5 when x = 3." Brett wrote that the answer was 41. Was Brett correct? Explain your answer.
In the expression 2x + 5 at x = 3 Brett is wrong as the correct answer is 11.
What is an expression?An expression is written in the form of numbers and variables with arithmetic operations.
According to the given question we have to evaluate 2x + 5 at x = 3 and match our answer with Brett which is 41.
To obtain the value of 2x + 5 at x = 3, we have to substitute x with 3 in the given expression which is,
= 2(3) + 5
= 6 + 5.
= 11.
So, our answer is correct which is 11 and Brett is wrong.
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Find the original price given the total amount and tip rate.
Total price: $307.32
Tip rate: 20%
Enter the correct answer in the box.
If the total price is $307.32 and tip rate is 20%, the original price given the total amount and tip rate is $256.10
What is the sum of the percentage of the original price and tip rate?
First and foremost, the tip rate is an added layer on the original price of 100%, which means that when the original price and the tip rate are added together, it gives 120%, hence, the total price of $307.32 is 120% of the original price
120% of original price=$307.32
1% of original price=$307.32/120
1% of original price=$2.561
100% of original price=$2.561*100
100% of original price=$256.10
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A piece of brass has a volume v cm'.
aIf there were 6 cm' more brass, its mass
would be 200 g. Write down an expression
in V for its density (g/cm').
Given data,
A piece of brass has a volume v cm'.
there were 6 cm'
mass would be 200 g
So,
We can write,
volume V = 6cm
brass mass M = 200g
Find density d.
Define Density :
Density, mass of a unit volume of a material substance. The formula for density is d = M/V, where d is density, M is mass, and V is volume. Density is commonly expressed in units of grams per cubic centi meter.
d = M/V
Where,
M: It is the mass
V: It is the volume
According to the data of the statement we have:
[tex]V = 6 cm^{1}[/tex]
[tex]M = 200g[/tex]
So, the density is given by:
d = M/V
d = [tex]\frac{200g}{6cm^{1} }[/tex]
d = [tex]33.33\frac{g}{cm^{1} }[/tex]
Therefore,
The density of the brass ornament is d = [tex]33.33\frac{g}{cm^{1} }[/tex]
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can someone help me with this one question pls i will give 50 points
Answer:
[tex]x \geq 7[/tex]
Step-by-step explanation:
First inequality
[tex]-27 > -4x - 7\\\to 4x > 20\\\to x > 5[/tex]
Second inequality
[tex]-35 \geq -4x - 7\\\to 4x \geq 28\\\to x \geq 7[/tex]
We are given that x is greater than 5 and greater or equal to 7.
We can summarize this down to [tex]x \geq 7[/tex]
Answer:
Inequality notation: [7, ∞)
Number Line:
7 (closed dot), point towards positive infinity.
Step-by-step explanation:
-27 > -4x - 7 and -35 ≥ -4x - 7
+7 +7 +7 +7
------------------ ------------------
-20 > -4x -28 ≥ -4x
÷-4 ÷-4 ÷-4 ÷-4
--------------- ---------------
5 < x 7 ≤ x or x ≥ 7
Inequality notation includes the numbers that are included or the"≥" symbol.
Number line:
--------->
<------------------------------|------------>
7
I hope this helps!
A florist buys a dozen roses for $12.96 and sells them for $48.48. Find the amount of markup on a single rose.
The amount of markup on a single rose is $2.74.
What is markup formula?The markup formula is defined as the profit per unit cost of an item and is given as,
Markup = 100 * profit/cost
We multiply by 100 because we express it as a percentage, not as a fraction.
Now it is given that,
Cost Price of a dozen roses = $2.96
Number of roses = 12
Thus, Cost Price of 1 rose = 12.96/12 = $.108
Now it is also given that, the these dozen roses are sold at $48.48
So, Selling price of 1 rose = 48.48/12 = $4.04
Thus, Profit = Selling Price - Cost Price
⇒ Profit = $4.04 - $1.08
⇒ Profit = $2.96
Thus,Amount of Markup of single rose = Profit/Cost of 1 rose
⇒ Amount of Markup of single rose = 2.96/1.08
⇒ Amount of Markup of single rose = 2.74
Thus, the amount of markup on a single rose is $2.74.
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PLEASE HELPP!!! 7(5h - 4) - 1 = 14 - 8h Show your work!!!!
Answer: h=1
Step-by-step explanation:
multiple 5h and -4 by 7
35h-28-1=14-8h
35h-29=14-8h
add 29 to both sides
35h=43-8h
43h=43
i think this is right...
The given equation is,
→ 7(5h - 4) - 1 = 14 - 8h
Now the required value of h will be,
→ 7(5h - 4) - 1 = 14 - 8h
→ 35h - 28 - 1 = 14 - 8h
→ 35h - 29 = 14 - 8h
→ 35h + 8h = 14 + 29
→ 43h = 43
→ h = 43/43
→ [ h = 1 ]
Hence, the value of h is 1.