According to the question, the given rational expression can be simplified which is as shown below:
Rational expression = [tex]\frac{12-4x}{x^{2} -9}=\frac{4(3-x)}{(x-3)(x+3)}[/tex]
For the simplification of the given expression, calculate the factors of the numerator as well as denominator terms and divide them from each other. In this change the sign of the expression before dividing with each other.
Rational expression = [tex]\frac{-4}{(x+3)}[/tex]
The rational expression are also known as polynomial expression. The highest degree of these expression is two. And these expression uses concept of factor rule.
Therefore, the final expression is [tex]\frac{-4}{(x+3)}[/tex]
What is polynomial expression?
Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.
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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
The y-coordinate of the y-intercept is the _____ term
Answer:
constant
Step-by-step explanation:
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]
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
add 4 to 6, then subtract y from the result
Answer:
10
4 plus 6 is equal to 10 there you go
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!
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)
write 0.243 as a repeating decimals, rounded to six digits
Answer:
[tex]0.243243[/tex]
6x+5y=39
3x+5y=27
grade 8
Answer:
y = 3 and x = 4
Step-by-step explanation:
Let's solve your system by substitution.
6x+5y=39;3x+5y=27
Step: Solve6x+5y=39for x:
6x+5y=39
6x+5y+−5y=39+−5y(Add -5y to both sides)
6x=−5y+39
6x/6=−5y+39/6
(Divide both sides by 6)
x=−5/6y+13/2
Step: Substitute −5/6y+13/2 for x in 3x+5y=27:
3x+5y=27
3(−5/6y+13/2)+5y=27
5/2y+39/2=27(Simplify both sides of the equation)
5/2y+39/2+−39/2=27+−39/2
(Add (-39)/2 to both sides)
5/2y=15/2
5/2y/5/2=15/2/5/2
(Divide both sides by 5/2)
y=3
Step: Substitute 3 for y in x=−5/6y+13/2:
x=−5/6y+13/2
x=−5/6(3)+13/2
x=4(Simplify both sides of the equation)
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.
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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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]
How can you test to see if a diagram made using digital tools is a construction or just a drawing based on estimation?
You can test to see if a diagram made using digital tools is a construction or just a drawing based on estimation by C. Look to see just how accurate the diagram appears. If needed, measure the screen using a ruler and protractor.
How to illustrate the information?The phrase "digital construction" is understood to refer to the use of digital technologies to improve and improve the quality of construction.
In this case, you can test to see if a diagram made using digital tools is a construction or just a drawing based on estimation by looking to see just how accurate the diagram appears. If needed, measure the screen using a ruler and protractor.
In conclusion, the correct option is C.
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How can you test to see if a diagram made using digital tools is a construction or just a drawing based on estimation? O Digital tools cannot be used to make a construction. Construction tools are limited to only straightedge and compass. O Look to see just how accurate the diagram appears. If needed, measure the screen using a ruler and protractor. O Drag a free point to see if the construction changes. Restart your computer and see if the diagram is found in the same location.
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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Write a rational function with the given characteristics.
A vertical asymptote at x=-4 and a horizontal asymptote at y=3
The rational function with the given characteristics is [tex]f(x) = \frac{3x + 1}{x - 4} [/tex].
How to find a rational function with the given characteristics?Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers,they can be found in any field K.
given that a vertical asymptote at x=-4.
A horizontal asymptote at y=3.
The denominator of the function cancels for this value and the numerator does not cancel at this value if the rational function has a vertical asymptote at x=4.
[tex]f(x) = \frac{p(x)}{(x - 4)} [/tex]
The degree of the numbered variable is equal to the degree of the denominator if the rational function has a horizontal asymptote at y=3, and the coefficient of the higher degree variable is three times larger.
Hence,
[tex]f(x) = \frac{3x + 1}{x - 4} [/tex]
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what has no length, no width, and no height
Answer:
line
Step-by-step explanation:
1, 6, 15, 28, ...
find nth term
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:
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.
Cam earns $400/week plus 2. 5% commission. He has been offered another job that pays $700/week but no commission.
a) Describe three strategies that you could use to compare Cam’s
earnings for the two jobs
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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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
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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What does g =
g-16
------
2
Answer:
8?
Step-by-step explanation:
Answer:
g = -8
Step-by-step explanation:
g-16
------ = -8
2
g = -8
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.
(-3x^4 – 5x – x^3)+(-12x^3 – 8x – 14x^4)
The simplified form of the expression is -17x⁴ -13x³ - 13x
Simplifying an ExpressionFrom the question, we are to simplify the given expression
The given expression is
(-3x⁴ - 5x - x³) + (-12x³ -8x -14x⁴)
To simplify the expression,
First clear the parentheses
(-3x⁴ - 5x - x³) + (-12x³ -8x -14x⁴)
-3x⁴ - 5x - x³ -12x³ - 8x - 14x⁴
Collect like terms
-3x⁴ - 14x⁴ - x³ -12x³ - 8x - 5x
Simplify further
-17x⁴ -13x³ - 13x
Hence, the simplified form of the expression is -17x⁴ -13x³ - 13x
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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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A/an is calculated by dividing the difference between a data value and the mean by the standard deviation.
Answer: Z-score
Step-by-step explanation:
(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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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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