What do you do the inequality symbol when you multiply or divide by a negative number?
In a sale there is 10% of all prices.a chair costs £63 in the sale.hoow mutch was it before the sale?
Could someone please help me. Thanks!!! 12 points!
Write an equation for a rational function with: vertical asymptotes at x = -4 and x = 4 x-intercepts at x = -6 and x = 5 horizontal asymptote at y = 8
A rational function with the required characteristics is f(x) = 8(x + 6)(x - 5) / (x + 4)(x - 4), considering vertical asymptotes, x-intercepts, and a horizontal asymptote.
Explanation:To write an equation for a rational function with given characteristics, we need to incorporate the vertical asymptotes, x-intercepts, and horizontal asymptote into our function.
Firstly, vertical asymptotes at x = -4 and x = 4 suggest that the denominator of our function will be in the form (x + 4)(x - 4), as setting x to -4 or 4 will make the denominator zero, which creates the asymptotes.
Secondly, x-intercepts at x = -6 and x = 5 indicate that the numerator will have factors that become zero at these x-values. Hence, the numerator should be(x + 6)(x - 5).
Finally, for the function to have a horizontal asymptote at y = 8, the degree of the numerator and denominator must be the same, and the leading coefficients of the numerator and denominator must have a ratio that equals 8. To achieve the horizontal asymptote, we multiply the numerator by 8, thus the leading coefficients of the numerator and denominator are in the ratio 8:1.
Combining all these elements gives us our rational function: f(x) = 8(x + 6)(x - 5) / (x + 4)(x - 4)
As Mercury revolves around the sun, it travels at a rate of approximately 30 miles per second. Convert this rate to miles per minute. At this rate, how many miles will Mercury travel in 4 minutes?
The number of miles that Mercury travels in 4 minutes will be 7,200 miles.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
As Mercury revolves around the sun, it travels at a rate of approximately 30 miles per second.
Convert the rate into miles per minute. Then we have
Rate = 30 x 60
Rate = 1,800 miles per minute
At this rate, the number of miles that Mercury travels in 4 minutes will be given as,
D = 1,800 x 4
D = 7,200 miles
The number of miles that Mercury travels in 4 minutes will be 7,200 miles.
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pilar wants to save $100. So far, she has saved $63. Find the length of each side of the square
What was the one item that was left out of the repeal.?
Given 7x + 11y = N, what is the highest number N can be to produce an answer of No solution. (X,y) must be positive.
Help please geometry
Tony is putting 42 oranges into 4 boxes. Each box holds 12 oranges.
How many more oranges are needed to fill all the boxes?
H=62.4Ns/33,000 solve for N
please help
Answer:
[tex]N=\frac{33,000H}{62.4s}[/tex]
Step-by-step explanation:
We have been given an equation [tex]H=\frac{62.4Ns}{33,000}[/tex]. We are asked to solve our given equation for N.
Multiply both sides by 33,000:
[tex]H*33,000=\frac{62.4Ns}{33,000}*33,000[/tex]
[tex]33,000H=62.4Ns[/tex]
Switch sides:
[tex]62.4Ns=33,000H[/tex]
Divide both sides by [tex]62.4s[/tex]:
[tex]\frac{62.4Ns}{62.4s}=\frac{33,000H}{62.4s}[/tex]
[tex]N=\frac{33,000H}{62.4s}[/tex]
Therefore, the value of N is [tex]\frac{33,000H}{62.4s}[/tex].
Is y=4x-1 and 12x=3y+7 parallel, perpendicular, or neither
Answer:
Neither is the answer.
Step-by-step explanation:
If a line y = m₁x + c₁ and y = m₂x + c₂ are perpendicular to each other then m₁ × m₂ = -1
If both the lines are parallel to each other then m₁ = m₂
Now two lines have been given as
y = 4x - 1 ----------(1)
12x = 3y + 7
3y = -12x + 7
y = -4x + [tex]\frac{7}{3}[/tex]------(2)
Now from equation (1) and equation (2),
m₁ = 4 and m₂ = -4
Since m₁ ≠ m₂
Therefore, these lines are not parallel
m₁ × m₂ = 4 × (-4) = -16
Therefore, both the lines are neither parallel nor perpendicular.
A car is traveling at a constant velocity. After two hours the car has traveled 90 miles. After five hours the car has traveled 225 miles. Assuming a linear equation fits this situation, what are the ordered pairs that you would use to find the linear equation
P(x) = x2 – 1 and q(x)=5(x-1), which expression is equivalent to (p – q)(x)?
Answer: The required expression is [tex]x^2-5x+4.[/tex]
Step-by-step explanation: We are given that
[tex]p(x)=x^2-1,\\\\q(x)=5(x-1).[/tex]
We are to find the expression that is equivalent to (p-q)(x).
We know that for any two functions f(x) and g(x), we have
[tex](f-g)(x)=f(x)-g(x).[/tex]
Therefore we get
[tex](p-q)(x)\\\\=p(x)-q(x)\\\\=(x^2-1)-(5(x-1))\\\\=x^2-1-5x+5\\\\=x^2-5x+4.[/tex]
Thus, the required expression is [tex]x^2-5x+4.[/tex]
Will a polynomial times a polynomial always equal a polynomial?
Answer:
yes, it will always be a polynomial but depending on how many terms it has, the answer may change
Step-by-step explanat
Given △ABC≅△JKL , m∠B=55° , and m∠L=25° , what is the measure of ∠J ? Enter your answer in the box.
Answer:
m∠J = 100° is the answer.
Step-by-step explanation:
Given : ΔABC ≅ ΔJKL,
m∠B = 55°
m∠L = 25°
To find : ∠J
Since in both the triangles ABC and JKL
m∠A ≅ m∠J
m∠B ≅ m∠K = 55°
m∠C ≅ m∠L = 25°
Since measure of ∠K and ∠L are known then we can calculate the third angle j
m∠J + m∠K + m∠L = 180°
55° + 25° + m∠J = 180°
80° + m∠J = 180°
m∠J = 180 - 80
= 100°
Therefore, m∠J = 100° is the answer.
Point R is located at (3,2) and point S is located at (8,15)
What are to coordinates of the point that partitions The directed line segment RS in a 1:4 ratio?
Answer:
was this right
Step-by-step explanation:
what is 875/1000 simplified
Please help with this question thank you!
A palm reader gets paid $80 for each palm she reads, and her goal is to earn $2240 reading palms this month. If she has already read 4 palms this month, how many more palms must she read in order to reach her goal?
A.24
B.28
C.20
D.32
Is 0.54 a rational number? Why or why not?
Samantha bought a shirt for $14.98. She gave the cashier a $20 bill. Which operation(s) finds the amount of change Samantha received?
subtract the cost of the shirt from the amount she gave the cashier
20.00 - 14.98 = 5.02
using subtraction she would get $5.02 back in change
a regular polygon must have ___ sides if each interior angle measure is four times the measure of each exterior angle
The sum of the interior angles of the polygon is 1440° and the number of sides of the polygon is 10 sides
What is the sum of the interior angles of a polygon?The sum of the interior angles of a polygon is given by the formula
Sum of Interior angles of a polygon with n sides is
nθ = 180 ( n - 2 )
where n is the number of sides
θ = angle in degrees
Given data ,
Let the sum of the interior angles of the polygon be S
Now , the number of sides = n
The sum of the exterior angles of a polygon = 360°
And , each interior angle measure is four times the measure of each exterior angle
Substituting the values in the equation , we get
180 ( n - 2 ) = 4 ( 360 )
On simplifying the equation , we get
180n - 360 = 1440
Adding 360 on both sides of the equation , we get
180n = 1800
Divide by 180 on both sides of the equation , we get
n = 10 sides
Hence , the number of sides of the polygon is 10 and it is a decagon
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You purchase a pair of jeans for $24.99 and a t-shirt for $12.49. Assume sales tax is 7.5%
What is your subtotal? $
What is the tax? $
What is your total? $
A car travels 0.75 every minute. Explain how could you use proportional reasoning to find how far the car travels in one hour
Answer:
Sample Response: Identify the unit rate as 0.75 miles per 1 minute. Since there are 60 minutes in an hour, multiply 0.75 time 60 to find how far the car travels in one hour.
Step-by-step explanation:
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Will give brainiest to first answer!
Which of the following inequalities is graphed on the coordinate plane?
A. y > x
B. y is less than or equal to x
C. y is greater than or equal to x
D. y < x
Answer:
u have a solid line...means there is an equal sign in the problem...so that eliminates 2 of them right away...so A and D are incorrectit is shaded below the line....this means it is less then...that eliminates option C leaving u with only one answer choiceso ur answer is : B. y is less then or equal to x
Step-by-step explanation:
The length of a rectangle is 6 cm longer than its width. if the perimeter of the rectangle is 36 cm , find its area.
Write a two proof column
Given: 4y=2x-10 ; y=6
Prove: x=17
Any large random sample from a group of people will be representative of the entire group.
a. True
b. False
Find the least common multiple of x 3 - x 2 + x - 1 and x 2 - 1. write the answer in factored form.
a. (x + 1) 2(x - 1)
b. (x + 1)(x - 1)(x 2 + 1)
c. (x 3 - x 2 + x - 1)(x 2 - 1)
d. (x + 1)(x - 1)(x 2 - 1)
The correct answer is d. [tex](x + 1)(x - 1)(x^2 - 1)[/tex].
To find the least common multiple (LCM) of the two polynomials[tex]\(x^3 - x^2 + x - 1\) and \(x^2 - 1\)[/tex], we need to factor each polynomial and then find the LCM of the factors.
First, let's factor [tex]\(x^3 - x^2 + x - 1\)[/tex]:
[tex]\(x^3 - x^2 + x - 1 = x^2(x - 1) + (x - 1) = (x^2 + 1)(x - 1)\)[/tex].
Now, let's factor [tex]\(x^2 - 1\)[/tex]:
[tex]\(x^2 - 1 = (x + 1)(x - 1)\)[/tex].
The LCM of two polynomials is the product of the highest powers of all the factors that appear in either polynomial. Here, we have the factors [tex]\(x - 1\), \(x + 1\), and \(x^2 + 1\)[/tex] from the first polynomial, and the factors [tex]\(x - 1\) and \(x + 1\)[/tex] from the second polynomial.
Since [tex]\(x^2 + 1\)[/tex] is already the highest power of [tex]\(x^2 + 1\) , \(x - 1\) and \(x + 1\)[/tex] are the highest powers of [tex]\(x - 1\) and \(x + 1\)[/tex] respectively, the LCM is simply the product of all these factors:
[tex]\((x + 1)(x - 1)(x^2 + 1)\)[/tex].
However, we notice that [tex]\(x^2 - 1\)[/tex] is actually equal to [tex]\((x + 1)(x - 1)\)[/tex], and since [tex]\(x^2 + 1\)[/tex] is not a factor of [tex]\(x^2 - 1\)[/tex], we do not include it in the LCM. Therefore, the LCM is just [tex]\((x + 1)(x - 1)\)[/tex].
But we must also consider the polynomial [tex]\(x^3 - x^2 + x - 1\)[/tex], which can be rewritten as [tex]\((x^2 + 1)(x - 1)\)[/tex]. Since [tex]\(x^2 + 1\)[/tex] is not a factor of [tex]\(x^2 - 1\)[/tex], it must be included in the LCM to account for the additional factor in the first polynomial.
Thus, the LCM of [tex]\(x^3 - x^2 + x - 1\) and \(x^2 - 1\)[/tex] is [tex]\((x + 1)(x - 1)(x^2 - 1)\)[/tex], which corresponds to option d. This is because we take the highest powers of the common factors [tex]\((x + 1)\) and \((x - 1)\)[/tex], and include the additional factor from the first polynomial, which is [tex]\(x^2 - 1\)[/tex] since [tex]\(x^2 + 1\)[/tex] is not a factor of[tex](x^2 - 1\))[/tex].
Therefore, the final answer is [tex]\(\boxed{(x + 1)(x - 1)(x^2 - 1)}\)[/tex].