60 POINTS!!! HELPFind any asymptotes or holes in the function below. Explain how you arrived at your answer. SHOW YOUR WORK AND THE STEPS YOU TOOK.
Answers
The function given is,
[tex]y=\frac{x-6}{(x-1)(x-6)}[/tex]Since , the leading coefficient of numerator is less than the leading coefficient of denominator .
Therefore, there is no horizontal asymptotes.
For finding the vertical asymptotes, substitute the denominator is equal to 0.
[tex](x-1)=0\text{ , }(x-6)=0[/tex][tex]x=\text{ 1,6.}[/tex]The vertical asymptotes are 1 and 6.
To find the hole in the function,
[tex](x-6)[/tex]is crossed out in numerator and denominator.
So, if we set up x-6 equals to 0.
The hole in the function is, when
[tex]x=6.[/tex]Related Questions
Estimate the side length of a square that has a 9 cm long diagonal. ( The perimeter of a square is typically 2.8 times bigger than the diagonal)
Answers
The diagonal and two adjacent sides of the square form an isosceles right triangle.
By the Pythagorean theorem
[tex]\begin{gathered} s^2+s^2=9^2 \\ 2s^2=81 \\ s^2=\frac{81}{2} \\ s=\sqrt[]{\frac{81}{2}} \\ s=\frac{9}{\sqrt[]{2}} \\ s=6.36\text{ cm} \end{gathered}[/tex]Use the following function rule to find f(9).
f(x) = x + 6
f(9) = [
What does f(9) =
Answers
Answer:
f(9) = 15Step-by-step explanation:
In order to find f(9) we substitute the value of x that's 9 into f(X) that's where there's x we substitute it with 9 and calculate.
We have
[tex]f(x) = x + 6[/tex]
[tex]f(9) = 9 + 6 \\ = 15[/tex]
We have the final answer as
f(9) = 15Hope this helps you
Please help asap now please Ik this easy for u not for me I’m not good whit shapes
Answers
The shape has some right angles .
The correct option is (D).
Given,
In the question:
Complete the sentences :
The shape has ____
Now, According to the question:
From the figure,
There are four option:
Select the one option according to the figure.
To see that :
The figure says that :
Correct Answer is some right angles because the sides are not exactly the same .
Hence, The shape has some right angles .
The correct option is (D).
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Simplify and determine the coefficient of (-x)(5y)(-2x).
Answers
Answer:
10x^2y
Step-by-step explanation:
In parallelogram EFGH the measure of angle E is (2x+3) and the measure of angle F is (3x-33) what’s is the measure of angle E
Answers
The measure of ∠E = 87° and ∠F = 93°.
What is Parallelogram? What is triangle?In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a parallelogram in which EFGH the measure of angle E is (2x+3) and the measure of angle F is (3x - 33).
We can write -
2(2x + 3) + 2(3x - 33) = 360°
4x + 6 + 6x - 66 = 360°
10x - 60 = 360
10x = 420
x = 42
∠E = 2 x 42 + 3 = 84 + 3 = 87°
∠F = 3 x 42 - 33 = 126 - 33 = 93°
Therefore, the measure of ∠E = 87° and ∠F = 93°.
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The table below represents the number of paintings, y, that Jordan completed in x years. Jordan's Paintings Year (x) Paintings (y) 1 4 2 7 3 10 4 13 Which equation describes the relmionship between the number of paintings and the year? A. y = x+3 B. y = 3x + 1 D.y = 4x + 3 C. y = 3x + 4
Answers
Method 1
Concept
Pick two points and find the equation of a line.
Point ( 1. 4 ) and ( 2, 7 )
Step 2: Represent each point
[tex]\begin{gathered} x_1\text{ = 1} \\ y_1\text{ = 4} \\ x_2\text{ = 2} \\ y_2\text{ = 7} \end{gathered}[/tex]Step 3: Substitute the values in the two points equation of a line formula
[tex]\frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} \frac{y\text{ - 4}}{x\text{ - 1}}\text{ = }\frac{7\text{ - 4}}{2\text{ - 1}} \\ \frac{y\text{ - 4}}{x\text{ - 1}}\text{ = }\frac{3}{1} \\ \frac{y\text{ - 4}}{x\text{ - 1}}\text{ = 3} \\ \text{Cross multiply} \\ y\text{ - 4 = 3(x - 1)} \\ y\text{ - 4 = 3x - 3} \\ y\text{ = 3x - 3 + 4} \\ y\text{ = 3x + 1} \end{gathered}[/tex]Step 4: Final answer
y = 3x + 1 Option B
-7/3 divided by 1/3 plus one
Answers
(-7/3)(3/1)+1
-21/3+1
-7+1
Answer: -6
Write an equation of the line that passes through (-5,0) and is parallel to the line y=-2/3x-1
Answers
The equation of the line that passes through (-5,0) and is parallel to the line y = -2/3x - 1 is y = - 2 / 3 x - 10 / 3
How to find the equation of a line?The equation of a line can be represented in different form such as point slope form, slope intercept form, standard form and general form.
The equation of a line in slope intercept form is as follow:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line passes through (-5,0) and is parallel to the line y = -2/3x - 1.
Parallel line has the same slope.
Therefore, the slope of the line is - 2 / 3.
Hence, let's find the y-intercept using (-5, 0)
0 = - 2 / 3(-5) + b
b = - 10 / 3
Therefore, the equation is y = - 2 / 3 x - 10 / 3
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The graph of the system of linear equations below is shown in the coordinate plane.
4y = -3x - 1
2y = x - 13
why is the point (5,-4) a solution to the system?
Answers
The point, (5, -4), is the solution to the given system of equations because the lines intersect at the point.
Graph of system of linear equationsFrom the question, we are to determine why the given point is a solution to the system of equations
The given system of equations is
4y = -3x - 1
2y = x - 13
When solving system of equations by the graphical method, the point where the lines intersect gives the solution to the system of equations.
From the given graph,
The two lines intersect at the point where x = 5 and y = -4.
That is,
The lines intersect at (5, -4), and thus, (5, -4) is the solution to the system of equations.
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iguyhuhhubbybbubuinnhunbubhb
Answers
shelbyblanchard15, this is the solution:
e. (7 * 10^6) * (8 * 10^5) = 5.6 * 10 ^12
f. 10,000,000 * 0.000 005
10,000,000 = 10 ^7
0.000 005 = 5 * 10 ^ -6
5 * 10^1 = 5 * 10
g. 30,000/0.0004
30,000 = 3 * 10^4
0.0004 = 4 * 10^-4
3 * 10^4/4 * 10^-4 = 7.5 * 10^7
Solve for x.
−4.5(x+3.21)=−33.21
Responses
x = 4.17
x, = 4.17
x = 6.67
x, = 6.67
x = 8.09
x, = 8.09
x = 10.59
Answers
Answer:
b
Step-by-step explanation:
Answer:
x = 4.17
Step-by-step explanation:
you just solve it using BIDMAS. I'm 100% sure I'm right
use two unit multipliers to convert 500 feet to centimeters
Answers
Answer:
15240.00 cm
Step-by-step explanation:
15240.00 cm
500 feet * 30.48x(cm)
x = centimeters per foot
The graph of a linear function is shown on the grid.Y(-3, 3.6(5,2)XYo -2What is the rate of change of y with respect to x for this function?Choose the grid that is labeled and bubbled with the correct answer.
Answers
(x, y) = (-3, 3.6); (5, 2)
Slope (m) = (y2 - y1) / (x2 - x1)
m = (2 - 3.6) / (5 - - 3) = - 1.6/8
m = -0.2
Isabella's baby weighed 8.5 lbs
when it was first born. 20 days
later, it weighed 10.8 lbs. what is the rate of change of the baby's weight per day?
Answers
0.115 lbs/day is the rate of change of baby's weight.
What is rate of change ?When anything changes over time, it does so at a certain rate, or ROC. Therefore, rather than the size of each change individually, it is the pace of change—or, more specifically, its acceleration or deceleration. Rate of change in the financial world is utilized to comprehend price returns and spot trend momentum.
Calculationrate of change in baby's weight will be = (10.8 - 8.5)/ 20
= 2.3 / 20
= 0.115 lbs/day
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The centre of a circle is the point with coordinates (-1, 3)
The point A with coordinates (6, 8) lies on the circle.
Find an equation of the tangent to the circle at A.
Give your answer in the form ax+by+c=0 where a, b and c are integers.
Answers
Answer:
[tex]7x-5y-2=0[/tex]
Step-by-step explanation:
The gradient of the line from the centre to [tex]A[/tex] is [tex]\frac{8-3}{6-(-1)}=\frac{5}{7}[/tex].
Perpendicular lines have gradients that multiply to -1, so the tangent at the point A has gradient 7/5.
So, the equation is:
[tex]y-8=\frac{7}{5}(x-6) \\ \\ 5(y-8)=7(x-6) \\ \\ 5y-40=7x-42 \\ \\ 7x-5y-2=0[/tex]
NEED HELP AGAIN FASTTT FOR GEOMETRY my time is running out
Answers
Answer:
d
Step-by-step explanation:
Answer:4/5
Step-by-step explanation:
sin is opposite/hypotenuse so its 16/20 which reduces to 4/5
The height of an iceberg above the
water is 23 meters. The bottom of the
iceberg is 15 meters below sea level.
What is the total height and depth of
the iceberg.
Answers
The total height of the iceberg is 38 meters and the total depth of the iceberg is 15 meters.
What is meant by height and depth?Height is a mathematical term that refers to the vertical distance between an object's top and base. Sometimes, it has the designation altitude. The measurement of an item along the y-axis in coordinate geometry is referred to as height in geometry.
The depth of an object is the separation between its closest and farthest ends. Jane, for instance, measures a box. Jane estimates the depth of the box by calculating the distance between the end of the box that is closest to her and the end that is farthest away.
Given, the height of an iceberg above the water is 23 meters.
And also given that the bottom of the iceberg is 15 meters below sea level.
Total height = above the water + below the water
Total height=23+15=38 meters
Depth= total height - iceberg above the water
Depth=38-23=15 meters
The total height of the iceberg is 38 meters.
The total depth of the iceberg is 15 meters.
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Solving Systems of linear equations by elimination
Answers
The solution of the systems of linear equations is x = 13.81 and y = 73.381. The average salaries were equal in the year 1999. The average salary that year was about $73381.
What is the system of linear equation?
A collection of two or more linear equations is a system of linear equations. The graph of a system of two equations is a pair of lines in the plane for two variables (x and y).
The intersection point of the lines is ( 13.81, 73.381).
The average salaries were equal after 14 years since 1985.
The average salaries were equal (1985 + 14) = 1999.
The average salary that year was about $73381.
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a health-conscious student faithfully wears a device that tracks his steps. suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. what percent of the time does he exceed 13,000 steps? group of answer choices 0.0228 0.05 0.95 0.972
Answers
The percentage of time he exceeds 13,000 steps is 2.28% or 0.0228.
Percentage
Use the percentage formula to express a number or percentage in terms of 100. % simply indicates one out of one hundred. An expression for a number between 0 and 1 can be made using the percentage formula. It is a number that is represented as a fraction of 100. The sign % is used to denote it and it is mostly used to compare and calculate ratios. The formula for percentage increases is the ratio of the increased value to the original value multiplied by 100. It is described in percentage form. If anything is valued more highly, both its value and proportion will rise.
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How many possible outcomes are therefor any set of linear systems?
Answers
The answer is three
None, one or infinitely many solutions
How many student tickets were sold if 150 general admission tickets were sold?
Answers
After simplification, 250 tickets sold to students if 150 general admission tickets were sold.
In the given question we have to find the how many student tickets were sold if 150 general admission tickets were sold.
The cost of concert ticket for general admission is $15.
The cost of concert ticket for student is $9.
Total sales of ticket is $4500.
The total 150 ticket sold to general admission.
So the total cost of ticket that received from the general admission is
=150*15 = 2250
Let x number of ticket sold to student.
Then total cost of students ticket is 9x.
Now the expression should be
9x+2250 =4500
Subtract 2250 on both side, we get
9x = 2250
Divide by 9 on both side we get
x = 250
Hence, 250 tickets sold to students if 150 general admission tickets were sold.
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The right question is
Concert ticket cost $15 for general admission, but only $9 with student ID. Ticket ales total $4500. How many student tickets were sold if 150 general admission tickets were sold?
can you help with this
Answers
In the given parallelogram ABCD:
CD=5x-18
BC=3x-6
AB=2x+12
From the properties of parallelogram: The opposite sides of parallelogram are equal
Pair of opposite sides are:
AB & CD
BC & DA
Opposite sides are equal:
[tex]\begin{gathered} AB=CD \\ 2x+12=5x-18 \\ 5x-2x=12+18 \\ 3x=30 \\ x=\frac{30}{3} \\ x=10 \end{gathered}[/tex]x = 10
Substitute the value of x = 10 in the expression of BC
BC = 3x - 6
BC = 3(10) - 6
BC = 30 - 6
BC = 24
Opposite sides are equal: BC = DA
BC = 24 = DA
DA = 24
Answer: DA = 24
During the 2003-2004 season, Kevin Weekes of the Carolina
Hurricanes saved 1506 out of 1652 shots on goal. To the nearest
what part of the time did Weekes save shots on goal?
Answers
Part of the time weekes save shots on goal is 0.911.
Given,
Total number of shots on goal=1652
Number of shots saved=1506
Part of time weekes save shots on goal,
[tex]\frac{Number of shots saved}{Total number of shots on goal}\\\\\\=\frac{1506}{1652}\\ \\=0.911[/tex]
Thus, Part of the time weekes save shots on goal is 0.911.
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The coordinate plane shows rectangle PQRS . The length of side QR is 4 units. What is the area of PQRS?
Answers
QR = 4 unit
Let us find RS, which is the length of the rectangle . Therefore
[tex]\begin{gathered} RS=\sqrt[]{(1-5)^2+(-4-6)^2} \\ RS=\sqrt[]{16+100} \\ RS=\sqrt[]{116} \end{gathered}[/tex][tex]\begin{gathered} \text{area}=lw \\ \text{area}=\sqrt[]{116}\times4 \\ \text{area}=4\sqrt[]{116\text{ }}unit^2 \end{gathered}[/tex]Mr. A drove to a city in New Jersey
that is 200 miles away. He got
there in 2 hours. What is his
2 rate of change (At what Speed
was Mr. A driving)
Answers
Answer:
100 miles per hour
Step-by-step explanation:
He drives 200 miles in 2 hours so just divide 200 by 2 to get the unit rate/ miles per hour
Qsn 1.4.1 have never done a problem of this kind before so will need background explanation for every step in the answer.
Answers
Answer
Maximum area = 4900 m²
Step-by-step explanation
1.4.1 The perimeter of a rectangle is calculated as follows:
[tex]P=2(l+w)[/tex]where l is the length and w is the width of the rectangle.
Substituting P = 280 m, l = 2x meters, and w = y meters, and solving for y:
[tex]\begin{gathered} 280=2(2x+y) \\ \frac{280}{2}=\frac{2(2x+y)}{2} \\ 140=2x+y \\ 140-2x=2x+y-2x \\ 140-2x=y \end{gathered}[/tex]The area of a rectangle is calculated as follows:
[tex]A=l\cdot w[/tex]Substituting l = 2x and w = y = 140 - 2x:
[tex]\begin{gathered} A=2x(140-2x) \\ A=2x(140)-2x(2x) \\ A=280x-4x^2 \end{gathered}[/tex]1.4.2 Given that Area's formula is a quadratic function, its maximum is placed at its vertex. The x-coordinate of the vertex is found as follows:
[tex]x_V=\frac{-b}{2a}[/tex]where a is the leading coefficient and b is the x-coefficient of the function. In this case, the coefficients are a = -4 and b = 280, then:
[tex]\begin{gathered} x_V=\frac{-280}{2(-4)} \\ x_V=\frac{-280}{-8} \\ x_V=35 \end{gathered}[/tex]Evaluating the Area at x = 35, the maximum Area is:
[tex]\begin{gathered} A=280(35)-4(35)^2 \\ A=4900\text{ m}^2 \end{gathered}[/tex](-x) + (-3) = x + 3
x =
Answers
Answer:
x = -3
Step-by-step explanation:
-x +- 3 = x + 3
-x - 3 = x + 3 (+- is equal to -)
- 3 = 2x + 3 (add x to both sides, to remove the x on the left side)
- 6 = 2x (subtract 3 on both sides)
x = -3 (divide by 2)
Factor the expression using the GCF.
84+28
Answers
Answer:
28(3 +1)
Step-by-step explanation:
You want the expression 84+28 to be factored using the GCF.
GCFThe Greatest Common Factor (GCF) of 84 and 28 can be found by looking at the remainder from division of 84 by 28.
84 ÷ 28 = 3 r 0
The remainder is 0, so 28 is a factor of 84. Since it is also the largest factor of itself, it is the GCF of the two numbers.
Distributive propertyFactoring out 28, we have ...
84 +28 = 28·3 +28·1 = 28(3 +1)
The factored expression is 28(3 +1).
<95141404393>
m = 4 through (3,-2)
Answers
The equation of the line is y = 4x - 14
The slope of the line m = 4
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the function
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
The point is (3, -2)
Substitute the values in the point slope form
y - (-2) = 4(x-3)
y + 2 = 4x - 12
Rearrange the equation and make slope intercept form
y = 4x - 12 -2
y = 4x - 14
Hence, the equation of the line is y = 4x - 14
The complete question is
Write the equation of the line when m = 4 and the passing through the point (3, -2)
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Write an equation in point slope form for the line that passes through (-3,5) with a slope of -3
Answers
The equation of line in point slope form is y = -3x -4
Given,
The points which the line passes through;
(x, y) = (-3,5)
Slope, m = -3
We have to find the equation in point slope form;
Point slope form;
The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.
Here,
Point slope form;
y - y₁ = m(x - x₁)
Then,
y - 5 = -3(x - -3)
y - 5 = -3x -9
y = -3x - 9 + 5
y = -3x - 4
That is,
The equation of line in point slope form is y = -3x -4
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