We have to create a function that has at least one asymptote and one removable discontinuity (a "hole").
We then have to list the type of feature.
We can start with a function like y = 1/x. This function will have a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.
We can translate it one unit up and one unit to the right and write the equation as:
[tex]y=\frac{1}{x-1}+1=\frac{1}{x-1}+\frac{x-1}{x-1}=\frac{x}{x-1}[/tex]Then, the asymptotes will be x = 1 and y = 1. We have at least one asymptote for this function.
We can now add a removable discontinuity. This type of discontinuity is one that is present in the original equation but, when factorizing numerator and denominator, it can be cancelled. This happens when both the numerator and denominator have a common root: the rational function can be simplified, but the root is still present in the original expression.
We than can add a removable discontinuity to the expression by multiplying both the numerator and denominator by a common factor, like (x-2). This will add a removable discontinuity at x = 2.
We can do it as:
[tex]y=\frac{x(x-2)}{(x-1)(x-2)}=\frac{x^2-2x}{x^2-3x+2}[/tex]This will have the same shape as y =x/(x-1) but with a hole at x = 2, as the function can not take a value that makes the denominator become 0, so it is not defined for x = 2.
Finally, we can find the x and y intercepts.
The y-intercepts happens when x = 0, so we can calculate it as:
[tex]\begin{gathered} f(x)=\frac{x^2-2x}{x^2-3x+2} \\ f(0)=\frac{0^2-2\cdot0}{0^2-3\cdot0+2}=\frac{0}{2}=0 \end{gathered}[/tex]The y-intercept is y = 0, with the function passing through the point (0,0).
As the x-intercept is the value of x when y = 0, we already know that the x-intercept is x = 0, as the function pass through (0,0).
Then, we can list the features as:
Asymptotes: Vertical asymptote at x = 1 and horizontal asymptote at y = 1.
Removable discontinuity: x = 2.
y-intercept: y = 0.
End behaviour: the function tends to y = 1 when x approaches infinity or minus infinity.
With that information, the function can be graphed.
If A is the image of A(3, 4) after a dilation with scale factor 7 about the origin, what is the distance between A and A? Hint: Use the distance formula: d = √√(x₂ − x₂)² + (Y₂ − 3₂)² .
0 7 units
○28 units
O 30 units
O 35 units
Answer:
Step-by-step explanation:
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Answer:
35
Step-by-step explanation:
sorry if im wrong sorry
how do I find the correct answer? (answers in the dropbox below)
A rhombus have 4 sides and angles
it first must be proven to have 4 sides, or 4 angles
thats a definition for Quadrilateral
then correct option is D
Calculate the five-number summary and the IQR from the following values given: {17, 20, 21, 25, 25, 29, 40}
Answer:
• 17, 20, 25, 29 and 40
,• IQR=9
Explanation:
(a)Given the set of values:
{17, 20, 21, 25, 25, 29, 40}
• The minimum value = 17
The first quartile
The first quartile is the median of the lower half of the data set.
The lower half of the data set = 17, 20, 21
• Therefore, the first quartile =20
The Median
The median is the number in the middle of the set of values.
The number in the middle is 25, therefore:
• Median = 25
The third quartile
The third quartile is the median of the upper half of the data set.
The upper half of the data set = 25, 29, 40
• Therefore, the third quartile =29
Finally, Maximum Value = 40.
The five-number summary of the set of values is: 17, 20, 25, 29 and 40
(b)Interquartile Range
Interquartile Range = Third Quartile - First Quartile
=29 - 20
IQR=9
given that the measure of arc AD=(17×+2), measure of arc AC=(7×-10),and measure of angle ABC=(4×+15) find the measure of angle ABC
In the given figure, angle ABC is formed by a tangent and a secant.
The angle formed by tangent and secant is given by
[tex]m\angle ABC=\frac{1}{2}(m\bar{AD}-m\bar{AC})[/tex]Where mAD and mAC are the intercepted arcs.
For the given case,
[tex]\begin{gathered} m\angle ABC=(4x+15)\degree \\ m\bar{AD}=(17x+2)\degree \\ m\bar{AC}=(7x-10)\degree \end{gathered}[/tex]Let us substitute the given values into the above formula and solve for x
[tex]\begin{gathered} m\angle ABC=\frac{1}{2}(m\bar{AD}-m\bar{AC}) \\ (4x+15)\degree=\frac{1}{2}\lbrack(17x+2)\degree-(7x-10)\degree\rbrack \\ 2\cdot(4x+15)\degree=(17x+2)\degree-(7x-10)\degree \\ 8x+30=17x+2-7x+10 \\ 8x-17x+7x=2+10-30 \\ -2x=-18 \\ x=\frac{-18}{-2} \\ x=9 \end{gathered}[/tex]The value of x is 9
So, the measure of angle ABC is
[tex]\begin{gathered} m\angle ABC=4x+15 \\ m\angle ABC=4(9)+15 \\ m\angle ABC=36+15 \\ m\angle ABC=51\degree \end{gathered}[/tex]Therefore, the measure of angle ABC is 51°
Karen is planning to drive 870 miles on a road trip. If she wants to complete the trip in 6 days, how many miles will she need to drive each day??
Answer:
145 miles
Step-by-step explanation:
870 ÷ 6 = 145
Question 19 of 25 Which of these is a factor in this expression? 6z^4 - 4+9 (y² +9) O A. (y +9 O B. 624 - 4 OC. 9 (y +9 OD. -4+9 (y +9)
1) In this expression, we have already a factored form. So the factor in this expression is 9(y³+9) Because multiplying "distributing it" we'll have the whole expression
6z^4 -4+9(y³+9)
6z^4 -4 +9y³+81
2) 9(y³+9)
Write the equation for a circle with the following informationcenter: (5,-3) radius: 7
Step 1: Problem
To determine the equation of a circle with centre (5, -3) and radius 7
Step 2: Substitute the centre value and radius to the equation
[tex]\begin{gathered} \text{Equation of a circle} \\ (x-a)^2+(y-b)^2=r^2 \\ \text{centre (5,-3) , radius =7} \\ a=5,\text{ b=-3, r=7} \\ (x-5)^2+(y-(-3))^2=7^2 \end{gathered}[/tex]Step 3: Simplify the above equation
[tex]\begin{gathered} (x-5)(x-5)\text{ + (y+3)(y+3) = 49} \\ x^2-5x-5x+25+y^2+3y+3y+9=49 \\ x^2-10x+25+y^2+6y+9=49 \\ x^2+y^2-10x+6y=49-25-9 \\ x^2+y^2-10x+6y=15 \\ x^2+y^2-10x+6y-15=0 \end{gathered}[/tex]Hence the equation of the circle is
[tex]x^2+y^2-10x+6y-15=0[/tex]35% of the employees in a company receive an incentive in the month of April. What is theprobability that among 4 employees chosen at random, all 4 do not receive the incentive inApril?
ANSWER :
0.1785
EXPLANATION :
35% will receive an incentive and (100% - 35% = 65%) will NOT receive an incentive.
So an employee has 65% chance of NOT receiving an incentive.
The probability that among 4 employees do not receive the incentive is :
[tex](0.65)^4=0.1785[/tex]Find the volume of the cone. Round to the nearest tenth.27 m-45°O 10,306,0 m320,612.0 m341,224.0 m3763.4 m3
The volume of a cone is given by the formula:
[tex]\begin{gathered} V=\frac{1}{3}\times\pi\times r^2\times h \\ r\text{ is the radius} \\ h\text{ is the height} \end{gathered}[/tex]From the question, we are provided with following:
[tex]\begin{gathered} h=27m \\ \theta=45^0 \end{gathered}[/tex]We have to use the given parameters to obtain the radius of the cone.
Thus, we have:
[tex]\begin{gathered} \text{Tan 45}^0=\frac{opposite}{\text{adjacent}} \\ 1=\frac{27}{\text{radius}} \\ \text{Therefore, radius=27m} \end{gathered}[/tex]Therefore, the volume of the cone is:
[tex]\begin{gathered} V=\frac{1}{3}\times\frac{22}{7}\times27^2\times27 \\ V=20,611.98m^3 \end{gathered}[/tex]Hence, the correct option is option BH
Jocelyn graphs a linear function that passes through three distinct points: A, B, and C. The coordinates ofpoint A (-3, -3) and point C (3,5) are shown.What are the possible coordinates of point B for Jocelyn’s linear function?
(0,1) is a possible coordinite through the points (-3,-3), (3,5)
find the value of expression if d = 10 and c= 5, 5d + c + 2
the water pressure on Mustafa as he dives is increasing at a rate of 0.992 atmospheres (atm) per meter
What is the rate of increase in water pressure in atm/km
The rate of increase in water pressure in atm/km = 992 atm/km
what is pressure?Pressure can be defined as the external or internal force that acts on an area of an object which can be measured in atmosphere per meter.
The rate at which Mustafa dives = 0.992atm/meter.
That is,
0.992 atm = 1 meter
X atm = 1 km
But 1000m = 1 km
make X atm the subject of formula;
x atm = 0.992 × 1000
X atm = 992 atm/km
Therefore, the rate in atm/ km would be = 992 atm/km
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according to recent study 7 out of every 500 Americans aged 13-17, years are vegetarian.in a group of 350 13 to 17- years old about how many would you expect to he vegetarian
7 out of every 500 Americans aged 13 -17 years are vegetarians
This implies that in a group of 500 Americans , 7 Americans that are within the age range of 13 - 17 years are vegetarians
7 ======== 500
x ======== 350
Introduce cross multiplication
7 x 350 = x * 500
2450 = 500x
Divide both sides by 500
2450/500 = 500x/ 500
x = 4.9
Approximately, 5
5 vegetarians aged 13 - 17 years will be present is in a group of 350 Americans
The answer is 5
Find the trigonometric ratio using the diagram. Write the fraction in itssimplest form.
Answer
KM = 30 units
Tan M = (8/15)
Explanation
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this question,
a = KM = ?
b = KL = 16
hyp = LM = 34
a² + b² = (hyp)²
KM² + 16² = 34²
KM² + 256 = 1,156
KM² = 1,156 - 256
KM² = 900
Take the square root of both sides
√(KM²) = √(900)
KM = 30 units
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
Using M as the given non-right angle,
Hypotenuse = LM = 34
Opposite = KL = 16
Adjacent = KM = 30
Using trignometric identities, we know that TOA means
Tan M = (Opp/Adj)
Tan M = (16/30)
Divide numerator and denominator by 2
Tan M = (16/30) = (8/15)
Hope this Helps!!!
draw a right triangle with a leg that as a length of 10 and the angle opposite to that side is 55 degrees. find the length of the hypotenuse. round your answer to nearest tenth.
Question:
Draw a right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees. find the length of the hypotenuse. round your answer to the nearest tenth.
Solution:
A right triangle with a leg that has a length of 10 and the angle opposite to that side is 55 degrees is given by the following picture:
In this case, the appropriate trigonometric identity is:
[tex]\sin (55^{\circ})\text{ = }\frac{y}{h}[/tex]where y is the opposite side, and h is the hypotenuse. Now, replacing the given data in the previous equation we obtain:
[tex]\sin (55^{\circ})\text{ = }\frac{10}{h}[/tex]and solving for h, we get:
[tex]h\text{ = }\frac{10}{\sin (55^{\circ})}\text{ = 12.207}\approx12.21[/tex]then, the correct answer is:
[tex]h\text{ =}12.21[/tex]im confused on what 43/25 as a percent would be
1------------------------------------>100%
43/25----------------------------->x%
So, using cross multiplication:
[tex]\begin{gathered} \frac{1}{\frac{43}{25}}=\frac{100}{x} \\ \text{solve for x:} \\ x=100\times(\frac{43}{25}) \\ x=172 \end{gathered}[/tex]Kara's original financial plan required that she save $220 amonth for two years in order to have $5,280 for the downpayment on a car. However, after one year she has onlymanaged to save $2,300. How much will Kara have to save each month in the second year in order to reach her original goal of $5,280?
given data:
the amount needed to pay the downpayment of the car = $5280.
original financial plan = $220 per month.
The amount kara saved after 1 year = $2300.
the balance amount she needed to save
[tex]\begin{gathered} =5280-2300 \\ =2980 \end{gathered}[/tex]now, divide the balance amount by 12, because 1 year =12 months.
[tex]\begin{gathered} =\frac{2980}{12} \\ =248.3 \end{gathered}[/tex]Thus, kara needs to save 248 dollors each month in order to have 5280 dollors after a year.
A 39 -ft ladder leans against a building so that the angle between the ground and the ladder is 85∘
How high does the ladder reach the building? __________ ft
The height of the building is 38.85 ft.
Given;
length of the ladder, x = 39 ft
the angle between the ground and the ladder, θ = 85°
let the height of the building be h.
Construct this triangle, the ladder forms the hypotenuse side of the right angle triangle, the height of the triangle is the opposite side of the triangle while the base of the triangle is the adjacent side of the triangle.
Apply the following trig ratio to determine the height of the triangle;
sin(θ) = opposite/hypotenuse
sin(85°) = h/39
h = 39sin(85°)
h = 38.85 ft
Therefore, the height of the building is 38.85 ft (approx.).
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Miscavage Corporation has two divisions: the Beta Division and the Alpha Division.
The Beta Division has:
sales of $320,000,
variable expenses of $158,100,
and traceable fixed expenses of $72,300.
The Alpha Division has:
sales of $630,000,
variable expenses of $343,800,
and traceable fixed expenses of $135,100.
The total amount of common fixed expenses not traceable to the individual divisions is $137,200.
What is the total company's net operating income?
The total company's net operating income (NOI) is $103,500.
What is a Net operating income?In accounting, a Net operating income refers to the figure that equals to all revenue from the property minus all reasonably necessary operating expenses.
The computation of the Net operating income is as follows:
= Gross Income - Operating Expenses
= (Sales+Sales) - [(variable expenses + variable expenses) + (fixed expenses + fixed expenses) + 137,200]
= (320,000+630,000) - [(158,100 + 343,800) + (72,300 + 135,100) + 137,200]
= 950,000 - (5,01,900 + 2,07,400 + 137,200)
= 950,000 - 8,46,500
= $1,03,500
In conclusion, the total company's net operating income (NOI) is $103,500.
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About how many points did the four students score in round 1. Estimate by rounding each point total to the nearest whole number
The total points that the four students score in round 1 is 75 points.
How to calculate the value?Based on the information given, it's important to convert the numbers to while numbers and then add.
John has 19.5. This will be 20.
Adam had 21.2. This will be 21.
Peter has 23.8. This will be 24.
Grace has 10.2. This will be 10.
The total points will be:
= 20 + 21 + 24 + 10
= 75
The complete question is given below.
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The points of four students are:
John 19.5
Adam 21.2
Peter 23.8
Grace 10.2
About how many points did the four students score in round 1. Estimate by rounding each point total to the nearest whole number
A parabola opening up or
equation in vertex form.
down has vertex (-1, 4) and passes through (-2, 17). Write its equation in vertex form.
Equation of parabola in vertex form is 13x² + 26x + 17
Define Parabola
A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile traveling under the pull of gravity will travel along a curve similar to this one.
Given,
vertex (h,k) = (-1, 4)
points (x,y) = (-2, 17)
We know, The equation in vertex form is
y = a(x - h)² + k
put the (h,k) values,
y = a(x - (-1))² + 4
y = a(x + 1)² + 4 --------- eq(i)
Next, find the value of 'a' by plug in the points of (x, y) in eq(i)
y = a(x + 1)² + 4
⇒17 = a(-2 + 1)² + 4
⇒17 = a(-1)² + 4
⇒17 = a + 4
⇒a = 13
Now, substitute 'a' value in eq(i) to find the equation of parabola
y = a(x + 1)² + 4
⇒ y = 13(x + 1)² + 4
⇒ y = 13(x² + 1 + 2x) + 4
⇒ y = 13x² + 13 + 26x + 4
⇒ y = 13x² + 26x + 17
Therefore, equation of parabola in vertex form is 13x² + 26x + 17
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what is the final cost of the purchase at discount heaven?
First, let's sum the single costs of each item.
[tex]32+32+20=84[/tex]Because they are buying 1 jacket, 2 pairs of jeans, and 1 vest. So, the subtotal of these items is $84. (At Discount Heaven)
Then, we apply a 7% sales tax.
[tex]84+0.07\cdot84=84+5.88=89.88[/tex]As you can observe, the sales tax is $5.88 for all the items purchased, and the total cost they have to pay is $89.88.
What is the probability that a randomly selected oar was purchased in the 2010s given that the oar was made from ash wood?Simplify any fractions
P (A) = probability of a car purchased in 2010's
P (B) = probability of the car being made from ash wood
P (A and B) = 4
P (B) = 4 +3 = 7
Conditional probability:
P (B/A) = P (A and B ) / P (B) = 4 / 7 = 0.5714
A runner has a track lap time of 3 minutes while at a run, 5 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/2 at a jog, and 1/10 at a walk, what is the total track lap time of the runner? Write the solution as a mixed number or a fraction in lowest terms.
The total track lap time of the runner is 4 11/15 and it has been written as a mixed number or a fraction in lowest terms.
Mixed fraction:
The fraction represented with its quotient and remainder is known as mixed fraction.
Given,
A runner has a track lap time of 3 minutes while at a run, 5 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/2 at a jog, and 1/10 at a walk.
Here we need to find the total track lap time of the runner.
Here we can compute the Total Lap Time by multiplying each fraction by its associated lap time, then we get,
Run Lap Time = (2/5)(3) = 6/5 minutes
Jog Lap Time = (1/3)(5) = 5/3 minutes
Walk Lap Time = (4/15)(7) = 28/15 minutes
So, the total lap time is, written as,
Total Lap Time = 6/5 + 5/3 + 28/15
Now, we have to make the fraction equal to each other,
=> (6x3)/(5x3) + (5x5)/(3x5) + (28 x 1)(15 x1)
=> 18/15 + 25/15 + 28/15
=> (18 + 25 + 28)/15 = 71/15
Now, we have to convert this into mixed fraction then we get,
=> 71/15 = 4 11/15
Therefore, the total Lap Time is 4 11/15 minutes.
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Suppose 72% of students chose to study French their freshman year, and that meant that there were 378 such students. How many students chose not to take French their freshman year?
Answer:
There were 378 students who chose to study French their freshman year. This means that 72% of the total number of students chose to study French their freshman year. Therefore, the total number of students must be 378 / 0.72 = 527.5. This means that there were 148.5 students who chose not to take French their freshman year.
Step-by-step explanation:
Using the image, identify the opposite rays (choose all that apply).
Solution
The answer is
In a certain chemical, the ratio of zinc to copper is 4 to 11. A jar of the chemical contains 528 grams of copper. How many grams of zinc does it contain.
If the ratio of zinc to copper is 4 to 11. A jar of the chemical contains 528 grams of copper. Then 192 grams of zinc does it contain
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that,
In a certain chemical, the ratio of zinc to copper is 4 to 11.
i.e 4:11 or 4 /11
If A jar of the chemical contains 528 grams of copper
We need to find how many grams of zinc does it contain.
Let us consider it as x.
Form a equation,
4/11=x/528
4×528=11x
2112=11x
Divide both sides by 11
192=x
Hence 192 grams of zinc does it contain.
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What is the midpoint of the line segment graphed below?10(5,9)(2-1)-1010- 10O A. (7,8)OB.OC (34)OD (710
ANSWER:
[tex](\frac{7}{2},4)[/tex]STEP-BY-STEP EXPLANATION:
To calculate the value of the midpoint, we use the formula of the midpoint which is the following:
[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Replacing and solving the midpoint:
[tex]\begin{gathered} (x_m,y_m)=(\frac{5+2_{}}{2},\frac{9-1_{}}{2}) \\ (x_m,y_m)=(\frac{7_{}}{2},\frac{8_{}}{2})=(\frac{7}{2},4) \end{gathered}[/tex]answer step by step please suppose AC is congruent with AD. what information would you need to conclude that ADB is congruent with ACE using ASA theorem?
Answer:
Angle ABD must be congruent to Angle AEC.
Explanation:
Angle: Triangles ADB and ACE share angle A in common.
Side: AD is congruent to AC.
For Triangles ADB and ACE to be congruent by the ASA Congruence Theorem, then the following must hold:
Angle: Angle ABD must be congruent to Angle AEC.
The population of the state of Colorado was about 5,846,000 people in 2020.
Which number best approximates the population as a single digit times a
power of 10?
OA. 6x 10-6
OB. 6 x 106
C. 5 × 105
D. 5 x 106
Answer: [tex]6 \times 10^6[/tex] which is choice B
==========================================
Method 1
5,846,000 rounds to 6,000,000 aka "6 million".
This converts to the scientific notation [tex]6 \times 10^6[/tex]
The first 6 is from "6 million", while the 6 as the exponent tells us to move the decimal point that many places to the right to go from 6.0 to 6,000,000
---------------
Method 2
Place a decimal point between the first two digits of 5,846,000 and erase the zeros at the end.
So we get 5.846
We must move the decimal point 6 spaces to the right to go from 5.846 back to 5,846,000 again
Therefore, [tex]5,846,000 = 5.846 \times 10^6[/tex]
Then the 5.846 rounds to 6.0 or simply 6 when rounding to the nearest whole number. This leads to [tex]6 \times 10^6[/tex]