ans (alpha particles) at Figure 127 Exercises 12.6. complete the following: Find the intercepts and domain and perform the symmetry test (a) 9x^2 - 16y^2 = 144
Answers
We have that the general equation of the hyperbola is the following:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]where 'a' and '-a' are the x-intercepts.
In this case, we have the following equation:
[tex]9x^2-16y^2=144[/tex]then, we have to divide both sides by 144 to get on the right side 1, thus, we have the following:
[tex]\begin{gathered} (9x^2-16y^2=144)(\frac{1}{144}) \\ \Rightarrow\frac{9}{144}x^2-\frac{16}{144}y^2=1 \\ \Rightarrow\frac{x^2}{16}-\frac{y^2}{9}=1 \end{gathered}[/tex]now, notice that we have that:
[tex]a^2=16[/tex]then, the x-intercepts are:
[tex]\begin{gathered} a^2=16 \\ \Rightarrow a=\pm\sqrt[]{16}=\pm4 \\ a_1=4 \\ \text{and} \\ a_2=-4 \end{gathered}[/tex]therefore, the x-intercepts are 4 and -4.
Now that we know that the intercepts are on those points, we can see that the hyperbola has the following graph:
we can see that the hyperbola is not defined between -4 and 4, therefore, the domain of the hyperbola is:
[tex](-\infty,-4\rbrack\cup\lbrack4,\infty)[/tex]finally, to perform the symmetry test, we have to check first both axis simmetries by changing x to -x and y to -y:
[tex]\begin{gathered} \frac{x^2}{16}-\frac{(-y)^2}{9}=1 \\ \Rightarrow\frac{x^2}{16}-\frac{y^2}{9}=1 \\ then \\ \frac{(-x)^2}{16}-\frac{y^2}{9}=1 \\ \Rightarrow\frac{x^2}{16}-\frac{y^2}{9}=1 \end{gathered}[/tex]since the hyperbola got symmetry about the x-axis and the y-axis, we have that the hyperbola got symmetry about the origin
Related Questions
1 - The Le Mans car race is a 24-hgur race. The longest distance erertraveled by a car in the race is 3,315 miles. What is the distancerounded to the nearest ten?2- The longest river in the world is the Nile. It is 4,184 miles long.What is the length of the Nile River rounded to the nearesthundred miles?3- Frank rounds 846,025 to the nearest hundred thousand and to the nearest ten thousand.Part A What is 846,025 rounded to the nearest hundred thousand?Part B What is 846,025 rounded to the nearest ten thousand?Part C Which rounded number is greater? Explain.
Answers
1. To find the nearest ten of 3315.
Since 15 is midway between 10 and 20.
So, the nearest ten of 3315 is 3320.
2. To find the nearest hundred miles of 4,184 miles:
184 is closest to 200.
Hence, the nearest hundred miles of 4,200 miles.
3.
A) To find the nearest hundred thousand of 846,025:
846,025 is closest to 800,000.
Hence, nearest hundred thousand of 846,025 is 800,000.
B) To find the nearest ten thousand of 846,025:
46,025 is closest to 50,000.
Hence, nearest ten thousand of 846,025 is 850,000.
C) Comparing the results of Part A and Part B,
The rounded number of Part B is greater.
find all other zeros of p (x)= x^3-x^2+8x+10, given that 1+3i is a zero. ( if there is more than one zero, separate them with commas.)edit: if possible please double check answers would high appreciate it.
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Since we have that 1 + 3i is one zero of p(x), then we have that its conjugate is also a root, then, we have the following complex roots for p(x):
[tex]\begin{gathered} x=1-3i \\ x=1+3i \end{gathered}[/tex]also, notice that if we evaluate -1 on p(x), we get:
[tex]\begin{gathered} p(-1)=(-1)^3-(-1)^2+8(-1)+10=-1-1-8+10 \\ =-10+10=0 \end{gathered}[/tex]therefore, the zeros of p(x) are:
x = 1-3i
x = 1+3i
x = -1
10x + 50 + 6x = 58 if x is the solution to the given equation, what is the value of 32x
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The solution to the given equation is;
[tex]\begin{gathered} 10x+50+6x=58 \\ \text{Collect all like terms,} \\ 10x+6x=58-50 \\ 16x=8 \\ \text{Divide both sides by 16} \\ \frac{16x}{16}=\frac{8}{16} \\ x=\frac{1}{2} \end{gathered}[/tex]Therefore, the value of 32x shall be;
[tex]\begin{gathered} 32x \\ =32(\frac{1}{2}) \\ =\frac{32}{2} \\ =16 \end{gathered}[/tex]The answer is 16
10 Natalie uses a 15% off coupon when she buys a camera. The original price of the camera is $45.00. How much money does Natalie save by using the coupon.?
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Given data:
The given discount through coupon is d=15%.
The original price of camera is c=$45.00.
The discount on the given amount is,
[tex]\begin{gathered} d=(\frac{15}{100})(45) \\ =6.75 \end{gathered}[/tex]Thus, the amount saved is $6.75.
The population P of a city is given by P = 115600e^0.024t, where t is the time in years. According to this model, after how many years will the population be 130,000?4.29 years4.89 years5.19 years4.49 years
Answers
Given:
The population P of a city is given by,
[tex]P=115600e^{0.024t,}[/tex]To find:
The time taken for the population to reach 130,000.
Explanation:
Substituting P = 130,000 in the given function, we get
[tex]\begin{gathered} 130000=115600 \\ e^{0.024t}=\frac{130000}{115600} \\ e^{0.024t}=1.1245 \\ 0.024t=\ln1.1245 \\ 0.024t=0.1174 \\ t=4.891 \\ t\approx4.89years \end{gathered}[/tex]Therefore, the number of years required for the population to reach 130,000 is 4.89years.
Final answer:
The number of years required is 4.89years.
find the value of x,y,z
Answers
Answer: x =116 degrees
y = 88 degrees
Explanation:
[tex]\begin{gathered} \text{ Find the value of x, y, and z} \\ To\text{ find z} \\ \text{Opposite angles are supplementary in a cyclic quadrilateral} \\ 101\text{ + z = 180} \\ \text{Isolate z} \\ \text{z = 180 - 101} \\ \text{z = 79 degre}es \\ To\text{ find x} \\ 2(101)\text{ = x + 86} \\ 202\text{ = x + 86} \\ \text{Collect the like terms} \\ \text{x = 202 - 86} \\ \text{x = 116 degr}ees \\ \text{ find y} \\ 2z\text{ = y + 70} \\ z=\text{ 79} \\ 2(79)\text{ = y + 70} \\ 158\text{ = y + 70} \\ \text{y = 158 - 70} \\ \text{y = 88 degre}es \end{gathered}[/tex]Therefore, x = 116 degrees, y = 88 degrees, and z = 79 degrees
5x + 4y = 12Step 1 of 2: Determine the missing coordinate in the ordered pair (0) so that it will satisfy the given equation,
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Answer:
Explanations:
Given the equation;
[tex]5x+4y=12[/tex]In order to get the missing coordinate in the ordered pair (0, ?), we will substitute x = 0 into the equation and get the corresponding y-value as shown:
[tex]\begin{gathered} 5(0)+4y=12 \\ 0+4y=12 \\ 4y=12 \end{gathered}[/tex]Divide both sides of the equation by 4;
[tex]\begin{gathered} \frac{4y}{4}=\frac{12}{4} \\ y=3 \end{gathered}[/tex]Therefore, the missing coordinate will be 3 to have (0, 3)
Can you help Turn this equation to the other equation
3x-y=-27
x+2y=16
y=_x+_
y=_x+_
Answers
Answer:
y=3x+27
2y= x+16or,
or,y= x+16/2
Do anyone know the answer to these questions? Please explain as well
Answers
given data:
[tex]\begin{gathered} \frac{7}{21}\text{ and }\frac{21}{24} \\ \end{gathered}[/tex]to find whether they form an proposition.
using cross product,
[tex]\begin{gathered} \frac{7}{21}\cdot\frac{21}{24} \\ 24\cdot7=21\cdot21 \\ 168\ne441 \end{gathered}[/tex]the cross product are not equal.
Thus, they donot form a proposition.
Becca wants to make a giant apple pie to try and break the world record. If she succeeds in making a pie with 20 foot diameter, what will the size of the crust covering the pie be?
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ANSWER :
62.83 feet
EXPLANATION :
The pie has a diameter of 20 feet.
The size of the crust covering is the circumference of the pie.
The circumference formula is :
[tex]C=2\pi r[/tex]We know that the radius is half of diameter.
So the radius is 20/2 = 10 feet.
Using the formula above :
[tex]\begin{gathered} C=2\pi(10) \\ C=62.83 \end{gathered}[/tex]The student Fun Club plans to go to the movies. At the matinee, tickets cost $6 and popcorn is $3. At evening shows, tickets cost $9 and popcorn is $4. The Fun Club attends a matinee and spends less than $60, and then attends an evening show and spends more than $36. If they purchased the same number of tickets and popcorns at each show, which of the following is a possible solution for the number of tickets and popcorns purchased?
Answers
Matinee
Cost of each ticket: $6
Cost of popcorn: $3
Evening:
Ticket: $9
Popcorn: $4
Number of tickets: x
Number of popcorns : y
The Fun Club attends a matinee and spends less than $60
6x + 3y < 60
Then attends an evening show and spends more than $36
9x+ 4y < 36
We have the system:
6x + 3y < 60 (a)
9x+ 4y >36 (b)
Graph each inequality:
The intersection of red and blue is the solution.
7 tickets and 5 popcorns (7,5) is inside the intersection, So, it is the solution.
IQ is normally distributed with a mean of 100 and a standard deviation of 15.a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 95.Write your answer in percent form. Round to the nearest tenth of a percent.P(10 greater than 95) =%b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125.Write your answer in percent form. Round to the nearest tenth of a percent.P(IQ less than 125) =%c) In a sample of 800 people, how many people would have an IQ less than 110?peopled) In a sample of 800 people, how many people would have an IQ greater than 140?peopleCheck Answer
Answers
To answer this questions we need to remember the standard score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x is the value we are looking for, mu si the mean and sigma is the standard deviation.
a.
We need the probability:
[tex]P(IQ>95)[/tex]using the standard score this is equivalent to:
[tex]\begin{gathered} P(IQ>95)=P(z>\frac{95-100}{15}) \\ =P(z>-0.3333) \end{gathered}[/tex]Using a normal distribution table we have:
[tex]P(z>-0.3333)=0.6306[/tex]Therefore the probability to select a person with more than 95 IQ points is 63.1%.
b.
Following the same reasoning as before we have:
[tex]\begin{gathered} P(IQ<125)=P(z<\frac{125-100}{15}) \\ =P(z<1.6667) \\ =0.9522 \end{gathered}[/tex]Therefore the probability to select a person with less than 125 IQ points is 95.2%
c.
To find how many people of this sample have more less than 110 points we need to find that probability:
[tex]\begin{gathered} P(IQ<110)=P(z<\frac{100-110}{15}) \\ =P(z<-0.666) \\ =0.7475 \end{gathered}[/tex]Multiplying this value with the sample size we have
[tex](800)(0.7475)=598[/tex]Therefore 598 people will have an IQ less than 110.
d.
By the same reasoning as before we have:
[tex]\begin{gathered} P(IQ>140)=P(z>\frac{140-100}{15}) \\ =P(z>2.6667) \\ =0.0038 \end{gathered}[/tex]Multiplying this value with the sample size we have
[tex](800)(0.0038)=3[/tex]Therefore 3 people will have an IQ greater than 140.
How many terms are in 6b+b2+5+2b-3f
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In that polynomial there are 5 terms, they are separated by signs.
If we simplify the new number of terms is 4
6b + b^2 + 5 + 2b - 3f
8b + b^2 + 5 - 3f
Given: D is the midpoint of segment AC, angle AED is congruent to angle CFD and angle EDA is congruent to angle FDCProve: triangle AED is congruent to triangle CFD
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Since Angle AED is congruent to angle CFD and angle EDA is congruent to angle FDS, we can use the midpoint theorem to get the following:
[tex]\begin{gathered} D\text{ is midpoint of AC} \\ \Rightarrow AD\cong AC \end{gathered}[/tex]therefore, by the ASA postulate (angle,side,angle), we have that triangle AED is congruent to triangle CFD
x[tex] {x}^{3} {y}^{8} term(x + y) ^{11} [/tex]find the coefficient of the given term in the binomial expansion
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Using the binomial theorem, we have that the expansion of (x+y)^11 is:
[tex]\begin{gathered} (x+y)^{11}= \\ x^{11}+11x^{10}y+55x^9y^2+165x^8y^3+330x^7y^4+462x^6y^5+462x^5y^6+330x^4y^7+165x^3y^8+55x^2y^9+11xy^{10}+y^{11} \end{gathered}[/tex]notice that the coefficient of the term x^3 y^8 is 165
A college had 5,000 students in 2018. The number of students decreased by 10% in 2019 andanother 5% in 2020. How many students did the college have in 2020? (1 point)
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Okay, here we have this:
Inicially we have 5000 students, let's calculate how many were left in 2019:
Students in 2019=5000*0.9
Students in 2019=4500
Now, let's finally calculate how many were left in 2020:
Students in 2020=4500*0.95
Students in 2020=4275
Finally in 2020 they were 4275 students
please help me I really need help in my math work
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we need to know the formula of the area of a rectangle
[tex]A=l\cdot w\text{ }[/tex]we already know A and l we need to clear w
[tex]w=\frac{A}{l}=\frac{2x^2+5x-12}{2x-3}[/tex]we need to do the division
[tex]undefined[/tex]step by step guide I am stuck at the part where you have to divide, I have split them up into 2 and got GCF for p on first term and 6 on second term
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We have the next expression:
[tex]pq\text{ - pr + 6q-6r}[/tex]Factorize using factor by grouping.
First, let's find the common terms. The one who is in all terms or majority terms.
In this case, let's use p:
[tex]p(q-r)+6q-6r[/tex]Factorize the common term 6.
[tex]p(q-r)+6(q-r)[/tex]Look at the expressions, both are multiply by (q-r), so we can rewrite the expression like this:
Factorize the common term (q-r)
[tex](q-r)(p+6)[/tex]7/8 = 7/16 =Reduce your answer to the lowest terms.
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You have a $250 gift card to use at a sporting goods store. a) Write an inequality that represents the possible numbers x of pairs of socks you can buy when you buy 2 pairs of sneakers. PRIO *12 SALE PRICE $80 b) Can you buy 8 pairs of socks? Explain.
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Sale price 12
number of socks =X
Sneakers sprice 80
Amount disposable 250
Then
Part a)
250 - 2•80 = 12X
250 - 160 = 12X
90 ≥ 12 X
Part b)Can buy 8 pairs?
Answer NO , because 90 < 12•8
1. If triangle ABC is congruent to triangle DEF, DE=17, EF =13, DF =9, and BC = 2x-5, then which of the following is the correctvalue of x?(1) 5(3) 9(2) 7(4) 11
Answers
If both trianlges are congruent, we get that:
[tex]BC=DE[/tex]This way,
[tex]2x-5=17[/tex]Solving for x :
[tex]\begin{gathered} 2x-5=17 \\ \rightarrow2x=17+5 \\ \rightarrow2x=22 \\ \Rightarrow x=11 \end{gathered}[/tex]This way, we get that x = 11
Answer: Option 4
Simplify the expression below. Share all work/thinking/calculations to earn full credit. You may want to do the work on paper and then upload an image of your written work rather than try and type your work. \sqrt[4]{ \frac{162x^6}{16x^4} }
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Use the long division method to find the result when 8x3 + 30x2 + 3x – 1 is divided by 4x + 1. If there is a remainder, express the result in the form q(x) + r(3) b(x)
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Answer:
[tex]2x^2+7x-1[/tex]Explanation:
Given the polynomial division:
[tex]\frac{8x^3+30x^2+3x-1}{4x+1}[/tex]The long division table is attached below:
Therefore, we have that:
[tex]\frac{8x^3+30x^2+3x-1}{4x+1}=2x^2+7x-1[/tex]Lucy sold some items at a garage sale. She spent 7/12 of her earnings on a new bike. She uses 3/5 of the remainder to purchase a gift for her mom. What fraction of her total earnings was spent on her mom's gift?
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First we have to find what fraction remained after buying the bike.
Subtracting 7/12 from 12/12 ( which represents the total)
The result is 5/12
Then, we are going to multiply 3/5 by 5/12 ( the remainder) to find our final answer.
[tex]\begin{gathered} \frac{3}{5}\cdot\frac{5}{12}=\frac{15}{60} \\ \frac{15}{60}=\frac{5}{20}=\frac{1}{4}\text{ Simplifying our fraction} \end{gathered}[/tex]The fraction of her total earnings spent on her mom's gift was 1/4
If f(x) = -2x + 8 and g(x) = v* + 9, which statement is true?
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We have the function;
[tex]f(x)=-2x+8[/tex]and
[tex]g(x)=\sqrt[]{x+9}[/tex]Let's obtain f(g(x) before we make conclusions on the statements.
[tex]f^og=-2(\sqrt[]{x+9})+8[/tex]The domain of f(g(x) starts from x= - 9, this is where the function starts on the real line.
But - 6 < -9 , and thus,
The answer is - 6 is in the domain of the function.
012Explanation34BCheck5Use the figure and the table to answer the parts below.67(a) Find the probability that a real number between 4 and 6 is picked.08(b) Find the probability that a real number between 4 and 7 is picked.0RegionABCXArea0.320.560.12 I need help with this math problem
Answers
Given:
The graph is:
Find-:
(a)
Find the probability that a real number between 4 and 6 is picked.
(b)
Find the probability that a real number between 4 and 7 is picked.
Explanation-:
The area of the region
[tex]\begin{gathered} \text{ Region }\rightarrow\text{ Area} \\ \\ A\rightarrow0.32 \\ \\ B\rightarrow0.56 \\ \\ C\rightarrow0.12 \end{gathered}[/tex]The probability is:
[tex]P(A)=\frac{\text{ Favorable outcome}}{\text{ Total outcome}}[/tex]The total outcomes is:
[tex]\begin{gathered} =0.32+0.56+0.12 \\ \\ =1 \end{gathered}[/tex](a)
Probability to the 4 and 6
The 4 to 6v region is B
[tex]\begin{gathered} P(B)=\frac{\text{ favorable outcomes for B}}{\text{ Total outcomes}} \\ \\ P(B)=\frac{0.56}{1} \\ \\ P(B)=0.56 \end{gathered}[/tex](B)
Probability for 4 to 7
The region B and C
[tex]\begin{gathered} 1. \\ \\ P(B\text{ and }C)=\frac{0.56+0.12}{1} \\ \\ =0.68 \end{gathered}[/tex]how do I have to search x in a triangle??
Answers
1) the value of x is 7
Explanation:1) From the diagram, the angles with the red ink are equal.
SInce the two angles at the base are equal, we call the triangle an isosceles triangle.
This triangle have two sides and two angle equal.
As a result, the sides opposite the angles given in the triangle are equal to each other.
The sides opposite the angles are x and 7. So, x is equal to 7.
Hence, the value of x is 7
The same principle or procedure can be applied to question number 2.
what is the scale factor from triangle PQR to triangle STU
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To find the scale factor from one triangle to another we need to divide the measurements of the second triangle by the corresponding measurements of the first triangle.
Since we need the scale factor from triangle PQR to triengle STU we need to divide the measurements of STU by the corresponding measurements of triangle PQR.
Sides PR and SU are corresponding sides, so we sivide 12 by 8:
[tex]\frac{12}{8}=\frac{3}{2}[/tex]To confirm, we also divide the measurements of sides UT and RQ:
[tex]\frac{9}{6}=\frac{3}{2}[/tex]Thus, the scale factor is: 3/2 = 1.5
Use the substitution property of equality to complete the following statement.
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Given:-
[tex]8x+y=12[/tex]To find x when y is 3.
So now we substitute,
[tex]\begin{gathered} 8x+y=12 \\ 8x+3=12 \\ 8x=12-3 \\ 8x=9 \\ x=\frac{9}{8} \end{gathered}[/tex]So the value is,
[tex]\frac{9}{8}[/tex]Marie requires 2 gallons of paint to cover an area of 400 square feet. Identify the graph that shows the relationship between the quantity of paint and the area covered and the parent function that best describes it. Then use the graph to estimate how many gallons of paint Marie requires to paint an area of 2,400 square feet.
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Given:
x = 2 gallons of paint
y = 400 square feet of area
The graph representing the given point (x,y) = (2, 400) is number 4: linear 12 gallons.
Then, to estimate how many gallons of paint Marie requires to paint an area of 2,400 square feet.
We locate the point y = 2400 and find the corresponding x value. This is:
x = 12
Answer:
* the graph is the fourth one
* 12 gallons