( (2 – 2)(y - 1214. Using the equation1 find the vertices. Select all that apply.94(21 + a, yı) and (x1 - a, yı)(1,5)(1, - 1)0 (-1,1)0 (-1, -1)(5,1)
Answers
we have the equation
[tex]\frac{(x-2)^2}{9}-\frac{(y-1)^2}{4}=1[/tex]this equation represent a horizontal hyperbola
so
a^2=9
a=3
b^2=4
b=2
(h,k)=(2,1)
so
x1=2
y1=1
x1+a=2+3=5
x1-a=2-3=-1
therefore
we have
(5,1) and (-1,1)Related Questions
Supercomputers have been developed that are much larger and can perform many more calculations than ordinary desktop or laptop computers. One such supercomputer, the Titan, has 4.4851010 transistors in its central processing unit (CPU) and another 1.32681011 transistors in its graphic processing unit (GPU). Find the total number of transistors in the Titan.
Answers
The total number of transistor in the Titan is 177532021 transistors
The number of transistors in the central processing unit = 44851010
The number of transistor in the graphic processing unit = 132681011
To find the total number of transistors in the Titan, we have to add the the number of transistors in the central processing unit and the number of transistor in the graphic processing unit
The total number of transistors in the Titan = The number of transistors in the central processing unit + The number of transistor in the graphic processing unit
= 44851010 + 132681011
= 177532021 transistors
Hence, the total number of transistor in the Titan is 177532021 transistors
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place the following vectors in the Phet simulation :) Please use the Colorado Edu Simulator
Answers
Magnitude = 11.2 direction = 153.4°
Magnitude =
Magnitude = 8.5 direction = 159.4°
A student says an association must be one of two things: positive or negative. What would you tell the student? Explain.
Answers
Explanation:
In a scatterplot showing the association between two variables, there are three possible outcomes:
• A positive association
,• No association
,• A negative association
Thus, the student missed out the third possibility, i.e. that there is no association between the two variables.
Find the equation that results from completing the square in the following equation
Answers
we have the equation
[tex]x^2+12x-85=0[/tex]step 1
Group similar terms and move the constant term to the right
[tex](x^2+12x)=85[/tex]step 2
Complete the square
[tex]\begin{gathered} (x^2+12x+6^2-6^2)=85 \\ (x^2+12x+6^2)=85+6^2 \\ (x^2+12x+6^2)=121 \end{gathered}[/tex]step 3
Rewrite as perfect squares
[tex](x+6)^2=121[/tex]Glven the following expressions: A. 5³.5-⁴ B. 3⁵/3-⁶ C. (1/4)³.(1/4)² D. (-7)⁵/(-7)⁷Part 1: Use operations of exponents to slmpllfy each expression (A-D). Include your work in your final answer. Part 2: For each simplified expression (A-D), tell whether or not the expression has a value between 0 and 1.
Answers
Step 1:
To answer each of the questions, you will apply the multiplication and division laws of the exponent.
[tex]\begin{gathered} \text{Multiplication law} \\ \text{If m}^n\text{ }\times m^t=m^{n+t} \\ \text{Division law} \\ \text{If m}^n\text{ }\frac{.}{.}m^t=m^{n-t} \end{gathered}[/tex]Step 2:
[tex]\begin{gathered} a)5^3\text{ }\times5^{-4}=5^{3-4} \\ =5^{-1} \\ =\text{ }\frac{1}{5} \\ \end{gathered}[/tex]4,2,1,3,51) What was the mean?2) What was the median?3) What was the minimum?4) What was the maximum?5) What was the range?6) What was the Q, (first quartile)?7) What was the Q, (third quartile)?
Answers
1. Mean = Sum of Numbers / Number of elements
Mean = (4 + 2 + 1 + 3 + 5) / 5 = 15 / 5 = 3
2. Arrange the numbers in ascending order
1, 2, 3, 4, 5
Median is the middle number
Since there are 5 elements that make up this data set, the median is the third element
Median = 3
3. Minimum = 1
4. Maximum = 5
5. Range = Maximum - Minimum = 5 - 1 = 4
6. Q (first quartile) is the median of the lower half of the data set or the middle value between the median and the lowest value of the data set
1, 2, 3, 4, 5
Q (first quartile) = 2
7. Q (third quartile) is the median of the upper half of the data set or the middle value between the median and the highest value of the data set
1, 2, 3, 4, 5
Q (third quartile) = 4
interquartile range = third quartile - first quartile = 4 - 2 = 2
find the missing side of the right angle round to the nearest tenth if necessary triangle is 6 meters by 12m
Answers
To get x, we will use the Pythagoras theorem
With the hypotenuse equal to 12m
[tex]\begin{gathered} x^2=12^2-6^2 \\ x^2\text{ = 144 - 36} \\ x^2\text{ = 108} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = }\sqrt[]{108\text{ }}=\text{ 10.39} \\ \text{ x = 10. 4m (to the nearest tenth)} \end{gathered}[/tex]Elijah says that 6.11212312... is a rational number. Deena disagrees and says the number isirrational Decide who is correct and what might likely cause one of them to make the error.Who is correct? What might likely cause one of them to make the error?a) Elijah is correct. Deena might think it is not showing a patternb) Deena is correct. Elijah might think it is showing a pattern.c) Both are correct. NUmbers like this are both rational and irrational.d) Nether is correct. The number cannot be rational or irrational.
Answers
for this problem we need to rememberwhat is the definition of a RATIONAL number defined as a number that canbe obtained from two integers
If we analyze the number given we can see that 6.11212312.... represent an Irrational number since this number cannot be obtained from the division of two integers
So then the best solution for this case would be:
b) Deena is correct. Elijah might think it is showing a pattern.
Algebraically what is the discriminant of the following image. 15 10 O Discriminant < 0 O Discriminant = 0 O Discriminant > 0 O Discriminant does not exist 1 2 3
Answers
We are asked to determine the discriminant of the given quadratic graph.
Refer to the image below
Comparing the given graph with the above image, we see that the given graph is vertically shifted upward (above the x-axis)
The graph does not intersect the x-axis which means no real solutions.
This means that the discriminant of the given graph must be negative (less than 0)
Therefore, the correct answer is the 1st option
[tex]Discriminant<0[/tex]There are no real solutions when the discriminant is less than 0.
In the figure below, the circle has center O and has radius 5. If the length of arc AB (shown in bold) is between 2n and 31, what is the lowest possible integer value of x. (72 doesn't work)
Answers
Given that
Radius = 5
[tex]\begin{gathered} \text{Length of the arc is betw}e\text{n 2}\pi\text{ and 3}\pi \\ \text{Length of the arc = }\frac{\theta}{360}\text{ x 2}\pi r \\ \text{Where }\theta\text{ = x} \\ \text{For L = 2}\pi \\ 2\pi\text{ = }\frac{x}{360\text{ }}\text{ x 2}\pi\text{ x 5} \\ 2\pi\text{ = }\frac{x\cdot\text{ 10}\pi}{360} \\ \text{Cross multiply} \\ 360\cdot\text{ 2}\pi\text{ = 10}\pi x \\ \text{Isolate x} \\ x\text{ = }\frac{720\pi}{10\pi} \\ x=72^o \\ \text{For 3}\pi \\ 3\pi\text{ = }\frac{x}{360}\text{ x 2}\pi\cdot\text{ 5} \\ 3\pi\text{ = }\frac{10\pi x}{360} \\ \text{Cross multiply} \\ 3\pi\text{ x 360 = 10}\pi x \\ \text{Isolate x} \\ \text{x = }\frac{1080\pi}{10} \\ \text{x = 108}^o \end{gathered}[/tex]Therefore, x can either be 72 or 108 degrees
The lowest possible integer is 72
Suppose that a savings account pays 7.4 percent interest compounded quarterly. What is the quarterly compound interest rate?Answer =____percent.
Answers
Answer
1.85 percent
Explanation
Note: there are 4 quarters in a year.
Since the savings account pays 7.4 percent interest compounded quarterly,
Therefore, the quarterly compound interest rate will be 7.4/4 = 1.85 percent
the total number of shares in abc corp is 750,000. henry owns 17% of the shares. how many shares of abc corp stocks does he own
Answers
The total number of shares is 750000
Henry owns 17%
percentage is expressed in terms of 100
Thus, the number of shares that he owns is
17/100 * 750000
= 127500
What is 1/5 of 80 ?
Answers
1/5 of 80 is the same as dividing 80 by 5, then it is:
[tex]\frac{1}{5}\cdot80=\frac{80}{5}=16[/tex][tex]1/5\\of\\80[/tex]
To find 1/5 of 80, we need to divide 80 by 5:
[tex]80/5[/tex]
[tex]=16[/tex]
Hope this helps!
What will be the coordinates of D'' after it has been reflected over the x-axis and then translated 3 units to the right?A. (-6, -4)B. (-9, -4)C. (-6, -2)D. (-9, -2)
Answers
Solution
Step 1:
Write the coordinate of point D = (- 9, 4 )
Step 2:
The rule for reflection over x-axis
A reflection of a point over the x -axis is shown. The rule for a reflection over the x -axis is (x,y)→(x,−y) .
Step 3
D = (- 9, 4 )
D' = (- 9, -4 )
Step 4
To translate the point P(x,y) , a units right and b units up, use P'(x+a,y+b) .
D' = (- 9, -4 )
D'' = (- 9+3, -4 )
D'' = (- 6, -4 )
Final answer
A. (- 6, -4 )
Quick question plss..
Does alcohol and water mix?
Answers
A model rocket is launched with an initial upward velocity of 202 ft/s. The rocket’s height h (in feet) after t seconds is given by the following.h=202t-16t^2Find the value of t for which the rocket’s height is 82 feet. Round your answers to the nearest hundredth
Answers
Solution:
Given:
[tex]h=202t-16t^2[/tex][tex]\begin{gathered} when\text{ the height is 82 feet,} \\ h=82 \\ \\ Hence, \\ h=202t-16t^2 \\ 82=202t-16t^2 \\ Collecting\text{ all terms to one side to make it a quadratic equation;} \\ 16t^2-202t+82=0 \\ Dividing\text{ the equation all through by 2,} \\ 8t^2-101t+41=0 \\ \\ To\text{ solve for t, we use the quadratic formula;} \\ \frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ where; \\ a=8,b=-101,c=41 \\ Hence, \\ t=\frac{-\left(-101\right)\pm\sqrt{\left(-101\right)^2-\left(4\times8\times41\right)}}{2\times8} \\ t=\frac{101\pm\sqrt{10201-1312}}{16} \\ t=\frac{101\pm\sqrt{8889}}{16} \\ t=\frac{101\pm94.28}{16} \\ t_1=\frac{101+94.28}{16}=\frac{195.28}{16}=12.205\approx12.21s \\ t_2=\frac{101-94.28}{16}=\frac{6.72}{16}=0.42s \end{gathered}[/tex]Therefore, to the nearest hundredth, the value of t for which the rocket's height is 82 feet is;
0.42 seconds or 12.21 seconds.
Which system of linear inequalities is graphed?
Responses
{y≤2x+1x+y≥−2
{y≥2x+1x+y≤−2
{y>2x+1x+y<−2
{y<2x+1x+y>−2
Answers
The option 3 is correct y>2x+1 x+y<-2 system of linear inequalities is graphed.
Let's check the slope of y-intercepts of the given lines in the graph.
The y-intercept of first line or above line is 1 and slope m = 2/1 = 2.
Hence the equation should be y =2x+1
y-intercept of second line is -2 and slope m = -1/1
Hence the equation is y = -x-2.
Now check the shaded portion for inequality sign.
Both lines are dotted.
so the inequality sign would be less than or greater than(< or >)
For equation y = 2x+1: shading on the left side.
on the left side of the equation or line y = 2x+1, the y values are greater than on right side.
Hence, we obtain inequality y>2x+1
on the down of the line y = -x-2 the y values are less than topside of the line.
hence second line inequality should be y<-x-2 or y+x<-2.
Hence the option 3 is correct y>2x+1 x+y<-2 system of linear inequalities is graphed.
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Fill in the blank. In the triangle below, x = decimal places. Round your answer to two لم 35
Answers
Right Triangles
Right triangles can be identified because they have one internal angle of 90°.
Right triangles have two shorter sided called the legs and one larger side called the hypotenuse.
The relationship between the side lengths and the angles are called the trigonometric ratios.
For example, the angle of 42° as shown in the figure has one adjacent side (35) one opposite side (x) and the hypotenuse (y).
It's required to find the value of x, knowing the value of the side (45) and the angle 42°.
The trigonometric ratio that relates the opposite leg and the adjacent leg is called the tangent.
[tex]\displaystyle\tan \theta=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]Substituting:
[tex]\displaystyle\tan 42^o=\frac{x}{35}[/tex]Solving for x:
x = 35 tan 42°
Calculating:
x = 35 * 0.9004
x = 31.51
The total cost to pay for parking at a state park for the day and rent a paddleboat are shown. Number of Hours Cost (5) 1 $17 2 $29 3 $41 4 $53 Part 1 Find the cost to park for a day and the hourly rate to rent a paddleboat. The cost to park for a day Is $ 5 and the hourly rate to rent a paddleboat is $ 12 Part 2 out of 2 What will Lin pay if she rents a paddleboat for 3.5 hours and splits the total cost with a friend? Complete the explanation. The total cost to rent the boat will be hours per hour + $ friend, they will each pay $ 1+2= If she splits the cost with a
Answers
We have the following:
The total cost to rent the boat will be:
3.5 hours x $ 12 per hour + $ 5 = $ 47. If she splits the cost with a friend, they each play $ 47 / 2 = $ 23.5
find the numbers of divisors of the composite number 231
Answers
The given number is 231.
Remember that a composite number means it can be expressed as factors.
In this case, if we multiply 3 x 7 x 11 we get 231.
Therefore, the number 231 has three divisors which are 3, 7, and 11.simplify : 8x - 4(x -1)
Answers
We want to simplify:
[tex]8x-4(x-1)[/tex]For doing so, we use the distributive property, and we get:
[tex]8x-(4x-4)[/tex]And we break the parenthesis to obtain:
[tex]8x-4x+4[/tex]Lastly, we simplify the similar terms and we get:
[tex]4x+4[/tex]This means that the expression simplified is 4x+4.
Select the correct answer.Which algebraic expression is equivalent to the expression below?3(5x + 7) - 6(4 – 2x)278 - 1212x + 312x + 3727x - 3
Answers
the given expression is
= 3(5x +7 ) - 6(4 - 2x )
= 15x + 21 - 24 + 12x
= 27x - 3
thus the answer is 27x - 3, correct option is D
The following are the annual salaries of 17 chief executive officers of major companies.here are salaries 84, 381, 542,338,542,338,224,248,495.676,767,405,271,723,814,428,452,1108,609(the salaries are written in thousands of dollars)find the30th and the 75th percentiles for the salaries
Answers
To determine the 30th and the 75th percentiles for the salaries:
The pth percentile is a data value such that at least p% of the data-set is less-than or equal to this data value and at least (100-p)% of the data-set are more-than or equal to this data value.
Arrange the data set in ascending order as follows:
84 ,224 , 248, 271, 338 , 381, 405 , 428, 452, 495 , 542, 609, 676 , 723 ,767 , 814, 1108
The formula to compute the position of the pth percentile is:
[tex]P^{th}\text{ percentile = }\frac{(n+1)\text{.p}}{100}[/tex]Compute the 30th percentile as follows:
[tex]30^{th}\text{ percentile = }\frac{(17+1).30}{100}=\frac{18}{100}.30\approx5^{th\text{ }}Obs[/tex]The 5th observation from the arranged data set is 338 .
Thus, the 30th percentile is 338.
Compute the 75th percentile as follows:
[tex]75^{th}\text{ percentile = }\frac{(17+1).75}{100}\approx14^{th\text{ }}Obs[/tex]The 14th observation from the arranged data set is 814.
Thus, the 75th percentile is 814
Therefore the 30th percentile is 338 and the 75th percentile is 814
Hi, can you help me answer this question please, thank you
Answers
SOLUTION
Write out the given parameters in the questions
[tex]\begin{gathered} \text{standard deviation =0.4 } \\ \text{sample ,n=20} \end{gathered}[/tex]The critical value is the measurement used to calculate the margin of error within a set of data and is expressed as
[tex]\begin{gathered} \text{Critical value =}1-\frac{\alpha}{2} \\ \text{where } \\ \alpha=0.05 \end{gathered}[/tex]Then
[tex]\text{critical value is the z=1.960}[/tex]Therefore the critical value is1.960
Then the standard error is given by
[tex]\begin{gathered} \sigma_{\bar{x}}=\frac{\sigma}{\sqrt[]{n}} \\ \\ \text{where } \\ n=\text{sample space=20 and }\sigma=0.4 \end{gathered}[/tex]Substituting the value we have
[tex]\sigma_{\bar{x}}=\frac{0.4}{\sqrt[]{20}}=\frac{0.4}{4.47}=0.089[/tex]Therefore the standard error is 0.089
The confidence interval is given by
[tex]\begin{gathered} \text{Confidence interval=}\bar{x}\pm(1.96)(S.E) \\ \text{where S.E= standard error } \end{gathered}[/tex]The mean for the sample will be
[tex]\bar{x}=\frac{sum\text{ of data}}{n}=\frac{3497.76}{20}=173.988[/tex]Substitute the value to obtain the confidence interval
[tex]\begin{gathered} \text{confidence interval=173.988}\pm1.96\times0.089 \\ C.I=173.988\pm0.174 \\ C\mathrm{}I=(173.814,174.162) \end{gathered}[/tex]Therefore, the confidence interval is (173.81,174.16) to 2d.p
i am so confused can you help on question 3 please and thank u
Answers
3.
y=3x + 1 (a)
y= 3x - 1 (b)
-y= -3x + 1 (c)
(a) and (b)
y= 3x + 1
y= 3x - 1
y=y
3x+1 = 3x - 1
3x -3x = -1 - 1
0 = -2
Since 0 is not equal to -2
There are NO solutions
Answer:
y=3x + 1 (a)
y= 3x - 1 (b)
what is rate of change for y=8x+1
Answers
Answer:
The slope (rate of change) is 8
Step-by-step explanation:
The formula for Slope-intercept form is [tex]y=mx+b[/tex] where m = slope. Based on this formula, the slope is 8.
Write a function s(t) that represents the situation. Your starting annual salary of $45,000 increases by 3% each year. We have to write it in y=a(1-r)^t format wherea: the initial amountt: the time period(1-r): the decay factor.
Answers
The function will be a compund interest
[tex]\begin{gathered} S(t)=P(1+r)^t \\ S(t)\text{ is the amount after t years} \\ P\text{ is the initial deposit} \\ r\text{ is the rate in \%} \\ t\text{ is the time in years} \end{gathered}[/tex]I need help with this practice problem solving It asks to answer (a) and (b)But please put these ^ separately so I know which is which
Answers
Given series,
[tex]\sum ^{\infty}_{n\mathop=1}(\frac{2n!}{2^{2n}^{}})[/tex]Thus the value of r is:
[tex]undefined[/tex]To get to his parent's house, Isaiah would have to drive due north 9 kilometers. To get to his grandparents' house, he would have to drive due east 12 kilometers. The straight-line distance between the parents' and grandparents' houses is __ kilometers.
Answers
let us represent the question with a diagram for better understanding.
Using Pythagoras theorem
[tex]\begin{gathered} c^2=12^2+9^2 \\ c^2=144+81 \\ c=\sqrt[\square]{225} \\ c=15\text{ km} \end{gathered}[/tex]The distance between the parents and grandparent house = 15 km
Fill in the following blanks with the appropriate matching words from the "word bank”. Some words may be used more than once.Intersection Union DisjunctionConjunctionWord bank: maybe, mostly, or, for, and, but
Answers
Intersection AND
Union AND, MOSTLY
Disjunction OR
Conjunction AND
For these words, we have:
Intersection, when we and the common results between two sets
So, Intersection A ∩ B A and B
A ={1,2,3} B= {3,4,5} A ∩ B ={3}
Disjunction, OR
When some conditions apply either to one set or to another.
A V B = OR
He is American OR He is British
A OR B
Union, AND, Mostly
When we want all the elements that belong to both Sets
So A ∪ B means A and all the elements from A and all the elements from B, no need no repeat the same element.
A = {1,2,3} B= {3,4,5} A ∪ B ={ 1,2,3,4,5}
Conjunction
A ^ B = AND,
In Logic and Set Theory and we have conjunction, we can use the word
He is a New Yorker AND He is American.