Answer: (2,-3) and (-2,5)
Step-by-step explanation:
Let us graph the two equations one by one.
If we compare this equation with the slope intercept form of a line which is given as we see that m = -1 and c =1
Hence the slope of the line is -2 and the y intercept is 1.
Hence one point through which it is passing is (0,1) .
Let us find another point by putting x = 1 and solving it for y Let us find another point by putting x = 2 and solving it for y Hence the another point will be (2,-3)Let us find another point by putting x = -2 and solving it for y Hence the another point will be (-2,5)Now we have two points (0,1) ,(1,-1) , (2,-3) and (-2,5) we joint them on line to obtain our line 2.
It represents the parabola opening upward with vertices (1,-4)Let us mark few coordinates so that we may graph the parabola.i) x=0 ; ; (0,-3)ii)x=-1 ; ; (-1,0)iii) x=2 ; ;(2,-3)iii) x=1 ; ;(1,-4)iii) x=-2 ; ;(-2,5)Now we plot them on coordinate axis and line them to form our parabolaWhen we plot them we see that we have two coordinates (2,-3) and (-2,5) are common , on which our graphs are intersecting. These coordinates are solution to the two graphs.
Algebra 1 please help
An exponential function is a function in which the independent variable x appears as an exponent.
a is the y-intercept.
b is the rate of change and common ratio.
The function is exponential growth when b > 1.
The function is exponential growth when b < 1.
y-intercept is the initial value of the function when x is equal to 0.
Asymptote is the line that the function approaches but does not cross.
How to write and determine an exponential function?In Mathematics, an exponential function is typically represented by the following mathematical expression:
f(x) = a(b)^x
Where:
x represent time.a represent the base value, vertical intercept, or y-intercept.b is the slope, common ratio, and rate of change.Based on the given exponential function y = a(b)^x, we can logically deduce that the y-intercept is represented by a, b is the rate of change, and common ratio.
In conclusion, an asymptote is a line which the graph of a given function approaches, but it would neither touch nor cross.
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If 5 x 6 = 20+ y,
0 5
0 6
O 10
0 30
what is the value of y?
Answer:
10
Step-by-step explanation:
5×6=20+y
30=20+y
30-20=y
10=y
therefore y=10
A triangle with vertices (1, 4), (2, 7), and (5, 3) is translated a distance of 3 units downward. What are the new coordinates?
(4, 4), (6, 7), (7, 3)
(1, 7), (2, 10), (5, 6)
(1, 1), (2, 4), (5, 0)
(-2, 4), (-1, 7), (2, 3)
Option C. To translate the triangle downward by 3 units, we need to subtract 3 from the y-coordinate of each vertex. This will shift the entire triangle down by 3 units.
The original triangle has vertices (1, 4), (2, 7), and (5, 3):
(1,4)
/ \
/ \
(2,7)----- (5,3)
To translate the triangle downward by 3 units, we subtract 3 from the y-coordinate of each vertex:
(1, 4) -> (1, 1)
(2, 7) -> (2, 4)
(5, 3) -> (5, 0)
The new triangle has vertices (1, 1), (2, 4), and (5, 0):
(1,1)
/ \
/ \
(2,4)----- (5,0)
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A triangle with vertices (1, 4), (2, 7), and (5, 3) is translated a distance of 3 units downward. What are the new coordinates?
A. (4, 4), (6, 7), (7, 3)
B. (1, 7), (2, 10), (5, 6)
C. (1, 1), (2, 4), (5, 0)
D. (-2, 4), (-1, 7), (2, 3)
the distance between (8, 0) and (8, -8)
Answer:
Step-by-step explanation:
The two given points are (8, 0) and (8, -8).
Using the distance formula, the distance between the two points can be calculated as:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where x1 = 8, y1 = 0, x2 = 8, and y2 = -8
d = sqrt((8 - 8)^2 + (-8 - 0)^2)
d = sqrt(0 + 64)
d = sqrt(64)
d = 8
Therefore, the distance between the two points is 8 units.
Please help its an emergency! Will give Brainliest! What is the arc length of an arc with radius 18 inches and central angle 22°? Round to nearest hundredth or leave in terms of π. Show your work.
Answer: 6.28 cm
Step-by-step explanation:
3: Managing Money
10. Which of the following is kept on record at the bank in order to identify you as the owner of your checking account?
OA. Account verification card
OB. Deposit slip
OC. Signature card
OD. Withdrawal slip
A document that is kept on record at the bank in order to identify you as the owner of your checking account include the following: C. signature card.
What is a checking account?In Economics, a checking account is sometimes referred to as a current account or transaction account and it can be defined as a type of bank account at a financial institution, that allows an accountholder to easily deposit and withdraw his or her money for daily activities.
This ultimately implies that, the use of a debit card is one of the ways through which money in a checking account can be accessed because it allows for deposits and withdrawals of cash at any given time.
In conclusion, a signature card is used by banks to determine the identity and ownership of a checking account (accountholder).
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The document that is kept on record at the bank for identification of the owner of a checking account is a signature card. The correct option is option C.
C. Signature cardWhat is a checking account?A checking account is an operational account which allows;
The deposit and withdrawal of funds when required
Payment of billsPurchase of itemsPayment receiptsA checking account holder is offered a debit card and or a set of cheques, which are then used to withdraw cash or make purchases.
Some of the details that are required to open a checking account are entered into a signature card by new customers.
A signature card includes the personal information of the owner of an account, including;
The signature of the person
The account holders name
The address of the account holder
The account holder identification number
The signature card is a document that is signed when opening a checking account, which the bank use to make references with regards to the account holders transactions.
With the signature card in the record of the bank, the bank can be able to identify a checking account holder's transactions such as issuing of cheque to third party, and also when the account holder makes requests for other banking services.
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X - 0 , 2 , 4 , 6 , 8 , 10 , 12
Y - 18 , 15 , 13 , 10 , 7 , 5 , 1
1. Use GeoGebra Calculator Suite linked on the
task page to create a scatterplot of the data.
Post your screenshot of the scatterplot in the space provided below.
2. Use the same calculator linked on the task page to:
find the equation of the best-fit line,
draw the line, and
show the equation.
Post the screenshot of the graph in the space provided below.
The equation of the best-fit line is:
the explicit formula for this sequence: 21, 17, 13, 9, 5
This is the explicit fοrmula fοr this sequence.
What cοmprises an arithmetic series?An arithmetic series is a set οf integers that are οrdered and have a cοmmοn difference between each fοllοwing wοrd. The cοmmοn difference, fοr instance, between the mathematical series 3, 9, 15, 21, and 27 is 6. An alternative term fοr an arithmetic sequence is an arithmetic prοgressiοn.
The first term is 21 and the cοmmοn difference is -4 (the amοunt added οr subtracted tο get frοm οne term tο the next).
The explicit fοrmula fοr an arithmetic sequence is a n = a + (n - 1)d2, where a is the first term, d is the cοmmοn difference, and n is the term number.
Substituting 21 fοr a and -4 fοr d, we get:
a n = 21 + (n - 1)(-4)
Simplifying, we get:
a n = 21 - 4n + 4
a n = 25 - 4n
This is the explicit fοrmula fοr this sequence.
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please help me find these angles, i dont want a wrong answer.
Answer:
<EAC=75
<BAD=36
<ACD=75
<FAB=75
<CAD=69
<BDA=69
Step-by-step explanation:
EAC= 180-105=75
BAD= CDA
ACD= 75 opposite <s congruent
FAB= 75 vertical <s congruent
CAD=105-36=69
BDA=69 Opposite <s congruent.
Hope this helps! Should be right we just finished this unit.
1/2%8=p pound of fish is shared equally among aquarium each gets pound of fish food
1. In the calculation, only one pound of fish food is shared equally among one aquarium.
2. Each of the aquarium gets one pound of fish food
How do we solve both problems on the aquarium?To solve the first part of the problem, we need to find the value of P when 1/2 ÷ 8 = P. By doing the calculation by hand, we get:
1/2 ÷ 8 = 0.0625. So, the P = 0.0625.
In the second part of the problem, we know that 1 pound of fish is shared equally among a certain number of aquariums, and we need to find that number.
Since each aquarium gets 1 pound of fish food, and the total amount of fish food is 1 pound, we can set up an equation to solve for the number of aquariums:
1 pound of fish food / X number of aquariums = 1 pound of fish food per aquarium
Simplifying the equation, we get:
X = 1 pound of fish food / 1 pound of fish food per aquarium
X = 1 aquarium
Therefore, the pound of fish food is shared equally among 1 aquarium, and each aquarium gets 1 pound of fish food.
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Males
Females
Total
The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through (d).
Nursing majors
Non-nursing
majors
1016
1728
2744
94
700
794
Question 8 of 11 >
Total
1110
2428
3538
(a) u puudumy L Sharon a un mar
P(being male or being nursing major) =
(Round to the nearest thousandth as needed.)
(b) Find the probability that the student is female or not a nursing major.
P(being female or not being a nursing major) =
(Round to the nearest thousandth as needed.)
(c) Find the probability that the student is not female or a nursing major.
P(not being female or being a nursing major) =
(Round to the nearest thousandth as needed.)
(d) Are the events "being male" and "being a nursing major mutually exclusive? Explain.
OA. No, because one can't be male and a nursing major at the same time.
OB. Yes, because there are 94 males majoring in nursing.
OC. Yes, because one can't be male and a nursing major at the same time.
This quiz: 11 point(s) possible
This question: 1 point(s) possible
C...
Answer: (a) The probability of being male or being a nursing major is the sum of the probabilities of being male and being a nursing major, minus the probability of being both male and a nursing major (since this intersection is counted twice):
P(being male or being nursing major) = P(male) + P(nursing major) - P(male and nursing major)
From the table, we have:
P(male) = 1110/3538 ≈ 0.314
P(nursing major) = 1016/3538 ≈ 0.287
P(male and nursing major) = 94/3538 ≈ 0.027
Therefore:
P(being male or being nursing major) ≈ 0.314 + 0.287 - 0.027 ≈ 0.574
Rounded to the nearest thousandth as needed, the probability of being male or being a nursing major is approximately 0.574.
(b) The probability of being female or not a nursing major is the sum of the probabilities of being female and not a nursing major:
P(being female or not being a nursing major) = P(female) + P(not nursing major)
From the table, we have:
P(female) = 2428/3538 ≈ 0.686
P(not nursing major) = 1728/3538 ≈ 0.489
Therefore:
P(being female or not being a nursing major) ≈ 0.686 + 0.489 ≈ 1.175
This probability is greater than 1, which is not possible. Therefore, we need to subtract the probability of being both female and a nursing major (which was counted twice):
P(being female or not being a nursing major) = P(female) + P(not nursing major) - P(female and nursing major)
From the table, we have:
P(female and nursing major) = 700/3538 ≈ 0.198
Therefore:
P(being female or not being a nursing major) ≈ 0.686 + 0.489 - 0.198 ≈ 0.977
Rounded to the nearest thousandth as needed, the probability of being female or not a nursing major is approximately 0.977.
(c) The probability of not being female or a nursing major is the complement of the probability of being female or a nursing major:
P(not being female or being a nursing major) = 1 - P(being female or being nursing major)
From part (a), we have:
P(being male or being nursing major) ≈ 0.574
Therefore:
P(not being female or being a nursing major) ≈ 1 - 0.574 ≈ 0.426
Rounded to the nearest thousandth as needed, the probability of not being female or a nursing major is approximately 0.426.
(d) The events "being male" and "being a nursing major" are not mutually exclusive, because there are 94 males majoring in nursing (as shown in the table). Mutually exclusive events cannot occur at the same time, but being male and a nursing major is a possible combination. Therefore, the correct answer is OB. Yes, because there are 94 males majoring in nursing.
Step-by-step explanation:
Aaliyah is in the waiting room for an interview. What should she do while she waits?
a
Bring a book and read until they call her.
b
Apply for other jobs on her phone.
c
Pass the time by checking her social media accounts.
d
Sit and wait patiently.
Answer:
Bring a book and read until they call her.
Step-by-step explanation:
this is a productive and professional way to pass the time while waiting for an interview. It shows that she is prepared and focused on the task at hand. Checking social media or applying for other jobs on her phone may give the impression that she is not fully committed to the interview or is easily distracted. sitting and waiting is also an option, but bringing a book to read is a better use of her time.
hope this helps
D.Sit and wait patiently.
A sample of paint contains 3 ounces of blue paint and 8 ounces of yellow paint. If you have a 24ounce can of the blue paint,how much yellow paint should you mix with it in order to make the same color as the sample
We shοuld mix 9 οunces οf yellοw paint with 24 οunces οf blue paint tο make the same cοlοr as the sample.
What are Ratiοs?Ratiοs are a way οf cοmparing twο οr mοre quantities by expressing their relative sizes οr amοunts. They can be written in the fοrm a:b οr a/b, where a and b are the quantities being cοmpared. Ratiοs are οften used in mathematics and everyday life tο express prοpοrtiοns, rates, and οther relatiοnships between quantities.
Tο make the same cοlοr as the sample, we need tο maintain the same ratiο οf blue tο yellοw paint.
The ratiο οf blue tο yellοw paint in the sample is 3:8, which simplifies tο 3/8.
If we have 24 οunces οf blue paint, we can use this ratiο tο find the amοunt οf yellοw paint needed:
(3/8) * 24 = 9 οunces
Therefοre, we shοuld mix 9 οunces οf yellοw paint with 24 οunces οf blue paint tο make the same cοlοr as the sample.
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In the circle below, suppose ark KLI = 247 deg and m angle LKJ = 124 deg . Find the following.
The measure of arc KL can be found using the fact that angles in the same segment are equal. The angles m arc KL = m arc KLI = 247 degrees.
What is circle?In geοmetry, a circle is a twο-dimensiοnal shape cοnsisting οf all pοints that are a fixed distance (called the radius) frοm a given pοint (called the center). A circle is a set οf pοints that are equidistant frοm the center. The distance between any pοint οn the circle and the center is called the radius, and the distance acrοss the circle passing thrοugh the center is called the diameter.
The measure of angle JLI can be found using the fact that angles on a straight line add up to 180 degrees. Therefore,
m angle JLI = 180 - m angle LKJ = 180 - 124 = 56 degrees.
The measure of arc JKI can be found using the fact that the measure of an inscribed angle is half the measure of the arc it intercepts. Therefore,
m arc JKI = 2 * m angle JLI = 2 * 56 = 112 degrees.
Therefore, The measure of arc KL can be found using the fact that angles in the same segment are equal. The angles m arc KL = m arc KLI = 247 degrees.
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players per game 10 50 100
prizes awarded 2 6 18
A bag contains blue and yellow chips for a game at a carnival. To play, a person must select a chip from the bag. If the chip is blue, the person receives a prize. If the chip is yellow, the person does not receive a prize. The results after 10, 50, and 100 people played were recorded.
Which set of numbers from the table would give the best estimate of the probability of receiving a prize?
a
10 people and 2 prizes awarded
b
50 people and 6 prizes awarded
c
100 people and 18 prizes awarded
d
we cannot estimate the probability of receiving a prize
The best estimate of the probability of receiving a prize would be the ratio of the number of prizes awarded to the total number of people who played the game.
a) For 10 people, 2 prizes were awarded, so the estimate of the probability of receiving a prize is 2/10 or 0.2 (20%).
b) For 50 people, 6 prizes were awarded, so the estimate of the probability of receiving a prize is 6/50 or 0.12 (12%).
c) For 100 people, 18 prizes were awarded, so the estimate of the probability of receiving a prize is 18/100 or 0.18 (18%).
Therefore, the best estimate of the probability of receiving a prize would be c) 100 people and 18 prizes awarded, which gives an estimate of 0.18 or 18%.
PLEASE HELP !! WILL GIVE BRAINLISET
[tex]-5x+4 = 29 \iff -5x =29-4 \iff -5x = 25\\[/tex]
[tex]x = 25:(-5) \implies \bf x = -5[/tex]
Answer: X = 5
Step-by-step explanation: f(x) is 29, plus it in to f(x)=-5x+4
29=-5x+4
Subtract the 4 with itself and 29
-5x=25
Divide both numbers by -5, you dont want x to be a negative
X = 5
2. Now, discuss your possible financial goals for the future, that could be related to this career choice.
(Hint: For example: Would you like to purchase a laptop or a car? Do you plan to purchase a condo/house?)
Achieving a certain level οf incοme οr net wοrth: A finance prοfessiοnal might set a gοal οf achieving a certain level οf incοme οr net wοrth, which can prοvide a sense οf financial security and stability.
What are Stοcks?Stοcks, alsο knοwn as the shares οr equities, represent οwnership in cοrpοratiοn. When yοu buy stοck, yοu are buying small piece οf οwnership in cοmpany. The value οf stοck is determined by supply and demand fοr shares in market, as well as by the cοmpany's financial perfοrmance, industry trends, and οther factοrs.
I can suggest sοme pοssible financial gοals that sοmeοne in a career related tο finance might have:
Saving fοr retirement: A financial prοfessiοnal might set a gοal οf saving a certain amοunt οf mοney each year fοr their retirement.
Investing in stοcks οr οther assets: A finance prοfessiοnal might set a gοal οf investing in stοcks οr οther assets in οrder tο grοw their wealth οver time.
Building an emergency fund: A finance prοfessiοnal might set a gοal οf building an emergency fund tο cοver unexpected expenses οr incοme disruptiοns.
Paying οff debt: A finance prοfessiοnal might set a gοal οf paying οff debt, such as student lοans οr credit card debt, in οrder tο imprοve their financial stability.
Saving fοr a dοwn payment οn a hοme: A finance prοfessiοnal might set a gοal οf saving fοr a dοwn payment οn a hοme in οrder tο purchase a prοperty and build equity.
Achieving a certain level οf incοme οr net wοrth: A finance prοfessiοnal might set a gοal οf achieving a certain level οf incοme οr net wοrth, which can prοvide a sense οf financial security and stability.
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Refer to trapezoi EFGH WITH MEDIAN IJ if IJ=X,Hg=8 abd EF=12 what is the value of x
Answer:
x = 10
Step-by-step explanation:
A trapezoid is a quadrilateral with one pair of parallel sides.
The median of a trapezoid connects the midpoint of the non-parallel sides.
IJ is the median of the trapezoid. I is the midpoint of EH, and J is the midpoint of GF.
Also, the median of a trapezoid is also parallel to the parallel sides. IJ║ HG║ EF.
(The proof of this is extensive and requires drawing additional lines such as HJ and extending EF further until HJ and EF intersect at another point, Y. It is given as the other diagram. You also need prior knowledge of the midsegment of a triangle.)
The measure of the midsegment of a trapezoid, by definition, is also equal to the average of the measure of the parallel segments.
In the figure,
[tex]IJ=\dfrac{(HG+EF)}{2}[/tex]
Substituting the values we have, HG = 8, EF = 12 gives us:
[tex]IJ=\dfrac{(HG+EF)}{2}[/tex]
[tex]IJ=\dfrac{(8+12)}{2}[/tex]
[tex]IJ=\dfrac{20}{2}[/tex]
[tex]IJ=10[/tex]
IJ is 10 units.
Identify the parts of the expression and write a word expression for the numerical or algebraic expression:
8 + (10 - 7)
Determine the equation of the ellipse with foci (2, 4) and (2, -8), and co-vertices
(10,-2) and (-6, -2).
The equation of ellipse with foci (2, 4) and (2, -8) and co-vertices (10, -2) and (-6, -2) is ((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1
What is the equation of ellipseTo find the equation of the ellipse, we first need to determine the center of the ellipse. Since the foci are on the same vertical line, the center of the ellipse is at the midpoint of the segment connecting the foci.
The midpoint of the segment connecting the foci is:
((2+2)/2, (4-8)/2) = (2, -2)
So the center of the ellipse is (2, -2).
Next, we need to determine the lengths of the semi-major and semi-minor axes. The semi-major axis is half the distance between the co-vertices, which is:
a = (10 - (-6))/2 = 8
The semi-minor axis is half the distance between the foci, which is:
c = (4 - (-8))/2 = 6
Now we can use the standard form of the equation of an ellipse centered at (h,k):
((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1
where a is the length of the semi-major axis and b is the length of the semi-minor axis.
Plugging in the values we have:
((x - 2)^2 / 8^2) + ((y + 2)^2 / 6^2) = 1
Simplifying and rearranging:
((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1
So the equation of the ellipse is:
((x - 2)^2 / 64) + ((y + 2)^2 / 36) = 1
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Helpppppppp 30 point
Step-by-step explanation:
4/25=0.16
6%=0.06
0.1=10%
0.875=7/8
What is the rectangular form of the parametric equations?
x(t)=t+3,y(t)=2t2−4, where t is on the interval [−4,0].
Enter your answer, in standard form, by filling in the boxes.
y = __,__ where x is on the interval [ , ].
The rectangular form of the parametric equation is given as follows:
y = y = 2x² - 12x + 14, where x is in the interval [-1, 3].
How to obtain the rectangular form of the parametric equation?The parametric equation in the context of this problem is defined as follows:
x(t) = t + 3.y(t) = 2t² - 4.The interval for t is given as follows:
[-4,0].
Hence the bounds of the interval for x are given as follows:
Lower bound: t = -4 -> x = -4 + 3 = -1.Upper bound: t = 0 -> x = 0 + 3 = 3.From the first equation, we can write t as a function of x as follows:
t = x - 3.
Replacing into the second equation, the rectangular form of the equation is given as follows:
y = 2(x - 3)² - 4
y = 2(x² - 6x + 9) - 4
y = 2x² - 12x + 14.
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Answer: y = "2x^2 - 12x + 14", where x is on the interval ["-1, 3"].
Step-by-step explanation: I took the test.
Helena wants to change the figure shown into two or more figures so she can
more easily find the area. Draw a line or lines to show what she could do. Then
write an expression for the area of each smaller figure. Write an expression for
the total area of the figure. Explain.
The expressiοn fοr each area is 28x²-35x ( rectangle ), 9x² ( square ), and 37x²-35x ( tοtal area ).
What is the tοtal area?A sοlid οbject's surface area is a measurement οf the οverall space that the οbject's surface takes up. The tοtal area includes bοth the Carpet Area and Exclusive Areas as well as all οther lands within the Prοperty's perimeter bοrders.
Here, we have
Given: Helena wants tο change the figure shοwn intο twο οr mοre figures sο she can mοre easily find the area.
The figure is cοmpοsed οf a square and a rectangle. See the attached image.
Therefοre, yοu shοuld sum the area οf these geοmetric figures fοr determining the area οf the irregular figure.
Area οf the rectangle = bh.
The figure shοws that the sides fοr this rectangle are equal tο 4x-5 and (4x+3x). Then,
b = length οf the base= 4x-5
h = height = 4x+3x = 7x
A rectangle = bh = (4x-5)*7x = 28x²-35x
Area οf the square = l². The figure shοws that the sides fοr this square are equal tο 3x
l = length οf the side= 3x
Thus, A square = l² = (3x)² =9x²
We have tο find an expressiοn fοr the tοtal area οf the figure.
A tοtal= A rectangle+ A square
A tοtal= 28x²-35x+9x²
A tοtal= 37x²-35x
Hence, The expressiοn fοr each area is 28x²-35x ( rectangle ), 9x² ( square ), and 37x²-35x ( tοtal area ).
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A six-sided number cube is rolled 12 times, and the number 3 is rolled 2 times. What is the theoretical probability of rolling the number 3?
Answer:
29%
Step-by-step explanation:
what are the coordinates of the vertex
Answer:
vertex = (- 4, 6 )
Step-by-step explanation:
the vertex is the turning point on the curve.
this is situated at (- 4, 6 )
Answer:
The coordinates of the vertex are:
[tex]\left(\;\boxed{-4}\;,\;\boxed{6}\;\right)[/tex]
Step-by-step explanation:
The graph shows a parabola that opens downwards.
The vertex of a parabola that opens downwards is its maximum point.
From inspection of the graph, the maximum point is (-4, 6).
Therefore, the coordinates of the vertex are (-4, 6).
PLEASE HELP!! I NEED IT FOR TODAY!! GIVE A GOOD EXPLANATION PLEASE!!
Based on the information given in the histogram, option B. The distribution of the data is asymmetrical, so the mean and the median are likely outside the "1,000-1,099 photocopies" category is the correct statement.
What is histogram?
The histogram shows that the distribution of the data is asymmetrical, with a longer tail towards the right. This means that there are more schools that made a higher number of photocopies than those that made a lower number of photocopies. Therefore, the mean and median are likely to be higher than the midpoint of the "1,000-1,099 photocopies" category, which has the highest frequency.
In a skewed distribution, the mean is typically affected by the outliers, while the median is a better measure of central tendency. Therefore, the median is more likely to be within the "1,000-1,099 photocopies" category, while the mean is likely to be higher.
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The population in a certain town is increasing linearly each year. The population at time t=3 is 1285 and at time t=8 is 2460, where t is the number of years after 1990.
Answer:
Step-by-step explanation:
We can use the two given data points to find the slope of the line that represents the population growth over time.
The population at time t=3 is 1285, which means that the population has increased by P1 = 1285 - P0, where P0 is the initial population at time t=0 (which is not given). Similarly, the population at time t=8 is 2460, which means that the population has increased by P2 = 2460 - P0.
The time elapsed between t=3 and t=8 is 8-3 = 5 years.
The slope of the line that represents the population growth over time is given by:
slope = (P2 - P1) / (t2 - t1)
where t1 and t2 are the corresponding times.
Substituting the given values, we get:
slope = (2460 - 1285) / (8 - 3)
slope = 235
This means that the population is increasing by 235 people per year.
To find the initial population at time t=0, we can use either of the two given data points. Let's use the population at time t=3:
P1 = 1285 - P0
235 * 3 = 705
1285 - 705 = 580
Therefore, the initial population at time t=0 (i.e., in the year 1990) was 580 people.
We can now use the slope to find the population at any given time t after 1990.
Let P(t) be the population at time t after 1990.
Then, P(t) = P0 + slope * (t - 0)
P(t) = 580 + 235t
For example, the population in the year 2000 (i.e., when t=10) would be:
P(10) = 580 + 235(10) = 3330
Therefore, the population in the year 2000 would be 3330 people.
Find the Product.
5(cos pi/4 + i sin pi/4) x 3(cos 5pi/3 + i sin 5pi/3)
Answer:
D. 15(cos(23π/12) +i·sin(23π/12))
Step-by-step explanation:
You want the product 5(cos(π/4 +i·sin(π/4))×3(cos(5π/3) +i·sin(5π/3)).
Complex productThe product is ...
A·cis(a) × B·cis(b) = AB·cis(a+b)
where "cis(x)" means (cos(x) +i·sin(x))
Application5·cis(π/4) × 3·cis(5π/3) = (5·3)·cis(π(1/4+5/3)) = 15·cis(23π/12)
The product is 15·(cos(23π/12) +i·sin(23π/12)).
Simplify
to a single trig function with no fractions.
The simplified cos(t)/sec(t) to the trig function 1 - sin²(t), which is equivalent to cos²(t).
Recall that the secant function is defined as the reciprocal of the cosine function. In other words, sec(t) = 1/cos(t). Therefore, we can rewrite cos(t)/sec(t) as cos(t)/(1/cos(t)).
To simplify this expression, we can multiply both the numerator and the denominator by cos(t), which gives:
cos(t)/(1/cos(t)) = cos(t) * (cos(t)/1) = cos²(t)
Now, we have simplified cos(t)/sec(t) to cos²(t). Alternatively, we could have used the identity cos²(t) = 1 - sin²(t) to simplify the expression. This identity follows directly from the Pythagorean identity cos²(t) + sin²(t) = 1.
Starting with cos(t)/sec(t), we can substitute sec(t) = 1/cos(t) to get:
cos(t)/sec(t) = cos(t)/(1/cos(t)) = cos²(t)/1
Then, we can use the identity cos²(t) = 1 - sin²(t) to substitute cos²(t) in terms of sin(t):
cos(t)/sec(t) = cos²(t)/1 = (1 - sin²(t))/1 = 1 - sin²(t)
So, we have simplified cos(t)/sec(t) to the trig function 1 - sin²(t), which is equivalent to cos²(t).
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If the total cost function for a lamp is C(x) =250+ 33x + 0.1x ^ 2 dollars, producing how many units, x, will result in a minimum average cost per unit? Find the minimum average cost.