The points where the graph intercepts the x-axis is the root of the function.
from the graph the points are 3.9 and 6.1
How to write the equation of the parabola in vertex formThe vertex v is at v ( 5, -4 ) this is equivalent to v ( h, k )
the equation of parabola in vertex form is y = a ( x- h )^2 + k
y = a ( x - 5 )^2 + {-4)
substituting point ( 4, -1 ) from the graph we have:
-1 = a ( 4 - 5 )^2 - 4
-1 = a - 4
a = 3
substituting the known values to y = a ( x- h ) + k
y = 3 ( x - 5 )^2 - 4
How to write the equation of the parabola in factored formy = 3 ( x - 5) ( x - 5 ) - 4
How to write the equation of the parabola in standard formy = 3 ( x - 5) ( x - 5 ) - 4
y = 3 ( x^2 - 10x + 25 ) - 4
y = 3x^2 - 30x + 75 - 4
y = 3x^2 - 30x + 71
Graph BHow to find the roots of the the function
The points where the graph intercepts the x-axis is the root of the function.
from the graph the points are 2 and 4
How to write the equation of the parabola in vertex form
The vertex v is at v ( 3, 2 ) this is equivalent to v ( h, k )
the equation of parabola in vertex form is y = a ( x- h )^2 + k
y = a ( x - 3 )^2 + 2
substituting point ( 0, -16 ) from the graph we have:
-16 = a ( 0 - 3 )^2 + 2
-16 = a - 9 + 2
-16 = a - 7
a = -9
substituting the known values to y = a ( x- h ) + k
y = -9 ( x - 3 )^2 + 2
How to write the equation of the parabola in factored formy = -9 ( x - 3) ( x - 3 ) + 2
How to write the equation of the parabola in standard formy = -9 ( x - 3) ( x - 3 ) + 2
y = -9 ( x^2 - 6x + 9 ) - 4
y = 3x^2 - 54x - 81 - 4
y = 3x^2 - 54x - 85
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101+102-103+104-105+106-…-199+200
Please answer asap!!! Will give brainliest!!!!
Answer:
252
Step-by-step explanation:
One way we could think about this problem is by grouping the numbers together into pairs: -103+104 would be a pair, -105+106 would be a pair and et cetera up to the pair -199+200.
As you can see, each of these pairs add to 1 (-103+104=1, -199+200=1 etc.), so to solve this problem we can simply find how many of these pairs there are and multiply the number by 1 since each pair will total to 1.
To find how many pairs there are we need to find the number of numbers between 103 and 200 (incl.) and divide it by 2.
200-103= 97 numbers, adding 1 to count the one we started with gives us 98 numbers between 103 and 200 (incl.).
98/2 = 49 pairs of numbers. Since each pair totals 1, 1x49 is the total sum of all these pairs of numbers.
Now we need to address the other two numbers. The sequence started with 101+102 before we looked at the remaining pairs, so to find the sum, we just need to add together 101+102+49.
101+102+49 = 252
Hope this helped!
Determine the following. Complementary angles
r= x + 9x
Solve the literal equation for x
Show steps please im confused
The linear equation in terms of the variable R is determined as x = R/10.
Given data:
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
The given equation is:
R = x + 9x
First, let's combine the like terms on the right side of the equation:
R = 1x + 9x
R = 10x
Now, we want to solve for x. To isolate x, divide both sides of the equation by 10:
R/10 = x
So, the solution for x is:
x = R/10
Hence, the expression for in terms of R is x = R/10.
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Invent two situations that you think would result in distributions with similar measures of variability
Explain your reasoning.
The two situations are:
Situation 1: Test Scores in Two ClassesSituation 2: Monthly Rainfall in Two CitiesSituation 1: Test Scores in Two Classes
Suppose we have two classes, Class A and Class B, taking the same exam with the same difficulty level.
The students in Class A are known to have a consistent level of performance, with most students scoring around the class average. The students in Class B, on the other hand, have a wider range of performance, with some students performing significantly better or worse than the class average.
In this situation, both classes are taking the same exam, so the central tendency (mean) of the test scores in Class A and Class B might be similar. However, the variability (spread) of the test scores in Class B is higher due to the wider range of performance among the students.
Situation 2: Monthly Rainfall in Two Cities
Consider two cities, City X and City Y, located in the same region. They experience a similar climate and weather patterns.
Over the course of a year, both cities receive roughly the same amount of rainfall on average. However, City X experiences more consistent monthly rainfall, with each month receiving rainfall close to the yearly average. In contrast, City Y has more variable monthly rainfall, with some months experiencing much higher or lower rainfall than the yearly average.
In this situation, the central tendency (mean) of the monthly rainfall in both cities will be similar since they receive the same average rainfall over the year.
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Find the midpoint of the given line segment with the given endpoints
(-3, 8) and (2, -4)
Answer:i have same question
Step-by-step explanation:
Which set of ordered pairs does not represent a function?
{(-8,-2), (0, 2), (-6, 2), (-4,-1)}
{(-6,-4), (-9, 0), (5, -7), (-3,-4)}
○ {(1,6), (-3, 6), (6, 3), (0, -4)}
{(6, 7), (-3, 8), (7,-2), (-3,-3)}
2y-4+5y=4-3y+5
How to solve this?
Answer:
You would first move all of the y numbers to one side so it should look like this: 2y-4+5y+3y=4+5. Then you would all the numbers that don't have y at the end to the other side: 2y+5y+3y=4+5+4.
Then you would add them all up: 10y=13
So your answer is 10y=13
Step-by-step explanation:
Suki is trying to solve the equation 62.75 + x = 92.
Determine whether Suki could use each statement below to reason and solve the equation.
Choose Yes or No for each statement.
A) Suki can add 62.75 to both sides of the equation.
[ Select ]
B) Suki asks, "What number can be added to 62.75 to get 92?"
[ Select ]
C) Suki thinks, "x is the difference between 92 and 62.75."
[ Select ]
D) Suki can divide 92 by x to get a value equal to 62.75.
[ Select ]
E) Suki knows that 62.75 + 0.25 = 63 and 63 + 29 = 92, so x must be 29.25.
[ Select ]
Answer:
picle scoops ina lane
Step-by-step explanation:
Answer:
29.25
Step-by-step explanation:
Q1: 1+2-3+4-5+6-…-99+100
Q2: 2+4-6+8-10+12-…-198+200
please help asap!!! Brainliest will be given if correct!!! Thanks <3
Answer:
Q1. 5050 Q2. 20100
Step-by-step explanation:
(a-b)(a+b)-c(c-2b) help me guys
Answer:
a^2-b^2+2bc-c^2
Step-by-step explanation:
We multiply a with a and negative b with b. Then multiply negative c with c and multiply negative c with negative 2b. After all add/ subtract like terms
Are 12,16,20 pythagorean triplets. Explain why.
Answer:Yes,these are pythagorean triplets because you can divide all three by the same number which is 4.
Step-by-step explanation:12 divided by 4 is 3. 16 divided by 4 is 4. And 20 divided by 4 is 5.
Answer:
Yes
Step-by-step explanation:
They all have a scale factor of 4 and 3,4,5 are also Pythagorean triplets
Zeke is making posters for the school play. He borrows 12 bottles of paint from the art teacher. Each bottle has 300 milliliters of paint. To make his posters really sparkle, he also brings 400 milliliters of glitter paint from home. How many liters of paint does he have in all?
Answer:
4 liters
Step-by-step explanation:
300 × 12 = 3600 ml
3600 + 400 = 4000 ml
1 liters = 1000 ml
liters to milliliters need to × 1000
milliliters to liters need to ÷ 1000
4000 ÷ 1000 = 4 liters
Answer two questions about systems a and b: ​ x−7y=−3 4x y=7 ​ ​ 4x y=7 x−7y=−3 ​
our ordered pair is ( 2 , 1/2).
What is linear equations in two variables?
If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.Let's first move the y's to the left side in the first equation.
4x - y = 3y + 7
4x - 4y = 7
Dividing both sides by 4,
x - y = 7/4
Our other equation is
x + 8y = 4
Subtracting the first equation from the second, we get
9y = 9/4
y = 1/4
We plug this into one of the equations
x + 2 = 4
x = 2
So our ordered pair is ( 2 , 1/2)
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find the indicated length.
Point R bisects segment ST. Find RT if ST = 16.9 meters.
RT=
The value of the indicated length RT is 8.45 meters
How to find the indicated length?The given parameters are
Point R bisects segment ST. ST = 16.9 meters.The above means that
RT = 1/2 * ST
So, we have
RT = 1/2 * 16.9
Evaluate the products
RT = 8.45
Hence, the value of the indicated length RT is 8.45 meters
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the length of a retangle is 4 times its width. The rectangles width is 8 m. What is the are of the rectangle?
The rectangle's width is 8m and the length is 4 times the width, so the length = 4 x 8 = 32m
To calculate the area of a rectangle, we take the width and multiply it with the length
A = 32 x 8 = 256m2
A 4-cup container of window cleaner costs $4. 48. What is the price per fluid ounce?
Answer:
14 cents
Step-by-step explanation:
because 4.48 divided by 4 = 1.12 BUT since there are 8 ounces in a cup 1.12 divided by 8 = 0.14
jackie's hair grows 3/4 in 1 and 1/2. how much hair grows per mouth
The answer is 1/2
The unitary technique, in its most basic form, is used to calculate the value of a single unit from a specified multiple. How to determine the value of one pen, for instance, if the cost of 40 pens is Rs. 400. The unitary approach can be used to complete it. Additionally, after determining the value of a single unit, we can multiply that value by the number of units needed to determine the value of the additional units. The concept of ratio and proportion is mostly applied using this way.
Jackie grow hair in 3/2 month = 3/4
Jackie grow hair in 1 month = 3/4 x 2/ 3
= 1/2
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161=wx14
161/14
w=11.5
16. The weather report gives the temperature as 35 degrees Celsius. Fin
equivalent temperature in degrees Fahrenheit. C = (F-32) X
35° = CF-32) F-32=5 (35)
E
■7.
17. A rectangle has perimeter 182 in. and length 52 in. What is the wic
182-104-78
78/2
8. A triangle has base 7 m and area 17.5 m². What is the height?
enVisionTM Algebra 1 Teaching Resources
. A triangle has a base 7 m and area 17.5m squared. What is the height?
Find the values of a and b.
Answer:
Step-by-step explanation:
7a + 33° = 10a - 12° ( being vertically opposite angle )
33° - 12° = 10a - 7a
21° = 3a
a = 21/3
a = 7°
Now,
6b - 42 = 3b ( vertically opposite angle )
6b - 3b = 42°
3b = 42°
b = 42/3
b = 14
hence , the value of a is 7°and b is 14°...
☘☘☘....
If M (-2, 5) is the midpoint of
CD and the coordinates of C are (4, 7), what are the coordinates of D?
Answer:
soln ,given,
midpoint of CD=M(-2,5)
let,
C(4,7)=(x1,y1)
D(x1,y2)=?
now by using midpoint formula =(x1+x2)/2+(y1+y2)/2
M(-2,5)=( 4+x2)/2+(7+y2)/2
comparing both sides
-2=(4+x2)/2
-4=4+x2
-4-4=x2
threfore,x2= -8
again
5=(7+y2)/2
10=7+y2
therefore,y2=3
thus , the coordinate of D is D(-8,3)
The Florida Fish and Wildlife Conservation Commission is conducting a study on wildlife patterns and behaviors in a specific area of the Florida
Everglades. A stationary camera is placed where the area being observed can be filmed and recorded for 96 hours. Researchers found that the footage
revealed that the Cape Sable Seaside Sparrows were observed in the area once every 4 hours and the Florida Leafwing Butterfly was observed in the
area once every 9 hours. What is the least amount of hours of footage the observers need to review to see the Cape Sable seaside sparrow and the
Florida leafwing butterfly in the area at the same time?
96
36
4
9
The least amount of hours of footage the observers need to review to see the Cape Sable seaside sparrow and the Florida leafwing butterfly in the area at the same time is B. 36 hours.
What is the least common multiple?The least common multiple (LCM) is the smallest multiple of two or more numbers.
The LCM of 9 and 4 is 36 (4 x 9).
Data and Calculations:The total number of hours of filming and recording by the stationary camera is 96.
The regularity of observing the Cape Sable Seaside Sparrows = every 4 hours
The regularity of observing the Florida Leafwing Butterfly = every 9 hours
Using their LCM as 36,
The Cape Sable Seaside Sparrows will be observed 9 times when they meet the Florida Leafwing Butterfly at its 4th observation.
Thus, the least amount of hours of footage the observers need to review to see the Cape Sable seaside sparrow and the Florida leafwing butterfly in the area at the same time is B. 36 hours.
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Assume there is a virus in a town, and there exists one patient on day 1.
Assume that the patient transmits the virus to another person once per day, then this other person becomes a patient, and that all carriers spread the virus at the same rate, i.e. each patient passes the virus on to one other person per day.
Once someone has caught the virus, they do not catch it again.
The town has a fixed population of 700000
and the borders are closed so that no one can enter or exit the town.
How many days does it take to make everyone in the town catch the virus?
Using an exponential function, it is found that it takes 20 days for everyone in the town to catch the virus.
What is an exponential function?An exponential function is given as follows:
[tex]y = ab^x[/tex]
In which:
a is the initial value.b is the rate of change.For this problem, we have that:
On the first day, one person has the virus.On the second day, the first person transmitted the virus to another person, hence two people have the virus.On the third day, each of the two people transmitted the virus to another two, hence four people have the virus.From this, we get that the parameters are given as follows:
a = 1, b = 2.
Hence the function for the number of contaminated people after t days is given by:
[tex]f(t) = 2^t[/tex]
Now, we have to solve for t when f(t) = 700000, hence:
[tex]2^t = 700000[/tex]
[tex]\log{2^t} = \log{700000}[/tex]
[tex]t\log{2} = \log{700000}[/tex]
t = log(700000)/log(2)
t = 19.4, rounded to 20.
It takes 20 days for everyone in the town to catch the virus.
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Consider this figure.
For A-C, select True or False for each statement about the sequences of transformation that can verify that traingle ABC is congruent to A'B'C'.
A. Triangle ABC is translated 1 unit to the left, followed by a reflection the x-axis. True/False
B. Triangle ABC is translated 1 unit to the right, followed by a reflection the x-axis. True/False
C. Triangle ABC is reflected across the x-axis, followed by a translation 1 unit to the right.
True/False
Answer is
A. False
B. True
C. False
According to the graph,
A (1, -2), B(b, - 2), C(1, -7), A'(-b , b), B'(-1 ,b), C'(-b , 1).
A. if ABC is reflected across x-axis. (x, y) reflected x-axis→ (x-y)
so A'(1,2), B' (b-2), C'(1-7) , it's no equal to title .
so A is false.
B. if ABC is translated 7 units to the left , up 8 units.
(x, y)→(x-7,y+8),
so A'(-b , b), B'(-1 ,b), C'(-b , 1)
it's equal to title. so B is true.
C. if ABC is translated 8 units down, 7 units to right
(x y)→(x+7, y-8),
so A' (8,-10),B'(13,-10), C'(8,-15)
it's not equal to title. so C is false.
A transformation is the movement of a figure. There are four types of transformations: reflection, rotation, translation, and dilation. Of these four types of transformations, a transformation can either be a congruent or similar shape to the original image. Congruent means that the shape or figure retains its size, shape, length, and angles of the original shape.
A rotation is a turn around a centre point. In a rotation, the distance from each point on the shape to the centre remains the same. A rotation is identified by a shape turning a specific amount degrees, usually 90, 180, or 270 degrees, around a point either clockwise or counter clockwise. This means with each rotation performed four things are given.
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write and solve an equation to answer the question Alan bought 3 pencils and a notebook. the notebook cost $6,and he spent a total of $12. how much did each pencil cost use p to represent the cost of each pencil.
Answer:
Each pencil costs $2
Step-by-step explanation:
3p + 6 = 12
3p = 6
p = 2
3 pencils for 2 dollars is 6 dollars, plus the 6 dollars he spent on a notebook, equals the 12 dollars he spent total.
Box
30 cm
32 cm
15 cm
A wooden box measures 30 cm by 15 cm by 32 cm.
The box has a lid.
Carton
Can James put all 110 cartons in the box and shut the lid?
Show your working clearly.
5 cm
A carton measures 5 cm by 5 cm by 5 cm.
James has 110 cartons.
He wants to put all these cartons in the box and be able to shut the lid.
5 cm
5 cm
D
ac
helppppspsosoosooooooooppo please I need to finish thsi
Answer:
The answer is correct.
Step-by-step explanation:
Negative means Below
Positive means above
Snorkel's age 15 years ago was 22. How old is Snorkel today?
find the cumulative frequency
We get the cumulative frequency as:
3
7
13
22
29
36
37
We are given the data:
Daily Low(°F) Frequency
35 - 39 3
40 - 44 4
45 - 49 6
50 - 54 9
55 - 59 7
60 - 64 7
65 - 69 1
We have to find the cumulative frequency of the data.
We will do this by adding the data values of previous interval.
Daily Low(°F) Frequency cumulative frequency
35 - 39 3 3
40 - 44 4 7
45 - 49 6 13
50 - 54 9 22
55 - 59 7 29
60 - 64 7 36
65 - 69 1 37
Therefore, we get the cumulative frequency as:
3
7
13
22
29
36
37
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Volume of Spheres find the volume
Step-by-step explanation:
Oke so basically we can calculate volume like this
1st: v=
[tex] \frac{4}{3} \times \pi \times r {3}^{?} [/tex]
Which equals:
[tex] \frac{4}{3} \times 3 \times {3}^{3} and \: it \: equals > 108 {\pi}^{3} [/tex]
Statistics involving collecting, organizing, and summarizing data is called ______. group of answer choices
Descriptive statistics are those that involve gathering, arranging, and summarizing data.
What does "descriptive statistics" mean?Brief informational coefficients known as descriptive statistics are used to sum up a given data set, which may be a sample of a population or a representation of the entire population. Measures of the central tendency or measures of variability make up descriptive statistics (spread).
What do descriptive statistics serve as their primary function?A descriptive statistic's main function is to summarize data. Only the data set from which they were derived are statements made by descriptive statistics; they never extend further than the data you have.
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