Answers
The leading coefficients and parabolic equations, considering the vertices, are given as follows:
1. a = 7/4, y = 7/4(x - 4)² - 1.
2. a = -2, y = -2(x + 1)² + 2.
Equation of parabola with vertex (h,k)
The equation of a parabola with vertex given by (h,k) is presented as follows:
y = a(x - h)² + k.
In which a is the leading coeffiicent.
For item 1, the coordinates of the vertex is given as follows:
(4,-1).
Hence:
h = 4, k = -1, and the equation is:
y = a(x - 4)² - 1.
When x = 6, y = 6, hence the leading coefficient is calculated as follows:
6 = a(6 - 4)² - 1
4a = 7
a = 7/4.
Thus the equation is:
y = 7/4(x - 4)² - 1.
For item 2, the vertex is:
(-1,2).
Hence:
y = a(x + 1)² + 2.
When x = 0, y = 0, hence the leading coefficient is calculated as follows:
0 = a(0 + 1)² + 2
a = -2.
Hence the equation is:
y = -2(x + 1)² + 2.
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Related Questions
researchers recruited over 1{,}0001,0001, comma, 000 patients with chronic back pain to participate in a study about the benefits of acupuncture. each subject was randomly assigned to one of these treatment plans: traditional chinese acupuncture, placebo acupuncture, and conventional pain treatment (medication and physical therapy). what is the primary purpose of randomly assigning subjects to the different treatment plans?
Answers
Accupunture is best these days for medication and health therapy.
What is accupunture.?Acupuncture is a traditional medical practice in which a doctor inserts needles into certain body parts of a patient. The earliest documents date back at least 2,500 years. [1] "Acupuncture points" are locations on the body where tiny metal needles are inserted. It is a type of complementary medicine[2], and it is fundamental to Traditional Chinese medicine[3] (TCM). [4] It makes use of the yin and yang principle.It is debatable and has yielded conflicting findings to research acupuncture using the concepts of "evidence-based medicine" (science research). [9] Although the majority of research indicates that acupuncture's effects are primarily attributable to placebo, certain studies indicate that acupuncture can reduce pain. [10] There is evidence that any advantages of acupuncture are transient. [11] When compared to conventional medical therapies, there is inadequate evidence to justify the use of acupuncture. [12] In the long run, acupuncture is not more effective than conventional medicine. [13]Learn more about accupunture click here:
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How long is long? Please help I need to know
Answers
Answer:
it depends on how long long is
A line includes the points (1, 10) and (0, 8). What is its equation in slope-intercept form?
Answers
Answer:
Y = 2x+8
Step-by-step explanation:
Y=mx=b equations
find the volume of the frustum by calculating the radius
Answers
The value of 'r' is 15 cm. Then the volume of the frustum will be 2625 cm³.
What is the volume?Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.
By the similar triangle, then the value of r is calculated as,
r/30 = 20/40
r = 15 cm
Then the volume of the frustum is calculated as,
V = 1/3 × (30/2)² × 40 - 1/3 × (15/2)² × 20
V = 1/3 × [9000 - 1125]
V = 1/3 × 7875
V = 2625 cm³
The value of 'r' is 15 cm. Then the volume of the frustum will be 2625 cm³.
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qiang drives 15 miles at an average speed of 30 miles per hour. how many additional miles will he have to drive at 55 miles per hour to average 50 miles per hour for the entire trip?
Answers
110 additional miles he will have to drive .
To calculate : additional miles qiang will have to drive
Let the additional no. of miles he has to drive be x .
⇒ Total Distance = 15 + x
Total Time ( in hrs ) = ( 15 / 30 ) + ( x / 55 ) = ( 1 / 2 ) + ( x / 55 )
The equation becomes ,
[ ( 15 + x ) ] / [ ( 1 / 2 ) + ( x / 55 ) ] = 50
On simplification we get ,
15 + x = 25 + ( 10x / 11 )
x = 110
Therefore , 110 additional miles he will have to drive .
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simplify (-2b⁵)2 step by step
Answers
-2^2 * b^5*2 =
4 * b^10 =
4b^10
find three consecutive integers such that 3 times the smallest is 18 more than the largest
Answers
The value of the three consecutive integers will be 10, 11, and 12.
What is Algebra?
The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Three consecutive integers are such that three times the smallest is 18 more than the largest.
Let the three consecutive number be x, x + 1, and x + 2. Then the equation will be:
3x = (x + 2) + 18
Simplify the equation, then the value of the variable x will be:
3x = x + 2 + 182x = 20x = 20 / 2x = 10
Then the value of the integers will be:
x + 1 = 10 + 1 = 11x + 2 = 10 + 2 = 12
The value of the three consecutive integers will be 10, 11, and 12
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Question #6 given f(x ) = x-4 g(x ) = 2x+2 c(x) = x+1 a. find the product of f(x) g(x) and simplify . b. use the result from part a and find the product of c(x ) and simplify c. describe the end behavior . question #6 given f(x ) = x-4 g(x ) = 2x+2 c(x) = x+1 a. find the product of f(x) g(x) and simplify . b. use the result from part a and find the product of c(x ) and simplify c. describe the end behavior . question #6 given f(x ) = x-4 g(x ) = 2x+2 c(x) = x+1 a. find the product of f(x) g(x) and simplify . b. use the result from part a and find the product of c(x ) and simplify c. describe the end behavior .
Answers
a) product of function f(x) and g(x) is 2x² - 6x - 8 and b) product of function that is in part a and an (x) is 2x³ - 4x² - 14x - 8.
Here are the three functions given:
f(x) = x -4
g(x) = 2x + 2
c(x) = x + 1
a) The product of function f(x) and g(x)
f(x). g(x) = (x -4). ( 2x + 2)
= x( 2x + 2) - 4(2x + 2)
= 2x² + 2x - 8x - 8
= 2x² - 6x -8
b) product of function f(x). g(x) and a(x)
f(x). g(x) . a(x) =( 2x² - 6x - 8 ). ( x + 1)
= x( 2x² - 6x - 8) + 1(2x² -6x - 8)
= 2x³ - 6x² -8x + 2x² - 6x -8
= 2x³ -4x² - 14x - 8
Therefore we get a) 2x² - 6x - 8 and b) 2x³ - 4x² - 14x -8.
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lupita rides a taxi that charges a flate rate of $6.75 plus $3.20 per mile . if the taxi charges lupita $40.03 in total for her trip , how many miles is her ride ?
Answers
50 miles because of the miles
hello can someone help me pls
Answers
Answer:
sum= 1080
Step-by-step explanation:
Answer:
The sum of an octagon is always 1080 degrees. The interior angles are usually all equal to 135 degrees, but this is an irregular octagon, making that not the case. Because the angles are not all equal, that does not mean that the octagon's sum is any different. Thus, the sum of the interior angles is 1080 degrees.
Hope this helps!
20 POINTS WILL MARK UR ANSWER THE BEST
Please help me solve this ASAP
can u also make sure there is a graph
Answers
Answer: The solution to this system is (1,3) as shown in the graph below.
Step-by-step explanation:
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NOTE: The red line is -x+y=2 and the blue line is y=3
Answer:
(x, y) = (1, 3)
Step-by-step explanation:
Four more than twice a number is less than negative fourteen. Solve the inequality for the unknown number. Solve the inequality for the unknown number.
Answers
Answer:
x < -9
Step-by-step explanation:
2x + 4 < -14
Solve for "x"
Subtract 4 from both sides
2x + 4 < -14
2x + 4 - 4 < -14 - 4
Simplify
Subtract all the numbers
2x + 4 - 4 < -14 - 4
2x < -14 - 4
2x < -18
Divide both sides by the same factor
2x < -18
[tex]\frac{2x}{2}[/tex] < [tex]\frac{-18}{2}[/tex]
Simplify
Cancel the terms that are in both numerator and denominator
[tex]\frac{2x}{2}[/tex] < [tex]\frac{-18}{2}[/tex]
x < [tex]\frac{-18}{2}[/tex]
Divide
[tex]x < \frac{-18}{2}\\ x < -9[/tex]
The answer is [tex]x < -9[/tex]
There is two function equations, f(x)=2x²+3x-4 and h(x)= -x²+8
If the input is f(1)+h(1), how exactly would I solve this
Answers
To solve f(1)+h(1) .....
plug in 1 for x in both equations f(x) and h(x):
f(1)=2(1)²+3(1)-4 = 2+3-4 = 1
h(1)= -(1)²+8 = -1+8 = 7
f(1)+h(1) = 1 + 7 = 8
Hope it helps!
Pls help due tomorrow!!!!!!!
Answers
We have : (a+b)^2 = a^2 + 2ab + b^2.
So, we can see here : the first term (3x) is a, the second term (a) is b.
For it to be expanded as such, the second term in the bracket must be equal to a^2 when it is squared.
Therefore, the missing term is a.
Recheck : (3x + a)^2 = (3x)^2 + 2.3x.a + a^2 = 9x^2 + 6ax + a^2.
a random sample of size 36 is taken from a population with mean 50 and standard deviation 5. what is (the mean of the sample mean)?
Answers
With the help of standard deviation we can conclude our answer.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean (also known as the anticipated value) of the collection.The lower case Greek letter (sigma), for the population standard deviation, or the Latin symbol s, for the sample standard deviation, are most frequently used in mathematical texts and equations to indicate standard deviation. Standard deviation may be written as SD.acc to our question-
Calculate the z-score of 51.5 using the formula:We substitute From the standard normal distribution table, the area to the left of 1.80 is0.9641Therefore it is 0.9461learn more about standard deviation here:
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Select the correct answer. Solve the following equation for x. x2 - 36 = 0
Answers
Answer:
Step-by-step explanation:
x2-36=0
+36 +36
x2=36
/2 /2
x=18
One bulldozer clears land twice as fast as another. Together they clear a large tract in 1.5 hours. How long would the larger bulldozer take?
Answers
The larger bulldozer would take about 30 minutes.
If I am wrong please let me know by commenting on this answer!
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Two congruent parallelograms are joined along their base
to make the shape below.
18 cm
Work out the total area of the shape.
11 cm
15 cm
Answers
The total area of the shape that is formed by the two congruent parallelograms is: 721 cm².
How to Find the Total Area of a Shape?To find the total area of the shape that is formed by the two congruent parallelograms, calculate the area of each face, then add all together.
The shape formed consist of:
2 identical parallelograms whose area = 2(base × height)2 identical right triangles = base × height1 rectangle = length × widthArea of the 2 identical parallelograms:
Base = 15 cm
Height = 11 cm
Area = 2(15 × 11) = 330 cm²
Area of the 2 identical right triangles:
Base = 11 cm
Height = 11 cm
Area = 11 × 11 = 121 cm²
Area of the rectangle = length × width = 18 × 15 = 270 cm²
Total area of the shape = 330 + 121 + 270
Total area of the shape = 721 cm²
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9 + x/10 = 10
Solve for x
Answers
Answer:i had forgot
Step-by-step explanation:
Answer:4
Step-by-step explanation:
u add den subtract den divide then there
Jodie wanted to match Mandy's obstacle course record of 74.6 seconds. She had already spent fifty and one fourth seconds on wall climbing and 10.56 seconds on the ropes. How much time did she have left to match the record?
60.81 seconds
64.04 seconds
10.60 seconds
13.79 seconds
Answers
Jodie has left 13.79 seconds to match the record.
What is a linear equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Here, we have
Jodie aimed to beat Mandy's 74.6-second mark on the obstacle course. She had already spent 10.56 seconds on the ropes and fifty-and-a-fourth seconds ascending the wall. To match the record, we must determine how much time she had remaining.
Jodie's total time for climbing the wall is fifty and one fourth seconds=50.25 seconds
The total time on ropes is 10.56 seconds
The total time she spent is 50.25+10.56=60.81
Left time = Record Time-Spent time
= 74.6-60.81 = 13.79
Hence, Jodie has left 13.79 seconds to match the record.
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Between his 9th and 10th birthdays jimmy read one book each week there are 52 weeks in a year if each book at about 95 pages about how many pages did he read during the year?
Answers
Answer:
he read 4940 pages in a year
Step-by-step explanation:
Given data:
1 year= 52 weeks
1 book= 95pages (takes 1 week to complete)
for 1 year = 52x95
=4940
What is the minimum number of lawns Wallace must mow in order for him to earn at least $8?
Answers
Answer:1
Step-by-step explanation:
The answer is one because the graph starts at 12$ and Wallace only needs $8.
it is given that I = PRT/100
express P in terms of I, R and T
Answers
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Let's express P (principle) in terms of I, R and T
[tex]\qquad \sf \dashrightarrow \: I= \dfrac{PRT}{100} [/tex]
[tex]\qquad \sf \dashrightarrow \: PRT = I \sdot 100[/tex]
[tex]\qquad \sf \dashrightarrow \: P = \dfrac{I \sdot 100}{RT} [/tex]
and that's it ~
P can be expressed in terms of I, R, T as P=100×I / (R×T)
Given equation
I=PRT/100
100 × I = PRT
100 × I / RT = P
P = 100 × I / RT
This formula is used to calculate Simple Interest, where P= Principal, I= Intrest to be Calculated. R= Annual rate of interest, T= Time (in years). Here one will shift the 100 from the denominator and multiply with the I next we will move the rate and time from the numerator to the denominator. The equation we now get will be in terms of I, R, and T and one can find the Principal using this equation.
I hope this answer helps.
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A roofing contractor uses shingles at a rate of 3 bundles for every 96 square feet of roof covered. At this rate, how many bundles of shingles will he need in order to cover a roof that is 416 square feet?
Answers
Answer:
13
Step-by-step explanation:
416/96 = 4.33333
416 is 4.333 times 96, so he needs 4.333 times 3 bundles.
4.3333 × 3 = 13
Answer: 13
Answer:
13
Step-by-step explanation:
you see how much it covers initially. (96/3=32) then 416/32=13
This shows a figure.
What is the value of x?
57
63
86
95
Answers
Answer:
57
Step-by-step explanation:
Straight line is 180 degrees
x+2x+9=180
3x=171
x=171/3
x=57
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is y=10.5x-5 proportional
Answers
The equation y = 10.5x - 5 is proportional
Given,
y = 10.5x - 5
We have to find this equation is proportional or not.
In mathematics, proportional relationships exist when two variables consistently change by the same multiple. The formula y = kx, where k is a constant multiplier that depicts the relationship between x and y, is used to represent proportional relationships. The line on the graph is always straight and goes through (0,0).
Here,
y = 10.5x - 5
10.5 is the constant multiplier that depicts the relationship between x and y.
So,
The equation y = 10.5x - 5 is proportional
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the freshman class of 63 students conducted a survey to compare how many students took spanish as opposed to french as a foreign language. the results are shown in the venn diagram. how many students studied neither spanish nor french?
Answers
With the help of sets we can conclude our answer.
What are sets?Simply put, a set in mathematics is a grouping of different items. Any group of objects, such as a collection of numbers, days of the week, different kinds of cars, etc., can be included in a set. An element of the set is any component of the set. When writing a set, curly brackets are utilized. An extremely basic set would look somewhat like this. Set A = {1,2,3,4,5}. The components of a set can be represented using a variety of notations. set is a well-defined collection of objects. Sets are named and represented using a capital letteracc to our qusetion-
Total students = 50Students taking french = 31Remaining Students= 50 - 31 = 19Students taking none = 10So remaining students have taken only spanish i.e. 19-10 = 9But total no of students taken spanish are 17So the students who had taken both are 17-9 = 8.Leran more about sets click here:
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a 3x3x3 cube is made of 27 small cubes of which one is blue and 26 are white. the surface of the cube is formed by 3x3 squares. the small cubes are arranged in such a way that the surface is as much white as possible. what fraction of the surface of the cube is white
Answers
The fraction of the surface of the cube which is white is 14/27
Given 27 cubes of 1 centimetre are conjoined to form a large cube of 3x3x3
To maximise the value of the surface area, in this case, taken as white, other than the cube in the centre, the rest of the cubes must have their white surface area exposed.
• Total Number of cubes where white surface area is exposed is = 27 – 1 = 26
Although, on each surface of the 3x3x3 cube, there are 9 smaller cube surfaces, and there will be a total of 6 surfaces for the bigger cube.
• Total number of cube surfaces exposed in blue = 9 * 6 = 54
• Therefore, the greatest fraction in blue= 26/54 = 13/27
Therefore the fraction of the surface of the cube is white is = 1-[tex]\frac{13}{27}[/tex]= 14/27
The fraction of the surface of the cube which is white is 14/27 is the answer
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The fraction of the surface area of the cube which is white is 14/27
Given 27 cubes of 1 centimetre are conjoined to form a large cube of 3x3x3
To maximise the value of the surface area, in this case, taken as white, other than the cube in the centre, the rest of the cubes must have their white surface area exposed.
• Total Number of cubes where white surface area is exposed is = 27 – 1 = 26
Although, on each surface of the 3x3x3 cube, there are 9 smaller cube surfaces, and there will be a total of 6 surfaces for the bigger cube.
• Total number of cube surfaces exposed in blue = 9 * 6 = 54
• Therefore, the greatest fraction in blue= 26/54 = 13/27
Therefore the fraction of the surface of the cube is white is = 1-(13/27)
= 14/27
The fraction of the surface of the cube which is white is 14/27 is the answer.
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m = 0; (x,- 3) and (5,x)
Find the given value of x so that the line through the pair of points is parallel and/or perpendicular to the slope given. (unless the slopes are 0 and undefined)
*Does this mean that the problem is completely undefined since there is a 0? Or can it also be parallel?
-personal note
Answers
Answer:
x=-3
Step-by-step explanation:
The values of y with respect to the points created is constant, hence the two points will have the same y values but difference their respective x values
m=[tex] \frac{y2 - y1}{x2 - x1} [/tex]hence, [tex] \frac{x +3}{ - 5 - x } = 0[/tex]x+3=0x=-3An estimated 3 out of every 25 men are left-handed.What percent of men are left-handed?
help me please
Answers
Answer:
12% of men are left handed.
Step-by-step explanation:
Percent of men who are left handed =
325×100=3×4=12 3 25 × 100 = 3 × 4 = .
12%
I hope this helps!