Answers
The x-intercept and coordinate of the vertex of the given parabola will be x = 1,7 and (4,-9) respectively.
What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).
As per the given parabola,
y = x² - 8x + 7
At x-intercept, y = 0
x² - 8x + 7 = 0
x² - 7x - x + 7 = 0
x(x - 7) - (x - 7) = 0
(x - 1)(x - 7) = 0
x = 1,7
For the vertex, the slope will be zero,
y' = 2x - 8 + 0 = 0
2x = 8
x = 4
Thus, y = 4² - 8 x 4 + 7
y = -9
Thus, the coordinate of the vertex is (4,-9)
Hence "The given parabola's x-intercept and vertex coordinates are x = 1,7 and (4,-9), respectively.".
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Related Questions
A shopkeeper sold a pen for Rs.13.20 to make a profit of 10 percent. In order to earn a profit
of 15 percent, he should have sold it for.
a. Rs.13.53
b. Rs.13.73
c. Rs.13.80
d. Rs.13.86
Answers
The selling price of the pen would be Rs. 13.80 to obtain a 15% profit
How to determine the valueLet the cost price of the pen be Rs. x.
The profit noted in Case 1 = 10% of CP, i.e., 10/100 x
The SP of the pen = 13.20
The CP of the pen is calculated as:
SP = CP + Profit
X + 10/100 x = 13.20
110/100 x = 13.20
x = 1320/ 110
x = 12
The Cost price of the pen is Rs 12.
If he wanted to acquire a profit of 15%, the selling price of the pen would be calculated as:
SP = CP + P
= 12 + (15 x 12)/100
= 12 + 180/100
SP = 13.80
Thus, the Selling price of the pen would be Rs. 13.80 to obtain a 15% profit
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Does someone mind helping me with this? Thank you!
Answers
4-2=x+2-2
2=x
Sqroot(2+2)+2
Sqroot(4)+2
2+2
4
Determine whether the line integral of each vector field (in blue) along the semicircular, oriented path (in red) is positive, negative, or zero.
Answers
Considering the images (a),(b),(c),(d),(e),(f) the oriented path is
(a) Negative
(b) Positive
(c) Positive
(d) Zero
(e) Zero
(f) Zero
calculating each quadrant's line integral and symmetry.
In calculus, a line integral is an integral where the function being evaluated is along a curve. A line integral is also known as a route integral, curve integral, or curvilinear integral.
What does a Line integral mean?
A line integral makes it possible to figure out a surface's area in three dimensions. Numerous situations call for the use of line integrals. They can be used, for instance, in electromagnetics to determine the work done on a charged particle moving along a curve in a force field that is represented by a vector field.Path, curvilinear, and curve integrals are other terms for line integrals. There are several uses for line integrals, including electromagnetics, where it is used to calculate the force exerted on a charged particle moving along a curve in a force field created by a vector field.To learn more about Line integral, visit:
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What is exponential form examples?
Answers
Exponential form is a way of representing repeated multiplications of the same number by writing the number as a base with the number of repeats written as a small number to its upper right.
In the exponential form, the exponent indicates the number of times the base is used as a factor.
For example, in the case of 16 it can be written as 2 × 2 × 2 × 2 = \(2^{4}\), where 2 is the “base” and 4 is the “exponent.
A product in which the factors are identical is called a power of that factor. The number that is repeated is called the base, and the number of times it repeats is called the exponent, power or degree. And the power that is written on the right upper side are called exponents. when multiplying the numbers having same base and different exponents then the base is kept same and the exponents are added.
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i need help with C i have no idea what to do
Answers
Answer: 3,086.96 ft²
Step-by-step explanation:
First, we will find the area of her square backyard.
A = L²
A = (60 ft)²
A = 3,600 ft²
Next, we will find the area of this fountain.
The diameter (6 feet) divided by 2 is equal to the radius.
A = πr²
A = (3.14)(6 ft)²
A = 113.04 ft²
Lastly, we will subtract the fountain area and the flowerbed area from the grass backyard area. You have already found the flowerbed area correctly, (10 ft * 10 ft) * 4 = 400 ft²
3,600 ft² - 400 ft² - 113.04 ft² = 3,086.96 ft²
Please help me quick
Answers
Answer :
She will need 7 cans to cover the court.It's given that, Abeer is staining the wooden floor of a court. The court is in the shape of a rectangle. Its length is 14 meters and its width is 11 meters.
Length of court = 14 m
Width of court = 11 m
Area of court = Length × width
Area of court = 14 × 11
Area of court = 154 m².
Each can of wood stain covers 22 square meters.
Cans she need to cover the courtt = Area of court / 22 square meters
= 154/22
= 7 cans.
Hence, she will need 7 cans to cover the court.
PLEASEE HELP ASAP I NEED HELP RIGHT NOW PLEASEEE
Answers
We have shown that h = 40 / √(\(tan^{2}\)70°+ \(tan^{2}\) 55° + 1.1472 tan 70° tan 55°).
What is trigonometry?
The relatiοnship between the sides and angles οf triangles is the subject οf the branch οf mathematics knοwn as trigοnοmetry.
A. Here is the diagram that represents the situatiοn:
T (top of tower)
/\
/ \
/ \
/ \
/ \
P Q
P is due sοuth οf the tοwer.
Q is 40 meters east οf the tοwer.
The angle οf elevatiοn frοm P tο the tοp οf the tοwer is 20 degrees.
The angle οf elevatiοn frοm Q tο the tοp οf the tοwer is 35 degrees.
B. Let's use trigοnοmetry tο sοlve fοr h.
Frοm triangle PTQ, we knοw that:
PT = h / tan 20° (using οppοsite οver adjacent)
TQ = h / tan 35° (using οppοsite οver adjacent)
PQ = 40 meters (given)
Frοm triangle PTQ, we can alsο use the Law οf Cοsines:
\(PQ^{2}\)= \(PT^{2}\) + \(TQ^{2}\) - 2 PT TQ cos 125° (using \(a^{2}\) = \(b^{2}\) + \(c^{2}\) - 2bc cos A)
Substituting the values we know:
\((40)^{2}\) =\((h/tan 20)^{2}\) + \(h/tan^{2}\)20° - 2 (h/tan 20°(h/tan 35°) cos 125°
Simplifying the equation, we get:
\((40)^{2}\) = \(h^{2}\) (\(1/tan^{2}\) 20° + 1/tan² 35° - 2/tan 20° tan 35° cos 125°)
\((40)^{2}\) = \(h^{2}\) (\(tan^{2}\) 70° + tan² 55° - 2 tan 70° tan 55° (-0.5736))
\((40)^{2}\) = \(h^{2}\) (\(tan^{2}\) 70° + tan² 55° + 1.1472 tan 70° tan 55°)
\(h^{2}\) = \((40)^{2}\) / (\(tan^{2}\) 70° + tan² 55° + 1.1472 tan 70° tan 55°)
h = sqrt[\((40)^{2}\) / (\(tan^{2}\) 70° + tan² 55° + 1.1472 tan 70° tan 55°)]
h = 40 / sqrt(\(tan^{2}\) 70° + \(tan^{2}\) 55° + 1.1472 tan 70° tan 55°)
Therefore, we have shown that h = 40 / √(\(tan^{2}\) 70°+ \(tan^{2}\) 55° + 1.1472 tan 70° tan 55°).
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Similar Graph
Problem 1. Suppose that the state of "fast speed" of a machine is denoted by the fuzzy
set F with membership function PF (v). Then the state of "very fast speed", where the
linguistic hedge "very" has been incorporated, may be represented by PF (v-vo) with vo
> 0. Also, the state "presumably fast speed", where the linguistic hedge "presumably"
has been incorporated, may be represented by PF
2 (v).
(a) Discuss the appropriateness of the use of these membership functions to represent the
respective linguistic hedges.
(b) In particular, if
F= { , , }
in the discrete universe V = {0, 10,20, ..., 190, 200} rev/s and vo = 50 rev/s,
determine the membership functions of "very fast speed" and "presumably fast
speed". Display both membership functions over the discrete Universe V.
Answers
The appropriateness of the membership functions PF(v-vo) and PF2(v) to represent the linguistic hedges "very" and "presumably" respectively can be discussed based on their ability to capture subjective interpretations and incorporate shifts or uncertainties in the membership values.
(a) The use of the membership functions PF(v-vo) and PF2(v) to represent the linguistic hedges "very" and "presumably" respectively can be considered appropriate. By incorporating these linguistic hedges into the membership functions, we are able to capture the subjective interpretations associated with the terms "very fast speed" and "presumably fast speed". The linguistic hedge "very" implies a higher degree or intensity of the property being described, which is reflected in the shift of the membership function PF(v) to PF(v-vo) where vo represents the offset or shift value. Similarly, the linguistic hedge "presumably" introduces an element of uncertainty or assumption, which can be represented by a different membership function PF2(v) capturing the corresponding interpretation.
(b) Given F = { , , } with V = {0, 10, 20, ..., 190, 200} rev/s and vo = 50 rev/s, we can determine the membership functions of "very fast speed" and "presumably fast speed" as follows:
For "very fast speed", the membership function PF(v-vo) can be calculated by subtracting vo from each element in the universe V and assigning appropriate membership values. For example, if PF(v) = {0, 0.2, 0.4, ..., 1.0}, then PF(v-vo) = {0, 0.2, 0.4, ..., 1.0} since vo = 50 and the membership values remain the same.
For "presumably fast speed", the membership function PF2(v) needs to be determined based on the specific interpretation associated with this linguistic hedge. Without further information, it is not possible to determine the exact form of PF2(v) and its membership values. However, it can be defined based on assumptions or expert knowledge to capture the intended meaning of "presumably fast speed" in the given context.
Both membership functions PF(v-vo) and PF2(v) can be displayed graphically over the discrete universe V to visualize the degrees of membership associated with the corresponding linguistic hedges.
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Tom reads books that he borrows from the library. After borrowing books for a while, he began recording at the beginning of each month the total number of books he has borrowed so far. The data for the first 5 months he recorded are shown below.
Answers
43 days are required on average to read 5 pages daily.
What will be the number of days?Given that the total number of pages is 300 and Tom has read 85 pages this means he has 300-85=215 pages unread. We are told that if he reads 5 pages per day how many days would he be done with the 215 pages left.
To solve for the number of days left, we have to divide 215 by 5
= 215 / 5
= 43 days
So Tom needs 43 days to read the 215 pages left and return the book to the Library.
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solve for b please help me
Answers
Answer:
B = 7 (?)
Step-by-step explanation:
(b + 3) / 5 = 2
5 (b + 3) / 5 = 2 x 5
Simplify it --> b + 3 = 10
b + 3 - 3 = 10 - 3 (subtract 3 from both sides)
B = 7
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
I’m just tryna keep it simple u got the answer
What percent of the customers paid less than $50 for their telephone service? A. 20 B. 25 C. 75 D. 80
Answers
Answer:
a
Step-by-step explanation:
Answer:D
there is 5 who pay more then 50$ and there is 15 who pay less then 50$
do the math 75% pay less
Step-by-step explanation:
what is the potential-energy function for f⃗ ? let u=0 when x=0 . express your answer in terms of α and x .
Answers
Potential energy can be defined as energy that is stored inside an object due to its position or configuration.The potential energy function for f⃗ is given by:-U = α (x^2 / 2)
Given a force vector f⃗ and its corresponding potential energy function u(x,y,z), the force is defined as the negative gradient of the potential energy function. In order to get the potential energy function for f⃗ , we need to integrate force with respect to distance. We know that force is equivalent to the derivative of potential energy with respect to distance, so we can use the fundamental theorem of calculus to solve for u(x).We are given that u=0 when x=0, so we can define our initial condition. Using the above equation, we get:-du/dx = f(x)⇒ du = -f(x)dx Integrating both sides, we get: u(x) = -∫f(x)dx + Cwhere C is a constant of integration. We can solve for C using our initial condition: u(x=0) = 0 = CSo, the potential energy function for f⃗ is:u(x) = -∫f(x)dx + 0Now, we can express f⃗ in terms of α and x, which yields :f⃗ = -αxî where î is the unit vector in the x-direction. Substituting this value for f⃗ into our equation for potential energy function, we get:u(x) = -∫(-αx)dx = 1/2αx² + C.
Therefore, the potential-energy function for f⃗ when u=0 at x=0, and expressed in terms of α and x, is given by u(x) = 1/2αx².
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In a survey of 150 students, 30 like baseball. In a population of 1000 students, how many would you expect to like baseball?
Answers
We can expect approximately 200 students to like baseball in a population of 1000 students.
To estimate the number of students who would likely like baseball in a population of 1000 students, we can use the concept of proportion.
Let's first calculate the proportion of students who like baseball in the survey of 150 students:
Proportion = Number of students who like baseball / Total number of students in the survey
Proportion = 30 / 150 = 0.2
Now, we can use this proportion to estimate the number of students who would likely like baseball in the population of 1000 students:
Number of students who like baseball = Proportion * Total number of students in the population
Number of students who like baseball = 0.2 * 1000 = 200
Therefore, based on the survey results, we can expect approximately 200 students to like baseball in a population of 1000 students.
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Please please help!! Please explain I will give brainly
Answers
Answer:
21
Step-by-step explanation:
See picture above for steps
Can someone help me? Right answer gets brainliest!!
Answers
Answer: Y=50x
Step-by-step explanation:
since the average is 50 mph and y represents the total distance with x representing the time in hours the soluition would be y=50x where however many hours multiplied by 50 equals the distance in miles Dee traveled
Plot A(2,3) and B(2,5). What is the midpoint of points A and B?
Answers
Answer:
(2,4)
Step-by-step explanation:
what is 2324132352413142536-1342536435241342536/2354253643524125363541+425364763524142536475
Answers
That is going to be a looong answer...
\(2324132352413142536 - \frac{1342536435241342536}{2.354254e} - 21 + 425364763524142536475\)
and done
-$-4-3/-2
V
Which equation represents a circle with the same radius
as the circle shown but with a center at (-1, 1)?
O(x-1)²+(v + 1)² = 16
O(x-1)² + (y + 1)² = 4
O (x + 1)² + (v-1)² = 4
O(x + 1)² + (y-1)² = 16
Answers
The equation represents a circle with the same radius as the circle shown but with a center at (-1, 1) is (x + 1)² + (y - 1)² = 16.
We know that, the center of a circle is (-1, 1).
We know that, the standard form for an equation of a circle is
(x - h)² + (y - k)² = r²
The (h, k) are co-ordinate of your Centre of circle, which in this case is (-1,1) and r is the radius of circle.
As we can see in the figure radius = 4units
From Centre (1,-2) to (1,-2)
Put these into the equation
(x + 1)² + (y - 1)² = 4²
(x + 1)² + (y - 1)² = 16
Therefore, option D is the correct answer.
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variables combining like terms
16. x+3
17. 5y+3
18. x+5y-5
Answers
Answer:
16.3x
17. 8y
18.x+y
I thing these are the answers of these equations
A right circular cone has a base radius of 4 and a height of 6. A right circular cylinder also has a base radius of 4 and a height of 6. Let A be the lateral surface area of the cone, and let B be the lateral surface area of the cylinder. Find A/B.
Answers
Answer:
A/B = 0.6Step-by-step explanation:
Given dimensions of
Right circular cone: r = 4 and h = 6Right circular cylinder: r = 4 and h = 6Find the lateral surface area of both figures
The cone\(A= \pi r\sqrt{h^2+r^2}=3.14*4\sqrt{6^2+4^2}= 90.57\)The cylinder\(B=2\pi rh=2*3.14*4*6 = 150.72\)Find the ratio A/B
A/B = 90.57/150.72 = 0.6 (rounded0Sydney was given 4 one thousand dollar bills, 2 one hundred dollar bills, 9 one dollar bills and 8 dimes, 3 pennies. Jacob was given 3 one thousand dollar bills, 9 one hundred dollar bills, 8 ten dollar bills, 7 one dollar bills, and 7 dimes, 6 pennies. Who had more money? How much more?
Answers
Answer:
Sydney has more money. She has $222.07 more than Jacob.
Step-by-step explanation:
Here are the values:
one thousand dollar bill=1,000
one hundred dollar bill=100
ten dollar bill=10
one dollar bill=1
dime=0.10
penny=0.01
From this, we can calculate the amount of money each person has:
Sydney=4(1,000)+2(100)+9(1)+8(0.10)+3(0.01)
Sydney=4,000+200+9+0.8+0.03
Sydney=$4,209.83
Jacob=3(1,000)+9(100)+8(10)+7(1)+7(0.10)+6(0.01)
Jacob=3,000+900+80+7+0.7+0.06
Jacob=$3,987.76
According to this, Sydney has more money.
$4,209.83-$3,987.76=$222.07
Sydney has $222.07 more than Jacob.
write down the equation of a straight line that is parallel to y = 4x+2
Answers
Answer:
y = 4x + 5
Step-by-step explanation:
anything with the slope of 4x is parallel to the given equation. therefore, there are an infinite amount of answers.
so, y = 4x + any number
hope this helps!<3
There are 36 donuts in the breakroom of an office. 24 of the donuts have sprinkles 13 of the donuts have walnuts The remaining donuts a filled with fruit. How many donuts are filled with fruit?
Answers
What nominal interest rate compounded monthly is equivalent to
2.50% compounded quarterly? Round to two decimal places
Answers
Rounding this to two decimal places, the equivalent nominal interest rate compounded monthly is approximately 2.53%.
To determine the equivalent nominal interest rate compounded monthly for a given nominal interest rate compounded quarterly, we can use the formula for nominal interest rate conversion.
The formula is:
r = (1 + i/n)^n - 1
Where:
r is the nominal interest rate compounded annually (we're looking for this),
i is the nominal interest rate compounded quarterly (2.50% in this case),
n is the number of compounding periods per year (4 for quarterly compounding).
Plugging in the values, we have:
r = (1 + 0.025/4)^4 - 1
Calculating this expression, we find:
r ≈ 0.025335
Rounding this to two decimal places, the equivalent nominal interest rate compounded monthly is approximately 2.53%.
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help please! i'll give brainliest :)
Answers
Answer:
120°
Step-by-step explanation:
These 2 angles are vertical angles which means they're equal to each other:
x + 96 = 5x
96 = 5x - x
96 = 4x
x = 24
x + 96
24 + 96
120
Answer: 120°
Step-by-step explanation: The angles are opposite from each other, so they are equal. So set them equal:
x + 96 = 5x
Solve the equation for x.
x + 96 = 5x
-x -x
96 = 4x
Divide both sides by 4 and x equals 24. Substitute 24 for x.
24 + 96 = 120
5³ + 4² + √81
Please help tyyy
Answers
Answer:
150
Step-by-step explanation:
First, we can simplify 5³:
5³ = 5 × 5 × 5 = 125
Then, we can simplify 4²:
4² = 4 × 4 = 16
Next, we can simplify √81:
√81 = √(9 × 9) = 9
Finally, we can add these simplified values:
5³ + 4² + √81
= 125 + 16 + 9
= 150
_____
Note:
An exponent shows how many times its base (the big number next to it) should be multiplied by itself.
A square root gives the number that is multiplied by itself to get the number under the root sign.
PLEASE HELP 30 POINTS
Answers
Answer:
B, B, C, and im not sure about the last one
Step-by-step explanation:
Declan said, "I know 3/4 is greater than 1/2, so that means 3/4 is greater than 6/12. " Does Declan’s reasoning make sense?
Answers
Declan's reasoning does make sense. This is because 3/4 and 1/2 have the same denominator, and 3/4 is a larger fraction than 1/2.
Therefore, it is reasonable to assume that 3/4 is greater than 6/12 because 6/12 simplifies to 1/2. Simplifying fractions means dividing the numerator and denominator by the same number, in this case, 6 is divisible by 2, so we can reduce the fraction to 1/2.
So, Declan is correct in his reasoning that 3/4 is greater than 6/12. It is important to understand the relationship between fractions and their denominators to make such comparisons accurately.
3/4 = 9/12
1/2 = 6/12
6/12 = 6/12
Since 9/12 (which is equivalent to 3/4) is greater than 6/12 (which is equivalent to 1/2), we can say that 3/4 is indeed greater than 6/12.
Therefore, Declan's reasoning is correct.
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Find the following if a+b/a-b=c
3(a+b)/2(a-b)
Answers
To find the value of 3(a+b)/2(a-b), we can substitute the given equation a+b/a-b=c into the expression and simplify.
Let's start by substituting the value of c into the expression:
3(a+b)/2(a-b) = 3(c)/2(a-b)
Now, we can substitute the given equation a+b/a-b=c:
3(c)/2(a-b) = 3(c)/(2(c))
Simplifying further:
3(c)/(2(c)) = 3/2
Therefore, the value of 3(a+b)/2(a-b) is 3/2.
A statistical technique that would allow a researcher to cluster such traits as being talkative, social, and adventurous with extroversion is called A. a case study B. Meta-analysis c. Statistical significance D. Factor analysis E. Z score.
Answers
Researcher can use factor analysis to cluster such traits as being talkative, social, and adventurous with extroversion.
What is a statistical technique?Statistical techniques such as extreme values, mean, median, standard deviations, interquartile ranges, and distance formulas are useful in exploring, summarizing, and visualizing data. These statistical techniques, though relatively simple, are a good starting point for exploratory data analysis.Given is that a researcher wants to cluster such traits as being talkative, social, and adventurous with extroversion.
Researcher can use factor analysis to cluster such traits as being talkative, social, and adventurous with extroversion. Factor analysis is a statistical procedure that identifies clusters of related items (factors) on a test; used to identify different dimensions of performance that underlie one's total score.Therefore, Researcher can use factor analysis to cluster such traits as being talkative, social, and adventurous with extroversion.
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