Answers
f (x) = ax ^ 2 + bx + c
To verify the equation of the parabola you need three points:
f (x) = ax ^ 2 + bx + c
We choose the points:
(x, y) = (- 1,7)
7 = a (-1) ^ 2 + b (-1) + c
7 = a - b + c
(x, y) = (0,5)
5 = a (0) ^ 2 + b (0) + c
5 = c
(x, y) = (- 2,5)
5 = a (-2) ^ 2 + b (-2) + c
5 = 4a - 2b + c
We solve:
c = 5
5 = 4a - 2b + 5
7 = a - b + 5
Rewriting
b = 2a
a-b = 2
Substituting:
a-2a = 2
a = -2
b = -4
The equation of the parabola is:
f (x) = - 2x ^ 2 -4x + 5
Related Questions
The common denominator of 3/4 and 9/10
Answers
So 3/4 would be 15/20, and 9/10 would become 18/20.
A graduated cylinder is filled with 36π of liquid. The liquid is poured into a different cylinder that has a radius of 3 cm. What will the height of the liquid be in the new cylinder?
Answers
Answer:
The height of the liquid in the new cylinder = 4 cm
Step-by-step explanation:
∵ The volume of the liquid = 36π cm³
∵ It poured into a cylinder that has radius 3 cm
∵ The volume of any cylinder = πr²h
∴ The volume of the liquid in the cylinder = π(3)²h = 9πh
- Where h is the height of the liquid inside the cylinder
∴ 9πh = 36π ⇒ divide both sides by π
∴ 9h = 36 ⇒ h = 36/9
∴ h = 4 cm
∴ The height of the liquid in the new cylinder = 4 cm
The height of the liquid in the new cylinder will be 4 cm. The term height is frequently used to describe someone's or something's height.
What is the height?Height is defined as the vertical distance between an object's top and bottom. It is measured in centimeters, millimeters, meters, and other units.
From the given conditions;
The volume of the liquid is, [tex]\rm V_L=36 \pi \ cm^3[/tex]
The radius of the cylinder is,[tex]\rm r=3 cm[/tex]
The volume of the cylinder is found as;
[tex]\rm V= \pi r^2 h \\\\ \rm V= \pi (3)^2 h \\\\ \rm V=9\pi h[/tex]
The height of the liquid is in the new cylinder is found as;
The volume of cylinder = Volume of liquid
[tex]\rm 9 \pi h= 36 \pi \\\\ \rm h=\frac{36}{9} \\\\ h= 4 \ cm[/tex]
Hence the height of the liquid in the new cylinder will be 4 cm.
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Find all real numbers X such that 4x+2>14 AND -21x+1>22
Answers
To solve the system of inequalities, we find the values of x that satisfy both conditions: x > 3 and x < -1.
Explanation:To solve this problem, we need to find the values of x that satisfy the given inequalities:
4x+2 > 14
-21x+1 > 22
For the first inequality, subtracting 2 from both sides gives us:
4x > 12
Dividing both sides by 4, we get:
x > 3
For the second inequality, subtracting 1 from both sides gives us:
-21x > 21
Dividing both sides by -21 (and flipping the inequality sign), we get:
x < -1
Therefore, the values of x that satisfy both inequalities are:
x > 3 and x < -1
The distance from Boulder City, NV to Santa Fe, NM is around 600 miles. If a map has a scale of 0.3 in for every 30 mi, how far is the scale distance between Boulder City, NV and Santa Fe, NM?
Answers
600 divided by 30 = 20 units
each unit is 0.3 inches
20*0.3 = 6
6 inches
Answer:
6 inches.
Step-by-step explanation:
The distance between two cities is around = 600 miles.
Map has a scale of 0.3 inches = 30 miles.
Therefore, on the scale 1 inches = [tex]\frac{30}{0.3}[/tex] miles
= 100 miles
Since on the map, 100 miles = 1 inches
The distance of 600 miles = [tex]\frac{600}{100}[/tex]
= 6 inches
The scale distance between cities is 6 inches.
A used bookstore will trade 2 of its books foe of yours, If Val brings in 18 books to trade,how many books can she get from the store
Answers
Hope this helps!
♤MidnightQueen
how many even 2-digit numbers have an odd number as the sum of their digits?
Answers
You are selling items from a catalog for a school fundraiser. Select two inequalities that you can use to find the range of sales that will earn you at least $40 and at most $50. Then find the range of sales. Let x represent the amount of sales (in dollars).
Answers
5(x/50)≤50
Selling between $400 and $500 will earn you between $40 and $50.
The range of sales that will earn at least $40 and at most $50 is represented by the inequalities x >= 40 and x <= 50. Hence, the range of possible sales is x such that 40 <= x <= 50.
Explanation:The subject of this question is inequalities and the concept of a range of numbers in mathematics. Here, we're looking at a range of sales values that will result in the organizer earning between $40 and $50.
The two inequalities that represent this scenario are: x >= 40 and x <= 50.
To find the range of sales, we look at the values that satisfy both conditions. Therefore, the range of sales is all the sales amounts (x) such that: 40 <= x <= 50. This means that any amount of sales that is greater than or equal to $40 and less than or equal to $50 will meet the criteria.
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A line has a slope of –3 and a y-intercept of (0, –1). What is the equation of the line that is parallel to the given line and passes through the point (–3, 1)?
A.
y = –3x – 8
B.
y = 3x + 10
C.
y = –3x + 4
Answers
a line parallel to that one, will have the same exact slope of -3.
now, we know about this other parallel line that it runs through -3,1, and of course, since is parallel, it has a slope of -3
[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1\\ &&(~ -3 &,& 1~) \end{array} \\\\\\ % slope = m slope = m\implies -3 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-1=-3[x-(-3)] \\\\\\ y-1=-3(x+3) \implies y-1=-3x-9\implies y=-3x-8[/tex]
The sum of two numbers is 46 and the difference is 14. What are the numbers?
Answers
.. x -(46 -x) = 14 . .the difference is 14
.. 2x = 60 . . . . . . simplify
.. x = 30 . . . . . . . divide by 2
The larger number is 30; the smaller is 16.
x + y = 46
x - y = 14 Add these two equations.
2x = 60 Divide by 2.
x = 60/2
x = 30
x + y = 46 Put 30 in for x
30 + y = 46 Subtract 30
y = 36 - 30
y = 16
the larger number is 30. The smaller is 16
A triangle has 3 sides, 10000, 1000, 10x. Find 10x. What 2 numbers can x be between.
answer format: ?<X<?
please help!!!!!!!!!!
Answers
a) 10000 < 1000 +10x
.. 1000 < 100 +x
.. 900 < x
b) 1000 < 10000 +10x
.. 100 < 1000 +x
.. -900 < x
c) 10x < 10000 +1000
.. x < 1100
x can be between 900 and 1100
Find the image of O (0,0) after two reflections, first across L1 and then across L2: L1: y = 2 L2: x = -3
Answers
[tex]S_x(x,y)\rightarrow(x,-y+2k)[/tex] reflection about horizontal line y=k
[tex]S_y(x,y)\rightarrow(-x+2h,y)[/tex] reflection about vertical line x=h
So for O(0,0), h=-3, k=2
First reflection about L1: y=2
(x,y)->(x, -y+2(k)) =>
O(0,0)->O'(0,-0+2(2) = O'(0,4)
Second reflection about L2: x=-3
(x,y)->(-x+2h,y) =>
O'(0,4)->O''(0+2(-3),4) = O"(-6,4)
Answer: after both reflections, the position of image is O"(-6,4)
Final answer:
After reflecting the origin (0,0) first across the line y=2, and then across the line x=-3, the final image of the point is at (-6,4).
Explanation:
The reflection of a point in the Cartesian coordinate system can be found using certain rules, depending on the line of reflection.
For the first reflection across L1: y = 2, imagine that every point has to move in a perpendicular motion to this line until it is on the opposite side but the same distance from L1.
The origin (0,0) will move up to (0,4) because it is 2 units away from y=2 and needs to move another 2 units up to be an equal distance on the opposite side of the line.
Next, for the reflection across L2: x = -3, use the same principle, but horizontally.
The point (0,4) is 3 units away from the line x=-3.
Reflecting over this line, you would move (0,4) to the left by 6 units (twice the distance from the line), giving us a final position of (-6,4).
The final position of the point O (0,0) after the two reflections is (-6,4).
3.1 Q19
Mona has 440 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?
Answers
x + x + y + y = 440
2x + 2y = 440
Divide by 2 through ...
x + y = 220
y = 220 - x
Area = xy
Area = x(220 -x) = 220x - [tex] x^{2} [/tex]
Given that that max length of x will be -b/2a
a = -1 b = 220
x = [tex] \frac{-220}{-2} [/tex] = 110
x = 110
y = 220 - 110 = 110
Therefore max area = 110 x 110 = 12100 square yards
Marge cut 16 pieces of tape for mounting pictures on poster board. Each piece of tape was 3/8 inch long. How much tape did Marge use?
Answers
Let's convert 3/8 to a decimal and then multiply the length of each piece of tape by how many pieces Marge used.
To convert a fraction to a decimal, simply divide its numerator by its denominator:
3 ÷ 8 = 0.375
Next, multiply this by the amount of pieces Marge cut.
0.375 × 16 = 6
Therefore, Marge used 6 inches of tape.
walter loves to paint. Every week day, he paints for 20 minutes. Every weekend day, he paints for 60 minutes. How many minutes does he spend painting in one week??
Answers
So Walter spends 220 minutes painting a week!
Hope this helps!
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A cone is cut parallel to its base. Write the best name for the plane section (or cross section).
Answers
Final answer:
A cone cut with a plane parallel to its base forms a circular cross section, a concept that is part of the study of conic sections.
Explanation:
When a cone is cut with a plane parallel to its base, the cross section or plane section that is created is a circle. This concept falls under the study of conic sections, which also includes other shapes like ellipse, parabola, and hyperbola, all of which are formed by the intersection of a plane with a cone. If the cut is made closer to the apex, the circle will be smaller, and if it's made closer to the base, the circle will be larger, but all such cross sections remain circular as long as the cut is parallel to the base.
A bag contains 15 red candies, 20 blue candies, and 10yellow candies. What is the probability of drawing a red candy? A blue candy? Something besides a yellow candy?
Answers
The probability of drawing a red, blue, and a candy that is not yellow from the bag is 1/3, 4/9, and 7/9 respectively.
Explanation:The question involves the concept of probability in mathematics, with a scenario of drawing candies from a bag. The total number of candies in the bag is 45 (15 red + 20 blue + 10 yellow).
The probability of drawing a red candy is the number of red candies divided by the total number of candies, which is 15/45 or 1/3.
The probability of drawing a blue candy is the number of blue candies divided by the total number of candies, which is 20/45 or 4/9.
If we want to find the probability of drawing something other than a yellow candy, this is essentially the sum of the probabilities of drawing a red or blue candy. This is 35 out of 45 (15 red candies + 20 blue candies), which reduces to 7/9.
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A box of 24 chocolate truffles cost $28.50 and individual truffle cost $1.50 how much do you save by purchasing a box of 24
Answers
[tex]1.50 \times 24 = 36 \\ 36 - 28.50 = 7.5[/tex]
you save $7.50
What is the ninth term in the binomial expansion of (x – 2y)13? 329,472x5y8 –329,472x5y8 –41,184x8y5 41,184x8y5
Answers
Please, see the detailed solution in the attached file.
Thanks.
A hacker is trying to guess someone's password. the hacker knows (somehow) that the password is 6 digits long, and that each digit cound be a number between 0 and 8. assume that the hacker makes random guesses. what is the probability that the hacker guesses the password on his first try? round to four decimal places.
Answers
The probability that the hacker guesses the password on his first try is 0
How to determine the probability?The password is given as:
Password = 6 digit long
The usable numbers are:
Digits = 0 to 8 i.e. 9 digits
If the digits can be repeated, then the number of passwords is:
Password = 9^6
Evaluate the exponent
Password = 531441
The probability that the hacker guesses the password on his first try is
P = 1/531441
Evaluate
P = 0.00000188167
Approximate
P = 0.0000
Hence, the probability that the hacker guesses the password on his first try is 0
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The probability of guessing the password on the first try is 0.000001881.
Explanation:To calculate the probability of guessing the password on the first try, we need to determine the number of possible passwords and divide it by the total number of possible guesses. In this case, the password is 6 digits long and each digit can be a number between 0 and 8.
So, there are 9 possible digits for each of the 6 positions, giving us a total of 9^6 = 531441 possible passwords.
The hacker makes random guesses, so there are 9^6 = 531441 possible guesses they can make.
The probability of guessing the password on the first try is therefore 1/531441 = 0.000001881, rounded to four decimal places.
Randall is going to the grocery store. It is 3 3/5 miles from his house. He walks 2 2/5 miles before it starts to rain. How far will he have to walk in the rain?
Answers
Which of the following is a polynomial function in standard form with zeros at 0, 2, and 4?
Answers
x(x² - 6x + 8)
x³ - 6x² + 8x
Answer:
polynomial x³ -6x² +8x .
Step-by-step explanation:
Given : polynomial function in standard form with zeros at 0, 2, and 4.
To find : Which of the following is a polynomial function.
Solution : we have given that
zeros at 0, 2, and 4.
x = 0 .
x = 2
x = 4
(x -0)(x -2) (x -4).
x (x-2)(x-4).
x( x² -4x -2x +8).
x (x² -6x +8).
x³ -6x² +8x .
Therefore, polynomial x³ -6x² +8x .
How do you multiply two scientific notation values? Explain the steps you would take to find the product of 6.7 × 106 and 3.2 × 105 written in scientific notation.
Answer is: Calculate the product of the coefficients and powers separately. Apply the product of powers rule to add the exponents. The product is not in scientific notation because the coefficient is greater than 10. Change the coefficient by moving the decimal one place to the left and increasing the exponent by one.
Answers
The answer to the above is
2.144 * 10^12
In scientific notation the product is written as [tex](2.144)\times10^{12}[/tex].
Given,Two scientific notation values are [tex]6.7\times10^6[/tex] and [tex]3.2 \times10^5[/tex].
We have to explain the steps to find the product of these values.
Scientific notation:Scientific notation is a widely used floating-point system in which numbers are expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10.
For the product of the above values we multiply coefficients separately like
[tex](6.7\times3.2=21.44)[/tex]
and powers of 10 separately
[tex](10^6\times10^5=10^{11} )[/tex].
So,
[tex]6.7\times10^6 \times 3.2\times10^5=(6.7\times3.2)\times(10^6\times10^5)[/tex].
[tex]6.7\times10^6 \times 3.2\times10^5=(21.44)\times10^{11}[/tex]
Or, in scientific notation form,
[tex]6.7\times10^6 \times 3.2\times10^5=(2.144)\times10^{12}[/tex].
Hence, in scientific notation the product is written as [tex](2.144)\times10^{12}[/tex].
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which answer is a reasonable estimate to the following problem? 94.689
Answers
What is the median of this set of data? 1, 2, 5, 6, 9 1 5 8 9
Answers
What is the surface area of the right cone below?
Answers
[tex]A= \pi r(r+ \sqrt{h^2+r^2} )[/tex]
Here Radius, r= 6 units
To find the height of cone, we use Pythagorean theorem.
c²=a²+b²
Put values
15²=6²+h²
225=36+h²
h²=189
Put values in formula.
A=6π(6+√189+36)
A=6π+(6+√225)
A=6π(6+15)
A=126π units²
Answer:
Te correct option B.
Step-by-step explanation:
The surface area of a cone is
[tex]A=\pi r(r+l)[/tex]
Where, r is the radius and l is slant height.
From the given figure it is noticed that the radius of the cone is 6 and slant height is 15.
The surface area of cone is
[tex]A=\pi \times 6\times (6+15)[/tex]
[tex]A=\pi \times 6\times 21[/tex]
[tex]A=126\pi[/tex]
The area of the cone is 126π units². Therefore option B is correct.
The five members of the Traynor family each buy train tickets. During the train ride, each family member buys a boxed lunch for $6.50. If the total cost of the trip is $248.50, what is the price of each train ticket? Enter your answer in the box.
Answers
248.5 - 32.5 = 216
216/5 = 43.2
each ticket is $43.20
Subtract 1.05 from a certain number. Multiply the difference by 0.8, add 2.84 to the product then divide the sum by 0.01 and get 700. What is the number?
Answers
We will set up an equation for this. Let x be the unknown number. Subtracting 1.05 from it gives us
(x-1.05)
Multiplying the difference by 0.8 would give us
0.8(x-1.05)
Adding 2.84 to the product would give us
0.8(x-1.05)+2.84
Dividing the sum by 0.01 would give us
[0.8(x-1.05)+2.84]/0.01 = 700
We will start working backward, cancelling the division by 0.01 first by multiplying:
([0.8(x-1.05)+2.84]/0.01)*0.01 = 700*0.01
0.8(x-1.05)+2.84 =7
Subtract 2.84 from both sides:
0.8(x-1.05)+2.84-2.84 = 7-2.84
0.8(x-1.05) = 4.16
Use the distributive property on the left side:
0.8*x - 0.8*1.05 = 4.16
0.8x - 0.84 = 4.16
Add 0.84 to both sides:
0.8x - 0.84+0.84 = 4.16+0.84
0.8x = 5
Divide both sides by 0.8:
0.8x/0.8 = 5/0.8
x = 6.25
Answer:
6.25
Step-by-step explanation:
I go to rsm and this answer worked
A circular rug has a radius of 3 ft. What is the circumference of the rug? Use 3.14 for mc014-1.jpg.
9.32 ft
9.42 ft
18.64 ft
18.84 ft
Answers
We must use a certain formula to find the circumference of anything circular.
The formula is:
C = 2 × pi × r
We know that pi = 3.14 approximately and the radius is 3 feet.
Substitute:
C = 2 × 3.14 × 3
C = 6.28 × 3
C = 18.84 ft
ANSWER:
The circumference of the circular rug is 18.84 ft. (Last option)
The circumference of a circular rug with a radius of 3 feet is equal to 18.84 feet.
Given the following data:
Radius of circular rug = 3 feet.π = 3.14.How to calculate the circumference of a circle?Mathematically, the circumference of a circle is calculated by using this formula:
Circumference = 2πr
Where:
r is the radius of a circle.
Substituting the given parameters into the formula, we have;
Circumference = 2 × 3.14 × 3
Circumference = 18.84 feet.
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Describe the relationship that must exist between a, b, and c in the equation ax^2+bx+c=0 in order for the equation to have exactly one solution
Answers
The [tex]b^2-4ac[/tex] bit is called the discriminant and it tells you what kind of solutions occur,
-if [tex]b^2-4ac \ \textgreater \ 0[/tex] then the equation has two different solutions
-if [tex]b^2-4ac=0[/tex] then the equation has exactly one solution
-if [tex]b^2-4ac\ \textless \ 0[/tex] then the equation has no (real) solutions.
So you are interested in exactly one solution which happens if [tex]b^2-4ac=0[/tex] or equivalently [tex]b^2=4ac[/tex].
The Harlowe school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table, where Low represents the fewest days attended and High represents the most days attended for a single student.
School Low High Range Mean Median IQR σ
High School A 98 180 82 158 148 55.5 35.2
High School B 105 180 75 145 124 48.5 28.2
High School C 102 180 78 169 151 53.5 31.3
Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justify your answer mathematically. (5 points)
Part B: If the school district wants to award the school with the highest average attendance, which school should it choose and why? Justify your answer mathematically.
Answers
Part B: High school A has the highest average attendance, because it has higher mean (82) than B and C. Mean is mathematically the same as average, total number of days attended by all students divided by the number of students.