The direction of the parabola is determined by the leading coefficient of the polynomial (a > 0 - Upwards, a < 0 - Downwards). The y-intercept of the polynomial is c and the two zeros of the polynomial are x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c).
What are the characteristics of quadratic equations?
Herein we have a quadratic equation of the form f(x) = a · x² + b · x + c. To determine the direction of the parabola, we must transform this expression into its vertex form and looking for the sign of the vertex constant:
f(x) = a · x² + b · x + c
f(x) = a · [x² + (b / a) · x + (c / a)]
f(x) + b² / (4 · a) - c = a · [x² + (b / a) · x + b² / (4 · a²)]
f(x) + b² / (4 · a) - c = a · [x + b / (2 · a)]²
If a > 0, then the direction of the parabola is upwards, but if a < 0, then the direction of the parabola is downwards.
The y-intercept is found by evaluating the quadratic equation at x = 0:
f(0) = a · 0² + b · 0 + c
f(0) = c
And the zeros are determined by the quadratic formula:
x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c)
The direction of the parabola is determined by the leading coefficient of the polynomial (a > 0 - Upwards, a < 0 - Downwards). The y-intercept of the polynomial is c and the two zeros of the polynomial are x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c).
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___________ statistics summarize numbers and _____________ statistics determine whether the results are significant.
Descriptive statistics summarize numbers and inferential statistics determine whether the results are significant.
What is statistics?
The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.
Statistics is the study and manipulation of data, including methods for data collection, evaluation, analysis, and interpretation.Descriptive statistics and inferential statistics are the two main subfields of statistics.Different levels of statistics communication are possible, from non-numerical descriptor (nominal-level) to numerical with reference to a zero-point (ratio-level).To gather statistical data, a variety of sampling methods can be utilized, including basic random, systematic, stratified, or cluster sampling.To know more about the statistics
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The ratio of height to the base radius of a cone is 3:4. If the volume of the cone is 2000πcm³, find its radium, in cm.
Who can help me to answer this question? Please and thank you very much .
Answer:
20 cm
Step-by-step explanation:
The volume, V, of a cone with radius r and height h is given by the formula
V = [tex](1/3) \pi r^2 h[/tex]
Since it is given that the ratio of h to r is 3/4 we have the relationship
h/r = 3/4 ==> h = (3/4)r
Substituting for h in the volume equation gives us an expression in terms of r
[tex](1/3)\pir^2h = (1/3) \pi r^2 (3/4)r\\(1/3 ) (3/4) = 1/4\\[/tex]
So the expression simplifies to[tex](1/4)\pi r^3[/tex]
We are given that this volume is 2000π cm³
So
(1/4)πr³ = 2000π
Eliminating π on both sides and multiplying by 4 on both sides gives
r³ = 8000
r = ∛8000 = 20 cm Answer
A deli sells sliced meat and cheese. One customer purchases 4 pounds of meat and 5 pounds of cheese for a total of $30.50. A sandwich shop owner comes in and purchases 11 pounds of meat and 14 pounds of cheese for $84.50. The system of equations below represents the situation.
4x + 5y = 30.50
11x + 14y = 84.50
The variable x represents the
The variable y represents the
The deli charges $
The quantity of meat and cheese sold by the deli according to the description accounts in the task content are; 4.5 and 2.5 pounds respectively.
What is the quantity of meat and cheese sold by the deli?The quantity of meat sold by the deli as represented by the variable X in the task content can be calculated by solving the systems of equations.
The quantity of cheese sold by the deli as represented by the variable y in the task content can be calculated by solving the systems of equations.
Consequently, solving the system of equations by means of substitution, we have;
y = (30.50-4x)/5
Hence, we have;
11x + 14((30.50-4x)/5) = 84.50
x = 4.5 pounds of meat and
y = 2.5 pounds of cheese.
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Use the elimination method to slice the system of equations Choose the correct ordered pair 6x+2y=8 12x+y=22
Answer:
x=2 and y=-2
Step-by-step explanation:
Solution Given:
6x+2y=8....................................................[1]
12x+y=22....................................................[2]
Multiplying equation in 1 by 2 and subtracting equation 1 by 2 we get
equation 1 becomes 12x+4y=16
and subtracting by equation 2 we get
12x+4y=16
-12x-y=-22[Note: while subtracting we must change sigh)
__________________
0x+3y= -6 [note: while subtracting we must keep the sigh which have greater value]
3y=-6
dividing both side by 3, we get
3y/3=-6/3
we get y=-2
Again similarly
Multiplying equation in 2 by 2 and subtracting equation 2 by 1 we get
equation 2 becomes 24x+2y=44
and subtracting by equation 1 we get
24x+2y=44
-6x-2y=-8
_____________________
18x-0y=36
18x=36
dividing both side by 18, we get
18x/18=36/18
x=2
The chart below shows conversion between kilometers and miles.
Conversion Chart
Kilometer
Miles
2
1.2
7
4.2
20
?
30
18
What is the missing value in the table?
Answer:Answer:
12 (D)
Step-by-step explanation:
The first one is 2:1.2 so i did x10 on it to get 20:12.
Step-by-step explanation:Oh and hey if it's right u have to make me brainliest i need award
what is 4^-2. ................................
Answer:0.0625
Step-by-step explanation:
Answer:
1/16.
Step-by-step explanation:
4 ^-2 = 1 / 4^2
= 1/16.
14²-34 divided by -9+7.2
Answer:
Let's go part by part:
14 raised to 2 = 196
-9+7x2=-9+14 = 5
196/5= 39,2 (final result)
Answer:
-3.2
Step-by-step explanation:
14 SQUARED is 196
196 - 34 = 5.7647
- 9 + 7.2 = - 1.8
5.7647 / -1.8 = -3.2
-3.2 would be your answer.
If -3(x+8)= -21, then x = -1.
Step-by-step explanation:
-3(x+8)=-21
open the bracket
-3x-24=-21
-3x=-21+24
-3x=3
x=-3/3
x=-1
What is the general form of the equation for the given circle centered at o(0, 0)? a. x2 y2 41 = 0 b. x2 y2 − 41 = 0 c. x2 y2 x y − 41 = 0 d. x2 y2 x − y − 41 = 0
The general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.
According to the question,
The general form of the equation for the given circle centered at o(0, 0) is (x-h)² + (y-k)² = r².
The given equation is x² + y² - 41 = 0 which is also represented by(x-0)² + (y-0)² = -(√41)². This is not possible.
The given equation is x² + y² - 41 = 0 which is also represented by (x-0)² + (y-0)² = (√41)²This means that the circle is centered at (0,0). Thus, the equation is correct The given equation is x² + y² +x+ y- 41 = 0 which is also represented by (x+1/2)² + (y+1/2)² = (√(83/2))²This means that the circle is centered at (-1/2,-1/2). Thus, this equation is incorrect. The given equation is x² + y² +x- y- 41 = 0 which is also represented by (x+1/2)² + (y-1/2)² = (√(83/2))²This means that the circle is centered at (1/2,-1/2). Thus, this equation is incorrect.Hence, the general form of the equation for the given circle centered at o(0, 0) is x² + y² - 41 = 0.
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Fatimah is x years old and nadia is 3 years older than fatmah. find expression, in it's simplest form in terms of x, for the sum of the girls ages in two years time and in y years time
The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.
How to derive an algebraic expression from a word problem
Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:
y - x = 3 (Expression that represents age difference between Fatimah and Nadia)
x + 3 = y, where x, y > 0 and y > x. (1)
The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.
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The slope-intercept form given (6,-5) & perpendicular to -5x - 7y = -17.
Answer:
[tex]y=\dfrac{7}{5}x-\dfrac{67}{5}[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slope.b is the y-intercept.Rearrange the given equation so that it is in slope-intercept form:
[tex]\implies -5x-7y=-17[/tex]
[tex]\implies -7y=5x-17[/tex]
[tex]\implies y=-\dfrac{5}{7}x+\dfrac{17}{7}[/tex]
Therefore, the slope of the given equation is -⁵/₇.
If two lines are perpendicular to each other (at right angles), the product of their slopes will be -1. Therefore, their slopes will be negative reciprocals of each other.
Therefore, the slope of the line perpendicular to the given equation is:
[tex]\sf m=\dfrac{7}{5}[/tex]
Substitute the found slope and the given point (6, -5) into the slope-intercept formula and solve for b:
[tex]\implies -5=\dfrac{7}{5}(6)+b[/tex]
[tex]\implies -5=\dfrac{42}{5}+b[/tex]
[tex]\implies b=-\dfrac{67}{5}[/tex]
Substitute the found slope and the found value of b into the slope-intercept formula to create the equation for the perpendicular line:
[tex]\implies y=\dfrac{7}{5}x-\dfrac{67}{5}[/tex]
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For a sample of size 300 from a population with the population proportion, p = 0. 45, compute μphat and σphat
For a sample of size 300 from a population with the population proportion, the μphat and σphat are 0.0287.
A share is an equation in which ratios are set equal to each other. for example, if there may be 1 boy and three women you can write the ratio as 1 : 3 (for each boy there are 3 women) 1 / 4 are boys and three / 4 are girls.
The formula for proportion is components /complete = percent/100. This system can be used to locate the percentage of a given ratio and to locate the lacking value of an element or an entire.
A proportion is generally written as equal fractions. for example: note that the equation has a ratio on each facet of the same signal. Every ratio compares the equal units, inches, and feet, and the ratios are equivalent due to the fact the devices are regular and equal.
Given 300 2 and p 0.45
p = 0.45 Up
and Õp-sqrt(p(1-p)/n) sqrt(0.45 * 0.55/300) sqrt(0.000825) =0.0287
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√32x+1
= 9x-2 minta tolong dengan ini
We have:
√32x + 1 = 9x - 2
<=> √32x - 9x = -2 - 1
<=> (√32 - 9)x = -3
<=> x = -3/(√32 - 9) = (27+12√2)/49
ANSWER: x = (27+12√2)/49
P/s: i'm not pretty sure
Ok done. Thank to me :3
If 3(x-3) = 5(2x + 1), then
x=-2
Step-by-step explanation:
Solution Given:
3(x-3) = 5(2x + 1)
Opening bracket we get
3x-9=10x+5
keeping common value in same side
-9-5=10x-3x
-14=7x
x=-14/7
x= -2
Answer:
-2 =x
Step-by-step explanation:
3(x-3) = 5(2x + 1)
To solve for x
Distribute
3x -9 = 10x +5
Subtract 3x from each side
3x-9-3x = 10x -3x+5
-9 = 7x+5
Subtract 5 from each side
-9-5 = 7x+5-5
-14 = 7x
Divide by 7
-14/7 = 7x/7
-2 =x
Select the correct answer. what is the probability that a person who is older than 35 years has a hemoglobin level between 9 and 11?
1. The probability that a person who exists older than 35 years has a hemoglobin level between 9 and 11 exists at 0.284.
2. The probability that a person who exists older than 35 years has a hemoglobin level of 9 and above exists at 0.531.
What is the probability that a person who exists older than 35 years contains a hemoglobin level between 9 and 11?Let the number of the person who is older than 35 years have a hemoglobin level between 9 and 11 be x.
From the given table it is clear that the total number of the person who is older than 35 years exists 162.
75+x+40 = 162
x+116 = 162
x = 162-116
x = 46
The number of people who are older than 35 years has a hemoglobin level between 9 and 11 exists at 46.
1. The probability that a person who exists older than 35 years has a hemoglobin level between 9 and 11 exists
P = Probability who is older than 35 years has a hemoglobin level
between 9 and 11 / Person who exists older than 35
P = 46/162 = 0.284
The probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 exists at 0.284.
2. Person who is older than 35 years has a hemoglobin level of 9 and above exists 46 + 40 = 86.
The probability that a person who exists older than 35 years has a hemoglobin level of 9 and above exists
P = Probability who is older than 35 years has a hemoglobin level
between 9 and above / Person who is older than 35
P = 86/162 = 0.531.
The probability that a person who is older than 35 years has a hemoglobin level of 9 and above exists at 0.531.
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You are playing a game with three cards. At the start, all three cards are face down. You know that a different real number is written on every card, but you do not know what the numbers are. The rules of the game are as follows: You can choose any card and turn it over (assuming that you have not already turned it over). You can either keep the card, or discard it. If you discard a card, then you cannot go back to it; you must choose a new card. If the card you have kept has the largest real number on it, then you win the game. If you use the optimal strategy, then what is the probability that you win the game
concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.
How to find the probability?
Now, we know that there are 52 cards in a normal deck, if we only keep the ones with real numbers, there are 40.
These numbers go from 1 to 10.
5.5 is the average real number in the cards, so, having a 6 or more in a card is what we expect.
This means that if the card that we turn up is smaller than 6, we discard it.
If the card has the value 6 or larger, we keep it.
In this case, the probability of losing is if one of the other cards has a value larger than 6.
The probability that a random card has a value larger than 6 is:
p = (number of cards with a value larger than 6)/(total number of cards)
p = (16/39)
(The quotient is 39 instead of 40, because we already know one of the cards)
This means that if keep the 6, the probability of winning is:
1 - 16/39 = 0.59
If instead, we got a 7, obviously we keep it, in that case the probability of winning is:
1 - 12/39 = 0.69
And so on, concluding, the idea is discarding cards until we get,at least, a 6, in that case, the smallest probability of winning the game is 0.59, which is more than in half of the cases.
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Which word describes their measures? linear congruent complementary supplementary
-7(-w-1)-2 simplest form
Find the ordered pair (s, t) that satisfies the system.
Answer:
s is antecedent t is consepuent
Worth 15 points!!!!!!!!!!!!!!
Make t the subject of the formula k=mt/[t*t]+f............**by t*t I mean square of T
Answer:
T tof = 2 ( v 0 sin θ 0 ) g . T tof = 2 ( v 0 sin θ 0 ) g . This is the time of flight for a projectile both launched and impacting on a flat horizontal surface.
Select the correct answer.
You are moving to a new apartment and need to hire a moving company. You’ve researched local moving companies and found these price options.
After the moving process has begun, you realize that it’s going to take closer to 7 hours to finish moving everything instead of the 4 hours you initially estimated. If you had planned for 7 hours of time for moving, which moving company would have given you the best deal?
Using a linear function, it is found that Company D would have given you the best deal for 7 hours of moving.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we consider:
The flat fee as the y-intercept.The hourly rate as the slope.Hence the costs for x hours of moving from each company are given as follows:
A(x) = 50 + 25x.B(x) = 40 + 30x.C(x) = 60 + 20x.D(x) = 150 + 5x.For 7 hours, the costs are given as follows:
A(7) = 50 + 25 x 7 = $225.B(7) = 40 + 30 x 7 = $250.C(7) = 60 + 20 x 7 = $200.D(7) = 150 + 5 x 7 = $185.Due to the lower cost, Company D would have given you the best deal for 7 hours of moving.
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Factor the greatest common factor: −5k2 20k − 30. −1(5k2 − 20k 30) −5(k2 − 4k 6) −5k(k2 − 4k 6) −5(k2 4k − 6)
The greatest common factor−5k2 20k − 30 is [tex]-5(k^{2} -4k-6).[/tex]
What is meant by the greatest common factor?The most common factor in mathematics is the highest number that may divide evenly into two other numbers.The largest factor that splits both numbers is the greatest common factor. List the prime factors of each integer before calculating the greatest common factor. One 2 and one 3 are shared by those aged 18 and 24. We multiply them to obtain the GCF. Therefore the GCF for 18 and 24 is 2 * 3 = 6.The biggest positive integer that divides evenly into all the numbers with no remainder is the greatest common factor (GCF, GCD, or HCF) of a collection of whole numbers.To find the greatest common factor:
−5k2 20k − 30.
Factor the expression: [tex]5(-k^{2} +4k-6)[/tex]
Factor the expression: [tex]5(-k^{2} -4k+6)[/tex]
Multiply the monomials: [tex]5(k^{2} +4k+6)[/tex]
The greatest common factor: [tex]-5(k^{2} -4k-6).[/tex]
The greatest common factor−5k2 20k − 30 is [tex]-5(k^{2} -4k-6).[/tex]
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The complete question is:
Factor the greatest common factor: [tex]-5k^2+ 20k - 30.[/tex]
a) [tex]-1(5k^2- 20k+ 30)[/tex]
b) [tex]-5(k^2 -4k+ 6)[/tex]
c)[tex]-5k(k^2 - 4k +6)[/tex]
d) [tex]-5(k^2 +4k - 6)[/tex]
The greatest common factor of −5k² + 20k − 30 exists -5( k² - 4k + 6 ).
Therefore, the correct answer is option a) -5 ( k² - 4k + 6 ).
What is greatest common factor (GCF)?The greatest common factor (GCF) of a set of numbers exists the biggest factor that all the numbers share.
Given : −5k² + 20k − 30.
Taking common -5 from each term, we get
−5k² + 20k − 30 = -5 ( k² - 4k + 6 ).
The greatest common factor of −5k² + 20k − 30 exists -5( k² - 4k + 6 ).
Therefore, the correct answer is option a) -5 ( k² - 4k + 6 ).
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pls help right now need pleaseee
Answer:
-1/2
Step-by-step explanation:
The cosine is equal to the x coordinate of the point where the terminal side of the angle intersects the unit circle.
ABCD is a rhombus. If AB = 2x + 12 , AC = 7x - 3, ∠=12°, and ∠ = (4y - 1)°.m ∠BAC = __ . (FIND BAC NOT CD)
Answer:
Step-by-step explanation:
Solve the inequality 6 > x² - 5x.
Answer:
Step-by-step explanation:
6 > x² - 5x.
The answer for the inequality is -1 the greater than sign x greater than 6
The interval notation is ( -1,6)
Answer:
[tex]-1 < x < 6[/tex]
Step-by-step explanation:
Moving all terms to one side, we get [tex]x^2-5x-6 < 0[/tex]. Notice that we can factor the left side. Doing so, we get [tex](x-6)(x+1) < 0[/tex]. The zeroes in this equation are [tex]x-6=0 \Rightarrow x=6[/tex] and [tex]x+1=0\Rightarrow x=-1[/tex]. Now, we must create test points in the intervals: [tex]x < -1, -1 < x < 6, x > 6[/tex]. For example, we can choose [tex]x=-2,x=0,x=7[/tex]. For [tex]x=-2[/tex], we get that [tex](-2-6)(-2+1) = 8 < 0[/tex] is false, since the expression is positive. Doing the same thing for [tex]x=0[/tex] and [tex]x=7[/tex], we get that only [tex]x=0[/tex] creates a negative value. This means that the values in the interval [tex]\boxed{-1 < x < 6}[/tex] all work.
find the solution of systems of equations
8x-5y=-8 -7x-5y=82
Answer:
x = -6, y = -8
Step-by-step explanation:
8x - 5y = -8
-7x - 5y = 82
minus them
15x = -90
x = -90 / 15
x = -6
8(-6) - 5y = -8
-48 - 5y = -8
-5y = -8 + 48
-5y = 40
5y = -40
y = -40 / 5
y = -8
What is the standard form polynomial representing the volume of this shipping container?
The image shows a blue shipping container with the numbers:
4x2 + 3x(along the length of the bottom)
x2 - 8 (Along the bottom of the 'front')
6x + 15 (going up the length of the 'front')
The standard form polynomial representing the volume of this shipping container is determined as: 24x^5 + 78x^4 - 147x^3 - 624x^2 - 360x.
What is a Standard Form Polynomial?A standard form polynomial is a polynomial expression written whereby the term with the highest degree or power on a variable is written first in the expression, followed by the least, then the constant of the polynomial comes last.
What is the Volume of a Rectangular Prism?
The Volume of a rectangular prism = (length)(width)(height).
The shipping container is a rectangular prism with the following dimensions:
Length of container = 4x² + 3x
Width of container = x² - 8
Height = 6x + 15
Plug in the values
Volume of container = (4x² + 3x)(x² - 8 )(6x + 15)
Expand
Volume of container = 24x^5 + 78x^4 - 147x^3 - 624x^2 - 360x
Thus, using the formula for the volume of a rectangular prism, the standard form polynomial representing the volume of this shipping container is determined as: 24x^5 + 78x^4 - 147x^3 - 624x^2 - 360x.
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The two hexagonal pyramids are similar. if the smaller pyramid has a surface area of 25.49 ft2, what is the surface area of the larger pyramid? round to the nearest hundredth. ft2
The largest pyramid's surface area is roughly 159.31 [tex]ft^2[/tex].
What is hexagonal pyramids?A hexagonal pyramid is one that has six isosceles triangles that meet at a point, each of which is supported by a hexagonal foundation. It is self-dual, just as any pyramid. It possesses C6v symmetry when the base of a right hexagonal pyramid is a regular hexagon.
A pyramid is a solid,
Additionally, the ratio of two solids' surfaces when they are comparable is equal to the square of the similarity scale factor.
The similarity scale factor in this instance
= (Hight of the larger pyramid)/(Height of smaller pyramid)
=15/6
Due to the aforementioned characteristic,
= (15/6)^2
Given that the smaller pyramid's surface area is 25.49 [tex]ft^2[/tex],
(The surface of larger pyramid)/(25.49) = 225/36
The surface of larger pyramid = (25.49*225)/36
= 5735.25/36
= 159.3125 ft^2
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Solve the equation
-18 + 24 = -2(x+6)
Answer:
x = -9
Step-by-step explanation:
-18+24 = -2(x+6) Distribute and simplify
6 = -2x-12 Add 12 to both sides
18 = -2x Divide by -2 on both sides
-9 = x Here's your answer
Hope this helps! :D
First, do -2 times x. that is -2x. Next, do -2 times +6. That should be -12. The last steps are in order, add 18 on both sides. it should be -18+18 and -12+18. now you have 24 on the left and -2x and +6. -6 on both sides. 6-6 and 24-6. now you have 18 and -2x. so get rid of the -2x by doing -2x/-2 and on the left side 18/-2. So the answer should be -9=x.
