The answers to each part of the question are mentioned above.
What is parabola?In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.The general equation of a parabola is given by -y = a(x – h)² + k or x = a(y – k)² +h.
where - (h, k) denotes the vertex.
Given is the equation of a parabola as -
(x - 1)² = y + 2
We can write the equation as -
y = (x - 1)² - 2
The coordinates of the vertex are : (h, k). So, we can write the coordinates of the vertex as V(1, - 2).The equation of a parabola is -[tex]$y=\frac{1}{4 \left(f - k\right)} \left(x - h\right)^{2} + k[/tex]
We can rewrite the equation of the parabola given as -[tex]$y=\frac{1}{4 \left(\frac{-7}{4} - (-2)\right)} \left(x - h\right)^{2} + k[/tex]
The coordinates of the focus are : (h, f). The coordinates of the focus will be - F(h, f) or F(1, -7/4)The distance from the focus to the vertex is the same as the distance from the vertex to the directrix so -- 2 - (- 7/4) = d - (- 2)
d = - 9/4
The equation of directrix will be :y = d
y = -9/4
The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: x = 1
Therefore, the answers to each part of the question are mentioned above.
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How many positive two-digit integers are multiples of 5 and of 7?
The number of positive two-digit integers that are multiples of 5 and 7 are 2
What ae multiples?In mathematics, multiples are the results of multiplying an integer by a given number.
The multiples of 5 and 7 within 10 to 100 are
35 and 70
multiples of 5: 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
multiples of 7: 7 14 21 28 35 42 49 56 63 70 77 84 91 98
The common numbers are 2 which are 35 and 70
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Math help quick guys where ya at
The required dimensions are solved using linear pair and vertical angle to get the result as
x = 40y = 35Angle AED = angle CEB = 125 degreesAngle DEB = Angle AEC = 55 degreesHow to find the value of x and yThe value of x and y is calculated using linear pair theorem, the theorem implies that
solving for x
(3x + 5) + (x + 15) = 180
3x + x + 5 + 15 = 180
collecting like terms
4x = 180 - 15 - 5
4x = 160
x = 40
solving for y
(y + 20) + (4y - 15) = 180
y + 4y + 20 - 15 = 180
collecting like terms
5y = 180 - 20 + 15
5y = 175
y = 35
Angle AED
= 3x + 5
= 3 * 40 + 5
= 125 degrees
Angle AED = angle CEB = 125 degrees (vertical angles)
Angle DEB
= x + 15
= 40 + 15
= 55 degrees
Angle DEB = Angle AEC = 55 degrees (vertical angles)
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Wenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows:
# of movies Frequency
0 4
1 9
2 5
3 6
4 1
a) Find the sample standard deviation, s. (Round your answer to two decimal places. )
b) Find the sample mean x^-
Answer: 35
Step-by-step explanation:
: i took this quiz before :)
Brent has goldfish that quadruple (become four times as many) every month, and Gretel has goldfish that double every month. If Brent has 4 goldfish at the same time that Gretel has 128 goldfish, then in how many months from that time will they have the same number of goldfish
On solving the provided question, we can say that by fraction they will have the same amount of fish in 5 months.
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
Month / Brent / Gretel
0/4/ 128
1/ 16 / 256
2 / 64 / 512
3 / 256 / 1024
4 / 1024 / 2048
5 / 4096 / 4096
They will have the same amount of fish in 5 months.
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Which quantity is proportional to 12/4?
Check all that are true.
48/18
36/12
35/15
2416
3/1
The quantities which are proportional to 12/4 are 36/12 and 3/1 .
What is proportional ?
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.
The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well. An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.
12/4 ⇒ 3/1
48/18= 24/9
= 8/3
The quantity 12/4 is not proportional to 48/18
36/12= 18/6
= 3/1
The quantity 12/4 is proportional to 36/12
35/15= 7/3
The quantity 12/4 is not proportional to 35/15
24/16= 12/8
= 6/4
= 3/2
The quantity 12/4 is not proportional to 24/16
3/1The quantity 12/4 is proportional to 3/1
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what is the legend of variables of combined gas law
The combined gas law for a gas is discussed below.
What is a gas?Gas is one of the four fundamental states of matter – the others being solid, liquid, and plasma. A pure gas may be made up of individual atoms, elemental molecules made from one type of atom, or compound molecules made from a variety of atoms.Given is the combined gas law.
The ideal combined gas law is given by →
PV = nRT
Where -
{P} = pressure {T} = temperature {V} = volume
{n} = number of moles {R} = gas constant
Non ideal gases are often modelled by the Van der Waals equation as →
(p + n²a/V²)(V - nb) = nRT
Where -
{a} and {b} = constants for a particular gas
{p} = pressure {v} = volume
{n} = number of moles {t} = temperature
{R} = gas constant
Therefore, the combined gas law for a gas is discussed above.
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What are the three types of algorithms?
The three types of algorithms are Brute Force algorithm, Greedy algorithm and Recursive algorithm.
What is Brute Force algorithm?As a very general approach to problem solving and an algorithmic paradigm, brute-force search or exhaustive search entails iteratively listing all potential candidates for the solution and determining if each one satisfies the problem's statement.
In order to find the divisors of a natural number n, a brute-force algorithm would count all integers from 1 to n & determine whether each one divides n without leaving a remainder.
A brute-force method might look at all possible configurations of 8 pieces on the 64-square chessboard and determine whether each queen piece may engage in mutually exclusive attacks for each configuration for the eight queens puzzle.
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If 7 is an element in the domain of f(x)= 6x-18/2, what is the corresponding element in the range?
The corresponding element in the range when 7 is an element in the domain is f(7)=33
Step-by-step explanation:
Given that the 7 is an element in the domain of f(x)
The function f is defined by f(x)=6x-18/2
To find the corresponding element in the range:
That is put x=7 in the given function f(x)
Therefore f(x) becomes
f(7) = 6(7)-18/2
=42-18/2
=42-9
=33
Therefore corresponding element in the range when 7 is an element in the domain is f(7)=33
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a 10-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 8feet from the base of the building. How high up does the ladder reach?
The ladder would reach a distance of 6 feet up the wall.
The Pythagorean theorem.This is a theorem that can be used to determine the unknown side of a right angled triangle. It is given as:
/hyp/^2 = /opp/^2 + /adj/^2
In the given question, the ladder is placed a against a vertical wall of a building. Given that the bottom of the ladder is 8 feet to the base of the building. Therefore this is would form a right angled triangle, such that the Pythagorean theorem can be applied.
So that, let the height of the ladder on the wall be represented by t. Then;
10^2 = t^2 + 8^2
100 = t^2 + 64
t^2 = 100 -64
= 36
t = (36)^1/2
t = 6 feet
Thus the ladder is placed 6 feet up the vertical wall.
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bonjour svp aide moi
Exercice 7: mon et nop sont deux angles adjacents supplémentaires tel que mOn = 60°.
1°) Calculer nOp.
Answer:
n0p = 120°
Step-by-step explanation:
m0n + n0p = 180°
60° + n0p = 180°
n0p = 120°
Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answer:
The values are 13 and 1
I hope this is correct
Find the nth term of the following sentence
-5,-2,3,10,19
On solving the provided question, we can say that An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.
what is arithmetic sequence?Arithmetic sequences are groups of integers that are arranged in a certain order and share a common difference between each term. The tolerance, for instance, is six in the mathematical progression 3, 9, 15, 21, and 27. Arithmetic progression can also be referred to as such. a series that is produced by adding the same value repeatedly. for instance, 1, 4, 7, 10, 13, 16, 19, 22, and 25. Sequences that have an arithmetic difference between two successive phrases are known as arithmetic sequences. A progression in math with a tolerance of 2 is 2,4,6,8,10.
An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. 2,4,6,8,10….is an arithmetic sequence with the common difference 2.
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How do you find the 3 side of a triangle?
Answer:
by using sine rule and cosine rule.
PLEASE HELP f(x)=x^2-12x+35 g(x)=x−5, find(f⋅g)(x)
Step-by-step explanation:
this is a multiplication dot, right ?
so,
(f.g)(x)
or
(f×g)(x)
any arithmetic operation (like +, -, ×, ÷) between 2 functions is done by applying that operation to the functional expressions.
(f×g)(x) = (x² - 12x + 35)(x - 5) =
= x³ - 5x² - 12x² + 60x + 35x -175 =
= x³ - 17x² + 95x - 175
Step-by-step explanation:
(f.g)(x) = f(x) . g(x)
= (x² - 12x + 35)(x - 5)
=x(x²-12x+35) - 5(x²-12x+35)
= x³-12x²+35x-5x²+60x-175
(f.g)(x)=x³-17x²+95x-175
H)
how many five- card hands are possible that contain at least three kings?
==========================================================
Explanation:
We'll break things up into cases. The phrasing "at least 3" means "3 or more".
We either will have 3 kings or 4 kings.
----------------------------------------------
Case A) There are exactly 3 kings.
Use the nCr combination formula. There are n = 4 kings total and we select r = 3 of them. That gives 4C3 = 4 ways to pick the 3 kings.
Put another way: there are 4 ways to leave a certain king out of the hand.
Then we have 52-4 = 48 cards that aren't a king, and we need to fill the remaining r = 2 slots. Through the nCr formula, you should find that 48C2 = 1128
To recap, we found
4 ways to pick the three kings1128 ways to pick the other two cards that aren't kingsThat gives 4*1128 = 4512 ways to have case A happen.
----------------------------------------------
Case B) There are exactly 4 kings
4C4 = 1, so there's only one way to select all the kings. The order doesn't matter. Then we have 48 cards to pick from for the fifth slot.
Overall there are 1*48 = 48 ways to have case B play out.
----------------------------------------------
There were 4512 ways to have case A happen, and 48 ways to have case B happen.
These cases are mutually exclusive to allow us to simply add the counts:
4512+48 = 4560
This is why the final answer is 4560
PLEASE HELPP
If A and B are supplementary angles and
m/B = 54, find m/A.
Answer:
m∠A=126°
Step-by-step explanation:
Supplementary means that they add up to 180°.
Therefore we can do 180-54 to get 126° for the m∠A.
Hope this helped! :)
Write an expression to represent the area of the shaded region in simplest from
We know that the area of a square/rectangle is the multiplication of its length by its width. We also know that this specific area does not include the blank region, therefore we need to subtract it from the area of the shaded region!
We can come up with two expressions:
Shaded Area:
[tex](5x + 2)(3x - 1)\\= 15x^2-5x+6x-2\\=15x^2+x-2[/tex]
Blank area:
[tex](x)(x+7)\\x^2+7x[/tex]
Now all we have to do is subtract the blank area's expression from the shaded area's and simplify since the question asks for the simplest form.
[tex](15x^2+x-2)-(x^2+7x)\\15x^2-x^2+x-7x-2\\14x^2-6x-2[/tex]
Therefore, your final answer should be:
14x^2 - 6x - 2
Is the triangle with sides of length 5 cm 3 cm and 4 cm a right angled triangle If yes why?
The triangle with sides of length 5 cm 3 cm and 4 cm is a right angled triangle because (3, 4, 5) is a Pythagorean triple.
We know that if non zero real numbers a, b, c follows Pythagoras theorem c² = a² + b², the numbers a, b, c is called as a Pythagorean triple.
And these numbers are nothing but the sides of right triangle.
Here we have been given the triangle with sides of length 5 cm 3 cm and 4 cm
Assume that p = 5 cm, q = 3 cm and r = 4 cm
p² = 25
q² = 9
and r² = 16
Consider q² + r² = 16 + 9
q² + r² = 25
q² + r² = r²
Since given numbers follows Pythagoras theorem, (3, 4, 5) is a Pythagorean triple.
And p = 5 cm, q = 3 cm and r = 4 cm are the lengths of sides of right triangle.
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(pesos and Php are philippine coins and money so just imagine pesos as coins if u arent filipino)
It has been Cheri's habit to collect 5 peso and 10 peso coins starting january of every year, to save up for her family's annual outreach to a local community at the end of the year. At the end of the year, she has saved a total of Php 2285 . If she has 11 more 10 pesos than 5 peso coins, how many coins of each does she have
Cheri collected 145 number of 5 peso coin and 156 number of 10 peso coin during her family's annual outreach
What is an equation?An equation is used to show the relationship between numbers and variables.
Let x represent the number of 5 peso coins and y represent the number of 10 peso coin
At the end of the year, she has saved a total of Php 2285, hence:
5x + 10y = 2285 (1)
Also, she has 11 more 10 pesos than 5 peso coins, hence:
y = x + 11 (2)
Solving both equations using elimination method gives:
x = 145, y = 156
Cheri had 145 number of 5 peso coin and 156 number of 10 peso coin.
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Thirty one divided by seven
Answer:
4.42857142857
Rounded:
4.4
If A=(7,9) and B=(3,12) what is the length of AB
The distance between two points A and B is 5 units.
WHAT?
Never in my life have I ever wanted to kill math
Answer:
Y-intercept: 15
Slope: 1.3
Equation: y = 1.3x + 15
Step-by-step explanation:
Base on the table:
# of haircuts = x
Cost ($) = y
Knowing that;
y-intercept = The starting point (y)
Thus, based on the table the y-intercept is 15.
Y-intercept: 15.
To find the slope.
We first have to pick two points on the line & determine their coordinates.
Then subtract y-coordinates of these two points and also subtract x-coordinates for these two points.
After that divide the y by the x.
Shown below:
I'm going to use;
(0,15) and (1,20.5)
0 = x₁
15 = x₂
1 = y₁
20.5 = y₂
Now we do;
20.5 - 1 = 19.5
15 - 0 = 15
19.5 / 15 = 1.3
Hence, Slope = 1.3
Slope: 1.3
The equation - y = mx + b
Knowing that;
b = y-intercept
m = Slope
Substitute it in we have;
y = 1.3x + 15
Equation: y = 1.3x + 15
RevyBreeze
Help ASAP!!!!
Which of the following statements is NOT true?
Flow chart to find the biggest of 3 numbers
The flowchart to find the biggest of 3 numbers is mentioned below:
Define Flowchart.A flowchart is a type of diagram that represents an algorithm, process, or workflow. It is a visual representation of the steps and decisions involved in a problem-solving or decision-making process. Flowcharts use a variety of symbols and shapes to represent different types of steps and decisions, such as inputs, outputs, process steps, and decision points. They are used to communicate the logic of a program or process to different stakeholders, such as developers, managers, and users.
Define Algorithm.An algorithm is a set of instructions or a step-by-step procedure for solving a problem or completing a task. It is a well-defined sequence of operations or actions that are taken in order to achieve a specific goal or outcome. Algorithms can be expressed using natural language, pseudocode, or programming languages. The steps in an algorithm must be unambiguous and have a clear stopping point.
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What are the top 5 formulas in math?
According to the use and the fundamental knowledge behind these formulas, The top 5 formulas in mathematics are quadratic, Pythagorean , slope-intercept , exponential and Euler's Formula.
What is mathematics?Mathematics is the study of numbers, shapes, and patterns. It is the science of studying the properties and relationships of quantities and shapes using logic, symbols and mathematical operations. It is a way of understanding the world and solving problems using quantitative reasoning.
What do you mean by formula?A mathematical formula is a set of symbols, numbers and mathematical operations that express a relationship or equation. These formulas are used to model, describe and explain phenomena in the natural and physical world, as well as in abstract mathematical theories. Formulas can take many forms, including equations, identities, and inequalities. They allow us to make predictions and calculations, and can be used in various fields of science, engineering and other fields to solve problems.
1. root of [tex]ax^2+bx+c[/tex] is [tex]x= \frac {-b+- \sqrt{b^2-4ac}}{2a}[/tex].
2.[tex]h^2 = p^2 +b^2[/tex]
3. [tex]y =mx+c[/tex]
4.[tex]e^x[/tex]
5.[tex]e^{ix} = cosx+isinx[/tex]
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Which function is shown on the graph?
of(x) = 1/2cos x
of(x) = -1/2cos x
Of(x) = -1/2sin x
Of(x) = 1/2sin x
The reasons and responses to the graphs in the question are as follows:
Graph 1.
The amplitude of the first graph is (1/2) which is the height from the midline to the peak
The value of the function at x = 0 is -(1/2), where sin(0) = 0, therefore, the function is a cosine function
The period of the graph is 2·π, which is the period of the parent cosine function
Therefore, the correct option is
Graph 2: Please find attached the graph of the function g(x) = 2×cos(x)
Graph 3: The frequency of a sinusoidal function is given as follows;
The period of the graph = π
Therefore;
The frequency of the sinusoidal graph is 2
Graph 4. Required:
To find the equation that represents the function of the graph
Solution;
The period of the function, T = π
The graph of the function has a maximum at x = 0, therefore, the graph is similar to a cosine function, y = cos(B·x)
Where;
B = 2·π/T
Therefore;
B = 2·π/π = 2
Therefore;
The equation that represent the function in the graph is f(x) = cos(2·x)
Question 5. The given function is f(x) = cos(2·x)
The frequency factor in the given function, B = 2
The period, T = 2·π/B
Therefore, T = 2·π/2 = π
The period of the function, f(x) = cos(2·x), is 2
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What value is X in math?
Answer:
Any value
Step-by-step explanation:
X is a variable, meaning it can be any number, and they are just using our variable, x, as a little mask to hide the exact value. In math, we will usually need to find x by solving different equations.
Examples:
x + 4 = 7
Know, x in this case is 3 because we just know 3 + 4 = 7, but x can be any value, and sometimes it gets more complicated than this. For example, we can have something like:
2x + 8 = 16
In this case, we need to have multiple steps to solve for x. First, we minus 8 from both sides:
2x = 8
Then we divide by 2:
x = 4
So, we know x = 4. In conclusion, x is a variable that is hiding a value, and you will need to either solve or substitute x. Meaning x can be any value.
Hope this Helped!
In ΔNOP,
m
∠
N
=
(
9
x
+
8
)
∘
m∠N=(9x+8)
∘
,
m
∠
O
=
(
4
x
+
13
)
∘
m∠O=(4x+13)
∘
, and
m
∠
P
=
(
2
x
−
6
)
∘
m∠P=(2x−6)
∘
. Find
m
∠
N
.
m∠N
Answer: 15
Step-by-step explanation: In ΔNOP,
m
∠
N
=
(
9
x
+
8
)
∘
m∠N=(9x+8)
∘
,
m
∠
O
=
(
4
x
+
13
)
∘
m∠O=(4x+13)
∘
, and
m
∠
P
=
(
2
x
−
6
)
∘
m∠P=(2x−6)
∘
. Find
m
∠
N
.
m∠N
Select the interval where the graph f is positive
Answer: A
Step-by-step explanation:
Based on the graph, we know that it is positive if it is above the x-axis. It is also indicated by the positive labels.
A: correct
Looking at choice A, it says the interval is from -2<x<-1. This means we have to find x=-2 and x=-1. On the graph, that interval is above the x-axis, so it is positive.
B: incorrect
Looking at choice B, it says the interval is from -1<x<0. This means we have to find x=-1 and x=1. On the graph, that interval is below the x-axis, so it is negative.
C: incorrect
Looking at choice C, it says the interval is from 0<x<1. This means we have to find x=0 and x=1. On the graph, that interval is below the x-axis, so it is negative.
Therefore, A is the correct answer.
There are two chords AB and CD in a circle. |AB| = 10 cm, |CD| 10 cm, |CD| = 8 cm and the radius of the circle is 12 cm. What is the distance of each chord from the centre of the circle?
The distance of each chord from the centre of the circle are √119 and √128 respectively .
Given,
Radius of a circle = 12 cm
AB = 10 cm
CD = 8 cm
Now, we get
BG = 10/2 = 5 cm
HD = 8/2 = 4 cm
(A perpendicular coming from the centre, which is not a diameter, bisects the chord.)
Now,
BE = ED = EF = 12 cm (All radii of a circle are equal.)
Now, by Pythagoras Theorem, we get
H² = P² + B²
For GE —
(BE)² = (GE)² + (BG)²
or, (12)² = GE² + (5)²
or, 144 = GE² + 25
or, GE² = 144 — 25
or, GE² = 119
or GE = ±√119
or GE = √119 (Since, length cannot be negative.)
For HE —
(DE)² = (HE)² + (HD)²
or, (12)² = HE² + (4)²
or, 144 = HE² + 16
or, HE² = 144 — 16
or, HE² = 128
or, HE = ± √128
or, HE = √128 or 8√2(Since, length cannot be negative.)
Hence , the distance of each chord from the centre of the circle are √119 and √128 respectively .
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