Answers
The equation of the parabola in vertex form is y = - (1 / 4) · x².
How to derive the equation of the parabola
In this problem we find a parabola whose axis of symmetry is on the y-axis and the directrix is above the parabola, which means that the least distance between the vertex and the directrix is negative. The equation of the parabola in vertex form is described below:
4 · p · (y - k) = (x - h)²
Where:
p - Least distance of the vertex from the directrix.(h, k) - Coordinates of the vertex.If we know that p = - 1 and (h, k) = (0, 0), then the equation of this parabola is:
4 · (- 1) · y = x²
- 4 · y = x²
y = - (1 / 4) · x²
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Related Questions
From 100 yards away, a marksman hit 9/10 of the targets last year.
Answers
From 100 yards away, a marksman hit probability of It means 90% of the targets were hit .
What is the probability?
Probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.Total no of targets = 10
number of targets hit = 9
= 100/10 = 10
= 10 * 9 ⇒ 90
It means 90% of the targets were hit .
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An earthquake of magnitude 9.1 occurred in 2004 in the Indian Ocean near Indonesia. It was about 74,900 times as strong as the greatest earthquake ever to hit Texas. Find the magnitude of the Texas earthquake. (Remember that an increase of 1.0 on the Richter scale means an earthquake is 30 times stronger.)
b. How does the solution of your equation help you find the magnitude?
Answers
The Magnitude of earthquake that hit Texas is 5.8; With the help of the logarithmic equation so found, we can get the value of M, with which we can get the magnitude of the Texas earthquake.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Given:
Magnitude of earthquake that hit Indian Ocean = 9.1 [tex]I_1[/tex] = Intensity of weaker earthquake[tex]I_2[/tex] = Intensity of greater earthquake.To find: Magnitude of earthquake that hit Texas.
Finding:
From the given, [tex]\frac{I_2}{I_1}[/tex] gives the ratio of the greater earthquake's intensity to the weaker earthquake's intensity.This ratio, when written as an exponential equation, equals [tex]30^M[/tex] where M is the increase in magnitude difference:=> [tex]\frac{I_2}{I_1}[/tex] = [tex]30^M[/tex]
For [tex]\frac{I_2}{I_1}[/tex] = 74900, the above expression becomes:
=> 74900 = [tex]30^M[/tex]
Taking logarithm on both sides, with base 10 gives:
=> log (74900) = log ([tex]30^M[/tex])
As [tex]log_b(a)^m = m(log_b(a))[/tex],
=> log (74900) = M ( log (30))
=> [tex]\frac{log(74900)}{log (30)}[/tex] = M
=> M ≈ 3.3, i.e., the increase in magnitude difference is approximately 3.3.
Thus, the magnitude of the earthquake that hit Texas = 9.1 - 3.3 = 5.8.
The logarithmic equation, in terms of exponents, so formed is: 74900 = [tex]30^M[/tex]. By finding the solution of this equation, we get the value of M, which gives us the value of the increase in the magnitude of the earthquakes.With the help of this value so found, we can find the required value of the magnitude of earthquake in Texas, as we already know that of Indian Ocean, by basic algebra.To learn more about logarithms, refer to the link: brainly.com/question/25710806
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A store is offering a 15% discount on all items. Also, employees get a 20 % employee discount. Write composite functions
a. to model taking the 15 % discount and then the 20 % discount.
Answers
The composite discount = 32%
The store offers 15% which on all items and employees get a 20% discount.
The composite discount formula is:
-x - y + ( x ×y / 100)
Here x = 15% and y = 20%
So by putting the value of x and y we get
- 15 - 20 + ( 15 × 20 /100)
- 15 -20 + 3
- 35+ 3
-32
Therefore we get the composite discount i.e., 32%
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Question Write a quadratic function in standard form whose graph has the given characteristics. vertex: (1,\ 9) ; passes through (4,\ 6)
Answers
The quadratic function of graph given characteristics vertex(1,\9); passes through (4,\6) is y=1/3x2+2/3x+26/3.
A quadratic function is a polynomial function with one or more variables where the highest exponent of the variable is two. Due to the fact that the biggest degree term in a quadratic function is of second degree, it is sometimes referred to as the polynomial of degree 2. There must be a quadratic function with at least one second-degree term. It performs algebraic operations.
Assum:y=ax2+bx+c
Point (1,9)(4,6) into it:{9=a+b+c/6=16a+4b+c} (point 1and 2)
Therefore, vertex(1,9) –b/2a=1→-b=2a
Point 3 into 1 and 2={9=-a+c/b=8a+c}
a=1/3, b=2/3, c=26/3
y=1/3x2+2/3x+26/3
For: y=ax2+bx+c
The graph intersects the x axis at x1 and x2,
X1= -b+√b2-4ac/2a , X2= -b-√b2-4ac/2a
The x-coordinate of the vertex must be in the middle of x1 and x2.
Assume the x-coordinate of the vertex as x
So : x=x1+x2/2 = -b+√b2-4ac/2a + -b-√b2-4ac/2a / 2 = -b/2a
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Evaluate each logarithm.
log 10,000
Answers
The value of the expression log 10,000 is 4.
The logarithmic function is the inverse of the exponential function. This means that the logarithm of a given number, say x, is the exponent to which another fixed number that is the base b, must be raised, so as to produce that number x.
Log a to the base b can be written as- log a/ log b.
Moreover, log [tex]a^{k}[/tex] = k log a, for all non negative values of a
Here, we are given a logarithmic expression- log 10,000
As the base is not given, we always assume it to be 10.
We can expand this as-
log 10,000 = log 10,000/ log 10
= log [tex]10^{4}[/tex]/ log 10
= 4 log 10/ log 10
= 4
Thus, the value of log 10,000 is 4.
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The length of a rectangle is 4 meters less than twice the width. If the area of the rectangle is 286 square meters, find the Dimensions.
Answers
Answer:
The dimensions of the rectangle are length = 22 meters and width = 13 meters.
Step-by-step explanation:
It is given that the length of a rectangle is 4 meters less than twice the width and if the area of the rectangle is 286 square meters we need to calculate the dimensions.
Firstly, let us look at the dimensions of the rectangle;
=> Let 'l' be the length and 'b' be the width of the rectangle.
Now, let us look at the area of a rectangle;
=> l × b
So, we get an equation from the above condition;
=> l = 2b - 4
Now, the area of the rectangle is given that is 286 square meters;
=> A = 286 sq. m.
Using the above-mentioned formula for the area of the rectangle we get;
=> A = l × b
=> 286 = (2b - 4) × b
=> 286 = 2b² - 4b
=> 2b² - 4b - 286 = 0
After solving it further we get;
=> 2b² - 4b - 286 = 0
=> b² - 2b - 143 = 0
=> b² - 13b + 11b - 143 = 0
=> (b - 13) + (b + 11) = 0
Now, after equating both the sides we get;
=> (b - 13) = 0
=> b = 13
and
=> (b + 11) = 0
=> b = -11
But, b = -11 is not possible so, the width of the rectangle is 13 meters.
And the length of the rectangle would be,
=> l = 2b - 4
=> l = 2 × 13 - 4
=> l = 22
Therefore, the dimensions of the rectangle are length = 22 meters and width = 13 meters.
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What is the slope of the line that passes through the points (8, 0) and (-4, -8)
Answers
The slope of the line that passes through (8, 0) and (-4, -8) is calculated as: m = 2/3.
How to Calculate the Slope of a Line that Passes through two Points?The slope (m) formula is given as:
Slope (m) = change in y/change in x = y2 - y1/x2 - x1.
Given the following points on the line:
(8, 0) = (x1, y1)
(-4, -8) = (x2, y2)
Plug in the values into the slope formula, x = y2 - y1/x2 - x1:
Slope (m) of the line = (-8 - 0) / (-4 - 8)
Slope (m) of the line = (-8) / (-12)
Slope (m) of the line = 2/3
Thus, the slope of the line that passes through (8, 0) and (-4, -8) is calculated as: m = 2/3.
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Solve each equation.
log 3 x=4
Answers
After solving the given equation log₃x = 4, the value of x = 81.
What is an equation?A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.So,
Given: log₃x = 4Then,
log₃x = 4logbx = n ⇔ x = bⁿlog₃x = 4 ⇔ 3⁴ = 81Therefore, after solving the given equation log₃x = 4, the value of x = 81.
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Leah has five older brothers and one identical twin sister.
Identify all the logical conclusions regarding Leah's siblings.
There are two girls in Leah's family.
There is one girl in Leah's family.
The firstborn child in Leah's family is a boy.
There are seven children in Leah's family.
Leah is the firstborn child in her family.
Leah and her sister look alike.
There are five boys in Leah's family.
There are six children in Leah's family.
Answers
the firstborn child in her family is a boy
her and her sister are identical
there are 5 boys
there are 7 children
A quadrilateral has four angles each angle is 90° Write down a mathematical name
Answers
Answer: A quadrilateral that has 4 sides is known as a rectangle.
Answer:
Step-by-step explanation:
This is either a rectangle or a square.
(A square is a special type of rectangle, with 4 equal sides).
Very confused how to do this please help
Answers
Part F
PLEASE HELP!!!
Complete the table to find the rule for the reflection, the coordinates of trapezoid PQRS, and the coordinates of the reflected image, trapezoid P′Q′R′S′.
Answers
The new coordinates after transformation of the original coordinates using the transformation rule (x, y) → (x, -y) are;
P(6, -4) → P'(6, 4)
Q(2, -2) → Q(2, 2)
R(2, -6) → R(2, 6)
S(6, -6) → S(6, 6)
What are the coordinates of the reflection transformation?The given reflection transformation of (x, y) → (x, -y) simply means a reflection across the x-axis.
Thus, the new coordinates after undergoing the above transformation are;
P(6, -4) → P'(6, 4)
Q(2, -2) → Q(2, 2)
R(2, -6) → R(2, 6)
S(6, -6) → S(6, 6)
Thus, we conclude that the new coordinates after transformation of the original coordinates using the transformation rule (x, y) → (x, -y) are;
P(6, -4) → P'(6, 4)
Q(2, -2) → Q(2, 2)
R(2, -6) → R(2, 6)
S(6, -6) → S(6, 6)
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Will give Branliest ASAP PLEASE
Answers
Answer: Evaluate x[tex]\frac{8}{3}[/tex]
DIFFERENTIATE W.R.T. X
[tex]\frac{8x\frac{5}{3} }{3}[/tex]
Step-by-step explanation:
What is the next number in this pattern? 1, 2, 4, 5, 8, 9, 13, 14, ... A) 15 B) 18 C) 19 D) 20
Answers
it’s pattern is +1, +2, +1, +3, +1, +4, +1 so the next would be +5
14 + 5 = 19
Help with basic algebra problem! Show the steps please!!!! Will give brainliest!!
Answers
Answer:
-18k
Step-by-step explanation:
-> -8k+ 10k
-> minus and plus is = minus
-> 8k+10k
-> -18k(ans)
Solve the following linear systems of equations using substitution. y = 3x + 5 y = 2x + 4
Answers
I may be wrong but here how I got this answer.
y = 3x + 5 y = 2x + 4
{ y = 2 x + 4
{3x + 5 y = 2x + 4
{ y = 2 x + 4
{ 3x + 5 y = 2x + 4
then simplify now.
{-2 x + y = 4
{3 x + 5 y = 2x + 4 |
|
|
{ - 2 x + y = 4
{ x + 5y = 4
Multiply 2 by both sides
{-2 x + y = y
{ 2x + 10 y = 8
Sum the equation to eliminate at least one variable
11 y = 12
Divide both sides of the equation by 11
y = 12/11
Substitute the given value of y into the equation -2 x + y = 4
-2 + 12/11 = 4
X = - 16/11 you solve the x and you will get that answer
Use the following information to fill in the blanks. On earth, there are about 1 quadrillion ants and about 8 billion people
Answers
The number of ants that are more than people will be 9800000.
How to illustrate the information?It should be noted that based on the information, it was stated that on earth, there are about 1 quadrillion ants and about 8 billion people.
Therefore, the difference between the values illustrated will be:
= 1 quadrillion - 8 billion
= 1 × 10^15 - 8 × 10^9.
= 9.2 × 10^5
Therefore, the number of ants that are more than people will be 9800000
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Use the following information to fill in the blanks. On earth, there are about 1 quadrillion ants and about 8 billion people.
On Earth, there are about ...... more ants than people.
suppose we have collected the weights of 100 main subjects as a part of a nutrition study. for your weight data we have values ranging from a low of 121 pounds to a high of 263 pounds determine reasonable class intervals for a frequency table
Answers
The reasonable class intervals for a frequency table in between 120-269 with 14 class interval in between is shown .
What is frequency in a table?
Frequency refers to the number of times an event or a value occurs. A frequency table is a table that lists items and shows the number of times the items occur.
Given:
The weights of 100 main subjects as a part of a nutrition study.
The values ranging from a low of 121 pounds to a high of 263 pounds.
According to given question we have
Total span =263 pounds- 121 pounds
=142 pounds
Interval frequency
120-134 4
135-149 14
150-164 16
165-179 28
180-194 17
195-209 8
210-224 7
225-239 6
240-254 2
255-269 3
Therefore, the reasonable class intervals for a frequency table in between 120-269 with 14 class interval in between is shown .
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5.450×10-4 x 3.550×10-7 in scientific notation
Answers
Answer:
[tex]1.93475*10^{-10}[/tex]
Step-by-step explanation:
To multiply the decimal numbers in scientific notation, multiply the decimals and add the powers of the 10.
[tex]\sf 5.45 * 10^{-4}* 3.55*10^{-7}=5.45*3.55 * 10^{(-4)+(-7)}[/tex]
[tex]\sf = 19.3475*10^{-11}[/tex]
Now, write the decimal 19.3475 in scientific notation.
As we have to move the decimal one count towards left, add 1 to the power.
[tex]\sf = 1.93475*10^{-11+1}\\\\ = 1.93475*10^{-10}[/tex]
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Simplify using order of operations. Show all of your work and do ONE operation at a time to receive all possible points
16 divided by 4 multiplied by 2
Answers
—- x2
4
Simplified; 4 x 2
Solution; 4x2, hence the answer 8.
HELP BRAINLEIST TO FIRST PERSON TO GET IT CORRRECT
Answers
The unknown angle in the triangle is as follows:
m∠A = 52°
How to find the angle in a triangle?External angle theorem states that If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
Therefore,
m∠D = m∠A + m∠B
m∠D = 116°
m∠A = (2x)°
m∠B = (x + 38)°
Hence,
116 = 2x + x + 38
116 = 3x + 38
3x = 116 - 38
3x = 78
divide both sides by 3
x = 78 / 3
x = 26
Therefore,
m∠A = 2(26)
m∠A = 52°
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Sketch the graph of the function by first making a table of
values.
[tex]f(x)=-x+3, -3\leq x\leq 3[/tex]
Answers
A pictorial representation or a diagram that represents data or values in an organized manner. For function f(x)=-x+3, -3≤x≤3 the graph is in attachment.
What is Graph?A pictorial representation or a diagram that represents data or values in an organized manner.
Given f(x)=-x+3, -3≤x≤3
It means x values lies from -3 to 3
x -3 -2 -1 0 1 2 3
f(x) 6 5 4 3 2 1 0
By taking the table values we can draw a graph.
Therefore the attached graph is the graph for f(x)=-x+3.-3≤x≤3.
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ANSWEE ASAPP !!! i’ll mark u brainliest
what point do the equations y=2x+1 , y=3x+1 and 5x+1 have in common?
a) 2,0
b) 0,3
c) the origin
d) they have no point in common
e) 0,1
Answers
Answer:
E) (0, 1)
Step-by-step explanation:
We can equalize the first two equations to find a certain point they share. We can then check if the third line also passes through this point if substituting that point's x coordinate into the third line's equation returns the point's correct y value.
[tex]2x + 1 = 3x + 1 \\\to 0 = x[/tex]
Therefore, the point is (0, 1) as substituting [tex]x = 0[/tex] into the first equation returns [tex]y = 1[/tex].
Substituting [tex]x = 0[/tex] into the third equation does also return [tex]y = 1[/tex], therefore, that line passes through the shared point (0, 1).
96x+23=265 solve for x
Answers
ANSWER- X is 2.52083333 or 2.52083 rounded
265-23 is 242. 242 divided into 96 is 2.52083333
(96 x 2.52083333)+23 = 265
This means our X is 2.52083...
HOPE THIS HELPS & GOOD LUCK
Answer:
[tex]\displaystyle \frac{121}{48}[/tex]
or
[tex]2.5208\bar3[/tex]
SolveTo begin, subtract 23 from both sides of the equation. This will move the constants to the right side.
[tex]96x=242[/tex]
Then, divide both sides of the equation by 96. This will isolate the unknown, x, and allow you to solve the equation.
[tex]\displaystyle \frac{96x}{96}=\frac{242}{96}[/tex]
[tex]\displaystyle x=\frac{121}{48}[/tex]
There are two different answers that are equivalent but will depend on what you are looking for.
For a fraction answer, your final answer is [tex]\displaystyle \frac{121}{48}[/tex].
For a decimal answer, your final answer is [tex]2.5208\bar3[/tex].
PLEASE HELP!!!
Find the value of x.
3, 6, X.
x = [ ? ]
Give your answer in simplest form
Answers
The value of x is 12.
What is triangle proportion?
According to the Triangle proportion rule, When a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
In the diagram;
The side with x is a reflexive side of both triangles and as such from triangle proportionality theorem we can say that;
⇒6/x = 3/6
⇒ 36 = 3x
⇒ x = 12
Hence, The value of x is 12.
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PLEASE HELP ME!!!!
ALGEBRA 1.
4 QUESTIONS PLEASE LOOK AT THE PHOTOS
Answers
The equation that shows the different and incorrect relationship is C. b = ✓(a² + c²)
How to illustrate the information?It should be noted that from the information the Pythagoras theorem was illustrated and given as c² = a² + b²
Therefore, the equations that can be gotten from it include b² = c² - a².
It should be noted that the equation that shows the different and incorrect relationship is b = ✓(a² + c²)
In conclusion, the correct option is C.
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solve for x 2x+3(5x-7)=47
Answers
I think the answer is x=4
Answer: x=4
Step-by-step explanation:
2x+3(5x-7)=47
2x+15x-21=47
17x-21=47
+21 +21
17x= 68
17 17
x=4
Sam evaluated the expression x2y for x = 7 and y = 9. He got a value of 49. Which of the following statements is correct?
Answers
Hey there!
x^2 * y
= 7^2 * 9
= 7 * 7 * 9
= 49 * 9
= 441
Thus, the answer should be:
441
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Solve. Check for extraneous solutions. (5 x-4)¹/₂-x=0
Answers
No extraneous solutions to this equation.
The equation is
[tex](5x- 4)^{1/2}[/tex] - x = 0
To find the value of x
[tex](5x- 4)^{1/2}[/tex] = x
Now square on both sides of the equation.
We get
5x - 4 =[tex]x^{2}[/tex]
[tex]x^{2}[/tex] - 5x + 4= 0
[tex]x^{2}[/tex] - 4x - x + 4 =0
x( x -4 ) - 1 ( x - 4) =0
( x- 4 ) ( x - 1)= 0
x = 4, 1
We get the value of x as 4 and 1
Now we have to put the value of x in the equation
First, put 4
[tex](5x - 4)^{1/2}[/tex] -x =0
[tex](5 * 4 - 4)^{1/2}[/tex] - 4= 0
[tex](20 - 4)^{1/2}[/tex] - 4 =0
[tex]16^{1/2}[/tex] - 4 = 0
4-4 =0
0 = 0
Now put 1
[tex](5 * 1 - 4)^{1/2}[/tex] - 1 = 0
[tex](5 -4)^{1/2}[/tex] - 1=0
1 - 1=0
0=0
Hence we get that both the value of x is not an extraneous solution.
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Solve each equation. Check for extraneous solutions.√x+6 +2=x+6
Answers
The solution for the equation √x + 6 + 2 = x + 6 is 4.
An extraneous solution is one that results from the process of addressing the problem but is not a legitimate solution to the problem, such as the answer to an equation.
A formula known as an equation uses the equals sign (=) to express how two expressions are equal.
Consider the equation,
√x + 6 + 2 = x + 6
Subtracting 6 from each side of the equation.
√x + 6 + 2 - 6 = x + 6 - 6
√x + 2 = x
Subtracting 2 from each side.
√x + 2 - 2 = x - 2
√x = x - 2
Squaring the above equation.
( √x )² = ( x - 2 )²
x = x² - 4x + 4
x² - 5x + 4 = 0
x² - x - 4x + 4 = 0
x( x - 1 ) - 4( x - 1 ) = 0
( x - 1 )( x - 4) = 0
x = 1, 4
Checking for extraneous solutions,
x = 1
√x + 6 + 2 = x + 6
√1 + 6 + 2 = 1 + 6
9 ≠ 7
Hence, x = 1 is not a solution.
For, x = 4
√x + 6 + 2 = x + 6
√4 + 6 + 2 = 4 + 6
2 + 6 + 2 = 4 + 6
10 = 10
The solution of equation √x + 6 + 2 = x + 6 is x = 4.
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