Write the quadratic equation in standard form that corresponds to the graph shown below.
Answers
The Quadratic equation in standard form that corresponds to the given parabola is (x + 1)^2 = 12y.
The quadratic equation in standard form that corresponds to the graph of the parabola passing through the points (2, 0) and (-4, 0), we can use the vertex form of a parabola equation, which is (x - h)^2 = 4a(y - k). the vertex of the parabola. The vertex is the midpoint of the line segment connecting the two given points.
The x-coordinate of the vertex is the average of the x-coordinates of the two points:
(2 + (-4))/2 = -2/2 = -1
The y-coordinate of the vertex is the same as the y-coordinate of both given points:
y = 0
Therefore, the vertex of the parabola is (-1, 0).
Now, let's find the value of 'a', which represents the coefficient in front of the y-term. We know that the distance from the vertex to either of the given points is equal to 'a'. In this case, the distance from the vertex (-1, 0) to either (2, 0) or (-4, 0) is 3 units.
So, 'a' = 3.
Now, we can write the quadratic equation in standard form:
(x - h)^2 = 4a(y - k)
Plugging in the values we found:
(x - (-1))^2 = 4(3)(y - 0)
Simplifying:
(x + 1)^2 = 12y
Therefore, the quadratic equation in standard form that corresponds to the given parabola is (x + 1)^2 = 12y.
To know more about Quadratic equation.
https://brainly.com/question/1214333
#SPJ8
Related Questions
These points are linear. Find the slope.
Answers
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.
\((\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{8 }{2 +4} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4 }{ 3 }\)
Joe works as a welder. He makes $8.50 an hour.
He gets time and a half for overtime(over 40 hours).
Joe worked 45 hours, what is his weekly pay
this week.
Answers
9514 1404 393
Answer:
$403.75
Step-by-step explanation:
Joe worked 45 -40 = 5 hours of overtime this week. "Time and a half" means he will be paid for an additional 5/2 = 2.5 hours, so his gross pay this week is ...
(45 +2.5)($8.50) = $403.75
Farhan has three pieces of rope with lengths of 140cm, 168cm and 210cm. He wishes to cut all the three pieces of ropes into smaller pieces of equal length and that there is no leftover rope. (i) What is the greatest possible length of each of the smaller pieces of rope? How many smaller pieces of rope can he get altogether?
give correct answer
Answers
Answer:
The greatest possible length is 14 cm.
The total number of smaller pieces is 37.
Step-by-step explanation:
The greatest common factor of these three numbers is 14.
Total number of smaller pieces = 10+12+15 = 37
Best Regards!
Find the surface area. Leave your answers in terms of π.A. 229.5π mi²B. 143.2π mi²C. 207.2π mi²D. 542.4π mi²
Answers
The surface area of a cone is found by
SA =π r^2 +π rl where r is the radius and l is the slant height
We know the diameter is 16 so we can find the radius by dividing the diameter in half
r = d/2 = 16/2 = 8
We know the slant height is 17.9
SA = π ( 8) ^2 + π ( 8) 17.9
= 64 π + 143.2π
=207.2π mi^2
GUYS YOU NEED TO SEE THE NEWS THERES A BIG THING ATTACKING NY RN
Answers
Answer:
what????????????????
fast hurry no link no bot please right
Answers
9514 1404 393
Answer:
(d) 972π in³
Step-by-step explanation:
The formula for the volume of a sphere is ...
V = 4/3πr³
The sphere has a diameter of 18 in, so a radius of 9 in. Its volume is ...
V = (4/3)π(9 in)³ = (4/3)729π in³ = 972π in³
The container can hold 972π in³ of water.
Diego is solving this system of equations:
4x + 3y = 10
-4x + 5y = 6
Here is his work:
4x + 3y = 10
-4x + 5y =6
-4x + 5y = 6 +
0 + 8y = 16
y = 2
4x + 3(2) = 10
4x + 6 = 10
4x = 4
x = 1
Answers
The solutions of the equations are x = 1 and y = 2
The system of equations are
4x + 3y = 10
-4x + 5y = 6
Here we have to use the elimination method. Eliminate the x term and find the value of y term
Add both equation
3y + 5y = 10 +6
Add the like terms
8y = 16
y = 16 / 8
Divide the terms
y = 2
Substitute the value of x in the first equation
4x + 3y = 10
4x + 3×2 = 10
Multiply the terms
4x + 6 = 10
4x = 10 - 6
4x = 4
x = 4 / 4
Divide the terms
x = 1
Hence, the solutions of the equations are x = 1 and y = 2
Learn more about elimination method here
brainly.com/question/14619835
#SPJ1
Graph slope =-3 y-intercept=4
Answers
Answer:
Step-by-step explanation:
slope intercept: y = mx + b
where m is the slope and b is the y-intercept
Equation: y = -3x + 4
Since y-intercept is given, then we have the first point of the line as (0,4)
Let's find the value of x when y is 0
y = -3x + 4
0 = -3x + 4
3x = 4
x = 4/3
(4/3,0) ---second point
Since there are two points/coordinates already then we can now plot/graph.
Pls help step by step, loves <3 (special right triangles)
Answers
Answer:
x ≈ 30,37
y ≈ 29,00
Step-by-step explanation:
Use trigonometry:
\( \sin(38°) = \frac{9}{x} \)
Now, use the property of the proportion to find x:
\(x = \frac{9}{ \sin(38°) } ≈30.37\)
Do the same thing to find y:
\( \tan(38°) = \frac{9}{y} \)
\(y = \frac{9}{ \tan(38°) } ≈29.00\)
is 49.220 bigger or 49.220?
is 10.001 bigger or 10.01?
is 20.10 bigger or 20.1?
Answers
Answer:
Step-by-step explanation:
49.220 = 49.220
10.001 < 10.01
20.10 = 20.1
49.220 = 49.220
10.001 < 10.01
20.10 = 20.1
On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞).
Answers
The statement that is true about the function is:
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).What is the function of a graph?A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
The minimum value of the curve = (1.9, -5.7),
The maximum value = (0, 2)
The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)
The point the function crosses the y-axis (the y-intercept) = (0, 2)
The given points can be plotted using MS Excel, from which we have:
F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5.
Hence, the correct option is A.
To know more about the function of a graph, visit:
https://brainly.com/question/32687137
Help me plz we’ll mark brainliest ONLY if u are correct L
Answers
Answer:
16/24+21/24
Step-by-step explanation:
Hope it helped!!
Answer: turtles
Step-by-step explanation:
In a bag of marbles, 12% were red, 16% were blue, and the rest are white. If the bag has 250 marbles how many were red or blue
Answers
Answer: 70
Step-by-step explanation: First, let's find how many are worth each in numbers. Use this formula:
Part Percent * Whole number / 100
Plug in the numbers:
Red = 12 * 250 / 100
3000/100
= 30 red marbles
Blue = 16* 250 / 100
4000 / 100
= 40 blue marbles
40 + 30 = 70
White = 250 - 70
= 180 white marbles
We can check our answer by adding 12 + 16. That's 28. So by multiplying 250 by 28, we get 7000. 7000 divided by 100 = 70
70 = 70
Therefore, both statements are true
I hope this helped!
For some constant c, the random variable X has probability density function
f(x)=(c(1-x)^9, 0≤x≤1
0, otherwise)
a) Find c.
b) Find P(X>0.6)
Answers
Answer:
b) Find P(X>0.6)
Explanation:
In order to find the product to the unknown variable you have to first solve the equation that has the parenthesis, The reason you should first find the parenthesis is because of The Order Of Operations, You have to first do parenthesis to find the unknown variable.
Find the probability that a student walks to school
Q6: The tree diagram below shows the likelihood that it rains or does not rain and whether students wall or do not walk to school.
Find the probability that a student walks to school.
Answers
The probability of walking to school is 7/15
How to determine the probability of walking to school?The tree diagram represents the given parameter
The following parameters are represented on the tree diagram
P(Rain) = 2/5P(Rain and walk) = 1/6P(No rain) = 3/5P(No rain and walk) = 2/3The probability that a student walks to school is then calculated as
P = P(Rain) x P(Rain and walk) + P(No rain) x P(No rain and walk)
Substitute the known values in the above equation
So, we have
P = 2/5 x1/6 + 3/5 x 2/3
Evaluate the products
P = 1/15 + 6/15
Evaluate the sum
P = 7/15
Hence, the probability is 7/15
Read more about probability at
brainly.com/question/24756209
#SPJ4
Can you help Turn this equation to the other equation
3x-y=-27
x+2y=16
y=_x+_
y=_x+_
Answers
Answer:
y=3x+27
2y= x+16or,
or,y= x+16/2
Function c
is defined by the equation c(n)=50+4n
. It gives the monthly cost, in dollars, of visiting a gym as a function of the number of visits, n
.
True or False? The inverse function is as follows:
n=(c(n) − 50)×4
Responses
Answers
Answer:
False
Step-by-step explanation:
1. The inverse function should have c(n) isolated
2. When finding the inverse of a function, the variables c(n) and n are interchanged (and then c(n) is isolated).
It would look like this --->c(n)=50+4n--->n=50+4(c(n)) ---> c(n)=(n-50)/4
7.
If one United States dollar is worth $6.46 in yen (Chinese currency) in Euro money,
how much is $100 in Yen worth in United States money, to the nearest cent?
Answers
Answer:
$15.48
Explanation:
100 ÷ 6.46 = 15.479876
Here is Takeshi's work determining a third point on the graph of an exponential function, `h(x)`.
Explain why the work is incorrect.
Answers
Answer:
Step-by-step explanation:
Let h(x) = y
The exponentail function is of the form :
\(y = ab^x\)
We have :
\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)
Given points : (4, 9) and (5, 34.2)
We have:
\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)
Writing the equation with x, y and b:
\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)
a = 0.043
b = 3.8
When x = 6, y will be:
\(y = (0.043)(3.8^6)\\\\y = 128.47\)
This is not the y value in the question y = 59.4
Therefore (6, 59.4) does not lie on the graph h(x)
a submarie decends to 1/6 of its maximum depth. Then it decends another 2/3 of its maximum depth. if it is now at 650 feet below sea level, what is it's maximum depth?
Answers
Answer:
975 feet.
Step-by-step explanation:
2/3 = 4/6
650/4 = 162.5
162.5 x 2= 325
650+325 = 975
Lightfoot Inc., a software development firm, has stock outstanding as follows: 20,000 shares of cumulative preferred 2% stock, $20 par, and 25,000 shares of $100 par common. During its first four years of operations, the following amounts were distributed as dividends: first year, $3,000; second year, $5,000; third year, $34,500; fourth year, $71,000.
Answers
The amount of Dividends of $3,000, $5,000, $34,500, and $71,000 were distributed to the 20,000 preferred and 25,000 common shareholders of Lightfoot Inc. over the first four years of operations.
To calculate the dividend per share of the preferred and common stock of Lightfoot Inc., the total amount of dividends paid out over the first four years must first be determined. This can be done by adding the given amounts of $3,000, $5,000, $34,500, and $71,000 to get a total of $113,500. To find the dividend per share for the preferred stock, the total dividend is divided by the number of shares (20,000) which gives a dividend per share of $5.68. To find the dividend per share for the common stock, the total dividend is divided by the number of shares (25,000) which gives a dividend per share of $4.54.
Learn more about amount here
https://brainly.com/question/8082054
#SPJ1
Given a sphere with a diameter of 6.2cm, find its volume to the nearest whole
Answers
Answer:
the answer is 12
Step-by-step explanation:
d=2r=2*6.2=12.4
A 50 inch board is to be cut into three pieces so that the second piece is 4 times as long as the first piece and the third piece is 5 tumes as long as the first piece. If x represents the length of the first piece, find the length of all three pieces.
Answers
Answer:
x = 5
Step-by-step explanation:
Piece 1 has length 5 inches
Piece 2 has length 20 inches
Piece 3 has length 25 inches
total length:50 inches
You are given the great circle of a sphere is a length of 25 miles. What is the volume of the sphere
Answers
The volume of the sphere is approximately 3431.82 cubic miles.
To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.
In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.
C = 2πr
60 = 2πr
Divide both sides of the equation by 2π:
r = 60 / (2π)
r = 30 / π
Now that we have the radius, we can use the formula for the volume of a sphere:
V = (4/3)πr³
V = (4/3)π(30/π)³
V = (4/3)π(27000/π³)
V = (4/3)π(27000/π³)
V = (4/3)π(27000/π³)
V = (4/3)(27000/π²)
V = (4/3)(27000/9.87) (approximating π to 3.14)
V ≈ 3431.82 cubic miles
Therefore, the volume of the sphere is approximately 3431.82 cubic miles.
for such more question on volume
https://brainly.com/question/6204273
#SPJ8
Question
You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?
What is the measure in radians for the central angle of a circle whose radius is 8 cm and intercepted arc length is 5.6 cm? Enter your answer as a decimal in the box. radians
Answers
The measure in radians for the central angle is approximately 0.7 radians.
To find the measure in radians for the central angle of a circle, we can use the formula:
θ = s / r
where θ is the central angle in radians, s is the intercepted arc length, and r is the radius of the circle.
In this case, the radius is given as 8 cm and the intercepted arc length is 5.6 cm.
Plugging these values into the formula, we have:
θ = 5.6 cm / 8 cm
Simplifying the expression:
θ = 0.7
We may use the following formula to get the centre angle of a circle's measurement in radians:
= s / r
s is the length of the intercepted arc, r is the circle's radius and is the centre angle in radians.
The intercepted arc length in this instance is 5.6 cm, while the radius is specified as 8 cm.
When these values are plugged into the formula, we get:
θ = 5.6 cm / 8 cm
Condensing the phrase:
θ = 0.7
For similar questions on radians
https://brainly.com/question/29058626
#SPJ11
Can someone help me find the solution for X? Please leave an explanation for me so I can do questions like this by myself!
Also, can you leave an equation that solves for x..?
Answers
The value of angle x in the straight line is 41 degrees.
How to find the angle x?The sum of angles on a straight line is 180 degrees. In other words, angles on a straight line add up to 180°. Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line.
Therefore, let's find the angles x.
Using sum of angles on a straight line,
x + 139 = 180
subtract 139 from both sides of the equation
x + 139 - 139 = 180 - 139
Hence,
x = 41 degrees
learn more angles here: https://brainly.com/question/29161085
#SPJ1
Black & Decker Manufacturing sold a set of saws to True Value Hardware. The list price was $3,800. Black & Decker offered a chain discount of 8/3/1. The net price of the saws is:
Answers
The net price of the saws that Black & Decker Manufacturing sold to True Value Hardware on a chain discount of 8/3/1 is $3,357.21.
What is a chain discount?A chain discount refers to a type of discount offered to customers, which is sequentially applied to the list price to arrive at the net price.
Chain discounts involve a series of trade discounts applied in sequence.
Data and Calculations:List price = $3,800
Chain discount = 8/3/1
First net price = $3,496 ($3,800 x 1 - 8%)
Second net price = $3,391.12 ($3,496 x 1 - 3%)
Third net price = $3,357.21 ($3,391.12 x 1 - 1%)
Thus, the net price based on a chain discount of 8/3/1 is $3,357.21.
Learn more about chain discounts at https://brainly.com/question/1515915
#SPJ1
For the function f(x) = x^1/3/3 find f^-1(x)
Answers
Answer:
To get f⁻¹(x), write f(x) = y = x^(1/3)/3, exchange x and y, so x = y^(1/3)/3, then y = (3x)³, this is just the f⁻¹(x) = (3x)³.
Step-by-step explanation:
Find an ordered pair (x,y) that is a solution to the equation x-2y=2
Answers
Answer:
An ordered pair is \((4,1)\)
Step-by-step explanation:
Rearranging the equation to isolate the y term and then make y the subject of the formula:
\(x - 2y - 2 = 0\)
\(2y = x - 2\)
The coefficient of y has to be '+1':
\(\frac{2}{2}y = \frac{1}{2}(x - 2)\)
\(y = \frac{1}{2}x -\frac{2}{2}\)
\(y = \frac{1}{2}x -1\)
This is the slope-intercept form of the equation.
Substitute any value of x in the above equation to determine the corresponding value of y. Together the x and y form an ordered pair.
For example:
For x = 4:
\(y = \frac{1}{2}\)(4) \(-1\)
\(= \frac{4}{2} - 1\)
\(= 2 - 1\)
y = 1
∴ An ordered pair = \((4, 1)\)
How could Marc mathematically try to prove that he hit the ball near the top of the tower?While on the golf course last weekend Marc hit into the rough, landing the ball behind a tall tree. To get out of the scenario, his best option was to hit the ball high enough so it goes over the tree and hopefully comes down in the fairway for his next shot. So with a mighty swing, he hit the ball into the air and was surprised to see it hit near the top of a 300 foot tall tower that he had not noticed. The formula for this shot is h(x) = -16xsquared + 120x , where h is the height of the ball and x is the number of seconds the ball is in the air. How could Marc mathematically try to prove that he hit the ball near the top of the tower?While on the golf course last weekend Marc hit into the rough, landing the ball behind a tall tree. To get out of the scenario, his best option was to hit the ball high enough so it goes over the tree and hopefully comes down in the fairway for his next shot. So with a mighty swing, he hit the ball into the air and was surprised to see it hit near the top of a 300 foot tall tower that he had not noticed. The formula for this shot is h(x) = -16xsquared + 120x , where h is the height of the ball and x is the number of seconds the ball is in the air. How could Marc mathematically try to prove that he hit the ball near the top of the tower?
Answers
Answer:
To mathematically prove that Marc hit the ball near the top of the tower, he could use the equation h(x) = -16x^2 + 120x, where h is the height of the ball and x is the number of seconds the ball is in the air.
First, Marc would need to determine the maximum height the ball reached during its flight. This can be found by using the vertex formula, which is x = -b/2a. In this case, a = -16 and b = 120, so x = -120/(2*-16) = 3.75 seconds.
Next, Marc can substitute this value back into the original equation to find the maximum height the ball reached. h(3.75) = -16(3.75)^2 + 120(3.75) = 135 feet.
Since the tower is 300 feet tall, Marc could conclude that if the ball hit near the top of the tower, it would have reached a height close to 300 feet. Since the ball reached a maximum height of 135 feet, it is unlikely that it hit the top of the tower.
However, this calculation assumes that the tower is directly in line with Marc's shot and that the ball did not have any horizontal movement. In reality, the tower could have been to the left or right of the shot, and the ball could have had some horizontal movement, which would affect its height at impact. Therefore, this calculation can only provide a rough estimate and cannot definitively prove whether or not the ball hit near the top of the tower.