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.
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Related Questions
Ayuda operaciones y respuesta es para ahora
Answers
The perimeter of the given window is 48 centimeter.
From the given figure,
Perimeter of window = 2(Length+Breadth)
= 2(10+14)
= 2×24
= 48 centimeter
Perimeter of house = 2(Length+Breadth)
= 2(37+35)
= 2×72
= 144 centimeter
Perimeter of roof = 2(Length+Breadth)
= 2(37+5)
= 2×42
= 84 centimeter
Therefore, the perimeter of the given window is 48 centimeter.
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the value stock in 1940 is $1.25. it’s value grows by 7% each year after 1940. write an equation representing the value of the stock V(t), in dollars, t years after 1940
Answers
This equation represents the value of the stock, V(t), in dollars, t years after 1940, taking into account the 7% annual Growth rate V(t) = $1.25 * (1 + 0.07)^t.
The value of the stock, V(t), in dollars, t years after 1940, we can use an exponential growth equation since the stock's value grows by 7% each year after 1940.
formulate the equation step by step:
1. We know that the initial value of the stock in 1940 is $1.25. This initial value serves as the starting point for our equation.
2.We are given that the value of the stock grows by 7% each year. This means that for every year that passes, the stock's value increases by 7% of its previous value.
3. In mathematical terms, if V(0) represents the initial value in 1940 ($1.25), then the value of the stock after t years can be represented as:
V(t) = V(0) * (1 + r)^t,
where r is the growth rate expressed as a decimal (in this case, 7% = 0.07).
4. Plugging in the given values, our equation becomes:
V(t) = $1.25 * (1 + 0.07)^t.
This equation represents the value of the stock, V(t), in dollars, t years after 1940, taking into account the 7% annual growth rate.
For example, if we wanted to find the value of the stock 10 years after 1940, we would substitute t = 10 into the equation:
V(10) = $1.25 * (1 + 0.07)^10.
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Choose the kind(s) of symmetry in the 2D number. (Select all that apply.)
plane
point
line
none
Answers
Answer:
plane
point
line
Step-by-step explanation:
Based on the options provided, the kinds of symmetry in a 2D number can be:
Plane symmetry: This refers to a symmetry where a figure can be divided into two identical parts by a plane. This symmetry is also known as reflectional symmetry.Point symmetry: This refers to a symmetry where a figure can be rotated 180 degrees around a central point to produce the same figure. This symmetry is also known as rotational symmetry.Line symmetry: This refers to a symmetry where a figure can be divided into two identical parts by a straight line. This symmetry is also known as bilateral symmetry.Therefore, the possible kinds of symmetry in a 2D number can be
plane symmetry,
point symmetry, or
line symmetry.
Change 0.12 to a ratio.
Answers
Answer:
3:25
Step-by-step explanation:
The photo shows how it's solved.
Answer: 3:25
Step-by-step explanation:
Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator
0.12 = 0.12/1
Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.
0.12 x 100
------------ = 12/100
1 x 100
Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)
12 ÷ 4
--------- = 3/25
100 ÷ 4
Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:
3
25 = 3:25
What is the value of x in the systems:
5x + 2y = 3
2x + 3y = -1
Answers
Answer: The value of x = 1 and y = -1
Step-by Step Explanation:
We have 5x + 2y = 3 -----(i)
and 2x + 3y = -1 -----(ii)
By substitution method,
from (i), x = 3-2y/5
Putting the value of x in equation (ii),
we get, 2(3-2y/5) + 3y = -1
6 - 4y/5 + 3y =-1
6 - 4y + 15y = -5
6 - 11y = -5
-11y = -5 - 6
-11y = -11
y = -1
And, x = 3-2(-1)/5
x = 3+2/5
x = 1
Therefore, x=1 and y=−1
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9. PUGS is a parallelogram. The equation of line PU is y = 4x-2. What is the slope of GS?
Answers
The equation of line PU is given as y = 4x - 2. This equation is in slope-intercept form (y = mx + b), where the coefficient of x represents the slope of the line.
In this case, the slope of line PU is 4.
Since the opposite sides of a parallelogram are parallel, the slope of GS will also be 4.
Therefore, the slope of GS is 4.
The function f(x)=√x is shown on the graph.
4
3+
2+
--5-4-3-2-1₁
-2+
-3+
4
1 2 3 4
Which statement is correct?
O The range of the graph is all real numbers less than
or equal to 0.
O The domain of the graph is all real numbers less
than or equal to 0.
O The domain and range of the graph are the same.
O The range of the graph is all real numbers.
Answers
Answer:
The domain and range of the graph are the same
Step-by-step explanation:
The domain and range of the graph are both [tex][0,\infty)[/tex] because you cannot take the square root of a negative number to produce a real result, and you cannot square a real number to get a negative number.
helppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer: $1.50 for every 1 pound
Step-by-step explanation:
If 2 pounds equal to $3.00 divide $3.00 by 2 and you end up with $1.50, you can also keep adding $1.50 to get the other prices.
What is the meaning of "If dom(f) = [tex]X^{n}[/tex], then f is an n-ary function on X"?
Answers
The statement "If dom(f) = Χ, then f is an n-ary functionon X" means that if the domain of the function f is equal to the set X, then f is considered an n-ary function on X.
How is this so?In other words, for each element in X, the function f can take n arguments or inputs to produce aunique output. The term "n-ary" indicates the number of arguments that the function can accept.
A statement in mathematics is a declarative utterance that is either true or untrue but not both. A proposal is anothername for a statement. The main point is that there should be no uncertainty.
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Answer:
The statement "If dom(f) = X, then f is an n-ary function on X" means that if the domain of a function f is equal to the set X, then f is a function that takes n arguments or inputs from the set X, where the value of n depends on the specific function.
Step-by-step explanation:
The statement "If dom(f) = X", then f is an n-ary function on X" means that if the domain of the function f is equal to the set X, then f is an n-ary function on X.
Here's a breakdown of the terms used in the statement:
- dom(f): The domain of a function f refers to the set of all possible input values for the function. It represents the set of values for which the function is defined.
- X: In this context, X represents a set. It could be any set, and it serves as the domain for the function f.
- n-ary function: An n-ary function is a function that takes n arguments or inputs. The value of n represents the number of inputs the function expects.
Therefore, the statement is saying that if the domain of the function f is equal to the set X, then f is an n-ary function on X. It implies that the function f takes n inputs from the set X, where n is determined by the specific function.
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.Mr. Kalada is three times as old as his son. After fifteen years, Mr. Kalada will be twice as old as his son's age at that time. Hence, Mr. Kalada's present age is
Answers
Answer:
Mr Kalada's present age is 45 years old
Step-by-step explanation:
P(-1; -1) S(-3; -7) Q(4; 2) R(7; -5) Determine (correct to one decimal place): 3.2 3.1 the acute angle between QR and the x-axis the angle of inclination of PQ POR 3.3 3.4 the angle of inclination of SP 3.5 SPR 3.6 PSR.
Answers
1. Acute angle between QR and the x-axis:
The angle between QR and the x-axis can be found by calculating the arctan of the slope of QR. The slope (m) can be found using the formula: m = (y2 - y1) / (x2 - x1).
Given points Q(4, 2) and R(7, -5):
m(QR) = (-5 - 2) / (7 - 4) = -7/3
Using the arctan function, we can find the acute angle (A1):
A1 = arctan(-7/3) ≈ -68.2 degrees
2. Angle of inclination of PQ:
The angle of inclination of PQ can be found using the same method as above with points P(-1, -1) and Q(4, 2):
m(PQ) = (2 - (-1)) / (4 - (-1)) = 3/5
The angle of inclination (A2) can be found by taking the arctan of the slope:
A2 = arctan(3/5) ≈ 30.96 degrees
3. Angle of inclination of POR:
The angle of inclination of POR can be found using points P(-1, -1) and R(7, -5):
m(POR) = (-5 - (-1)) / (7 - (-1)) = -6/8 = -3/4 = -0.75
The angle of inclination (A3) can be found using the arctan function:
A3 = arctan(-0.75) ≈ -36.87 degrees
4. Angle of inclination of SP:
To find the angle of inclination of SP, we can use points S(-3, -7) and P(-1, -1):
m(SP) = (-1 - (-7)) / (-1 - (-3)) = 6/2 = 3
The angle of inclination (A4) can be found using the arctan function:
A4 = arctan(3) ≈ 71.57 degrees
5. Angle SPR:
To find angle SPR, we can use the Law of Cosines. Using the distance formula, we can find the lengths of sides SP, SR, and PR. Let's denote SP as a, SR as b, and PR as c:
a = sqrt((-3 - (-1))^2 + (-7 - (-1))^2) = sqrt(4^2 + 6^2) = sqrt(52) ≈ 7.21
b = sqrt((-3 - 7)^2 + (-7 - (-5))^2) = sqrt(10^2 + 2^2) = sqrt(104) ≈ 10.2
c = sqrt((-1 - 7)^2 + (-1 - (-5))^2) = sqrt((-8)^2 + 4^2) = sqrt(80) ≈ 8.94
Now we can apply the Law of Cosines to find the angle SPR (A5):
cos(A5) = (a^2 + b^2 - c^2) / (2ab)
A5 = arccos((7.21^2 + 10.2^2 - 8.94^2) / (2 * 7.21 * 10.2)) ≈ 42.1 degrees
6. Angle PSR:
To find angle PSR, we can subtract the angle SPR (A5) from the angle of inclination of SP (A
Inputs: People at concession stand Outputs: Cost of their order
this relation a function?
it a constant function?
it a 1-1 function?
Answers
People at the concession stand as input Cost of their order's output.
(1) The relation in question is a function.
(II) This function is not constant. (Each category of concession has a different order cost.)
Not a 1-1 function (iii). (Several persons arrived seeking the same sort of concession. So they all pay the same price for their order.)
A function describes the relationship between patrons' inputs at the concession stand and the cost of their order as an output. A function is a relationship between a set of possible inputs and outputs, where each input is associated to exactly one output.
The quantity of patrons at the concession stand serves as the input in this scenario, while the cost of their order serves as the output.
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Suppose that the volume, V,
of a right circular cylinder is
1280 cubic centimeters and
the radius of its base is
8 centimeters. What is the
height of the cylinder?
D
Answers
Answer:
[tex]\huge\boxed{\sf h \approx 6.4\ cm}[/tex]
Step-by-step explanation:
Given data:Volume = v = 1280 cm³
Radius = r = 8 cm
π = 3.14
Required:Height = h = ?
Formula:V = πr²h
Solution:Put the given data in the above formula.
Finding height of cylinder.
1280 = (3.14)(8)²(h)
1280 = (3.14)(64)(h)
1280 = 200.96 (h)
Divide both sides by 200.961280 / 200.86 = h
h ≈ 6.4 cm[tex]\rule[225]{225}{2}[/tex]
how much time will it take to get to New Orleans by boat from Houston, Texas
Answers
Tom's estimated travel time is approximately 13.6 hours.
Based on the given scenario, Tom is traveling a distance of approximately 340 nautical miles from Houston to New Orleans by boat. He will be using a medium-sized recreational boat with an average speed of 25 miles per hour.
To estimate the time it will take for his journey, we can use the formula:
Time = Distance / Speed
Substituting the values, we have:
Time = 340 miles / 25 miles per hour
Calculating the division, we find that Tom's estimated travel time is approximately 13.6 hours.
However, it is important to note that this estimate assumes a continuous journey without considering other factors that may affect the travel time. Various elements can impact the actual duration, such as weather conditions, water currents, navigational challenges, refueling stops, and any necessary rest breaks.
Additionally, it is essential for Tom to adhere to all boating regulations and safety guidelines to ensure a smooth and secure voyage.
To obtain a more accurate estimate, Tom should consult local boating authorities, marinas, or experienced sailors familiar with the route.
They can provide valuable insights into the specific conditions and offer guidance on potential challenges that may affect the travel time. Planning for additional buffer time is also recommended to account for unforeseen circumstances and to prioritize safety during the journey.
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The complete question may be like:
Tom plans to travel by boat from Houston, Texas, to New Orleans, Louisiana. He wants to estimate the time it will take for his journey. The distance between the two cities by water is approximately 340 nautical miles. Tom will be traveling on a medium-sized recreational boat that has an average speed of 25 miles per hour. Considering normal weather conditions and assuming a continuous journey, how long will it take Tom to reach New Orleans?
Please provide an answer based on this scenario, taking into account the distance, average speed, and any other relevant factors.
in the histogram above I'm which interval does most of the data lie
Answers
Answer: The Mode
Step-by-step explanation:
The mode is the data value that occurs the most often in a data set
How mant times does 9 go into 18
Answers
Answer:
2 times, with a remainder of 0.
Step-by-step explanation:
If you had 2 friends and you had to divide 18 between both you would get 9. each with no left over
the region in the first quadrant enclosed by the curves y=0, x=2, x=5 and y=1/sqrt(1+x) is rotated about the x-axis. The volume of the solid generated is A. πIn(2) B. πIn(3/4) C. πIn(10) D. πIn(5) E. πIn(4/3)
Answers
The volume of the solid generated by rotating the region enclosed by the curves y=0, x=2, x=5, and [tex]y=1/\sqrt(1+x)[/tex] about the x-axis is πln(2),
(option A).
To find the volume of the solid generated by rotating the region enclosed by the curves y=0, x=2, x=5, and[tex]y=1/\sqrt(1+x)[/tex] about the x-axis, we need to use the formula for the volume of a solid of revolution.
The formula is ∫[a,b] [tex]π(f(x))^2dx[/tex], where a and b are the limits of integration and f(x) is the function that describes the distance between the axis of revolution and the curve being rotated.
In this case, we need to use the function f(x) = 1/sqrt(1+x), since this function describes the distance between the x-axis and the curve being rotated. The limits of integration are from x=2 to x=5, since these are the values of x that define the region being rotated.
Using the formula, we can set up the integral as follows:
[tex]∫[2,5] π(1/\sqrt(1+x))^2dx[/tex]
= π∫[2,5] 1/(1+x) dx
= π[ln(1+x)]|[2,5]
= π[ln(6) - ln(3)]
= πln(2) (option-A)
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Find the missing angle and side measures of Delta*ABC , given that
m angle A = 50 deg , m angle C = 90 deg , and CB = 16
Answers
The missing angle is <B= 40 degree and missing side length is AB = 12.25 and AC = 19.068.
To find the missing angle and side measures of ΔABC, we can use the properties of a triangle.
Given:
∠A = 50°
∠C = 90°
CB = 16
We can start by finding the measure of ∠B:
∠A + ∠B + ∠C = 180° (Sum of angles in a triangle)
50° + ∠B + 90° = 180°
∠B + 140° = 180°
∠B = 180° - 140°
∠B = 40°
Now, using Sine law
CB/ sin A = AB / sin C
16 / sin 50 = AB / sin 90
16 / 0.766044 = AB
AB = 12.25
Again 12.25 = AC/ sin B
12.25 = AC / sin 40
AC = 19.068
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
area of A = πr² = π7² = 153.9 m²
area of B = πr² = π9² = 254.5 m²
What is the area of a trapezoid with bases that are 7 meters and 10 meters in length and a height of 12 meters? 42 m2 60 m2 102 m2 204 m2
Answers
A = (b1 + b2) * h / 2
where b1 and b2 are the lengths of the two bases, and h is the height.
Plugging in the values given in the problem, we get:
A = (7 + 10) * 12 / 2
= 17 * 6
= 102
Therefore, the area of the trapezoid is 102 square meters. Answer: 102 m2.
(-20,13) (16,15)
Can some find the slop for this question
Answers
Slope (m) = (y2 - y1) / (x2 - x1)
Given the points (-20, 13) and (16, 15), we can assign the coordinates as follows:
x1 = -20, y1 = 13
x2 = 16, y2 = 15
Now, we can substitute these values into the slope formula:
Slope (m) = (15 - 13) / (16 - (-20))
= 2 / 36
= 1 / 18
Therefore, the slope of the line passing through the points (-20, 13) and (16, 15) is 1/18.
El valor de la asintota vertical
Answers
The vertical asymptote of the function are x = ±1/2
Given that we need to determine what is value of the vertical asymptote of the function =
(2x + 1) / (4x²-1)
To find the vertical asymptote of the function f(x) = (2x + 1) / (4x² - 1), we need to determine the values of x for which the denominator becomes zero.
This is because division by zero is undefined, and the function may have vertical asymptotes at those points.
The denominator of the function is 4x² - 1.
To find the values of x that make the denominator zero, we can set it equal to zero and solve for x:
4x² - 1 = 0
Adding 1 to both sides:
4x² = 1
Dividing both sides by 4:
x² = 1/4
Taking the square root of both sides:
x = ±√(1/4)
Simplifying further, we get:
x = ±1/2
Therefore, the values of x that make the denominator zero are x = -1/2 and x = 1/2. These are the vertical asymptotes of the function.
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Translation =
What is value of the vertical asymptote of the function =
(2x + 1) / (4x²-1)
These shapes are similar.
Find X.
X
9
5
27
15
21
Answers
Answer:
15
Step-by-step explanation:
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 graph is [tex]f(x) = (-4/9)(x + 2)^2 + 4[/tex]
To determine the quadratic equation in standard form that corresponds to the given graph, we need to identify the key features of the parabola. From the graph, we can see that the parabola opens upwards and intersects the y-axis at the point (0, c). We can also observe that the vertex of the parabola lies at the point (h, k).
The standard form of a quadratic equation is given as follows:
[tex]f(x) = a(x - h)^2 + k[/tex]
Where (h, k) represents the coordinates of the vertex, and 'a' is a constant that determines the shape and direction of the parabola.
Looking at the graph, we can determine the vertex by identifying the x-coordinate where the parabola reaches its highest or lowest point. Let's assume the vertex is located at the point (h, k).
From the graph, it appears that the vertex lies at (-2, 4). Therefore, we have h = -2 and k = 4.
Now we can rewrite the equation as:
[tex]f(x) = a(x + 2)^2 + 4[/tex]
Next, we need to determine the value of 'a'. To do this, we can use another point on the graph. Let's consider the point (1, 0).
Plugging in the coordinates (1, 0) into the equation, we get:
[tex]0 = a(1 + 2)^2 + 4[/tex]
0 = 9a + 4
9a = -4
a = -4/9
Now we have the value of 'a'. Substituting it back into the equation, we get:
[tex]f(x) = (-4/9)(x + 2)^2 + 4[/tex]
Thus, the quadratic equation in standard form that corresponds to the given graph is:
[tex]f(x) = (-4/9)(x + 2)^2 + 4[/tex]
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The value of x in the given right triangle HJK include the following: C. 10.
What is a 30-60-90 triangle?In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):
Hypotenuse, x = 5 × 2
Hypotenuse, x = 10.
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Factor each expressions using the greatest common factor.
1:3x + 6
2:4x-8
4:2x-4
7:9x + 18
5: 6x + 12
8: 8x - 16
3: 5x + 10
6:7x-14
Answers
1. 3x + 6 = 3(x + 2)
2. 4x - 8 = 4(x - 2)
3. 5x + 10 = 5(x + 2)
4. 2x - 4 = 2(x - 2)
5. 6x + 12 = 6(x + 2)
6. 7x - 14 = 7(x - 2)
7. 9x + 18 = 9(x + 2)
8. 8x - 16 = 8(x - 2)
Therefore, the factored expressions are:
1. 3(x + 2)
2. 4(x - 2)
3. 5(x + 2)
4. 2(x - 2)
5. 6(x + 2)
6. 7(x - 2)
7. 9(x + 2)
8. 8(x - 2)
a) Su-Lo scored 45% in her test out of 80.
what mark did she
score?
Answers
Answer:
Step-by-step explanation:
To calculate Su-Lo's score on the test, we can multiply her percentage by the total marks for the test.
Su-Lo scored 45% out of 80, so her score can be calculated as follows:
Score = Percentage × Total marks
Score = 45% × 80
To find the score, we need to convert the percentage to a decimal by dividing it by 100:
Score = (45/100) × 80
Score = 0.45 × 80
Score = 36
Therefore, Su-Lo scored 36 marks on the test.
Steve is going shopping. This matrix shows his shopping list:
How much will Steve spend if he shops at S2?
Round to the nearest cent
Answers
$27.71 is the amount Steve spend if he shops at S2.
Given that Steve is going shopping
The shopping list of steve has 2 cereal, 4 soups , 2 soda, 1 milk and 4 candy.
We have to find the cost spend by Steve when he purchase in shop 2, S2.
In S2, the cereal cost 2.15, soup cost 2.75, soda cost is 3.00, Milk cost 3.25 and candy costs 0.79.
Total cost = 2×2.15 + 4×2.75+2×3+1×3.25+4×0.79
=4.3+11+6+3.25+3.16
=27.71
Hence, $27.71 is the amount Steve spend if he shops at S2.
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A circular hot spring has a diameter of 110 meters. Over time, the diameter
of the spring decreases by 3 meters. By how many square meters does the
area of the hot spring decrease? PLEASEE IM BEGGING ANSWER ;(
Answers
Answer:
Step-by-step explanation:
Hello!
We want to know the area of the original circle - the now circle.
The original circle's diameter is 110 meters.
To figure out the area you use this formula: [tex]r^2*pi[/tex]
The diameter is 107 meters, so the equation is [tex]55^2[/tex][tex]*\pi[/tex].
The area is about 9503.3 meters.
The next area is the "now circle".
The now circle's diameter is 107 meters.
When you use this formula, you end up with [tex]53.5^2*\pi[/tex].
The area is about 8892 meters.
So it's just basic subtraction!
I'll let you figure out the rest.
:)
Which of the following exponential regression equations best fits the data shown below?
(-4,0.05), (-3, 0.20), (-2, 0.75)
Answers
The exponential regression equation is y = 11.37 * 3.87ˣ
How to determine the exponential regression equationFrom the question, we have the following parameters that can be used in our computation:
(-4,0.05), (-3, 0.20), (-2, 0.75)
To calculate the exponential regression equation that best fits the data shown, we use a graphing tool
An exponential function is represented as
y = abˣ
From the graphing tool, we have
a = 11.37
b = 3.87
substitute the known values in the above equation, so, we have the following representation
y = 11.37 * 3.87ˣ
Hence, the exponential regression equation is y = 11.37 * 3.87ˣ
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