The value of the double integral is ∬D 2y dA = 131/150.
To determine which is easier to integrate, let's first sketch the region D:
From the sketch, we see that D is more naturally expressed as a function of y, rather than x. Therefore, it is easier to integrate using option B, which is ∬D 2y dy dx.
To evaluate the double integral using option B, we can set up the integral as follows:
∬D 2y dy dx = ∫[0,1] ∫[[tex]y^2,(3y+10)/10][/tex] 2y dx dy
= ∫[0,1] [[tex](3y^2 + 10y)/5 - y^{5/5}][/tex]dy
= [[tex]y^{3/5}+ y^2 - y^6/30[/tex]] evaluated from 0 to 1
= 1/5 + 1 - 1/30 = 131/150
Therefore, the value of the double integral is ∬D 2y dA = 131/150.
for such more question on double integral
https://brainly.com/question/22008756
#SPJ11
What is midpoint formula Class 11?
The midpoint formula helps us to find the midpoint of a line given to us on a coordinate system.
The coordinate system in geometry is a plane space in which points are located using paired numerical values called coordinates. It is of two types Cartesian coordinate system and polar coordinate system
The cartesian coordinate system is further divided into majorly two parts i.e., 2-Dimensional and 3- dimensional systems. A 2-D system has 2 axis X and Y whereas a 3-D system has X, Y, and Z axes. The plane is divided into 4 quadrants
The midpoint formula is used to find the center of a line or a figure. It is a mathematical equation used in geometry and economics. On a line from point (x1,y1) to (x2,y2) the midpoint P= (x1+y1)/2 , (x2+y2)/2. It divides the line in a 1:1 ratio.
To know more about the Midpoint theorem visit:
https://brainly.com/question/28443113
#SPJ4
Solving systems of equations by substitution worksheet
1. y = 6x-11
-2x-3y = -7
2. 2x-3y = -1
y = x-1
1. steps to find the value of x
The first step is to equalize the form of the equation.
y = 6x-11 = -6x+y= -11
-2x-3y = -7
thus becoming:
-6x+y= -11
-2x-3y = -7
Then eliminate y:
-6x+y= -11 | times -3| becomes 18x-3y=33
18x-3y=33
-2x-3y = -7
y in the equation can be eliminated to become:
20x=40
x=40/20
x=2
steps to find the value of y:
The first step is to equalize the form of the equation.
y = 6x-11 = -6x+y= -11
-2x-3y = -7
thus becoming:
-6x+y= -11
-2x-3y = -7
Then eliminate x:
-2x-3y = -7 | multiplied by 3| becomes -6x-9y=-21
-6x+y= -11
-6x-9y=-21
x in the equation can be eliminated to become:
10y=10
y=-10/10
y=1
2.
1. steps to find the value of x
The first step is to equalize the form of the equation.
2x-3y = -1
y = x-1 becomes -x+y=-1
thus becoming:
-2x-3y = -1
-x+y=-1
Then eliminate y:
-x+y=-1| times -3| to 3x-3y=3
-2x-3y = -1
3x-3y=3
y in the equation can be eliminated to become:
-5x=-4
x=4/5
Steps to find the value of y:
The first step is to equalize the form of the equation.
2x-3y = -1
y = x-1 becomes -x+y=-1
thus becoming:
-2x-3y = -1
-x+y=-1
Then eliminate x:
-x+y=-1| multiplied by 2| becomes -2x+2y=-2
-2x-3y = -1
-2x+2y=-2
x in the equation can be eliminated to become:
-5y=1
y=-1/5
Learn more about elimination at https://brainly.com/question/1076697.
#SPJ4
The sum of all interior angles in a polygon is 9 degrees. How many sides does the polygon have? Please show your working.
In the triangle below, what is the side adjacent?? HELP
The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where × represents the number of years since 2012, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the calendar year in which the number of new cases would reach 1171.
Regression equation:
Final answer:
The linear regression equation is y = 22.086x + 898.620 and the year for 1171 cases is 2024
How to determine the linear regression equationFrom the question, we have the following parameters that can be used in our computation:
The table of values
Using a graphing calculator, we have the following summary
Sum of X = 15Sum of Y = 5723Mean X = 2.5Mean Y = 953.8333Sum of squares (SSX) = 17.5Sum of products (SP) = 386.5The regression equation is represented as
Regression Equation = ŷ = bX + a
Where
b = SP/SSX = 386.5/17.5 = 22.08571
a = MY - bMX = 953.83 - (22.09*2.5) = 898.61905
So, we have
ŷ = 22.08571X + 898.61905
Approximate
y = 22.086x + 898.620
When the new cases is 1171, we have
22.086x + 898.620 = 1171
This gives
x = 12
i.e. year = 2012 + 12 = 2024
Hence, the year is 2024
Read more about linear regression at
https://brainly.com/question/10209928
#SPJ1
Find the sales tax selling price 20$ rate of sales tax 3%
Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) is dilated using a scale factor of one fourth to create polygon A′B′C′D′. Determine the vertices of polygon A′B′C′D′.
A′(−0.8, 1.2), B′(−0.4, 0.4), C′(0.8, −0.4), D′(0.8, 0.8)
A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)
A′(−2, 3), B′(−1, 1), C′(2, −1), D′(2, 2)
A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)
The vertices of the new polygon A'B'C'D' is A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1) (optionB)
What are vertices of a polygon?A vertex is a corner point of a polygon, polyhedron, or other higher-dimensional polytope, formed by the intersection of edges, faces or facets of the object.
The vertices of the polygons are given as B(−2, 2), C(4, −2), D(4, 4) . The polygon is reduced by using a scale factor one fourth. i.e 1/4.
This means that each coordinates of the vertices will be reduced by 4 to give the vertices of the new polygon.
A = (-4,6) , A' = ( -1, 1.5)
B = ( -2,2) B' = ( -0.5, 0.5)
C = ( 4, -2) C' = ( 1, -0.5)
D = ( 4,4) , D' = ( 1, 1)
Therefore the vertices of the new polygon is A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)
learn more about vertices from
https://brainly.com/question/28747454
#SPJ1
Answer:
its not b i tried and it was wrong
Step-by-step explanation:
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answer:
The following equations are equivalent:
2 + x = 5
x + (negative 4) = 7
Negative 5 + x = negative 2
All of these three equations are equivalent because they all represent the same mathematical relationship between x and other numbers. The variable x is the same in each equation. We can see this by applying the same operation on both sides of the equations, and the variable x will cancel out and the two sides will be equal.
How do I olve thi ytem of equation uing the elimination method. (I don't jut want the anwer, I want an explanation on how to get the anwer. )
y=3x13
2x=y-9
Answer:
-4
Step-by-step explanation:
y=3x13
2x=y-9
2x=3x+13-9
2x=3x+13-9
2x=3x+4
-3 -3
-x=4
-x/ -x/
x=-4
(You said "3x13" so i'm going to guess you meant to say "3x+13").
(If you meant "3x-13" I can also help you with that too)!
Perform the following composition of transformation for point P (6, -4.)
T (-1,2) o R (180)
So, on solving the provided question we can say that coordinates are -
(6, -4.) and T (-1,2) y-y1 = m(x - x1) => 2x - y -16 =0
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.
here,
coordinates are -
(6, -4.) and T (-1,2)
y-y1 = m(x - x1)
y +4 = 2(x -6)
y+ 4 = 2x - 12
2x - y -16 =0
To know more about coordinates visit:
https://brainly.com/question/27749090
#SPJ1
11
1 point
Which is the slope of the proportional relationship?
3/4
2
1/2
4/3
X3456
Y
3 6
69
8
5 10
6 12
Answer:
The number line that represents the inequality 6x - 12 > -6 is (D)
How to determine the number line?
The inequality is given as:
6x - 12 > -6
Add 12 to both sides
6x > 12 - 6
Evaluate the difference
6x > 6
Divide both sides by 6
x > 1
The number line that represents the above inequality is (D)
Read more about number lines at:
brainly.com/question/10851163
What is the measure of 23 if clld?
Answer:
i tink im doing this complete wrong but 1.380649×10−23 J
Step-by-step explanation:
Look at the image down below
Using the concept of ratios, the constant of proportion between middle school and high school is 3/4
What is ProportionalityProportionality is a fundamental concept in mathematics and physics. It is a relationship between two or more variables where a change in one causes a proportional change in the other. In other words, the ratio between the two remains constant. Proportionality is an important concept in mathematics because it is used to make predictions and solve problems. The constant of proportionality is the ratio between the two variables that remain constant in a proportional relationship.
To determine the constant of proportionality in this relationship, we can write an equation in the form
y = kx
k = constant of proportionOr we can easily use ratio to find the constant of proportion
Number of girls in middle school = 6
Number of girls in high school = 8
The ratio = 6/8 = 3 / 4 = Option B
Learn more on proportionality here;
https://brainly.com/question/28413384
#SPJ1
5. Principal = $ 6750, rate = 62/3 % p.a. and time = 3 years.
Answer:
Interest is $4185.00
Please give me brainliest
Step-by-step explanation:
[tex]i = \frac{p \: r \: t}{100} \\ i = \frac{6750 \times \frac{62}{3} \times 3 }{100} \\ i = \frac{418500}{100} \\ i = 4185[/tex]
Answer:
Step-by-step explanation:
Formula for simple interest =S= (P*R*T)/100
Here P=$6750,R=62/3% T=3Years
Simple interest for given is S= 41.85
What is the equation for the line in slope-intercept form?
Answer: y = 8x
Step-by-step explanation:
The line passes through points (1,8) and (2,16).
Using this, we can first find the slope.
Slope = Δy/Δx = 8/1 = 8
So the slope is 8.
The equation is now
y = 8x + b
Let's use the point (1,8) to find the value of b now.
8 = 8 +b
b = 0
Therefore, y = 8x is the answer.
(you can skip the last step by noticing that the graph passes through the origin)
Answer:
y = 8x
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
From inspection of the given graph, two points on the line are:
(0, 0)(2, 16)Substitute the points into the slope formula to find the slope of the line:
[tex]\implies m=\dfrac{16-0}{2-0}=\dfrac{16}{2}=8[/tex]
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
The y-intercept is the y-value of the point where the line crosses the y-axis. From inspection of the given graph, the y-intercept is zero. So b=0.
Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:
[tex]\implies y=8x+0[/tex]
[tex]\implies y=8x[/tex]
Therefore, the equation for the line in slope-intercept form is:
y = 8xA geometry student named Mary claims that the two triangles in the diagram below are not similar to one another. She asserts that the ΔABC is not similar to ΔXYZ because triangle XYZ is bigger. Explain why Mary is mistaken in her conclusions about ΔABC and ΔXYZ. In writing your response, be sure to explain the difference between similarity and congruence. Also be sure to include important math concepts such as similarity, proportionality, and corresponding sides.
Mary is mistaken in her conclusion that the two triangles are not similar because size does not determine similarity. Similarity is determined by the proportionality of corresponding sides and the congruence of corresponding angles. Congruence is the equality of all the measures of the corresponding parts of two figures.
In order to determine if two triangles are similar, we must compare the ratios of corresponding sides. If the ratios of corresponding sides are equal, then the triangles are similar. In the diagram, it is not specified what the measures of the sides of the triangles are, so it is not possible to determine if the triangles are similar based on the information given. However, if the ratio of corresponding sides are same, then the triangles are similar.
It is important to note that similarity and congruence are different concepts. Congruence refers to the equality of all measures of corresponding parts of two figures, including side lengths and angles. Similarity refers to the proportionality of corresponding parts, including side lengths and angles. A triangle can be similar to another triangle without being congruent, and congruent triangles are always similar.
In summary, Mary is mistaken because the size of the triangle does not determine similarity, it is determined by the proportionality of corresponding sides and congruence of corresponding angles. Without knowing the measures of the sides of the triangles, it is impossible to determine if the triangles are similar based on the information given.
why is there a limit
Term limits have been approved almost everywhere they’ve been on the ballot.
Are term limits helpful?
However, the evidence suggests that at the margin, term limits are helpful to the cause of individual liberty. Elhauge’s report showed that term limits lessen the influence of seniority. His research demonstrated that long-term lawmakers from both major parties vote for more bureaucracy than do lawmakers who have been in office for shorter times.
Therefore, term limits have been approved almost everywhere they’ve been on the ballot
Learn more about limits here: https://brainly.com/question/8533149
#SPJ2
How many square meters are in 280 square centimeters
We can perform a change of units to see that 280 square centimeters is equivalent to 0.028 square meters.
How many square meters are in 280 square centimeters?We want to perform a change of units between square centimeters and meters.
Remember the relation:
100cm = 1m
Now we can square both sides of that equation, then we will get:
(100 cm)^2 = (1m)^2
10,000 cm^2 = 1m^2
Then if we have a measure in square centimeters, to transform it into square meters we need to divide that measure by 10,000.
Then:
280 cm^2 = (280/10,000) m^2 = 0.028 m^2
Learn more about changes of units at:
https://brainly.com/question/141163
#SPJ1
True or False? If false, state the correct solution.
Answer:
TRUE
Step-by-step explanation:
(2x^2-5x-3)/(x-3) = (2x+1)
(2x^2)/(x-3) - (5x)/(x-3) - 3/(x-3) = (2x+1)
[separated each term on the left side]
(2x^2)- (5x) - 3 = (2x+1)(x-3)
2x^2- 5x - 3 = (2x+1)(x-3)
(2x+1)*(x-3) = (2x+1)(x-3)
Both sides are the same. The equation is TRUE.
A cubical tank full of water is emptied in a cylindrical tank. If the edge of cubical tank is 77cm, find the height to which the water rises in the cylinder whose bbase diameter 1.4m.
Answer:
Step-by-step explanation:
H=456,533/pier^2
H=456533×7/22×7×7*. Here 7 as radius
H=29.645cm
Translate this sentence into a equation
38 is the product of Dellas score and 2.
Use the variable d to represent Della’s score
The required translation of the given statement into an equation is given as 38 = 2d.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
38 is the product of Della's score and 2.
Let the variable d to represent Della’s score,
2 × d = 38
2d = 38
Thus, the required translation of the given statement into an equation is given as 38 = 2d.
Learn more about models here:
https://brainly.com/question/22591166
#SPJ1
(a) The area of a rectangular parking lot is 8428 m²
If the width of the parking lot is 86 m, what is its length?
Length of the parking lot: _ m
(b) The perimeter of a rectangular pool is 376 m.
If the length of the pool is 99 m, what is its width?
Width of the pool: _m
Answer:
a) Length of the parking lot: 98 m
b) Width of the pool: 89 m
Step-by-step explanation:
a) The formula for the area of a rectangle is [tex]A=lw[/tex].
We need to evaluate the length. Lets solve for [tex]l.[/tex]
[tex]A=lw[/tex]
Divide both sides of the equation by [tex]w[/tex].
[tex]\frac{A}{w} =l[/tex]
We are given
[tex]A=8428\\w=86[/tex]
Lets evaluate [tex]l[/tex].
[tex]\frac{8428}{86}=l[/tex]
[tex]l=98[/tex]
b) The formula for the perimeter of a rectangle is [tex]P=2l+2w[/tex].
We need to evaluate the width. Lets solve for [tex]w[/tex].
[tex]P=2l+2w[/tex]
Subtract [tex]2l[/tex] from both sides of the equation.
[tex]P-2l=2w[/tex]
Divide each term by 2.
[tex]\frac{P}{2} -\frac{2l}{2} =\frac{2w}{2}[/tex]
Simplify.
[tex]w=\frac{P}{2}-l[/tex]
We are given
[tex]P=376\\l=99[/tex]
Lets evaluate [tex]w[/tex].
[tex]w=\frac{376}{2}-99[/tex]
[tex]w=188-99[/tex]
[tex]w=89[/tex]
Answer:
a) 98m , b) 89m
Step-by-step explanation:
(a) Given,
The area of a rectangular parking lot is 8428 m²width of the parking lot is 86 mTo Find : Length of the Parking lot
Length of a rectangle shape can be derived by the formula,
[tex]l = \frac{A}{w}[/tex]
[tex]l = \frac{8428}{86}[/tex]
[tex]l = 98m[/tex]
Hence , the length of a rectangular parking lot is 98m
(b) Given ,
The perimeter of a rectangular pool is 376 mlength of the pool is 99 mTo Find : The width of the rectangular pool
We take the width as variable 'x'
Now we plug it into the perimeter of a rectangle equation
[tex]376 = 2(99 + x)[/tex]
Using distributive property we,
[tex]376 = 198 + 2x[/tex]
We now flip the equation
[tex]2x + 198 = 376[/tex]
[tex]2x = 376 - 198[/tex] ( Transposing into the right hand side)
[tex]2x = 178[/tex]
[tex]x = \frac{178}{2}[/tex]
[tex]x = 89[/tex][tex]m[/tex]
Hence , the width of the rectangular swimming pool is 89m
Rewrite 5 square root 3^4 as an expression with a rational exponent. Then mark this number on the graph of f (x) = 3^x. Explain how you know where to place it.
Step-by-step explanation:
the nth root of something can be expressed as 1/n as exponent.
e.g. sqrt(2) = 2^(1/2).
so, the 5th root of 3⁴ = 3^(4/5)
for f(x) = 3^x
that means that x = 4/5 = 0.8.
so, I go on the x-axis to the right to 0.8, and from there straight up to the actual curve.
that is the desired point.
How do you find the coordinates of a midpoint example?
To find the coordinates of the midpoint of two points in a plane, you can use the midpoint formula. The midpoint formula is:
(x,y) = ((x1 + x2) / 2, (y1 + y2) / 2)
Where (x1, y1) and (x2, y2) are the coordinates of the two points, and (x,y) are the coordinates of the midpoint.
For example, if you have two points (3, 4) and (7, 10), you can use the midpoint formula to find the coordinates of the midpoint:
(x,y) = ((3 + 7) / 2, (4 + 10) / 2)
(x,y) = (5, 7)
The midpoint of points (3,4) and (7,10) is (5,7).
Read more about the Midpoint formula:
brainly.com/question/28443113
#SPJ4
Which equation represents a line perpendicular to the line with equation 2x + 3y = 12?.
The equation of the line perpendicular to 2x + 3y = 12 will be y = 3x/2 + c where c ∈ R.
The equation of the line given here is 2x + 3y = 12
Now rearranging it to the slope-intercept form we get
3y = -2x + 12
or, y = -2x/3 + 4
Now any 2 lines are perpendicular when the product of their slopes results in -1.
Hence, let the equation of the line perpendicular to the given line be
y = mx + c, where m is the slope of the line and c is the intercept.
Hence,
-2m/3 = -1
or, m = 3/2
Hence the equation of the line will be
y = 3x/2 + c where c ∈ R
To learn more about Straight Lines visit
https://brainly.com/question/402319
#SPJ4
Two Places P and q have thesame Longitude. Their Latitude are 15°N and 36°s, Draw diagrams and calculate the great circle distance q
Therefore , the solution of the given problem circle comes out to be
straight line distance from Sydney to Capetown ≈11139 km
A circle is what?A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is axis of rotation equal about the center at every angle. Every set of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetrical about the center at every angle.
Here,
The distance between Sydney and Cape Town's longitudes is 151.13° and 18.22°, respectively, for the little circle, which equals 533.669 km. Sydney to Capetown distance in a straight line is
151.13∘−18.22∘=132.91∘
Straight line distance from Sydney to Capetown
d= √53372+53372−2×5337×5337× cos132.91∘
= 9785 km
θ=cos⁻¹ (6400²+6400²−9785² / 2 x 6400×6400)=99.72∘
Great Circle route from Sydney to Cape Town
=>πR / 180∘ ×θ
=> 6400π180∘×99.72∘
=> 11138.831…≈11139 km
Therefore , the solution of the given problem circle comes out to be
straight line distance from Sydney to Capetown ≈11139 km
To know more about circle visit:
https://brainly.com/question/29142813
#SPJ1
a bag contains 3 red marbles and 4 blue marbles. a marbleis taken at random from the bag and replaced. another marble is taken rom the bag. work out the probability that the 2 marbles taken from the bag are the same colour
The probability that the 2 marbles taken from the bag are the same color is 25/49.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
Number of red marbles = 3
Number of blue marbles = 4
Total marbles = 7
Now,
The probability of taking two blue marbles consecutively with replacement.
= 4/7 x 4/7
= 16/49
The probability of taking two red marbles consecutively with replacement.
= 3/7 x 3/7
= 9/49
Since the two marbles of the same color can be blue or red.
The probability that the 2 marbles taken from the bag are the same color.
= 16/49 + 9/49
= 25/49
Thus,
The probability that the 2 marbles taken are the same color is 25/49.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ1
The boatbill is present in a density of at least one pair per 20 acres at the same time that two different types of plants are dominant. What are these plants?.
The two types that the boatbill will dominate are grasses and shrubs according to the attached table.
What is density?The density of an item is defined as its mass divided by its volume. Density is commonly expressed in grams per cubic centimeter (g/cm3). Remember that grams are a unit of mass and cubic centimeters are a unit of volume (the same volume as 1 milliliter). “Density = mass divided by volume.” Density is a compound metric that tells us about an object's mass in proportion to its volume. The density of a substance is the measure of how densely it is packed together. It is expressed as mass per unit volume. Density Symbol: D or ρ Density Formula: = m/V, where is the density, m is the object's mass, and V is its volume.
Here,
According to the accompanying data, the boatbill will predominate among grasses and bushes.
To know more about density,
https://brainly.com/question/27672452
#SPJ4
Solving a Mixed-Degree
Consider the following system of equations:
10 + y = 5x + x2
5x + y = 1
The first equation is an equation of a
The second equation is an equation of a
What are the solutions of the system?
Answer:
The solutions are:
(1,-4), and (-11,56)
Step-by-step explanation:
10 + y = 5x + x^2
5x + y = 1
Rearrange both equations to isolate y:
y = x^2 + 5x - 10
y = -5x+1
Since y=y, we set set the right sides of both equations equal to each other:
-5x+1 = x^2 + 5x - 10
Rearrange
-x^2 - 10x + 11 = 0
x^2 +10x - 11 = 0
Factor
(x+11)(x-1) = 0
x = -11 and 1
Use these two values of x to find y. We'll use the simpler equation of
y = -5x+1.
x _y
1 -4 (1,-4)
-11 56 (-11,56)
See the attached graph for proof.
Write a quadratic equation in standard form that has an axis of symmetry of x=-2and y intercept of 0,6
The quadratic equation in standard form that has an axis of symmetry of x=-2 and y-intercept of (0,6) is x² + 4x - 6 = 0.
A quadratic equation in standard form is of the form ax² + bx + c, where a, b, and c are constants.
The axis of symmetry of a quadratic equation is given by the line x = -b/2a, so if the axis of symmetry is x=-2, we can set -b/2a = -2, which gives b = 4a.
To find the y-intercept of the quadratic equation, we can set x = 0 and substitute that into the equation: y = a(0)² + b(0) + c = c
So, if the y-intercept is (0,6) then c = 6.
By using above two information, we can write the quadratic equation in standard form as:
a(x+2)² + 4a(x+2) + 6 =0
=> a(x²+4x+4) + 6 = 0
=> a(x²+4x+4) = -6
=> a(x²+4x+4) = -6
=> x² + 4x + 4 = -6/a
=> x² + 4x + 4 = -6/a +10
=> x² + 4x - 6 = 0
So, the quadratic equation in standard form that has an axis of symmetry of x=-2 and y-intercept of (0,6) is x² + 4x - 6 = 0.
To learn more about quadratic equations:
https://brainly.com/question/1214333
https://brainly.com/question/28038123