Answers
According to the intercepts and points, the equation is of the parabola is y = (1/2)*(x + 2 + √2)*(x + 2 - √2)
Equation of the parabola:
The general form of a parabola with the x-intercepts (a, 0) and (b, 0) can be written as:
y = a*(x - a)*(x - b).
Given.
Here we have the x - intercepts (-2 - √2, 0) and (-2 + √2, 0) and the points (-1, 1).
Now, we have to find the equation of the parabola.
Here we know that the x-intercepts are (-2 - √2, 0) and (-2 + √2, 0)
When we apply the values on the general form of the equation of the parabola, then we get the equation as:
=> y = a*(x + 2 + √2)*(x + 2 - √2)
Here we also know that the y-intercept is (-1, 1), which means that when x = -1, we must have y = 1, replacing that we get:
=> 1 = a*(2 + √2)*( 2 - √2)
=> 1 = a*(4 - 2)
=> 1 = 2a
=> a = 1/2
Therefore, the equation of the parabola is written as,
=> y = (1/2)*(x + 2 + √2)*(x + 2 - √2)
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Related Questions
Enter the repeating digit:
2/3 = 0.?
Answers
Answer:
6
the recurring digit is 6
ANS: 0.6
integration of ∫x³+1/x³-x dx
Answers
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits \frac{x^3+1}{x^3-x} dx }} \end{gathered}$}[/tex]
We rewrite the integrand.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\frac{x^3+1}{x^3+x}=1+\frac{1}{x-1}-\frac{1}{x} }} \end{gathered}$}[/tex]
We integrate terms by terms:
The integral of the constants have this constant multiplied by the variable of integration.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits 1 \ dx=x } } \end{gathered}$}[/tex]
That u = x -1. Then that du = dx and we put du.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits\frac{1}{u} \ du }} \end{gathered}$}[/tex]
Integral 1/u is log(u). If you now substitute u further into:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{log(x-1) }} \end{gathered}$}[/tex]
The integral of the product of a function by a constant is the constant times the integral of this function:
[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{\sf{\int\limits\left(-\frac{1}{x}\right)dx=-\int\limits\frac{1}{x}dx }} \end{gathered}$}[/tex]
Integral 1/u is log(x). Therefore, the result is: -log(x).
The result is: x - log(x) + log(x - 1)
Hey can someone please find the area of this shape? Thank you so much I’ll give brainly. Please explain
Answers
Answer:
44.63
Step-by-step explanation:
( The heart shape makes two half circles and a square )
1 ) The two half circles together make a whole, so we can first find the area of that circle!
2 ) We can see that the dynamiter is 5in. We can cut this in half to find the radius...
5 ÷ 2 = 2.5
3 ) The area of a circle is found with the equation ( A = πr2 ). We can plug in the radius ( 2.5 ) to find the area...
A = π( 2.5 )2 = 19.635in
4 ) Now that we know the area of the circle we can find the area of the square. To find this we can use the equation ( A = a2 ) where a represents the edge length in this case 5in.
A = ( 5 ) 2 = 25in
5 ) We can now add the area of the circle and the area of the square to get the area of the heart!
19.635 + 25 = 44.63
Hope this helps! :)
There are 1255 students in Sarah's high school. 40% of the students are taking Spanish. How many students are not taking spanish?
Answers
40% of 1255 = 502
1255 - 502 = 753
753 aren’t taking Spanish
A rental car company charges $53 per day to rent a car and $0.08 for every mile driven. Rashaad wants to rent a car, knowing that: He plans to drive 475 miles. He has at most $250 to spend. Use the drop-down menu below to write an inequality representing dd, the total number of days Rashaad can rent the car while staying within his budget.
Answers
The inequality that can be used to represent the total number of days Rashaad can rent the car while staying within his budget is d ≤ 4 .
How to represent inequality?The rental car company charges $53 per day to rent a car and $0.08 for every mile driven.
Rashaad wants to rent a car, knowing that: He plans to drive 475 miles. He has at most $250 to spend.
Therefore, the inequality to represent the total number of days Rashaad can rent the car can be represented as follows:
Therefore,
53d + 0.08(475) ≤ 250
53d + 38 ≤ 250
53d ≤ 250 - 38
53d ≤ 212
divide both sides of the inequality by 53
53d / 53 ≤ 212 / 53
d ≤ 4
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Count on from 6. Write the number
that shows 2 more.
Answers
Using the addition, the number that shows 2 more count from 6 is 8.
In the given question we have to write the number that shows 2 more.
We have to start counting from 6.
To write the number that shows 2 more we add 2 in 6, then again add 2 in the result of add of 2 and 6 and so on.
Hence the number that shows 2 more starting from 6 is
6+2=8
So the number that shows 2 more is 8.
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NO LINKS!! Please assist me with this problem Part 1m
Answers
Answer:
(x + 8)² + (y - 8)² = 64=======================
Given ConditionsTangent to x-axis,Tangent to y-axis,In the second quadrant,Radius is 8 units.SolutionEquation of circle:
(x - h)² + (y - k)² = r², where (h, k) is center and r - radiusThe center is the radius long distance from the x- axis to left and y-axis up same distance, this makes it in the second quadrant.
So the coordinates of the center are:
x = - 8, y = 8The equation is:
(x - (-8))² + (y - 8)² = 8²(x + 8)² + (y - 8)² = 64Answer:
[tex](x+8)^2+(y-8)^2=64[/tex]
Step-by-step explanation:
Required conditions:
Tangent to both axes.Center in the second quadrant.Radius = 8 units.If the circle is tangent to both axes, its center will be the same distance from both axes. That distance is its radius.
If the center of the circle is in quadrant II, the center will have a negative x-value and a positive y-value → (-x, y).
Therefore, the coordinates of the center will be (0-r, 0+r) where r is the radius.
If the radius is 8 units, then the center is (-8, 8).
[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]
Substitute the found center and given radius into the formula to create an equation for the circle that satisfies the given conditions:
[tex]\implies (x-(-8))^2+(y-8)^2=8^2[/tex]
[tex]\implies (x+8)^2+(y-8)^2=64[/tex]
solve by using substitution 2x-3y=-12 and x+y=9
Answers
Explanation:
So in this question, you have to rearrange the second equation so that either x or y is isolated. I’m going to stick with x for now. First, subtract y from both sides to get x=-y+9. Then, substitute x into the first equation and solve:
2(-y+9)-3y=-12
-2y+18-3y=-12
-5y+18=-12
-5y=-30
y=6
Then, substitute y=6 into any of the 2 equations (preferably the second one) in order to get x:
X+6=9
x=3
You can also check this by substituting x and y into both equations. Hope this helps!
A standard die is rolled. Find the probability that the number rolled is greater than 1. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Answers
As there are 6 numbers on a standard die the required probability is 5/6.
The black graph is the graph of y = f(x).
Choose the equation for the red graph.
A. y - 1 = f(x)
B. = f(x)
C. y = f(x - 1)
D. y = f()
1
Answers
Answer:
It's A.
Step-by-step explanation:
If you subtract from y, the graph moves to the right. If you add, it moves to the left.
A stadium has 51,000 seats. Seats sell for $28 in Section A, $16 in Section B, and $12 in Section C. The number of seats in Section A equals the total number of seats in sections B and C. Suppose the stadium takes in $1,078,400 from each sold-out event. How many seats does each section hold?
Answers
Answer:
A: 25,500
B: 14,600
C: 10,900
Step-by-step explanation:
This is what we know:
a = b + c
a + b + c = 51,000 Substitute in a for b + c
a + a = 51000 Combine like terms.
2a = 51000 Divide both sides by 2
a = 25,500
28a + 16b + 12c = 1078400 Substitute in 25.600 for a
28(25500) + 16b + 12c = 1078400
714000 + 16b + 12c = 1078400 Subtract 714000 from both sides
16b + 12 c = 364400
25500 +b + c = 51000 Subtract 25500 from both sides
b + c + = 25500 Multiply this equation all the way through by -12 and add it to the bold equation above it.
-12b -12c = -306000
16b + 12c = 364400
4b = 58400 divide both sides by 4
b = 14600
a + b + c = 51000 Plug in what we know
25500 + 14600 + c = 51000
40100 + c = 51000 Subtract 40100 from both sides
c = 10900
What is the curved surface area of a cylinder with the circumference of 4 and height of 6
Answers
The curved surface area of a cylinder is 24cm²
Given the following data;
Base circumference = 4 cm
Height = 6 cm
How to find the curved surface area of a cylinder?Suppose that:
Radius of the considered cylinder = 'r' units
Height of the considered cylinder = 'h' units
Then, the curved surface area of that cylinder is 2πr h
To find the curved surface area (CSA) of the cylinder we have;
CSA of a cylinder = 2πrh
But 2πr = 4 cm
Now Substituting the values into the equation, we have,
CSA of a cylinder = 6 x 4
CSA of a cylinder = 24 cm²
Hence, The curved surface area of a cylinder is 24cm²
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How do you find Circumcenter of a triangle?
Answers
Answer:
The circumcenter of a triangle is the point where the three perpendicular bisectors of the sides of the triangle intersect.
Step-by-step explanation:
The process of calculation of circumcenter has been given below.
What is circumcenter of a triangle?
Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.
Let the coordinate of A, B, C [tex]\Delta[/tex] ABC be ([tex]x_1, y_1[/tex]), [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] respectively and let the coordinate of circumcenter of [tex]\Delta ABC[/tex] is (x, y)
We need to find the length of AB, BC and AC
The length will be obtained in terms of x and y
On solving the equations, we will obtain the value of x and y
The value of x and y is the required coordinate of the circumcenter.
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The mean age of 12 women in an office is 22 years old. The mean age of 3 men in an office is 24 years old. What is the mean age (nearest year) of all the people in the office?
Answers
The mean age (nearest year) of all the people in the office is 22.4.
How to find the mean age?Using this formula to find the mean age
Mean age = Sum of men and women age / Number of men and women
Let plug in the formula
Mean age = ( 12 women × 22 years old) + (3 men × 24 years old) / 12 women + 3 men
Mean age = 264 + 72 / 12 +3
Mean age = 336 /15
Mean age = 22.4
Therefore the mean age is 22.4.
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Write an equation for the line in the following problems.
I NEED THIS ASAP
Answers
Answer:
Graph 1: y = (-3x/5) + 1
Graph 2: y = 4
Step-by-step explanation:
Both functions are linear, so we can use a linear equation to model these functions. Using slope-intercept form, "y=mx+b" will be easiest, since the graph is shown.
Graph 1:
(1 - (-2))/(0 - 5) = (1 + 2)/-5 = -3/5 = slope
y-intercept (0, 1)
y = (-3x/5) + 1
Graph 2:
(4 - 4)/(1 - 0) = 0 = slope
y-intercept (0, 4)
y = 0x + 4
y = 4
Answer:
First equation : [tex]y=-\frac{3}{5}x +1[/tex]
Second equation : y = 4
Step-by-step explanation:
We want to write equations for the two given lines in slope intercept form
y = mx + b
Where m = slope and b = y intercept
Identifying the y intercept
First lets find the y intercept.
The y intercepts is where the line passes the y axis.
By looking at the first line it appears that the line passes the y axis at (0,1) meaning the y intercept is 1 so b = 1
Identifying the slope
We can find the slope using the slope formula
slope = (y1-y2)/(x1-x2)
Where the values of x and y derive from any two points on the line. (x1,y1) and (x2,y2)
The points used may vary as there are many options however I have chosen (0,1) and (-5,4)
So (x1,y1) = (0,1) and (x2,y2) = (-5,4)
Meaning x1 = 0 , y1 = 1 , x2 = -5 and y2 = 4
( we now plug these into the slope formula )
Again recall slope = (y1-y2)/(x1-x2)
==> plug in x1 = 0 , y1 = 1 , x2 = -5 and y2 = 4
slope = (1-4)/(0-(-5))
==> reduce subtraction
slope = -3/5
so our slope(m) is -3/5
Plugging in slope and y intercept into slope intercept form
Finally we plug in the values of m and b into slope intercept form to get the equation
Again we have y = mx + b
m = -3/5 and b = 1
So our equation is y = -3/5x + 1
Identifying equation for second line
When we have a horizontal line our equation is going to be put in y = b form where b = the y value that the line crosses. (or y intercept)
Here the line goes through the y value of 4 so b = 4
Hence, the equation of the second line would be y = 4
m∠7 = 100° . Find the measure of ∠5
Answers
The measures of angles 5 and 3 is 100 degrees.
How to find the measure of angles in intersecting lines?When parallel lines are cut by a transversal, angle relationships are formed such as corresponding angles, alternate angles, vertically opposite angles, linear angles etc.
Therefore,
m∠7 = m∠5 (corresponding angles)
corresponding angles are congruent.
Therefore,
m∠5 = 100 degrees
m∠3 = m∠7(alternate angles)
m∠3 = 100 degrees.
Alternate angles are congruent.
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if a 10800 cm^2 of material is available to make a box with a square base and an open top find the largest possible volume of the box
Answers
The largest possible volume of the box is 108000cm^3.
How can the largest possible volume of the box be found?The concept is the concept of
We can represent the length of the square box as x
we can also represent the surface of the box as S
we can represent the height of the square box as y
we can represent the volume as V= xy
Then since the top of the box is open and we can equate the material of the box is equal with surface area of box.
then S=[x^2 +2xy +2xy]
= x^2 +4xy
Then substitute the value of S we have
10800= x^2 +4xy
y= [10800-x^2/4x]
V=2700 * 1/4X^2
V=2700 * 1/4X^2
Then substitute the value of y into
V= xy
= x[10800-x^2/4x]
V= 2700x - 3/4X^2
Differentiate the volume to 0
=3x^2 = 2700
X^2 = 3600
X = 60 and Y = 30
V=2700 * 1/4X^2
V= 270(60) - 1/4* (60)^2 = 108000cm^3
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If the premier is 97 what is the square value of x
Answers
Answer: 21
Step-by-step explanation
if the premier is 97 the square value of x is 21
Bucket a and bucket b have the same shade of blue paint. If white paint is added to bucket b, which bucket would have the darker shade of blue paint
Answers
Answer:
Bucket a would be a darker shade because the white makes bucket b lighter.
Question
An advertising sales representative has sales totaling $4500. For these sales, the representative earns a commission of $360.
Which proportion could be used to find the commission amount for sales totaling $15,000?
Answers
The commission amount for sales totaling $15,000 is $600.
How to calculate the value?From the information, the advertising sales representative has sales totaling $4500 and for these sales, the representative earns a commission of $360.
Therefore, the commission fraction will be:
= Commission / Sales
= 360 / 4500
= 1/25
Therefore, the commission on $15000 will be:
= 1/25 × $15000
= $600
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Answer:
(1) where y = 18 when x = 2.
What is the value of x when y = 36?
= 4
(2) when x is 4, y is 11.
What is the constant of proportionality for this relationship?
= 2.75
(3) What is 34% of 650?
=4.875
(4) 28 7
16 4
12 3
=1/4x
(5) Last month 288 people attended the monthly bingo night. This month 243 people attended bingo night.
= 15.6
(6) Over 6.8 months, a tree grew 7.48 inches.
=1.1
(7) A party-size bag of chips contains 15 ounces. This is 750% of the amount in the snack-size bag.
=2
(8) An advertising sales representative has sales totaling $4500. For these sales, the representative earns a commission of $360.
Which proportion could be used to find the commission amount for sales totaling $15,000?
=360/4500=x/15,000
(9) Brad's dinner bill, including a 16% tip, is $10.44.
= 9
(10) Do the values in the table represent a proportional relationship?
x 2 4 6 8
y 3.2 6.4 9.6 12.8
Select from the drop-down menu to correctly complete the statement.
response - correct
All of the y-values are a constant multiple of the corresponding x-values, so the relationship is proportional.
(11) Molly estimated the width of a poster to be 21 inches. The actual width is 26 inches.
=19.2
(12) Solve for x.
x−9= −5/24
=1 7/8
(13) Each 1/2 inch on a scale model represents an actual length of 1/6 of a yard.
=3
(14) Landon is buying a shirt priced at $19.99. The sales tax is 8.5%.
= 21.69
(15) A sprinter ran 100 meters in 15 seconds.
=400
(16) Two gears are connected and rotating at the same time. The smaller gear completes 3 2/3 rotations every time the larger gear completes 1/3 of a rotation.
=11
(17) Jasmine dumped her box of spare change and found out that she had saved 128 coins. She separated them and counted 48 dimes.
What percent of Jasmine's coins are dimes?
= 37.5
(18) A pair of boots costing $299 is marked down 45%.
= 164.45
(19) Figure 1 is dilated to get Figure 2.
What is the scale factor?
Enter your answer in simplest form in the box.
=5/8
(20) y=5/x Not proportional
y=5(−2x) Proportional
y=x/4 Proportional
y=6x+4 Not proportional
Step-by-step explanation:
Hey here u go i so tired lol completely POOPED God bless u have a great test
Dave rented a limousine for his wife's birthday. The hourly rate is $70. They used the limousine for 3 hours, plus Dave gave the driver a 10% tip. How much did he spend in total for the hourly charges plus tip?
A.
$252
B.
$189
C.
$287
D.
$231
Answers
Answer:
$231
Step-by-step explanation:
3 hours for 70 dollars an hour we multiply 70 by 3
70x3
210
And then to get the 10 percent tip we multiply 210 by .10
210x.10
21
And now we add 210 and 21 to get 231
Hopes this helps please mark brainliest
Humberto walks 3 miles due north then turns around and walks 5 miles due south how far is Humberto from his starting point
Answers
Humberto's displacement is 2 miles due south far from his starting point.
How is the displacement completed?We understand that displacement is a vector quantity with both magnitude and direction, while distance is a scalar quantity with only magnitude.
Displacement, unlike distance, shows the direction and position of an object from its original base. This means that displacement refers to how far an object has traveled out of its original position with the direction included.
In other words, displacement shows the object's overall change in position and the direction of the new position from the former.
Starting point = 0
Distance covered toward the north = 3 miles
Distance covered toward the south = 5 miles
Displacement = 2 (0 - 3 + 5) miles
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Erica worked 14 hours last week and 20 hours this week. If she earns $9 per hour how much did she earn during these two weeks?
Answers
Answer: $306
Step-by-step explanation:
You can find the answer by multiplying 9 by each of the values.
14 * 9 = 126
20 * 9 = 180
Add these values together and you get 306 !
Which expression is equivalent to 8 ^ -3
Answers
The expression 1 / 8^3 is equivalent to 8^-3. Option B is correct.
First, let us understand the exponents or power:
A power, or index, is a little floating number that appears next to a number or letter.
It is denoted as a^m.
where a = base number
and m = power or index number.
Some laws of exponents are:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹a⁻¹ = 1 / aWe are given:
8^-3
We can solve as;
8^-3 = 8^(3 * -1) = (8^3) ^ -1 = 1 / 8^3 [since a⁻¹ = 1 / a]
So, 8^-3 = 1 / 8^3.
Thus, the expression 1 / 8^3 is equivalent to 8^-3. Option B is correct.
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Determine which set of side measurements could be used to form a right triangle.
5, 10, 30
2, 3, 4
square root of 26, square root of 34, 60
square root of 11, 7, square root of 60
Answers
Answer:
the 4th one
Step-by-step explanation:
because we determined by Pythagorean theorem (the square root of 11)2 + 7 the power of 2 =
(the square root of 60)2 .....square root cancelled by power of 2
11 + 49 = 60
60 = 60
2sin3x - sqrt3 = 0
express as: x = _____ + _____ pi n
Answers
The trigonometric equation 2sin3x - √3 = 0 is expressed as x = π/9 + 2πn/3, 2π/9 + 2πn/3
How to solve trigonometric equations?
A trigonometric equation is defined as an equation involving one or more trigonometric ratios of unknown angles
Given: 2sin3x - √3 = 0
2sin3x - √3 = 0
2sin3x = √3
sin3x = √3/2
3x = sin⁻¹√3/2 (Note: sin⁻¹√3/2 = 60° = π/3 in radian)
3x = π/3, π -3 (Note: sine is positive in 1st and 2nd quadrant)
3x = π/3, 2π/3
x = π/9, 2π/9
x = π/9 + 2πn/3, 2π/9 + 2πn/3
Therefore, 2sin3x - √3 = 0 can be expressed as x = π/9 + 2πn/3, 2π/9 + 2πn/3
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The graph of a quadratic function with vertex (4, 2) is
Find the range and the domain.
Write the range and domain using interval notation.
Answers
For the given graph of quadratic function whose vertex is (4,2) , the domain and the range in the interval notation is given by :
Domain = ( -∞ , ∞ )
Range = ( 2 , ∞ )
As given in the question,
For the given graph of quadratic function ,
Given graph represents the parabola.
Standard equation of the parabola with vertex ( h, k) is given by,
y = a ( x - h )² + k
Substitute the value ( h ,k ) = ( 4, 2 )
y = a ( x - 4 )² + 2
As it is a parabola in the first quadrant and faces in the upward direction,
Value of x tends to -∞ to ∞
Domain = ( -∞ , ∞ )
Minimum value of y coordinate is 2 and increases to ∞.
Range = ( 2, ∞ )
Therefore, for the given graph of quadratic function whose vertex is (4,2) , the domain and the range in the interval notation is given by :
Domain = ( -∞ , ∞ )
Range = ( 2 , ∞ )
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(-3y)^4 write the power as a product of powers
Answers
Answer: 81y^4
Step-by-step explanation:
expand then calculate, -3 to the power of 4+81 then 81 added to y ^4 81y^4 is your finally power.
Order these numbers from least to greatest.
2.8, 2.5081, 1.935, 2.58
2.8
<
2.5081
<
1.935
2.58
Answers
Answer:
Step-by-step explanation:
1.935<2.5081<2.58<2.8
∵1.9350<2.5081<2.5800<2.8000
Find tα/2 for n = 18 and a 99% confidence interval.
Answers
The value of tα/2 of the t-test is 2.898
How to determine tα/2?A t-test is a statistical test that is used to compare the means of two groups. tα/2 refers to the t critical value from the t-distribution table that corresponds to α/2
Given: n = 18 and a 99% confidence interval
We have to find the critical t value for 99% confidence level and sample size of 18
Degrees of freedom = n - 1 = 17
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
In the t table (check the attached image), we have to check the value against the column 0.005 and for 17 degrees of freedom.
The value obtained from the table is 2.898
Therefore, tα/2 = 2.898
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