Answers
(x - h)² = 4a(y - k)
(x - h)² = -4a(y - k)
(y - k)² = 4a(x - h)
(y - k)² = 4a(x - h)
You will notice that the equation contains an x². So, our choices will be narrowed down to:
(x - h)² = 4a(y - k)
(x - h)² = -4a(y - k)
where, the vertex has the coordinates (h.k)
y = 6x² - 24x + 30
Divide both sides by 6,
y/6 = x² - 4x + 5
y/6 - 5 = x² - 4x
Completing the squares, add (-4/2)² = 4 to both sides,
y/6 - 5 + 4 = x² - 4x + 4
y/6 - 1 = (x - 2)²
1/6(y - 6) = (x - 2)²
Thus, h=2 and k=6. The vertex is at point (2,6).
The vertex of the quadratic equation y = 6x^2 - 24 + 30 is (2, -6).
Explanation:The given equation is y = 6x^2 - 24x + 30.
To find the vertex of this quadratic equation, we can use the formula x = -b/2a.
In this equation, a = 6 and b = -24. Plugging these values into the formula, we get x = -(-24)/(2*6) = 24/12 = 2.
Now, substitute this value of x into the equation to find the corresponding y-coordinate of the vertex.
Substituting x = 2, we get y = 6(2)^2 - 24(2) + 30 = 12 - 48 + 30 = -6.
Therefore, the vertex of the given quadratic equation is (2, -6).
Related Questions
What The length of AC?
Answers
sin 42°/85=sin 85°/AC
==>AC=sin 85° *85 /sin 42°=126.54711....
A woman is 43 years old, and her daughter is 15 years old. How many years will it be before the woman’s age is just twice her daughter’s?
Answers
43+x=2(15+x)
43 +x = 2(15+x)=
43 + x = 30 +2x
43 = 30 +x
13 =x
13 years
43+13 = 56
15 +13 = 28 ( 28*2 = 56)
Find the slope of a line through a pair of points (2,-3) and (8,4)
Answers
m = (y2-y1) / (x2-x1)
from the given points:
(x1,y1) = (2,-3)
(x2,y2) = (8,4)
substituting in the equation, we can get the slope as follows:
m = (4--3) / (8-2) = (4+3) / (8-2) = 7/6
suppose you deposit $500 into an account earning 7.8% interest compound annually. what will your balance be after 5 years?
Answers
539 x 5
2695
A swimming pool in the shape of a rectangle is surrounded by 3 feet of walkway. the pool is 23 feet wide and 32 feet long. how long would the fence be that just encloses the walkway and the pool?
Answers
Perimeter: 2(l+w)
= 2 (26ft + 35ft)
= 122 ft fence would be required to enclose the walkway and the pool.
You are making cookies for a bake sale and need to make enough cookies to fill 24 boxes containing 6 cookies each. How many dozen cookies do you need to make?
Answers
To make enough cookies to fill 24 boxes containing 6 cookies each, you need to make 12 dozen cookies.
Explanation:To find out how many dozen cookies you need to make, you need to divide the total number of cookies by 12.
In this case, there are 24 boxes with 6 cookies each, so the total number of cookies is 24 x 6 = 144.
Dividing 144 by 12 gives us 12 dozen cookies.
Identify the vertex the axis of symmetry the maximum or minimum value and the range of each parabola
Answers
of each parabola
f(x) = a(x- h)²+k
the vertex is the point : A( h , k)
the axis of symmetry is the line : x = h
the maximum or minimum value is : f(h) = k
the range i s : R
write a system of linear equations with -3,9 as its solution
Answers
Solution of the equation is given to us, hence,
x = -3 and x = 9
x + 3 = 0 and x - 9 = 0
Multiplying,
(x + 3)(x - 9) = x² - 9x + 3x - 27 = x² - 6x - 27
Hence, the linear equation with solution -3 and 9 is x² - 6x - 27.
Final answer:
To create a system of linear equations with the solution (-3, 9), we need to construct two equations that intersect at this point, for example, y = -3x + 18 and y = 2x + 15.
Explanation:
To write a system of linear equations with the solution (-3, 9), we can create two separate equations that intersect at this point. Using the equation provided, y = 9 + 3x, we can see that the point (-3, 9) satisfies this equation since plugging in x = -3 gives us y = 9 + 3(-3) = 9 - 9 = 0, which is incorrect. We must correct the mistake and ensure that the solution (-3, 9) satisfies both equations in our system.
A correct form of the first equation would be y = -3x + 9 (not y = 9 + 3x as provided), since plugging x = -3 yields y = -3(-3) + 9 = 9 + 9 = 18, which is also incorrect. Therefore, we need to be careful in constructing our equations.
Let's construct two new equations correctly:
First, we start with the equation y = -3x + 18, which does satisfy the condition when x = -3 and y = 9. Next, we can create a different equation with the same solution. For instance, if we want another equation, we might use the slope-intercept form, y = mx + b. We can choose a different slope (m), for example, m = 2, and find b such that when x = -3, y = 9:
y = mx + b
9 = 2(-3) + b
9 = -6 + b
b = 15
So, the second equation is y = 2x + 15. The system of linear equations with the solution (-3, 9) is:
1. y = -3x + 18
2. y = 2x + 15
Raymond just got done jumping at Super Bounce Trampoline Center. The total cost of his session was \$43.25$43.25dollar sign, 43, point, 25. He had to pay a \$7$7dollar sign, 7 entrance fee and \$1.25$1.25dollar sign, 1, point, 25 for every minute he was on the trampoline. Write an equation to determine the number of minutes (t)(t)left parenthesis, t, right parenthesis that Raymond was on the trampoline.
Answers
1.25t = 43.25 - 7
1.25t = 36.25
t = 36.25 / 1.25
t = 29 <== he was jumping for 29 minutes
Answer:
Answer:M=29
subtract 43.25 by 7 because it's a one time fee. But the 1.25 is for each minute so you subtract by 7 and you get 36.25. once you have 36.25 you divide it by 1.25. You should then get 29 mins.
can someone help am not sure how to do this -2x+3y=-10
2x+y=-14
HELP
Answers
B) 2x+y=-14
Adding the equations we get
4y = -24
y = -6
Inserting y = -6 into equation B)
B) 2x -6 = -14
2x = -8
x = -4
Find four consecutive integers whose sum is 106
Answers
Bob likes to prepare personal pizzas. He begins with a circle of dough that is 12 inches in diameter. On top of the dough, he places slices of salami. All of the slices are round and have a 4-inch diameter. If Bob doesn't overlap the slices or allow any of the slices to extend beyond the edge of the pie, what is the maximum number of salami slices he can add?
Answers
Zoe and Hannah share tips in the ratio 3:7 Last week , Zoe received £24. how much did Hannah receive Last week?
Answers
hannah : 7x8 = 56
hannah received £56
Answer:
£56 did Hannah receive Last week
Step-by-step explanation:
Let the number be x.
As per the statement:
Zoe and Hannah share tips in the ratio 3:7.
Then;
Total Zoe share = 3x
Total Hannah share = 7x
It is also given that Last week , Zoe received £24.
⇒3x = 24
Divide both sides by 3 we have;
x = 8
Hannah receive Last week = 7x = 7(8) = £56
Therefore, £56 did Hannah receive Last week
Solve the equation by factoring. 9 xsquared +21x -8= 0
Answers
a =9, x' = the 1st root and x" = the 2nd root..
Find the roots:
x'= [-b+√(b²-4.a.c)]/2.a and x"= [-b-√(b²-4.a.c)]/2.a
x' = 1/3 and x" = -8/3 and the initial factorized equation becomes:
9(x-1/3)(x+8/3)
After reduction to same denominator and simplifying by 9, you get:
(3x-1)(3x+8) ( = 9x² + 21x - 8)
What is the x value in the solution to this system of linear equations?
2x-y=11
x+3y=-5
a.-3
b.-1
c.2
d.4
Answers
x+3y=-5
So, 6x-3y=33
x+3y=-5
Using elimination, 7x=28 or x=4.
Answer with Step-by-step explanation:
We have to determine the value of x on solving the system of linear equations:
2x-y = 11
x+3y = -5
2x-y=11
Adding y on both sides and subtracting by 11 on both sides, we get
y=2x-11
Putting value of y in x+3y = -5
x+3(2x-11) = -5
x+6x-33 = -5
7x -33 = -5
adding 33 on both sides, we get
7x= 28
Dividing by 7 on both sides, we get
x=4
Hence, Correct option is:
d. 4
What is the length of line RS? Use the law of sines to find the answer.Round to the nearest tenth.
Answers
Let x = length of line segment RS.
Let Q = ∠RQS.
Let S = ∠RSQ
According to the Law of Sines,
[tex] \frac{sinS}{2.4} = \frac{sin80^{o}}{3.1} \\\\sinS = (\frac{2.4}{3.1}) sin 80^{o}= 0.7624 \\\\ S = sin^{-1}0.7624 = 49.68^{o}[/tex]
Because the sum of angles in a triangle is 180°, therefore
∠Q = 180 -(80 + 49.68) = 50.32°
Apply the Law of Sines again to obtain
[tex] \frac{x}{sinQ} = \frac{3.1}{sin80^{o}} \\\\ x = ( \frac{sin50.32^{o}}{sin80^{o}})3.1 = 2.423[/tex]
Answer: The length of RS = 2.4 (nearest tenth)
Answer:
Answer: The length of RS = 2.4 (nearest tenth)
I am a number less than 100. Two of my factors are three and five. My digits are one apart. What number am I?
Answers
factors 3 & 5
3*5 = 15
15, 30, 45, 60, 75, 90 are all the possible choices
so the answer would be 45 since the numbers are only 1 apart
Line segment YV of rectangle YVWX measures 24 units. What is the length of line segment YX? 8 units units 12 units units
Answers
The length of the line segment YX in rectangle YVWX is [tex]\rm 8\sqrt{3} \; units[/tex] and it can be determine by using the trignometric properties and properties of rectangle.
Given :
YV = XW = 24 units[tex]\rm \angle VXW = 30^\circ[/tex][tex]\rm \angle XWV = 90^\circ[/tex][tex]\rm \angle XVW = 60^\circ[/tex]The length of the line segment YX in rectangle YVWX can be determine by using the trignometric properties.
[tex]\rm tan \theta = \dfrac{Perpendicular}{Base}[/tex]
[tex]\rm tan 60 = \dfrac{24}{VW}[/tex]
[tex]\rm \sqrt{3} = \dfrac{24}{VW}[/tex]
[tex]\rm VW =8\sqrt{3}\;units[/tex]
In rectangle opposite sides are equal. Therefore, [tex]\rm VW=YX = 8\sqrt{3}\;units[/tex].
For more information, refer the link given bellow:
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[tex]\rm VW=YX = 8\sqrt(3)\;units.[/tex]
The length of the line segment YX in rectangle YVWX is \rm 8√(3) \; units and it can be determine by using the trignometric properties and properties of rectangle.
Given :
YV = XW = 24 units
[tex]\rm \angle VXW = 30^\circ\\\rm \angle XWV = 90^\circ\\\rm \angle XVW = 60^\circ[/tex]
The length of the line segment YX in rectangle YVWX can be determine by using the trignometric properties.
[tex]\rm tan \theta = (Perpendicular)/(Base)\rm tan 60 = (24)/(VW)\rm √(3) = (24)/(VW)\rm VW =8√(3)\;units[/tex]
In rectangle opposite sides are equal. Therefore, [tex]\rm VW=YX = 8√(3)\;units[/tex].
A circle is centered on point B, Points A, C and D lie on its circumference. if ABC measures 46 degrees, what does ADC measures?
Answers
---------------------------------------
---------------------------------------
Explanation:
Using the inscribed angle theorem we can connect the central angle ABC and the inscribed angle ADC. The reason why is because they both cut off the minor arc AC
Angle ABC is given to be 46 degrees, the formula we use is shown below
central angle = 2*(inscribed angle)
angle ABC = 2*(angle ADC)
46 = 2*(angle ADC)
46/2 = 2*(angle ADC)/2 ... divide both sides by 2
23 = angle ADC
angle ADC = 23 degrees
If ABC measures 46 degrees, then the central angle ADC measures 23 degrees.
Using the inscribed angle theorem we can connect the central angle ABC and the inscribed angle ADC.
The reason why is because they both cut off the minor arc AC
Angle ABC is given to be 46 degrees,
The formula we use is shown below
What is the formula for the central angle?The central angle = 2*(inscribed angle)
The angle ABC = 2*(angle ADC)
46 = 2*(angle ADC)
46/2 = 2*(angle ADC)/2 ... divide both sides by 2
23 = angle ADC
angle ADC = 23 degrees.
Therefore, If ABC measures 46 degrees, then the central angle ADC measures 23 degrees.
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What is767,074 rounded to the nearest hundred thousand
Answers
An Internet service company earned $770 in set-up fees for new homes in a neighborhood. They charged $35 for each new set-up. How many new set-ups did they perform? A.19 B.22 C.25 D.26
Answers
An Internet service company earned $770 in set-up fees for new homes in a neighborhood. For each new set-up they charged $35. Then they performed 22 new set ups. So option B is correct.
What is equation?Two expressions with an equal sign is called equation.
An Internet service company earned $770 in set-up fees for new homes in a neighborhood. They charged $35 for each new set-up, then number of new setups we have to find,
Internet service company earned =$770
For each new set-up they charged $35
Number of set ups they perform = x
35x=770
x=770/35
x=22
Therefore 22 new setups are performed.
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round 87600.2 to 1 significant figure
Answers
Answer:
90000
Step-by-step explanation:
A significant figure is a number different from zero that assigns the value of the quantity.
In this case, you have four significant figures, not counting the zeros. To round this, you need the first upper number with only one significant figure.
For that, we use 9 because is the next number from 8, and then complete the value with zeros.
87600.2 will be 90000.0
If ab=37 and xy=1/37, what is the value of the product xxbxyxa
Answers
In this case, we are simply asked to find for the value of:
xbya or abxy
Since we know that given values of ab and xy, therefore abxy is:
abxy = 37 * (1 / 37)
abxy = 37 / 37
abxy = 1
30 packages a minute are unloaded from a truck that has 2700 packages. How long would it take to unload the truck?
Answers
Please vote my answer brainliest. thanks!
It would take 90 minutes to unload a truck containing 2700 packages at a rate of 30 packages per minute.
Explanation:This problem involves performing a simple division operation. Given that 30 packages are unloaded from a truck each minute and there are a total of 2700 packages on the truck, we find the time it would take to unload the truck by dividing the total number of packages by the number of packages that can be unloaded each minute.
Solution:
We solve the problem as follows:
First, state the number of packages in the truck, which is 2700 packages. Next, note the rate at which packages are being unloaded per minute, which is 30 packages a minute. Then, we simply divide the total number of packages by the number of packages that can be unloaded per minute. This gives us the total time required to unload the entire truck, which is 2700⁄30 = 90 minutes.Therefore, it would take 90 minutes to unload the entire truck.
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The probability that Shania is on time for school is 1/2. Find the probability that Shania arrives on time for school for the next 5 days. Express your answer as a percent, to the nearest tenth of a percent. A. 50% B. 15.6% C. 11.4% D. 3.1%
Answers
= 1/2!
= 1/32
= 0.0313
= 3.1%
The answer is D.
Hope this helps. :)
Answer: 3.1 %
Step-by-step explanation:
Given : The probability that Shania is on time for school is [tex]\dfrac{1}{2}[/tex]
Since the each day is independent of other.
Then , the probability that Shania arrives on time for school for the next 5 days will be :_
[tex]=(\dfrac{1}{2})^5=\dfrac{1}{32}=0.03125\approx3.125\%\approx3.1\%[/tex]
Hence, the probability that Shania arrives on time for school for the next 5 days. = 3.1 %
Use the figure to answer the question that follows:
Which angles form a pair of corresponding angles?
A: Angles PRL and RSN
B: Angles PRL and QSN
C:Angles PRK and QRK
D:Angles PRK and QSN
Answers
Reason being, because corresponding means the same angle in two different places. PRL and RSN are the same exact angles just one is higher than the other!
Hope This Helps!
Solve w = t(r1 + r2) for t.
Answers
w / (r1 + r2) = t
But I'm not sure
Answer:
The solution for t is [tex]\frac{w}{(r_1+r_2)}[/tex]
Step-by-step explanation:
The given expression is [tex]w = t(r_1+r_2)[/tex]
We need to solve for the 't' ,
To solve for t, divide [tex]w = t(r_1+r_2)[/tex] by [tex](r_1+r_2)[/tex]
[tex]\frac{w}{(r_1+r_2)} = t[/tex]
Hence, The solution for t is [tex]\frac{w}{(r_1+r_2)}[/tex]
The dashed-line triangle is a dilation image of the solid-lined triangle.
A graph is shown with x and y axes that extend from negative 8 to positive 8 in increments of 2.
A triangle formed by solid black line segments is shown with vertices at negative 9 comma 4, negative 9 comma negative 8, and 7 comma negative 8.
A second smaller triangle formed by dashed line segments is shown with vertices at negative 5 comma 6, negative 5 comma 2, and 0 comma 2.
Is the dilation an enlargement or a reduction? What is the scale factor of the dilation? (1 point)
reduction; one-third
enlargement; one-third
reduction; 3
enlargement; 3
Answers
Triangles ABC and A'B'C' are similar because of AAA.
Also,
[tex] \frac{AB}{A'B'}= \frac{15}{5}=3 \\\\ \frac{AC}{A'C'}= \frac{12}{4}=3 [/tex]
Therefore
ΔA'B'C' is 1/3 the size of ΔABC.
This means that the scale factor from ΔABC to ΔA'B'C' is a 3-factor reduction.
Answer: reduction; one-third.
The dilation is a reduction.
The scale factor of the dilation is one-third.
Are these all correct?
Answers
Problem 2) I agree. Nice work on getting the correct answer. The folding line is a vertical line through the center
Problem 3) It's hard to say for sure, but I think the top left corner is NOT reflective over any line of symmetry no matter how you rotate it. So I would uncheck that box. I agree with your other choices though. Great job with those.
Jose wants to put a fence around his rectangular garden. His garden measures 31 feet by 33 feet. The garden has a path around it that is 3 feet wide. How much fencing material does Jose need to enclose the garden and path?
Answers
so the dimensions become 34 feet and 36feet
hence the fencing length required or the perimeter= 2(l+b)
= 2( 34+36)
= 2(70)
= 140feet fence