Answers
Answer:
[tex](-9.5,2.63)[/tex]
Step-by-step explanation:
In essence, this problem asks one to find the vertex of the given equation. An easy way to find the vertex of a quadratic equation in standard form is to complete the square.
Completeting the square involves grouping the quadratic and linear term, then factoring out the coefficient of the quadratic term. After doing so, one will add a term to make the grouped terms a perfect square trinomial and then balance the equation. Finally, one will simplify the equation and get the quadratic equation in vertex form. From there, finding vertex is quite easy, the x-coordinate is the additive inverse of the quadratic term, and the y-coordinate is the constant.
Once a quadratic equation in standard form has been converted to vertex form by the process of completing the square, its equation is amongst the lines of the following,
[tex]a(x-k)^2+h[/tex]
(k, h) is the vertex of the parabola.
The quadratic equation in standard form,
[tex]2x^2+19x+42.5[/tex]
Group the quadratic and linear terms,
[tex](2x^2+19x)+42.5[/tex]
Factor out the coefficient of the quadratic term,
[tex]2(x^2+9.5x)+42.5[/tex]
Add a term to make the grouped part a perfect square trinomial, then balance the equation,
[tex]2(x^2+9.5x+22.5625)+42.5-2(22.5625)[/tex]
Simplify,
[tex]2(x^2+9.5x+22.5626)+42.5-45.125[/tex]
[tex]2(x+9.5)^2+2.625[/tex]
The vertex of the equation is the following,
[tex](-9.5,2.625)[/tex]
Rounded,
[tex](-9.5,2.63)[/tex]
Related Questions
A shipping box is in the shape of a rectangular prism. It has a volume of 9,000 in.3, and the dimensions of the base are 20 in. by 30 in. What is the height of the box?
15 in.
20 in.
300 in.
600 in.
ITS NOT 20 I TOOK THE TEST AND GOT IT WRONG
Answers
Answer:
15 in.
Step-by-step explanation:
Volume of rectangular prism = length × width × height
Length = 30 in
Width = 20 in
Height = x
Volume of rectangular prism = 9000 in³
Volume of rectangular prism = length × width × height
9000 = 30 × 20 × x
9000 = 600x
x = 9000/600
x = 15 in
Answer:
15
Step-by-step explanation:
the formula of finding the volume of a rectangular prism is base times height. the base dimensions are 20*30 so its 600 square inches, 9000/600=15.
What is the perimeter of thsi shape ??!
Answers
Answer:
D. 180 mm
Step-by-step explanation:
At the bottom of the shape, we can see the base is 60mm. The next side(left or right) is shown as 20mm. The next side right before the missing piece is 20mm. The width of the missing piece is 10mm. The length of the missing piece is 20mm because:
20 + 20 = 40
60mm - 40mm = 20mm
60mm + 20mm + 20mm + 10mm + 20mm + 10mm + 20mm + 20mm
180 mm
An investment doubles its value in 3 years. A) what is the average rate of change in the value of this investment over the 3 year period? B) what continuously compounded interest rate would yield this return?
Answers
1/3 times 1/4 a,1/12 b,1/16 c,1/7 or d, 1/2
Answers
Answer:
a,1/12
Step-by-step explanation:
HELP ASAPUse the table to identify values of p and q that can be used to factor
x2 + x - 12 as (x + p)(x + 4).
P
p +
2.
-2.
9
-6
6
4
3
-1
1
-3
4
A. 2 and -6
B. -3 and 4
C. -2 and 6
D. 3 and -4
Answers
Option B is correct, the values of p and q in expression are -3 and 4.\
The given expression is x²+x-12.
This is expressed as (x+p)(x+q)
We have to find the values of p and q.
x²+x-12
Let us factorize the expression:
x²+4x-3x-12
x(x+4)-3(x+4)
(x-3)(x+4)
When we compare this with (x+p)(x+q) we get:
p=-3 and q=4
Hence, the values of p and q in expression are -3 and 4.
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A 6-foot tall man has a 9-foot shadow. At the same time, a tree he is standing next to has a 30-foot shadow.
A. 20 ft
B. 27 ft
C. 45 ft
D. 21 ft
E. 24 ft
Answers
Answer:
A.20 ft
Step-by-step explanation:
the shadow is double the height of the object.
What is the area of the parallelogram?
36 m 2
18 m 2
24 m 2
72 m 2
Answers
Answer:
I would need the picture please
Step-by-step explanation:
Thank you! Let me know when you've added the question!
You can just give me the height and base.
$35,200 at 2% for 2 years
Answers
Answer:
Um 1408
Step-by-step explanation:
2% of 35,200 is 704 and 304*2= 1408
Answer:
36622.80
Step-by-step explanation:
I don't know how to do it I used an app on my phone
PLEASE HURRY!!!
NO LINKS OR FILES, JUST THE CORRECT ANSWER AND I WILL GIVE BRAINLIEST IF THERE ARE ANY LINKS I'LL REPORT YOUU
Answers
Answer:
so the 2 questions i see are surveys so... you have to answer them with truth on your own self
Step-by-step explanation:
Answer:
hi i am the person that you are talking to with all the comments give him brainliest
Step-by-step explanation:
Use the dropdown to complete the following inequality
Answers
Answer:
c+2<1
Step-by-step explanation:
Since c is located slightly less than -1, and -1+2 = 1; then adding 2 to c would make it slightly less than 1.
A cube has side length of 1 meter. Determine the volume of the cube. Include all of your calculations in your final answer.
Answers
Answer:
look at the picture i sent......
PLSSS HELP ASAP WILL GIVE BRAINLIEST
Solve by completing the square: 5x² + 20x + 32 = 0
Answers
Answer:
5x2 + 20x + 32 = 0 - 16977324
Step-by-step explanation:
What value of x makes 6x + 5 equal to 12?
Answers
Answer:
x = 7/6
Step-by-step explanation:
6x+5 = 12
Subtract 5 from each side
6x+5-5 = 12-5
6x = 7
Divide each side by 6
6x/6 = 7/6
x = 7/6
Answer:
x=7/6
Step-by-step explanation:
6x+5 = 12
subract 5 from both sides
6x = 7
divide by 6 on both sides
x=7/6
Write a rule for the n th term of the sequence for which az = 4 and r= 2.
=
Answers
Answer:
Step-by-step explanation:
The general form for a geometric sequence is:
a
n
=
a
1
⋅
r
n
−
1
With this, you can write a system of equations:
a
2
=
a
1
⋅
r
2
−
1
a
5
=
a
1
⋅
r
5
−
1
2
=
a
1
⋅
r
1
0.25
=
a
1
⋅
r
4
r
4
r
1
=
0.25
2
r
3
=
0.125
r
=
0.5
Now, find the first term.
a
2
=
a
1
⋅
0.5
1
2
=
a
1
⋅
0.5
a
1
=
4
Using the formula stated above, we get:
a
n
=
4
⋅
0.5
n
−
1
what is the answer to 4x-3=37
Answers
Answer:
4x - 3 = 37
+3 +3
4x = 40
Divide by 4 on both sides:
X = 10
Step-by-step explanation:
x=10
.......................
PLEASE HELP
I am quite confused
Answers
4) Jerry cuts a piece of paper from one corner to the other, as shown. How long is the cut edge (look at photo)
A) 20 cm
B) 30 cm
C) 40 cm
D) 50 cm
Pls don’t put answer in a link
Answers
The required length of the cut edge will be 50 cm. which is the correct answer would be an option (D).
What is Pythagoras's theorem?Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
The piece of paper from one corner to the other, as shown figure.
Let the length of the cut edge would be x cm, which is equal to the hypotenuse in the given right triangle.
According to Pythagoras's theorem,
⇒ c² = a² + b² ....(i)
As per the given question, we have
c = x, a = 40 cm and b = 30
Substitute the values in the above formula, and solve for x
⇒ x² = 40² + 30²
⇒ x² = 1600 + 900
⇒ x² = 2500
⇒ x² = 50²
⇒ x = 50
Therefore, the required length of the cut edge will be 50 cm.
Learn more about Pythagoras's theorem here:
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Fred has a spinner that is split into four equal sections: red, blue, green, and yellow. Fred spun the spinner 500 times. Which of
the following would be a good estimate of the number of times the spinner lands on the green section?
Answers
Answer:
125 times ..................... but it's not their so c is correct
HOw do I find the range of a funtion
Answers
because you start off with no pairs of waited plates, then add them (Which is 20 for both) and that is the range
How do I solve this problem?
Answers
Answer:
3240
Step-by-step explanation:
Sum=n/2(2a+(n-1)d)
=80/2(2*1+(80-1)1)
=40(2+79)
=40*81
=3240
Answer:
6480.
Step-by-step explanation:
This is an arithmetic series with first term 2, last term 160 and common difference 2.
Sum = n/2 [ a1 + L)
= (80/2)(2 + 160)
= 40 * 162
= 6480.
Predict how many times you will roll a number less than 4 if you roll a standard number cube 200 times.
Round to the nearest integer, if necessary.
times.
You will roll a number less than 4 about
Answers
Answer:
100 times
Step-by-step explanation:
you have a 3/6 chance of rolling less than 4 once
so you multiply 3/6 times 200- you get 600/6
you simplify 600/6 to 100
100 times is the answer.
Have a fantasical day.
Ray is late for work but would like to drink some coffee before he leaves. The coffee in the pot is too hot, so Ray puts 20 small ice cubes in a mug before pouring in the coffee. The ice cubes measure 1 cm per side. The mug is cylindrical and has a height of 9 cm and a base of 7 cm. What is the volume of the coffee that will fill the mug after the ice cubes have been added (round to the nearest whole number)?
A) 113 cm3.
B) 326 cm3.
C) 346 cm3.
D) 424 cm3.
Answers
Answer:
V,cube = sidelength^3
V,cube = (1 cm)^3
V,cube = 1 cm^3
Since there are 20 ice cubes, V = 20 cm^3
V,cylinder = pi * r^2 * h
V,cylinder = 3.14 * 3.5^2 * 9
V,cylinder = 346.185 cm^3
This is the volume of mug when full.
Since 20 cm^3 is allotted for the ice cube, thus,
346.185 - 20 = 326.185 cm^3
Yes it's B.
Hope this helps~ `u`
Step-by-step explanation:
MRK ME BRAINLIEST PLZZZZZZZZZZZZZ
You opened a checking account with $250 and have been spending $35 every week. How much will
you have your account after 6 weeks?
$35
$40
$210
$75
Answers
Answer:
$35
Step-by-step explanation:
multiply 35 by the number of weeks (6) to get $210, subtract $210 from $250 to get $35
Mackenzie surveys 80 of her classmates and finds that 85% of them like sports. She also finds that 75% of her 84 relatives like sports. How many
more of her classmates like sports as compared to her relatives?
Answers
80 of 85%
80 times 85/100 = 68
Relatives
84 of 75%
84 times 75/100 = 63
68-63 = 5 more of her classmates like sports than her relatives
Can someone help me find out how to solve this problem I just need to find what function to use
Answers
Answer: tangent
Step-by-step explanation: from the diagram the adjacent and the opposite are given. From SOHCAHTOA , tan is the only trig ratio with opposite and adjacent.
Thus tan teta= opposite÷adjacent
tan teta= 3÷6= 0.5
teta=tan invers of 0.5
=26.6°
Can you please help me out????
Answers
Answer: B.) 19.6 feet.
Draw a right triangle ABC. AB will represent the ladder, with point A being on the ground and point B being against the building.
Label: AC=6 ft, m<A=73° and <C is a right angle.
Use the trig mnemonic "SOHCAHTOA" to identify that BC/AC=tan<A. So BC, which is the height the ladder reaches, equals AC*tan<A=6*tan(73)=19.6 feet.
Step-by-step explanation:
What is the quotient of 15,048 and 76
Answers
Answer:
If you mean 15,048 ÷ 76, the quotient is 198.
If you mean 76 ÷ 15,048, the answer is 0.00505050505. But I doubt that’s what you mean.
The quotient for the given problem is 198.
What is division?
Division is a simple operation in which a number is divided. The splitting of a large group into smaller groups such that every group will have an equal number of items.
By using division concept, we can find the quotient when the divisor is divided by the dividend.
The divisor is 15048
The dividend is 76
Division is performed by using the division operator ÷
⇒ [tex]15048[/tex] ÷ [tex]76[/tex]
⇒ [tex]198[/tex]
Hence the quotient for the given problem is 198.
Learn more about division here
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Which point on the number line has the least absolute value?
Answers
Answer:
P
Step-by-step explanation:
The least absolute value is what number is closest to zero.
A bird sanctuary has 14 bags of bird seed. Each bird feeder holds 1/6 of a bag. How many bird feeders can be filled with the bird seed?
Answers
Answer:
84 bird feeders can be filled
Step-by-step explanation:
Considering there is 14 bags, all you'd have to do is see how many bird feeders can be filled... and to do that, just multiply 14 x 6, because it every bag fills up 6 feeders. 14 x6 =84 bird feeders can be filled.
angie needs 8 cups of oliv oil to make a recipe if olive oil costs $4.00 a pint how much money will she need to buy the olive oil
Answers
Answer:
i have tht too but i dont know the answrr :(
Step-by-step explanation: