How to calculate y=6x^2+1
Answers
Hi there!
~
⇒ Graph : [tex]y=6x^2+1[/tex]
∴ Rewrite the equation in vertex form.
⇒ [tex]y = 6 ( x + 0)^2 + 1[/tex]
∴ Use the vertex form, [tex]y = a(x - h)^2 + k[/tex] , to determine the values of [tex]a , h ,[/tex] and [tex]k[/tex]
[tex]a = 6 \\h = 0\\k = 1[/tex]
∴ Since the value of [tex]a[/tex] is positive, the parabola opens up.
⇵
∴ Find the vertex [tex]( h,k)[/tex].
[tex](0,1)[/tex]
∴ Find [tex]p[/tex], the distance from the vertex to the focus.
[tex]\frac{1}{24}[/tex]
∴ Find the focus.
[tex]( 0 , \frac{25}{24} )[/tex]
∴ Find the axis of symmetry by finding the line that passes through the vertex and the focus.
[tex]x = 0[/tex]
∴ Find the directrix.
[tex]y = \frac{23}{24}[/tex]
∴ Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Up
⇒ Vertex: [tex]( 0 , 1)[/tex]
⇒ Focus: [tex]( 0 , \frac{25}{24} )[/tex]
⇒ Axis of Symmetry: [tex]x = 0[/tex]
⇒ Directrix: [tex]y = \frac{23}{24}[/tex]
∴ Select a few [tex]x[/tex] values, and plug them into the equation to find the corresponding [tex]y[/tex] values. The [tex]x[/tex] values should be selected around the vertex.
[tex]x : -2 , -1 , 0 , 1 , 2 \\y : 25 , 7 , 1 , 7 , 25[/tex]
Hope this helped you!
Related Questions
Translate the phrase into an algebraic expression, then simplify.
The sum of -23 and 9,
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Answer:
69
Step-by-step explanation:
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Answer:
it dilated by two
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The power generated by an electrical circuit (in watts) as a function of its current c cc (in amperes) is modeled by P ( x ) = − 15 x ( x − 8 ) P(x)=−15x(x−8) What is the maximum power possible?
Answers
The maximum power is 4A.
What is Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The given function
P(x) = - 15x (x-8)
P(x) = - 15x² + 120x
The standard form of a quadratic function is:
y = ax² + bx + c
For which x is the maximum of the parabola
x = - b/2a
So, a = -15 and b = 120.
Then, x = - 120/(2 · (-15))
x = - 120/ (-30)
x = 4A
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what is 42,456 divided by 36 also what is 7,456 divided by 215 please do in step by step
Answers
Answer:
1179 rem 12
36 /42456
36_
64
-36_
285
-252_
336
-324_
12*
this is for number 1
_ are where you put lines under the number to do the subtraction
What is the answer for -4-(7t-4)^2=-49
Answers
t₁ = (3√5 + 4)/7
t₂ = -(3√5 - 4)/7
Step-by-step explanation:- 4 - (7t - 4)² = - 49
- (7t - 4)² = - 49 + 4
- (7t - 4) = - 45 | (-)
(7t - 4)² = 45
(7t - 4)² = 3√5
7t - 4 = ± 3√5
7t - 4 = 3√5 => 7t = 3√5 + 4 => t₁ = (3√5 + 4)/7 7t - 4 = - 3√5 => 7t = - 3√5 + 4 => t₂ = -(3√5 - 4)/7Solve for t in terms of q, r, and s.
S = rqt
T=
Answers
multiply out
qt=rs+rt
The solution is: the value of x, and the angles m∠SQT and m∠RQS are:
x = 23, m∠RQS = 72°, m∠SQT = 83°.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
Here, we have,
Since we are not told what to look for, we can as well look for the value of x, m∠SQT and m∠RQS
Given
m∠RQS=(4x-20)°
m∠SQT=(3x+14)°
m∠RQT=155°
The addition postulate is true
m∠RQT= m∠RQS + m∠SQT
Substitute the given parameters into the formula
155 = 4x-20+3x+14
155 = 7x-6
7x = 155+6
7x = 161
x = 161/7
x = 23
Solve for m∠RQS
m∠RQS = 4x-20
m∠RQS = 4(23)-20
m∠RQS = 92-20
m∠RQS = 72°
Solve for m∠SQT
m∠SQT = 3x+14
m∠SQT = 3(23)+14
m∠SQT = 69+14
m∠SQT = 83°
Hence, The solution is: the value of x, and the angles m∠SQT and m∠RQS are: x = 23, m∠RQS = 72°, m∠SQT = 83°.
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complete question:
S is in the interior of ∠RQT. m∠RQS=(4x-20)°,m∠SQT=(3x+14)°, and m∠RQT=155°
A car travels 200 ft before stopping.How many meters is this?
Answers
Answer:
the answer is 60.96
Step-by-step explanation:
*please give me brainliest, i only need four more*
what times what times what times what equals -5/24 i need two different ways please help
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Answer:
;fjk;rofkfk;;fkslgl;fkfls'rfi;,dfei;se;feieirjeiljlaejre
sfe;jflejflseleijflskfeselselehf
Step-by-step explanation:
ueufaepfsfjseuefkeou;oiwrrsdkuijksgukuisdjyfekefaehkf
How does a tree feel after a hard day at work?
(Math question. It one of those math riddles where you have to answer a bunch of problems to decode the answer)
Answers
B - -36
U - 9
S - 10
H - 16
E - 6
D - -3
When registering their cars, owners must identify the color that covers the largest portion of the vehicle. In one region, the probability that car was mainly white was 0.24, the probability that it was mainly silver was 0.22 and the probability that it was mainly black was 0.19. In this region, are the events "silver" and "black" mutually exclusive? Find the probability that a randomly selected car from this region is mainly silver OR mainly black.
Answers
Answer:
0.41 probability
Step-by-step explanation:
0.22 + 0.19 = 0.41
Answer:Yes they are mutually exclusive!
0.22 + 0.19 = 0.41
Solve problem step by step 3(2x-4)=8
Answers
Answer:
x = 10/3
Step-by-step explanation:
3(2x-4) = 8
3*2x + 3*-4 = 8
6x - 12 = 8
6x = 8 + 12
6x = 20
x = 20/6
x = 10/3
Check:
3((2*10/3) - 4) = 8
3(20/3 - 4) = 8
20 - 3*4 = 8
20 - 12 = 8
n – 8 = 16 in a verbal sentence
Answers
Answer:
N minus eight equals sixteen.
Step-by-step explanation:
i need help please :(
Answers
Answer:
B
Step-by-step explanation:
Recall the product property of exponents, where:
[tex]x^a\cdot x^b=x^{a+b}[/tex]
In our expression, x is 3, a is -8, and b is 4. Thus:
[tex]3^{-8}\cdot 3^{4}=3^{-8+4}[/tex]
Add in the exponent.
[tex]=3^{-4}[/tex]
So, our answer is B.
And we're done!
The perimeter of a rectangular window is 104 ft. The length is three times the width. Write a equation and solve for the width.
Answers
Answer:
L2 + W2 = P
L = 3W
2(3W) + 2W = 104
6W + 2W = 104
8W = 104
W = 13
Step-by-step explanation:
perimeter is 2 times length plus two times width.
add these togethter to get 104 (the given number)
then create an equation to find length based on the given number
simplify and find w.
Answer: width = 13 ft
Step-by-step explanation:
Perimeter (P) = 2 × Length (L) + 2 × width (w)
Given: P = 104, L = 3w
P = 2L + 2w
104 = 2(3w) + 2w
104 = 6w + 2w
104 = 8w
13 = w
the volume of a gas varies inversely as the pressure on it. if the volume is 240 cm^3 under a pressure of 30 kg/cm^2, what pressure must be applied to have a volume of 120cm^3
Answers
Answer:
V varies 1/P.
V=K/P.
K=VP.
K=240×30.
=7200.
Therefore 7200=VP.
so.....
7200=120P.
P=7200/120.
P=60kg/cm^2.
tickets to a school dance are sold for $10 each the student council spent a total of $400 on setup cost for the dance the school's profit p in dollars from the dance depends on the number of tickets sold which function describes the relationship between p and t
Answers
Answer:
I think it’s p(t)=10t-400
Answer:
t(p) = 10p-400
Step-by-step explanation:
What is the simplified form of the expression 3 + 8x − 2y − x + 1 + 4y? Enter your answers in the boxes.
Answers
Answer:
=7x+2y+4
Step-by-step explanation:
Answer:
7x+2y+4
Step-by-step explanation:
combine like terms:
8x-x=7x
-2y+4y=2y
3+1=4
so the simplified form of the equation is 7x+2y+4
22
O Rational
0 Irrational
Is it rational or irrational
Answers
Answer:
22 is irrational I think
Answer:
22 is a Rational number
Step-by-step explanation:
All integers, whole numbers and natural numbers are rational numbera
Which statement best describes the zeros of the function h(x) = (x-4)2(x - 7x + 10)?
Answers
Answer:
where are the options
Step-by-step explanation:
Answer: The answer is THE FUNCTION HAS THREE DISTINCT REAL ZEROS
Step-by-step explanation:
I’m pretty sure I still need to check if I got it right
What is the difference between the absolute value of 4 and the absolute value of –3?
Answers
Answer:
The absolute value of -3 is three the absolute value of 4 is 4.
Answer:
k bro the correct answer is 7
Step-by-step explanation:do 4 - 4 which equals 0 right then minus 3 more to get -3 therefore your answer is 7 Mark brainliest plz
Show that cos3(B)+cos(B)sin2(B) = 1 sin(B)cos2(B)+sin3(B) tan(B)
Answers
Answer:-90
Step-by-step explanation:
Explain the difference between the associative addition and the commutative addition
Answers
Answer:
Associative states you can regroup numbers and you will get the same answer and the commutative property states that you can move numbers around and still have the same answer.
Example:
Commutative a+b=b+a
Associative a+ (b+c) = (a+b) +c= a+b+c
Answer:
what that person said lol.
Which value would make the statement true? StartFraction 2 Over question mark EndFraction greater-than StartFraction 4 Over 12 EndFraction 4 6 12 24
Answers
Answer:
4
Step-by-step explanation:
Given the expression 2/? > 4/12, to find the value of ? that will make the expression true, we will cross multiply first
On cross multiplying:
2×12 > 4 × ?
24 > 4 × ?
Divide both sides by 4
24/4 > 4×?/4
6 > ?
This means that ? < 6
The answer will be a value that is less than 6. According to the option, the only value less than 6 is 4. Hence the correct answer is 4.
Answer: 4
Step-by-step explanation:
Brandy borrowed $12,500 from her dad and made an agreement to pay him back over 4 years at an annual simple interest of 3%. What is the TOTAL amount she will pay her dad back over the 4 years?
Answers
Answer:
1400 if not compounded
Step-by-step explanation:
12500x.03
Answer:
14,000
Step-by-step explanation:
Step 1:
- 12,500x0.03=375
- 375x4=1500
1500 is the interest amount
but it's asking for the total so
Step 2:
- 12500+1500=14,000
- 14,000 is the TOTAL account balance.
A statistics professor wants to know the average GPA of the students enrolled in their class. They look up information on Canvas about the students enrolled in the class and compute the average GPA as 3.29.a) trueb) false
Answers
Complete question :
A statistics professor wants to know the average GPA of the students enrolled in their class. They look up information on Canvas about the students enrolled in the class and compute the average GPA as 3.29
a. State whether the following statement is true or false. The population is all students enrolled in the accounting class.
b. Does the value 3.29 represent the population parameter or the sample statistic?
Answer:
True ; population parameter
Step-by-step explanation: The population comprises of all sets or participants relating to a study or experiment. For example, a population of male adults in the United States refers to the entire pool of adult population in the country. Hence, in the scenario above, the population refers to the entire student in the accounting class since the accounting class represents the entire pool of students.
B.) population parameter
Statistical estimates derived from a population is called the a parameter, since 3.29 represent the average score of the entire class.
Same statistic represents estimates derived from a sample (subset of the entire population).
The diameter of the Sun is 1.4 x 10⁶ km. The diameter of the planet mars is about 7000km. What is the approximate ratio of the diameter of the Sun to the diameter of Mars?
Answers
Answer:
200 : 1
Step-by-step explanation:
Given that,
The diameter of the Sun is 1.4 x 10⁶ km and the diameter of the planet mars is 7000 km.
We need to find the ratio of the diameter of the Sun to the diameter of Mars. Let the ratio is R. So,
[tex]R=\dfrac{\text{diameter of the Sun}}{\text{diameter of Mars}}\\\\R=\dfrac{1.4\times 10^6\ km}{7000\ km}\\\\R=\dfrac{200}{1}[/tex]
Hence, the ratio is 200:1.
Which number sentence states that x is at most 50?
A. x < 50
B. x < 50
C. x = 50
D.x > 50
E. x > 50
idk this one is kind of confusing me
Answers
Answer:
its A & B, x<50
Step-by-step explanation:
atmost means till 50.
atleast means more than 50.
The number sentence that states that x is at most 50 is option B: x ≤ 50.
In mathematical notation, the symbol "≤" means "less than or equal to." So, x ≤ 50 translates to "x is less than or equal to 50."
This means that x can be any value that is less than 50 or exactly 50.
Option A (x < 50) would mean "x is less than 50," excluding the value 50 itself.
Option C (x = 50) would mean "x is equal to 50," but it doesn't include any values less than 50.
Option D (x > 50) would mean "x is greater than 50," excluding the value 50 itself.
Option E (x ≥ 50) would mean "x is greater than or equal to 50," which includes values greater than 50, but it doesn't allow any values less than 50.
So, the correct choice to state that x is at most 50 (including the value 50) is option B: x ≤ 50.
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How do I solve -2x +6-(-5) +5x
Answers
Answer:
3x+11
Step-by-step explanation:
-2x +6-(-5) +5x
-2x+11+5x
3x+11
Which is the length of x? 1 7/9 2 1/2 1 1/4 1 3/5
Answers
Answer:
option D. x = 1 3/5
Step-by-step explanation:
ratio and proportion
4 = x
5 2
X multiply:
5x = 4(2)
5x = 8
x = 8 / 5
x = 1 3/5
Answer:
x = 1 3/5
Step-by-step explanation:
x = 1 3/5
Simplify the expression completely.
-3V24 - V.
Answers
Answer:
-V (3 V^23 + 1)
Step-by-step explanation:
Simplify the following:
-3 V^24 - V
Factor -V out of -3 V^24 - V:
Answer: -V (3 V^23 + 1)