Answer:
7 2/5
Step-by-step explanation:
7.08 to improper fraction:
708/100
= 7 2/25
an inch worm is how long in general
Answer:
A inch
Step-by-step explanation:
what is 7k+1<8. and what would it look like on a number line
_
Answer:
[tex]\huge \boxed{k<1}[/tex]
Step-by-step explanation:
[tex]7k+1<8[/tex]
Subtract 1 from both sides.
[tex]7k+1-1<8-1[/tex]
[tex]7k<7[/tex]
Divide both sides by 7.
[tex]\displaystyle \frac{7k}{7} <\frac{7}{7}[/tex]
[tex]k<1[/tex]
Find the vertex and the length of the latus rectum. x= 1/2 (y - 5)² + 7
Answer:
Vertex = (7,5)
Length of latus rectum = 2 units
Step-by-step explanation:
The vertex form of a parabola is
[tex]x=a(y-k)^2+h[/tex] ...(1)
where, (h,k) is vertex and length of latus rectum is [tex]\left|\dfrac{1}{a}\right|[/tex].
The given equation is
[tex]x=\dfrac{1}{2}(y-5)^2+7[/tex] ...(2)
On comparing (1) and (2), we get
[tex]h=7,k=5,a=\dfrac{1}{2}[/tex]
So, vertex of parabola is (7,5).
Length of latus rectum is
[tex]L.R.=\left|\dfrac{1}{a}\right|=\left|\dfrac{1}{\frac{1}{2}}\right|=2[/tex]
Therefore, the length of the latus rectum is 2 units.
A grocery sold 5kg of wheat flour at Rs30 per kg and gained 20%. If he had sold it at Rs27 per kg, what would be his gain or loss percent.
Answer:
His gain percent would have been 8%
Step-by-step explanation:
The key to answering this question is to first calculate the price at which the wheat flour was bought.
Mathematically;
% profit = (selling price-cost price)/cost price * 100%
Let the cost price be $x
Thus;
% profit = (30-x)/x * 100
20 = 100(30-x)/x
20x = 3000-100x
100x + 20x = 3000
120x = 3000
x = 3000/120
x = Rs 25
So let’s assume he sold at Rs 27
His profit would have been 27-25 = 2
His gain or loss percentage would’ve been;
2/25 * 100/1 = 200/25 = 8% (gain, since selling price is greater than the cost price)
Evaluate 6 · 3 ÷ √9 - 1. plz help, will mark brainliest A. 2 B. 3 C. 5 D. 6
Answer: C. 5
Step-by-step explanation:
[tex]6 \cdot3\div \sqrt{9}-1[/tex]
[tex]6 \cdot 3=18[/tex]
[tex]\sqrt{9}=3[/tex]
[tex]18\div \:3-1[/tex]
[tex]18\div \:3=6[/tex]
[tex]6-1[/tex]
[tex]=5\\[/tex]
The value is 16.
What is square root?The square root of a number is that factor of a number which when multiplied by itself gives the original number. Squares and square roots are special exponents. Consider the number 9. When 3 is multiplied by itself, it gives 9 as the product. This can be written as 3 × 3 or 3^2. Here, the exponent is 2, and we call it a square.
We can use four methods to find the square root of numbers and those methods are as follows:
Repeated Subtraction Method of Square RootSquare Root by Prime Factorization MethodSquare Root by Estimation MethodSquare Root by Long Division MethodGiven:
6 · 3 ÷ √9 - 1
6*3 = 18
√9 - 1 = 3-1 = 2
So,
6 · 3 ÷ √9 - 1
=18- 2
=16
Learn more about square root here:
https://brainly.com/question/3120622
#SPJ2
Which function is a quadratic function? a(x) = –2x3 + 2x – 6 b(x) = 5x3 + 8x2 + 3 c(x) = –8x2 + 3x – 5 d(x) = 6x4 + 2x – 3
Answer:
c(x) = –8x² + 3x – 5
Step-by-step explanation:
Function is quadratic if there is x² and no higher exponent with any x
Answer:
C
Step-by-step explanation:
for edge
Remember, a percent is a fractional part
of 100. In a bag of candy, 15 of the 50
pieces are red. What percentage of the
candy is red?
mex
B 50%.
C 3006
D 659
Answer:
Step-by-step explanation:
B
Answer:
The answer would be 30% (although I don't see that as an answer).
Step-by-step explanation:
This is because when you multiply the denominator times a number that makes the denominator 100 and multiply that same number by the numerator you get the percentage of the sample you are looking at on the numerator.
15/50 = (15*2)/(50*2) = 30/100 = 30%
A carpenter has a 10 1/2 foot wood plank. He cuts off 4 1/4 feet to replace a deck board as well as 3 2/3 feet to repair a step. He uses the rest of the plank for a shelf. How many feet of wood does the carpenter have for the shelf? PLEASE SHOW YOUR WORK AND EXPLAIN HOW YOU GOT THE ANSWER PLEASE I WILL MARK YOU BRAINIEST.
Answer:
The carpenter used 2 7/4 feet of plank for the shelf
Step-by-step explanation:
Total length of plank =10 1/2 foot
He used
For Deck board=4 1/4 feet
Step=3 2/3 feet
Shelf=x feet
Total plank=deck board + step + shelf
10 1/2 = 4 1/4 + 3 2/3 + x
Change the fractions
21/2 = 17/4 + 11/3 + x
Add 17/4 + 11/3
21/2 =51+44/12 + x
21/2= 95/12 + x
Collect like terms
21/2 - 95/12 =x
126-95/12 = x
31/12=x
2 7/12 =x
Therefore, the carpenter used 2 7/4 feet of plank for the shelf
Answer:
Step-by-step explanation:
Total length of plank =10 1/2 foot
He used
For Deck board=4 1/4
Step=3 2/3
Shelf=x
Total plank=deck board + step + shelf
10 1/2 = 4 1/4 + 3 2/3 + x
Combine like terms to create an equivalent expression. -3.6-1.9t+1.2+5.1t
Answer:
3.2t-2.4Step-by-step explanation:
[tex]\\-3.6-1.9t+1.2+5.1t\\\mathrm{Group\:like\:terms}\\\\=-1.9t+5.1t-3.6+1.2\\\\\mathrm{Add\:similar\:elements:}\:-1.9t+5.1t=3.2t\\\\=3.2t-3.6+1.2\\\\=3.2t-2.4[/tex]
Answer:
3.2t -2.4
Step-by-step explanation:
-3.6-1.9t+1.2+5.1t
Like by terms = -1.9t+5.1t - 3.6 +1.2
Solve left to right step 1 = 3.2t - 3.6 +1.2
Solve step 2 = 3.2t - 2.4
Choose all properties that were used to simplify the following problem:
(38 +677) + (-38)
[677 + 38) + (-38)
677 + [38 + (-38)]
677 + 0
677
additive identity
additive inverse
commutative property of addition
associative property of addition
distributive property
The properties 1‚ 2‚ 4‚ and 5. are used
The properties used to simplify problem are 1 , 2 and 4.
A problem which is simplified is given ; (38 +677) + (-38).
What are the correct options ?
How will you represent the associative properties of addition ?
Associative properties are represented by ; (A + B ) + C = A + ( B + C ).
As per the data given in question ;
Let's check which options are suitable.
( 38 + 677 ) + ( -38 ) = 38 + ( 677 - 38 )
(A + B ) + C = A + ( B + C )
So , this is the associative property.
677 + 0 = 677
A + 0 = A
So , this is the additive identity.
677 + [38 + (-38)]
Here ; 38 + ( -38 ) represents ;
A + (-A) = 0.
So , this is the additive inverse.
Thus , the properties used to simplify problem are 1 , 2 and 4.
To learn more about addition properties click here ;
https://brainly.com/question/643393
#SPJ2
Witch of the following numbers are greater then or equal to 4/7
A 2/5
B .57
C 2/3
Answer:
2/3
Step-by-step explanation:
Its simple. Ona calculator, if you type in these fractions, you can compare then decimal form values and see which is the biggest:
4/7 = .5714
2/5 = .04
.5/7.0714
2/3 = .66667
Since .6667 is greater than .5714, 2/3 is greater than 4/7
Answer:
B: .57
C: 2/3
Step-by-step explanation:
Divide 4/7 = .57
A: divide 2/5 = 0.4, which is less than 4/7 so we won't include this number as one of the answers
B: .57, which is equal to 4/7
C: divide 2/3 = 0.67, which is greater than 4/7
This question has two answers (B and C), because it is asking which numbers are greater than or equal to.
Evaluate 5(14 - 2³) +8 ÷ 2.? Plz help me, will mark you as brainliest A. 26 B. 34 C. 44 D. 56
Answer:
[tex]\large \boxed{\sf B. \ 34}[/tex]
Step-by-step explanation:
[tex]5(14 - 2^3 ) +8 \div 2[/tex]
[tex]\sf Solve \ brackets.[/tex]
[tex]2^3 =8[/tex]
[tex]5(14 - 8 ) +8 \div 2[/tex]
[tex]14-8=6[/tex]
[tex]5(6 ) +8 \div 2[/tex]
[tex]\sf Multiply \ and \ divide.[/tex]
[tex]5(6)=30[/tex]
[tex]8 \div 2 = 4[/tex]
[tex]30 +4[/tex]
[tex]\sf Add.[/tex]
[tex]34[/tex]
Answer: 34
Step-by-step explanation: It's very easy to make mistakes in order of operations problems if you try to do too much of the problem in your head.
It really is worth the extra time it takes to write out every step.
P E M D A S
Parenthses
Exponents
Multiplication/Division
Addition/Subtraction
In this problem, simplify (14 - 2³) first
because it's located inside the parenthses.
2³ is 8 so our second step reads 5(14 - 8) + 8 ÷ 2.
14 - 8 is 6 so we have 5(6) + 8 ÷ 2.
Now multiplication and division are based on order of appearance.
Since multiplication comes first, we do it first.
5(6) is 30 so we have 30 + 8 ÷ 2.
Now we can do the division.
8 ÷ 2 is 4 and we have 30 + 4 which is 34.
show that (2x+3)^3 = 8x^3+36x^2+54x+27 for all values of x
Answer:
see explanation
Step-by-step explanation:
Given
(2x + 3)³
= (2x + 3)(2x + 3)(2x + 3) ← expand the last 2 factors using FOIL
= (2x + 3)( 4x² + 12x + 9)
= 2x(4x² + 12x + 9) + 3(4x² + 12x + 9) ← distribute parenthesis
= 8x³ + 24x² + 18x + 12x² + 36x + 27 ← collect like terms
= 8x³ + 36x² + 54x + 27
Simplify. Can you explain it also?
[tex] \frac{9 {c}^{3} {de}^{2} }{12 {c}^{2}d {e}^{3} }[/tex]
Answer:
The answer is
[tex] \frac{3c}{4e}[/tex]Step-by-step explanation:
[tex] \frac{9 {c}^{3}d {e}^{2} }{12 {c}^{2} d {e}^{3} } [/tex]To solve the fraction reduce the fraction with d
That's we have
[tex] \frac{9 {c}^{3} {e}^{2} }{12 {c}^{2} {e}^{3} } [/tex]Next simplify the expression using the rules of indices to simplify the letters in the fraction
For c
Since they are dividing we subtract the exponents
We have
[tex] {c}^{3} \div {c}^{2} = {c}^{3 - 2} = c^{1} = c[/tex]For e
[tex]e^{2} \div {e}^{3} = e^{2 - 3} = {e}^{ - 1} = \frac{1}{e} [/tex]Substituting them into the expression we have
[tex] \frac{9c}{12e} [/tex]Reduce the fraction by 3
We have the final answer as
[tex] \frac{3c}{4e} [/tex]Hope this helps you
1 - Os coeficientes numéricos de uma equação do 2º grau (ax² + bx + c = 0), são números reais representados pelas letras “a, b e c”. Para que uma equação do 2º grau possa existir, é necessário que o coeficiente “a” seja DIFERENTE de: * 1 ponto a) -2 b) -1 c) 0 d) 1 2) Usando o método de Tentativa e Erro, visto na aula, qual das alternativas abaixo representa uma raiz da equação: x²-5x+6=0 * 1 ponto a) x = 0 b) x = 1 c) x = 2 c) x = -2
Answer:
1) La opción correcta es;
c) 0
2) La opción correcta es;
c) x = 2
Step-by-step explanation:
1) La forma general de una ecuación cuadrática se puede escribir en la forma;
a · x² + b · x + c = 0
Dónde;
a, y b son los coeficientes de x², x y c es el término constante
Por tanto, para que exista un polinomio de 2º grado es necesario que el coeficiente a sea diferente de 0
De lo que tenemos;
(0) × x² + b · x + c = 0, lo que da;
(0) × x² + b · x + c = b · x + c = 0 que es una ecuación lineal o un polinomio de primer grado
Por tanto, la opción correcta es c) 0
2)
La ecuación dada se presenta como sigue;
f (x) = x² - 5 · x + 6 = 0
Usando el método de prueba y error, tenemos;
Cuando x = 0
f (0) = 0² - 5 · (0) + 6 = 6 que no es igual a 0 y, por lo tanto, no es una solución
Cuando x = 1
f (1) = (1) ² - 5 · (1) + 6 = 1 que no es igual a 0 y por lo tanto, no es una solución
Cuando x = 2
f (2) = (2) ² - 5 · (2) + 6 = 0 que es igual a 0 y por lo tanto, es una solución
Cuando x = -2
f (1) = (-2) ² - 5 × (-2) + 6 = 20 que no es igual a 0 y por lo tanto, no es una solución
Por tanto, la opción correcta es c) x = 2
ANSWER QUICKLY PLZZZZZZ ASAP
Answer:
m = 2G² + 5Step-by-step explanation:
[tex]G = \sqrt{ \frac{m - 5}{2} }[/tex]
To make m the subject square both sides of the equation
That's
[tex] \frac{m - 5}{2} = {G}^{2} [/tex]
Cross multiply
m - 5 = 2G²
Move 5 to the right side of the equation to make m stand alone
We have the final answer as
m = 2G² + 5Hope this helps you
Answer:
A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for .
The rectangle is 4 inches long and 3 inches wide. The semi-circle sits on top of the rectangle on a side that is 4 inches long.
Step-by-step explanation:
The number that is 75% of one less than a number n.
Answer:
The number is n-0.75
Step-by-step explanation:
Here in this question, we are interested in giving a number which is 75% of 1 less than a number n.
The first thing we do here is to calculate the value of 75% of 1.
That would be;
75/100 * 1 = 0.75
So this value less than n will be;
n- 0.75
Ohm's law states That the current That the current (I) In amps equals the voltage (E) In volts divided by the resistance (R) in ohms. If you connected a two megohm resistor (2 x 10 6 ohms) Across a 2.4 kilovolt Voltage source parentheses 2.4Times 10 to the third power volts) What would be the current in amps
Answer:
1.2 milli ampsStep-by-step explanation:
From ohms law the expression for voltage is given as
[tex]V= IR[/tex]
Now given that
Voltage, V= [tex]2.4*10^3[/tex] volts
Resistance R= [tex]2*10^6[/tex] ohms
Applying ohms law the current can be calculated by making I the subject of formula
that is I= V/R
[tex]I= \frac{2.4*10^3}{2*10^6} \\\\I= \frac{2.4}{2} *10^(^3^-^6^)\\\\I=1.2*10^-^3[/tex]
The current in amps is 1.2 milli amps
1. An atom consist of charged particles called electrons and protons. Each proton has a charge of +1 and each electron has a charge of -1.Remember number of electrons is equal to number of protons, while answering these questions i) What is the charge on an atom? Ii) What will be the charge of an atom if it loses an electron? Iii) What will be the charge of an atom if it gains an electron?
Answer:
I) no charge
ii) it will be positively charged
iiI) it will be negatively charged
Step-by-step explanation:
An atom is composed of electrons, neutrons and protons. Electrons are negatively charged while protons are positively charged. The number of electrons and protons in a neutral atom are exactly the same. This ensures the electrical neutrality of the atom.
However, if an atom looses an electron, there are now more protons than electrons present in the atom hence the atom is positively charged.
Similarly, if an atom gains an electron, it now contains more electrons than protons, hence it is negatively charged.
Please answer it now in two minutes
Answer:
x = 84
Step-by-step explanation:
∠ UWV is an angle in a semicircle and is right = 90°
VW = UW thus Δ UVW is right isosceles, thus
∠ UVW = ∠ WUV = 45° ( sum of angles in triangle ) , thus
x - 39 = 45 ( add 39 to both sides )
x = 84
ANSWER QUICKLY PLZZZZZZ
ANSWER QUESTION C
Answer:
[tex] \boxed{12}[/tex]Step-by-step explanation:
E is 5 more than d
f is 7 less than d
a) e = d + 5
b) f = d - 7
c) plug the values of e and f
[tex] = d + 5 - (d - 7)[/tex]
When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression
[tex] = d + 5 - d + 7[/tex]
Since, two opposites add up to zero , remove them from the expression
[tex] = 5 + 7[/tex]
Add the numbers
[tex] = 12[/tex]
Hope I helped!
Best regards!
Water flows through a pipe at a rate of 4 quarts per day. Express this rate of flow in liters per week. Round your answer to the nearest tenth.
Answer:
26.5 liters
Step-by-step explanation:
We know that 1 gallon is 4 quarts, and 1 gallon is approx. 3.78 liters. There's 7 days in a week, so 7 gallons of water is being flowed through. Multiplying 3.78 by 7, we get 26.46 liters per week. Rounding to the nearest tenth, and we get 26.5 liters.
Can anyone help me with this question ?
Answer:
each shirt costs $17.50.
Step-by-step explanation:
we have the equation 4(12.50) + 4(2x) = 190
because each friend (4 total friends) get one hat and two shirts.
we simplify the equation to 50 + 8x = 190
subtract 50 from both sides
8x = 140
divide both sides by 8
x = 17.5
therefore, each shirt costs $17.50.
SUPER URGENT HELP NEEDED! BRAINLIEST AVAILABLE!
HELP IN NEED THESE ANSWERED ASAP! WILL GIVE BRAINLIEST TO THE PERSON WHO CAN ANSWER THESE QUICKEST AND I NEED ANSWERS TO ALL 4, BUT DON'T NEED ANY WORKING OUT, BUT IF YOU WANT TO YOU CAN! ALSO IF YOU ONLY KNOW THE ANSWER TO 1 OR 2 OF THEM, JUST SEND THAT, AND I WILL STILL GIVE YOU BRAINLIEST!
Answer:
1B)[tex] 11[/tex]
1C)$ 5104$
1D) $A=3 B=-51$
1E) [tex] \frac{1}{8}[/tex]
Step-by-step explanation:
The above answer!
Pattern A starts at 20 and has the rule 'subtract 2 Pattern B starts at 20 and has
the rule 'subtract I". Which shows the first several terms of Patterns A and B?
Pattern A: 20, 17, 15, 13, 11,
Pattern B: 20, 19, 18, 17, 16, 15
Pattern A: 20, 18, 16, 14, 12, 10
Pattern B: 20, 21, 22, 23, 24, 25
Pattern A: 20, 18, 16, 14, 12, 10
Pattern B: 20, 19, 18, 17, 16, 15
Pattern A: 20, 22, 24, 26, 28, 30
Pattern B: 20, 21, 22, 23, 24, 25
Answer:
The correct option is C.
Step-by-step explanation:
The two patterns are defined as follows:
Pattern A starts at 20 and has the rule 'subtract 2'.Pattern B starts at 20 and has the rule 'subtract 1'.Form the two patterns as follows:
Pattern A : 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0
Pattern B : 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
The first several terms of Patterns A and B are shown by:
Pattern A: 20, 18, 16, 14, 12, 10
Pattern B: 20, 19, 18, 17, 16, 15
Thus, the correct option is C.
a number is multiplied by 5 and the results is twice the number added to 2 find the number
Answer:
5x=2x+2
3x=2
X=2/3
Hope this helps ФωФ
In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from $1$ to $10$, and one SuperBall is drawn (at random) from ten red balls numbered from $11$ to $20$. When you buy a ticket, you choose three numbers from $1$ to $10,$ and one number from $11$ to $20$. If the numbers on your ticket match at least two of the white balls or match the red SuperBall, then you win a super prize. What is the probability that you win a super prize?
nCr(20, 2) = 190 ways of selecting 2 from 20
nCr(10, 1) = 10 ways of selecting 1 from 10
To find the over all probability of winning,
Calculate the Harmonic Mean (19) and divide by 2
Equivalent to
1/ (1//190 + 1/10) =9.5
So the probability is 1/9.5 = 2/19.
PlZ HELP NOW ASAP!!!
Answer:
x=33
Step-by-step explanation:
x for ?
sinx=opposite/hypotenuse
sinx=162.5/298=0.54530201
convert to degrees using arcsin(0.54530201)= 33.043
33 degrees rounded to the nearest ones
Solve for xxx. 12x+7 4012x+7 40
Answer:
[tex]x = 2.75[/tex]
Step-by-step explanation:
I'm assuming you have an equation
[tex]12x + 7 = 40\\[/tex]
and you want to solve for x.
This is easy. First, subtract 7 from each side of the equation.
[tex]12x+7-7 = 40-7[/tex]
[tex]12x = 33[/tex]
Then divide both sides by 12, to get x alone on the left side.
[tex]\frac{12x}{12} = \frac{33}{12}[/tex]
[tex]x = \frac{33}{12} = 2.75[/tex]
20 POINTS! Please help.! 1) Given the following three points, find by hand the quadratic function they represent. (0,6), (2,16), (3, 33) A. f(x)=4x2−3x+6 B. f(x)=4x2+3x+6 C. f(x)=−4x2−3x+6 D. f(x)=−4x2+21x+6 2) Given the following three points, find by hand the quadratic function they represent. (−1,−8), (0,−1),(1,2) A. f(x)=−3x2+10x−1 B. f(x)=−3x2+4x−1 C. f(x)=−2x2+5x−1 D. f(x)=−5x2+8x−1 3) Find the equation of a parabola that has a vertex (3,5) and passes through the point (1,13). A. y=−3(x−3)2+5 B. y=2(x−3)2+5 C. y=−2(x−3)2+5 D. y=2(x+3)2−5
Answer:
1) f(x) = 4·x² - 3·x + 6
2) f(x) = -2·x² + 5·x - 1
3) y = 2·(x - 3)² + 5
Step-by-step explanation:
1) The quadratic function that is represented by the points (0, 6), (2, 16), (3, 33) is found as follows
The general form of a quadratic function is f(x) = a·x² + b·x + c
Where, in (x, y), f(x) = y, and x = x
Therefore for the point (0, 6), we have;
6 = 0·x² + 0·x + c
c = 6
We have c = 6
For the point (2, 16), we have;
16 = a·2² + b·2 + 6
10 = 4·a + 2·b.............................(1)
For the point (3, 33), we have;
33 = a·3² + b·3 + 6
27 = 9·a + 3·b............................(2)
Multiply equation (1) by 1.5 and subtract it from equation (2), we have;
1.5 × (10 = 4·a + 2·b)
15 = 6·a + 3·b
27 = 9·a + 3·b - (15 = 6·a + 3·b) gives;
27 - 15 = 9·a - 6·a+ 3·b - 3·b
12 = 3·a
a = 12/3 = 4
a = 4
From equation (1), we have;
10 = 4·a + 2·b = 4×4 + 2·b
10 - 4×4 = 2·b
10 - 16 = 2·b
-6 = 2·b
b = -3
The function, f(x) = 4·x² - 3·x + 6
2) Where the points are (-1, -8), (0, -1), (1, 2), we have;
For point (-1, -8), we have -8 = a·(-1)² - b·(-1) + c = a - b + c......(1)
For point (0, 1), we have -1 = a×0² + b×0 + c = c.........................(2)
For point (1, 2), we have 2 = a×1²+ b×1 + c = a + b + c..............(3)
Adding equation (1) to equation (3) gives
-8 + 2 = a - b + c + a + b + c = 2·a + 2·c where, c = -1, we have
-8 + 2 = -6 = 2·a + 2
2·a = -6 + 2 = - 4
a = -8/2 = -2
From equation (3), we have;
2 = a + b + c
b = 2 - a - c = 2 - (-2) - (-1) = 2 + 2 + 1 = 5
f(x) = -2·x² + 5·x - 1
3) The equation of a parabola that has vertex (3, 5) and passing through the point (1, 13) is given by the vertex equation of a parabola
The vertex equation of a parabola is y = a(x - h)² + k
Where;
(h, k) = Vertex (3, 5)
(x, y) = (1, 13)
We have
13 = a·(1 - 3)² + 5
13 = a·(-2)² + 5
13 - 5 = a·(-2)² = 4·a
4·a = 8
a = 8/4 = 2
The equation is y = 2·(x - 3)² + 5.
