Answer:
a = -5/11
Step-by-step explanation:
You want to solve the equation -1/4-a-4=7/4a-3.
SolutionThe first step in solving this 3-step equation can be to add the opposite of (-a) so that the variable 'a' appears only on one side of the equation:
-1/4 -a -4 +a = 7/4a -3 +a
-17/4 = 11/4a -3 . . . . . . . . . . . simplify
The second step is to add the opposite of the constant (-3) so that the constant is on one side of the equation, and the variable is on the other side.
-17/4 +3 = 11/4a -3 +3
-5/4 = 11/4a . . . . . . . . . . simplify
The third step is to multiply by the inverse of the coefficient of the variable:
(4/11)(-5/4) = (4/11)(11/4a)
-5/11 = a . . . . . . . . . . . . . . . simplify
Check-1/4 -(-5/11) -4 = (7/4)(-5/11) -3
-17/4 +5/11 = -35/44 -3
(-187 +20)/44 = (-132 -35)/44
-167/44 = -167/44 . . . . . . answer checks OK
17. Copy each statement. Insert +, -, x, or ÷ symbols to make each statement
true.
a. 17 ? 2? 3 ? 8 = 3
b. 33 ? 3? 2 ? 5 = 1
Answer:
a. 17 - 2 × 3 - 8 = 3
b. 33 ÷ 3 - 2 × 5 = 1
Step-by-step explanation:
a. 17 - 2 × 3 - 8 = 3
b. 33 ÷ 3 - 2 × 5 = 1
determine the midpoint of the line segment connecting (6,-5) and (-1,-6)
The midpoint of the line joining (6,-5) and (-1,-6) is (-5/2,-11/2).
How to determine the midpoint of the line joining two points (a,b) and (p,q)?
To get the midpoint of the line joining two points (a,b) and (p,q), we first have to add the x coordinates of two points and divide it by 2. So the midpoint's x coordinate will be (a+p)/2 . Similarly, we have to do the same with y. Then the midpoint of the line joining two points (a,b) and (p,q) will be [(a+p)/2,(b+q)/2}.
To get the midpoint of (6,-5) and (-1,-6) , first, we have to add the x coordinates and divide it by 2 . And have to do the same with y.
so, the midpoint will be [(6+(-5)]/2,[-5+(-6)]/2.
Hence ans will be ,(-5/2,-11/2)
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4. Which statement about the lines below is true?
7x=-21 and 11y = 55
Select all that apply.
A. Line 11y = 55 is vertical.
B. Line 7x=-21 is vertical.
C. For both lines, all points on the line have an x- and a y-coordinate.
D. For either line, one of the coordinates of all of the points is always the same value.
The statements about lines that is true are
A. Line 11y = 55 is vertical.
C. For both lines, all points on the line have an x and a y-coordinate.
D. For either line, one of the coordinates of all of the points is always the same value.
Lines given to us are
1. 7x = -21
x = -3
2. 11y = 55
y = 5
Now let us check the statements.
A. Line 11y = 55 is vertical.
Yes, it is absolutely true as y = 5 will be a straight vertical line from origin of the graph (0 , 0) to (0 , 5)
B. Line 7x= -21 is vertical.
No, this statement is not true as this will be a horizontal line from (0 , 0) to (-3 , 0)
C. For both lines, all points on the line have an x- and a y-coordinate.
Yes, for both the lines there will be both x and y coordinate as every point on graph has x and y coordinates to represent them.
D. For either line, one of the coordinates of all of the points is always the same value.
Yes, this statement is true as for first line x coordinate is a constant value of 0 and for second line y is a constant value of 0.
Therefore the statements about lines that is true are A, C and D.
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Solve 5x² + 1 = 51 by finding square roots.
x = 50, -50
x = √10,-√10
x = 10, −10
x = √50,-√√/50
Answer:
x = √10,-√10
explanation:
5x2 + 1 = 51
you would carry the +1 to the other side making it
5x2=51-1
which is 5x2=50
this equation above can then be turned into
x2=50÷5
which goes on to form the equation
x2=10
this can then be turned into x=the square root of ten
and since it is know that when an equation is x2 whether it is negative or positive it would result in the same answer
but yeah I'm not smart or whatever but I hope this helps
not too sure it's correct though
Write an equation of the line that passes through each pair of points.(5, −2), (7, −1)
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{5}}} \implies \cfrac{-1 +2}{2} \implies \cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{1 }{ 2 }}(x-\stackrel{x_1}{5}) \implies y +2 = \cfrac{1 }{ 2 } ( x -5) \\\\\\ y+2=\cfrac{1 }{ 2 }x-\cfrac{5 }{ 2 }\implies y=\cfrac{1 }{ 2 }x-\cfrac{5 }{ 2 }-2\implies {\Large \begin{array}{llll} y=\cfrac{1 }{ 2 }x-\cfrac{9}{2} \end{array}}[/tex]
Answer:
y=1/2x-9/2
Step-by-step explanation:
First you want to find the slope by doing -2-(-1)/5-7
Therefore the slope is 1/2
Next you want to add in any set of points, either (5, -2) or (7, -1)
Substitute the x- point in place of x and the y in place of y in y=1/2x+b
Once you do this you should get -2=1/2(5)+b
You should get -2=2 1/2+b
Then subtract 2 1/2 from -2
You should get -4 1/2
Once you have the slope and y- intercept you can put together your problem
y=1/2x-4 1/2
don't forget to convert, y=1/2x-9/2
Hope this helps
At Happy Tails Animal Boarding, cat food and dog food is purchased weekly, Last week, Karen purchased 6 bags of cat food and 9 bags of dog food for a total of 117$. This week, she purchased 4 bags of cat food and 7 bags of dog food for a total of 87$.
Assuming the prices for cat and dog food have not changed over the past two weeks, find and solve the system of equations which can be used to determine the cost of a bag of cat food, c, and the cost of a bag of dog food, d.
c=cost of a bag of cat food
d=cost of a bag of dog food
Write Two Equation
?
?
One bag of cat food costs $6 and one bag of dog food costs $9.
What is system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
The problem states that c equals the cost of bag of cat food and d equals the cost of bag of dog food.
Last week she paid $117 for 6 bags of cat food and 9 bags of dog food.
Therefore, the equation becomes,
6c + 9d = 117 ..(1)
This week she paid $87 for 4 bags of cat food and 7 bags of dog food.
Therefore, the equation becomes,
4c + 7d = 87 ..(2)
Now to solve the system of equations
To solve the first equation for c.
6c + 9d = 117
6c = 117 - 9d
[tex]c = \frac{117}{6}-\frac{9d}{6}[/tex]
Plug value of c in equation (2).
[tex]4(\frac{117}{6}-\frac{9d}{6}) +7d = 87\\78 - 6d + 7d = 87\\d = 87-78\\d = 9[/tex]
Plug d = 9 in equation (1)
6c + 9(d) = 117
6c + 9(9) = 117
6c + 81 = 117
6c = 117 - 81
6c = 36
c = 6
Hence, one bag of cat food costs $6 and one bag of dog food costs $9.
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what is (18x45) divided by 8
The solution for (18x45) divided by 8 = 101.25
Simplify (18x45) divided by 8
Step 1: Rewrite the equation in mathematical terms
we have:
[tex]\frac{18 x 45}{8}[/tex]= [tex]\frac{810}{8}[/tex]
= 101.25
Therefore, the solution for (18x45) divided by 8 = 101.25
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A standard deck of playing cards has 4 different suits (hearts, spades, clubs and diamonds) and 13 different ranks for the cards (ace, 2-10, jack, queen, king). In a poker game you are dealt a hand of 5 cards.
How many ways are there to get dealt exactly a single pair? A pair is a hand with two cards of the same rank. (so two pairs, three of a kind, four of a kind, full house etc. aren't included)
The number of ways that there are to get dealt exactly a single pair is; 6,589,440 ways
What is the probability of Selection?The combination in probability selection is defined as a method where we count the number of ways a certain number of objects can be arranged in "n" different ways. If the number of different objects are "n", then it means that the number of ways that we can select "r" number of different objects is expressed as:
nCr = n!/(r!(n - r)!)
The total number of cards that we have in a deck of cards = 52.
There total number of different cards are 13 in number and this tells us that we can possibly have a pair of any one of the 13 cards. There are also 4 cards of the same rank and this means that the number of ways of selecting two cards of the same rank is; 4C2 = 6 ways
After selecting a card for the pair, we have 48 different cards as an option for the third card. Thereafter, we will have a total of 44 cards as an option for the fourth card and then 40 cards will be an option for the fifth card (due to the fact that none of the cards can be of same rank except for the pair of cards).
Therefore, the total number of ways that we can deal with exactly a single pair can be expressed as:
Number of ways = number of ways for the pair × number of ways for the third card × number of ways for the fourth card × number of ways for the fifth card
Plugging in the relevant values gives;
Number of ways = (13 × 6) × 48 × 44 × 40
= 6,589,440 ways
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What does the transformation f(x) → f(x + 3) - 7 do to the graph of f(x)? choose answer below:
translates it 7 units left and 3 units up
translates it 3 units left and 7 units up
translates it 7 units right and 3 units up
translates it 3 units left and 7 units down
Answer:
3 units left 7 units down
Step-by-step explanation:
if the sign is inside the bracket opposite sign
if the sign is outside the bracket leave it as it is
so (x+3)=0 which means x= -3 so 3 units left since it is on x axis. 7 is on y axis and since it is negative so 7 units down.
Hey can someone please explain this to me I’m a bit confused. Thank you I appreciate it!
The area of given figure is 93mm².
75 less than the product of 30 and a number is -225. What is the number?
Answer:
The Number is -5
Step-by-step explanation:
We will form the Equation and solve for the Number
Let the Number be x
Product of 30 and a Number = 30x
75 less than the Product of 30 and a Number = 30x - 75
75 less than the Product of 30 and a Number is -225
Then 30x - 75 = -225
Now solve for x (the Number)
add 75 for both sides
30x = -225 + 75 = -150
Divide both sides by 30
x = -150 / 30 = -5
Glad to Help
Raina, Trey, and Deandre have a total of $145 in their wallets. Raina has $10 more than Trey. Deandre has 3 times what Raina has. How much do they have in their wallets?
Trey, Raina, and Deandre have $21,$31, and $93 in their wallets respectively.
From the question the sum of the money in their wallets is:
Raina + Trey +Deandre=$145
R + T + D =$145................(i)
Raina has $10 more than Trey= ($10 + T)
Deandre has 3 times more Raina =3($10 + T)
substituting the values of Raina and Deandre in Eqn (i) we have
R + T + D =$145
($10 + T) + T +{3$(10 + T)}=$145
$10 +T +T+ $30 + 3T =$145
5T +$40 = $145
5T = $145 - $40
5T = $105
T = $105/5
T = $21
i.e Trey = $21
Raina has $10 more than Trey= ($10 + T)
i.e = ($10 + $21)
Raina =$31
Deandre has 3 times more Raina =3($10 + T)
=3($10 + $21)
=$30 +$63
Deandre =$93
Therefore the total sum of money in thier wallet is:
Raina + Trey +Deandre=$145
$31 + $21 + $93= $145
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The ratio of teachers to students on a field trip is 2:13. If there are 132 more students than adults on the field trip, how many adults are there and how many students are there?
There are 284 number of students and 152 number of adults.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The ratio of teachers to students on a field trip is 2:13
Let x be the number of adults
If there are 132 more students than adults on the field trip, then 132+x
To find the number of adults and number of students formulate a equation as below
2/13=(x+132)/x
Apply cross multiplication
2x=13(x+132)
Apply distributive law on RHS
2x=13x+1716
11x=1716
Divide both sides by 11
x=152
x+132=152+132=284
Hence there are 284 number of students and 152 number of adults.
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Please help question from 4 through 12 thank you very much
The answer to the questions from 4 through 12 are below:
4. z³ + 5z² + 5z + - 35. 4d + 6c - 66. 20a - 2b - 17. 40x8. 10x + 16y + 149. a² + 8a - 1010. 15v + 22w11. 10c² + 4c12. z³ - 8z² + 5z + 23What is the perimeter of a rectangle and triangle4. z³ + 5z + 3z² + 1 - 4 - 2z²
= z³ + 5z² + 5z + - 3
5. Perimeter of the square = Addition of all the sides
= (2d - 3) + (3c) + (2d - 3) + (3c)
= 2d - 3 + 3c + 2d - 3 + 3c
= 4d + 6c - 6
6. Perimeter of the triangle = Addition of all the sides
= (4a - 2b) + (9a - 4) + (7a + 3)
= 4a - 2b + 9a - 4 + 7a + 3
= 20a - 2b - 1
7. Perimeter of a square = 4 × side length
= 4 × 10x
= 40x
8. Perimeter of a rectangle = 2(length + width)
= 2{(2x + 7) + (3x + 8y)}
= 2(2x + 7 + 3x + 8y)
= 2(5x + 8y + 7)
= 10x + 16y + 14
Simplify the following
9. 3a + a² + 5(a - 2)
= 3a + a² + 5a - 10
= a² + 8a - 10
10. 8(v + w) + 7(v + 2w)
= 8v + 8w + 7v + 14w
= 15v + 22w
11. 4c² + 6(c + c²) - 2c
= 4c² + 6c + 6c² - 2c
= 10c² + 4c
12. z³ + 5(z + 3) + 4(2 - 2z²)
= z³ + 5z + 15 + 8 - 8z²
= z³ - 8z² + 5z + 23
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What is the product of 1.45 and 0.34 rounded off to one decimal place
Answer: 0.5
Step-by-step explanation:
1.45*0.34 = 0.493
Rounded to the tenth place is 0.5
Find the equation of the line
Answer:
[tex]y= \frac 12 x -3\\y=0.5x -3[/tex]
Depending if you can imput fractions, or decimal numbers.
Step-by-step explanation:
The slope can easily calculated as [tex]m=\frac{\Delta y}{\Delta x} = \frac {0-(-3)}{6-0} = \frac 36 = \frac12[/tex]
The y intercept can be easily read from the graph as and is -3
For the functions f(x)=2x4+2x3−x2+2x+3 and g(x)=x+1 find (fg)(x) and (fg)(−4)
The value of the function (fg(x) is 2x⁵ + 2x⁴ + x³ + x ² +5x +3 and the value of f(g)(-4) is -1089.
What is polynomial?A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
Given function is f(x) = 2x⁴ + 2x³− x²+ 2x + 3
The value of the function is calculated as,
f(x) = 2x⁴ + 2x³− x²+ 2x + 3
(fg)(x) = (2x⁴ + 2x³− x²+ 2x + 3)(x+1)
(fg)(x) = (2x⁵ + 2x⁴ + x³ + x ² +5x +3)
The value of (fg)(x) is calculated as,
(fg)(x) = (2x⁵ + 2x⁴ + x³ + x ² +5x +3)
(fg)(-4) = (2(-4)⁵ + 2(-4)⁴ + (-4)³ + (-4)² +5x-4 +3)
(fg)(-4) = -2048 +1024-64+16-20+3
(fg)(-4) = -1089
Therefore, the value of the function (fg(x) is 2x⁵ + 2x⁴ + x³ + x ² +5x +3 and the value of f(g)(-4) is -1089.
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Write an equation in slope-intercept form for the line that passes through (3, 1) and (1,2).
The equation of the line that passes through (3, 1) and (1,2) in slope intercept form is y = - 2 / 2 x + 5 / 2.
How to find equation of a line?The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.
Therefore, let's write the equation of a line that passes through (3, 1) and (1, 2).
using slope intercept form,
y = mx + b
where
m= slopeb = y-interceptTherefore, let's find slope
m = 2 - 1 / 1 - 3
m = 1 / - 2
m = - 1 / 2
Let's find y-intercept using (1, 2)
2 = - 1 / 2(1) + b
b = 2 + 1 / 2
b = 5 / 2
Therefore, the equation is y = - 2 / 2 x + 5 / 2
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A room is 12 m long,10m broad and 6 m high. It has a door of size 1m×2m and a windows of size 2m × 1.5m. Calculate the cost of plastering the walls at the rate of Rs 15/m².
The cost of plastering the rectangle walls at rate of Rs.15/[tex]m^2[/tex] is Rs.5565.
What is rectangle?
With four sides, four corners, and four right angles (90°), a rectangle is a closed 2-D object. A rectangle's opposing sides are equal and parallel. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The opposite sides of a quadrilateral are equal and parallel, and all the angles are equal. Around us, there are several rectangle-shaped items. Two dimensions, the length and breadth, define each rectangle shape. The width and length of a rectangle are its longer and shorter sides, respectively.
Given,
Length of room =12m
Breadth of room =10m
Height of room =6m
So, Area of four walls =2(l+b)×h
=>area of four wall=2(12+10)×6=264[tex]m^2[/tex]
Now Area of 2 doors and 3 windows =(2×1×2+3×2×1.5)
=> area of 2 doors and 3 windows = 13[tex]m^2[/tex]
Area of ceiling =l×b=12×10=120 [tex]m^2[/tex]
Thus, total area for plastering =(264−13+120)= 371[tex]m^2[/tex]
Hence, the cost of whitewashing =Rs.(371×15)=Rs.5565.
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Young Frankenstein has two brothers, Pugsley and Gomez. The sum of their ages is 34. Frankenstein is older than Pugsley, but Pugsley is not the youngest. Gomez is 8 years younger then Frankenstein and Pugsley and Gomez’s ages differ by 5 years. How old are the three brothers?
The age of the three brothers, based on the relationship between the ages of Frankenstein, Pugsley, Gomez, is:
Frankenstein - 15 years Pugsley - 12 years Gomez - 7 yearsHow to find the ages?Frankenstein is older than Pugsley and so is not the youngest. Pugsley is not the youngest according to the question so Gomez must be the youngest.
Assuming Gomez's age is x, the relationship between their ages is:
Gomez age + Pugsley age + Frankenstein age = 34
x + x + 5 + x + 8 = 34
3x + 13 = 34
x = (34 - 13) / 3
x = 7 years
Pugsley's age is:
= x + 5
= 7 + 5
= 12 years
Frankenstein's age is:
= x + 8
= 7 + 8
= 15 years
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Can you write 6 x 10^5 x 0.08 in scientific notation.
Please.
4.8 × 10^4
Step-by-step explanation:= 4.8 × 10^4 {scientific notation}= 4.8e4 {scientific e notation}= 48 × 103 {engineering notation - thousand; prefix kilo- (k)}= 4.8 × 104 {standard form}4 {Order of Magnitude - for scientific and standard forms}= 48000 {real number}= forty-eight thousand {word form}A car dealership increased the price of a certain car by 13%. The original price was $39,400.
Answer:
find the increased dollar amount by finding the percentage amount first:
$ 39,400 * .13
= $ 5,122
then take $ 5,122 and add it to the original price
$ 39,400 + $ 5,122 = $ 44,522 (new price)
Step-by-step explanation:
A rectangular-prism-shaped toy chest is 2 \text { m}2 m2, start text, space, m, end text by 1 \text { m}1 m1, start text, space, m, end text by 1 \text { m}1 m1, start text, space, m, end text.
A shipping crate is packed with 181818 of these toy chests. There is no extra space in the crate.
What is the volume of the crate?
The volume of the crate if there is no extra space in the crate is 36m³.
How calculate the volume?From the information illustrated, the prism is 2m by 1m by 1m abd the shipping crate is packed with 18 of these.
In this case, the volume will be:
= Length × Width × Height
= 2 × 1 × 1
= 2m³
Since there are 18 crates, the total volume will be:
= 2m³ × 18
= 36m³
The volume is 36m³.
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Complete question
A rectangular-prism-shaped toy chest is 2m by 1m by 1m. A shipping crate is packed with 18 of these toy chests. There is no extra space in the crate. What is the volume of the crate?
Identify the values of the variables. Give your answers in simplest radical form. HELP!
The value of the variables in the right triangle are as follows;
[tex]v = \frac{3\sqrt{2} }{2}[/tex][tex]w=\frac{3\sqrt{6} }{2}[/tex]How to find the side of a right tringle?A right triangle is a triangle that has one of its angles as 90 degrees.
The side of a right triangle can be found by using trigonometric ratios.
Therefore, let's find the variable length of the right triangle as follows;
sin 30 = opposite / hypotenuse
sin 30 = v / 3√2
1 / 2 = v / 3√2
cross multiply
3√2 = 2v
divide both sides by 2
v = 3√2 / 2
Let's find the variable w.
cos 30 = adjacent / hypotenuse
cos 30 = w / 3√2
√3 / 2 = w / 3√2
cross multiply
√3 × 3√2 = 2w
3√6 = 2w
divide both sides by 2
w = 3√6 / 2
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Use the summation formulas to rewrite the expression without the summation notation.
The expression without the summation notation is Sₙ = 4(n² - 1)/n²
How to rewrite an expression without the summation notation?
Summation notation is used to write a very long sum (of elements) in a very concise manner. It is also called Sigma notation
Given:
[tex]\displaystyle \sum\limits_{i = 1}^n \frac{12k(k-1)}{n^{3} }[/tex]
Below are the useful summation formulas you will need in order to rewrite the expression without the summation notation:
[tex]\displaystyle \sum\limits_{i = 1}^n i = \frac{{n\left( {n + 1} \right)}}{2}[/tex]
[tex]\displaystyle \sum\limits_{i = 1}^n {{i^2}} = \frac{{n\left( {n + 1} \right)\left( {2n + 1} \right)}}{6}[/tex]
Where i is a variable
Since 12 and n are constants, we can rewrite the given equation as follows:
[tex]\displaystyle \sum\limits_{i = 1}^n \frac{12k(k-1)}{n^{3} } = \displaystyle \frac{12}{n^{3} } \displaystyle\sum\limits_{i = 1}^n k(k-1)[/tex]
[tex]= \displaystyle \frac{12}{n^{3} } \displaystyle\sum\limits_{i = 1}^n k(k-1)[/tex]
[tex]= \displaystyle \frac{12}{n^{3} } \displaystyle\sum\limits_{i = 1}^n (k^{2}-k)[/tex]
[tex]= \displaystyle \frac{12}{n^{3} } ( \displaystyle\sum\limits_{i = 1}^n k^{2} - \displaystyle\sum\limits_{i = 1}^n k )[/tex]
Using the formula, we have:
= 12/n³ ( n(n+1)(2n+1)/6 - n(n+1)/2 ) Factorise n(n+1) out
= 12n(n+1)/n³ ( (2n+1)/6 - 1/2 )
= 12(n+1)/n² ( (2n+1-3)/2 )
= 12(n+1)/n² ( (2n-2/6) )
= 2(n+1)/n² (2n-2)
= ( (2n+2)(2n-2) )/n²
= (4n² - 4)/n²
= 4(n² - 1)/n²
Therefore, using summation formulas to rewrite the expression without the summation notation gives Sₙ = 4(n² - 1)/n²
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5 miles is 8km Convert 22.3miles to km
Answer:
13.9375
Step-by-step explanation:
this is your answer 1234
Harry is paid semimonthly. His
Semimonthly salary is $2,052. What is his
annual salary?
Answer:
$12,312
Step-by-step explanation:
$2,052 * 6 = $12,312
help for brainlest please???
Answer:
45
Step-by-step explanation:
the pattern adds 3 if you look at it care fully
Jason watched a caterpillar move 10 feet in 2 minutes. Jason says that the caterpillar's unit rate is 0.2 feet per minute, Is Json correct? Explain.
Rewrite the equation in standard form from vertex form: y = -4(x - 3)² + 6
The equation of the parabola, in standard form is ______________
y = -4x²+24x-30 is the standard form of parabola whose equation is y = -4(x - 3)² + 6
What is Parabola?Parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
The given equation is y = -4(x - 3)² + 6.
We need to write this equation as standard form of parabola.
the equation of a parabola in standard form is.
y=ax² +bx+c
The given equation should be expanded y = -4(x - 3)² + 6.
y = -4(x²+9-6x)+6
Now apply distributive property
y = -4x²-36+24x+6
y = -4x²+24x+6-36
y = -4x²+24x-30
Hence y = -4x²+24x-30 is the standard form of parabola whose equation is y = -4(x - 3)² + 6
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