Answer:
[tex]y = (x - 3)^2 - 12[/tex]
[tex](3,-12)[/tex]
Step-by-step explanation:
Given
[tex]y = x^2 - 6x - 3[/tex]
Solving (a): In vertex form
The vertex form of an equation is:
[tex]y = a(x - h)^2 + k[/tex]
To do this, we make use of completing the square method.
We have:
[tex]y = x^2 - 6x - 3[/tex]
------------------------------------------------------------------
Take the coefficient of x (i.e. -6)
Divide by 2; -6/2 = -3
Square it: (-3)^2 = 9
Add and subtract the result to the equation
------------------------------------------------------------------
[tex]y = x^2 - 6x - 3[/tex]
[tex]y = x^2 - 6x + 9 - 9 - 3[/tex]
[tex]y = x^2 - 6x + 9 - 12[/tex]
Factorize [tex]x^2 - 6x + 9[/tex]
[tex]y = x^2 - 3x-3x + 9 - 12[/tex]
[tex]y = x(x - 3)-3(x - 3) - 12[/tex]
Factor out x - 3
[tex]y = (x - 3)(x - 3) - 12[/tex]
Express as squares
[tex]y = (x - 3)^2 - 12[/tex]
Hence, the vertex form of [tex]y = x^2 - 6x - 3[/tex] is: [tex]y = (x - 3)^2 - 12[/tex]
Solving (b): State the coordinates of the vertex.
In [tex]y = a(x - h)^2 + k[/tex]; the vertex is: (h,k)
The vertex of [tex]y = (x - 3)^2 - 12[/tex] will be [tex](3,-12)[/tex]
HELP‼️‼️‼️‼️‼️‼️‼️‼️
Answer:
a. x^(5/6) + 2x^(7/3)
Step-by-step explanation:
____
5x²—3x—2=0 by completing the square method
Answer:
{1, -2/5}
Step-by-step explanation:
5x^2 - 3x -2 = 0
x^2 - (3/5)x - 2/5 = 0
( x - (3/10) )^2 - (3/10)^2 - 2/5 = 0
( x - (3/10) )^2 = 2/5+9/100
( x - (3/10) )^2 = (7/10)^2
Take square roots on both sides
x - 3/10 = +/- 7/10
x = 3/10 +/- 7/10
= { 1, -2/5 }
Can i get help on this, Ill give brainliest to best explaination
Answer:
x= -3,-2,-1,0,1,2,3..
PLEASE HELP WITH THIS QUESTION
Answer:
3/5
Step-by-step explanation:
There are 12 window seats and 8 aisle seats giving us a total of 20 seats.
12/20 = 3/5
Therefore, the probably the next person will be assigned a window seat is 3/5.
Is this a function? Or is it not a function ? I’ll give brainlist.
Answer:
its a function something to remember is if anything on the y line (up and down) touches its not a function otherwise it is
Step-by-step explanation:
how do i solve this (see image)
Answer:
replace w with -4.
(7-4)-(-4+7)
3-3
p
Answer:
0
Step-by-step explanation:
(7+w) - (w+7)
Distribute the minus sign
7+w - w -7
Combine like terms
w-w +7-7
0
9.
For the graph of the function, identify the axis of symmetry, vertex and the formula for the function.
A. Axis of symmetry: x = 0.5; Vertex: (0.5, –0.75); f(x) = –x2 – x – 1
B. Axis of symmetry: x = 0.5; Vertex: (0.5, –0.75); f(x) = –x2 + x – 1
C. Axis of symmetry: x = –0.5; Vertex: (–0.5, –0.75); f(x) = –x2 + x – 1
D. Axis of symmetry: x = 0.5; Vertex: (0.5, –0.75); f(x) = –x2 + 2x – 1
Answer:
Axis of symmetry: x = 0.5; Vertex: (0.5, –0.75); f(x) = –x2 + x – 1
Step-by-step explanation:
The answer is A because the axis of symmetry is in between 0 and 1, the vertex lies on 0.5 and -0.75, and the parabola opens down so the coefficient of a is -1, and the y-int or the value of c is -1
The vertex of the function is axis of symmetry is and the formula for the function is Option (a) is correct.
Further Explanation:
Given:
Calculation:
The standard form of the parabola is shown below.
Here, the parabola has vertex at and has the symmetry parallel to x-axis and it opens left.
The general form of the parabola can be expressed as follows,
The graph is a downward parabola.
From the graph it has been observed that the vertex of the parabola is
Symmetry of the graph is
The -intercepts of the graph is Therefore, the value of is
The value of is -1 as the graph is a downward parabola.
The vertex of the function is axis of symmetry is and the formula for the function is Option (a) is correct.
Learn more:
1. Learn more about unit conversion brainly.com/question/4837736
2. Learn more about non-collinear brainly.com/question/4165000
3. Learn more aboutbinomial and trinomial brainly.com/question/1394854
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Conic sections
Keywords: vertex, symmetry, symmetric, axis, y-axis, x-axis, function, graph, parabola, focus, vertical parabola, upward parabola, downward parabola.
whats 2+2 then subtracting 3 which you then add 4 more?
Answer:
5
Step-by-step explanation:
2+2-3+4=5
(2+2)=4
(4-3)=1
(1+4)=5
can anybody tell me if this is correct please? thank you.
Answer:
Yep
Step-by-step explanation:
You're correct, Well done!
Answer:
Yes that is correct!
Step-by-step explanation:
(38 x 25)/100 = $9.50
38 - 9.50 = $28.50
f(x) = |x| transforms into function g by a horizontal reflection, shifts left 3 times and 1 time down. What is
g(x)?
Answer:
[tex]g(x) = -|x+3|-1[/tex]
Step-by-step explanation:
1. horizontal reflection - reflection on x-axis: [tex]g(x) = - f(x)[/tex]
[tex]g(x) = -|x|[/tex]
2. shift left 3: [tex]g(x) = f(x+h)[/tex]
[tex]g(x) = -|x+3|[/tex]
3. shift down 1: [tex]g(x) = f(x) - k[/tex]
[tex]g(x) = -|x+3|-1[/tex]
PLZ HELP ILL GIVE BRAINLY!!!!!!!!!!!!
Answer:
Step-by-step explanation:
(3-[tex]\sqrt{2[/tex])(3+[tex]\sqrt{2[/tex])
=(3)^2-([tex]\sqrt{2[/tex] )^2
=9-2
=7
The numbers m, n, p, and q are different, and
each is equal to one of the numbers 1,2,3,6, or 12. If 2m 69 = 2n= = P, what is the value of p?
Confused a bit, can you make sure you copy and pasted it right?
PLEASE HELP GIVING BRAINLY!
Answer:
Opposite angles are equal, all add to 360:
10x-7=83
10x=90
X=9
Z = (360-(83*2))
Z = 97
PLEASE HELP ASAP - ILL GIVE BRAINIEST
can somebody help me pleeaaassseee? 5 star rate
Answer:
x < 3/14
Step-by-step explanation:
-14x > -3
divide each side by -14
however, whenever multiplying or dividing an inequality by a negative value then you must reverse the inequality symbol
x < 3/14
Answer:
divide by -14:
[tex]x<3/14[/tex]
when you divide by a negative the sign flips
Find the slope of the line that passes through the pair of points
(3,-3), (3,-4)
A undefined
B 0
C -7/6
D -6/7
Answer:
undefined
Step-by-step explanation:
To find the slope through 2 points
m = ( y2-y1)/(x2-x1)
= ( -4 - -3)/(3 - 3)
= ( -4+3)/(3-3)
= -1/0
Since it is a number divided by zero, the slope is undefined
I NEED HELP ASAP PLEASE !!!!!
12 men or 15 women can do a piece of work in 21 days find the number of days to complete the same work by 6 men and 10 women
In which quadrant is the point (-5, -4) in?
III
IV
II
I
Answer:
quadrant 3
Step-by-step explanation:
only quadrant 3 contains both negative values for x & y
Answer:
III
Step-by-step explanation:
First, remember the order of the quadrants; quadrant I is in the top right corner then the quadrants increase moving counterclockwise. So, the third quadrant is the bottom left. Each quadrant consist of (x,y) values of different signs.
They are as follows:
I - (x,y)
II - (-x,y)
III - (-x,-y)
IV - (x,-y)
Since, (-5,-4) has two negative coordinates, it must be in the III quadrant.
¿ Cuál es la ecuación de la circunferencia que pasa por punto (-4,2) y
su diámetro es 8 ?
Porfaaaa
Answer:
(x+4)² + (y-k) ² = 16
Step-by-step explanation:
The equation of the circumference is expressed as;
(x-h) ² + (y-k) ² = r²
(h,k) is the centre
r is the radius
Given that diameter = 8
radius = 8/2
radius = 4units
Given that h = -4 and k = 2
(x-h) ² + (y-k) ² = r²
(x-(-4)) ² + (y-2) ² = 4²
(x+4)² + (y-k) ² = 16
This gives the required equation
someone help plsplspls
Answer/Step-by-step explanation:
Volume of a cone = ⅓*π*r²h
Where,
Radius (r) = 7 mm
Height (h) = 8 mm
Plug in the value into the equation
V = ⅓*3.14*7²*8
V = ⅓*3.14*49*8
V = 410.293333
V ≈ 410.3 mm³ (nearest tenth)
what is the remainder of f(x)=x^4-2x^3-27x^2-9x+18 when divided by binomial x+4
Answer:
The remainder will be 6.
Step-by-step explanation:
We have the function:
[tex]f(x)=x^4-2x^3-27x^2-9x+18[/tex]
And we want to find the remainder after it is divided by the binomial:
[tex]x+4[/tex]
We can use the Polynomial Remainder Theorem. According to the PRT, if we have a polynomial P(x) being divided by a binomial in the form (x - a), then the remainder will be given by P(a).
Here, our divisor is (x + 4). We can rewrite this as (x - (-4)).
Therefore, a = -4.
Then according to the PRT, the remainder will be:
[tex]f(-4)=(-4)^4-2(-4)^3-27(-4)^2-9(-4)+18=6[/tex]
The remainder will be 6.
A snow cone is a tasty treat with flavored ice and a spherical bubble gum ball at the bottom, as shown below:
Snow cone with spherical bubble gum ball at the bottom
The radius of the cone is 1.25 inches, and its height is 2.75 inches. If the diameter of the bubble gum ball is 0.5 inches, what is the closest approximation of the volume of the cone that can be filled with flavored ice? (4 points)
Group of answer choices
4.43 in3
0.07 in3
13.50 in3
4.50 in3
==========================================================
Explanation:
The volume of the cone is...
V = (1/3)*pi*r^2*h
V = (1/3)*3.14*(1.25)^2*2.75
V = 4.49739583333333
which is approximate.
-----------
The volume of the sphere is
V = (4/3)*pi*r^3
V = (4/3)*3.14*(0.25)^3 ... note the radius is half the diameter
V = 0.06541666666667
which is approximate as well
-----------
Subtract the two volumes to finish things up
4.49739583333333-0.06541666666667 = 4.43197916666667
The result 4.43197916666667 then rounds to 4.43
This is the approximate amount of empty space in the cone that isn't taken up by the spherical gum. The units are in "cubic inches" or "in^3" for short.
Help Please Pythagorean Theorem
Answer:
1. x = 15
2. x = 26
3. x = 7.6157731059 (you can round this answer to 8 or 7.6)
4. x = 11.7
5. x = 25
6. x = 1.4
7. x = 22.5
8. x = 38.4
9. x = 10.3 v = 5.8
For some of them, I had to use estimation.
I used this formula : a^2 + b^2 = c^2
Help me for 40 points. Thank you very much
Answer:
answer is 11/16 plz give me brainlist
Si alicia se gasta 2 pesos, le quedaría el doble de dinero que si se gastara 4 pesos ¿cuantos tiene alicia?
Answer:
La cantidad de dinero que tiene Alicia es 6 pesos.
Step-by-step explanation:
Un sistema de ecuaciones lineales es un conjunto de dos o más ecuaciones lineales, en el cual se relacionan dos o más incógnitas.
Resolver un sistema de ecuaciones consiste en encontrar el valor de cada incógnita para que se cumplan todas las ecuaciones del sistema. Es decir, se debe buscar los valores de las incógnitas, con los cuales al reemplazar, deben dar la solución planteada en las ecuaciones.
Siendo:
x= cantidad de dinero que tiene Alicia.y= dinero que le quedaría a Alicia si gasta 4 pesos.Entonces el sistema de ecuaciones a resolver es:
[tex]\left \{ {{x-2=2*y} \atop {x-4=y}} \right.[/tex]
Sustituyendo la ecuación 2 en la primer ecuación:
x-2= 2*(x -4)
Resolviendo:
x -2= 2*x -2*4
x -2= 2*x -8
-2 + 8= 2*x -x
6= x
Entonces, la cantidad de dinero que tiene Alicia es 6 pesos.
A rectangle has an area of square unit inside length of 2 1/4 unit find the other side length of the Rectangle
Answer:
Therefore, the other side length of the Rectangle b = 4 (4/9)
Step-by-step explanation:
Although crucial information that area of the rectangle is missing we can assume it be 10 square units for understanding purposes.
Let the sides of the rectangle be a and b.
Given a = 2 1/4 units
a = 9/4 units
b=?
Area of a rectangle = product of its sides = a×b
⇒ a×b= 10
⇒ 9b/4 = 10
⇒ b= 40/9 = 4 (4/9)
Therefore, the other side length of the Rectangle b = 4 (4/9)
What is the perimeter of a rectangle whose length is 1472 m and breadth is 1072 m ?
2472 m
4872 m
25 m
50 m
Answer:
5088 is the perimeter of the rectangle.
Answer:
5088 is the right answer
The formula of perimeter of rectangule is 2(l+b)
So, l=1472 b=1072
2(1472+1072)
2(2544)
2×2544 IS 5088
Bernardo is converting a fraction, StartFraction a Over b EndFraction, to a percent. Both a and b are whole numbers and not equal to zero. Which expression represents the percent? (a divided by b) divided by 100
(b divided by a) divided by 100
100 (a divided by b)
100 (b divided by a)
Answer:
100(a/b)
Step-by-step explanation:
Fraction
a/b
To a percent
100(a/b)
100(a/b)
________________took the test review
(got 100%)
1\tfrac{2}{5} \div \frac{8}{9}
1 5/2 ÷ 9/8
Answer:
Step-by-step explanation:
What you wrote below the top line and the bottom line are not the same thing.
I think you really want the second line, but one can't be sure.
(1*2 + 5)/2 div (9/8)
7/2 // 9/8
7/2 * 8*9
7*8/18 = 56/18 = 28/9
If you really do want the top line (the latex) it is different.
1 2/5 div (8/9) Is there such a thing as tfrac? I didn't know this but there is.
(1*5 + 2)5 // (8/9)
7/5 // 8/9 Invert the bottom fraction and multiply
7/5 * 9 / 8
63 / 40
1 23/40
