Answer:
see explanation
Step-by-step explanation:
Given a quadratic in standard form , y = ax² + bx + c ( a ≠ 0 ), then
The x- coordinate of the vertex, which is also the equation of the axis of symmetry is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = x² + 12x + 32 ← is in standard form
with a = 1, b = 12 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{12}{2}[/tex] = - 6
Substitute x = - 6 into y for corresponding y- coordinate
y = (- 6)² + 12(- 6) + 32 = 36 - 72 + 32 = - 4
Thus
equation of axis of symmetry is x = - 6
vertex = (- 6, - 4 )
To find the y- intercept , let x = 0
y = 0² + 12(0) + 32 = 32 ← y- intercept
The axis of symmetry is x = -6, vertex is (-6,-4) and y-intercept is 32.
Quadratic function:Important information:
The given quadratic function is [tex]y=x^2+12x+32[/tex].Substitute [tex]x=0[/tex] to find the y-intercept.
[tex]y=(0)^2+12(0)+32[/tex]
[tex]y=32[/tex]
The vertex form of a quadratic function is:
[tex]y=a(x-h)^2+k[/tex] ...(i)
Where a is constant, (h,k) is vertex and x=h is the axis of symmetry.
Adding and subtracting the square of half of coefficient of x, the given quadratic function can be written as:
[tex]y=x^2+12x+32+6^2-6^2[/tex]
[tex]y=(x^2+12x+6^2)+32-36[/tex]
[tex]y=(x+6)^2-4[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=1,h=-6,k=-4[/tex]
Therefore, the axis of symmetry is x = -6, vertex is (-6,-4) and y-intercept is 32.
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What 2 numbers multiply to make -48 and combine to make 2?
____ and ___
4 and -12 are equal to -48
Is (3,5) a solution of y>x-3?
Answer:
no it's not
Step-by-step explanation:
Chris had 30 dollars to spend on 3 gifts. He spent 9 7 10 dollars on gift A and 3 2 5 dollars on gift B. How much money did he have left for gift C?
Answer:
4 dolars left
Step-by-step explanation:
im smart
Help me please :(((( I need the formula and faces
Answer:
for prism
let n= no.of sides of the shape of end face
face=n+2
vertices=2n
edge=3n
atq...shape of prism. F. V. E
triangle n=3. 5. 6. 9
rectangle. 6. 8. 12
Pentagon. 7. 10. 15
hexagon. 8. 12. 18
by puuting value of n in above formulas a for f v and e
Your cat is 8 years younger than your friend. In 4 years, your friend will be twice as old as your cat. How old is your cat now?
years old
Answer:
your cat will be 12 your friend will be either 16 or 24
Step-by-step explanation:
Friend is 12 years old and cat is 4 years old.
What is equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side.
Given,
Cat is 8 years younger than your friend
Let age of friend be x
then, age of cat be x - 8
But In 4 years, your friend will be twice as old as your cat
x + 4 = 2(x - 8 + 4)
x + 4 = 2x - 16 + 8
x + 4 = 2x - 8
-2x + x = - 12
x = 12
Age of friend = 12 years
Age of cat = 12 - 8 = 4 years
Hence, 12 years is age of friend and 8 years is age of cat.
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Jessica loves to walk. She walks 3 miles each day. If she wants to walk a total of 57 miles how many days should she walk? Write an equation to show this problem along with the answer. *PLEASE SHOW WORK
Answer:
the answer is 57÷3 =19 days
What is the domain in interval notation of f(x)=(x+3)^2
Given:
The function is
[tex]f(x)=(x+3)^2[/tex]
To find:
The domain of the given function in interval notation.
Solution:
We have,
[tex]f(x)=(x+3)^2[/tex]
Domain is the set of x-values or input values.
The given function is a quadratic function and domain of the quadratic function is all real number. The function is defined for all values of x. So, domain of the given function is the set of all real numbers.
Domain = Set of all real numbers
Domain = (-∞,∞)
Therefore, the domain of the given function is (-∞,∞).
Please Help me! ASAP
A recipe uses 214 cups of flour for a batch of cookies. Henry makes 10 batches of cookies for a bake sale.
A model shows a total of c cups divided into 10 sections, each labeled 2 and 1 fourth.
Part A
Which equation models the total number of cups of flour, c, Henry needs?
c+214=10
214×c=10
10+c=214
214×10=c
Part B
How many cups of flour does Henry need?
2014cups
2212cups
2434cups
2512cups
Part C
Estimate how much flour Henry would need to make 15 batches of cookies. Explain.
I would round 214 to 2, so Henry would need about 30 cups of flour.
I would round 214 to 3, so Henry would need about 45 cups of flour.
I would round 214 to 1, so Henry would need about 15 cups of flour.
I would round 214 to 234, so Henry would need about 30 cups of flour.
Answer:
Step-by-step explanation:
A recipe uses 214 cups of flour for a batch of cookies. Henry makes 10 batches of cookies for a bake sale.
A model shows a total of c cups divided into 10 sections, each labeled 2 and 1 fourth.
Part A
Which equation models the total number of cups of flour, c, Henry needs?
c+214=10
214×c=10
10+c=214
214×10=c
Part B
How many cups of flour does Henry need?
2014cups
2212cups
2434cups
2512cups
Part C
Estimate how much flour Henry would need to make 15 batches of cookies. Explain.
I would round 214 to 2, so Henry would need about 30 cups of flour.
I would round 214 to 3, so Henry would need about 45 cups of flour.
I would round 214 to 1, so Henry would need about 15 cups of flour.
I would round 214 to 234, so Henry would need about 30 cups of flour.
In a game, Annie needs three cards that have a sum of 4. Pick on three cards that Annie could choose.
A). 2
B). -8
C). 3.5
D). -1.5
E). 1
Answer:
A, C, and D
Step-by-step explanation:
2 + 3.5 - 1.5 = 4
What percent of 700 is 364
Answer:
52%
Step-by-step explanation:
4x^2-4x+1 factoring special cases
Answer:
(2x−1)(2x−1)
Step-by-step explanation:
Factor 4x2−4x+1
4x2−4x+1
=(2x−1)(2x−1)
Translate: Four less than twice a number is
twelve
the question is in image!!!!!! plz answer you’ll get 95 points!!
Answer:
Option A is correctStep-by-step explanation:
Given functions f(x) and g(x). f(x) is:
f(x) = x^2 + 4x + 6Converted into vertex form, it is:
f(x) = (x + 2)^2 + 2g(x) has vertex at (-2, -14), it's vertex form is:
g(x) = (x + 2)^2 - 14Comparing f(x) and g(x) we see both have same x- coordinate of the vertex (x = -2).
Both have positive leading factors, therefore the vertex is their minimum point.
Function f(x) has vertex above the x-axis as y-coordinate of the vertex is positive. Hence no intersection with x-axis.
Function g(x) has negative y-coordinate of the vertex, so it has two intersections with x-axis.
Correct choice is A
Answer:a
Step-by-step explanation:
Did it
What is the solution to the equation 4x + 2(x – 3) = 3x + x - 12? (1 point)
1)-3
0 2 -1
3) 1
4) 3
Answer:
the answer to this problem is -3
how many yards are there in 14 1/2 miles?
Answer:
25520 yds
Step-by-step explanation:
Answer:
25,520
Step-by-step explanation:
The formula for yards to miles is that you have multiply the length value by 1760.
So 14.5 * 1,760 = 25,520
Please help it's due today. Also please don't help if you don't know.
Answer:
[tex] {x}^{16} {y}^{22} [/tex]
Step-by-step explanation:
multiple the top exponents by 3 and the u subtract the bottoms
could someone me please
Answer:
0.12 = 1.1 / 9
Step-by-step explanation:
0.12 (2 with a "hat") = 0.12222222222222222222222
0.12 = 1.1/9
1/2(x+10)-2(2 1/2 +3x)
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
Find the volume of the given shape. Round your answer to the nearest
hundredth if necessary.*
Answer:
Step-by-step explanation:
It is a sphere with radius r = 5 cm
volume = (4/3)πr³
= (4/3)π(5³)
≅ 523.60 cm³
During the American Revolution, women... i need help now please i will give 11 points
1.ran family businesses.
2.cared for the troops.
3.helped raise money for the war.
4.all of the above
Answer:
its 4 or d
Step-by-step explanation:
hope this helps!
please mark me brainliest! thanks!
10-+19 please be quick lol
Answer:
Are u asking what 10 +19 is its 29
Please help me answer #2 and #3.
Answer:
#2 - Definition of midpoint
#3 - Vertical Angles Theorem
Nationally, the proportion of red cars on the road is 0.12. A statistically
minded fan of the Philadelphia Phillies (whose team color is red) wonders if Phillies fans are
more likely to drive red cars. One day during a home game, he takes a random sample of 210
cars parked at Citizens Bank Park (the Phillies home field), and counts 35 red cars.
(a) State appropriate hypotheses for performing a significance test. Be sure to define the
parameter of interest.
Answer:
Null hypothesis: proportion of red Phillies cars is 0.12.
Alternate hypothesis: proportion of red Phillies cars is not 0.12.
Step-by-step explanation:
Which is the better deal ‐ $0.20 off of every dollar or 1/4 off every dollar?
Answer:
1/4
Step-by-step explanation:
Answer:i dont know so sorry
Step-by-step explanation
But i think 1/4 or 0.25
7 5/8 =____
+6 6/7=+____
____= ____
The scale drawing of a rectangular playground is shown.
27. 24 cm Playground 20 cm
The actual length of the playground is 36 feet. Using the scale drawing of the rectangle, what is the actual width of the playground?
A. 19 feet
B. 30 feet
C. 32 feet
D. 40 feet
How many unique triangles can be drawn with side lengths 12 cm and 16 cm, and a 50° included angle?
A. 0
B. 1
C. 2
D. an infinite number
HELPPPPPP ASAPPPPPP PLSSS
You bought a Pokemon card at Walmart that costs $5. You found out that it was a rare collectible and that its price was increasing by double every month. How much will the Pokemon card cost after 1 year? (*hint * how many months in a year?)
Answer:
5^12 = $244,140,625.00
Step-by-step explanation:
Restaurant has an early bird special of $7 per plate before 4 PM. The regular price after 4 PM is $9 per plate. If the restaurant sold 93 plates and made $733, how many of those plates were early bird specials
Answer:
the early bird special plate is 52
Step-by-step explanation:
Let us assume the early bird special be x
And, regualr price be y
Now the equations are
x + y = 93
7x + 9y = 733
Now multiply by 7 in equation (1)
7x + 7y = 651
7x + 9y = 733
Now subtract these two equations
-2y = 82
y = 41
x = 93 - 41
= 52
hence, the early bird special plate is 52