100 POINTS !!! Find the axis of symmetry and the vertex of the graph of y = 6x2 − 24x + 11. x = 2; (2, −13) x = 4; (4, 11) x = −2; (−2, 83) x = −4; (−4, −11)
Answers
Let's see
[tex]\\ \rm\rightarrowtail y=6x^2-25x+11[/tex]
Graph attached
vertex(-2,-13)Axis of symmetry
x=-2
Answer:
axis of symmetry: x = 2
vertex: (-2, 13)
Step-by-step explanation:
Given function
[tex]\sf y=6x^2-24x+11[/tex]
Vertex form
[tex]\sf y=a(x-h)^2+k[/tex]
where (h, k) is the vertex
Expand vertex form:
[tex]\sf \implies y=ax^2-2ahx+ah^2+k[/tex]
Compare coefficients of expanded vertex form with given function:
coefficient of [tex]\sf x^2[/tex]:
⇒ a = 6
coefficient of [tex]\sf x[/tex]:
⇒ -2ah = -24
⇒ ah = 12
⇒ 6h = 12
⇒ h = 2
constant:
⇒ [tex]\sf ah^2+k=11[/tex]
⇒ [tex]\sf 6 \cdot 2^2+k=11[/tex]
⇒ [tex]\sf 24+k=11[/tex]
⇒ [tex]\sf k=-13[/tex]
Vertex
Vertex = (2, -13)
Axis of symmetry
Axis of symmetry is when x = h
Therefore, axis of symmetry is x = 2
Related Questions
100 BRAINLY POINTS!!!!
The cost, y, in dollars, to purchase x school T-shirts includes a one-time setup fee, plus a charge per T-shirt. The cost is modeled with the linear function y = 6.67x + 35. What is the cost to purchase each T-shirt after the beginning setup cost is paid?
A. $41.67
B. $35.00
C. $28.33
D. $6.67
PLEASE HELP CUH
EXPLAIN YOUR ANSWER
SHOW YOUR WORK
Answers
Let's check our given function.
y=6.67x+35Compare to y=mx+b(Slope intercept)
Slope=m=6.67Y intercept=b=35So beginning set up is fixed i.e 35 .
per shirt cost the rate of change which is slope
option D is correct
ZA and ZB are vertical angles. If mA = (2x - 4)º and mZB = (4x - 30),
then find the value of x.
Answers
Answer:
x=13
Step-by-step explanation:
2x-4 = 4x - 30
-4 = 2x - 30
26 = 2x
x = 13
I need help on this question I’m confused I think a &b are the same and c &d are different but I’m not to sure !
Answers
====================================================
Reason:
[tex]2^6[/tex] means we have 6 copies of "2" multiplied out as shown in choice B. That explains how A and B are the same, and we can say
[tex]2^6 = (2*2*2)*(2*2*2)[/tex]
The parenthesis are optional, but I find they're handy to count the '2's easier.
----------------
Now notice that
[tex]2^3 = 2*2*2[/tex]
So,
[tex]2^6 = (2*2*2)*(2*2*2)\\\\2^6 = (2^3)*(2^3)\\\\2^6 = (2^3)^2\\\\[/tex]
The last step is possible because we have two copies of [tex]2^3[/tex] multiplied together.
This shows that choice C is equivalent to A and B.
-------------------
Lastly,
[tex]2^6 = (2*2*2)*(2*2*2)\\\\2^6 = (2*2)*(2*2)*(2*2)\\\\2^6 = (2^2)*(2^2)*(2^2)\\\\2^6 = (2^2)^3\\\\[/tex]
The jump to the last step is possible because we have three copies of [tex]2^2[/tex] multiplied together.
This shows choice D is equivalent to the others.
All four expressions are the same.
They represent different ways to say the same number. That number being 64.
Given the function h of x equals 8 times the cube root of x minus 6 end root plus 16, what is the x-intercept of the function?
–6
–2
2
16
Answers
The x-intercept of the function h(x) is when the function h(x) = 0
The x-intercept of the function is -2
How to determine the x-intercept?From the question, the function is given as:
[tex]h(x) = 8 * \sqrt[3]{x - 6} + 16[/tex]
Set the function h(x) to 0, to calculate the x-intercept
[tex]8 * \sqrt[3]{x - 6} + 16= 0[/tex]
Subtract 16 from both sides of the equation
[tex]8 * \sqrt[3]{x - 6} +=-16[/tex]
Divide through by 8
[tex]\sqrt[3]{x - 6} =-2[/tex]
Take the cube of both sides
[tex]x - 6 =-8[/tex]
Add 6 to both sides
[tex]x =-2[/tex]
Hence, the x-intercept of the function is -2
Read more about x-intercept at:
https://brainly.com/question/3951754
Answer:
-2
Step-by-step explanation:
The person above me explained it perfectly! Also, I got this answer correct on my test.
b. Maria is watching cell growth in a lab. The cells double every 30 minutes. If there were 3 cells
initially, how many cells are there in 5 hours
Answers
Answer:
3072
Step-by-step explanation:
The number of cells is initially 3 and is multiplied by 2 every time t increases by 1/2 hour. This means the exponential function describing the number of cells can be written ...
y = (initial value) × (growth factor)^(t/(growth period)
y = 3 × (2^(t/(1/2)) = 3×2^(2t)
After 5 hours, the number of cells will be ...
y = 3×2^(2·5) = 3×2^10 = 3×1024
y = 3072
There are 3072 cells in 5 hours.
_____
Additional comment
The function could be simplified to ...
y = 3×4^t
Blue Tide Swim Shop is having its annual summer sale, when every item in the store gets marked down. During the sale, rashguards sell for $5 less than full price. Miguel purchases 3 rashguards and pays a total of $60.
Which equation can you use to find how much money, f, each rashguard costs at full price?
How much does each rashguard cost at full price?
Answers
Original price be x
Discount price be y
The equation is
y=x-5So
y=3(x-5)60=3x-153x=75x=25$Answer:
3(f - 5) = 60
$25
Step-by-step explanation:
Let f = full price of rash-guard
Given:
during the sale, rash-guards sell for $5 less than full pricecost of 3 rash-guards during sale is $60Therefore, the equation you can use to find how much money each rash-guard costs at full price is:
3(f - 5) = 60
To calculate the full price of the rash-guard, solve the equation for f:
⇒ 3(f - 5) = 60
Expand:
⇒ 3f - 15 = 60
Add 15 to both sides:
⇒ 3f = 75
Divide both sides by 3:
⇒ f = 25
Therefore, the full price of each rash-guard is $25.
Answer number 9 please. Thank you.
Answers
The above attachment is the answer. Hope it helps?
The ratio of green marbles to yellow marbles is
4 green marbles to 6 yellow marbles.
If there are 2 green marbles,
how many yellow marbles are there?
Answers
Answer:
There are three yellow marbles.
Step-by-step explanation:
The way i figure it is since they are both even numbers divide them both by two and you have your answer.
Hannah travels 6 times as many minutes to work as Raoul does. Together,
they travel for 63 minutes. How many minutes does Hannah travel? Draw
a model and write an equation to solve.
Answers
Answer:
hannah 54
raoul 9
Step-by-step explanation:
hannah _ 6x
raoul _ x
6x+x=63
7x=63
x=9
hannah _ 6×9=54
raoul _ 9
HELP PLEASE FOR NUMER 3 and 4 PLEAESE ASAP ANI WILL GIVE BRANILESS FOR THE FIRST PERSON
Answers
Step-by-step explanation:
I don't understand this question
come again
let f(x)=3x+4 and g(x)=2x-5 find (f+g)(x)
Answers
Answer:
(f+g)(x) = 5x - 1
Step-by-step explanation:
Let f(x) = 3x + 4 and g(x) = 2x - 5 find (f+g)(x)
f(x) = 3x + 4 and g(x) = 2x - 5, find (f+g)(x)
(f+g)(x) =
f(x) + g(x)
3x + 4 + 2x - 5 (combine like terms)
5x - 1
Therefore, (f+g)(x) = 5x - 1
Hope this helps!
Answer:
5x -1
Step-by-step explanation:
(3x + 4) + (2x - 5) = 3x + 4 + 2x - 5 = 3x + 2x + 4 - 5
5x - 1
What is the solution set of the quadratic inequality f
Answers
Answer:
A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. The solutions to quadratic inequality always give the two roots. The nature of the roots may differ and can be determined by discriminant (b2 – 4ac).
Find the AREA of the figure. (Sides meet at right angles.)
Answers
Answer:
47
Step-by-step explanation:
3 x 4 = 12
7 x 5 = 35
35 + 12 = 47
Is πxy=4 a linear equation?
Answers
Answer:
Yes
Step-by-step explanation:
It is a first-degree equation. Look at the exponents of each variable (x, y), they are not written because they are 1
Hope this helps
Find the area. :)
please and thx
Answers
Answer:
132 cm²
Step-by-step explanation:
To find the area of the figure, start by dividing the figure into smaller rectangles.
Area of figure
= area of shaded rectangle +area of unshaded rectangle
[tex]\textcolor{steelblue}{\text{Area of rectangle= length ×breadth}}[/tex]
Shaded rectangle
Length= 4 cm
Breadth= 6 cm
Area
= 4(6)
= 24 cm²
Unshaded rectangle
Length= 9 cm
Breadth= 12 cm
Area
= 9(12)
= 108 cm²
After finding the area of each rectangle, we can add the two areas together to obtain the total area of the figure.
Area of figure
= 108 +24
= 132 cm²
what are the possible values of remainder r, when a positive integer 'a' is divided by 3
Answers
Answer:
0, 1, 2
Step-by-step explanation:
Euclid's division Lemma states that for any two positive integers ‘a’ and ‘b’ there exist two unique whole numbers ‘q’ and ‘r’ such that , a = bq + r, where 0≤ r < b.
Here, a= Dividend, b= Divisor, q= quotient and r = Remainder.
According to Euclid's division lemma a 3q+r, where 0≤r≤3 and r is an integer.
Therefore, the values of r can be 0, 1 or 2.
The equation to model Exponential Decay is:
y = a[1 – r)
y= total amount
a= starting amount
r= the growth rate as a decimal
t= number of growth periods
Question 1 (1 point)
Sarah takes 550 mg of an antibiotic. Every hour,
her body breaks down 25% of the remaining drug.
How much will be left after 12 hours?
Guys help me please I really don’t understand this
Answers
I will give some hints. We know most values, we have to solve for y as that is the remaining amount.
y = We have to find.
a = 550 mg (She takes this much)
r = 0.25 (This is 25% as a decimal, don't forget to subtract 1)
t = 12 (This is because over the 12 hours, each hour it breaks down so (12 hours total * 1 hour periods) gives us 12 periods.
I hope this helps!
how do you find the circumference, radius, and diameter in area?
Answers
Answer:
Sample Respond: Let's assume it's equal to 14 cm. Substitute this value to the formula for circumference: C = 2 * π * R = 2 * π * 14 = 87.9646 cm . You can also use it to find the area of a circle: A = π * R² = π * 14² = 615.752 cm² . Finally, you can find the diameter - it is simply double the radius: D = 2 * R = 2 * 14 = 28 cm .
Step-by-step explanation:
I got 100% on the quiz
A golfer hits from a tee for a 300-yard hole. Her drive carries 275 yards but it’s 13 degrees off the line from the hole. How much farther must the golfer now hit the ball to reach the hole?
Answers
By using the cosine rule, we will see that the distance between the golfer and the hole is 69.7 yd.
How to find the distance?Basically, we need to find the length of the missing side of the shown triangle.
So, one side measures 300yd, other side measures 275 yd, and the angle between these sides measures 13°.
Now we can use the cosine rule, where for sides a, b, and c, and angle A (A is the opposite angle to the side a) the rule says:
a^2 = b^2 + c^2 - 2bc*cos(A).
In this case we define:
b = 300ydc = 275 ydA = 13°Replacing that we get:
a^2 = (300yd)^2 + (275yd)^2 - 2*(300yd*275yd)*cos(13°) = 4,853.94 yd^2
a = √(4,853.94yd^2) = 69.7 yd
So the distance between the golfer and the hole is 69.7 yd.
If you want to learn more about triangles, you can read:
https://brainly.com/question/2217700
Why is the Area for my shape not correct and can you explain why?
Answers
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Here, We have given
2 squares , In which 1 square is enclosed within the another square and it arranged in a form that it forms 4 right angled triangle The height and base of the given right angled triangles are 6 and 3 each.We know that,
Area of triangle
[tex]{\sf{=}}{\sf{\dfrac{1}{2}}}{\sf{ {\times} base {\times} height }}[/tex]
Subsitute the required values,
[tex]{\sf{=}}{\sf{\dfrac{1}{2}}}{\sf{ {\times} 3 {\times} 6}}[/tex]
[tex]\sf{ = 3 {\times} 3 }[/tex]
[tex]\bold{ = 9 }[/tex]
Therefore,
Area covered by 4 right angled triangles
[tex]\sf{ = 4 {\times} 9 }[/tex]
[tex]\bold{ = 36}[/tex]
Now,
We have to find the area of the big square
The length of the side of the big square[tex]\sf{ = 6 + 3 = 9 }[/tex]We know that,
Area of square
[tex]\sf{ = Side {\times} Side }[/tex]
Subsitute the required values,
[tex]\sf{ = 9 {\times} 9 }[/tex]
[tex]\bold{ = 81 }[/tex]
Therefore,
The total area of shaded region
= Area of big square - Area covered by 4 right angled triangle
[tex]\sf{ = 81 - 36 }[/tex]
[tex]\bold{ = 45 }[/tex]
Hence, The total area of shaded region is 45 .
Part 2 :-Here,
We have to find the area of non shaded region
According to the question
Hypotenuse = The length of squareLet the hypotenuse of the given right angled triangle be x
Therefore,
By using Pythagoras theorem,
This theorem states that the sum of the squares of the base and perpendicular height is equal to the square of hypotenuse.That is,
[tex]\sf{ (Perpendicular)^{2} + (Base)^{2} = (Hypotenuse)^{2} }[/tex]
Subsitute the required values
[tex]\sf{ (6)^{2} + (3)^{2} = (x)^{2} }[/tex]
[tex]\sf{ 36 + 9 = (x)^{2} }[/tex]
[tex]\sf{ x = \sqrt{45}}[/tex]
[tex]\bold{ x = 6.7 }[/tex]
That means,
The length of the small square = 6.7We know that ,
Area of square
[tex]\sf{ = Side {\times} Side }[/tex]
Subsitute the required values,
[tex]\sf{ = 6.7 {\times} 6.7 }[/tex]
[tex]\bold{ = 44.89 \:\: or \:\: 44.9 }[/tex]
Therefore ,
Area of non shaded region
= Area of big square - Area of small square
[tex]\sf{ = 81 - 44.9 }[/tex]
[tex]\bold{ = 36.1 }[/tex]
Hence, The total area of non shaded region is 36.1 or 36 (approx) .
Part 3 :-Here, we have to
find the total area of the figure Therefore,The total area of the figure
= Non shaded region + Shaded region
[tex]\sf{= 36 + 45 }[/tex]
[tex]\bold{= 81}[/tex]
Hence, The total area of the given figure is 81 .
Explain why the fractions in question number 2 are equivalent?
Answers
Answer:
its 2/6ths its only multiplied by 2
Step-by-step explanation:
Find the distance between the two points in simplest radical form.
Answers
Answer:
13 units
Step-by-step explanation:
A right triangle can be drawn using the grid lines for legs and the line segment between the two points as the hypotenuse. You can count grid squares or subtract coordinates to find the vertical leg is 12 units and the horizontal leg is 5 units. The Pythagorean theorem tells you the length of the hypotenuse (distance between the points) is ...
d² = 12² +5² = 144 +25 = 169
d = √169 = 13
The distance between the two points is 13 units.
_____
Additional comment
This set of dimensions, {5, 12, 13}, is one of several "Pythagorean triples" that often show up in math problems. Other common triples are {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}, and multiples of these.
in the figure line segment AB is tangent to the circle at point A. find the length of line segment AB 8 in. And 10 in.
Answers
Answer:
the answer is just ab
Step-by-step explanation:
dats what it is added up
The length of line segment AB is 12 inches for the given figure.
What is a secant?A secant is a straight line that touches a circle twice.
As per the given figure, we have
Secant segment BD = (8+10) in.
External secant segment BC = 8 in.
Tangent segment = AB
When a secant segment and a tangent segment intersect at an exterior location, the square of the tangent segment's measure equals the product of the secant segment's and its external secant segment's measures.
So, AB² = BC × BD
Substitute the values in the above equation,
AB² = 8 × (8+10)
AB² = 8 × 18
AB² = 144
AB = 12
Thus, the length of line segment AB is 12 inches.
Learn more about secants theorems here :
brainly.com/question/15532257
#SPJ3
The complete question has been attached below.
WHAT IS THE AVERAGE NUMBER OF POINTS THAT CHANGED HANDS
Answers
Which effect did World War II have on the United States?
a) The United States became the richest, most powerful nation in the world.
b) The war caused the United States to enter another severe depression.
c) The war had little effect on the United States.
d) The United States became second in power only to England.
Answers
Answer:
the anwer is A cause jobs and industials had 96 percent and corperate profits after taxes doubled
Answer:
a
Step-by-step explanation:
world War 2 did in fact cause the United States to become the richest and most powerful
Can the GCF of a pair of numbers ever equal one of the numbers? Explain how you know
Answers
Answer:
It can
Step-by-step explanation:
For example, the GCF of 44 and 22 is 22.
Eg: 13, 26
13 is the factor of 26. 26= 13*2
So, GCF of 13 and 26 = 13
Which trig ratio will be helpful in finding the missing side length sin(24)
Answers
The sin ratio will be helpful in finding the missing side length and the missing side length is 29.50 units.
What is the trigonometric ratio?The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
We have a right-angle triangle in the figure in which:
Length of the hypotenuse = x unit
Length of the side opposite to the angle = 12
And the angle is given between sides adjacent to the angle to the hypotenuse = 24°
We know the:
[tex]\rm sin\theta = \frac{Side \ opposite \ to \ the \ angle}{hypotenuse }[/tex]
[tex]\rm sin24 = \frac{12}{x}[/tex]
[tex]\rm x = \frac{12}{sin24}[/tex]
x = 29.50 units
Thus, the sin ratio will be helpful in finding the missing side length and the missing side length is 29.50 units.
Know more about trigonometry here:
brainly.com/question/26719838
6x+9=45 how do you solve it
Answers
[tex] \huge\mathbb\orange{ANSWER} [/tex]
[tex] \mathsf \purple{6x + 9 = 45}[/tex]
[tex] \mathsf \pink{6x + 9 - 9 = 45 - 9}[/tex]
[tex] \mathsf \purple{6x = 36}[/tex]
[tex] \mathsf \pink{ \frac{6x}{6} = \frac{36}{6} }[/tex]
[tex] \mathsf \purple{x = 6}[/tex]
[tex] \mathbb\orange{Hope\: It\: Helps} [/tex]
A surveyor determines that the angle of elevation between herself and the top of an observation tower is 60^o. She determines that the distance between her position and the base of the tower is 20 meters. Approximately how tall is the tower?
Answers
For water to be a liquid, its temperature must be within 50 Kelvin of 323 Kelvin. Which equation can be used to determine the minimum and maximum temperatures between which water is a liquid?
|323
Answers
Answer:
its 323 so you were right :) if 323 is your answer lol
Step-by-step explanation:
abs(T-50)=323 Where T is in degrees Kelvin.
abs () means absolute value.
So T=323 plus or minus 50