Identify the axis of symmetry, vertex, and y intercept of y=-6x^2+12x-8
Answers
Answer:
See below for answers and explanations (with attached graph)
Step-by-step explanation:
It helps to transform the equation into vertex form by completing the square because it tells us a lot about the characteristics of the parabola:
[tex]\displaystyle y=-6x^2+12x-8\\\\y=-6\biggr(x^2-2x+\frac{4}{3}\biggr)\\\\y-6\biggr(-\frac{1}{3}\biggr) =-6\biggr(x^2-2x+\frac{4}{3}-\frac{1}{3}\biggr)\\\\y+2=-6(x^2-2x+1)\\\\y+2=-6(x-1)^2\\\\y=-6(x-1)^2-2[/tex]
Since vertex form is [tex]y=a(x-h)^2+k[/tex], we identify the vertex to be [tex](h,k)\rightarrow(1,-2)[/tex] and the axis of symmetry to be [tex]x=h\rightarrow x=1[/tex]. The y-intercept can be found by setting [tex]x=0[/tex] and evaluating:
[tex]y=-6(x-1)^2-2\\\\y=-6(0-1)^2-2\\\\y=-6(-1)^2-2\\\\y=-6(1)-2\\\\y=-6-2\\\\y=-8[/tex]
Hence, the y-intercept of the parabola is [tex]y=-8[/tex], or [tex](0,-8)[/tex] as an ordered pair.
Related Questions
PLEASE HURRY!!
What is the slope of the line that passes through (1, 4) and (-3, -3)?
A. -7/4
B. 7/4
C. -4/7
D. 4/7
Answers
Answer:
The slope of the line is option B
what is the slope this? please help thanks
Answers
Answer: the area of the X???
Step-by-step explanation:
the slope is 1/4
because it goes across by 4 and up by 1
A printer can print 12 pages in 9 seconds. What is the closest estimate of the
number of pages it can print in one minute?
120
100
45
72
Answers
Answer:
72 is the closest.The printer will primt 80 pages in one minute
Answer:
72
Step-by-step explanation:
12 pgs in 9 sec
*[tex]\frac{20}{3}[/tex] *[tex]\frac{20}{3}[/tex]
≈80 pgs in 60 sec
Hope this helps!!!
Please mark me as brainliest!!!
A geometry teacher asked Charlene to define “acute triangle.” Charlene said that an acute triangle is a triangle whose three interior angles have measures less than 90°. Is Charlene’s definition valid?
Answers
Answer:
YES BECAUSE THIS DEFINITION FITS ALL ACUTE TRIANGLES AND DOES NOT FIT TRIANGLES THAT ARE NOT ACUTE
Step-by-step explanation:
i got it right on TTM
HOWW DO I DO THIS????
WEIRD EXACT TRIG QUESTION (cannot use a calculator)
Answers
Answer:
[tex]\huge{\red{\angle ABC = \boxed{30}\degree}}[/tex]
Step-by-step explanation:
[tex]\sin \angle ABC =\frac{p}{30}......(1)[/tex] (Given)In [tex] \triangle ABC,[/tex] sin ratio of [tex] \angle ABC[/tex] can be given as:[tex]\sin \angle ABC =\frac{AC}{AB}[/tex][tex]\implies \sin \angle ABC =\frac{2p+10}{80}......(2)[/tex]From equations (1) and (2), we find:[tex] \frac{p}{30}=\frac{2p+10}{80}[/tex][tex]\implies 80(p)=30(2p+10)[/tex][tex]\implies 80p=60p+300[/tex][tex]\implies 80p-60p=300[/tex][tex]\implies 20p=300[/tex][tex]\implies p=\frac{300}{20}[/tex][tex]\implies p=15[/tex][tex]\implies \sin \angle ABC =\frac{15}{30}[/tex][tex]\implies \sin \angle ABC =\frac{1}{2}[/tex][tex]\implies \sin \angle ABC =\sin 30\degree\:\:\:\:(\because \sin 30\degree=\frac{1}{2})[/tex][tex]\implies \huge{\red{\angle ABC = \boxed{30}\degree}}[/tex]Convert the polar coordinates (3, -5 pi/3). to rectangular coordinates.
Answers
Answer:
See below
Step-by-step explanation:
x = 3 cos (-5pi/3) = 1.5
y = 3 sin (-5pi/3) = 2.598
please explain every step
Answers
761680
Explanation:[tex]\sf \boxed{\sum _{n=1}^{44}\:60\left(1.2\right)^{n-2}}[/tex]
Identify the following's:
First Term [a] = 60(1.2)ⁿ⁻² = 60(1.2)¹⁻² = 50
Common ratio [r] = 1.2
Total Terms [n] = 44
===========================
[tex]\sf Geometric \ Sum \ of \ Terms = \dfrac{a(r^n - 1)}{r-1}[/tex]
===========================
Solving Steps:
[tex]\rightarrow \sf \dfrac{a(r^n - 1)}{r-1}[/tex]
[tex]\rightarrow \sf \dfrac{50(1.2^{44} - 1)}{1.2-1}[/tex]
[tex]\rightarrow \sf 761679.5808[/tex]
[tex]\rightarrow \sf 761680 \ \ \ (rounded \ to \ nearest \ integer)[/tex]
Which transformations would result in the image shown?
ABCD is reflected over both axes.
ABCD is translated right 4 units and down 3 units.
ABCD is reflected over the x-axis and translated right 4 units.
ABCD is reflected over the y-axis and translated down 3 units.
Best answer gets brainliest!
Answers
Answer:
the answer is reflected over both axes hope this helped
Simplify the expression. Write your answer as a power.
64⁴/64³
The simplified expression is
Answers
Answer:
[tex]64^1\:\text{or}\:64[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{64^4}{64^3}=64^{4-3}=64^1=64[/tex]
Step-by-step explanation:
64^4/64^3= 64^(4-3)= 64^1= 64
Can someone help
kaitlin buys candy that costs $8 per pound. she will spend less than $40 on candy. what are the possible numbers of pounds she will buy?
use p for the number ofpounds kaitlin will buy.
write your answer as an inequality solved for p.
Answers
Answer:
x≤5p
Step-by-step explanation:
40/8=5 Kaitlin can buy UP TO 5 pounds of candy at $8/pound. So she will buy less than or equal to 5 pounds
What is the best way to get points on DRFROSTMATHS? BRAINLIEST TO BEST ANSWER!
Answers
Answer:
You can see your total points on your dashboard. You can see points for individual topics on the Topic Explorer. After answering each question you will see how your points have changed.
Step-by-step explanation:
Ships arriving in U.S. ports are inspected by Customs officials for contaminated cargo. Assume, for a certain port, 20% of the ships arriving in the previous year contained cargo that was contaminated. A random selection of 50 ships in the current year included 5 that had contaminated cargo. Does the data suggest that the proportion of ships arriving in the port with contaminated cargoes has decreased in the current year
Answers
The value of the np is 10, and the value of the nq is 40 which is less than 5 also the hypothesis H0: p = 0.20 versus H1: p<0.20
What are the null hypothesis and alternative hypothesis?The null and alternative hypotheses are two generalizations about a population that are strictly contradictory. The null hypothesis can be denoted by H₀ and the alternative hypothesis can be denoted by H₁.
We have:
n = 50
p = 20% = 0.02
q = 1-p = 1- 0.02 = 0.08
[tex]\rm n_p = 50 \times 0.20 = 10\\\\\rm n_q = 50\times 0.80 = 40[/tex]
[tex]\rm n_q > 5\\\\\rm n_p > 5[/tex]
The conditions are verified for this test.
Null hypothesis H0: The number of ships arriving in ports with hazardous cargoes has remained constant.
Alternative hypothesis H1: The number of ships arriving in port with polluted goods has dropped.
H0: p = 0.20 versus H1: p<0.20
Thus, the value of the np is 10, and the value of the nq is 40 which is less than 5 also the hypothesis H0: p = 0.20 versus H1: p<0.20
Learn more about the null hypothesis and alternative hypothesis here:
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A hotel with 80 rooms has 45 for doubles
and 35 singles. Singles can be booked in
any room, but reservations for two or
more people must be booked in double
rooms.
Let x be the number of single reservations and y
the number of reservations for two or more.
Which system of inequalities represents this
situation?
Click on the correct answer.
x ≥ 35 x + y ≤ 80
y ≤ 45 x + y ≤ 80
x≤ 35 x+y≤ 80
y≥ 45 x + y ≤ 80
Answers
Answer:
y ≤ 45
Step-by-step explanation:
First y must be less than or equal to 45.
y ≤ 45 x + y ≤ 80
And total number of reservations cannot exceed 80:
x + y ≤ 80.
Consider the following trapezoid.
Find the value of X.
Answers
Answer:
106º
Step-by-step explanation:
Because both the base angles are 74º. The known angles so far are 148º.
The top angles also have to be equal as they are on parallel lines so:
360 - 148 = 212º
212 / 2 = 106º
Answer:
x = 106 degrees
Step-by-step explanation:
74 plus 74 = 148
360 is the interior angle sum of all trapezoids
360-148=212
212 is the sum of both x and y
x and y are the same measure.
212/2 = 106
What is the range of the function represented by this graph?
Answers
Answer:
The range of the function given in the graph is the values of all y for any input x.
Therefore, as shown in the graph the value of y for any input of x is below y = 1. Therefore, the range is y <= 1
......................
[tex]3 \times (6 + 2) - 3 + 4 \div 2 =[/tex]
Answers
Answer:
23
Step-by-step explanation:
Follow the PEMDAS order of operations
3 x (6 + 2) - 3 + 4 ÷ 2
Parenthesis (P):
(6 + 2) = (8)
Exponents (E):
none
Multiply/Divided (MD) left to right:
Multiply: 3 x 8 = 24
= 24 - 3 + 4 ÷ 2
Divided: 4 ÷ 2 = 2
= 24 - 3 + 2
Add/Subtract (AS) left to right:
Subtract: 24 - 3 = 21
= 21 + 2
Add: 21 + 2 = 23
A circle is centered at (−4, 9) and has a radius of 11.
What is the equation of the circle?
Answers
Answer:
(x +4)² +(y -9)² = 121
Step-by-step explanation:
The equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
__
We are given that (h, k) = (-4, 9) and r = 11. When we put these values into the equation, it becomes ...
(x -(-4))² +(y -9)² = 11²
We can simplify this a bit to ...
(x +4)² +(y -9)² = 121
Please can anybody help me with this:
Show that (x − 9)(x − 1) ≡ x^2 − 10x + 9
Answers
We will expand the factored form of (x − 9)(x − 1) into the same form as x² − 10x + 9 to show they are equal.
Distribute and multipy out:
(x − 9)(x − 1)
x * x = x²
x * -1 = -x
x * -9 = -9x
-9 * -1 = 9
Add together:
x² + -x + -9x + 9
x² − 10x + 9
Use the Reflexive property:
x² − 10x + 9 = x² − 10x + 9 ✓
What is the scale factor of the dilation of triangle def? three-tenths three-sevenths seven-thirds 7
Answers
The scale factor of the dilation of triangle def is three-tenths i.e. 3/10
How to determine the scale factor of dilation?From the complete question, the corresponding sides are:
DE = 10
D'E' = 3
The scale factor k is then calculated using"
DE * k = D'E'
So, we have:
10* k = 3
Divide both sides by 10
k = 3/10
Hence, the scale factor of the dilation of triangle def is three-tenths i.e. 3/10
Read more about dilation at:
https://brainly.com/question/3457976
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Answer: 3/10
Step-by-step explanation:
please solve this for me ASAP
Answers
The correct answer is thermoelectric generator because it transfers heat to electricity directly or converts electrical energy to thermal power for heating or cooling.
What is a thermoelectric generator?Thermoelectric generators are semiconductor solid-state devices that convert a temperature difference and heat flow into a usable DC power source.
The Seebeck effect is used to create voltage in thermoelectric generator semiconductor devices. This voltage is used to drive electrical current and generate usable power at a load.
From the statement given, it is a thermoelectric generator because a thermoelectric power generator transfers heat to electricity directly or converts electrical energy to thermal power for heating or cooling.
Thus, the correct answer is thermoelectric generator because it transfers heat to electricity directly or converts electrical energy to thermal power for heating or cooling.
Learn more about the thermoelectric generator here:
https://brainly.com/question/2289126
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Can someone say the answer to this question with steps?
¬
Answers
Answer:
729
Step-by-step explanation:
Can someone please answer this, ill give you brainliest Would be very appreciated.
Answers
Answer:
x-intercept: (4, 0), (-5, 0)
y-intercept: (0, -20)
Explanation:
x² + x - 20x² + 5x -4x -20x(x+ 5) -4(x +5)(x-4)(x + 5)Their x-intercept: (at x intercept, y will be 0)
(x-4)(x + 5) = 0x = 4, x = -5Their y intercept: (at y intercept, x will be 0)
y = (x-4)(x + 5)y = (0-4)(0 + 5)y = -20Answer:
x-intercepts : (4, 0) and (-5, 0)y-intercept : (0, -20)Step-by-step explanation:
Finding x-intercept(s)
The x-intercept's y-coordinate will be 0⇒ 0 = (x - 4)(x + 5)⇒ x = 4 and x = -5The x-intercepts are : (4, 0) and (-5, 0)Finding y-intercept
The y-intercept's x-coordinate will be 0⇒ y = 0² + 0 - 20⇒ y = -20The y-intercept will be (0, -20)A $52.50 screen door is on
sale for $42. Find the percent
of discount on the door.
Answers
Answer:
20%
Step-by-step explanation:
Given/To Find:
A $52.50 screen door is on
sale for $42. Find the percent
of discount on the door.
Solve:
Formula: Value 1 - Value 2 ÷ Original Value × 100
Hence we have:
52.50 - 42 = 10.5
10.5 ÷ 52.50 = 0.20
0.20 × 100
=20%
Check Answer:
52.50 × 20% = 10.5
52.50 - 10.5 = 42
Hence, the percent of discount on the door is 20%
Kavinsky
Graph the following system of inequalities.
y≤ 2c + 1
y<-x-1
Answers
For equation 1:
y ≤ 2c + 1y intercept = (0, 1)
x intercept = (-0.5, 0)
Graph Plotted Below the LineFor equation 2:
y < -x -1y intercept = (0, -1)
x intercept = (-1, 0)
Graph Plotted Below the LineOption B is correct
what is the area of a cylinder
Answers
A cylinder's volume is =
π r² h,
and its surface area is =
2π r h + 2π r².
see attached image.
Answers
Answer:
whats the question?
Step-by-step explanation:
100 divided by 360 please help I’m gonna cry
Answers
360 ÷ 100 = 3.6
[tex]\bf{\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace3.\emptyspace6\:\:\:\:\:\:\:\:\:\\ 100\overline{|\smallspace360.0}\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\underline{\emptyspace3\emptyspace0\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace6\emptyspace0\emptyspace0\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\underline{\emptyspace6\emptyspace0\emptyspace0}\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\:\:\:\:\:\:\:\:\:\:\end{matrix}}[/tex]
I hope it helps you...Salu2!!!!
Answer:
0.277778
Step-by-step explanation:
hope this helps also please don't cry everyone loves you
how do you find surface area of a rectangular prism
Answers
Answer:
To find the surface area of a rectangular prism, measure the length, width, and height of the prism. Find the area of the top and bottom faces by multiplying the length and width of the prism. Then, calculate the area of the left and right faces by multiplying the width and height.
Can someone help me with this please
Answers
#95 will give brainliest to best answer!
Answers
Answer:
3/10
Step-by-step explanation:
The probability of drawing a blue card first is 3/5 (3 blue cards out of a total of 5 cards). Then the probability of drawing a blue card again will be 2/4 (the blue card you drew first is removed so there are only 2 blue cards and 4 total cards). Now we multiply the probabilities together to get the probability of drawing a blue card, not replacing it, and then drawing another blue card = (3/5)(2/4) = 6/20 = 3/10.
Hope this helps! :)