Which statement describes the graph of f(x) = x² - 6x + 9?
a line with an x-intercept of (-3, 0)
a parabola with an x-intercept of (-3, 0)
a line with an x-intercept of (3, 0)
a parabola with an x-intercept of (3, 0)
Answers
Answer:
A parabola with an x-intercept of (3, 0)
Step-by-step explanation:
We can immediately rule out the first and third options, because the equation of a second degree function is a parabola.
Your equation is
ƒ(x) = x² - 6x + 9 = 0
We can factor this equation as
ƒ(x) = (x - 3)²
The parent parabola, y = x², has its x-intercept at (0,0).
Your function subtracts three from x, so the intercept is shifted three units to the right.
The graph of your function is a parabola with an x-intercept of (3, 0).
The figure below shows the graph of your function shifted three units by subtracting three from x.
Related Questions
The distance between Quebec City and New York City is 520 miles if Kate leaves Quebec and will leaves New York at 9:09 a.m. And they tried toward each other at 55 miles per hour and 75 miles per hour respectively at what time will they meet?
Answers
Kate and Will meet at 1 : 09 pm
Solution:
The distance between Quebec City and New York City is 520 miles.
At the point where Kate and Will meet, they would have traveled 520 miles.
Let "t" represent the time it takes Kate to travel a certain distance before they met.
[tex]Distance = speed \times time[/tex]
If Kate drives at 55 mph, the distance covered would be
[tex]Distance = 55 \times t = 55t[/tex]
If Will drives at 75 miles per hour, then the distance covered will be
[tex]Distance = 75 \times t = 75t[/tex]
Since the total distance covered is 520 miles
Which means,
[tex]55t + 75t = 520\\\\130t = 520\\\\t = \frac{520}{130}\\\\t = 4[/tex]
Given that in question,
If Kate leaves Quebec and will leaves New York at 9:09 a.m
4 hours after 9: 09 am, Kate and Will will meet
9: 09 am + 4 hours = 1: 09 pm
Thus they would meet at 1 : 09 pm
7/12 times 7. Note: the answer is a mixed number :)
Answers
Answer:
[tex]4\frac{1}{12}[/tex]
Step-by-step explanation:
7/12 * 7
7 = 7/1
7/12 * 7/1
49/12
12 goes into 49 four times, with a remainder of 1
[tex]4\frac{1}{12}[/tex]
Hope this helps :)
Answer:
4 1/12
Step-by-step explanation:
7/12 X 7
7/12 which is 7/12
do 7/12 times 7 which is 49/12
12 goes 4 times into 49 (up to 48)
there's one remaining
and its over 12
4 1/12
how can you determine if a polygon is a convex?
Answers
Answer:
You can determine if a polygon is a convex, by which way the edges points out
Convex is when all the points are facing out, so a polygon is a convex if all the edges are pointing out.
Answer:
No side of the polygon crosses any other, even when extended indefinitely.
Step-by-step explanation:
If no sides of the polygon cross each other, it is convex when it has no internal reflex angles (angles measuring more than 180°). If sides of the polygon cross each other, it is not convex.
Another way to describe a convex polygon is that extending any one side indefinitely will not cause it to cross any other side.
If log4(x) = –2 , which of the following is the correct value of X?
a. x = -16
b. x =
c.x = -8
d.x=1
Answers
Answer:
c
Step-by-step explanation:
4*-8=-2
What is 77 divided by 13690
Answers
Answer: 0.00562454
Step-by-step explanation:
Did I save you a lot of time? Lol hope I helped
Answer:
the answer would be 0.00562454346 or if u want it as a fraction it would be 281227173/50000000000
Step-by-step explanation:
given f (x) = 5x + 1 find f(-3)
Answers
Answer:
x=-4/5
Step-by-step explanation:
So first, since it says find f(-3) put -3 in the place of x in F(x)
So, f(-3)=5x+1
-3=5x+1
-4=5x
x=-4/5
or
x=-.8
What’s 36x^2 + 24xy + 4y^2?
Explain the steps.
Answers
Answer:
4(3x+y)^2
Step-by-step explanation:
36x^2+24xy+4y^2
=9*4x^2+6*4xy+4y^2
=4(9x^2+6xy+y^2)
=4(3x+y)*(3x+y)
=4(3x+y)^2
Find the slope of the line
y=-6x+\frac{1}{4}[/tex]
Answers
The equation given is the equation of a line in slope-intercept form.
The slope of the line is the numerical value associated with the variable X.
The number in front of X is -6, so the slope of the line would be -6
Answer: To find an equation that is parallel to
y
=
−
6
x
+
1
, the slopes must be equal. Using the slope of the equation, find the parallel line using the point-slope formula.
(
6
,
0
)
m
=
−
6
So the answer would be -6
Step-by-step explanation:
When a number is decreased by 79%, the result is 13. What is the original number to the nearest tenth?
Answers
If a number is decreased by 79%, we are left with 21%.
so let's devide by 21 to get down to 1%, then multiply by 100 to get to the origininal number:
13 / 21 * 100 = 61.9047619048
To the nearest tenth it's 61.9
Final answer:
To find the original number when decreased by 79% to result in 13, we solve the equation 0.21x = 13, which gives us 61.9047619. Rounding this to the nearest tenth gives us 61.9.
Explanation:
To find the original number, we need to translate the percentage decrease back into the original number. Here's the step-by-step calculation:
We understand that after decreasing the original number by 79%, we have 21% of it left, which is equivalent to the number 13.So to find the original number (let's call it x), we set up the equation 0.21x = 13.Divide both sides by 0.21 to solve for x: x = 13 / 0.21 which equals 61.9047619.Round to the nearest tenth. We look at the hundredth's digit, which is 0, we round down the tenth's place to get the final answer, 61.9.So the original number to the nearest tenth is 61.9.
Four to the power of three times four to the power of negative six is equal to four to the power of five times four to the power of blank
Answers
The blank is -8
Step-by-step explanation:
Let us revise some rules of indices:
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{m+n}[/tex] [tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{m-n}[/tex] [tex]a^{m}[/tex] = [tex]a^{n}[/tex] , them m = n∵ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{5}[/tex] × [tex]4^{x}[/tex]
∵ All bases are equal
∴ Use the first and third rule above to find x
∵ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{3+-6}[/tex]
∴ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{-3}[/tex] ⇒ L.H.S
∵ [tex]4^{5}[/tex] × [tex]4^{x}[/tex] = [tex]4^{5+x}[/tex] ⇒ R.H.S
Equate L.H.S and R.H.S
∴ [tex]4^{-3}[/tex] = [tex]4^{5+x}[/tex]
Equate the indices of the two sides
∴ -3 = 5 + x
- Subtract 5 from both sides
∴ -8 = x
∵ x represents the blank
∴ The blank = -8
The blank is -8
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Four to the power of three times four to the power of negative six is equal to four to the power of five times four to the power of negative eight.
To solve for the missing exponent, we can use the following properties of exponents:
Multiplying exponents with the same base: When multiplying powers with the same base, we add their exponents.
Negative exponents: A number raised to a negative exponent is equal to its reciprocal raised to the positive exponent.
Applying these properties:
4^3 * 4^-6 = 4^(3 - 6) = 4^-3 (since 4^-6 = 1/4^6)
4^5 * 4^x = 4^(5 + x)
Setting these equal to find x:
4^-3 = 4^(5 + x)
Therefore, x = -3 - 5 = -8.
what is the quotient when (x+3) is divided into the polnomial 2x^2+x-15
Answers
Answer:
2x-5
remainder of 0
Step-by-step explanation:
Check the image
2, -10, 50, -250,...
Answers
2 x -5 = -10
-10 x -5 = 50
And so on
Answer:
Multiply by 5
-250, 1250
Step-by-step explanation:
2 x -5 = -10
-10 x -5 = 50
50 x -5 = -250
-250 x -5 = 1250
A concert hall has three sections: the main floor, the balcony, and the gallery. For a recent concert, 1020 tickets were sold. There were twice as many balcony tickets sold as gallery tickets, and 225 more main floor tickets than balcony tickets. If g represents the number of gallery tickets sold, which expressions represents this situation?
A. Gallery: g Balcony: g Main Floor: g + 225
B. Gallery: g + g + 225 Balcony: 2g Main Floor: g
C. Gallery: g Balcony: g + 225 Main Floor: 2g + 225
D.Gallery: g Balcony: 2g Main Floor: 2g + 225
Answers
Answer:
c is the answer i am preety sure
Step-by-step explanation:
Gallery = g
Balcony = 2g (twice as many gallery)
Main floor = 2g + 225 ( 225 more than balcony)
The answer would be D.
Will earns $98 a week bagging groceries. He saves 80% of what he makes per week and spends the rest on lunches. How much does Will spend each week on lunches
Answers
Answer:
$19.60
Step-by-step explanation:
$98 is made each week.
80% is saved, and the rest is spend on lunch, so 20% is spent on lunch.
20%=.20
98•.20=19.6
$19.60 is spend on lunches each week.
What is the least common multiple of 30 and 13
Answers
Answer: it would be 390
Just keep counting how many times one number goes into the other, start with the smallest
Janet can read 3.6 pages of a book in a minute. If she read for 2.71 minutes. How much would have she had read
Answers
Final answer:
It would have taken Janet about 9.7536 pages to read..
Explanation:
To determine Janet's reading progress, her reading speed is multiplied by the duration she read. With a reading speed of 3.6 pages per minute, if Janet read for 2.71 minutes, the calculation is 3.6 multiplied by 2.71, resulting in 9.7536. Hence, Janet would have read approximately 9.7536 pages. This calculation showcases how the product of reading speed and time provides a quantitative measure of reading accomplishment. It's a straightforward way to estimate the amount of material covered within a specific timeframe, offering insights into reading efficiency and progress.
Which transformation of the red triangle on the graph maps it onto the missing piece of the square? A. a translation 16 units right
B. a reflection across the y-axis
C. a 90° counterclockwise rotation about the origin
D. a 90° clockwise rotation about the origin
E. a 180° rotation about the origin
Answers
Answer:
D.) A 90 degree clockwise rotation about the origin
Step-by-step explanation:
The red triangle should have a 90° clockwise rotation about the origin. Option C is correct.
Given that,
A graph of figures is shown in the pictures,
Which transformation of the red triangle on the graph maps it onto the missing piece of the square is to be determined.
The translation is defined as the change of position through linear distance and angle.
What is simplification?The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.
In order to occupy the required space on the green figure by red triangle, it should be rotated to 90° clockwise about the origin.
Thus, the red triangle should have a 90° clockwise rotation about the origin. Option C is correct.
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If a chessboard were to have pennies placed on each square such that 1 penny was placed on the first square, 2 on the second, 4 on the third, and so on (doubling the number of pennies on each subsequent square), how many pennies would be on the chessboard when finished?
How many squares are on the chessboard?
Answers
This is just like the rice chessboard problem! To quickly get the answer, we can simply do (2^64)-1.
Take a look at the following:
1+2+4+8=15=2^4-1
1+2+4+8+16=31=2^5-1
There's that rule involved, and we can simply use 2^64-1 instead of adding too many numbers.
Hope this helped!
Total number of pennies on the chessboard is equals to [tex]2^{64} -1[/tex].
Total number of squares on the chessboard = 64
What is pattern?" Pattern is defined as the numbers are arranged in such a way that it follow certain rule or formula."
According to the question,
Number of pennies in first square = 1
Number of pennies in second square = 2
Number of pennies in third square = 4
Condition given,
Doubling the number of pennies on each subsequent square.
Calculate pattern follow as per given condition we have,
Total Number of pennies in first square = 1
= [tex]2^{1} -1[/tex]
Total Number of pennies till second square = 1 + 2
= [tex]2^{2} -1[/tex]
Total Number of pennies till third square = 1+ 2 + 4
= [tex]2^{3} -1[/tex]
Total Number of pennies till fourth square = 1+ 2 + 4 +8
= [tex]2^{4} -1[/tex]
Total number of squares on the chessboard = 64
Therefore, as per the pattern follow on each subsequent square we get,
Total number of pennies till 64th squares chessboard = [tex]2^{64} -1[/tex]
Hence, total number of pennies on the chessboard is equals to [tex]2^{64} -1[/tex].
Total number of squares on the chessboard = 64.
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In September there were 16 members in the music club. In October the member of members was 24. What was the percent increase?
Answers
Answer:
9%
Step-by-step explanation:
It is simple because you just count to get to 24 and that is the percentage.
The surface area of a cell phone screen is 6800 mm2. Use the fact that 10 mm = 1 cm to convert this area to cm2. Round your answer to the nearest whole number. Do not type the units in the space below.
Answers
Answer:
[tex]68 \: {cm}^{2} [/tex]
Step-by-step explanation:
You can use 1 cm = 10 mm very well to help you with this.
The small two at the end of the unit (cm^2) refers, that the shape of an object is two dimensional. If we make 1 cm two dimensional by multiplying it with the original 1 cm, we get a total area of
[tex]1 \: {cm} \times 1 \: {cm} \: = 1 \: {cm}^{2} [/tex]
We have created an equation. Since we know 1 cm = 10 mm, we can replace the centimetres in the equation with the millimetres, like so:
[tex]10 \: mm \times 10 \: mm = 1 \: {cm}^{2} \\ 100 \: {mm}^{2} = 1 \: {cm}^{2} [/tex]
From there, its just a simple matter of calculation:
[tex]6800 \: {mm}^{2} \times \frac{1 \: {cm}^{2} }{100 \: {mm}^{2} } = 68 \: \: {cm}^{2} [/tex]
write an equation in slope intercept form of the line that passes through (-1 5) and is parallel to the graph of 2y+4x= -8
Answers
Answer:
Therefore, equation of the line that passes through (-1,5) and is parallel to the line
[tex]2y+4x=-8[/tex]
is
[tex]y=-2x+3[/tex]
Step-by-step explanation:
Given:
[tex]2y+4x=-8[/tex] .Equation of line
can be written as
[tex]y=-2x-8[/tex] ...which is in Slope intercept form
To Find:
Equation of line passing through ( -1, 5) and is parallel to the line 2y+4x=-8
Solution:
[tex]y=-2x-8[/tex] ...........Given
Comparing with,
[tex]y=mx+c[/tex] ....general form in slope intercept
Where m =slope
We get
[tex]Slope = m = -2[/tex]
We know that parallel lines have Equal slopes.
Therefore the slope of the required line passing through (-1 , 5) will also have the slope = m = -2.
Now the equation of line in slope point form given by
[tex](y-y_{1})=m(x-x_{1})[/tex]
Substituting the points and so we will get the required equation of the line,
[tex](y-5)=-2(x-(-1))=-2(x+1)\\\\y-5=-2x-2\\y=-2x+3......Equation\ of\ line[/tex]
Therefore, equation of the line that passes through (-1,5) and is parallel to the line
[tex]2y+4x=-8[/tex]
is
[tex]y=-2x+3[/tex]
5. People get energy from the food they eat. This energy is measured
in calories. When you exercise, you use up or burn calories. The
picture at the right shows about how many calories a 125-pound
person burns each minute bowling. How many calories does a
125-pound person burn in 2 hours of bowling?
ASAP! please help!
Answers
Answer:
Step-by-step explanation:
I don't have all the information, but all you need to do it convert 2 hours to minutes (which would be 120 minutes) and setup a proportion.
amount of calories burnt per minute x (total amount of calories burnt)
____________________________ = ________________
1 minute 120 minutes
Hope this helps!
They would burn 360 calories doing 2 hr of bowling.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
We are given that this energy is measured in calories. When you exercise, you use up or burn calories.
The information shows about how many calories a 125-pound person burns each minute bowling.
We need to do it convert 2 hours to minutes which would be 120 minutes and setup a proportion.
The amount of calories burnt per minute x (total amount of calories burnt)
1 minute = 120 minutes
Multiply 120 x 3 = 360.
Hence, they would burn 360 calories doing 2 hours of bowling.
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E=IZ
Where E=(5+9i) and I=(8+7i)
How do I solve for Z?
Answers
Answer:
[tex]Z = \frac{37i }{113 } - \frac{23}{113} [/tex]
Step-by-step explanation:
We have the complex number relationship as:
E=IZ
Where E=(5+9i) and I=(8+7i)
We solve for Z to get;
Z=E/L
We then substitute the expressions to get:
[tex]Z = \frac{5 + 9i}{8 + 7i} [/tex]
We rationalize to get:
[tex]Z = \frac{5 + 9i}{8 + 7i} \times \frac{8 - 7i}{8 - 7i} [/tex]
We simplify to obtain:
[tex]Z = \frac{40 - 35i + 72i - 63}{ {8}^{2} + {7}^{2} } [/tex]
This gives
[tex]Z = \frac{37i - 23}{113 } [/tex]
Or
[tex]Z = \frac{37i }{113 } - \frac{23}{113} [/tex]
25 kids took a math test. If 20 kids passed the test, what percent of kids did not pass the test?
Answers
Answer: 20%
Step-by-step explanation:
25 = 100%
25/5 = 5
100/5 = 20
That means 80% passed and 20% didnt.
Answer:
20%
Step-by-step explanation:
If 20 kids passed, that means 5 did not. 5/20 is 0.2. Write that in percentage is 20%.
Kristin spent 40$ on pampers. If they cost 8$ / package , how many packages did she buy
Answers
Answer:
5 Packages
Step-by-step explanation:
40 / 8 = 5
Worth 20 points PLZ HELP ASAP
An F note has a frequncy of 689.46Hz calculate the wavelegnth in meters
Answers
Answer:
434822.11875961m
Step-by-step explanation:
this is because the formula is λ = C/f
Where,
λ (Lambda) = Wavelength in meters
c = Speed of Light (299,792,458 m/s)
f = Frequency
If 80 inches is equivalent to 44 inches, then 28 inches would be equivalent to what?
Answers
Answer:
Well no cheating not from me
Step-by-step explanation:
Brain May, guitarist for Queen, does not know how to price his signature Antique Cherry Special that cost £280 to make. He know he wants 85% markup on cost. What price should Brian May ask for the guitar?
Answers
Answer:
£518
Step-by-step explanation:
Asking price = original cost × markup%
A = 280(1.85) = 518
Brian May needs to price his Antique Cherry Special guitar at £518. This price is determined by the original cost, £280, and a 85% markup, £238, on this cost.
Explanation:Brian May needs to define a price for his signature Antique Cherry Special guitar that was costed at £280 and he wants an 85% markup on this cost. Markup is calculated by multiplying the cost by the markup percentage. In this case, the markup is £280 * 85/100 = £238. Therefore, to determine the final price Brian needs to add the original cost and the markup, which is £280 + £238 = £518. So the price Brian should ask for the guitar is £518.
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What is the measurement of angle R
Answers
Round the number to the nearest hundred. 281
Answers
Answer:
300
Step-by-step explanation:
because you said nearest hunderd and 281 would be 200 if it was 149 but since its 281 its further to 300
your welcome
lex <3
Answer:
300
You first look to the right of the hundred and if it is 5 and above u add 1 to the hundreds place. If its 4 and below u keep it the same. You just have to remember that all the place values after the one rounded would have a value of 0