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hopefully this helps
Related Questions
Which second-degree polynomial function has a leading coefficient of –1 and root 5 with multiplicity 2?
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[tex]\displaystyle{f(x)=ax^2+bx+c[/tex], where [tex]a\neq0[/tex].
The leading coefficient is a, so we have a=-1.
5 is a double root means that :
i) f(5)=0,
ii) the discriminant D is 0, where [tex]D=b^2-4ac[/tex].
Substituting x=5, we have
f(5)=a(5)^2+b(5)+c,
and since f(5)=0, and a is -1 we have:
0=-25+5b+c
thus c=25-5b.
By ii) [tex]\displaystyle{b^2-4ac=0[/tex].
Substituting a with -1 and c with 25-5b we have:
[tex]\displaystyle{b^2-4ac=0[/tex]
[tex]\displaystyle{b^2-4(-1)(25-5b)=0[/tex]
[tex]\displaystyle{b^2+4(25-5b)=0[/tex]
[tex]\displaystyle{b^2-20b+100=0[/tex]
[tex]\displaystyle{(b-10)^2=0[/tex]
[tex]\displaystyle{b=10[/tex]
Finally we find c: c=25-5b=25-50=-25
Thus the function is [tex]\displaystyle{f(x)=-x^2+10x-25[/tex]
Remark: It is also possible to solve the problem by considering the form
[tex]f(x)=-1(x-5)^2[/tex] directly.
In general, if a quadratic function has leading coefficient a, and has a root r of multiplicity 2, then its form is [tex]f(x)=a(x-r)^2[/tex]
Answer:
f(x) = 2x2 – 4x – 30
Step-by-step explanation:
Got it right
Ernie's favorite movie of the year is now in its fourth week in the theaters. He is gathering data about its earnings each week. He is also interested in knowing how other recently released movies are doing at the box office compared with his favorite movie. The table gives the earnings of the top-five movies during the third week that Ernie’s favorite movie, movie A, was showing in theaters. Movie Earnings Average Ticket Price A $26,088,808.74 $8.35 B $60,394,938.12 $9.72 C $23,659,617.52 $8.12 D $34,311,887.98 $7.57 E $10,505,611.08 $8.46
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To compare the relative success of his favorite movie to others, the student can calculate each movie's ticket sales by dividing its total earnings by the average ticket price. This provides a clearer idea of the viewership each movie had, which can be more informative than simple box office earnings.
Explanation:The student is interested in the earnings of his favorite movie in relation to other recently released films. To compare these films, one could calculate each movie's ticket sales by dividing its earnings by the average ticket price. For instance, the ticket sales for the movie A would be calculated by dividing its earnings, $26,088,808.74, by its average ticket price, $8.35. This calculation would need to be repeated for each movie to have a clear comparison.
These calculations will help Ernie understand how many people, roughly, saw each movie, since box office earnings alone can be skewed by differing ticket prices. In other words, a movie could have higher earnings than another but still have fewer viewers if its tickets were significantly more expensive.
Learn more about Comparison of Movie Earnings here:https://brainly.com/question/33342471
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how do i graph y=1/2Sinø/2?
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[tex]\bf \bullet \textit{ stretches or shrinks}\\ \left. \qquad \right. \textit{horizontally by amplitude } |{{ A}}|\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}[/tex]
[tex]\bf \bullet \textit{function period or frequency}\\ \left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ \left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)[/tex]
now, with that template in mind,
[tex]\bf \stackrel{parent~function}{y=sin(\theta )}\qquad \qquad y=\stackrel{A}{\frac{1}{2}}sin\left(\stackrel{B}{\frac{1}{2}}\theta \right) \\\\\\ Amplitude\implies \frac{1}{2} \\\\\\ Period\implies \cfrac{2\pi }{B}\implies \cfrac{2\pi }{\frac{1}{2}}\implies 4\pi [/tex]
which is pretty much the same sin(θ) function, but squished by 1/2 and elongated up to 4π, check the picture below.
-1/2(7z+4)+1/5(5z-15)
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Round the decimal to the nearest hundredths 983.625
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9 = hundreds
8 = tens
3 = ones
6 = tenths
2 = hundredths
5 = thousandths
You want to round to the nearest hundredths
Look at the number on the right, if it's bigger than 5, round up, if it's 4 or lower, round down.
In this case, the number to the right is a 5, so you round the 2 (hundredths) up one so:
983.63
Beth sold half of her comic books and then bought nine more she now has 28 how many did she have to start with
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19 + 19 = 38
she started with 38 comics
Kelly wants to buy 5.6 feet of wood for a bookshelf. The wood costs $3.25 per foot. If Kelly has $18.50 to spend, how much change will she receive?
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store decreased its price on a computer by $112 to $478. What was the original price
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Answer:
$590.
Step-by-step explanation:
Let x be the original price of computer.
We have been given that a store decreased its price on a computer by $112 to $478.
This means x minus 112 equals to 478. We can represent this information in an equation as:
[tex]x-\$112=\$478[/tex]
Let us add $112 to both sides of our equation.
[tex]x-\$112+\$112=\$478+\$112[/tex]
[tex]x=\$590[/tex]
Therefore, the original price of computer was $590.
this number is the same as 31 + 880000
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hope this helps
The tank for a car holds
18
18
gallons. The gasoline gauge shows the tank is
1
3
13
full. How much gas is still in the tank? Give your answer as a whole number or as a mixed fraction reduced to lowest terms
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[tex]\bf 18\cdot \cfrac{1}{3}\implies \cfrac{18}{3}\implies \stackrel{gallons}{6}[/tex]
To calculate the amount of gas left in the tank, you should multiply the total capacity of the tank, which is 18 gallons, by the fraction that represents the amount of gas remaining, which is 1/3. Thus, there are 6 gallons of gas still in the tank.
Explanation:
To answer this question, we should multiply the total capacity of the tank, which is 18 gallons, by the fraction that represents the amount of gas remaining, which is 1/3. This will give us the number of gallons of gas left.
Now, apply the multiplication: 18 gallons * 1/3 = 6 gallons.
So, there are 6 gallons of gas still in the tank.
Learn more about multiplication of fractions here:https://brainly.com/question/9281754
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What is the largest place value of 585
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Which would most likely be graphed using a continuous graph? Check all that apply. (Medal for correct answer.
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Question:
Which would most likely be graphed using a continuous graph? Check all that apply.
Answer:
B. Total cost, c, of buying g pounds of broccoli.
C. Speed of a car, s, as it accelerates over time, t.
E. total distance, d, that has been driven over time, t.
F. decrease in outside temperature, F, one evening over time, t.
Hope this helped!
What is the equation of a line, in point-slope form, that passes through (−2, −6) and has a slope of 13 ?
A)y−2=13(x−6)
B) y+6=13(x+2)
C) y−6=13(x−2)
D) y+2=13(x+6)
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Suppose it costs $ 20 per day and $ 0.12 per mile to rent a car. What is the total bill if the car is rented for 3 days and is driven 140 miles?
The total bill is $_
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0.12 per mile for 140 miles = 0.12(140) = 16.80
for a total cost of : 60 + 16.80 = 76.80 <==
what percent of 29.5 is 10.03
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[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 29.5&100\\ 10.03&p \end{array}\implies \cfrac{29.5}{10.03}=\cfrac{100}{p}\implies p=\cfrac{10.03\cdot 100}{29.5}[/tex]
If a bottle rotates through 270 degrees in 3 seconds how many degrees does it rotate in 2 seconds
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I divided 270 by 3, which was 90. Then, I multiplied 90 by 2. Which was 180.
90 sec per spin
then you multply by two for two spins
90x2=180
Answer is 180 per sec
Which metric unit would you use to measure: 1.The length of a newspaper. 2. The height of a lamp post. 3. The length of a bus route. 4. The width of a ruler.
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liters is liquid
meters is how long or wide
grams is weight
i would use meters
How do I solve a-5/5=5
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a - 1 = 5
a - 1 (+1) = 5 (+1)
a = 6
if you mean (a-5)/5 = 5
((a - 5)/5) (5) = 5(5)
a - 5 (+5) = 25 + 5
a = 30
hope this helps
First, rewrite 9/10 and 23/25 so that they have a common denominator.
Then, use
<, =, or > to order 9/10 and 23/25
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[tex]\bf \cfrac{9}{\boxed{10}}\qquad \qquad \cfrac{23}{\boxed{25}} \\\\\\ \cfrac{9\cdot \boxed{25}}{10\cdot \boxed{25}}\implies \cfrac{225}{250}\qquad \qquad \qquad \cfrac{23\boxed{10}}{25\cdot \boxed{10}}\implies \cfrac{230}{250}\\\\ -------------------------------\\\\ \textit{so, which is larger then?}\qquad \cfrac{225}{250}~or~\cfrac{230}{250}?[/tex]
surely you can tell.
9/10=45/50 (multiply by 5)
23/25=46/50 (multiply by 2)
46/50 > 45/50 therefore
23/25 > 9/10.
Hope this helps :)
Can you answer all of these please?!?!
1. Kim's age is twice that of her sister. When you add Kim's age to her sister's age, you get 36. How old is each sister?
(a) Write an equation that represents the situation. Explain any variable used.(1 point)
(b) Solve the equation from Part (a). Show your work. State your solution as a complete sentence. (3 points)
Answer:
2. Solve each given equation and show your work. Tell whether it has one solution, an infinite number of solutions, or no solutions, and identify each equation as an identity, a contradiction, or neither.
(a) (2 points)
(b) (2 points)
(c) (2 points)
Answer:
3. At a bargain store, Tanya bought 3 items that each cost the same amount. Tony bought 4 items that each cost the same amount, but each was $2.25 less than the items that Tanya bought. Both Tanya and Tony paid the same amount of money. What was the individual cost of each person's items?
(a) Write an equation. Let x represent the cost of one of Tanya's items. (1 point)
(b) Solve the equation. Show your work. (2 points)
(c) Check your solution. Show your work. (1 point)
(d) State the solution in complete sentences. (1 point)
Answer:
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kim-2x
x+2x=36
3x=36
x=12
2x=24
Kim is 24 years old and her sister is 12 years old.
3) Tanya-3x
Tony-4y
x-2.25=y
3x=4y
3x=4x-9
9=x
6.75 =y
Tanya's was 9 $ and Tony's was 6.75 $
Alexandria wants to go hiking on Saturday. She will consider these conditions when she chooses which of several parks to visit:
• She wants to hike for 2 hours.
• She wants to spend no more than 6 hours away from home.
• She can average 50 miles per hour to and from the park.
Write and solve an inequality to find possible distances from Alexandria’s home to a park that satisfies the conditions.
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Answer: 27
i would say 54/2=27
Step-by-step explanation:
I'll give BRAINIEST
.............
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Why do you sometimes have only one multiplication sentence for an array?
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Graph y−5=−23(x+9) using the point and slope given in the equation. Use the line tool and select two points on the line.
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i think it may be correct
Answer here is correct hope this helps :)
What integer is equivalent to 9 3/2
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Answer: 21/2
I need help please 4x-10=2(2x-5)
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What is the sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2?
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Answer:
[tex]\frac{765}{128}[/tex]
Step-by-step explanation:
We have been given that 1st term of a geometric series is 3 and common difference is 1/2 . We are asked to find the sum of 1st 8 terms of the given series.
We will use geometric series formula to solve our given problem.
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]
Upon substituting our given values in the above formula we will get,
[tex]S_8=\frac{3(1-(\frac{1}{2})^8)}{1-\frac{1}{2}}[/tex]
[tex]S_8=\frac{3(1-\frac{1^8}{2}^8)}{\frac{2-1}{2}}[/tex]
[tex]S_8=\frac{3(1-\frac{1}{256})}{\frac{1}{2}}[/tex]
[tex]S_8=\frac{3(\frac{256-1}{256})}{\frac{1}{2}}[/tex]
[tex]S_8=\frac{3(\frac{255}{256})}{\frac{1}{2}}[/tex]
[tex]S_8=3(\frac{255}{256}\times\frac{2}{1})[/tex]
[tex]S_8=3(\frac{255}{128})[/tex]
[tex]S_8=\frac{765}{128}[/tex]
Therefore, the sum of our given series is [tex]\frac{765}{128}[/tex].
How does translating a figure using the formal definition of a translation compare to the previous method of translating a figure?
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This method is easy to understand and easy to apply to any figure than the other methods.
What is a translation of the figure?When the figure is moved from one place to another place is called translation of the figure.
When we add in x then the figure will translate toward the left.
And when we subtract in x then the figure will translate toward the right.
If we add in y then the figure will translate downward.
And when we subtract in y then the figure will translate upward.
This method is easy to understand and easy to apply to any figure than the other methods.
More about the translation of the figure link is given below.
https://brainly.com/question/933695
How many sixteens are in 15/16
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hope this helps
at the metal-casting company where i work, i must set up a conveyor system to move castings from the furnace to the heat treatment area 55 yards away. the castings cool at the rate of 0.03 degrees fahrehnheit per second and must not be allowed to cool more that 7 degree's fahrenheit before being heat rtreated. what is the minimum speed per second that the conveyor must move?
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Minimum speed = 55 yd * 3 ft/yd / 233.3 s
= 0.707 ft/s