Answers
Answer:
Step-by-step explanation:
You have to solve this as a system. We have 3 coordinates given; the first 2 are given as zeros of the quadratic, the 3rd one is given as a regular coordinate. The zeros of a quadratic are where the y values of a coordinate are 0's because the x-intercepts of a quadratic (aka zeros) exist where y = 0. We use each of those points in the standard form of a quadratic to solve for a, b, and c. First, (0, 0):
[tex]0 = a(0)^2+b(0)+c[/tex] which gives us that c = 0. We'll use that value of c as we move forward with the problem. Next we'll use (3, 0):
[tex]0=a(3)^2+b(3)+0\\0 =9a+3b[/tex]Hold that thought for a minute or 2. Next we'll use the coordinate (1, 6):
[tex]6=a(1)^2+b(1)+0\\\\6=a+b[/tex] Now we have a system that we can solve using either substitution or elimination for a and b. I used elimination:
6 = a + b
0 = 9a + 3b and multiply the top equation by -3:
-18 = -3a - 3b
0 = 9a + 3b
so
-18 = 6a and
a = -3. Now back solve for b:
6 = -3 + b so
b = 9 and our quadratic is
[tex]y=-3x^2+9x+0[/tex] or just
[tex]y=-3x^2+9x[/tex]
Related Questions
-7p+2(5p-8)=6(p+6)-7
Answers
Answer:
-15
Step-by-step explanation:
-7p+10p-16=6p+36-7
3p-16=6p+29
3p-6p=29+16
-3p=45
p=45/-3
p=-15
-7p+2(5p-8)=6(p+6)-7
Distribute
-7p+10p-16=6p+36-7
Add -7p and 10p together
3p-16=6p+36-7
Subtract 7 from 36
3p-16=6p+29
+6p (on both sides)
9p-16=29
+16 (on both sides)
9p=45
Divide both sides by 9
P=5
what are the order of operations for integers ?
Answers
Answer:
PEMDAS
Step-by-step explanation:
P - Parentheses (Brackets also!)
E - Exponents
M and D - Multiplication and division. Many people think multiplication has to be done first as said in "PEMDAS" but it doesn't. Do multiplication and division according to which ever one is farthest to the left (left to right).
A and S - Addition and subtraction. Same thing applies here, neither addition or subtraction has to be done first, just do them according to which one is farthest to the left when reading the expression from left to right.
Directions: Using the digits 0 to 9, fill in the boxes so that the chart is accurate. Use each digit only once per blue box and once per red box. Logs are base 10. Please help me out with this would really appreciate it, thanks.
Answers
Step-by-step explanation:
log 10 = 1. So if log x < 1, then x < 10. And if log x > 1, then x > 10.
The upper left number is the smallest, and can't be smaller than 1. If the exponent is 0, we can put any number in the red box.
The fractions in the upper right and lower left need to be as large as possible. The denominators will be small, and the numerators will be large.
From there, a little trial and error does the rest. The are many possible answers. I've included one.
What is the equation of the line that passes through the point (3,-7) and has a undefined slope
Answers
Answer:
x = 3
Step-by-step explanation:
A vertical line has undefined slope. Its equation is of the form x=c, for some constant c.
Line through (3, -7)To make sure the line passes through a point with an x-coordinate of 3, the constant in the equation must be 3:
x = 3 . . . . . . vertical line through (3, -7)
[tex]5^{-3}[/tex] rewrite as an equivalent expression
Answers
Answer:
the equivalent equation of
[tex]5^{-3}[/tex]=[tex]\frac{1}{5^{3}}=\frac{1}{125}[/tex]
What is the quotation of 6 and -1/2?
1. -12
2. -1/12
3. 1/12
4. 12
Answers
Answer: Option 2: -1/12
Explanation
= -1/2÷6
= -1/2×1/6
= -1/12
Must click thanks and mark brainliest
Kyrin picked 40 apples from the trees behind his house. Later, he gave two to each of his friends. He only has 8 remaining. How many friends does he have?
Answers
Answer:
kyrin had 16 friends
Step-by-step explanation:
40 - 2 (x) = 8 make x as friends
- 2x = 8 - 40
- 2x/ - 2 = - 32/ -2
x = 16
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
Find the mode of the data set that consists of 8, 18, 4, 2, 3, 7, 11, 13, 5, 1.
A. 6
B. 7.2
C. no mode
D. 17
Answers
Answer:
No mode
Step-by-step explanation:
There are no any numbers which are repeated. So there is no mode.
Answer:
The answer is C.no mode because the mode of a data set is the number that occurs most frequently in the set. To easily find the mode, but the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!
Combine like terms in the given polynomial. Then, evaluate for x = 4, y = – 2.
xy – 2xy + 3x2 y — 4x y2 + 2xy2
3x2 y + 2xy2 – xy; – 56
C - xy – 2xy2 + 3x2y; – 56
Cx? y2 – 2; 62
C
– 2x y2 + 3x2y – xy; – 120
Need explanation please
Answers
Answer:
- 2 x y^2+3 x^2 y -xy
-120
Step-by-step explanation:
xy – 2xy + 3x^2 y — 4x y^2 + 2xy^2
Combine like terms
xy – 2xy + 3x^2 y — 4x y^2 + 2xy^2
- x y+3 x^2 y - 2 x y^2
Let x = 4 y = -2
-(4)(-2) +3(4)^2 (-2) -2(4)(-2)^2
Exponents first
-(4)(-2) +3(16) (-2) -2(4)(4)
Multiply
+8 -96-32
Add and subtract
-120
Any help would be nice
Answers
Answer:
11. angles on a straight line add up to 180
so 180 -133 equal to b.b=47
12.Vertical opposite angles are equal.
therefore b=50
lilly just paid off a 400$ loan. she had to pay 60 in interest at a simple annual interest rate of 5%. how many years did lily have this loan?
•A.) 2
•B.) 3
•C.) 4.5
•D.) 5
Answers
Answer:
B.) 3
Step-by-step explanation:
Interest = prinipical ^ interest rate ^ year
60 = 400 ^ 5% ^ year
year = 60/400^5%
3years
In the town of Rockville, 35 of the students in middle school participate in organized sports after school. If 14 of them play basketball, what fraction of the students play basketball?
Answers
Answer:
2/5
Step-by-step explanation:
The fraction that play basketball is the number that play basketball over the total
14/35
Divide the top and bottom by 7
2/5
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
A ___________________ summarizes all values in a data set and lists how many times they occur.
A. tally chart
B. data value
C. data summary
D. frequency table
Answers
Answer:
Step-by-step explanation:
B) data summary its in the words it sums up the answers to all the data you've collected over timew
G
Antranig has a glass that holds 9.75 fluid ounces. He drinks 3.5 glasses of water in one day. To the nearest hundredth of a fluid ounce, how much water does Antranig drink?
He drinks about ounces of water
(Do not round antil the final answer. Then round to the nearest hundredth as needed.)
HELP MAN
Answers
Answer:
34.13 ounces
Step-by-step explanation:
Total amount of water drunk=3.5*9.75=34.13
Which is the simplified form of r to the negative 7th power plus s to the negative twelve
Answers
Answer:
1/r^7 + 1/s^12
Step-by-step explanation:
Since there is a negative exponent, the term becomes a fraction. As we do not know the value of the term, it remains in its variable form with a positive exponent
What were Malcolm's and Ravi's maximum speeds?
Answers
Answer:
Malcom's maximum speed = 200 km/h
Ravi's maximum speed = 320 km/h
Step-by-step explanation:
Let m = Malcom's maximum speed
Let r = Ravi's maximum speed
Average of their maximum speed would be represented as [tex] \frac{m + r}{2} = 260 [/tex]
[tex] m + r = 520 [/tex].
Make m the subject of the formula by subtracting r from both sides:
[tex] m = 520 - r [/tex]. Let this be equation 1.
Given that Malcom's speed (m), when doubled is 80 km/h more than that of Ravi (r). This can be expressed as: [tex] 2m = r + 80 [/tex]. This is equation 2.
Plug in (520 - r) into equation 2 to replace m:
[tex] 2(520 - r) = r + 80 [/tex]
[tex] 1040 - 2r = r + 80 [/tex]
Solve for r. Subtract 1040 from both sides:
[tex] 1040 - 2r - 1040 = r + 80 - 1040 [/tex]
[tex] - 2r = r - 960 [/tex]
Subtract r from both sides
[tex] - 2r - r = r - 960 - r [/tex]
[tex] - 3r = - 960 [/tex]
Divide both sides by -3
[tex] \frac{-3r}{-3} = \frac{-960}{-3} [/tex]
[tex] r = 320 [/tex]
To find m, plug in the value of r into equation 1.
[tex] m = 520 - r [/tex]. =>Equation 1
[tex] m = 520 - 320 [/tex]
[tex] m = 200 [/tex].
Malcom's maximum speed = m = 200 km/h
Ravi's maximum speed = r = 320 km/h
In a naval engagement, one-third of the fleet was captured, one-sixth was sunk, and two ships were destroyed by fire. One-seventh of the surviving ships were lost in a storm after the battle. Finally, the twenty-four remaining ships sailed home. How many ships were in the fleet before the engagement?
Answers
Answer:
60 ships.
Step-by-step explanation:
Let the total number of ships in the naval fleet be represented by x
One-third of the fleet was captured = 1/3x
One-sixth was sunk = 1/6x
Two ships were destroyed by fire = 2
Let surviving ships be represented by y
One-seventh of the surviving ships were lost in a storm after the battle = 1/7y
Finally, the twenty-four remaining ships sailed home
The 24 remaining ships that sailed home =
y - 1/7y = 6/7y of the surviving fleet sailed home.
Hence
24 = 6/7y
24 = 6y/7
24 × 7/ 6
y = 168/6
y = 28
Therefore, total number of ships that survived is 28.
Surviving ships lost in the storm = 1/7y = 1/7 × 28 = 4
Total number of ships in the fleet(x) =
x = 1/3x + 1/6x + 2 + 28
Collect like terms
x - (1/3x + 1/6x) = 30
x - (1/2x) = 30
1/2x = 30
x = 30 ÷ 1/2
x = 30 × 2
x = 60
Therefore, ships that were in the fleet before the engagement were 60 ships.
WILL GIVE BRAINLIEST:
Elanor wants to estimate the number of frogs in a reservoir.
She catches 90 frogs from the reservoir and marks them with a non-harmful dye.
Elanor then returns the frogs to the reservoir.
The next day she catches another 70 frogs and 10 of these are marked with the dye.
Work out an estimate for the total number of frogs in the reservoir.
Answers
Answer:
approximately 150 frogs
Step-by-step explanation:
To find your estimate, you have to add 90 + 60 because from the 70 that Elanor caught the second day, 10 of them were the ones that she had caught the day before so you have to do 70 - 10 = 60. Therefore, 90 + 60 = 150 estimated frogs.
Please help!! What is the volume of four cubes with a side length of fraction 1 over 4 foot? V = s3, where s is the side length. fraction 1 over 4 ft3 fraction 1 over 3 ft3 fraction 1 over 12 ft3 fraction 1 over 16 ft3
Answers
Answer:
1/16 is the answer!!Hope this helps. sorry for no explanation but i already did this flvs quiz and i don't remember how to f=do it
Step-by-step explanation:
Point B is on line segment AC. Given BC=9 and AB=11, determine the length AC.
Answers
Answer:
20
Step-by-step explanation:
If point B is on line segment AC, then we know for sure AB + BC = AC.
To understand this better, draw a line segment, then put a point anywhere on the line segment. There are two line segment divided by that point. If you combine those two line segments then you have your original figure.
So 11 + 9 = 20.
Shawn wanted to model the number 13,450 using 13,450 using base-ten blocks how many large cubes, flats, and longs does he need to model the number
Answers
Answer:
13 cubes, 4 flats, 5 longs
Step-by-step explanation:
Base-ten is basically just analyzing the place values of each number in the given value.
A cube represents 1,000, a flat represents 100, and a long represents 10.
Looking at the number 13,450, we can see that there are 13 thousands in this (13,000). This means that we will need 13 cubes.
We can also see that there are 4 hundreds in this (400), meaning we need 4 flats.
Also, there are 5 tens in this (50), so we need 5 longs.
Hope this helped!
Which ordered pair is a solution to the following linear system?
y = x
y = –x
Question 3 options:
(0, 0)
(0, 1)
(1, 1)
(1, 0)
Answers
(0,0)
How?
Putting values
[tex]\\ \sf\longmapsto y=x[/tex]
[tex]\\ \sf\longmapsto 0=0[/tex]
And
[tex]\\ \sf\longmapsto y=-x[/tex]
[tex]\\ \sf\longmapsto 0=-0[/tex]
Hence verified
let the cp be rs x. if a man gains 20% profit by selling an article for rs 816. find cp
Answers
Answer:
Let, the c.p be x.
Given,
profit % = 20%
S.P = rs 816
c.p = x
We know,
profit = p% of c.p
= [tex]\frac{20}{100}[/tex] * x
= [tex]\frac{x}{5}[/tex]
now,
C.p = profit + s.p.
x = [tex]\frac{x}{5}[/tex] + 816
x = [tex]\frac{x+ 4080}{5}[/tex]
5x = x + 4080
5x-x = 4080
4x = 4080
x = [tex]\frac{4080}{4}[/tex]
x = Rs 1080
Hence, the c.p is Rs. 1080
PLEASE HELP!! Find the slant height of the come
Answers
...
s=√h2+b22
s = slant height.
h = vertical height.
b = base.
Anyone who can help me with this?
Answers
Answer:
C
Step-by-step explanation:
We know that the first integer will be "l" so the second will be l + 1, third will be l + 2, fourth will be l + 3, and the fifth will be l + 4. The question says "the greatest is g" so that means that the fifth integer is the greatest meaning that is the value of g. Now that we know the value of g, we can substitute it into the equation they gave us and simplify.
l+(l+4)/2
2l+4/2
l + 2
Best of Luck!
Answer:
C
Step-by-step explanation:
say your 5 consecutive numbers are 6-10
if 6 is l and 10 is g then
6+10 over 2 equals 8
this proves that l+2 is correct since 6+2=8
what is
f(x)= (x-12)(x+1)
in standard form?
Answers
Answer:
x^2-11x-12
Step-by-step explanation:
I use the box method, which makes a 2x2 box. Then you arrange you numbers based on the equation (show in image)
Then you multiply it out and get the equation
F(x)= x^2+x-12x-12
Simplify your equation and you get
F(x)= x^2-11x-12
ASAP PLZ ANSWER 50 POINTS How do I determine if -3x+y =8 is a function?
Answers
Answer:
To determine if Y=-8 is a function, you must do the vertical line test. If you were to plot Y=-8 on a coordinate plane, you would see that at the point of (0,-8)[which is what Y=-8 is also] is on the Y axis and makes a horizontal linet hat passes through (o,-8).
Step-by-step explanation:
Answer:
graph
Step-by-step explanation:
did you mean in graph
Does this graph show a function? explain how you know
Answers
Which is the best estimate of -14 1/9 (-2 9/10)
Answers
Answer:
Step-by-step explanation:
-14 1/9 is close to - 14
-2 and 9/10 is close to - 3
The best estimate would be 42 (14 * 3)
Estimate means you put your calculator on the kitchen counter until you've done this question.
Let's see what the actual answer is. 40.92222 which is close to 41.
42 is a pretty good estimate.
whats the answer to this problem/how to figure it out?!
Answers
6x^2+4x+8
6x7^2+4x+8
blah blah blah
ANSWER
330
pls say if im right
Answer:
330Step-by-step explanation:
[tex]6x^2 +4x +8\\x =7\\\\6(7)^2 +4(7) +8\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:exponents}\:\left(7\right)^2\::\quad 49\\\\=6\cdot \:49+4\left(7\right)+8\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:6\cdot \:49\::\quad 294\\\\=294+4\left(7\right)+8\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:4\left(7\right)\::\quad 28\\\\=294+28+8\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:294+28+8\:\\:\quad 330[/tex]