Write an equation of the parabola that passes through the points (-1,4), (0,1), and (2,7)
y = _____
Answer:
y = -6x^2 + 15x -5
Step-by-step explanation:
equation step 1 for parabola
y2-y1 /x2-x1
= 1 - 4 / 0 - - 1
= -3 / 1
y = -3
We try again different points
y2-y1 / x2-x1
= 7 - 1 / 2 - 0
= 6 / 2
y = 3
we can see that one side is descending and 1 side is ascending
The start of the parabola is 0,1 as x = 0 and crosses the line.
we try again
y2-y1 /x2-x1
7-1 / 2-0
= 6 / 2
y = 3
You should know that a parabola is determined by 3 points, so unless your points happen to be collinear, they will determine a parabola. A straight forward, if not always the easiest way would be to take the general equation
y = ax^2 + bx + c
plug in each point, eg.y = y1 and x = x1 eg) y = y2 and x = y2 eg) y = y3 x=x3
Top equation re-used last see at end.
4 = a(-1)^2 + b(-1 ) + c = a+b+c=4
1 = a(0)^2 +b(0) + c = c =1
7 = a(2)^2 + b(2) + c = 4a+2b=7
a= -1-0 = -1 b = -1-0 = -1 and 4-1 = 3
-a +-b = 3
2nd set of equations
4a-0a = 4a
2b-0b = 2b
7-1 = 6
4a +2b=6 and previous
-a +-b = 3 here we can multiply by -2 to get 2b equality to 1st equation
2a + 2b = -6
4a + 2b = 6
2a = -12
2a = -12 / 2
a = -6
plug a
4(-6) + 2b = 6
-24 + 2b = 6
2b = 6 +24
2b = 30
b = 15
then put a + b+ c into top equation
(-6) + (15) + c = 4
9 + 0 = 4
9 -9 = 4 -9 cancel
c = -5
Then put into first equation as c and complete equation
To find that;
y = -6x^2 + 15x -5 = is our equation of the parabola.
This is how to solve your two linear equations in three unknowns.
The equation of parabola passing through (-1, 4), (0, 1), and (2, 7) is y = 2x² - x + 1.
To find equation of parabola that passes through the given points, we use the general-form of quadratic equation: y = ax² + bx + c.
Since we have three points, we substitute the coordinates of each point into the equation to create a system of equations. Solve for a, b, and c:
Substitute (-1, 4), We get,
4 = a(-1)² + b(-1) + c,
4 = a - b + c,
Next, Substitute (0, 1):
1 = a(0)² + b(0) + c
1 = c
Next, Substitute (2, 7):
7 = a(2)² + b(2) + c
7 = 4a + 2b + c
Now, we have a system of equations:
a - b + c = 4 ...equation(1)
c = 1 ...equation(2)
4a + 2b + c = 7 ...equation(3)
From equation(2), we know that c = 1. Substituting this into equation(1) and 3, we get,
a - b + 1 = 4
4a + 2b + 1 = 7
Solve equation(1) for a - b:
We get, a - b = 3,
Solve equation(3) for 4a + 2b:
4a + 2b = 6
Now we have a system-of-equations as :
a - b = 3
4a + 2b = 6
Solving the system for "a" and "b", We get,
a = 2; b = -1
Now we can write the equation of the parabola:
y = ax² + bx + c ⇒ y = 2x² - x + 1,
Therefore, the required equation of parabola is y = 2x² - x + 1.
Learn more about Parabola here
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3x - 5 < -14 or 2x - 1 > 7 for x
Answer:
see below
Step-by-step explanation:
x < -3 for the first equation
x > 4 for the second equation
Find the GCF (Greatest Common Factor) of each pair of numbers:
9 and 36
35 and 42
100 and 120
84 and 42
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The Answers are :
9 and 36 [tex]\rightarrow[/tex] 935 and 42 [tex]\rightarrow[/tex] 7 100 and 120 [tex]\rightarrow[/tex] 2084 and 42 [tex]\rightarrow[/tex] 42Answer:
9 and 36 = 9
35 and 42 = 7
100 and 120 = 20
84 and 42 = 42
Plz I am really stuck on this question, your time is appreciated.
Answer: 0.05
Step-by-step explanation:
1) Re-arrange the formula given to find the rate (r)
I = Prt
becomes r = I / Pt
Now we add in the values we know
P = 3000, t = 3 years, I = 450
r = 450 / ( 3000 × 3 )
r = 0.05 or 5% / year
b) Write 25 x 10^6 in standard form
Answer:
The final answer is 25000000.
Step-by-step explanation:
Answer:
25000000
Step-by-step explanation:
10^6 = 1000000
25 x 10^6 = 25000000
How do you Factor out greatest common factor of 30x³y³z²+12x²y²z³-18x⁵y⁶z ?
Step-by-step explanation:
30x³y³z²+12x²y²z³-18x⁵y⁶z
6x²y²z(5xyz+2z²-3x³y⁴).
hope this helps you.
what number is not a common denominator of 2/4 and 3/8
Scale the numerator and the denominator down by a factor of 4 (divide) to write a fraction equivalent to 8/56. (i really need help with this)
8/56 = ??
Answer:
2/14
Step-by-step explanation:
when you scale the numerator and denominator down by 4, you just divide both of them by 4. So since 8 divided by 4 is 2 and 56 divided by 4 is 14, the answer is 2/14
Answers?..............
How many variable terms are in the expression 3x3y + 5xz − 4y + x − z + 9?
(Input a numeric value only.)
Answer:
3
Step-by-step explanation:
there are only x y and z used in the expression no matter how many times they multiply.
Two jars of sweets have the same amount of sweets inside.
25% of the sweets in jar A are orange.
2 fifths of the sweets in jar B are orange.
10 sweets in jar A are orange. How many are orange in jar B?
Answer:
4 sweets are orange in jar B
Step-by-step explanation:
scale the numerator and the denominator up by a factor of 5 (multiply) to write a
fraction equivalent to 3/10.
Answer:
15/50
Step-by-step explanation:
5*3=15
5*10=50
so 15/50.
A plane travels 800 metres along the runway before taking off at an angle of 10∘
.It travels a further 1 000 metres at this angle as seen in the figure. Work out the distance of the plane from its starting point. Give your answer to 2 decimal places.
I hope this step by step explanation helps.
A plane travels 800 meters along the runway before taking off, then the distance travelled from the starting point will be equal to 1793.24 meters.
What is Velocity?Velocity is the rate at which a moving object's direction changes as perceived from a certain vantage point and measured by a particular unit of time. Kinematics, the area of special relativity that investigates how bodies move, starts with the fundamental idea of speed.
In order to be explained, the scientific vector quantity known as velocity needs to have both a magnitude and a direction.
As per the given data in the question,
Distance travelled by plane = 800 meters
Use the equation,
a² = b² + c² -2bc cos A
d² = 800² + 1000² - (2 × 800 × 1000 × cos 170°)
d² = 1640000 - 1600000(cos 170°)
d² = 3215692.405
d = 1793.24
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Solve for x: 7x-3/2 = -2/3
Hence, the value of x ix 5/21.
★ Solution (1) :-[tex]\sf \leadsto \dfrac{7x - 3}{2} = \dfrac{-2}{3}[/tex]
[tex]\sf \leadsto 3(7x - 3) = -2(2)[/tex]
[tex]\sf \leadsto 21x - 9 = -4[/tex]
[tex]\sf \leadsto 21x = -4 + 9[/tex]
[tex]\sf \leadsto 21x = 5[/tex]
[tex]\sf \leadsto x = \dfrac{5}{21}[/tex]
Answer:
5/42
Step-by-step explanation:
7x - 3/2 = -2/3 (Take -3/2 to the other side so it becomes +3/2)
7x = -2/3 +3/2 (Add the two fractions)
7x = 5/6 (7 is taken to the other side so 5/6 ÷ 7)
x = 5/42
If a snail travels 2/5 of an inch in 2/3 of a minute, then how far can it travel in 1 full minute? ___Inches
Answer:
4 in / min
^Speed of snail
1min × 60 = 1hour
(4 in / min) × 60 = 240 in / hour
12 in = 1 ft.
240in / 12 = 20ft. every. hour OR 20ft. / h
Step-by-step explanation:
Find the train fares. Assume one half of adult fare for children 1-12. Children
under 1 ride free.
Adult fare: $260
Adults: 2
Children:
4 mo.
2 yr.
4 yr.
6 yr.
7 yr.
Answer:
(D) 6yr
Step-by-step explanation:
Help me answer this please quickly!
Answer:
Step-by-step explanation:
When two lines intersect, the non adjacent angles formed are called vertical angles and they are congruent.
∠FZG = ∠HZJ {Vertical angles are congruent.
∠FZG = 38°
The figure below has what type of symmetry?
Answer:
c both point and line symmetry.
Plz help me I just need the answer
the sum of three numbers is 131. the third number is 4 times the first. the second number is 5 more than the first. what are the numbers
Step-by-step explanation:
let the numbers are:
a, b, and c
the equation would be:
a+b+c = 131
c = 4a
b = a+5
=>
a + a+5 +4a = 131
6a +5 = 131
6a = 131-5
6a = 126
a= 126/6
a = 21
b = a+5 = 21+5
b = 26
c = 4a = 4(21)
c = 84
The points (0, 3) and (1, 9) fall on a particular line. What is its equation in slope-intercept form?
Answer:
y = 6x + 3
Step-by-step explanation:
y2 - y1 / x2 - x1
9 - 3 / 1 - 0
6/1
= 6
y = 6x + b
3 = 6(0) + b
3 = 0 + b
3 = b
Answer:
y = 6x+3
Step-by-step explanation:
[tex]\frac{y2-y1}{x2-x1}\\\\= \frac{9-3}{1-0}\\\\= \frac{6}{1}\\\\= 6[/tex]
Hence, the slope is 6.
Substituting the slope value to the equation 'y=mx+c',
y = 6x +c
Substituting (0,3):
3 = 0 + c
c = 3
Hence,
y = 6x + 3
Feel free to mark this as brainliest! :D
PLZZZ HELPP REALLLY QUICKKK I WILL GIVE SOMEONE BRAINLEST PLZZ HELLPPP AND EXPLAINNNN PLZZZ EXPLAINNN
Hi there!
The ratio of the base to the height is 4:1, so:
12 cm : x cm
12/4 = 3, which is the scale. Thus, x = 3 cm.
Find the area using the equation A = b × h
A = 3 × 12 = 36 cm²
Which expression describes 10−7?
Unless we are missing more information (which I think we may be as this is a simpler question)
10 - 7 = 10 - 7 = 3
If you need it in words:
Ten minus seven
- or -
Seven subtracted from ten
Which is the equation of the line that passes through (-2,2) and (4,-5)
Answer:
here you go
Step-by-step explanation:
Algebra questions and answers. Write an equation of the line that passes through (4,5) and is parallel to the line defined by 4x+y=-2. Write the answer in slope-intercept form (if possible) and in standard form (Ax+By=C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable.
after a 60% reduction, you purchase a new soft drink machine on sale for $200. what was the original price of the soft drink
your answer is 740 {:
Step-by-step explanation:
let x be the original price
then we write our equation
x-60%x=200 (x=100%x)
100%x-60%x=200
40%x=200
(40/100)x=200
x=(200*100)/40
x=20000/40=500
so the original price was $500
One of the greatest assets of a secretary is often his/her ability on the keyboard of a computer. Mrs. Garcia has been recognized as the Most Outstanding Typist at a prestigious firm because of her outstanding typing speed. The table below displays data collected from her most recent evaluation.
Write an equation to represent the total number of words, y, that Mrs. Garcia can type in x minutes_________
If Mrs. Garcia maintains a constant speed consistent with the results above, how many words will she type in 49 minutes?_______
Answer:
y = 70x3,430Step-by-step explanation:
The table shows that Mrs. Garcia types 70 words in the first minute and 70 additional words in each additional minute.
That is, in x minues, Mrs. Garcia types 70x words:
y = 70x . . . . words Mrs Garcia can type in x minutes
__
When x=49, the number of words Mrs. Garcia is expected to type is ...
y = 70×49 = 3,430
She will type 3,430 words in 49 minutes.
make x the subject
h=4(x+3y)+2
Answer:
x=(h-12y-2)/4
Step-by-step explanation:
h=4x+12y+2
4x=h-12y-2
x=(h-12y-2)/4
Mrs. Alejandro places four cards on the board. Which does not represent the same distance?
A. 36 yards
B. 432 feet
C. 1296 inches
D. 108 feet
Answer:
B. 432 feet
Step-by-step explanation:
36 yards * 3 = 108 feet
108 feet * 12 = 1296 inches
HELPPPPPPPPPPPPPPPPPPPPPP
Answer:
11
Step-by-step explanation:
1. You could solve this as a way of just knowing that 6+11=17.
2. You could also solve this algebraically by subtracting 6 on both sides and getting y=11 because 17-6=11.
Answer:
y=11
Step-by-step explanation:
6+y=17
y=17-6
y=11
Can you solve this? I'm terrible at math