Answer:
y = [tex]\frac{1}{3}[/tex] x² - 2x - 2
Step-by-step explanation:
x-coordinate of the vertex of a parabola is ( [tex]- \frac{b}{2a}[/tex] )
y = f(x) = ax² + bx + c
(x, y) ∈ f(x)
~~~~~~~~~
{ (0, - 2), (3, - 5) } ⊂ { (x, y): y = ax² + bx + c }
a(0)² + b(0) + c = - 2 ⇒ c = - 2
a(3)² + b(3) + ( - 2) = - 5
9a + 3b - 2 = - 5 ⇒ 3a + b = - 1
[tex]- \frac{b}{2a}[/tex] = 3 ⇒ b = - 6a
[tex]\left \{ {{3a+b=-1} \atop {b=-6a}} \right.[/tex]
3a + ( - 6a) = - 1
a = [tex]\frac{1}{3}[/tex]
b = - 2
y = [tex]\frac{1}{3}[/tex] x² - 2x - 2
The equation of the parabola for the given values is y = x²/3 - 2x - 2.
What is a parabola?A parabola is the part of the conic section of which the points are equidistant from a fixed line called as directrix and a fixed point known as focus.
The general equation for the parabola is given as,
y = ax² + bx + c
Where c is the y-intercept.
Substitute c = -2 as per the question to obtain,
y = ax² + bx - 2
At (3,-5) the parabola has minimum value which implies y' = 0 as below,
y' = 2ax + b = 0
Substitute x = 3 to obtain,
2a × 3 + b = 0
=> -6a = b
And, y = -5 at x = 3 which gives,
-5 = 3²a + 3b - 2
=> 9a + 3b = -3
Substitute b = -6a to get,
9a - 18a = -3
=> a = 1/3
Which implies b = -6 × 1/3 = -2
Now, the equation for the parabola becomes as below,
y = x²/3 - 2x - 2
Hence, the required equation of the parabola is obtained as y = x²/3 - 2x - 2.
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Four cubes are lined up to form a solid. The side lengths of the cubes are 2 ft, 3 ft 4 ft. and 5 ft. What is the volume of the solar A. 196 ft B 224 ft C.374 ft3 d 2,744ft3
Answer:
A
Step-by-step explanation:
If side 1 is 13, side 2 is 12, and side 3 is 18, can a triangle be made?
Answer:
no
Step-by-step explanation:
I want its solution and the unit is about algebraic fraction.
Answer:
3x²/(3x - 9y)
This should be the simplest form.
Step-by-step explanation:
Combine the fractions:
(5x² - 2x²)/((6x - 6y) - (3y - 3x))
Combine like terms:
3x²/(6x - 3x - 6y - 3y)
Solve.
3x²/(3x - 9y)
Answer:
9x^2
======
6(x - y)
Step-by-step explanation:
Begin by switching the - to a plus. Switch the x and y in the second denominator.
5x^2 2x^2
===== + ======
6x - 6y 3x - 3y
Pull out the common factors in both denominators. Use the distributive property.
5x^2 2x^2
===== + ======
6(x - y) 3(x - y)
Multiply both the numerator and denominator by 2 on the left had fraction.
5x^2 2*2x^2
===== + ======
6(x - y) 2*3(x - y)
5x^2 4x^2
===== + ======
6(x - y) 6(x - y)
Put both numerators over a common denominator. Notice that the + sign shifts up. It shifts up because both fractions have been changed to a common denominator.
5x^2 + 4x^2
===================
6(x - y)
Combine the two numerators since they are of the same power.
9x^2
======
6(x - y)
The graph of a linear function is shown.
Which word describes the slope of the line?
• positive
• negative
O zero
O undefined
The slope of the line as shown in the graph of the linear function in the image below is: negative.
What is the Slope of a Line of a Linear Function?The slope of a line of a linear function = change in y/change in x.
The value of the slope would be positive if the graph increases upwards from your left to your right.
The value of the slope would be negative if the graph decreases downwards from your left to your right.
Thus, the slope of horizontal lines are always zero while the slope of vertical lines are undefined.
Therefore, the slope of the line as shown in the graph of the linear function in the image below is: negative.
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help I literally got a 4/10 in my math test and my mom is like REALLLLY mad that she took my phone so I’m using my sisters ipad and she gave me advice on this app so i don’t even know if this could help but this is the page I need to complete/it’s for term 2 (week2) basically on my test well it’s apart of it so pls help- ~btw don’t look at the top cause I already completed it, I just need the 2 and 3 helppppp ima die ANDDD I used all the points I think that’s what it’s called~
Answer:
3/8 < 2/4
2/3 > 7/12
i could be wrong sorry
It should look like this:
A baseball team wins one out of every three games. How many wins
would they have after 27 games?
Answer:
9 wins
Step-by-step explanation:
[tex]\frac{1}{3} =\frac{x}{27} \\\\3x=27\\x=9[/tex]
They'd have 9 wins after 27 games.
which set of ordered pairs could be generated by an exponential function
Answer:
Option C represents an exponential function
Step-by-step explanation:
Generally, we have an exponential function in the form ;
y = a.b^x
Where in fact, a is not 0
In this case, let us have a as 1 and b as 2
So we have;
for x = -1
y = 2^-1 = 1/2
for x = 0
y = 2^0 = 1
for x = 1
y = 2^1 = 2
for x = 2
y = 2^2 = 4
So the correct choice here is the third option
Find the product of (2a+b)^2
Answer:
(2a+b)^2
4a^2 + 4ab + b^2
product=4
Answer:
4a²+b²+4abStep-by-step explanation:(2a+b)²=(2a)²+(b)²+2×2a×b(a+b)²=a²+b²+2abanswer:- 4a²+b²+4abIron Man's arc reactor has a diameter of 71mm. How much of his chest does it cover?
Answer:
your not in highschool
Step-by-step explanation:
The sum of the age of mother and daughter is 66 years.Mothers age is 5 times of daughters age.What is the age of daughter??
Answer:
I think it might be 13 or 14 I'm not completely sure though.
Step-by-step explanation:
who ever answer this get a brainliest and a thank you i need it answered asap
Answer:
a = 9
Step-by-step explanation:
For solve the problem we can use the Pythagorean theorem in this way
a^2 + (3√3)^2 = (6√3)^2
If we solve the equation we have
a^2 + 27 = 108
a^2 = 81
a = +/-9
we take only the the positive value because a length can’t be negative
a = 9
what are the factors of -9 that have a sum of 0
Answer:
3 and -3
Step-by-step explanation:
+3 -3 =0
sum mean adding
Oliver has created a plot of his backyard on the given coordinate plane, so that each unit length is one yard. He wants to design a right triangular plant bed for his backyard that has an area of eight square yards. After placing one vertex of the base of the plant bed at (3, 8) and one vertex at (7, 8) on his coordinate plane, he has to determine where to place the last vertex. Locate the possible locations of the last vertex on the coordinate plane.
Answer:
The possible locations are;
(3, 4), (3, 12), (7, 4), and (7, 12)
Please find attached the plot of the points created with Microsoft Excel
Step-by-step explanation:
The given parameters of the plot of Oliver's backyard are;
The area of the right triangular plant bed Oliver wants to design, A = 8 yd²
The length of a/each unit of the plot = 1 yard
The location of one of the vertex of the right triangular area = (3, 8)
The location of the other vertex of the right triangular area = (7, 8)
We note that the area of a triangle, A = 1/2 × Base length, B × Height, h
Let the distance between the two plotted point represent the base length, 'B', therefore;
B = 7 - 3 = 4 (We subtract only the x-values (7 and 3) given that the y-values (8 and 8) are the same;
Therefore, the base length, B = 4 yards
A = 1/2 × B × h
∴ A = 8 yd.² = 1/2 × 4 yd. × h
h = 8 yd.²/ 2 yd. = 4 yd.
The height of the right triangle, h = 4 yd.
Therefore the possible locations of the last vertex the right triangle on the coordinate plane, given that the first two points are parallel with the x-axis, are points 4 units above or the y-axis value of the plotted points with the x-value of the last vertex being either 3, or 7 as follows;
(3, 8 ± 4) or (7, 8 ± 4) which give points, (3, 4), (3, 12), (7, 4), and (7, 12).
Answer:
3,4 7,4
Step-by-step explanation:
Help plzz need the answer and that explanation plz don't send a file I need help with question 21!! thx so much
Answer:
No, they cannot be becuase the points are too different- no same numerical
values.
Step-by-step explanation:
Determine the value of a so that the following system has no solution.
ax+5y=10
6x+2y=7
HURRY PLSSSS
Answer:
z
Step-by-step explanation:
pls help with this !!
Answer:
25.12 so the nearest 10 is 25.10
please help me with this math problem, the question is on the picture that i attached, ill mark brainliest if the answer is correct. NO links!
Answer:
5/12
Step-by-step explanation:
Think SohCahToa
Soh- Sin: opposite/hypotenuse
Cah- CoSin: adjacent/hypotenuse
Toa- Tan: opposite/adjacent
Opposite: The length on the opposite side of the angle.
Adjacent: The length next to the angle.
Hypotenuse: The longest side of the angle.
HELP MEEEEEEEEE I REALLY DONT KNOW THIS ONE
Answer:
[tex]volume = \pi {r}^{2} h \\ = \pi( {5}^{2} ) \times 6 \\ 150\pi \: cubic \: units[/tex]
Answer:
471
Step-by-step explanation:
Using Pi=3.14
First find the area of the bottom circle:
3.14*([tex]5^{2}[/tex])
=78.5
Then multiply the result by the height
78.5*6=471
therefore,
Volume of clylinder: 471 units squared
Please give me brainliest if corrrect :)
Which system of equations could be represented by the graph?
is the Square root of 18 divided by 3 a rational or irrational number? explain using full sentences
Answer:
irrational
Step-by-step explanation:
[tex]\sqrt{18}[/tex] = [tex]\sqrt{9}[/tex] · [tex]\sqrt{2}[/tex] which is the same as 3[tex]\sqrt{2}[/tex]
3[tex]\sqrt{2}[/tex] divided by 3 equals [tex]\sqrt{2}[/tex], which is irrational
Lines CD and DE are tangent to circle A shown below: Lines CD and DE are tangent to circle A and intersect at point D. Arc CE measures 112 degrees. Point B lies on circle A. If Arc CE is 112°, what is the measure of ∠CDE? (4 points) Question 5 options: 1) 124° 2) 136° 3) 68° 4) 56°
Answer:
Option (3)
Step-by-step explanation:
By the theorem, angle between two tangents intersecting each other outside the circle is half of the difference between intercepted arcs.
From the figure attached,
Two tangents CD and DE are intersecting each other at point D outside the circle A.
Two intercepted arcs are minor arc CE and major arc CBE,
Measure of arc CE = 112°
Therefore, measure of major arc CBE = 360° - 112°
= 248°
m(∠CDE) = [tex]\frac{1}{2}(\text{arcCBE}-\text{arcCE})[/tex]
= [tex]\frac{1}{2}(248-112)[/tex]
= [tex]\frac{1}{2}\times 136[/tex]
= 68°
Option (3) will be the correct option.
Answer:
C
Step-by-step explanation:
1. A signal tower has two lights that are 30 feet apart from each other, one directly above the other. From
a boat, the angle of elevation of the lower light is 14 degrees, and the angle of elevation yo the upper
light is measured to be 32 degrees.
a) Find to the nearest foot the distance from the boat to the lower light.
b) The boat and the foot of the tower are in the same horizontal plane. Find to the nearest foot the
distance from the boat to the foot of the tower.
Solution :
It is given that the distance between the two lights is 30 feet.
The angle of elevation of the upper light from the boat, ∠ ABP = 32 degree
The angle of elevation of the lower light from the boat, ∠ ABQ = 14 degree
∴ ∠ PBQ = ∠ ABP - ∠ ABQ
= 32 - 14
= 18 degree
In triangle PAB
∠ PAB = 180 - (90 + 32)
= 58 degree
Similarly in triangle AQB
∠ AQB = 180 - (90 + 14)
= 76 degree
Now considering triangle PBQ and applying the sine theorem,
[tex]$\frac{PQ}{\sin 18}=\frac{BQ}{\sin 58}$[/tex]
we know PQ = 30 feet
∴ [tex]$BQ =\frac{\sin 58}{\sin 18} \times 30$[/tex]
= 82.33 feet
Again taking the right triangle ABQ and applying sine theorem,
[tex]$\frac{BQ}{\sin 90}=\frac{AB}{\sin 76}$[/tex]
[tex]$\frac{82.33}{\sin 90}=\frac{AB}{\sin 76}$[/tex]
∴ [tex]$AB = 82.33 \times \sin 76$[/tex]
= 79.88 ft
= 80 feet
I Mark Brainliest ! No Bots Plz
Select All that apply
Answer:
Option 2
Step-by-step explanation:
Using The exterior angle Theorem solve for the identified angle
Answer:
107
Step-by-step explanation:
180-(65+42) = SQR = 73
180-73 = 107
Graph this function: y =3/4x - 4 (you can just put the cordinants)
Pls help with this I have limited time
Answer:
x = 8
z = 86
Step-by-step explanation:
6x + 46 = 13x - 10 (Because they're vertical angles)
6x - 13x = -10 - 46
-7x = -56
x = 8
6x + 46
6(8) + 46
94
z + 94 = 180
z = 86
Brenna wants to learn more about stingrays. Which of the following is a statistical question Brenna could ask?
A. Do stingrays live in oceans or rivers?
B. Are stingrays an endangered species?
C. What is the heaviest stingray ever recorded?
D. How long does a stingray live?
Answer:d
Step-by-step explanation:because that would come up with the most information from sciencetist and professors
Answer:
Probably B or A
Step-by-step explanation:
Because learning about stingrays asking a question like that can tell you how many are left and how long you have to study them while they are here. and A because you wanna get to know their surroundings and what's better for them in an environment before you actually get to know about the stingrays, studying the environment can give you an idea of what to look for when you are diving in the ocean. Meaning you know exactly what to look for when diving so you can get as much information as you need.
Solve the system by substitution.
x = 9y
x-5y=20
Step-by-step explanation:
hope this helps you! have a great day
The solutions of the system of equations are x = 45 and y = 5.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
The system of equations,
x = 9y .... (1)
x-5y=20 ......(2)
Substituting the value of x from the equation 1 to equation 2,
we get,
9y - 5y = 20
4y = 20
y = 5
Then, x = 5(9) = 45
Therefore, the solutions of the equations are x = 45 and y = 5
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HELPP!!!!!!!!!!!!!!!!
Answer:
D.4 3/4
Step-by-step explanation:
hope it helps you
Answer the question above
Answer:
MJ
Step-by-step explanation:
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