Answers
so.. .hmmm the vertex is at the origin... and we know the parabola passes through those two points... let's use either.. say hmmm 100,-50, to get the coefficient "a"
keep in mind that, the parabolic dome is vertical, thus we use the y = a(x-h)²+k version for parabolas, which is a vertical parabola
as opposed to x = (y-k)²+h, anyway, let's find "a"
[tex]\bf y=a(x-0)^2+0\implies y=ax^2\qquad \begin{cases} x=100\\ y=-50 \end{cases}\implies -50=a100^2 \\\\\\ \cfrac{-50}{100^2}=a\implies -\cfrac{1}{200}=a \\\\\\ thus\qquad \qquad y=-\cfrac{1}{200}x^2\implies \boxed{y=-\cfrac{x^2}{200}}[/tex]
now.. .your choices, show.... a constant on the end.... a constant at the end, is just a vertical shift from the parent equation, the equation we've got above.. is just the parent equation, since we used the origin as the vertex, it has a vertical shift of 0, and thus no constant, but is basically, the same parabola, the one in the choices is just a shifted version, is all.
Related Questions
How many hours is from 9:00am to 6:00 pm?
Answers
The value of a $225,000 house increases at a rate of 3.5% each year. Use a graph to predict the value of the house in 8 years.
A) ≈ $276,582
B) ≈ $286,263
C) ≈ $306,652
D) ≈ $296,282
Answers
V (t)=V0 (1+r)^t
V (t) ?
V0 225000
R 0.035
T 8 years
V (8)=225,000×(1+0.035)^(8)
V (8)=296,282
The value of the house in 8 years. (D) ≈ $296,282
How to predict the value?The given parameters are:
Initial value, a = $225,000
Rate, r = 3.5%
The scenario is an illustration of an exponential growth function.
So, we have:
V(x) = a * (1 + r)^x
Substitute known values
V(x) = 225000 * (1 + 3.5%)^x
This gives
V(x) = 225000 * (1.035)^x
Next, we plot the graph of V(x)
See attachment
From the attached graph
V(x) = $296,282
Read more about exponential functions at:
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Find the greatest common factor for the group of numbers. 12 , 28 , 24
Answers
Final answer:
The greatest common factor (GCF) of the numbers 12, 28, and 24 is found by identifying the smallest powers of their common prime factors, which are 2 and 3. Multiplying these together, 2 squared times 3, gives us the GCF of 12.
Explanation:
To find the greatest common factor (GCF) of the numbers 12, 28, and 24, we break each number down into its prime factors:
28 = 2 x 2 x 7
The smallest power of 3 that is common is just 3.
Therefore, the GCF of 12, 28 and 24 is 22 x 3 = 4 x 3 = 12.
PLEASE HELP!!!! If a function, f(x) is shifted to the left four units, what will the transformed function look like?
Answers
So that means f(x) turns into f(x+4)
For example, say we had the function f(x) = 5x^2 + 10x
Shifting f(x) four units to the left leads to
f(x) = 5x^2 + 10x
f(x+4) = 5(x+4)^2 + 10(x+4) ... notice the replacements in bold
f(x+4) = 5(x^2+8x+16) + 10(x+4)
f(x+4) = 5x^2 + 40x + 80 + 10x + 40
f(x+4) = 5x^2 + 50x + 120
A perfect circle figure has four lines of symmetry. True or false?
Answers
determine the valie of x for which v || w if m2 =100 and. m7 =4x+10
Answers
What is the simplified expression for ?
Answers
What is the graph of the function f(x) = the quantity of x squared plus 3 x plus 5, all over x plus 2
Answers
Answer:
Your answer is in the picture below
The graph approaches x=−2 asymptotically, has no x-intercepts, and the y-intercept of the graph is the point (0, 5).
Attached graph.
The graph of the function f(x) = (x² + 3x + 5 )/(x+ 2) is a parabola that is shifted to the left by 2 units.
The parabola is similar to the graph of the function y = x², but it is narrower because the denominator of the fraction is x + 2.
The graph also has a hole at the point (-2, 5), which is the point where the denominator of the fraction is 0.
Attached graph.
Here are the steps on how to sketch the graph of the function:
Sketch the graph of the function y = x².
Shift the graph to the left by 2 units.
Add a hole at the point (-2, 5).
The attached figure shows the graph of the function f(x) = (x² + 3x + 5 )/(x+ 2):
The graph of the function has the following features,
The domain of the function is all real numbers except for -2.
The range of the function is all real numbers except for 5.
The function has a minimum point at (-4, 1).
The function has a hole at the point (-2, 5).
learn more about graph here
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Find the equation of the quadratic function with zeros -1 and 1 and vertex at (0, -4).
Answers
bear in mind that, a zeor or solution of say -1 and 1, simply means x-intercepts at -1, 0 and 1,0.
[tex]\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ vertex\ (0,-4)\ \begin{cases} h=0\\ k=-4 \end{cases}\implies y=a(x-0)^2-4\implies y=ax^2-4 \\\\\\ \textit{we also know that } \begin{cases} y=0\\ x=-1 \end{cases}\implies 0=a(-1-0)^2-4 \\\\\\ 0=a(-1)^2-4\implies \boxed{4=a}\qquad thus\implies \boxed{y=4x^2-4}[/tex]
A person died leaving behind inheritance of Rs. 300000. Distribute the amount among 4 sons and 3 daughters so that each son gets double of what a daughter gets. Find the share of each when a debt of Rs. 80,000 was also to be paid.
Answers
4s+3d=300000-80000
4s+3d=220000, now using s=2d in this equation you get:
4(2d)+3d=220000
8d+3d=220000
11d=220000
d=20000
So each daughter gets 20000 and each son gets 40000.
The inheritance problem deals with distributing Rs. 300,000 among 4 sons and 3 daughters after a Rs. 80,000 debt is paid. Using algebra and ratios, it is determined that each daughter receives Rs. 20,000 while each son receives Rs. 40,000.
The situation given is that a person dies leaving behind an inheritance of Rs. 300,000, which must be divided among 4 sons and 3 daughters such that each son receives double what each daughter gets. Additionally, a debt of Rs. 80,000 is to be taken out of the inheritance before distribution.
First, we need to consider the debt. Subtracting the debt from the total inheritance, we have:
Total inheritance after debt = Rs. 300,000 - Rs. 80,000 = Rs. 220,000
Now, let's assume each daughter gets x amount. Therefore, each son gets 2x the amount. We can set up the equation accounting for all sons and daughters:
3x (daughters' shares) + 4(2x) (sons' shares) = Rs. 220,000
Simplifying:
3x + 8x = Rs. 220,000
11x = Rs. 220,000
x = Rs. 20,000 (share of each daughter)
Consequently, the share of each son will be double that of a daughter, which is:
2x = 2(Rs. 20,000) = Rs. 40,000 (share of each son)
I NEED THIS QUICK
Alvin’s first step in solving the given system of equations is to multiply the first equation by 2 and the second equation by –3. Which linear combination of Alvin’s system of equations reveals the number of solutions to the system?
9x + 4y = 36
6x + 2.5y = 24
Answers
After multiplying by the given coefficients and adding, the new equation obtained is:
8y - 7.5y = 0
after doing the calculations the answer is:
y = 0
x = 4
Because the two equations formed were independent, they had one solution
Answer:
its C
Step-by-step explanation:
What is the length of the side opposite the 30° angle? HELP
Answers
√3 times as long as the side opposite the 30 degree so the side opposite the 30 degree angle is 5/√3 inches long.
Solve each system of equations by using elimination.
7)2t-u=17
3t+u=8
8)2j-k=3
3j+k==2
9)3c-2d=2
3c+4d=50
Answers
t= 5. 15+u=8
u=-7
8. 5j= 5. 3(1)+ k= 2
j=1. k= -1
9. 6c - 4d= 4. 3(6)+4d= 50
3c +4d= 50. 18 + 4d= 50
9c = 54. 4d= 32
d= 8
c = 6
The tip of a 15-inch wiper blade wipes a path that is 36 inches long. What is the angle of rotation of the blade in radians to the nearest tenth?
2.4 radians
1.2 radians
2.8 radians
0.4 radians
Answers
L = (2πr) x (θ /360)
where L is the length of arc, r is the radius, and θ is the intercepted angle in terms of degrees.
Substituting the known values to the equation,
36 = (2π)(15) x (θ / 360)
We translate the equation to find the value of θ,
θ = (36)(360) / 2π(15)
The value of θ is equal to 137.51°.
This can be coverted to radians through the equation below,
θ (in radians) = 137.51° x (2π rad / 360°) = 2.4 rad
a telephone pole casts a shadow that is 34 m long. find the height of the telephone pole if a statue that is 36cm tall casts a shadow 77cm long
Answers
[length of the post]/[length of the shadow]=[length of the statue]/[length of the shadow of statue]
thus;
suppose the length of the pole is x m
thus;
x/34=36/77
x=36/77*34
x=15.8 m
the answer is 15.9 m
HELP ASAP 30 POINTS
Evaluate f(3) for the piecewise function: f(x) = Which value represents f(3)?
–11
8
12.5
16
Answers
Answer:
-11
Step-by-step explanation:
A triangle has one leg measuring 10 inches and the hypotenuse measuring 20 inches. the other leg measures 10\sqrt[]{3} 10 3 inches. what type of triangle is represented here?
Answers
c^2 = a^2 + b^2
where c is the hypotenuse or the longest side and a, b are the two shorter sides.
To prove that the triangle is indeed a right triangle, we use the equation above.
c^2 = a^2 + b^2
c^2 = 20^2 = 10^2 + (10sqrt(3))^2
400 = 100 + (100(3))
400 = 400
Two mechanics worked on a car. the first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. together they charged a total of $1450 . what was the rate charged per hour by each mechanic if the sum of the two rates was $160 per hour
Answers
the second mechanic = b
the first mechanic works for 4 hours = 4 * a
the second mechanic works for 15 hours = 15 * b
total charged = t
t = 4a + 15b
sum of their rates:
a + b = 160
b = 160 - a
t = 4a + 15b
1450 = 4a + 15 * (160 - a)
1450 = 4a + 2400 - 15a
now let's make the formula easier.
15a - 4a = 2400 - 1450
11a = 950
a = 86.36
b = 160 - 86.36 = 73.64
Find the value of x if B is between A and C, AB = 4x – 9, BC = 3x + 5 and AC = 17.
Answers
4x- 9 + 3x+5 = 17
7x = 21
x = 3
4x - 9 + 3x + 5 = 17
7x - 4 = 17
add 4 to both sides
7x = 21
divide both sides by 7
x = 3
George plays basketball in a week-long camp. On Day 2, he scored 8 points. On day 4, he scored 12 points. Explain how to measure his average rate of change
Answers
avg rate of change is x+2=y
Triangle END is translated using the rule (x, y) → (x − 4, y − 1) to create triangle E'N'D'. If a line segment is drawn from point E to point E' and from point N to point N', which statement would best describe the line segments drawn? (1 point
Answers
They are parallel and congruent.
They are perpendicular to each other.
They share the same midpoints.
They create diameters of concentric circles.
The transformation that is done is a translation. Which means that the coordinates will be translated or moved in the coordinate plane without changing the size and the orientation of the image. If is a line was drawn from E to E' and another line was drawn from N to N', the two lines would be parallel and congruent since the translation done to E is the same to that of N.
The answer is
They are parallel and congruent.
This answer is right!!!!! They are parallel and congruent.
what is the sum of 27 and 5 times a number is 187
Answers
5x=160
x=32
.
A bag contains 20 candies: 3 cherry, 4 orange, 7 lemon, and 6 grape. if two candies are selected simultaneously, what is the probability that they are both the same flavor?
Answers
Erica purchased adult and youth tickets for a movie. She bought x adult tickets for $7 each and y youth tickets for $5. Write an expression that can be used to show the total cost, C, of all tickets.
Answers
Answer:
7x + 5y = C
Step-by-step explanation:
X is the number of people buying an adult ticket
Y is the number of people buying a youth ticket
Using this we can find C, cost
A scale model of a human heart is 198 inches long. The scale is 34 to 1. How many inches long is the actual heart? Round your answer to the nearest whole number.
Answers
The area of a rectangle is 33 m2 , and the length of the rectangle is 5 m less than double the width. find the dimensions of the rectangle.
Answers
A = LW = 33
L = 2W-5
Substituting the second equation to the first,
A = 33 = (2W - 5)W
33 = 2W² - 5W
2W² - 5W -33 = 0
W = 5.5 and -3
Since the equation is quadratic, there are two possible roots: 5.5 and -3. However, we can only use the positive value. Thus, W=5.5 m. Consequently,
L = 2(5.5)-5
L = 6 m
Therefore, the dimensions of the rectangle is 6 m by 5.5 m.
Determine the slope of a line that makes an angle of 5pi/4 radians with the x-axis.
Answers
π radians is the angle 180 degrees, so π/4 radians is 180°/4=45°.
to construct the angle [tex]5 \frac{ \pi}{4} [/tex] we can proceed as shown in the figure, that is, we open an angle equal to 5 half right angles.
We see that the line making the angle 5pi/4 is the same line making the angle pi/4 radians, that is 45 degrees.
A line making the angle 45 degrees with the x axis, has slope equal to 1.
Remark, we have considered a line passing through the origin, as it represents all other lines making 5pi/4 radians.
Answer: slopi=1
How many three-letter "words" can be made from 5 letters "fghij" if repetition of letters (a) is allowed?
Answers
Also, for the second letter of the word, we can also have 5 choices because it is stated that repetition is allowed. Similarly, there are also 5 choices for the last letter of the word. By fundamental principle of counting, we multiply the numbers identified in the sentences above,
n = 5 x 5 x 5 = 125
Thus, 125 words can be formed from the given letters.
Write the sum using summation notation, assuming the suggested pattern continues.
-1 + 2 + 5 + 8 + ... + 44
A) summation of negative three times n from n equals zero to fifteen
B) summation of the quantity negative one plus three n from n equals zero to fifteen
C)summation of negative three times n from n equals zero to infinity
D) summation of the quantity negative one plus three n from n equals zero to infinity
Answers
Find the value of each variable for the right triangles. Make sure all answers are in reduced radical form. Show your work.
Answers
#1
[tex]t= \sqrt{13^2-12^2}= \sqrt{169-144}= \sqrt{25}=5 [/tex]
#2
[tex]a= \sqrt{12^2-9^2}= \sqrt{144-81}= \sqrt{63}= \sqrt{9*7}=3 \sqrt{7} [/tex]
#3
[tex]x= \sqrt{6^2+9^2}= \sqrt{36+81}= \sqrt{117}= \sqrt{9*13}=3 \sqrt{13} [/tex]
Answer:
i) t = 5
ii) a = 3√7
iii) x =3√13
Step-by-step explanation:
We have right triangles.
Know the two sides of the triangle and need to find the third missing side.
In order to find the third side of the right triangle, we use pythagoras theorem.
It is,
(Hypotenuse)² = (base)² + (height)²
i)
13² = 12² + t²
169 = 144 + t²
t² = 25
t = 5.
ii)
12² = 9² + a²
144 = 81 + a²
144 - 81 = a²
a² = 63
a = √63
iii)
x² = 9² + 6²
x² = 81 + 36
x² = 117
x = √117
x = 3√13