15 POINTS
What is the equation of the following graph in vertex form?
(parabolic function going down from the left through the point negative four comma zero and turning at the point negative three comma negative one and going up through the point negative two comma zero and then through the point zero comma eight and continuing up towards infinity)
y = (x − 3)2 − 1
y = (x + 3)2 − 1
y = (x − 4)2 − 2
y = (x − 4)2 + 8
Answers
And y coordinate of vertex is -1 so the answer is B.
Answer with explanation:
→The given curve is Quadratic,having two real roots,as it cuts X axis at two distinct points that is at ,-2 and -4.
→Graph is symmetrical about line , x=-3.
→This curve is a Parabola,opening in upward direction ,that is having Y axis as Axis of Symmetry.
→Parabola is defined as locus of all the points such that distance from fixed point called focus, to distance from fixed line called Directrix ,is always Constant.
→Point which divides PARABOLA in two symmetrical parts is called Vertex having coordinates (-3,-1).
Equation of parabola having vertex ,(-3,-1) and opening in Upward Direction,that is in vertical direction, is given by:
General Equation: Equation of parabola passing through point (a,b) and opening in upward direction and having focus (k,h) is
y-b=4 k× (x-a)²
So, the equation of parabola will be
→y-(-1)=4 k[x-(-3)]²
→y+1==4 k(x+3)²-----(1)
This parabola also passes through (-4,0) and (-2,0).
→0+1=4 k×(-4+3)²
→1=4 k×(-1)²
[tex]1=4 k\\\\k=\frac{1}{4}[/tex]
If you will substitute , x=-2 and y=0 in equation 1,you will get same value of k.
Equation of Parabola ,that is equation 1,can be written as
[tex]y+1=4\times\frac{1}{4}(x+3)^2\\\\y+1=(x+3)^2\\\\ y=(x+3)^2-1[/tex]
Option B: y=(x+3)²-1
Related Questions
ONE LAST QUESTION!!!!!!!!!!WILL GIVE THE BRAIN!!!!!!!!!!
Answers
Shifting upwards by 3 units means, adding 3 to the function value. So the resulting function after these two transformations will be:
[tex]g(x)=- \sqrt{x}+3 [/tex]
Thus, option C gives the correct answer
in the polynomial function F(x)=1/2x^2+8-5x^3-19x what is the leading the coefficient
Answers
So its -5.
Answer:
-5
Step-by-step explanation:
The leading term in a polynomial consist on the highest degree term. To get the highest degree term, we need to reorder the polynomial from left to right, starting with the highest degree term.
In this case:
[tex]f(x)=\frac{1}{2} x^{2} +8-5x^{3} -19x[/tex]
reordering
[tex]f(x)=-5x^{3} +\frac{1}{2}x^{2} -19x+8[/tex]
So, the leading coefficient is the one with the leading term:
[tex]-5x^{3}[/tex]
So, it is -5
Suppose a term of a geometric sequence is a4 = 121.5 and the common ratio is 3. write the formula for this sequence in the form an = a1 ⋅ rn−1. explain how you arrived at your answer.
Answers
a ⇒⇒⇒ the first term
r ⇒⇒⇒ common ratio
Given: the fourth term (a4) = 121.5 and the common ratio = 3 and n = 4
∴ [tex]121.5 = a* 3^{4-1} [/tex]
∴ a = 121.5/3³ = 121.5/27 = 4.5
So, The formula for this sequence will be [tex]4.5 * 3^{n-1} [/tex]
Answer:
First I substituted 121.5 for an, 4 for n, and 3 for r in the general form. Then I solved to find a1 = 4.5. Finally, I substituted 4.5 for a1 and 3 for r in the general form to get an = 4.5 ⋅ 3n−1.
An equation of a function y(t) is shown.
y(t)=−t²+14t−40
Which of the following statements are true about the graph of y(t) for
6≤t≤8 and WHY?
a. The value of y(t) increases over the interval 6≤t≤7
b. The value of y(t) increases over the interval 7≤t≤8
c. The average rate of change over the interval 6≤t≤8 is 0
d. The value of y(t) is constant over the interval 6≤t≤8
e. The average rate of changer over the interval 6≤t≤7 is the same as the average rate of change over the interval 7≤t≤8
Answers
y(t)=-t^2+14t-40
thus the graph will be as shown in the figure:
From the graph we deduce that the correct statement is:
y'(t)=-2t+14=0
thus
t=7
thus
y(7)=0
thus the correct statement is:
c. The average rate of change over the interval 6≤t≤8 is 0
The graph of y(t) increases over the interval 6≤t≤7 because the derivative is positive. The average rate of change over the interval 6≤t≤8 is 0 due to symmetry about the vertex of the parabola at t=7. The rate of change over the intervals 6≤t≤7 and 7≤t≤8 are equal in magnitude but opposite in direction.
Given the quadratic function y(t)=-t²+14t-40, we need to analyze its behavior over the interval 6≤t≤8. The first derivative y'(t) of the function, which represents the slope of the tangent line to the graph at any point t, is -2t + 14. To determine the intervals of increase and decrease, we can set the first derivative to zero to find the vertex of the parabola, yielding t=7, which means the function increases on the interval 6≤t≤7 and decreases on 7≤t≤8.
The average rate of change over an interval is calculated by taking the difference in the function values at the endpoints of the interval over the difference in t. For the interval 6≤t≤8, since this is a symmetrical interval around the vertex, the average rate of change is 0. Furthermore, it follows from symmetry that the average rate of change over the intervals 6≤t≤7 and 7≤t≤8 should be equal in magnitude but opposite in sign.
Considering the stated properties and analyzing the equation, we can conclude that:
The value of y(t) increases over the interval 6≤t≤7.The value of y(t) decreases over the interval 7≤t≤8, so statement b is false.The average rate of change over the interval 6≤t≤8 is 0, making statement c true.The value of y(t) is not constant over the interval 6≤t≤8.The average rates of change over both intervals 6≤t≤7 and 7≤t≤8 are not equal in value; they are opposite, making e false.A shipping box in the shape of a rectangular prism has a volume of 18x^3+5x^2-2x. what are three expressions that can represent possible dimensions of the shipping box?
Answers
Volume=length×width×height
but
V=18x^3+5x^2-2x
V=x(18x^2+5x-2)
V=x(9x-2)(2x+1)
Hence the possible expression for the dimensions of the shipping box is x by (9x-2) by (2x+1)
Answer:
[tex](x), (9x-2), (2x+1)[/tex]
Step-by-step explanation:
[tex]18x^3+5x^2-2x=x(18x^2+5x-2)=x(9x-2)(2x+1)[/tex]
An archway is modeled by the equation y = -2x^2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B?
A. 8 units
B. 6 units
C. 5 units
D. 3 units
Answers
1. You have that the the archway is modeled by the equation y=-2x^2+8x and the angle mentioned in the problem is defined by the equation x−2.23y+10.34=0.
2. Therefore, you must susbtitute y=-2x^2+8x into x−2.23y+10.34=0, as below:
x−2.23(-2x^2+8x)+10.34=0
3. When you apply the distributive property, you obtain:
x−2.23(-2x^2+8x)+10.34=0
x+4.46x^2-17.84x+10.34=0
4.46x^2-16.84x+10.34=0
4. When you solve the quadratic equation, you obtain:
x=3 units
Therefore, the answer is the option D: D. 3 units.
Answer
The answer is 6
Step-by-step explanation:
Original tv cost: 700$
Current tv cost: 500$
Find the percent of decrease
Round to the nearest whole percent
Answers
100%------------> $700 (is the Original tv cost)
X %--------------> $500 (is the Current tv cost)
x=500*100/700----> 71.43%
the percent of decrease=100%-71.43%-----> 28.57%-----> 29%
the answer is
the percent of decrease is 29%
Hi
The answer : the percent of decrease is 29%
Brenda’s bank offers car financing for 3, 4 or 5 years. If brenda chooses 5-year financing, how many monthly payments will she have?
Answers
Number of payments=[Number of years]×[number of months]
Number of years=5
Number of months=12
hence
# Payments=5*12=60 monthly payments
Given a possible triangle ABC with a=5,b=11,and a=23, find a possible value for
Answers
Given a possible triangle ABC with a=5, b=11, and A=23 degrees, find a possible value for angle B. Round to the nearest tenth.
A. 10.2° B. 11.2° C. 59.3° D. no solution
========================================================
a = 5 , b = 11 , and ∠A = 23°
By applying the Law of Sines:
[tex] \frac{sin \ A}{a} = \frac{sin \ B}{b} [/tex]
[tex] \frac{sin \ 23}{5} = \frac{sin \ B}{11} [/tex]
∴ sin B = 11* (sin 23°)/5 ≈ 0.8596
∴ ∠B = [tex] sin^{-1} 0.8596 [/tex] ≈ 59.3°
∴ The correct choice is option (C)
C. 59.3°
Are the two events “choosing a sophomore” and “choosing someone who replied ‘Yes’” independent events?
Answers
Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of β if β < α.
sin(7x − 15) = cos(3x + 5)
Answers
in a right triangle
if sin A= cos B
then
angle A and angle B are complementary angles
so A+B=90
therefore
(7x-15)+(3x+5)=90-----> 10x-10=90----> 10x=100----> x=10°
so
7x-15------> 7*10-15----> 55°
3x+5------> 3*10+5----> 35°
we know that
β < α
therefore
the answer is
β =35°
α=55°
Answer:
The answer is B). 35
Step-by-step explanation:
I did it on USA Test Prep
Solve the following quadratic equation using the quadratic formula.
5x^2 − 8x + 5 = 0
Write the solutions in the following form, where r, s, and t are integers, and the fractions are in simplest form.
x = r − si/t,x = r + si/t
Answers
[tex]5x^2-8x+5=0\to a=5;\ b=-8;\ c=5\\\\\Delta=(-8)^2-4\cdot5\cdot5=64-100=-36\\\\\sqrt\Delta=\sqrt{-36}=6i[/tex]
[tex]x_1=\dfrac{-(-8)-6i}{2\cdot5}=\dfrac{8-6i}{10}=\dfrac{4-3i}{5}\\\\x_2=\dfrac{-(-8)+6i}{2\cdot5}=\dfrac{8+6i}{10}=\dfrac{4+3i}{5}[/tex]
Quadratic equations can be solved using several methods; one of them, is by using quadratic formula
The solution to [tex]5x^2 - 8x + 5 = 0[/tex] is: [tex]x = \frac{4 + 3i}{5}, x = \frac{4 - 3i}{5}[/tex]
The equation is given as:
[tex]5x^2 - 8x + 5 = 0[/tex]
The quadratic formula is:
[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
In the given equation;
[tex]a = 5\\b = -8\\c = 5[/tex]
So:
[tex]x = \frac{-(-8) \± \sqrt{(-8)^2 - 4 \times 5 \times 5}}{2 \times 5}[/tex]
[tex]x = \frac{8 \± \sqrt{-36}}{10}[/tex]
Expand
[tex]x = \frac{8 \± \sqrt{36} \times \sqrt{-1}}{10}[/tex]
[tex]x = \frac{8 \± 6 \times \sqrt{-1}}{10}[/tex]
In complex numbers;
[tex]i = \sqrt{-1}[/tex]
So, we have:
[tex]x = \frac{8 \± 6 \times i}{10}[/tex]
[tex]x = \frac{8 \± 6i}{10}[/tex]
Simplify
[tex]x = \frac{4 \± 3i}{5}[/tex]
Split
[tex]x = \frac{4 + 3i}{5}, x = \frac{4 - 3i}{5}[/tex]
Hence, the solution to [tex]5x^2 - 8x + 5 = 0[/tex] is: [tex]x = \frac{4 + 3i}{5}, x = \frac{4 - 3i}{5}[/tex]
Read more about quadratic formulas at:
https://brainly.com/question/9701183
Consider the function graphed below
Answers
For x <1:
In this interval we have the following equation:
f (x) = x ^ 2
For x> 1:
In this interval we have the following equation:
f (x) = (1/3) x + 2/3
Answer:
The graph represents the following function:
f (x) = x ^ 2 (x <1)
f (x) = (1/3) x + 2/3 (x> 1)
Verify the equation below with each of the values listed for t to find a solution.
4 = 2t +8
Answers
4 = 2t + 8
4 + (-8) = 2t + 8 + (-8)
-4 = 2t
-4 / 2 = 2t / 2
-2 = t
t = -2
Square root of -1 divided by (3+8i)-(2+5i)
Answers
Used:[tex](a+b)(a-b)=a^2-b^2[/tex]
Will mark 5 stars
The variable used to show correlation is r, which is also known as the correlation complement.
A.True
B.False
Answers
B. False
Dustin is driving his car at speed of 50 kilometres per hour. he going to texas which is located 345 kilometres from his starting point.how long will it take him to reach texas?
Answers
help me please...
Problem: The standard form of a circle is (x-h)2+(y-k)2=r2 and for the parabola, y-k=a(x-h)2. The (h,k) pair will be the center of the circle and the vertex of the parabola. The radius of the circle is ‘r’ and the focal length of the parabola is f=1/(4a). For the following General Conic Equation: x2+y2-4x-6y-12=0 complete the following problems showing all your work:
Complete the square showing all your work to convert to Standard Form:
If this is a circle, state the coordinates of the center and give the radius. If this is a parabola, state the coordinates of the vertex and give the focal length. Show all your work.
Sketch the Conic. Label the values you found in part B. Be sure to draw or show the radius or focal length.
Answers
x²+y²-4x-6y-12=0
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(x²-4x)+(y²-6y)=12
Complete the square twice. Remember to balance the equation by adding the same constants to each side
(x²-4x+4)+(y²-6y+9)=12+4+9
Rewrite as perfect squares
(x-2)²+(y-3)²=25
the answer part A) is
(x-2)²+(y-3)²=5²-----> this is the standard form of the equation of a circle
Part B) (x-2)²+(y-3)²=5²
the center is the point (2,3) and the radius is r=5 units
Part C)
using a graph tool
see the attached figure
A drawer of loose socks contains 2 red socks, 2 green socks, and 6 white socks. Which best describes how to determine the probability of pulling out a white sock, not replacing it, and pulling out another white sock?
Answers
So, if you were to not replace the first drawn white sock, your percentage goes to 55.5556%! This is because you now have 5/9 socks remaining in the drawer being white!
Answer:
The probability that the first sock is white is 6/10 and that the second sock is white is 5/9, so the probability of choosing a pair of white socks is 30/90 = 1/3! Hope that helps.
Step-by-step explanation:
PLEASE PLEASE HELP
question is attached
Answers
x1 = 4.8284
x2 = - 0.828
Remark
Substitute the value for y from the first equation into the second equation. Multiply by 4 and then see if it factors out. Solve for x first and then y.
Step one
Solve for y in the first equation. Subtract x from both sides.
y = 2 - x
Step Two
Equate the two ys.
2 - x = - 1/4x^2 + 3
Step Three
Bring the left side over to the right side.
0 = -1/4 x^2 + x + 3 - 2 Combine the like terms.
0 = -1/4 x^2 + x + 1
Step Four
0 = -1/4 x^2 + x + 1 Multiply through by 4
0 = - x^2 + 4x + 4
Step five
This won't factor. The only thing you can do is use the quadratic equation for roots.
a = - 1
b = 4
c = 4
[tex]\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac} }{2a}[/tex]
[tex]\text{x = }\dfrac{ -(4) \pm \sqrt{4^{2} - 4(-1)4}}{-2}[/tex]
[tex]\text{x = }\dfrac{ -(4) \pm \sqrt{16 + 16}}{-2} [/tex]
[tex]\text{x = } 2 \pm \sqrt{32 }\div -2 [/tex]
x = 2 +/- sqrt(4^2 * 2) / (- 2)
x = 2 +/- 4 sqrt(2) / - 2
x = 2 -/+ 2 sqrt(2)
x = 2 -/+ 2 *(1.414)
x = 2 -/+ 2.828
x1 = 4.8284
x2 = - 0.828
Short Answer
x1 = 4.8284
x2 = - 0.828
Remark
Substitute the value for y from the first equation into the second equation. Multiply by 4 and then see if it factors out. Solve for x first and then y.
Step one
Solve for y in the first equation. Subtract x from both sides.
y = 2 - x
Step Two
Equate the two ys.
2 - x = - 1/4x^2 + 3
Step Three
Bring the left side over to the right side.
0 = -1/4 x^2 + x + 3 - 2 Combine the like terms.
0 = -1/4 x^2 + x + 1
Step Four
0 = -1/4 x^2 + x + 1 Multiply through by 4
0 = - x^2 + 4x + 4
Step five
This won't factor. The only thing you can do is use the quadratic equation for roots.
a = - 1
b = 4
c = 4
x = 2 +/- sqrt(4^2 * 2) / (- 2)
x = 2 +/- 4 sqrt(2) / - 2
x = 2 -/+ 2 sqrt(2)
x = 2 -/+ 2 *(1.414)
x = 2 -/+ 2.828
x1 = 4.8284
I hope this helps
x = 2 +/- sqrt(4^2 * 2) / (- 2)
x = 2 +/- 4 sqrt(2) / - 2
x = 2 -/+ 2 sqrt(2)
x = 2 -/+ 2 *(1.414)
x = 2 -/+ 2.828
x1 = 4.82
Which of the following would triple the volume of the Egyptian square-based Pyramid below?
A. Multiply only the height by 3.
B. Add 3 to each dimension of the Pyramid.
C. Multiply every dimension of the Pyramid by 3.
D. Add 3 to the slant height.
Answers
Final answer:
To triple the volume of a square-based Egyptian pyramid, you must multiply every dimension of the pyramid by 3. This is because volume is proportional to all three dimensions of the shape, and changing just one dimension won't achieve the desired effect.
Explanation:
The question asks which action would triple the volume of a square-based Egyptian pyramid. The volume (V) of a pyramid is calculated using the formula V = (1/3) × base area × height. To triple the volume, you would need to triple the factor of each dimension because volume is a three-dimensional measurement, and changing one dimension alone would not be sufficient.
Option A suggests multiplying only the height by 3, but this would not triple the volume as the base area remains the same. Option B suggests adding 3 to each dimension, but adding a constant to linear dimensions does not maintain a proportional relationship to volume.
Option D suggests adding 3 to the slant height, which does not directly correlate to the volume. Therefore, option C is correct: Multiplying every dimension of the Pyramid by 3 would indeed triple the volume because changing each dimension equally maintains the proportion. This is similar to how if a block's dimensions were doubled (2L × 2L × 2L), the new volume would be 8 times the original (8L³).
You are required to choose two topics from a list of six to write about on your science test. How many different pairings are possible?
10
15
20
12
Answers
The answer is 12 :)
simplify
can u plz help me on this its a math question !!!!!
theres an image below!!!
Answers
_________________________________________________________
Explanation:
_________________________________________________________
We are asked to simplify:
→ [tex] (\frac{2}{9})^3 [/tex]
_________________________________________________________
Note the following property of exponents:
_________________________________________________________
[tex]( \frac{a}{b})^n [/tex] = [tex] \frac{(a^n)}{(b^n)} [/tex] ; { b [tex] \neq [/tex]0 } .
_________________________________________________________
As such:
→ [tex]( \frac{2}{9})^3 [/tex] ;
=[tex]\frac{2^3}{9^3}[/tex] = [tex] \frac{(2*2*2)}{(9*9*9)}[/tex] = [tex] \frac{8}{729} [/tex] .
_____________________________________________________________
The answer is: " [tex] \frac{8}{729} [/tex] " ;
→ which is: "Answer choice: [A]: " [tex] \frac{8}{729} [/tex] " .
_____________________________________________________________
Hope this answer—and explanation—is of some help to you.
Please comment below or otherwise respond to me if you have any questions or if I can be of further assistance.
Best wishes!
Answer:
6
----------- 6 over 729
729
Step-by-step explanation:
2/9 * 2/9 * 2/9
If GP=PH, GA =17, mED = 37, and mAB = 87, find each measure.
Answers
mAB = 87°
mED = 37°
mEFA=mBCD
360°=mAB+mED+mEFA+mBCD
360=87+37+2mBCD------> mBCD=[360-87-37]/2----> mBCD=118°
therefore
m BCD=118°
m FA=m EFA/2-----> m FA=118/2----> 59°
m FA=59°
m DC=m BCD/2----> m DC=118/2----> 59°
m DC=59°
HB=GA------> HB=17
DB=2*HB----> DB=2*17-----> DB=34
EG=GA------> EG=17
the answers are
DB=34
EG=17
mBCD=118°
mFA=59°
mDC=59°
Frank owns 250 acres of land. If he divides the land into 1/3 acre plots, how many plots will he have?
Answers
Hope this helps you.
All you really have to do is 250 divided by 1/3 and you get 83.3333 (repeating) but you can just say 83.3.
The length of a rectangle is twice it’s width.The length is 12cm.Work out the area of the rectangle
Answers
Answer:
Step-by-step explanation:
As with all word problems we first have to convert it to an equation or equations.
L = length of the Rectangle and W = its width
So L = 2 * W
A = area of the rectangle which is 128 cm^2
So A = L * W = 128 cm^2
substitute 2W for L from the 1st equation to give A = 2 * W * W = 2 * W^2 = 128 cm^2
Thus W^2 = 64 cm^2
finally W = 8 cm and therefore L = 2 * W = 16 cm
The perimeter P = 2 * (L+W) = 2* (8cm + 16cm) = 2 * 24cm = 48 cm
In the figure below, lines that appear to be tangent are tangent. Point O is the center of the circle. Which of the following is the value of x?
a. 60 degrees
b. 90 degrees
c. 100 degrees
d. 120 degrees
Answers
Answer:
(D) 120 degrees
Step-by-step explanation:
From the figure drawn, we have
∠ABC=60°
And ∠OAB=∠OCB=90° (angles made by tangent on the circle is 90°)
Thus, ∠AOC+∠OCB∠CBA+∠OAB=360° (Angles sum property of quadrilateral)
[tex]x+90^{\circ}+90^{\circ}+60^{\circ}=360^{\circ}[/tex]
[tex]x+240^{\circ}=360^{\circ}[/tex]
[tex]x=120^{\circ}[/tex]
Therefore, the value of x is [tex]120^{\circ}[/tex]
Hence, option D is correct.
Answer: d. 120 degrees
Step-by-step explanation:
From the given figure drawn, we can see that
∠ABC=60°
Also we know that tangents are radius are perpendicular at the point of tangency
And ∠OAB=∠OCB=90° (∵ tangents are radius are perpendicular at the point of tangency)
Therefore, we have
[tex]\angle{AOC}+\angle{OCB}+\angle{ABC}+\angle{OAB}=360^{\circ}\text{ ( By Angle sum property of quadrilateral)}\\\\\Rightrarrow\ x+90^{\circ}+60^{\circ}+90^{\circ}=360^{\circ}\\\\\Rightarrow\ x=360^{\circ}-240^{\circ}\\\\\Rightarrow\ x=120^{\circ} [/tex]
Bobby is testing the effectiveness of a new cough medication. There are 100 with a cough in the study. Seventy patients received the cough medication, and 30 other patients did not receive treatment. Thirty-four of the patients who received the medication reported no cough at the end of the study. Twenty of the patients who did not receive medication reported no cough at the end of the study. What is the probability that a patiebt chosen at random from this study took the medication, given that they reported no cough?
A. 63%
B. 53%
C. 38%
D. 43%
Answers
[tex]=\frac{34}{54}=63\%[/tex]
The probability that a patient chosen at random from this study took the medication, given that they reported no cough is 63%.
Answer:
The answer to this question is 63%
If you want to put a 4x8 piece of plywood through a 3 foot square opening in your ceiling by turning it diagonally is the opening big enough? use a 45-45-90 since its a square
Answers
c^2=a^2+b^2
The diagonal of the opening will be:
c^2=3^2+3^2
c^2=9+9
c^2=18
c=3√2 ft
The diagonal of the wood will be:
c^2=4^2+8^2
c^2=16+64
c^2=80
c=4√5 ft
The space will not be enough for the plywood to pass
A number is chosen at random from 1 to 50. find the probability of selecting numbers with 3 in the tens places