the graph of the parabola y=3(x+5)2-2 has vertex (-5,-2). if this parabola is shifted 1 unit down and 6 units to the right, what is the equation of the new parabola?
Answers
Answer:
y = 3(x-1)^2 -3
Step-by-step explanation:
y = 3(x+5)^2 - 2
vertex: (-5, -2)
1 unit down :
-2 - 1 = -3
6 units to the right:
3(x+5-6)^2 -2
3(x-1)^2 - 2
make what's in the parenthesis equal to 0:
(x-1)^2 = 0
x = 1
or
-5 + 6 = 1
new vertex : (1, -3)
equation : y = 3(x-1)^2 -3
Translation involves shifting of points from one position to another. The equation of the new parabola is: [tex]y = 3(x - 1)^2 - 3[/tex]
Given that:
[tex]y = 3(x + 5)^2 - 2[/tex]
[tex](h,k) = (-5,-2)[/tex] --- vertex
The general equation of a parabola is:
[tex]y = a(x - h)^2 + k[/tex]
By comparison:
[tex]a = 3\\ h = -5 \\ k= -2[/tex]
When the vertex is shifted 1 unit down, the rule is:
[tex](x,y) \to (x,y-1)[/tex]
So, we have:
[tex](x,y) \to (-5,-2-1)[/tex]
[tex](x,y) \to (-5,-3)[/tex]
When the vertex is shifted 6 unit right, the rule is:
[tex](x,y) \to (x + 6,y)[/tex]
So, we have:
[tex](h,k) \to (-5 + 6,-3)[/tex]
[tex](h,k) \to (1,-3)[/tex]
This means that:
[tex]h = 1\\ k =-3[/tex]
Recall that:
[tex]a =3[/tex]
Substitute these values in:
[tex]y = a(x - h)^2 + k[/tex]
[tex]y = 3(x - 1)^2 - 3[/tex]
Hence, the equation of the new parabola is: [tex]y = 3(x - 1)^2 - 3[/tex]
Read more about translations at:
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Related Questions
The perimeter of rhombus EFGH is 48 cm and the measure of ZFE) = 60
Answers
9514 1404 393
Answer:
a. 12 cm
b. 90°
c. 60°
Step-by-step explanation:
The relevant relationships are ...
all sides of a rhombus have the same lengththe diagonals of a rhombus are perpendicular bisectors of each otherthe diagonals of a rhombus divide the figure into 4 congruent triangles__
a) The perimeter, 48 cm, is the sum of four equal side lengths, so any given side is (48 cm)/4 = 12 cm.
GH = 12 cm
__
b) Angle EJF is where the diagonals meet. It is a right angle.
∠EJF = 90°
__
c) Angle EFJ is the complement of the one marked, so is 30°. Angles EHJ and GHJ are congruent to that, so both are 30°. Angle EHG is the sum of those two congruent 30° angles, so is ...
∠EHG = 60°
Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and values of the rate at two hour time intervals are shown in the table. Find lower and upper estimates for the total amount of oil that leaked out.
t (h) 0 2 4 6 8 10
r(t) (L/h) 8.8 7.6 6.8 6.2 5.7 5.3
V=_____ upper estimate
V= ______lower estimate
Answers
The exact amount of oil that leaks out for 0 ≤ t ≤ 10 is given by the integral,
[tex]\displaystyle\int_0^{10}r(t)\,\mathrm dt[/tex]
Then the upper and lower estimates of this integral correspond to the upper and lower Riemann/Darboux sums. Since r(t) is said to be decreasing, this means that the upper estimate corresponds to the left-endpoint Riemann sum, while the lower estimate would correspond to the right-endpoint sum.
So you have
• upper estimate:
(8.8 L/h) (2 h - 0 h) + (7.6 L/h) (4 h - 2h) + (6.8 L/h) (6 h - 4h) + (6.2 L/h) (8 h - 6h) + (5.7 L/h) (10 h - 8 h)
= (2 h) (8.8 + 7.6 + 6.8 + 6.2 + 5.7) L/h)
= 70.2 L
• lower estimate:
(7.6 L/h) (2 h - 0 h) + (6.8 L/h) (4 h - 2h) + (6.2 L/h) (6 h - 4h) + (5.7 L/h) (8 h - 6h) + (5.3 L/h) (10 h - 8 h)
= (2 h) (7.6 + 6.8 + 6.2 + 5.7 + 5.3) L/h)
= 63.2 L
Write the following as an inequality.
x is greater than – 3 and less than or equal to 4
Use x only once in your inequality.
Answers
Answer:
-3<x≤4
Step-by-step explanation:
Answer:
4 [tex]\geq[/tex] x > -3
Step-by-step explanation:
I just put the written form into inequality form.
9. Which is a true statement about the denominator in a fraction?
(Select one answer)
It is always a negative number
It cannot be 0
It has to be an even number
It is always smaller than the numerator
Answers
Answer:
It cannot be 0
Step-by-step explanation:
it can also be positive number :2/4
it can be odd number too:3/9
it is bigger than numerator bcoz we have to divide it for numerator
So, 0 number cannot be put as denominator in fraction is true statement
Let $f(x) = x^2 - 2x$. Find all real numbers $x$ such that $f(x) = f(f(x))$. List your solutions separated by commas in any order
Answers
==========================================================
Explanation:
The given function is f(x) = x^2 - 2x
Let's apply function composition like so
[tex]f(x) = x^2 - 2x\\\\f(f(x)) = (f(x))^2 - 2(f(x))\\\\f(f(x)) = (x^2-2x)^2 - 2(x^2-2x)\\\\[/tex]
In the second step, I replaced every x with f(x). Then in the third step, I replaced f(x) with x^2-2x on the right side.
Setting this equal to f(x) gets us
[tex]f(f(x)) = f(x)\\\\(x^2-2x)^2 - 2(x^2-2x) = x^2-2x\\\\[/tex]
which is a bit cluttered. However, we have "x^2-2x" show up three times. Let's say w = x^2-2x
If we replaced all those "x^2-2x" expressions with w, then we get,
[tex](x^2-2x)^2 - 2(x^2-2x) = x^2-2x\\\\w^2 - 2w = w\\\\[/tex]
Which looks more manageable
-----------------------------------------------
Let's solve for w
w^2 - 2w = w
w^2 - 2w-w = 0
w^2 - 3w = 0
w(w - 3) = 0
w = 0 or w-3 = 0
w = 0 or w = 3
----------------------------------------------
If w = 0, then,
w = x^2 - 2x
x^2 - 2x = w
x^2 - 2x = 0
x(x - 2) = 0
x = 0 or x-2 = 0
x = 0 or x = 2 are two solutions (out of four total)
-------------------------------------------------
Or, if w = 3, then,
w = x^2 - 2x
x^2 - 2x = w
x^2 - 2x = 3
x^2 - 2x - 3 = 0
(x - 3)(x + 1) = 0
x-3 = 0 or x+1 = 0
x = 3 or x = -1 are the other two solutions
-----------------------------------------------
To summarize, the four solutions are: x = -1, x = 0, x = 2, x = 3
What is the surface area of the composite figure?
Answers
9514 1404 393
Answer:
382 cm²
Step-by-step explanation:
The side facing is a trapezoid with bases 8 and 14 cm, and height 7 cm. Its area is ...
A = 1/2(b1 +b2)h
A = (1/2)(8 +14)(7) = 77 . . . . cm²
The perimeter of the face is ...
7 cm + 8 cm + 9 cm + 14 cm = 38 cm
The total surface area is the sum of the lateral area and the base area.
SA = LA + BA
SA = (38 cm)(6 cm) + 2×(77 cm²) = 228 cm² + 154 cm²
SA = 382 cm²
The surface area of the composite figure is 382 square centimeters.
_____
Additional comment
The lateral area is the width of a rectangular face (6 cm) times the total of all of the lengths of those faces. That total is the perimeter of the trapezoidal base (38 cm).
There are two trapezoidal bases that contribute area. The first calculation figured the area of one of them.
Please help me with this question and don't report
Answers
Answer:
50 ft
Step-by-step explanation:
For this problem we will use the Pythagorean theorem which is: a^2+b^2= c^2
I found the length for both of the legs on this triangle which are: 30 ft (for the side on the far left) and 40ft (for the other leg of the triangle whose hypotenuse is the walkway).
Now that we know the two legs we can use the Pythagorean theorem:
40^2 + 30^2 = 2500
then take the square root of 2500 in order to find the hypotenuse length:
Square root of 2500= 50ft
plz consider marking me as brainliest, it truly helps me!
Answer:
50ft
Step-by-step explanation:
trust me on this answer
A student is chosen at random from a large statistics class and asked how much time (in whole hours) she spent studying during the past 24 hours. Describe the sample space S of possible outcomes:
Answers
Answer:
24
Step-by-step explanation:
The sample space is the total possible values of an experiment or research. Since the total number of hours is 24, then the total possible number (or the limit she can use have) is 24. This she cannot exceed this 24 hour limit. Then we call this the total possible outcome and thus the sample space.
!!!HELP PLEASE ASAP!!! I don’t know how to solve this problem nor where to start? Can some please help me out and explain how you got the answer please. Thank you for your time.
Answers
Answer:
population standard deviation = 7.68sample standard deviation = 8.87Pick only one of these values. So if the first one doesn't work, then try the other one. Unfortunately, your teacher isn't clear on which value to go with.
===========================================================
Explanation:
Nice work on getting the mean so far.
To get the standard deviation, we'll use the value 236 in the table. This value is the sum of everything above it. So it's the sum of the [tex](x-\overline{x})^2[/tex] values. We call this the sum of the squared errors. The errors themselves being [tex]x-\overline{x}[/tex]
So we'll divide 236 over n = 4 to get 236/4 = 59
This will get us the population variance. Apply the square root to get [tex]\sqrt{59} \approx 7.68[/tex] which is the population standard deviation.
So if your teacher wants the population standard deviation, then the answer is 7.68
------------
If that answer doesn't work, then try this section.
Unfortunately, there are two flavors of standard deviation. The good news is that we don't have to do much work to find the sample standard deviation.
Instead of dividing by n = 4, we'll divide by n-1 = 4-1 = 3.
So 236/3 = 78.667
Since the value is approximate, I'll leave it as a fraction.
This represents the sample variance.
Apply the square root to get the sample standard deviation
[tex]\sqrt{\frac{236}{3}} \approx 8.87[/tex]
and that value is the sample standard deviation.
If the answer in the previous section doesn't work, then the answer must be 8.87
A satellite orbits earth at a speed of 22100 feet per second (ft/s). Use the following facts to convert this speed to miles per hour (mph). 1 mile = 5280 ft 1 min = 60 sec 1 hour = 60 min
Answers
15,068 mi/hr
Step-by-step explanation:
[tex]22100\:\frac{\text{ft}}{\text{s}}×\frac{1\:\text{mi}}{5280\:\text{ft}}×\frac{60\:\text{s}}{1\:\text{min}}×\frac{60\:\text{min}}{1\:\text{hr}}[/tex]
[tex]=15,068\:\text{mi/hr}[/tex]
The speed of 22100 feet per second will be 15068.18 miles per hour.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Unit conversion is the expression of the same property in a different unit of measurement. Time, for example, can be expressed in minutes rather than hours, and distance can be converted from miles to kilometres, feet, or any other length measurement.
Given that the speed of the satellite is 22100 feet per second. The speed in miles per hour will be calculated as,
22100 ft /s = ( 22100 x 3600 ) / 5280
22100 ft/s = 79560000 / 5280
22100 ft/s = 15068.18 miles per hour
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35. Graph the following system of equations and find the x-coordinate of the solution.
3x+ 3y=3
Y=-1/2x+2
x=2
x= -2
X = 3
x=0
Answers
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Answer:
(b) x = -2
Step-by-step explanation:
The graph shows the lines intersect at (x, y) = (-2, 3).
The x-coordinate of the solution is x = -2.
A pair of fair dice are rolled. Find the probability of rolling a sum that is a multiple of 3 or a multiple of 4.
Answers
Answer:
0.5555 = 55.55% probability of rolling a sum that is a multiple of 3 or a multiple of 4.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Possible outcomes:
For the pair of dice:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
So 36 total outcomes.
Desired outcomes:
Sum being multiplies of 3 or multiples of 4, so:
(1,2), (1,3), (1,5)
(2,1), (2,2), (2,4), (2,6)
(3,1), (3,3), (3,5), (3,6)
(4,2), (4,4), (4,5)
(5,1), (5,3), (5,4)
(6,2), (6,3), (6,6)
3 + 4 + 4 + 3 + 3 + 3 = 20
Probability:
[tex]p = \frac{20}{36} = 0.5555[/tex]
0.5555 = 55.55% probability of rolling a sum that is a multiple of 3 or a multiple of 4.
Does the point (0, 0) satisfy the equation y = x2?
Answers
Answer:
The point is a solution
Step-by-step explanation:
y = x^2
Substitute the point into the equation and see if it is true
0 = 0^2
0=0
True
The angles in a triangle are 100, 40, and 40 degrees. Classify the triangle by its angles and sides.
A. Right isosceles
B. Right Scalene
C. Obtuse scalene
D. Acute isosceles
E. Acute scalene
F. Obtuse isosceles
Answers
Answer:
F. Obtuse isosceles
Step-by-step explanation:
Since we have an angle that is 100 degrees, we have an obtuse angle
We have two angles that are 40, which means we have two sides that are equal length, because two angles have the same measure. That means it is isosceles
The triangle is an obtuse isosceles
In this problem, y = 1/(1 + c1e−x) is a one-parameter family of solutions of the first-order DE y' = y − y2. Find a solution of the first-order IVP consisting of this differential equation and the given initial condition. y(0)=-1/3
Answers
If y (0) = -1/3, then
-1/3 = 1 / (1 + C e ⁻⁰)
Solve for C :
-1/3 = 1 / (1 + C )
-3 = 1 + C
C = -4
So the particular solution to the DE that satisfies the given initial condition is
[tex]\boxed{y=\dfrac1{1-4e^{-x}}}[/tex]
what sum of money must be invested the interest of 4% to given on interest Rs900 in 5 yearr
Answers
Answer:
5
Step-by-step explanation:
trust
help
The points (63, 121), (71, 180), (67, 140), (65, 108), and (72, 165) give the weight in pounds as a function of height in inches for 5 students in
a class. Give the points for these students that represent height as a function of weight
{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}
{(121, 140), (180, 71), (140, 67), (108, 65), (165, 72);
{(121, 71), (180, 63), (140, 67), (108, 65), (165, 72)}
{(63, 121), (71, 180), (67, 140), 65, 108), (72, 165))
Answers
Answer:
{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}
Step-by-step explanation:
We have:
Weight as a function of height.
Give the points for these students that represent height as a function of weight:
Inverse of the input, that is, in the (x,y) format, (x,y) -> (y,x), the coordinates are exchanged, and thus, the correct option is:
{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}
Given the flag ABCDE, determine the single rule (x,y) that creates the
transformed figure A'B'C'D'E'. Fill in your answer below in the format (x,y)--
>
WILL GIVE BRAINLIEST
Answers
Answer:
(y, -x)
Step-by-step explanation:
Rotation of 90°
(Clockwise)
(x, y) ---> (y, -x)
Rotation of 90°
(CounterClockwise)
(x, y) --> (-y, x)
Rotation of 180°
(Both Clockwise and Counterclockwise)
(x, y) ---> (-x, -y)
Rotation of 270°
(Clockwise)
(x, y) ---> (-y, x)
Rotation of 270°
(CounterClockwise)
(x, y) ---> (y, -x)
(12 1/3 * 2) + (10 3/4 * 2)
Answers
Answer:
[tex](12\frac{1}{3} *2)+(10\frac{3}{4} *2)\\\\=(\frac{12(3)+1}{3} *2)+(\frac{10(4)+3}{4} *2)\\\\=\frac{37*2}{3} +\frac{43*2}{4} \\\\=\frac{74}{3} +\frac{86}{4} \\\\=\frac{74(4)+86(3)}{3*4} \\\\=\frac{296+258}{12} \\\\=\frac{554}{12}[/tex]
Find the domain of fg. f(x) = x2 +1 g(x) = 1/x a. all real numbers c. all real numbers, except -1 b. all real numbers, except 0 d. all real numbers, except 1
Answers
The function fg is not defined if the denominator = 0 which means x can’t be 0
So B is the right answer to this question
HELP. Need help on this
Answers
Answer:
what are the answers
Step-by-step explanation:
8b²+7b factorize it i want the explantion also pll help
Answers
b(8b+7)
Answer:
Solution given;
8b²+7b
let look what is common there;
8*b*b+7*b
over here b is common
take common and keep other remaining on bracket
b(8b+7)
In a simple way b(8b+7) is a factorise form of
8b²+7b
A ladder leans against the side of the a house. The ladder is 19 feet long and forms an angle of elevation of 75 degree when leaned against the house. How far away from the house is the ladder? Round your answer to the nearest tenth.
Answers
=============================================================
Explanation:
Focus entirely on the triangle on the right side. The other parts of the drawing are not necessary. In my opinion, they are distracting filler.
Refer to the diagram below.
We have an unknown adjacent side, let's call it x, that's along the horizontal part of the triangle.
The hypotenuse however is known and it is 19 ft
We use the cosine ratio to tie the two sides together
cos(angle) = adjacent/hypotenuse
cos(75) = x/19
19*cos(75) = x
x = 19*cos(75)
x = 4.9175618569479 which is approximate
x = 4.9
The base of the ladder is roughly 4.9 feet away from the base of the house.
Side note: make sure your calculator is in degree mode.
Which expression is equivalent to 27 + 45?
Answers
Answer:
8 x 9
Have a nice day!
What is the solution to the equation x^2 + 10x + 75 = 0?
Answers
Hope this helps!!!!!
Help ASAP PLEASE (STATISTICS) !!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
i cant see it good
Step-by-step explanation:
prob its me
Need Help this is due in 30 minutes!
Answers
Answer:
E
Step-by-step explanation:
Since all the numbers are hundredths decimals, let multiply by the power of 2 of the base 10. So let multiply the equation by
[tex]10 {}^{2} [/tex]
So our new equation is
[tex]3 3{x}^{2} + 71x - 14 = 0[/tex]
Solve by AC method
[tex]ac = - 462[/tex]
[tex]b = 71[/tex]
We must think of two numbers that
Multiply to -462 and Add to 71. Set up equation
The numbers are 77 and -6.
So our new equation is
[tex] {33x}^{2} + 77x - 6x - 14 = 0[/tex]
Solve by factoring by grouping
[tex](33 {x}^{2} + 77x) - (6x - 14)[/tex]
Factor out 11 for the first equation
[tex]11x(3x + 7) - 2(3x + 7)[/tex]
So our factors are
[tex](11x - 2)(3x + 7)[/tex]
Set each equal to zero
[tex]11x - 2 = 0[/tex]
[tex]11x = 2[/tex]
[tex]x = \frac{2}{11} [/tex]
[tex]3x + 7 = [/tex]
[tex]3x = - 7[/tex]
[tex]x = \frac{ - 7}{3} [/tex]
Question 1
The perfect square among the following options is
8
Say
27
216
256
Answers
Answer:
217 is the perfect swuare i think
A drink bottler needs to fill 16 one-pint bottles and he has two tanks: one that contains 2 gallons of soda and a second that contains 3 gallons which will he need to fill the bottles?
Answers
Answer:
2 Gallons of Soda
Step-by-step explanation:
that is the answer above
Find the slope, if it exists, of the line containing the points (10,-3) and (10,-8).
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
m=
Answers
Answer:
The slope is undefined.
Step-by-step explanation:
The line must pass through the points (10,-3) and (10,-8), meaning that it must be vertical. The slope of a line is undefined if the line is vertical.
