Which statement describes the translation of . y= -1/2(x-2) ^2 from standard position? A) Moved up and to the right. B) Moved up and to the left. C) Moved down and to the left. D) Moved down and to the right. .
Answers
Answer: The correct option is
(D) Moved down and to the right.
Step-by-step explanation: We are given to select the statement that best describes the translation of the following function from the standard position.
[tex]y=-\dfrac{1}{2}(x-2)^2~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
This is an equation of a parabola.
The standard position of a parabola of this type is
[tex]y=x^2,[/tex]
where the vertex is at (0, 0). Since the coefficient of x² is positive, so the parabola opens upwards.
Now, from equation (i), we have
the vertex of the parabola is at (2, 0) and since the coefficient of x² is negative, so the parabola opens downwards.
Also, the vertex (0, 0) has been shifted to (2, 0), so the parabola is moved 2 units to the right.
Therefore, the given parabola is moved down and 2 units to the right as compared to the standard position.
The images of the given parabola (i) and the standard parabola are shown in the attached figure below.
Thus, (d) is the correct option.
Related Questions
How many terms are in the algebraic expression 11;; +3 ?
Answers
PLEASE HELP on these problems! I really need the help and these are due in a few hours. Very urgent. I would really appreciate the help, so please help!!!
1. If f(x) = a(r)^x is an example of exponential decay, what must be the value of a and r?
2. The population of Greenfield was 52,500 at the beginning of 1980. Its population steadily decreased by 2.5% per year from 1980 through 1990. What is the population of Greenfield at the end of 1990?
3. If g(x) is the inverse of f(x) - 2x + 1, find a point on g(x) for which both coordinates are positive integers less than 10.
Answers
For 2, we apply that formula, getting 52500*(1-2.5%)^10 (because it's for 10 years and compounded annually). Since 100% is 1, 2.5% is 0.025, and
1-0.025=0.975. Plugging that in, we get 52500*(0.975)^10=around 40757 people.
For inverse functions, what we do is have y=2x+1, so we switch x and y and solve for y, so in x=2y+1 we subtract one from both sides to get x-1=2y. Next, dividing both sides by 2, we get (x-1)/2=y as our inverse. Since we want positive integers less than 10, (x-1) has to be even and therefore x has to be odd. Using a bit of guess and check, we get that x can be 9 while y can be 4 for (9, 4)
.help me with this please. thank you
Answers
Slope of line passing through A(8,8) and B(4,6)→
m = (6-8)/(4-8) = (-2)/(-4) = 1/2
m = 1/2
What will the equation be if mowing need help. I need my lawn mowed every week from June through the middle of July. I will pay 35 dollars for each mowing for 7 weeks
Answers
[tex]\bf \stackrel{payment}{p}=35\stackrel{weeks}{w}\implies p=35w\qquad 1\le x\le 7[/tex]
John paid $100 for renting a canoe for 5 hours. Which graph shows the relationship between the cost of renting a canoe for different hours?
Answers
Answer:
The first one :)
Step-by-step explanation:
The sides of ABC are 30 units, 40 units, and 60 units in length. If the corresponding sides of XYZ are r times as long as the sides of ABC, which expression gives the perimeter of XYZ? 130r 3 x 130r
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What is the length of TW¯¯¯¯¯¯ ?
segment T W with point U between T and W. segment T U is marked congruent to segment U W. segment T U is labeled as 16 units long.
Enter your answer in the box.
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The length of TW of the given Line segment is; 32
How to find the length of a Line segment?From the given line segment with partition, we can see that;
Segment TU = 16
From the partition, we see that;
Segment TU is equal to Segment UW. Thus;
TU = UW = 16
Thus;
TW = TU + UW
TW = 16 + 16
TW = 32
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what is the converse of the linear pairs theorem
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Simplify 3(3y + 2) + 8y. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
23y
–17y + 2
17y + 6
–17y + 6
Answers
9y + 6 + 8y
17y + 6 is your answer
hope this helps
Add like terms: 17y+6
The answer is 17y+6
Simplify. −64x6y9−−−−−−−√3 assume all variables are nonnegative.
Answers
-64 = (-4)(-4)(-4)
Then,
x6 = x2 (x2) (x2)
and,
y9 = (y3)(y3)(y3)
If we take the cube root, we consider only one item per product. Thus, the answer is,
-4x²y³
Answer:
[tex]-4x^2y^3[/tex]
Step-by-step explanation:
We have been given an expression [tex]\sqrt[3]{-64x^6y^9}[/tex]. We are asked to simplify our given expression.
Applying radical rule [tex]\sqrt[n]{-a}=-\sqrt[n]{a}[/tex], when n is odd, we will get:
[tex]-\sqrt[3]{64x^6y^9}[/tex]
We can rewrite terms of our given expression as:
[tex]-\sqrt[3]{(4)^3(x^2)^3(y^3)^3}[/tex]
Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:
[tex]-4x^2y^3[/tex]
Therefore, simplified form of our given expression is [tex]-4x^2y^3[/tex].
A circle has its center at the origin, and (5, -12) is a point on the circle. How long is the radius of the circle?
5
12
13
Answers
Answer:
r = 13
Step-by-step explanation:
The radius of a circle that its center at the origin, and passes through point (5, -12) is 13 units
How to determine the length of the radius?The given parameters are:
Center, (a,b) = (0,0)Point, (x,y) = (5,-12)The length of the radius is calculated using:
[tex]r = \sqrt{(x - a)^2 + (y - b)^2}[/tex]
So, we have:
[tex]r = \sqrt{(5 - 0)^2 + (-12 - 0)^2}[/tex]
Evaluate
[tex]r = \sqrt{169}[/tex]
Solve the square root
r = 13
Hence, the radius is 13 units long
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Ken is making gift bags for a party. He has 64 colored penes and wants to put the same number in each bag. How many bags will ken make if he puts 4 in each bag?
Answers
64 pens = 1/4 x 64
= 16 bags
Ken will make 16 gift bags if he puts 4 in each bag.
What is the measure of ∠B?
Answers
m<B = 360 - 285
m<B = 75
Solve each problem and write your answer in scientific notation
Answers
subtract 6/8 - 1/4 enter your answer in the box below as a fraction in lowest terms using the slash ( / ) as the fraction bar
Answers
The difference of the given fractions is 1/2.
Given that, 6/8 - 1/4.
Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators same first and then subtract them.
Here, 6/8 - 1/4
= 6/8 - 2/8
= (6-2)/8
= 4/8
= 1/2
Therefore, the difference of the given fractions is 1/2.
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1. If x-1 is a factor of p(x)=x^3-7x^2+15x-9, which of the following represents the complete factorization for p(x)?
A. (x-3)(x+4)(x+1)
B. (x-3)(x-3)(x-1)
C. (x-3)(x+3)(x-1)
D. (x-3)(x+3)(x+1)
2. The point (1,0) lies on the graph of p(x)=x^4-2x^3-x+2
True or false
Answers
Answer:
1. Option B is the correct answer.
2. The point (1,0) lies on the graph of p(x)=x⁴-2x³-x+2.
Step-by-step explanation:
1. Dividing x³-7x²+15x-9 with (x-1).
[tex]\frac{x^3-7x^2+15x-9}{x-1}=x^2-6x+9[/tex]
Factorizing x²-6x+9 we will get
x²-6x+9 = (x - 3)(x-3)
x³-7x²+15x-9 = (x-1)(x - 3)(x-3)
Option B is the correct answer.
2. We have p(x)=x⁴-2x³-x+2
That is y = x⁴-2x³-x+2
We have coordinates (1,0), substituting
y = 1⁴-2 x 1³-1+2 = 0
So when we are substituting x value as 1 we are getting y as zero, so the point lies in curve.
Solve the equation n times 50 equals 5000 explain your solution
Answers
n = 100.
Hope this helped :)
Use the drop-down menus to identify the values of the parabola.
Vertex = ____
Domain = {x| ____ }
Range = {y| y ≤ ____ }
Answers
The answer is
Vertex: 0,4
Domain: x is a real number
Range: 4
:D
Answer:
Vertex - (0,4)
Domain - [tex]D=[x|x\in\mathbb{R}][/tex]
Range - [tex]R=[y|y\leq 4][/tex]
Step-by-step explanation:
Given : The graph of a parabola
To find : The values of the parabola - Vertex ,Domain and Range
Solution :
To identify the vertex the given parabola given by equation
[tex]y=-x^2+4[/tex]
Vertex is given by [tex]y=a(x-h)^2+k[/tex]
where (h,k) are the vertex.
Comparing with equation,
Vertex is (h,k)=(0,4)
Domain is the set of value where function is defined.
The domain of given function is all real numbers.
[tex]D=[x|x\in\mathbb{R}][/tex]
Range is the set of value that corresponds to the domain.
[tex]R=[y|y\leq 4][/tex]
2v+46=8(v-1)
I got -54/10 which I know is wrong. Please help.
Answers
2v+46 = 8v-8
then, we will gather the terms with the variables on one side of the equation and the terms with no variables on the other side.
46+8 = 8v-2v
54 = 6v
to get the value of v, we will divide both sides of the equation by 6
v = 54/6 = 9
The length is 5 units more than the width. The perimeter is 9 times the width. Find the length and width of the rectangle. Can you also include the steps thanks!
Answers
The length, width, and perimeter of the rectangle are 7 units, 2 units, and 18 units.
What is the perimeter?Perimeter is the sum of the length of the sides used to make the given figure.
Let the width of the rectangle be represented by x. The length is 5 units more than the width. The perimeter is 9 times the width. Therefore, we can write,
Width = x
Length = 5 + x
Perimeter = 9x
Now, the length, width, and perimeter of the rectangle together can be written as,
Perimeter = 2(Length + Width)
9x = 2[(5+x) + x]
9x = 2(5 + x + x)
9x = 2(5 + 2x)
9x = 10 + 4x
9x - 4x = 10
5x = 10
x = 10/5
x = 2
Further, the dimensions can be written as,
Width = x = 2 units
Length = 5 + x = 2 + 5 = 7 units
Perimeter = 9x = 9(2) = 18 units
Hence, the length, width, and perimeter of the rectangle are 7 units, 2 units, and 18 units.
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What is the solution to the system of linear equations?
6x+7y=59
4x+5y=41 how do you do it
Answers
Answer:
The correct answer is 4, 5 :)
Step-by-step explanation:
A system of linear equations can be solved by elimination, substitution or using graphs.
The values of x and y for [tex]6x + 7y= 59[/tex] and [tex]4x + 5y =41[/tex] are 4 and 5, respectively.
Given
[tex]6x + 7y= 59[/tex]
[tex]4x + 5y =41[/tex]
Make x the subject in [tex]4x + 5y =41[/tex]
[tex]4x = 41 - 5y[/tex]
Divide by 4
[tex]x = \frac 14(41 - 5y)[/tex]
Substitute [tex]x = \frac 14(41 - 5y)[/tex] in [tex]6x + 7y= 59[/tex]
[tex]6 \times \frac 14(41 - 5y)+ 7y = 59[/tex]
[tex]\frac 32(41 - 5y)+ 7y = 59[/tex]
Multiply through by 2
[tex]2 \times \frac 32(41 - 5y)+ 2 \times 7y = 2 \times 59[/tex]
[tex]3(41 - 5y)+ 14y = 118[/tex]
Open brackets
[tex]123 - 15y+ 14y = 118[/tex]
Collect like terms
[tex]- 15y+ 14y = 118 - 123[/tex]
[tex]-y = -5[/tex]
[tex]y = 5[/tex]
Substitute [tex]y = 5[/tex] in [tex]x = \frac 14(41 - 5y)[/tex]
[tex]x = \frac 14(41 - 5 \times 5)[/tex]
[tex]x = \frac 14(41 - 25)[/tex]
[tex]x = \frac 14(16)[/tex]
[tex]x = 4[/tex]
Hence, the solution to the system of linear equations is:
[tex]x = 4[/tex]
[tex]y = 5[/tex]
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the water level of a pond drops an inch every 7 days without rain how many days will it take the ponds water level to drop by 12 inches
Answers
1 inch in 7 days
multiply 7 by 12
7 *12 = 84 days
cross multiply
(1)(x) = (7)(12)
x = 84 days <===
if x and y are both negative when is x-y positive
Answers
For example
x = -2
y = -5
x-y = -2-(-5) = -2+5 = 3
Find dy/dx by implicit differentiation. y cos x = 5x2 + 3y2
Answers
To find dy/dx by implicit differentiation, differentiate both sides of the equation with respect to x. Apply the product rule and isolate dy/dx by moving terms.
Explanation:To find dy/dx by implicit differentiation, we'll differentiate both sides of the equation with respect to x. Let's start by differentiating y cos x = 5x2 + 3y2:
Using the product rule, we have: dy/dx * cos x + y * (-sin x) = 10x + 6y * dy/dx
Next, isolate dy/dx by moving terms:
dy/dx * cos x - 6y * dy/dx = 10x - y * (-sin x)
dy/dx * (cos x - 6y) = 10x + y * sin x
dy/dx = (10x + y * sin x) / (cos x - 6y)
Which Algebraic expression has a term with a coefficient of 3?
A:5y-7
B:-2y+5+3
C:3(y-6)
D:3y+1
Answers
Answer:
D:3y+1
Step-by-step explanation:
find the Algebraic expression has a term with a coefficient of 3
The number before the variable is the coefficient
A:5y-7
y has a coefficient of 5
B:-2y+5+3
y has a coefficient of -2
C:3(y-6)
y or 1y are same
Here , y has a coefficient of 1
D:3y+1
y has a coefficient of 3
what are three ways to name a line with 5 points?
Answers
EGJ
EFFHJ
Hope I helped
find the quotient.
-7 ÷ 14/3.
a. -2/3
b. -98/3
c. -1/2
d. -3/2
Answers
To find the quotient of -7 ÷ 14/3, simplify the fraction 14/3 to 42/3 and then divide -7 by 42/3. The quotient is -1/2.
Explanation:To find the quotient of -7 ÷ 14/3, we can simplify the fraction 14/3 to an improper fraction or a mixed number. Let's convert it to an improper fraction. We multiply the denominator (3) by the whole number (14) and add the numerator (0) to get the new numerator. This gives us 42/3. Next, we divide -7 by 42/3. When dividing by a fraction, we multiply by its reciprocal. So, -7 ÷ 42/3 is the same as -7 × 3/42. This simplifies to -21/42 which reduces to -1/2.
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The Ye Ol' Sandwich Shop sells 4 different sandwiches, 6 different drinks, and 3 different desserts. How many different orders could you place if you decided to buy a sandwich and a drink?
Answers
1 of 4 options for a sandwich
1 of 6 options for a drink
These categories are not dependent on each other. 4*6=24 possible combinations.
so 4 x 6 = 24
you have 24 different combinations you can do
hope this helps
Which logical form represents this statement?
Either it is not cold today or I am wearing woolen coat.
p : It is cold today. q : I am wearing woolen coat.
~p ∧ ~q
~p ∧ q
~p ∨ q
~(p ∨ q)
Answers
A rectangle of area 350 square feet is 14 times as wide as it is long. Find its length and width
Answers
Let length be x
then width = 14x
Now, just area = [tex]14x \times x [/tex]
[tex]350 = 14x^2 \\ x^2 = 25 \\ x = 5 [/tex]
so length = 5
and width = 14 x 5 = 60