Describe the transformation of the graph of f into the graph of g as either a horizontal or vertical stretch. f(x)=sqrt(x) and g(x)=sqrt(0.5x)
Answers
[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]
with that template in mind, let's see [tex]\bf f(x)=\sqrt{x}\qquad \begin{array}{llll} g(x)=&\sqrt{0.5x}\\ &\quad \uparrow \\ &\quad B \end{array}[/tex]
so B went form 1 on f(x), down to 0.5 or 1/2 on g(x)
B = 1/2, thus the graph is stretched by twice as much.
The transformation of the function f(x) to g(x) is a horizontal stretch.
Step-by-step explanation:The parent function f(x) is given by:
[tex]f(x)=\sqrt{x}[/tex]
and the transformed function g(x) is given by:
[tex]g(x)=\sqrt{0.5x}[/tex]
Now we know that the transformation of the type:
f(x) → f(bx)
is a horizontal stretch if 0<b<1
and is a horizontal shrink if b>1
Here we have:
[tex]b=\dfrac{1}{2}=0.5[/tex]
i.e.
[tex]0<b<1[/tex]
This means that the transformation of the function f(x) to g(x) is a horizontal stretch by a factor of 2.
Related Questions
Which statements are true for solving the equation 0.5 – |x – 12| = –0.25? Check all that apply.
The equation will have no solutions.
A good first step for solving the equation is to subtract 0.5 from both sides of the equation.
A good first step for solving the equation is to split it into a positive case and a negative case.
The positive case of this equation is 0.5 – |x – 12| = 0.25.
The negative case of this equation is x – 12 = –0.75.
The equation will have only 1 solution
Answers
we have
[tex]0.5-\left|x-12\right|=-0.25[/tex]
we know that
The absolute value has two solutions
Subtract [tex]0.5[/tex] both sides
[tex]-\left|x-12\right|=-0.25-0.5[/tex]
[tex]-\left|x-12\right|=-0.75[/tex]
Step 1
Find the first solution (Case positive)
[tex]-[+(x-12)]=-0.75[/tex]
[tex]-x+12=-0.75[/tex]
Subtract [tex]12[/tex] both sides
[tex]-x+12-12=-0.75-12[/tex]
[tex]-x=-12.75[/tex]
Multiply by [tex]-1[/tex] both sides
[tex]x=12.75[/tex]
Step 2
Find the second solution (Case negative)
[tex]-[-(x-12)]=-0.75[/tex]
[tex]x-12=-0.75[/tex]
Adds [tex]12[/tex] both sides
[tex]x=-0.75+12[/tex]
[tex]x=11.25[/tex]
Statements
case A) The equation will have no solutions
The statement is False
Because the equation has two solutions------> See the procedure
case B) A good first step for solving the equation is to subtract 0.5 from both sides of the equation
The statement is True -----> See the procedure
case C) A good first step for solving the equation is to split it into a positive case and a negative case
The statement is False -----> See the procedure
case D) The positive case of this equation is 0.5 – |x – 12| = 0.25
The statement is False
Because the positive case is [tex]0.5-(x-12)=-0.25[/tex] -----> see the procedure
case E) The negative case of this equation is x – 12 = –0.75
The statement is True -----> see the procedure
case F) The equation will have only 1 solution
The statement is False
Because The equation has two solutions------> See the procedure
The equation 0.5 - |x - 12| = -0.25 has no solutions because an absolute value cannot be negative. Attempting to split the equation into positive and negative cases or solving for x is fruitless because the left side of the equation will always be at least 0.5.
Explanation:When solving the equation 0.5 - |x - 12| = -0.25, we can immediately notice that it will have no solutions because the absolute value is always non-negative, and therefore the left-hand side cannot be less than 0.5. Hence, subtracting 0.5 from both sides is not a good first step. Instead, you would typically isolate the absolute value on one side, but given that the equation equals a negative number, we know it has no solutions without additional steps.
Additionally, splitting the equation into a positive case and a negative case isn't useful here, because no matter what's inside the absolute value, the output cannot lead to a negative result, thus making both cases moot.
The statements that say "The positive case of this equation is 0.5 - |x - 12| = 0.25" and "The negative case of this equation is x - 12 = -0.75" are incorrect as they misinterpret how the absolute value works. Lastly, the equation does not have any solution, so it cannot have only one solution.
Learn more about Absolute Value Equations here:https://brainly.com/question/35209059
#SPJ3
The following is an incomplete paragraph proving that ∠WRS ≅ ∠VQT, given the information in the figure where segment UV is parallel to segment WZ.:
Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively
According to the given information, segment UV is parallel to segment WZ while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem. Because angles SQU and WRS are corresponding angles, they are congruent according to the Corresponding Angles Postulate. Finally, angle VQT is congruent to angle WRS by the _____________________.
Which Property of Equality accurately completes the proof?
Reflexive
Substitution
Subtraction
Transitive
Answers
The Subtraction Property does not apply here, and the Reflexive Property is used to show something is equal to itself (a = a).
Given that ∠VQT is congruent to ∠SQU by the Vertical Angles Theorem and ∠SQU is congruent to ∠WRS by the Corresponding Angles Postulate, ∠VQT is congruent to ∠WRS because of the Transitive Property of Equality.
Basically, Angle 1 = Angle 2, Angle 2 = Angle 3, therefore Angle 1 should also equal Angle 3.
Answer:
Transitive
Step-by-step explanation:
Just took the test
Hope it helps :)
Which expression is equivalent to r^9/r^3
Answers
Answer:
The correct option is B.
Step-by-step explanation:
The given expression is
[tex]\frac{r^9}{r^3}[/tex]
According to the property of exponent,
[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
Using this property of exponent, we get
[tex]\frac{r^9}{r^3}=r^{9-3}[/tex]
[tex]\frac{r^9}{r^3}=r^{6}[/tex]
The expression [tex]r^{6}[/tex] is equivalent to the given expression.
Therefore the correct option is B.
Write | √3 - 2i | in a + bi form.
Answers
[tex]\bf |\sqrt{3}-2i|\implies \begin{cases} +(\sqrt{3}-2i)\\ -(\sqrt{3}-2i) \end{cases}\implies \begin{cases} \sqrt{3}-2i\\ -\sqrt{3}+2i \end{cases}[/tex]
What is the initial value of the function represented by this graph?
A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 2 with the ordered pair 7, 5.
0
1
2
5
Answers
The initial value of a function is the value of the function when x = 0
o when x = 0, y = 2 so the initial value is 2
Answer:
2
Step-by-step explanation:
The initial value is what you start off with, so it is 2! :)
How do you graph y^2=x^3?
Answers
To graph these types of equations, we need to remember our rules about graphing squared values and cubed values. A squared function will create a parabola, while a cubed function will create a curvy line over the y-axis.
Find the limit of the function algebraically. limit as x approaches negative nine of quantity x squared minus eighty one divided by quantity x plus nine.
Answers
lim x→-9 (x²-81)/(x+9)
Initially, we solve this by substituting x=-9 to the equation.
((-9)²-81)/(-9+9) = 0/0
The term 0/0 is undefined. This means that the solution is not see on the number line because it is imaginary. Other undefined terms are N/0 (where N is any number), 0⁰, 0×∞, ∞-∞, 1^∞ and ∞/∞. One way to solve this is by applying L'Hopitals Rule. This can be done by differentiating the numerator and denominator of the fraction independently. Then, you can already substitute the x=-9.
(2x-0)/(1+0) = 2x = 2(-9) = -18
The other easy way is to substitute x=-8.999 to the original equation. Note that the term x→-9 means that x only approaches to -9. Thus, you substitute a number that is very close to -9. Substituting x=-8.999
((-8.999)²-81)/(-8.999+9) = -18
A baby wriggled so much that weighing him at the clinic was a problem. So the doctor held the baby and stood on a scale. Then the nurse held the baby and stood on the scale. Then the doctor held the nurse who held the baby and stood on the scale. the three results were 78 kg, 69 kg and 142 kg respectively. What was the weight of the baby.
Long question but help me out ( it was 69 kg I mean)
Answers
y = weight of the doctor.
z = weight of the nurse.
x + y = 78 so y = 78 - x
x + z = 69 so z = 69 - x
x + y + z = 142
substitute y = 78 - x and z = 69 - x into x + y + z = 142
x + y + z = 142
x +78 - x + 69 - x = 142
-x + 147 = 142
-x = - 5
x = 5
answer
the weight of the baby was 5 kg
weight of the Nurse be N
weight of the Doctor be D
Now if we fit those into equations we have:
1. B+D= 78
2. B+N= 69
3. B+D+N= 142
Now take 1 and 3:
B+D= 78 so substitute 78 in the thrid equation were B+D is
78+N= 142 ( what plus 78 will get you 142)
78+64= 142
The nurse's weight is 64 kg
Now that we have the nurses weight. You take the combined weight of the baby and nurse and subtract 64
The baby weighs 5kg
now take the doctors and babies combine weight and subtract 4
The Doctor weighs 73 kg
ANSWER:
The baby weighs 5kg, the nurse weighs 64, and the doctor weighs 74.
Sorry for the long answer but hope this helps.
What is the solution of the equation 6x - 8 = 4x? X=
Answers
hope this helps you
Solve for z: 3z -5 +2z=25 -5z
Answers
To answer this question you will have to combine like terms.
3z-5+2z=25-5z
Combine 3z and 2z first because they have z in common and are on the same side: 3z+2z=5z
Now you have -5+5z=25-5z
Now you will go ahead and distribute since you can't combine anymore on certain sides.
You can add 5 to 25 on the other side: 25+5=30
Then add 5z to 5z on the other side: 5z+5z=10z
So now your equation should look like this: 10z=30
From here you will have to divide both sides by 10: 10/10=1(since it came to 1 it will just stay as z instead of 1z) 30/10=3
So your solution should come to: z=3
Sam picked a card from a standard deck. What is the probability that Sam picked a heart or a king?
A. 1/13
B. 16/52
C. 17/52
D. 16/53
Answers
P(HorK)=16/52
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
Number of cards in a deck = 52
Number of heart = 13
Number of king = 4
But we know that heart contains one king too.
So, to avoid double counting we have to subtract 1 from it.
so, Number of king = 3
So, Probability that Sam picked a heart or a king is given by
[tex]\frac{13}{52}+\frac{3}{52}\\\\=\frac{16}{52}\\\\[/tex]
Hence, Option 'B' is correct.
How do I solve this? (Geometry)
Answers
7x4 = 28
5 x z = 28
z = 28/5 = 5.6
Your job pays $8 per hour. (a) Write an algebraic expression for your pay in dollars for working h hours. (b) What is your pay if you work 36 hours?
Answers
if u work 36 hrs...
P = 8(36)
P = 288 <==
b. Plug in 36 for h
8*36
288
Final answer: $288
How many cookies will Tanya have if she bakes 6batches more than the maximum number of batches in the table
Answers
We can form an equation for this linear relationship.
The relationship is in the form [tex]y=ax+b[/tex] where
y = number of cookies of 'x' batches
x = number of batches
a = changing rate = 16
b = the number of cookies when the batch is 0
We need to find the value of 'b' and we can achieve this by keep subtracting 16 from 165, which is batch 5 until we get to batch 0.
Batch 5 = 165
Batch 4 = 165 - 16 = 149
Batch 3 = 149 - 16 = 133
Batch 2 = 133 - 16 = 117
Batch 1 = 117 - 16 = 101
Batch 0 = 101 - 16 = 85 ⇒ this is the value of 'b'
So the equation is [tex]y=16x+85[/tex]
We will use this equation to work out the number of cookies if we cook another 6 batches.
6 batches more than batch 9 will give us batch number 15
We have: x=15, a=16, b=85
y = 16(15) + 85 = 325 cookies
Answer:
325 cookies
Step-by-step explanation: I just took the test and got it right.
A party rental company has chairs and tables for rent. The total cost to rent 3 chars and 2 tables is $20. The total cost to rent 8 chairs and 4 tables is $45. What is the cost to rent each chair and each table?
Answers
Equations:
8c + 4t = 45
3c + 2t = 20
Modify for elimination: ( multiply 2nd eq by -2)
8c + 4t = 45
-6c + -4t = -40
Subtract and solve for "c":
2c = 5
c = $2.50 (cost of one chair)
Solve for "t":
3c + 2t = 20
3(2.50) + 2t = 20
7.50 + 2t =20
2t=12.50
T= 12.50/2 =6.25
t = $ 6.25 (cost of one table)
Table = 6.25 each
Chair = 2.50 each
Check:
3(2.50) + 2(6.25) =
7.50 +12.50 = 20
8(2.50) + 4(6.25) =
20.00 + 25.00 = 45.00
Below are the steps to solve an equation: Step 1: |x − 5| + 2 = 5 Step 2: |x − 5| = 5 − 2 Step 3: |x − 5| = 3 Which of the following is a correct next step to solve the equation?
Answers
Equation 1: x-5=3
Equation 2: x-5=-3
The answers would be x=8 and x=2.
Answer: [tex]x-5=\pm 3[/tex] will be the next step of the given expression.
Step-by-step explanation:
Since, Given expression is |x-5|+2=5
On solving the above expression,
Step 1. [tex]|x-5|+2=5[/tex]
step 2. [tex]|x-5| = 5-2[/tex]
Step 3. [tex]|x-5| = 3[/tex]
Step 4. [tex]x-5=\pm 3[/tex] (because mode takes both positive and negative values)
1 + 4 + 7 + 10 ... what is last number that makes sum go over 1 million.
Answers
[tex]\displaystyle\sum_{k=0}^n(3k+1)=n+1+3\sum_{k=1}^nk=n+1+\dfrac{3n(n+1)}2[/tex]
[tex]=\dfrac32n^2+\dfrac52n+1[/tex]
The sum will exceed 1 million for [tex]n[/tex] satisfying
[tex]\dfrac32n^2+\dfrac52n+1>1000000[/tex]
[tex]3n^2+5n+2>2000000[/tex]
[tex]3n^2+5n-1999998>0[/tex]
The least integer that satisfies this is [tex]n=816[/tex].
Plato-Match each set of conditions with the corresponding relationship between ∆ABC and ∆XYZ and the criterion (if any) that proves the relationship.
Answers
The second one on the left is matched with the last one on the right, because it says that two of the angles are equal, and one side is equal, hence, AAS, or ASA.
The last one on the left is matched with the first one on the right, because it says all three sides are equal, therefore, SSS.
The third one on the left is matched with the second one on the left. I'll be honest, I'm not sure why this is, (geometry isn't my best subject either Dx) but by the process of elimination, this is it.
the questionnnnnnnn issssssssss
Answers
Ф=angle of the arc
r=radius
Data:
Ф=140º
r=diameter/2=(100 m)/2=50 m
π=3.14
arc length=(140º/360º)(2)(3.14)(50 m)=122.1111...m=122.1 m
Answer: A) 122.1 m
Hans the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 6 clients who did Plan A and 5 who did Plan B. On Tuesday there were 2 clients who did Plan A and 3 who did Plan B. Hans trained his Monday clients for a total of 7 hours and his Tuesday clients for a total of 3 hours. How long does each of the workout plans last?
Answers
A = hours for plan A
B = hours for plan B
Monday: 6A + 5B = 7
Tuesday: 2A + 3B = 3
use elimination by multiplying the 2nd equation by 3.
Doing that we get 3(2A + 3B = 3) = 6A + 9B = 9
So the two equations are now:
6A + 9B = 9
6A + 5B = 7
Subtract and we have 4B = 2
B = 2/4 = 1/2 of an hour
Now put 1/2 back into either equation to solve for A
6A + 5(1/2) = 7
6A + 5/2 = 7
6A = 14/2 -5/2
6A = 9/2
divide by 6 to get A = 9/12 = ¾ hours
Plan A = 3/4 hour
Plan B = 1/2 hour
Final answer:
By setting up and solving a system of equations, we find that Plan A lasts for 45 minutes per session and Plan B lasts for 30 minutes per session.
Explanation:
Solving for the Duration of Workout Plans
We have information regarding the total duration of workouts and the number of clients for two consecutive days. To find the duration of each workout plan, we use a system of equations. Let A represent the duration of Plan A and B represent the duration of Plan B. The equations based on the given information are:
6A + 5B = 420 minutes (7 hours on Monday)
2A + 3B = 180 minutes (3 hours on Tuesday)
Multiplying the second equation by 3 gives us:
6A + 9B = 540
Subtracting the first equation from this result gives us:
4B = 120 minutes, therefore, B = 30 minutes
Now we substitute B = 30 in the first equation:
6A + 150 = 420, which simplifies to 6A = 270, hence A = 45 minutes
Thus, Plan A lasts for 45 minutes and Plan B lasts for 30 minutes.
Need help with this question! Will attach pic! A satellite is to be put into an elliptical orbit around a moon as shown below.The moon is a sphere with radius of 1000 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 953 km to 466 km
Answers
x²/a² + y²/b² = 1
Here is: a - semi-major axis and b - semi-minor axis.
Radius of the moon is 1,000 km and the distance from the surface of the moon to the satellite varies from 953 km to 466 km.
a = 1,000 + 953 = 1,953 km
b = 1,000 + 466 = 1,466 km
Answer:
The equation is x² / 1,953² + y² / 1,466² = 1
or: x²/3,814,209 + y²/2,149,156 = 1
what can 4 and 22 divided into equally the answer is smaller than 88
Answers
11x4
22x2
The variable Z is directly proportional to X. When X is 15, Z has the value 45.
What is the value of Z when X = 23
Answers
If variable Z is directly proportional to X, this means that the value of X increases a certain amount when Z increases. The same will apply to decreasing of either variable.
If Z = 45, X = 15. This means Z is 3 times as much as X.
X is currently 23. We can now figure out for Z.
Since Z is 3 times as much as X, multiply 23 by 3.
23 * 3 = 69
The value of Z is 69 when X is 23.
I hope this helps!
Zeus Industries bought a computer for $2857. It is expected to depreciate at a rate of 24% per year. What will the value of the computer be in 3 years?
Round to the nearest penny. Do not type the "$" sign in your answer
******PLEASE HELP******
Answers
Write the number in the form a +bi
Answers
can someone pls help me
Answers
circle=4 <=======
Plug circle value in
diamond+2= 5*(4)
diamond+2=20
diamond=18 <=====
Plug circle and diamond value in
2(4)=18+2*triangle
8=18+2*triangle
-10=2*triangle
-5= triangle <=======
Evaluate the following expression using the values given:
Find 3x2 − y3 − y3 − z if x = 3, y = −2, and z = −5.
Answers
When $n$ is divided by 10, the remainder is $a$. when $n$ is divided by 13, the remainder is $b$. what is $n$ modulo 130, in terms of $a$ and $b$?
Answers
If
N = a (mod 10)
N = b (mod 13)
gcd(10,13) = 1
then
N = 10 bx + 13 ay (mod 130)
Where
10x + 13y = 1
-> (10x + 13) (mod 2) = 1 (mod 2)
-> y (mod 2) = 1
y = -3, x = 4
-> N = 40b – 39a (mod 130)
It is given that ra + sb should be non-negative:
N = 40b – 39a (mod 130)
N = 40b + (130 – 39)a (mod 130)
N = 40b + 91a (mod 130)
Therefore, N modulo 130, in terms of a and b is: N = 40b + 91a (mod 130).
Final answer:
To find the value of n modulo 130 in terms of a and b, one must solve two congruences using the Chinese Remainder Theorem. The solution would require computations beyond the scope of this response and would result in n expressed as a linear combination of a and b modulo 130.
Explanation:
To solve for the values of n modulo 130, given that when n is divided by 10, the remainder is a, and when n is divided by 13, the remainder is b, we can express n in the following forms:
n = 10k + a, where k is some integer
n = 13l + b, where l is some integer
Since 10 and 13 are coprime, Chinese Remainder Theorem tells us that there is a unique solution for n modulo 130 that satisfies both of these congruences. To find n in terms of a and b, we must find k and l such that these two equations give the same n for a particular value of n between 0 and 129 inclusive. This can be done through careful calculations or using a method designed for solving simultaneous congruences.
Once the suitable k and l values are found, the value of n modulo 130 can be stated. Since the exact solution requires more context or computational techniques, we can't provide the specific number in this case, but the final answer will be in the form: n ≡ (something involving a and b) (mod 130).
What is the measure of RST?
Answers
Answer:
∠TSR = 93°
Step-by-step explanation:
In the figure attached as we know ∠S = [tex]\frac{mQR+mPT}{2}[/tex] [ By the theorem of angles of the intersecting secants in a circle]
∠S = [tex]\frac{131+43}{2}[/tex]
= [tex]\frac{174}{2}[/tex]
= 87°
Now we have to find the measure of ∠RST
Since ∠QSR + ∠TSR = 180° [ supplementary angles]
87° + ∠TSR = 180°
∠TSR = 180 - 87 = 93°
Therefore, m∠TSR = 93° is the answer.
Jessica plans to purchase a car in one year at a cost of $30,000. how much should be invested in an account paying 10% compounded semiannually to have the funds needed?
Answers
A=p (1+r/k)^kt
A fund needed 30000
p Amount invested?
R interest rate 0.1
K compounded semiannual 2
T time 1 year
Solve the formula for p to get
P=A÷(1+r/k)^kt
P=30,000÷(1+0.1÷2)^(2×1)
P=27,210.88