The function transformations are:
The function (a) y = -1/2(x + 2)^2 + 4 is translated to the left by 2 units, reflected across the x-axis, compressed vertically by a factor of 1/2 and translated up by 4 unitsThe function (b) y = -(x - 1)^2 - 2 is translated right by 1 unit, reflected across the x-axis, and translated down by 2 unitsThe function (c) y = (4x)^2 is stretched horizontally by a factor of 1/4The function (d) y = 4x^2 is stretched vertically by a factor of 4What are transformations?Transformations involve translating, reflecting, rotating and dilating a function across the coordinate plane
How to determine the transformations?The parent function of a quadratic function is represented as:
y = x^2
When the function is stretched horizontally by a factor of k, where k is between 0 and 1, we have:
y = (x/k)^2
Assume k = 1/4. we have:
y = (4x)^2
This means that the function (c) y = (4x)^2 is stretched horizontally by a factor of 1/4
When the function is stretched vertically by a factor of k, where k is greater than 1, we have:
y = k(x)^2
Assume k = 4. we have:
y = 4x^2
This means that the function (d) y = 4x^2 is stretched vertically by a factor of 4
Translating the function left is represented as:
y = (x + k)^2
Assume k = 2. we have:
y = (x + 2)^2
Reflecting the function across the x-axis is represented as
y = -(x + 2)^2
When the function is compressed vertically by a factor of k, where k is between 0 and 1, we have:
y = -k(x + 2)^2
Assume k = 1/2. we have:
y = -1/2(x + 2)^2
Translating the function up is represented as:
y = -1/2(x + 2)^2 + k
Assume k = 4. we have:
y = -1/2(x + 2)^2 + 4
Hence, the function (a) y = -1/2(x + 2)^2 + 4 is translated to the left by 2 units, reflected across the x-axis, compressed vertically by a factor of 1/2 and translated up by 4 units
Translating the function right is represented as:
y = (x - k)^2
Assume k = 1. we have:
y = (x - 1)^2
Reflecting the function across the x-axis is represented as
y = -(x - 1)^2
Translating the function down is represented as:
y = -(x - 1)^2 - k
Assume k = 2. we have:
y = -(x - 1)^2 - 2
Hence, the function (b) y = -(x - 1)^2 - 2 is translated right by 1 unit, reflected across the x-axis, and translated down by 2 units
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If the triangle are similar, write a similarity
statement and tell whether you would use
AA similarity, SAS similarity, or SSS
similarity. If not similar, explain why.
Explanation
Answer:
The triangles are similar due to AAA
Step-by-step explanation:
'The triangles ABC and DBE are similar because they have a common angle < B, and also angle < E is marked as congruent to angle < A. Then the third angle <C is going to be congruent to angle D as well due to the property of addition of internal angles of a triangle must add to 180 degrees.
Then the triangles are similar due to AAA
Mrs. Brownstone brought 56 liters of juice for the fifth grade party. How many milliliters of juice did she bring?
Answer:
56000 milliliters
1 liter = 1000 milliliters
56(1000)=56000
Step-by-step explanation:
WHERE ARE THE BLACK DOTS LOCATED?!?
Answer:
The first one (on the bottom) is (2, -3)
The second one (the top one) is (-1, 3)
Answer:
(-1, 3) and (2, -3)
Step-by-step explanation:
The x-value always goes first and the second is always the y-value.
What is the measurement of angle D
HELP PLS
9514 1404 393
Answer:
68°
Step-by-step explanation:
Alternate interior angles are congruent, so we have ...
123° = d° +55°
d = 123 -55 = 68
Angle D measures 68°.
_____
For those of you inclined to use this answer for other questions, here are the other angles in this figure.
A = 55° . . . . alternate interior with 55°, so congruent
B = C = 180° -123°
B = C = 57°
X/4=8
Solve that using the opposite operation
Answer:
x = 32
Step-by-step explanation:
4 • (x/4) = 8 • 4
x = 32
Step-by-step explanation:
[tex]\qquad\sf\dashrightarrow x/4=8 [/tex]
[tex]\qquad\sf\dashrightarrow x=4×8 [/tex]
[tex]\qquad\sf\dashrightarrow x=32 [/tex]
Solve the system y = 3x + 2 and 3y = 9x + 6 by using graph paper or graphing technology. What is the solution to the system?
No solutions
Infinite solutions
(32)
(9,2)
Which expression is equivalent to 1/4(12x + 16) + 3x + 7
Please help!!!
a. 15/4x + 7
b. 15x + 23
c. 6x + 23
d. 6x + 11
Answer:
the answer is 6x+11
Step-by-step explanation:
1/4(12+16)+3x+7
1/4×4(3x+4)+3x+7
(3x+4)+3x+7
3x+4+3x+7
6x+11
what is domain and range because I got it wrong is not the right one
Answer:
You most likely got it wrong because you didn't plot all the points that are actually in the table, the domain and range are both right.
Mary has a large sum of money to deposit, but since she has heard many stories from her grandmother about the Great Depression, when many banks lost their customers’ deposits, she is worried that the bank might not keep her money safe. Give Mary some recommendations about what she can do to make sure that her money stays protected.
Mary should make sure to choose a bank that is FDIC insured. Furthermore, if she has more than maximum deposit insurance amount to deposit, she should spread her deposits out among several separate banks. These should be totally different banks, not simply different branches of the same bank. The FDIC will insure up to the maximum deposit insurance amount at each bank, even if the bank fails.
Choose the equations that are equivalent. Select all that apply.
A. 52 = 8n +4
B. 42n + 1) = 52
C. 4 = 52 - 8n
D. 4n = 48
Answer:
A. 52 = 8n +4
C. 4 = 52 - 8n
What is the solution to the equation 1/3 n =6
Answer:
n=18
Step-by-step explanation:
2. Pierre works full time and is paid an hourly rate of $12.50 for 35 hours a week. He is paid for 52
weeks of the year. What are his total earnings for ONE YEAR?
Answer:
$22,750
Step-by-step explanation:
First, find out how much Pierre is paid per week: $12.50 x 35 -> $437.5/week
Then, multiply to find how much he is paid the whole year: $437.5 x 52 -> $22,750
It's urgent, Please answer, Make Sure you Round it
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
460, 451,442
Find the 37th term.
Answer:
136
Step-by-step explanation:
This is an arithmetic sequence
The formula is an = a1 + f × (n-1)
n= the number we are trying to find = 37
a= the number in any given space on the sequence
a1= 460
f= the common difference between the numbers
f= -9 because you subtract 9 from each to get the number
a37= 460-9(37-1)
a37= 460-9(36)
a37= 460- 324
a37= 136
[tex] \\ [/tex]
The first three terms of a sequence are 460, 451, 442[tex] \\ [/tex]
To Find :[tex] \\ [/tex]
37th term of sequence = ?[tex] \\ [/tex]
Solution :[tex] \\ [/tex]
Clearly these three terms are making an arithmetic sequence, with :
First term, a = 460 Common difference, d = 451 - 460 = - 9[tex] \\ [/tex]
Now, we have to find 37th term of sequence = [tex] \tt a_{37}[/tex]
[tex] \\ [/tex]
Now, we know that :
[tex] \large \underline{\boxed{\bf{a_{n} = a + (n-1)d}}}[/tex]
[tex] \\ [/tex]
[tex] \tt : \implies a_{37} = a + (37-1)d[/tex]
[tex] \tt : \implies a_{37} = a + 36d[/tex]
[tex] \\ [/tex]
Now, by substituting values of a and d :
[tex] \tt : \implies a_{37} = 460 + 36 \times (-9)[/tex]
[tex] \tt : \implies a_{37} = 460 - 324[/tex]
[tex] \tt : \implies a_{37} = 136[/tex]
[tex] \\ [/tex]
Hence, value of 37th term of given sequence is 136.
PLZ HELP ME PLZ I NEED IT
Answer:
Step-by-step explanation:
The intersection occurs at the point (3,-3) so those are the coordinates.
If
f(x) = x^2 + 2x - 4
and
g(x) = 3x + 1
Find
f(g(x)) = ?
Answer;
f (x) = 2x-4g (x) =x^2
Step-by-step explanation:
The solution is 9x² + 12x - 1
The composition function f ( g ( x ) ) is 9x² + 12x - 1
What is Composition of functions?
Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Given data ,
Let the first function be represented as f ( x )
The value of f ( x ) = x² + 2x - 4
Let the second function be represented g ( x )
The value of g ( x ) = 3x + 1
Now , the composition function f ( g ( x ) ) is calculated by
Substitute the value of x as 3x + 1 , in f ( x ) , we get
f ( g ( x ) ) = f ( 3x + 1 )
f ( 3x + 1 ) = ( 3x + 1 )² + 2 ( 3x + 1 ) - 4
On simplifying the equation , we get
f ( 3x + 1 ) = ( 9x² + 6x + 1 ) + ( 6x + 2 ) - 4
f ( 3x + 1 ) = 9x² + 12x - 1
Therefore , the value of f ( 3x + 1 ) is 9x² + 12x - 1
Hence , the composition function f ( g ( x ) ) is 9x² + 12x - 1
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Somebody help me please
Answer:
The second one
A car corporation produced 1980 fewer cars this month than last.
Write a signed number to represent this month's change in production.
Answer:
there was 1300 fewer cars so your answer would be -1300 :-)
Find the degree of the following polynomial:
7xy223 + 8y5 – 3x4 + 4
Answer:
224
Step-by-step explanation:
polynomial degree:224
leading term:7x^223
leading coefficient:7
write the following decimals in the form of p\ q= 0 and p,q are con-primes 1) 15.265
Given:
The decimal number is 15.265.
To find:
The decimals in the form of [tex]\dfrac{p}{q}[/tex] and p,q are co-primes.
Solution:
Let the decimal number be [tex]x=15.265[/tex].
It can be rewritten as
[tex]x=15.265\times \dfrac{1000}{1000}[/tex]
[tex]x=\dfrac{15265}{1000}[/tex]
[tex]x=\dfrac{5\times 3053}{5\times 200}[/tex]
Cancel out the common factors.
[tex]x=\dfrac{3053}{200}[/tex]
Here, p=3053 and q=200 and the HCF of (p,q) is 1. So, p and q are co-primes.
Therefore, the requited fraction form is [tex]\dfrac{3053}{200}[/tex].
a cylindrical tank has a radius of 3 m and a height of 12 m.
What is the volume of the tank?
Answer:
Volume = 339.12 m^3
Step-by-step explanation:
Volume = Pi(r^2)(height)
Volume = 3.14(3^2)(12)
Volume = 339.12 m^3
URGENT!!!!!!
Use scientific notation to estimate the number of inches in 1,225 miles. Include all calculations in your final answer.1 inch ≈ 1.578 × 10 -5 miles.
Answer: The number of inches in 1225 miles is [tex]7.763\times 10^7[/tex]
Step-by-step explanation:
Scientific notation is defined as the representation of expressing the numbers that are too big or too small and are represented in the decimal form with one digit before the decimal point times 10 raise to the power.
Example: 3000 is written as [tex]3.0\times 10^3[/tex]
Given : [tex]1.578\times 10^{-5}[/tex] miles = 1 inch
Thus 1 mile = [tex]\frac{1}{1.578\times 10^{-5}}=0.634\times 10^5[/tex] inches
1225 miles = [tex]\frac{0.634\times 10^5}{1}\times 1225=776.3\times 10^{5}=7.763\times 10^7[/tex] inches
Help me plz i will give brainlest
Answer:
the answer should be (3,-2)
y=7x+8 can somebody help me
Solve 11=h-14 please
Answer:
25
Step-by-step explanation:
25-14=11
Answer:
25
Step-by-step explanation:
11=25-14
Since 11+14 is 25 then h in 11=h-14 must be 25
The masses of 4 containers loaded on a ship are 28 tonnes,45 tonnes,16.8tonnesand 48500kg .What is 5he total mass in tones?
Step-by-step explanation:
first of all we have to change kg into ton= 48500kg into ton =53.462ton(48500/907.168)
after that we add all the weight of 4 container = 28+45+16.8+53.462
total will be his total mass of tones he had =143.262
Help help help help help help help help help
Answer: a: 23.4
Step-by-step explanation:
Answer:
A.23.4
Step-by-step explanation:
first find the volume of the tank 18x12x25=5400 then find how many gallons of water tank can hold 5400/231=23.4
hope this helps have a blessed day :)
Please help! Thank tou
Answer:
220mL
780mL
600mL
480mL
Step-by-step explanation:
500-280=220
500+280=780
280/8=35, so 35 mL is in one L, 35x5=175
875-175=600
750-280=480
Answer:
Step-by-step explanation:
perrys bikes rents bikes for $18 plus $4 per hour. Lea paid $42 to rent a bike for how many hours did she rent the bike?
Answer:
5 hours 30 min
Step-by-step explanation:
Can someone help me, I forgot how to solve this
Answer:
y = mx + b
Step-by-step explanation:
Select the equivalent expression.
3-5 = ?