Given:
The functions are:
[tex]h(x)=x^2[/tex]
[tex]k(x)=-\dfrac{1}{7}x^2[/tex]
To find:
The transformation from the graph of h to the graph of k.
Solution:
The transformation is defined as
[tex]k(x)=ah(x+a)=[/tex] .... (1)
Where, a is stretch factor
If 0<|a|<1, then the graph compressed vertically by factor |a| and if |a|>1, then the graph stretch vertically by factor |a|.
If [tex]a<0[/tex], then the graph of h(x) reflected across the x-axis.
We have,
[tex]h(x)=x^2[/tex]
[tex]k(x)=-\dfrac{1}{7}x^2[/tex]
It can be written as
[tex]k(x)=-\dfrac{1}{7}h(x)[/tex] ...(2)
On comparing (1) and (2), we get
[tex]a=-\dfrac{1}{7}<0[/tex]
The graph of h(x) reflected across the x-axis.
[tex]|a|=\dfrac{1}{7}<1[/tex]
So, the graph is compressed vertically.
It means the graph of h reflection over the x-axls and a vertical stretch to get the graph of k.
Therefore, the correct option is B.
In ΔDEF, the measure of ∠F=90°, the measure of ∠D=54°, and EF = 39 feet. Find the length of FD to the nearest tenth of a foot.
Answer:
yuphsjsjanananajqjqjwjejreis
Answer:
28.3
Step-by-step explanation:
(Absolute value inequalities) 50 points!
-6|4p+2|+8 > -34
Answer
p>5/4 or p<-9/4
Step-by-step explanation:
1. first isolate the absolute value by subtracting 8 and then dividing by -6
2. you then split the absolute value inequality into 4p+2>7 and 4p+2<-7
3. When you solve those, you get p>5/4 and p< -9/4
Answer:
[tex] - \frac{9}{4} < p < \frac{5}{4} [/tex]
Step-by-step explanation:
1) Subtract 8 from both sides.
[tex] - 6 |4p + 2| > - 34 -8[/tex]
2) Simplify -34 - 8 to -42.
[tex] - 6 |4p + 2| > - 42[/tex]
3) Divide both sides by -6.
[tex] |4p + 2| < \frac{ - 42}{ - 6} [/tex]
4) Two negative numbers makes a positive.
[tex] |4p + 2| < \frac{42}{6} [/tex]
5) Simplify 42/6 to 7.
[tex] |4p + 2| < 7[/tex]
6) Rewrite the inequality without the absolute value.
[tex] - 7 < 4p + 2 < 7[/tex]
7) Subtract 2 from the whole equation.
[tex] - 7 - 2 < 4p < 7 - 2[/tex]
8) Simplify.
[tex] - 9 < 4p < 5[/tex]
9) Divide the whole equation by 4.
[tex] - \frac{9}{4} < p < \frac{5}{4} [/tex]
Therefor, the answer is - 9/4 < p < 5/4.
Somebody help me out please
Answer:
So need me to solve it?
Step-by-step explanation:
A quilt was originally priced at $25 but went on sale for 20% off. If Pamela bought the quilt and paid 10% sales tax, how much did she pay in total?
Answer:
22.20
Step-by-step explanation:
25 × .80 ×1.10=22.20
Riki cuts two decagons out of cardboard.Then he glues yarn around theedges. How much yard does riki use if each edge of the decagon is 8 centimeter?
Answer:
0.00736 Sq. Yard size of decagon is used
Step-by-step explanation:
Given
Each side of Decagon [tex]= 8[/tex] centimeter
Area of Decagon
[tex]A = \frac{5}{2} a \sqrt{5+2\sqrt{5} }[/tex]
Here a is the side of decagon
Substituting the given values, we get -
[tex]A = 2.5 * 8 * 3.077\\A = 61.54[/tex]Square centimeter
1 square centimeter = 0.000119599 square yard
Area in yard = 0.00736 Sq. Yard
In the year 2006, a person bought a new car for $24000. For each consecutive year after that, the value of the car depreciated by 10%. How much would the car be worth in the year 2010, to the nearest hundred dollars?
Answer:
$15,746.400
Step-by-step explanation:
The computation of the car value in the year 2010 is shown below:
Since the new car brought in the year of 2006 at $24,000
And, it would be depreciation by 10%
So, in the year 2010 the car value would be
= $24,000 × (1 - 0.10)^4
= $24,000 × 0.9^4
= $15,746.400
Diego had 3 letters D,E, and N. How many orders/sets can Diego create with the letters?
3
9
6
12
Answer:
6
Step-by-step explanation:
DEN
DNE
NDE
NED
END
EDN
Suppose m is the line with equation y = −4 and ΔA'B'C is mapped to ΔA"B"C" by applying the glide reflection T⟨3, 0⟩ ∘ Rm. What are the coordinates of ΔA″B″C″?
Answer:
[tex]A" = (-1,-3)[/tex] [tex]B" = (-2,-6)[/tex] [tex]C" = (1,-7)[/tex]
Step-by-step explanation:
Given
See attachment for graph
[tex]A' = (-4, -5)[/tex]
[tex]B'=(-5, -2)[/tex]
[tex]C' = (-2, -1)[/tex]
First, reflect over [tex]y =-4[/tex]
The rule is: [tex](x,y) ==> (x,y+h)[/tex]
Where [tex]h =-4[/tex]
So:
[tex]A' = (-4, -5)[/tex] [tex]==>[/tex] [tex]A'' = (-4, 1-4) = (-4, -3)\\[/tex]
[tex]B'=(-5, -2)[/tex] [tex]==>[/tex] [tex]B'' = (-5, -2-4) = (-5, -6)[/tex]
[tex]C' = (-2, -1)[/tex] [tex]==>[/tex] [tex]C'' = (-2, -3-4) = (-2, -7)[/tex]
So, we have:
[tex]A" = (-4,-3)[/tex] [tex]B" = (-5,-6)[/tex] [tex]C" = (-2,-7)[/tex]
Next translate A''B''C'' by T(3, 0), we have;
The rule is: [tex](x,y)==>(x+3,y+0)[/tex]
[tex]A" = (-4,-3)[/tex] [tex]==>[/tex] [tex]A" = (-4 + 3, -3+0) = (-1, -3)[/tex]
[tex]B" = (-5,-6)[/tex] [tex]==>[/tex] [tex]B" = (-5 + 3, -6) = (-2, -6)[/tex]
[tex]C" = (-2,-7)[/tex] [tex]==>[/tex] [tex]C" = (-2 + 3, -7) = (1 , -7)[/tex]
Hence, A''B''C'' are:
[tex]A" = (-1,-3)[/tex] [tex]B" = (-2,-6)[/tex] [tex]C" = (1,-7)[/tex]
I would also appreciate anyone that can help w this :)
Answer:
Step-by-step explanation:
Each term is 4 more than the preceding term.
Common difference d = 4
nth term = a₁ + (n-1)d = -6 + (n-1)4
a₁₀ = -6 + 9⋅4 = 30
Among all positive numbers , whose sum is 12, find those for which the product of the two numbers and their difference is largest. (Hint: Let =− and express in terms of alone.)
Answer: The numbers whose sum equals 12 and whose product and difference is largest is 6 and 6
Step-by-step explanation:
numbers whose sum is 12
Sum =12 Product Difference Product- Difference
11 +1 11 10 1
10 +2 20 8 12
9 +3 27 6 21
8 +4 32 4 28
7 +5 35 2 33
6+6 36 0 36
The numbers whose sum equals 12 and whose product and difference is largest is 6 and 6
plss. pa answers ?
thanks po
Answer:
Graph 3Line starting at x = -2
Domain: x ≥ -2Range: y ≥ 0Graph 4Vertical line
Domain: x = 3Range: y = any real numberGraph 5Quadratic function with negative leading coefficient and max value of 3
Domain: x = any real numberRange: y ≤ 3Graph 6Curve with non-negative domain and min value of -2
Domain: x ≥ 0Range: y ≥ -2Graph 7Line with no restriction
Domain: x = any real numberRange: y = any real numberGraph 8Quadratic function with positive leading coefficient and min value of 4
Domain: x = any real numberRange: y ≥ 4Graph 9Parabola with restriction at x = -4
Domain: x = any real number except -4Range: y = any real numberGraph 10Square root function with star point (2, 0)
Domain: x ≥ 2Range: y ≥ 0Tell whether the rates are equivalent. Justify your answer.
60 centimeters every 2.5 years
30 centimeters every 15 months10
Answer:
30 centimeters every 15 months is correct the other one isnt.
Step-by-step explanation:
The rates are equivalent, and we can justify this by converting the time units to make a valid comparison.
To determine if the rates are equivalent, we need to compare the ratios of centimeters to time between the two rates.
Rate 1: 60 centimeters every 2.5 years
Rate 2: 30 centimeters every 15 months
Let's convert both rates to a common time unit to make a valid comparison. We can convert years to months or months to years.
Converting Rate 1:
2.5 years * 12 months/year = 30 months
Rate 1 becomes 60 centimeters every 30 months.
Now, let's compare the rates:
Rate 1: 60 centimeters every 30 months
Rate 2: 30 centimeters every 15 months
The rates are equivalent because the ratios of centimeters to time are the same for both rates. In both cases, the ratio is 2 centimeters per month.
Therefore, the rates are equivalent, and we can justify this by converting the time units to make a valid comparison.
To know more about "rates." here
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Help!!!!!!!!!!! I need help with my math sorry if too easy.
Answer:
whats the question? I'll help!!
A certain bacteria can double in 6 hours. How long will it
take the bacteria to increase from 20 to 140? (Hint: First find
the constant k)
Answer:
it can go to 160 on in 18 hours so the the answer could be 26 hours
HELP ASAP
Expand the expression: 3(n+4)
Multiply 3 and n, and 3 and 4.
3n+12
---
hope it helps
5(y+ 2/5) = -13
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Simplify combining the like terms : a-(a-b)-b-(b-a)
Answer:
: a-(a-b)-b-(b-a)
-a^2+ab+b^2+ab
Guided Practice
Use the formula to estimate the temperature when n = 120 chirps/min. Round to the nearest whole number, if necessary.
The forumla F = n/4 + 37 estimates the temperature F in degrees Fahrenheit when crickes chirp n times per minute.
A.
157°F
B.
67°F
C.
39.25°F
Answer:
B.
67°F
Step-by-step explanation:
I'M SORRY BUT I CAN'T FIND IT ANYWHERE AND I HAVE NO IDEA WHAT IT IS
ahhhhhhhhhh
Please help will mark brainiest
Answer:
length= 34
width= 61.5
if vx=11u and vz=u+30 find the value of u that makes the Quadrilateral WXYZ a parallelogram
Plz helpppp if u cannn
Answer:
57ft
Step-by-step explanation:
Since 5 inches = 3 ft and there is a total of 95 inches, we need to first figure out how many 5s are in 95.
95/5=19
There are 19 5s in 95.
Now we multiply 19 by 3 to find out how many feet it represents.
19x3=57
find the value of given expression
[tex] \sqrt{66 + 15} [/tex]
Answer:
9
Step-by-step explanation:
Hope this helps, let me know if im correct
Answer:
√{66+15}=√81=√9²=±9 is your answer
In AVWX, v = 21 cm, w = 64 cm and X=23°. Find the length of x, to the nearest
centimeter.
Answer:45cm
Step-by-step explanation:delta
Need help will give you the brainliest
Answer:
164,160 just do 96% of it
Answer:
i think its 164,160
Step-by-step explanation:
A pond contains 3,000,000 liters of water. How is this number written in scientific notations?
So bassically I have to write this as it is too short, but the answer is = 3 x 10^7
The given number 3,000,000 written in scientific notations is [tex]3\times10^6[/tex].
Given that, a pond contains 3,000,000 liters of water.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.57×10³.
The given number written in scientific notations is
3,000,000 = [tex]3\times10^6[/tex]
Therefore, the given number 3,000,000 written in scientific notations is [tex]3\times10^6[/tex].
To learn more about the Scientific notation visit:
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Solve the inequality. Graph the solution.
z−2−6≤−2
Answer:
z ≤ 6
Step-by-step explanation:
z − 2 − 6 ≤ −2
z - 8 ≤ −2
z ≤ -2 + 8
z ≤ 6
≤ means it will be a CLOSED circle and go in the LEFT direction starting AT 6
In a circle with a radius of 2725 in., an arc is intercepted by a central angle of 7π/4 radians.
What is the arc length?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
Answer:
150.56
Step-by-step explanation:
I took the test
Answer:
150.56
Step-by-step explanation:
Who know this please I need help asap !!
Answer:
Step-by-step explanation:
[tex]tan\theta =\frac{12}{5}\\ \\ \theta =tan{-1}\frac{12}{5}\\ \\ \theta =67.38^o\\ \\ \theta \approx 67^o[/tex]
Can someone pls help me with this?
Answer:
14 is A
15 is B
Step-by-step explanation:
14 . the answer is a because first off the slope is negative so we can immediately eliminate B and D second of all the slope is 1/2 so we can eliminate D and get that the answer has to be a
15. answer is B for this one because first of all the slope is negative so we can immediately eliminate A and c and second of all the y-intercept would be 120 because 90 is what x=1 so we would have to add 30 to get what y would equal when x=0 if that makes sense
m<2 = 50°, m<1=
40
90
50
130
Answer:
50
Step-by-step explanation: