Answers
#b
Attached
#a
y=x²y=2(x-2)²+1So
General equation of parabola
y=a(x-h)²+klet's note the changes
The value of a is changed from 1 to 2 ,hence change in focus .x² is turned to (x-2)² ,hence change in x axis (2 units right)+1 is added hence the y coordinate of vertex goes 1 units up .Vertex of first one is at (0,0) but second one is at (2,1)
Answer:
Transformation of f(x) to g(x):
Translation of 2 units rightVertical stretch by a factor of 2Translation of 1 unit up(see attachment for graphs)
Step-by-step explanation:
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\!\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
Parent function:
[tex]f(x)=x^2[/tex]
Translated 2 units to the right:
[tex]\implies f(x-2)=(x-2)^2[/tex]
Stretched vertically by a factor of 2:
[tex]\implies 2f(x-2)=2(x-2)^2[/tex]
Translated 1 unit up:
[tex]\implies 2f(x-2)+1=2(x-2)^2+1[/tex]
Therefore, the transformation of f(x) to g(x) is:
Translation of 2 units rightVertical stretch by a factor of 2Translation of 1 unit upLearn more about translations here:
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Related Questions
there are a total of 126 cats and dogs at an animal shelter. for every 5 dogs, there are 4 cats . how many cats are there in the shelter?
Answers
5+4 = 9
How many iterations are there?
126/9 = 14
How many cats in 14 iterations?
14* 4 = 56
5star:)
what is the cost of each shirt using the equation 10x+40?
1 shirt=
5 shirts=
10 shirts=
50 shirts=
Answers
The cost of 1 shirt would be 10
you would need to multiply the cost of one shirt by the number of shirts bought (x)
Which expression represents a number that is 4 times as great as the quotient of 25 and 5?
A. (25 x 5) x 4
B. 4 ÷ ( 25 ÷ 5 )
C. 4 x ( 25 ÷ 5 )
D. (25 ÷ 5 ) ÷ 4
Answers
Answer:
(25 ÷ 5 ) ÷ 4
Step-by-step explanation:
solve the equation for the variable. Then plug that variable value into the expression and simplify to get the answer.
Answer:
C
Step-by-step explanation:
the quotient of 25 and 5 is 25 ÷ 4 , then multiply this by 4 , so
4 × (25 ÷ 5 ) → C
In a candy box, there are 5 times as many candies with nuts as candies without nuts. There are 24 candies in the box: How many candies with nuts are in the box?
Answers
Answer:im pretty sure its 20
Step-by-step explanation: because 4x5=20 and theres 24
re for Question 1: of 5 points)
Sandy has a ladder that is 16.5 ft long. He wants to lean the ladder against a vertical wall so that the top
the ladder is 15.9 ft above the ground. For safety reasons, he wants the angle the ladder makes with th
ground to be no greater than 76°. Will the ladder be safe at this height? Show your work and draw a diagram
to support your answer.
Answers
The ladder will be safe at this height .
What is trigonometric ratios?There are six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
According to question
Sandy has a ladder whose length = 16.5 feet
He wants to lean the ladder against a vertical wall 15.9 feet above the ground.
And he wants the angle the ladder makes with the
ground to be < 76°.
As Perpendicular = 15.9 feet
and Hypotenuse = 16.5
Sin Ф = [tex]\frac{Perpendicular }{Hypotenuse}[/tex]
Sin Ф = [tex]\frac{15.9}{16.5}[/tex]
Sin Ф = 0.9636
Therefore, Ф ≈ 74.49 (approx.)
That means it is safe .
Hence, The ladder will be safe at this height as it is not greater than 76° .
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# SPJ2
The scientist had a 35% saline solution that he mixed with 10 milliliters of a 75% saline solution to get a 40% saline solution. How many milliliters of the 35% solution were used?
Answers
x mL of the 35% saline solution contains 0.35x mL of salt.
10 mL of the 75% solution contains 0.75 • 10 mL = 7.5 mL of salt.
After mixing, the scientist would have a total volume of (x + 10) mL. We know its concentration is 40%, so it contains 0.40 (x + 10) mL of salt.
The total amount of salt before and after mixing must be the same, so
0.35x + 7.5 = 0.40 (x + 10)
Solve for x :
0.35x + 7.5 = 0.40x + 4.0
0.10x = 3.5
x = 35
The scientist used 35 mL of the 35% solution.
HELP NOwwwwWWWW ILL GIVE BRAINLIEST
line A is a perpendicular to line B. if the slope of line A is 3/7 what is the slope of line b?
Answers
Answer: -7/3
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals of each other.
PLEASE HELP 90 POINTS & WILL GIVE BRAINLIEST
In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Alexander sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
8 visitors purchased no costume.
340 visitors purchased exactly one costume.
28 visitors purchased more than one costume.
If next week, he is expecting 600 visitors, about how many would you expect to buy more than one costume? Round your answer to the nearest whole number.
Answers
Answer:
45 people
Step-by-step explanation:
1) Add all of the origanal visitors (376)
2) Find the ratio (28/376) = 0.0744
3) Either 28/376 * 600 OR 0.0744 * 600 (I would recomend the fraction for more accurate answers, but because it says to round to the nearest whole number either will work, but you should still use fraction)
4) 44.6908
5) Round to 45 people
One can find an angle bisector using a compass and a straightedge construction or a straightedge and tracing paper construction. True or false?
Answers
Answer: true
Step-by-step explanation:
Answer:
it's true
Step-by-step explanation:
25POINTSSSS
does anyone have the answers to End of Semester Test: Geometry B
Edmentum/plato
Answers
Answer:
nah i need them too
Step-by-step explanation:
plato
PLS HELP
No links pls and Ty<333!!!
A circle's diameter is 8 centimeters.
What is the circle's area (use 3.14 for pi and round to the nearest
tenth)?
Answers
Answer:
16 pi cm^2
Step-by-step explanation:
Area = pi r^2 r = 1/2 d
= pi (4^2) = 16 pi cm^2
Four more than three times a number x is 48
Answers
Answer:
x = 14 2/3
Step-by-step explanation:
4 more, +4
3 times a number x
3 * x
= 48
3x + 4 = 48
3x = 44
x = 44/3
x = 14 2/3
Four more 3x+4
3x+4=48
someone please help me with this problem
Answers
Answer:
B
Step-by-step explanation:
x = y²z² ( multiply both sides by y ) , then
xy = y² × y × z² = y³z²
ASAP
Which statement is an example of causation?
o When it rains, the playground gets wet.
The height of children increases as their running speed increases.
O The increase in the number of ice-cream cones a vendor sells causes an increase in temperature.
O Students who eat a good breakfast each day are more physically active than those who skip breakfast.
Answers
Answer:
I beleive the fist one is.
Step-by-step explanation:
The first one is a possibility, the second has a correlaition, and the third, I believe is a correlation.
PLEASE HELP URGENT
Given \tan \theta =0.6, find the value of b.
Answers
Answer:
b=8.5cm
Step-by-step explanation:
tanx (this represents tan theta, it's just easier to type) is equal to 0.6 and since the tanx ratio is opp/adj, we know that opp/adj = 0.6
To find what b is (adjacent as it is adjacent to the angle being used and it is not the hypotenuse), we just have to rearrange.
0.6=5.1/adj
to solve for adj, we can switch 0.6 and adj. (This works because to get adj by itself on one side you would multiply it to the other side and then divide 0.6 from both sides --> simple algebra)
so then you have
adj=5.1/0.6
adj=8.5cm
(if you want to check your solution you can use pythagoeran theorem, a^2+b^2=c^2) and sub everything in and make sure all the numbers equal the right thing!
Please help me and the answer is not 6.4
Answers
Answer:
4.9
Step-by-step explanation:
The box-and-whisker plot below represents some data set. What is the range of the
data?
Answers
Explanation: range is the highest number subtracted by the lowest number, therefore it would be 85-35 which equals 50!
In order for the data in the table to represent a linear function with a rate of change of 5, what must be the value of a? a = 3 a = 8 a = 18 a = 33
Answers
To represent the linear function in order for the data the value of a=18.
What is a linear function?
In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
It is given that for a linear function the value is changing at the rate of 5 so we can see in the table as the function independent value is changing then the value of the dependent linear function increases by 5.
So the value of a will be equal to 18.To represent the linear function in order for the data the value of a=18.
To know more about linear function follow
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If 3K is x% of 3000, then an expression for x is..?
Answers
well, let's see it this way, we know that 3000 is the 100%, and we also know that 3K is x% of 3000, so then
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 3000 & 100\\ 3K& x \end{array} \implies \cfrac{3000}{3K}=\cfrac{100}{x} \\\\\\ 3000x=300K\implies x=\cfrac{300K}{3000}\implies x=\cfrac{K}{10}[/tex]
Find the perimeter of the rectangle
Answers
Answer:
Step-by-step explanation:
perimeter = 2 (l + b)
= 2 {(2/3x+ 10) + (1/3x + 5)}
= (4/3x + 10) + (2/3 + 10)
= 4/3x + 20 +2/3 + 10
= 6/3x + 30
= 3x + 30
For triangle xyz , the measures of angles x,y, and Z are known. Which method should be used to start solving triangle xyz?
law of sines
law of cosines
neither law can be used
both laws can be used
Answers
Answer:
neither law can be used
Step-by-step explanation:
to solve the given triangle the given measurements are not enough (one more value should be known).
Graph the points K(-2, -1), L(-1, 2), M(2, 4), and N(1,1) in desmos geometry. What is the distance from point M to point N?
options:
4
√10
3
√8
Answers
Quadrilateral KLMN has vertices K(-2,-2), L(1,1), M(0,4), and N(-3,5)
It is first translated by (x + 2,y - 1)
then
K(-2,-2) ---> K'(-2 + 2,-2 - 1) = (0,-3)
L(1,1), ---> L'(1 + 2,1 - 1) = (3,0)
M(0,4), ---> M' (0 + 2,4 - 1) = (2,3)
and
N(-3,5) ---> N' (-3 + 2,5 - 1) = (-1,4)
and then translated by (x - 3,y + 4)
K'(0,-3) ---> K''(0 - 3,-3 + 4) = (-3,1)
L'(3,0) ---> L''(3 - 3,0 + 4)= (0,4)
M'(2,3) ---> M'' (2 - 3, 3 + 4)= (-1,7)
and
N'(-1,4) ---> N'' (-1 - 3,4 + 4) = (-4,8)
the coordinates of K" L" M" N" after both translations are
K''= (-3,1)
L''= (0,4)
M''= (-1,7)
and
N'' = (-4,8)
hope im right if not im sorry but it going to be right cuz im good at this stuff for you
which expression is equivalent to (7x^3)^2(x^8)1/2
Answers
Answer: 49x^14
Step-by-step explanation:
Triangle N P O is shown. Line O N extends through point M to form exterior angle P N M. Angle N P O is 38 degrees. Angle P O N is 39 degrees. Exterior angle P N M is x degrees.
Which statement about the value of x is true?
x > 38
x < 39
x < 77
x > 103
Answers
Answer: x > 38
Step-by-step explanation:
Charlie buys a bag of 15 tangerines for 2.85
Find the unit price in dollars per tangerine.
If necessary, round your answer to the nearest cent.
Answers
$2.85/15 = $0.19 per tangerine.
what is -4(x+3) - 12x + 5 distributed
Answers
-4x -12- 12x + 5 (Distributed)
-16x - 7 ( Combine like terms)
Answer-16x - 7.
You plan on supplementing your income. you would like to withdraw a semiannual salary of $6,951.20 from an account paying 1.75% interest, compounded semiannually. determine the amount needed in the account such that you can withdraw the needed amount at the end of each period for 15 years. round to the nearest cent. a. $239,364.66 b. $182,713.25 c. $184,311.99 d. $237,288.39
Answers
The amount needed in the account is 182,713.25 dollars then the correct option is B.
What is a monthly payment?The term loan refers to a sort of credit vehicle in which a sum of money is lent to another party in exchange for the value or principal amount being repaid in the future.
Then the formula of monthly payment (MP) will be
[tex]\rm MP = P \times \dfrac{r(1+r)^n}{(1+r)^n - 1}\\[/tex]
The formula can be written as
[tex]\rm P = MP \times \dfrac{(1+r)^n-1}{r(1+r)^n}\\[/tex]
You plan on supplementing your income. you would like to withdraw a semiannual salary of $6,951.20 from an account paying 1.75% interest, compounded semiannually.
The amount needed in the account is such that you can withdraw the needed amount at the end of each period for 15 years will be
MP = $6951.20
r = 0.00875
n = 30
Then we have
[tex]\rm P = 6951.20 \times \dfrac{(1+0.00875)^{30}-1}{0.00875(1+0.00875)^{30}}\\\\P = \$182713.25[/tex]
More about the monthly payment link is given below.
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Which system of equations can be used to find the roots of the equation 4 x squared = x cubed 2 x? startlayout enlarged left-brace 1st row y = negative 4 x squared 2nd row y = x cubed 2 x endlayout startlayout enlarged left-brace 1st row y = x cubed 4 x squared 2 x 2nd row y = 0 endlayout startlayout enlarged left-brace 1st row y = 4 x squared 2nd row y = negative x cubed minus 2 x endlayout startlayout enlarged left-brace 1st row 4 x squared 2nd row y = x cubed 2 x endlayout
Answers
The system of equations can be used to find the roots of the considered equation is y = 4+x^2 and y= x^3 + 2 + x
How can we find the solution to an equation?We do same operations on both the sides so that equality of both expressions doesn't get disturbed. Solving equations generally means finding the values of the variables used in it for which the considered equation is true.
Sometimes we can find such value, and sometimes it is not possible at all, or sometimes, there are infinite number of solutions.
For the given case, we are given with the equation [tex]4+x^2 = x^3 + 2 + x[/tex]
We can take two equations as:
[tex]y = 4+x^2 \\y= x^3 + 2 + x[/tex]
And when we will try to solve this system of equation, we will end up substituting the value of y in terms of x, and therefore, ending up on the same equation [tex]4+x^2 = x^3 + 2 + x[/tex]
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Answer:
D
y=4x^2
y=x^3+2x
Step-by-step explanation:
im trying to pass just like yall, Good luck to all
WILL GIVE BRAINLIEST - What is the length of the hypotenuse of the base?
*Picture linked below*
Answers
Answer:
4sqrt(2) cm
Step-by-step explanation:
a^2 + b^2 = c^2
4^2 + 4^2 = c^2
32 = c^2
sqrt(32) = c
c = 4sqrt(2)
(7x-3) (3x-17) y find value of x and y
Answers
Answer:
[tex]21yx^{2}-128xy+51y[/tex]
Step-by-step explanation: