For all of the Following use the function LaTeX: P\left(x\right)\:=\:\left(x+3\right)^2+2 . My original vertex is
Answers
Answer:
A) Q(x) = (x + 3)² + 5, and the vertex is (-3, 5)
B) R(x) = (x - 3)² + 2, and the vertex is (3, 2)
C) S(x) = (x - 1)² - 5, and the vertex is (1, -5)
Step-by-step explanation:
The given function is P(x) = (x + 3)² + 2
The given function is a parabolic function in vertex form, f(x) = a·(x - h)² + k, and vertex, (h, k)
By comparison, the vertex of the function P(x) = (x + 3)² + 2 is (-3, 2)
A) A function f(x) translated α units UP gives
f(x) (translated α units UP) → f(x) + α
A translation of the function 3 units UP is given by adding 3 to the given function as follows;
Q(x) = P(x) + 3
∴ Q(x) = (x + 3)² + 2 + 3 = (x + 3)² + 5
Q(x) = (x + 3)² + 5, and the vertex by comparison to f(x) = a·(x - h)² + k, and vertex, (h, k) is (-3, 5)
B) A function f(x) translated b units RIGHT gives;
f(x) translated b units right → f(x - b)
∴ P(x) = (x + 3)² + 2 translated 6 units RIGHT gives;
P(x) = (x + 3)² + 2 (translated 6 units RIGHT) → R(x) = (x + 3 - 6)² + 2 = (x - 3)² + 2
R(x) = (x - 3)² + 2, and the vertex by comparison is (3, 2)
C) A function translated α units DOWN and b units RIGHT is given as follows;
[tex]f(x) \ translated \ by\ \dbinom{b}{a} \rightarrow f(x - b) - a[/tex]
Therefore, the given function, P(x) = (x + 3)² + 2, translated 7 units DOWN and 4 units RIGHT gives;
[tex]P(x) = (x + 3)^2 + 5 \ translated \ by\ \dbinom{4}{-7} \rightarrow P(x - 4) - 7 = S(x)[/tex]
S(x) = P(x - 4) - 7 = (x + 3 - 4)² + 2 - 7 = (x - 1)² - 5
[tex]P(x) = (x + 3)^2 + 5 \ translated \ by\ \dbinom{4}{-7} \rightarrow (x - 1)^2 - 5= S(x)[/tex]
S(x) = (x - 1)² - 5, and the vertex by comparison is (1, -5)
Related Questions
find the values of the sine,cosine and tangent of the following angles.
a.153°
b.204°
c.320°
Answers
Answer:
a)sin153°=0.454
cos153°= -0.891
tan153°= -0.510
b)sin 204°= -0.407
cos204°= -0.914
tan204° = 0.445
c)sin320°= -0.643
cos320° = 0.766
tan320°= -0.839
Step-by-step explanation:
please help asap!!! this is almost due!!!
Answers
Answer:
i'm pretty sure the answer is option C. (x^2 + 9x) = 6^2
Step-by-step explanation:
i'm not 100% sure, but i hope this helps.
please help, i will give brainliest!
Answers
Answer:
yes please, ask the question
ax^2-y^2-x-y factorize
Answers
Answer:
x(ax-1)-y(y+1)
Step-by-step explanation:
you have to group the like terms
ax^2-x-y^2-y
x(ax-1)-y(y+1)
I hope this helps
A cage holds two litter of rats. One litter comprises one female and five males. The other litter comprises seven females and two males. A random selection of two rats is done. Find the probability that the two rats are from the same litter.
Answers
Answer:
The probability that the two rats are from the first litter is 14.28%, and the probability that the two rats are from the second litter is 34.28%.
Step-by-step explanation:
Since a cage holds two litter of rats, and one litter comprises one female and five males, while the other litter comprises seven females and two males, and a random selection of two rats is done, to find the probability that the two rats are from the same litter the following calculation must be performed:
6/15 x 5/14 = 0.1428
9/15 x 8/14 = 0.3428
Therefore, the probability that the two rats are from the first litter is 14.28%, and the probability that the two rats are from the second litter is 34.28%.
What is the range of the absolute value function shown in the graph?
A. 3 ≤ y < ∞
B. -∞ < y ≤ 3
C. -6 ≤ y < ∞
D. -∞ < y < ∞
Answers
Answer:
C
Step-by-step explanation:
as we can see on the graph, the lowest y value is the vertex/corner at x=3, y=-6.
all other y values are above (=are larger) that level.
and it goes up without appearant limit, so up to infinity.
8 lb. 9 oz.
X 15 _______
Answers
Step-by-step explanation:
where is the steps to this question you can't answer it without a question too it SMH
Find the number of all the 2-digit numbers satisfying the
following congruences x = 3(mod7), x = 2(mod5).
OLEASE HELP
Answers
Use the Chinese remainder theorem.
Start with x = 3×5 + 2×7 = 15 + 14 = 29. Now,
• 29 ≡ 15 ≡ 1 (mod7)
• 29 ≡ 14 ≡ 4 (mod5)
Adjust for this by multiplying the first term in x by 3, and the second term by 3 (because 4×3 ≡ 12 ≡ 2 (mod5)).
So now x = 3×5×3 + 2×7×3 = 45 + 42 = 87, and
• 87 ≡ 45 ≡ 3 (mod7)
• 87 ≡ 42 ≡ 2 (mod5)
The CRT then says that x ≡ 87 (mod(7×5)) ≡ 87 (mod35), which is to say any number x = 87 + 35n satisfies both congruences (where n is any integer).
So there are 3 possible 2-digit numbers that work: {17, 52, 87}.
To confirm:
• 17 ≡ 15 + 2 ≡ 2 (mod5) and 17 ≡ 14 + 3 ≡ 3 (mod7)
• 52 ≡ 50 + 2 ≡ 2 (mod5) and 52 ≡ 49 + 3 ≡ 3 (mod7)
• 87 ≡ 85 + 2 ≡ 2 (mod5) and 87 ≡ 84 + 3 ≡ 3 (mod7)
Can someone help me out with this
Answers
We know
[tex]\boxed{\Large{\sf Circumference=\pi d}}[/tex]
[tex]\\ \Large\sf\longmapsto Circumference=\dfrac{22}{7}\times 23.4[/tex]
[tex]\\ \Large\sf\longmapsto Circumference=\dfrac{514.8}{7}[/tex]
[tex]\\ \Large\sf\longmapsto Circumference=73.5in[/tex]
Describe how to determine the average rate of change between x = 4 and x = 6 for the function f(x) = 2x3 + 4. Include the average rate of change in your answer.
Answers
In this question, we want to find the average rate of change of a function over an interval, it represents by how much f(x) changes when x changes by 1.
Average rate of change:
The average rate of change of a function over an interval [a,b] is given by:
[tex]A = \frac{f(b) - f(a)}{b - a}[/tex]
In this question:
[tex]f(x) = 2x^3 + 4[/tex]
Between x = 4 and x = 6, so [tex]a = 4, b = 6[/tex]. Then
[tex]f(a) = f(4) = 2*4^3 + 4 = 132[/tex]
[tex]f(b) = f(6) = 2*6^3 + 4 = 436[/tex]
Then
[tex]A = \frac{436 - 132}{6 - 4} = 152[/tex]
Thus, the average rate of change of the function is of 152, that is, when x changes by 1, y changes by 152.
For another problem involving an average rate of change, you can check https://brainly.com/question/14481908
pls help. even if it’s just one question
Answers
Answer:
a, (5;1) R = [tex]\sqrt{7}[/tex]
b, (-2; 4) R = [tex]2\sqrt{2}[/tex]
c, (4;7) R = 7
d, (-3; -6) R = 7
Step-by-step explanation:
What is the slope of the line?
Answers
Answer:
A number that describes both the direction and the steepness of the line is known as slope of the line .
Square Root of 9801
With Steps Please
Answers
Answer:
99
Step-by-step explanation:
First give it as a product of prime factors. Divide 9801 with prime numbers. The first picture divides 9801 fron prime numbers. Prime numbers are 2,3,5,7, 11. We can only divide using 3 and 11. So we get 3⁴ and 11². The second picture shows how I got the square root of 9801. Square root is ½. So we multiply each power with ½ so we finally get 99. You can recheck for yourself using a calculator. It is 99.
The sets A and L are given below.
A = (a, b, e}
L={c, k,j}
Find the intersection of A and L.
Find the union of A and L.
Write your answer using notation (in roster form)
Help plzzz
Answers
Step-by-step explanation:
A n L =null
A U L= a,b,c,e,k,j
How do you find the volume of this pyramid with what is given? pls
Answers
Answer:
373.3333... in^3
Step-by-step explanation:
V = lwh / 3
V = 10 * 8 * 14 / 3
V = 1120 / 3
V = 373.3333... in^3
I'm probably wrong, I haven't done volume in a looong time.
I miss the equation, point D.
Answers
how to find volume of this prism?
Answers
5984cm^3
Detailed explanation:
The t distribution should be used whenever _____. Group of answer choices the sample size is less than 30 the population is not normally distributed the sample standard deviation is used to estimate the population standard deviation None of the answers is correct.
Answers
Answer:
A: the sample size is less than 30
Step-by-step explanation:
Usually, the t-distribution is used instead of normal distribution in calculation of the mean of a normally distributed population when the sample size is small (n < 30) and if the population standard deviation is not known.
Thus, looking at the options, the correct one is Option A.
que es la razon de una figura semejante
Answers
Answer:
English for fast response
Solve for 2. Round to the nearest tenth, if necessary.
135°
X
78
BO
Submit
answer
Answer: 2 =
Submit Answer
PLS HELP I really need to get this done
Answers
Answer:
x = 63.9
Step-by-step explanation:
Since this is a right triangle, we can us trig functions
cos theta = adj/ hypotenuse
cos 35 = x/78
78 cos 35 =x
x=63.89385
Rounding to the nearest tenth
x = 63.9
Not sure how to do this! I’m supposed to find the area of each shape, but the slits in the shapes are confusing me and I’m not too sure how to do these problems!
Answers
sorry i don't know answe're of this question
The freezing point of oxygen is –218.790C and hydrogen is –252.80C. A lab is lowering the temperature inside a fridge. Which freezes first? How much colder does it have to be for both to freeze?
Answers
Answer:
Oxygen; 34.01°C
Step-by-step explanation:
The oxygen freezes first as it has a higher (warmer) freezing point. For both to freeze, the temperature must drop a further 34.01°C as:
-218.79 - (-252.8)
= 252.8 - 218.79
= 34.01
help someone!! which one is it?
Answers
Answer:
not great with math but I'm sure it's the second circle
A and B can do the work in 8 days ; B and C can do the work in 12 days ;A ,B and C together can finish it in 6 days .In how many days A and C together will do the same work
Answers
The graph represents a functional relationship.
Which value is an input of the function?
Iy
8
0-14
6
0-2
4
.
0 0
2
4
2
4
8 10 12 14 16 18
Х
-2
-6
-B
-10
-12
-14
Answers
I hope this helps I’m sorry if it’s wrong
By analyzing the graph we conclude that the value that is an input is x = 4.
Which value is an input of the function?
For the inputs, we need to look at the horizontal axis. In the graph we can see a closed dot at x > 0 (we can't see the exact value).
This means that the minimum of the domain is positive.
From that, we conclude that the only correct option, that we can be sure that belongs to the domain (set of the inputs), is x = 4, the third option.
If you want to learn about domains:
https://brainly.com/question/1770447
#SPJ5
Find the distance between the two points.
(5,5)
(2.2)
✓ [?]
Enter the number that
goes beneath the
radical symbol.
Answers
Answer:
[tex]{18}[/tex]
Step-by-step explanation:
[tex] \sqrt{(2 - 5) {}^{2} + ( 2 - 5) {}^{2} } [/tex]
[tex] = \sqrt{( - 3) {}^{2} + ( - 3) {}^{2} } [/tex]
[tex] = \sqrt{9 + 9} [/tex]
[tex] = \sqrt{18}[/tex]
Answered by GAUTHMATH
what is the value of x in a decagon
Answers
Answer:
x = 54
y = 144
Step-by-step explanation:
y = (10-2)×180/10 = 144
x = 180-90-(180-144) = 54
Answered by GAUTHMATH
Which complex number is represented by the point graphed on the complex plane below?
On a coordinate plane, a point is graphed at (3, negative 4).
–4 + 3i
3 + 4i
3 – 4i
4 + 3i
Answers
Answer:
3-4i because it is negative in a graph
Answer:
C.) 3-4i
Step-by-step explanation:
because it is negative in a graph
Match the answers……………..
Answers
9 in 8956 = 900
9 in 95675 = 90000
9 = 9 in 124569
9 in 68795 = 90
90000 = 9 in 2549652.........
hope it helps...
G.C.D of 55 and 121 is are
Answers
Common factor of 55 and 121 is 11
Answer:
= 11
Find the Greates Common Deviser :
55 = 5, 11, 55.121 = 11, 121.