Answers
Answer:
(1,4)
Step-by-step explanation:
Let's this of [tex]y=\sqrt{x}[/tex] which is it's parent function.
How do we get to [tex]y=-\sqrt{x-1}+4[/tex] from there?
It has been reflected about the a-axis because of the - in front of the square root.
It has been shifted right 1 unit because of the -(1) in the square root.
It has been moved up 4 units because of the +4 outside the square root.
In general:
[tex]y=a(x-h)^2+k[/tex] has the following transformations from the parent:
Moved right h units if h is positive.
Moved left h units if h is negative.
Moved up k units if k is positive.
Moved down k units if k is negative.
If [tex]a[/tex] is positive, it has not been reflected.
If [tex]a[/tex] is negative, it has been reflected about the x-axis.
[tex]a[/tex] also tells us about the stretching factor.
The parent function has a starting point at (0,0). Where does this point move on the new graph?
It new graphed was the parent function but reflected over x-axis and shifted right 1 unit and moved up 4 units.
So the new starting point is (0+1,0+4)=(1,4).
Answer:
(1, 4)Step-by-step explanation:
You must specify the domain of the function.
We know: There is no square root of the negative number.
Therefore
x - 1 ≥ 0 add 1 to both sides
x ≥ 1
The first argument for which the function exists is the number 1.
We will calculate the function value for x = 1.
Put x = 1 to the equation of the function:
[tex]y=-\sqrt{1-1}+4=-\sqrt0+4=0+4=4[/tex]
Therefore the starting point of the graph of given function is (1, 4).
Related Questions
Someone Please Help Me With This
n
_ = 1 6
3
Answers
Answer:
n=48
Step-by-step explanation:
n
_ = 1 6
3
Multiply each side by 3
n/3 * 3 = 16*3
n = 48
find the perimeter of the triangle to the nearest unit with vertices A(-2,4) B(-2,-2) and C(4,-2)
Answers
Answer:
20
Step-by-step explanation:
Use the distance equation to find the length of each side:
d = √((x₂ − x₁)² + (y₂ − y₁)²)
where (x₁, y₁) and (x₂, y₂) are the points (the order doesn't matter).
AB:
d = √((-2 − (-2))² + (-2 − 4)²)
d = 6
BC:
d = √((4 − (-2))² + (-2 − (-2))²)
d = 6
AC:
d = √((-2 − 4)² + (4 − (-2))²)
d = 6√2
So the perimeter is:
AB + BC + AC
6 + 6 + 6√2
≈ 20
please help!!!
Which ordered triple represents all of the solutions to the system of equations shown below?
2x - 2y - z = 6
-x + y + 3z = -3
3x - 3y + 2z = 9
a(-x, x + 2, 0)
b(x, x - 3, 0)
c(x + 2, x, 0)
d(0, y, y + 4)
What is the solution to the system of equations shown below?
2x - y + z = 4
4x - 2y + 2z = 8
-x + 3y - z = 5
a (5, 4, -2)
b (0, -5, -1)
c No Solution
d Infinite Solutions
Answers
Answer:
b (x, x - 3, 0)d Infinite SolutionsStep-by-step explanation:
1. A graphing calculator or any of several solvers available on the internet can tell you the reduced row-echelon form of the augmented matrix ...
[tex]\left[\begin{array}{ccc|c}2&-2&-1&6\\-1&1&3&-3\\3&-3&2&9\end{array}\right][/tex]
is the matrix ...
[tex]\left[\begin{array}{ccc|c}1&-1&0&3\\0&0&1&0\\0&0&0&0\end{array}\right][/tex]
The first row can be interpreted as the equation ...
x -y = 3
x -3 = y . . . . . add y-3
The second row can be interpreted as the equation ...
z = 0
Then the solution set is ...
(x, y, z) = (x, x -3, 0) . . . . matches selection B
__
2. The second equation is 2 times the first equation, so the system of equations is dependent. There are infinite solutions.
A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce: f(n) = 9(0.7)n What does the number 9 in the function represent?
Answers
Answer:
9 represents the initial height from which the ball was dropped
Step-by-step explanation:
Bouncing of a ball can be expressed by a Geometric Progression. The function for the given scenario is:
[tex]f(n)=9(0.7)^{n}[/tex]
The general formula for the geometric progression modelling this scenario is:
[tex]f(n)=f_{0}(r)^{n}[/tex]
Here,
[tex]f_{0}[/tex] represents the initial height i.e. the height from which the object was dropped.
r represents the percentage the object covers with respect to the previous bounce.
Comparing the given scenario with general equation, we can write:
[tex]f_{0}[/tex] = 9
r = 0.7 = 70%
i.e. the ball was dropped from the height of 9 feet initially and it bounces back to 70% of its previous height every time.
Give an example of each of the following or explain why you think such a set could not exist.
(a) A nonempty set with no accumulation points and no isolated points
(b) A nonempty set with no interior points and no isolated points
(c) A nonempty set with no boundary points and no isolated points
Answers
The nonempty set with no accumulation points and no isolated points cannot exist. An example of a nonempty set with no interior points and no isolated points is the set of all rational numbers within the interval (0, 1). A nonempty set with no boundary points and no isolated points also cannot exist.
Explanation:(a) A nonempty set with no accumulation points and no isolated points cannot exist. An accumulation point in a set is a value that every open interval contains a point from the set different than itself. An isolated point is a point that has an open interval containing only itself. Every point in a nonempty set must be either an accumulated point or an isolated point.
(b) An example of a nonempty set with no interior points and no isolated points is the set of all rational numbers within the interval (0, 1). An interior point is a point where an open interval around the point lies completely within the set, which doesn't exist for this set. Also, this set does not contain any isolated points because between any two rational numbers, there always exists another rational number.
(c) A nonempty set with no boundary points and no isolated points cannot exist. A boundary point is a point that every neighborhood contains at least one point from the set and its complement. If a set does not have any boundary points, it means it cannot be separated from its complement, so it must be an empty set.
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HELP!
What is the solution set of |2x + 1| > 5?
A {x|1 < x < –3}
B {x|–1 < x < 3}
C {x|x > 2 or x < –3}
D {x|x < 2 or x > –3}
Answers
Answer:
Answer choice C
Step-by-step explanation:
When the values of x are greater than 2, the solution works. When the values oclf x are less than 3, the solution also works. :)
Answer:
C
Step-by-step explanation:
Inequalities of the form | x | > a have solutions of the form
x < - a OR x > a, thus
2x + 1 < - 5 OR 2x + 1 > 5 ( subtract 1 from both sides of both )
2x < - 6 OR 2x > 4 ( divide both sides of both by 2)
x < - 3 OR x > 2
Solution set is
{ x | x > 2 or x < - 3 } → C
Help please if you can?
If f(x) = -2x - 5 and g(x) = x^4 what is (gºf)(-4)
Answers
Answer:
81
Step-by-step explanation:
g(x) = x^4 put f(x) in for x in g(x)
g(f(x)) = (f(x))^4 Substitute the value for f(x) which is (-2x - 5) put - 4 in for the x in f(x)
g(f(x) = (-2x - 5)^4
g(f(x)) = (- 2*(- 4) - 5)^4 Combine
g(f(x)) = (8 - 5)^4 Subtract
g(-4) = (3)^4 Raise 3 to the 4th power
g(-4) = 81 Answer.
A firefighter determines that 350 feet of hose is needed to reach a particular building. If the hoses are 60 feet in length, what is the minimum number of lengths of hose needed?
Answers
Answer:
6 lengths
Step-by-step explanation:
You essentially want the smallest integer solution to ...
60x ≥ 350
x ≥ 350/60
x ≥ 5 5/6
The smallest integer solution to this is x = 6.
The minimum number of lengths of hose needed is 6.
_____
Informally, you know that dividing the required total length by the length of one hose will tell you the number of required hoses. You also know the ratio 350/60 is equivalent to 35/6 and that this will be between 5 and 6. (5·6 = 30; 6·6 = 36) The next higher integer value will be 6.
If angle A is 45 degrees and angle B is 60 degrees.
Find sin(A)cos(B)
½ (sin(105) + sin(345))
½ (sin(105) - sin(345))
½ (sin(345) + cos(105))
½ (sin(345) - cos(105))
Answers
Answer:
(1/2)(sin(105°) +sin(345°))
Step-by-step explanation:
The relevant identity is ...
sin(α)cos(β) = (1/2)(sin(α+β) +sin(α-β))
This falls out directly from the sum and difference formulas for sine.
Here, you have α = 45° and β = 60°, so the relevant expression is ...
sin(45°)cos(60°) = (1/2)(sin(45°+60°) +sin(45°-60°)) = (1/2(sin(105°) +sin(-15°))
Recognizing that -15° has the same trig function values that 345° has, this can be written ...
sin(45°)cos(60°) = (1/2)(sin(105°) +sin(345°))
Given that angle A is 45 degrees and angle B is 60 degrees, we use the product-to-sum identity in Trigonometry to find sin(A)cos(B). The correct answer after simplifying the formula sin(A)cos(B) = ½ [sin(A + B) + sin(A - B)] is ½ [sin(105) + sin(345)].
Explanation:In Mathematics, especially Trigonometry, there is a formula known as product-to-sum identities. One of the identities is Sin(A)Cos(B) = ½ [sin(A + B) + sin(A - B)].
Given that angle A is 45 degrees and angle B is 60 degrees, we will find sin(A)cos(B) by substituting A and B in the formula.
On substitution you get ½ [sin(45 + 60) + sin(45 - 60)], which simplifies to ½ [sin(105) + sin(-15)]. Note that sin(-15) is equivalent to sin(345) in the unit circle, therefore the expression further simplifies to ½ [sin(105) + sin(345)].
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Please help with these partial sum questions??
Answers
a. If c is a constant then the sum of such constants is the same as multiplication of constants. Therefore [tex]\Sigma_{k=1}^{n}c=nc[/tex]
b. [tex]\Sigma_{k=1}^{n}k=1+2+3+\dots+\infty=\infty[/tex]
c. [tex]\Sigma_{k=1}^{n}k^2=1+4+9+\dots+\infty=\infty[/tex]
d. [tex]\Sigma_{k=1}^{n}k^3=1+8+27+\dots+\infty=\infty[/tex]
Hope this helps.
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