Answer:
0.267949192 8s the value of tan 195°
match each function with its inverse function. use function composition to determine your answers.
QUESTION 1
[tex] \boxed {f(x) = 2x + 6 \to \: g(x) = \frac{1}{2}x - 3 } [/tex]
The reason is that:
[tex]g(f(x)) = 2( \frac{1}{2} x - 3) + 6[/tex]
Expand:
[tex]g(f(x)) = x - 6+ 6 [/tex]
[tex]g(f(x)) = x[/tex]
QUESTION 2
[tex]\boxed {f(x) =3 - 2x \to \: g(x) = - \frac{1}{2}(x - 3)} [/tex]
The reason that
[tex]g(f(x)) = - \frac{1}{2} (3 - 2x - 3)[/tex]
[tex]g(f(x)) = - \frac{1}{2} (- 2x )[/tex]
[tex]g(f(x)) =x[/tex]
QUESTION 3
[tex]\boxed {f(x) = \sqrt[3]{3x}+ 2 \to \: g(x) = \frac{ {(x - 3)}^{3} }{3} } [/tex]
The reason is that:
[tex]f(g(x)) = \sqrt[3]{ \frac{3 {(x - 2)}^{3} }{3} } + 2[/tex]
[tex]f(g(x)) = x-2 + 2[/tex]
[tex]f(g(x))=x[/tex]
QUESTION 4
[tex]\boxed {f(x)=3\sqrt[3]{x + 2} \to \: g(x) = \frac{1}{27} {x}^{3} - 2} [/tex]
The reason is that
[tex]f(g(x)) = 3 \sqrt[3]{ \frac{1}{27} {x}^{3} - 2 + 2} [/tex]
[tex]f(g(x)) = 3 \sqrt[3]{ \frac{1}{27} {x}^{3} } [/tex]
[tex]f(g(x)) = 3 \times \frac{1}{3} x[/tex]
[tex]f(g(x)) =x[/tex]
What function does this graph represent?
Answer:
I'm not sure if this is the answer answer but this what the graph is a parabola
The function represented by the graph is y = 1/4(x - 2)^2 + 1
What function does this graph represent?
From the question, we have the following parameters that can be used in our computation:
The graph
The graph is the graph of a quadratic function
By definition:
A quadratic function is represented as
y = a(x - h)^2 + k
Where
Vertex = (h, k)
From the graph, we have
Vertex = (2, 1)
So, we have
y = a(x - 2)^2 + 1
Using the point (0, 2) on the graph, we have
a(0 - 2)^2 + 1 = 2
4a + 1 = 2
4a = 1
a = 1/4
So, we have
y = 1/4(x - 2)^2 + 1
Hence, the function this graph represent is y = 1/4(x - 2)^2 + 1
Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30?
To change the graph of f(x) = [tex]x^2[/tex] into g(x) = 4[tex]x^2[/tex] + 24x + 30, the transformations include a vertical stretch by a factor of 4 and a shift to the left by 3 units and up by 6 units. Completing the square helps identify these shifts.
Explanation:To transform the graph of f(x) = [tex]x^2[/tex] into the graph of g(x) = 4[tex]x^2[/tex] + 24x + 30, we can analyze the changes applied. First, the coefficient of x2 in g(x) is 4, which means the original parabola is vertically stretched by a factor of 4. Second, the term 24x indicates a horizontal transformation, specifically a shift, which is revealed when we complete the square.
To complete the square for the quadratic part of g(x), we rewrite the equation as 4([tex]x^2[/tex] + 6x) + 30 and add and subtract the square of half the coefficient of x inside the parentheses, giving us 4((x + 3)2 - 9) + 30. This simplifies to 4(x + 3)2 + 6, indicating that the graph of f(x) was also shifted to the left by 3 units and up by 6 units.
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what is 11/7 as a mixed number
Answer:
1 4/7
Step-by-step explanation:
11/7 As A Mixed Number Would Be 1 And 4/7
I need help with geometry, please Find area of kite.
Answer:
90 units²
Step-by-step explanation:
The area (A) of a kite is calculated as
A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ← diagonals
d₁ = 3 + 3 = 6 and d₂ = 20 + 10 = 30, hence
A = 0.5 × 6 × 30 = 90 units²
Two functions are shown below. For which value of x does f(x) = g(x)?
f(x) = 4x-4, g(x) = 2(3)^x-6
This question was on my Math 1 review so I think that the answer should be relatively uncomplicated. I looked around and only managed to find stuff dealing with logarithms, which I don't understand. Any help would be appreciated.
Answer:
x=0 and x=1
Step-by-step explanation:
4(1)-4=0
2(3)^(1)-6=0
4(0)-4=-4
2(3)^(0)-6=-4
A group surveyed a mix of people below and above 40 years old about whether or not they visit a dentist once a year. This table gives the survey results.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 8 22
Above 40 17 13
Which table shows the relative frequency of people above 40 years old who do not visit a dentist once a year? Round your answers to the nearest hundredth.
Answer: is D
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.27 0.73
Above 40 0.57 0.43
Work: 8+22=30 17+13=30 turn into a fraction then simplify to get answer;
22/30 simp= 73.0 (0.73)
13/30 simp= 43.0 (0.43)
8/30 simp= 26.667 (0.27)
17/30 simp= 56.667 (0.57)
Answer with Step-by-step explanation:
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 8 22
Above 40 17 13
Relative frequency of people above 40 years old who do not visit a dentist once a year
=Number of people above 40 years old who do not visit a dentist yearly/Number of people above 40
=13/(17+13)
=13/30
=0.43
Hence, Relative frequency of people above 40 years old who do not visit a dentist once a year is:
0.43
The first equation in the following system gives the company's cost of making x purses. The second equation gives the company's income for selling x purses.
3111-04-10-10-07
You used substitution to obtain the equation
0 = -0.01x2-10x+1,989 from the system.
What are the solutions to the system of equations?
(-23,400, 3,400) and (-1,170,170)
(-1,170, -23,400) and (170, 3,400)
(274, 726) and (5,480, 14,520)
(274, 5,480) and (726, 14,520)
The solution (-1170, -23,400) should be eliminated in the context of this situation.
The company will break even when its cost of making x purses equals its income for selling x purses. The company must make and sell purses to break even. (Just need help with the last part of this.)
1st Answer: B.) (-1,170, -23,400) and (170, 3,400)
2nd Answer: 170
Answer:
that answer is verified 100% correct
Step-by-step explanation:
PLEASE HELP
find the vertex of f(x)=x^2+2x+3 (make sure you show your work)
Answer:
(- 1, 2)
Step-by-step explanation:
Given a quadratic in standard form y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
f(x) = x² + 2x + 3 ← is in standard form
with a = 1 and b = 2, hence
[tex]x_{vertex}[/tex] = - [tex]\frac{2}{2}[/tex] = - 1
Substitute x = - 1 into f(x) for corresponding value of y
f(- 1) = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2
vertex = (- 1, 2 )
An inconsistent linear system has _ solutions
Answer:
zero im pretty sure
Step-by-step explanation:
Answer:
An inconsistent linear system has no solution(s).
Step-by-step explanation:
Just took the test.
2200 dollars is placed in an account with an annual interest rate of 7.25%. How much
will be in the account after 29 years, to the nearest cent?
Answer:
A = $2200(7.612) = $16,747.28
Step-by-step explanation:
You don't say whether this is simple interest or compound interest. I will assume you meant compound interest, for which the appropriate formula is
A = P(1 + r)^t, where P is the principal amount, r is the interest rate as a decimal fraction, and t is the time in years. Then:
A = $2200(1 + 0.0725)^29, or
A = $2200(1.0725)^29, or
A = $2200(7.612) = $16,747.28
The amount in the account after 29 years will be approximately $8484.64.
Explanation:To calculate the amount of money that will be in the account after 29 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount ($2200 in this case), r is the annual interest rate (7.25% or 0.0725 as a decimal), n is the number of times interest is compounded per year (in this case, it's compounded annually, so n is 1), and t is the number of years (29 in this case). Plugging in the values, we get:
A = 2200(1 + 0.0725/1)^(1*29)
A = 2200(1.0725)^29
A ≈ $8484.64
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3. What’s the answer to this question?
Answer:
Opt B. y=5-3x
Step-by-step explanation:
We need to write the given equation in slope-intercept form, so we can obtain the slope and the 'y' axis intercept point.
To do this, we need to isolate 'y' variable with a possitive sign, hence we perform the following operation:
Subtraction of -5 in both sides of equality sign.
-y=3x-5
Lets multiply by -1 the equation from above:
y= 5-3x.
From the above we can find the slope, is the coefficient of x. in this case -3
And the y-intercept point is 5.
Which one show factor pairs of 16
Answer:
There is not enough information
Step-by-step explanation:
If you wanted to find all the factors, here’s a list.
1,2,4,8,16
Find the value of x? I need help I don't understand what to do
Answer: (1) 120° (2) 6.5
Step-by-step explanation:
(1)
[tex]\dfrac{major\ arc-minor\ arc}{2}=intercepted\ angle\\\\\\\dfrac{(360-x)-x}{2}=60[/tex]
360 - 2x = 120
- 2x = -240
x = 120
(2)
2.5² + 6² = x²
6.25 + 36 = x²
42.25 = x²
6.5 = x
1 year, 27 weeks =
weeks
Answer:
Around 79.17 weeks
Step-by-step explanation:
Answer:
if you want to know how many weeks are in one year and 27 weeks, i can help out
Step-by-step explanation: 1 year has 365 days in it and one week has 7 days in it. Divide 365 by 7.
365/7= about 52 weeks.
52+27=79 weeks.
The exact amount of weeks is 79.177457
hope this helped!!
If the original dimensions of a rectangular prism are doubled, how will the volume be affected? 2 times bigger 4 times bigger 6 times bigger 8 times bigger
The answer is 8 times bigger.
Hope this helps!
Answer:
2times bigger.
Step-by-step explanation:
Original volume of a rectangular prism = length × width × height
V = lwh... (1)
If the original dimension is doubled
New volume V2 = 2l × 2w × 2h
V2 = 2(lwh)...(2)
Taking the ratio of both volumes
V2/V = 2(lwh)/lwh
V2/V = 2
V2 = 2V
This shows that the new volume was two times bigger than the original volume
the area of a square is 64 cm. what is the length of one side of the square?
Answer:
8cm
Step-by-step explanation:
Since the area of a square is Side X Side (s x s) it is also s². The s² is also equivalent = 64cm². To find the length of a side you do the √64cm² and you get 8cm for a side. Great Job!
Write 1,000 as a power of 100
Answer:
10 or 100
Step-by-step explanation:
Answer:
100^1,000 if that's what you mean or 100 ^10 to make 1,000
Step-by-step explanation:
IF RIGHT PLZ MARK BRAINLIEST!! PLZZZ!!!!!!!!!!!!!
Solve x⁄6 = 20.
A. x = 14
B. x = 26
C. x = 120
D. x = 3
Answer:
120
Step-by-step explanation:
x/6=20
×=20×6
=120
The data represents the number of traffic tickets written by two police officers in one day over the course of a week. Officer 1: 21, 11, 14, 16, 10, 18, 5 Officer 2: 16, 19, 20, 17, 6, 13, 23
(a) Draw a box and whiskers plot for each officer (b) Compare the median values of the data sets. What does this comparison tell you in terms of the situation the data represent?
Answer and Explanation :
Given : The data represents the number of traffic tickets written by two police officers in one day over the course of a week.
Officer 1: 21, 11, 14, 16, 10, 18, 5
Officer 2: 16, 19, 20, 17, 6, 13, 23
To find : (a) Draw a box and whiskers plot for each officer
(b) Compare the median values of the data sets. What does this comparison tell you in terms of the situation the data represent?
Solution :
a) We plot the box plot with the help of graphing calculator of both data.
Refer the attached figure below.
Figure 1 shows the data 1 with Median 14.
Figure 2 shows the data 2 with Median 17.
b) On comparing the median of both Officer's are different first officer has 14 median and second officer has 17 median.
A rectangular garden sits next to a house. Three sides of the garden are fenced, and the fourth side is the house. The length of the garden is 9 meters. A total of 21.5 meters of fencing is used. If w stands for the width of the garden in meters, which equation can be used to find its width?
A. 2w+9=21.5 C. 2w - 21.5 = 9
B. 2w + 18 = 21.5 D. 2w +21.5=18
the equation that can be used to find width is B
Answer:
It's a
Step-by-step explanation:
I did it
PLEASE HELP Match each function formula with the corresponding transformation of the parent function y = - (x + 2)2. 1. y = - (x + 4)2 Reflected across the x-axis and the y-axis 2. y = - (x + 2)2 - 2 Translated right by 2 units 3. y = (x - 2)2 Translated left by 2 units 4. y = 2 - (x + 2)2 Translated down by 2 units 5. y = -x2 Translated up by 2 units 6. y = (x + 2)2 Reflected across the x-axis
So we are given the following function: [tex]y=-(x + 2)^{2}[/tex].
Before we can solve this problem, we need to know the following:
Given g (x) = f (x) + k; The graph of g(x) equals f(x) shifted k units vertically. If k > 0, the base graph shifts k units upward, and if k < 0, the base graph shifts k units downward. Given g(x) = f (x - k); The graph of g(x) equals f(x) shifted k units horizontally. If k > 0, the base graph shifts k units to the right, and if k < 0, the base graph shifts k units to the left.The reflection of the point (x,y) across the x-axis is the point (x,-y).The reflection of the point (x,y) across the y-axis is the point (-x,y).Know we can solve the problem!
1. [tex]y=-(x + 4)^{2}[/tex]. Translated left by 2 units.
2. [tex]y=-(x + 2)^{2} - 2 [/tex] Translated down by 2 units
3. [tex]y=(x - 2)^{2}[/tex] Reflected across the x-axis and the y-axis
4. [tex]y= 2-(x + 2)^{2}[/tex] Translated up by 2 units
5. [tex]y=-(x)^{2}[/tex] Translated right by 2 units
6. [tex]y=(x + 2)^{2}[/tex] y = (x + 2)2 Reflected across the x-axis
For the simple harmonic motion equation d=4sin(pi/8t) what is the maximum?
Answer:
Maximum value of the function is 4.
Step-by-step explanation:
Given function of simple harmonic motion is [tex]d=4\sin\left(\frac{\pi}{8}t\right)[/tex].
Now we need to find about what is the maximum value of [tex]d=4\sin\left(\frac{\pi}{8}t\right)[/tex].
We know that value of sine function varies from -1 to 1.
that means for any value of t, maximum value of sine function is 1.
[tex]\sin\left(\frac{\pi}{8}t\right) \leq 1[/tex]
[tex]4 \sin\left(\frac{\pi}{8}t\right) \leq 4[/tex]
[tex]d \leq 4[/tex]
Hence maximum value of the function is 4.
formula for area of polygon
Answer:
The formula for the area of a polygon is 1/2*a*p.
a = apothem, which is a line segment that is the shortest distance from the center to a side.
p = perimeter
Hope this helps. :)
Answer:
Step-by-step explanation:
There's no one formula for finding the area of any polygon.
There are specialized formulas for finding the area of a square, of a triangle, of a trapezoid, etc. Beyond these, you have to invent approaches, such as breaking up an octagon into 8 triangles, finding the area of 1 such triangle, and then multiplying that area by 8.
Type an inequality statement using the < or > for the inequality symbols solve for x 6x-11-13x<7-5x
Answer:
-9 < x
Step-by-step explanation:
6x-11-13x<7-5x
Combine like terms
-11-7x<7-5x
Add 7x to each side
-11-7x+7x<7-5x+7x
-11 < 7+2x
Subtract 7 from each side
-11-7 < 7-7+2x
-18 < 2x
Divide by 2
-18/2 < 2x/2
-9 < x
****BRAINLIEST The graph shows the solution for which inequalities?
y ≥ x + 2 and y ≤ 2x + 3
y ≥ x - 2 and y ≤ 2x - 3
y ≥ 3x - 2 and y ≤ x + 3
y ≤ 3x - 2 and y ≥ x + 3
Answer:
[tex]y\geq 3x-2[/tex] and [tex]y\leq \frac{1}{2} x+3[/tex]
Step-by-step explanation:
Blue:
The inequality for the blue line is
[tex]y\geq 3x-2[/tex]
Yellow
The inequality for the yellow line is
[tex]y\leq \frac{1}{2} x+3[/tex]
This means that the correct answer is the third option,
[tex]y\geq 3x-2[/tex] and [tex]y\leq \frac{1}{2} x+3[/tex]
The graph shows the solution for the inequalities y ≥ 3x - 2 and y ≤ x + 3.
How can find the inequalities?The inequalities can be found by substituting the coordinates of a point within the shaded area in both inequalities and seeing if they are satisfied.
We can find the inequalioties as follows:The options are given.
Let us take the options one by one:
Option A: y ≥ x + 2 and y ≤ 2x + 3Now, substitute (0,0) in the inequalities:
0 ≥ 2 and 0 ≤ 3
This is not true.
Option B: y ≥ x - 2 and y ≤ 2x - 3Now, substitute (0,0) in the inequalities:
0 ≥ - 2 and 0 ≤ - 3
This is not true.
Option C: y ≥ 3x - 2 and y ≤ x + 3Now, substitute (0,0) in the inequalities:
0 ≥ - 2 and 0 ≤ 3
This is true.
Option D: 0 ≤ - 2 and 0 ≥ 3Now, substitute (0,0) in the inequalities:
0 ≥ - 2 and 0 ≤ - 3
This is not true.
Therefore, we have found that the inequalities are y ≥ 3x - 2 and y ≤ x + 3. The correct answer is option C.
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r(x)=x-3
s(x)= 4x²
write the expressions for (s+r)(x) and (s-r(x) and evaluate (s.r)(2)
What we are given:
r( x ) = x - 3
s( x ) = 4x²
We have to find:
( s + r )( x ) = ( x - 3 + 4x² )
→ 4x² + x - 3
( s - r )( x ) = ( x - 3 - 4x² )
→ -4x² + x - 3
For the last function, I am confused whether it is a multiplication or composite function, so I am going to do both.
Multiplication:
( x - 3 ( 4x² ))( 2 )
( 4x³ - 12x² )( 2 )
4(2)³ - 12(2)²
4(8) - 12(4)
32 - 48
→ -4
Composite function:
r(s(x))(2) = r(4x²) = 4x² - 3 = 4(2)² - 3 = 4(4) - 3 = 16 - 3
→13
Final answer:
The expressions for (s+r)(x) is 4x^2 + x - 3 and (s-r)(x) is 4x^2 - x + 3. The value of (s.r)(2) is 16.
Explanation:
To find the expression for (s+r)(x), we need to add the functions s(x) and r(x). Adding the two functions, we get (s+r)(x) = 4x^2 + (x-3). Simplifying this expression, (s+r)(x) = 4x^2 + x - 3.
To find the expression for (s-r)(x), we need to subtract the function r(x) from s(x). Subtracting the two functions, we get (s-r)(x) = 4x^2 - (x-3). Simplifying this expression, (s-r)(x) = 4x^2 - x + 3.
To evaluate (s.r)(2), we need to substitute 2 for x in the expression s(x) * r(x). Substituting 2 for x in the expression 4x^2, we get (s.r)(2) = 4(2)^2 = 16.
PLEASE HELP FAST In the diagram below, Xy and yz are tangent to o. What is the measure of
Xwz?
Answer:
240
Step-by-step explanation:
since that arc is 120 you subtract that form 360 and voila!
Which is the same as moving the decimal point 3 places to the right in a decimal number
Answer:
Multiplying the decimal number by 1000
Step-by-step explanation:
consider the number 12.2345.
For you to move the decimal point three places to the right, you have to multiply the number with 10³=1000
12.2345×1000= 12234.5
The decimal has moved from three places as it has skipped three places values to the right.
The choice which is the same as moving the decimal point 3 places to the right in a decimal number is; Multiplying the number by 1000.
Which is the same as moving the decimal point 3 places to the right in a decimal number?According to the task content;
We are required to determine which is the same as moving the decimal point 3 places to the right in a decimal number.Since, a decimal point movement one space to the right indicates a multiplication by 10, hence, it follows that the required multiplication is 1000.
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The graph of y =
[tex] \sqrt[3]{x} [/tex]
is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph of f(x)?
ANSWER
See attachment.
EXPLANATION
The given parent function is:.
[tex]y = \sqrt[3]{x} [/tex]
If this graph is reflected over the x-axis and then translated down 2 units to form f(x), then the f(x) has equation
[tex]f(x) = - \sqrt[3]{x} - 2[/tex]
The graph of this function is shown in the attachment.
Answer:
the second graph
Step-by-step explanation: