Answer:
-1
Step-by-step explanation:
-b+10b+2b+17=6
9b+2b+17=6
11b+17=6
11b=6-17
11b=-11
b=-1
Consider the function f(x)=8x3−2. If f(g(x))=x and g(f(x))=x, find g(x)
I can give you a hint. So when we do the composition of functions, if we plug 2 functions into each other and get x by itself, that means the functions are inversely related.
For this problem, simply find the inverse of f(x).
If you are stuck, I could provide you with a solution below...
f(x) = 8x³ - 2
y = 8x³ - 2
y + 2 = 8x³
(y + 2)/8 = x³
cube root((y + 2)/8) = x
g(x) = cube root((x + 2)/8)
The value of function g(x) after solving will be ∛(x + 2) / 2.
What is Function?
A relation between a set of inputs having one output each is called a function.
Given that;
The value of function,
f(x) = 8x³ − 2
And, f(g(x)) = x and g(f(x)) = x
Now,
Since, f(g(x)) = x
And, f(x) = 8x³ − 2
The substitute x = g (x) in above equation we get;
f (g(x)) = 8 (g(x))³ - 2
x = 8 (g(x))³ - 2
Add 2 both side;
x + 2 = 8 (g(x))³
Divide by 8;
(x + 2)/8 = (g(x))³
Take cube root both side;
∛(x + 2)/8 = g(x)
g(x) = ∛(x + 2) / 2
So, The value of function g(x) after solving will be ∛(x + 2) / 2.
Learn more about the function visit:
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If the diameter of a circle is 10 inches, what is the area of a circle?
Answer:
25[tex]\pi[/tex]
Step-by-step explanation:
because area is pi r^2
Answer:
78.54 or 25π (if in terms of pi)
Step-by-step explanation:
A = πr² = π*5² ≈ 78.53982
What is the factorization of the trinomial below?
x^3 - 12x^2 + 35x
A. (x - 7)(x + 5)
B. x(x - 7)(x - 5)
C. (x^2 - 7)(x + 5)
D. x(x - 7)(x + 5)
mr bernstein owns 14 paintings, but has only enough wall space in his home to display three of them at any one time. How many ways can Mr Bernstein display three paintings in his home
Answer:
2,184
Step-by-step explanation:
PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)
X2 -2x -24=0 is equivalent to
Answer(S):
Answer:
x= 6, -4
Step-by-step explanation:
x^2 - 2x - 24 = 0
(x-6) (x+4) = 0
x = 6, x= -4
Pls help im struggling :p
When creating a histogram it is best to create a range for the different variables that are available.
So for the sake of covering all the possible ranges from 1 - 22, let's divide it into 5 categories.
0 - 5 6 - 10 11 - 15 16 - 20 21 - 25
Now that we have set ranges for the different variables, we then find the frequencies.
0 - 5 : 3
6 - 10 : 2
11 - 15 : 3
16 - 20 : 1
21 - 25 : 3
Now that we have all the values we can then create our histogram.
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i’ll try to mark the right answer as brainliest<: ( 20 points )
Help picture below problem 8
Answer:
Together they equal 180 l so you need to do 180-128 which equals 52. The answer is <D measures 52
Step-by-step explanation:
The following table gives the partial results from a company sampling their employees to see how many years they had worked for the company. The data for both samples was right-skewed.
Department Quality assurance Service
Mean (years) 4.2 2.6
Standard deviation (years) 1.1 1.7
The company wants to use these results in a two-sample t test to see whether there is a significant difference between lengths of time for employees in the quality assurance and service departments.
Which of the following are conditions for this type of test?
Choose all answers that apply:
A. The samples represent no more than 10% percent of the employees in each department.
B. The sample includes equal numbers of employees from each department.
C. The sample includes at least 30 employees from each department.
Using the Central Limit Theorem, it is found that the condition that applies to this test is:
C. The sample includes at least 30 employees from each department.
What does the Central Limit Theorem state?It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.
From this, since we have a skewed variable, it is found that a sample size of at least 30 is needed, hence option C is correct.
More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213
Maggie is making a necklace using string and identical beads.The 12 beads fill 4 inches of the string.How many beads are in 1 inch of string
Answer:
3
Step-by-step explanation:
Divide 12 by 4 since the ratio is 12 to every 4 inches
Special Right Triangles
Isosceles Right Triangle
30-60-90 Triangle
help 1-12 please
Step-by-step explanation:
remember, the sum of all angles in a triangle is always 180°.
1.
since it is a right-angled triangle, and one of the leg angles is 45°, then the other leg angle is also 45°.
which makes this an isoceles triangle.
so, the second leg is 6 too.
the baseline (Hypotenuse) is then per Pythagoras
baseline² = 6² + 6² = 36 + 36 = 72 or 2×36
baseline = sqrt(72) = 6×sqrt(2)
2.
this is then a 30-60-90 triangle.
the left leg (a) is then 2a/2 = 10/2 = 5.
and the bottom leg is 5×sqrt(3).
3.
isoceles triangle.
so, left and right legs (a) are both 3 (from the 3×sqrt(2)).
4.
30-60-90 triangle
upper leg is then 6×sqrt(3).
the baseline is 2 times the left leg : 2×6 = 12
5.
isoceles triangle
both legs are 2 (from the 2×sqrt(2)).
6.
30-60-90 triangle
left leg is 4 (from the 4×sqrt(3)).
the baseline is 2×4 = 8.
7.
isoceles triangle.
6 = a×sqrt(2)
a (both legs) = 6/sqrt(2)
8.
30-60-90 triangle
9 = a×sqrt(3)
a (left leg) = 9/sqrt(3)
baseline = 2a = 2×9/sqrt(3) = 18/sqrt(3)
9.
due to the equal leg angles this is an isoceles triangle.
4 = a×sqrt(2)
a (both legs) = 4/sqrt(2)
10.
30-60-90 triangle
the bottom leg (a) = 2a/2 = 6/2 = 3
the left leg is then 3×sqrt(3)
11.
isoceles triangle
left leg is also 5.
baseline is 5×sqrt(2)
12.
30-60-90 triangle
12 = a×sqrt(3)
a (left leg) = 12/sqrt(3)
the baseline is then 2a = 2×12/sqrt(3) = 24/sqrt(3)
Factor 2x2 + 7x + 10x + 35 by grouping.
Answer:
(x+5)(2x+7)
Step-by-step explanation:
x(2x+7) + 5(2x+7)
(x+5)(2x+7)
I hope this helps!!
A hot air balloon rising vertically is tracked by an observer located 5 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is π4 , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?
Answer:
Step-by-step explanation:
aThe person and the hot air balloon form a right triangle, with the lift-off point as the vertex that form the right angle. If you were to try to solve for the height of the balloon, you would need to use tangent to do so:
tanθ = opp/adj = y/x
y = xtanθ
What this problem ultimately wants to know, is how the distance of the balloon is changing with respect to time: dy/dt. So we need to take the derivative of the above equation (you need to product rule to do so):
dy/dt = (dx/dt)tanθ + xsec2θ(dθ/dt)
We need to find out values for all of the variables:
The observer is not moving, therefore dx/dt = 0.
The observer is standing 4 miles away from the lift-off point, so x = 4.
The angle between the horizontal and the observer's line of sight is π/3, therefore θ = π/3.
The rate of change for the angle, dθ/dt, is 0.1.
Just plug all the numbers in:
dy/dt = (0)tan(π/3) + (4)sec2(π/3)(0.1)
dy/dt = 0 + 1.6
dy/dt = 1.6 mi/min
If the number of equally likely sample outcomes of a single experiment is 4, what is the total number of elements in the sample space if the experiment has 3 stages?
How do I find the volume?
Answer:
150m^3
Step-by-step explanation:
The formula for the volume a triangular prism, like the one you have, is 1/2 base x height. For your prism the volume would be 1/2 (30 x 10) which equals 150. Now just add the measurment m (meters) and you're set.
What is the range of this data set? 64°, 72°, 74°, 68°, 70°, 68°, 68°, 75°, and 44°
Answer:
31
Step-by-step explanation:
First put your numbers in order
44 , 64 , 68 , 68 , 68 , 70 , 72 , 74 ,
Then subtract the Highest and Lowest numbers by each other
75 - 44 = 31
3. For each triangle, find the length of the labeled side.
Answer:
see explanation for detailed analysis
how many times should you expect to see heads if a fair coin is tossed 3500 times?
Answer:
1750
Step-by-step explanation:
If you flip a coin, you should theoretically get heads 50% of the time and tails 50% of the time. So in this case you would get heads 1,750 times.
Triangle ABC has vertices A (-4,4), B(0, 3), and C(1,-1). Find the vertices of triangle A'B'C' after a
reflection across the x-axis.
Reflection is flipping. The x axis is the horizontal line. If you flip a shape over the x axis, it will still stay in the same area for the horizontal points, it's the vertical points that will change, but only their signs will because a reflection isn't moving a shapes location completely. Think of it like Flipping the page of a book. If you drew a triangle on your book page and flipped the page, it would still be in the same area just the opposite side/direction. Just make the y axis (second number in brackets) points the opposite sign to solve
-4,-4 0,-3. 1,1
find m<DAC= x in circle O given that m<BOA= 66° and m<DB= 20°. (The figure is not drawn to scale.)
Answer:
66+20+x=180(sum of angle in a triangle)
x=180-(66+20)
x=180-86
x=94
Determine the type of symmetry of r =5-sin11ø from the equation, if any. Make sure to confirm graphically. Symmetric with respect to the:
A) pole
B) line /2
C) polar axis
D) none of these
well, let me not bore you to death on how we test it and test it.
[tex]\underline{\textit{testing for symmetry to the }\frac{\pi }{2}~line\qquad \qquad r=-r~~,~~\theta =-\theta } \\\\\\ r=5-sin(11\theta )\implies (-r)=5-sin[11(-\theta )]\implies -r=5-sin(-11\theta ) \\\\\\ \stackrel{symmetry~identity}{-r=5-\stackrel{\downarrow }{[-sin(11\theta )]}}\implies\implies r=-5-sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underline{\textit{testing for symmetry to the polar axis}\qquad \qquad \theta =-\theta} \\\\\\ r=5-sin(11\theta )\implies r=5-sin[11(-\theta )]\implies r=5-sin(-11\theta ) \\\\\\ r=5-[-sin(11\theta )]\implies r=5+sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underline{\textit{testing for symmetry to the pole}\qquad \qquad r=-r} \\\\\\ r=5-sin(11\theta )\implies -r=5-sin(11\theta )\implies r=-5+sin(11\theta )\qquad \textit{no dice}[/tex]
so the symmetry tests didn't pass, notice the picture below though, looks a bit deceiving, it looks as if it'd have π/2 symmery, but it doesn't show in the test.
The sum of three consecutive odd integers is 39. Find the three integers.
Answer:
11 13 15
Step-by-step explanation:
n + n + 2 + n + 4 = 39
3n + 6 =39
3n = 33
n = 11
the three odd integers are 11 , 13 ,15
The square root of the cube of 4 is equal to
3 or 4 or 16 or 8 or 2
Answer:
Step-by-step explanation: 1.587401052
Answer:
8
Step-by-step explanation:
this means
[tex] \sqrt{ {4}^{3} } [/tex]
4³ = 4×4×4 = 64
the square root of 64 is 8.
Can you find the missing side length?
Step-by-step explanation:
you need to calculate all the sides that are given to get the other side
It seems like they have shown you how to calculate so give it a try
Please help i need it done before tomorrow. thank you.
What is the area of the trapezoid?
Enter your answer in the box.
Answer:
Step-by-step explanation:
A = [tex]\frac{b_{1} +b_{2} }{2}[/tex] × h
~~~~~~~~
[tex]b_{1}[/tex] = 15 in.
[tex]b_{2}[/tex] = 6 + 15 + 6 = 21 in.
h = 18 in.
A = [tex]\frac{15+21}{2}[/tex] × 18 = 324 in.²
Westford Lake was originally blue because it only had 810 algae plants. Then towns and farms cropped up by the lake. This caused 9,772 more algae plants to grow, which turned the lake green. How many algae plants are now in Westford Lake?
Answer:
10,582 algae plants
Step-by-step explanation:
10,582 algae plants. You have to add 810 and 9,772 to get 10,582 algae plants.
if 60% of class is girls, and there are 30 students in the class. How many boys are in class?
Answer:
12
Step-by-step explanation:
60% of 30 is 18 (girls)
40% of 30 is 12 (boys)
Answer:
12 boys
Step-by-step explanation:
60% is the same as 6/10, and if you make the denominator 30, you must make the denominator multiply by three as well as the numerator. this makes the number 18/30 girls in a class. if you subtract the girls from the total number of people, you get 12 boys, or 40% of the class.
you can also find that 100% - 60% = 40%, which is equal is equal to 4/10. After it's multiplied by 3 again, it becomes 12/30 or 12 boys.
Help picture below problem 11
The sum of all the angles of any triangle is 180 degrees
--> Therefore the missing angle is:
x = 180 - 60 - 75 = 45
Hope that helps!
The sum of the angles of a triangle is 180 degrees
--> to put that into mathematical terms
Angle O + Angle K + Angle C = 180
60 + 75 + Angle C = 180
Angle C = 45 degrees
Therefore the missing angles' measure is 45 degrees
Hope that helps!
Using the equation 5x=4y, if y=10, what is x?
Answer:
x = 8
Step-by-step explanation:
plug 10 into the other equation for y then solve...
5x = 4(10)
5x = 40
x = 8 [Answer]
PLEASE RATE!! I hope this helps!!
If you have any questions comment below
Answer:
x = 8
Step-by-step explanation:
Using the equation 5x = 4y, if y = 10, what is x?
5x = 4y
5x = 4(10) <== substitute 10 for y
5x = 40
/5 /5 <== divide both sides by 5
x = 8 <== value of x, our final answer
Hope this helps!
Find the sum of the arithmetic sequence 1, 4, 7, 10, ...,94; n=32
Answer:
Step-by-step explanation:
hello :
the sum is : Sn = n/2(U1 + Un ) and U n = U1+(n-1)r
given : U1 = 1 r=4-1=7-4=...= 3 n= 32
so : U 32 = 1+(32-1)3= 94
S32 = 32/2 (1+94) = 1520