Answer:
[tex]f(g(2)) = 2[/tex]
Step-by-step explanation:
Given
[tex]x \to f(x)[/tex]
[tex]-6 \to 1[/tex]
[tex]-3 \to 2[/tex]
[tex]g(x) = f^{-1}(x)[/tex] --- inverse
Required
[tex]f(g(2))[/tex]
For two functions f(x) and g(x) where f(x) and g(x)are inverse;
[tex]f(g(x)) = x[/tex]
So, by comparison:
[tex]f(g(2)) = 2[/tex]
hlo all here is your question in this question the chooses are below
Answer:
1. centimeter
2. kilogram
3. gram
4. milligram
5. centimeter
6. meter
7. kilometer
8. liter
9. kiloliter
10. millimeter
Step-by-step explanation:
you really cannot answer that yourself ?
you don't understand yet the difference between length or distance, area, volume, weight, ... ?
I how this helps then
1. is length, and it is rather short. so, we use a rather small unit to express it.
2. is weight. and a big one. so, we use a bigger unit.
3. is weight. but a small one.
4. is weight. and a really tiny one.
5. is length. similar dimension of size as the finger.
6. is length. and a bigger one.
7. is length. and a truly big one.
8. is volume. liquid volume at that. but rather small.
9. is volume. and again liquid volume. also very big. but still, kiloliter is practically never used by anybody ...
10. is length. and a very tiny one.
what is answer if 2xyx5
Answer:
Answer is 3bu2(DeEZ)=1
Step-by-step explanation:
solve the quadratic equation x²+x-2
Step-by-step explanation:
ii hope this will help you
please mark me as brinalist friend
Answer:
x = 1
x = -2
Step-by-step explanation:
Hello!
We can solve the quadratic by factoring the equation.
Standard Form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]
Given our equation: [tex]x^2 + x - 2 = 0[/tex]
a = 1b = 1c = -2Find two numbers that multiply up to "ac" but add up to "b". The two numbers are 2 and -1. Expand x into 2x and -1x.
Factor by Grouping[tex]x^2 + x - 2 = 0[/tex][tex]x^2 + 2x - x - 2 = 0[/tex][tex]x(x + 2) -1(x + 2) = 0[/tex][tex](x - 1)(x + 2) = 0[/tex]Set each factor to 0 and solve for x:
[tex]x - 1 = 0\\x = 1[/tex][tex]x + 2 = 0\\x = -2[/tex]The solutions for x are 1 and -2.
Please help with this question!?
Answer:
7
Step-by-step explanation:
Substitute 2 for x.
[tex] {2}^{2} + 3 = 7[/tex]
Find the area of the figure
Please help :)
9514 1404 393
Answer:
372 m²
Step-by-step explanation:
A vertical line down the center of the figure will divide it into two congruent trapezoids, each with bases 13 and 18, and height 12.
The area of one of them is ...
A = 1/2(b1 +b2)h
So, the area of the two of them together is ...
A = (2)(1/2)(b1 +b2)h = (b1 +b2)h
A = (13 m + 18 m)(12 m) = 372 m²
the number of cases of a new diease can be modeled by the quadratic
Step-by-step explanation:
The number of cases of a new disease may be modeled by the quadratic regression equation y=-2x^2+44x+8 , what is the best prediction for the number of cases after 20 years ( the carrot symbol (^) means the following number is the exponent)
I’m confused with this question
9514 1404 393
Answer:
(a) max: None; min: -5
(b) max: 5; min: None
Step-by-step explanation:
a) The upward pointing arrow on the end of the graphed curve tells you that the graph extends upward indefinitely. There is no absolute maximum value.
The solid dot at (-4, -5) is the lowest point on the graph. That tells you the absolute minimum is -5.
__
b) The solid dot at (-4, 5) is the highest point on the graph. That tells you the absolute maximum is 5.
The open dot at (3, -5) is the lowest point on the graph. This means values of the function can be arbitrarily close to -5, but -5 is not one of them. There is no absolute minimum value.
If it is 9:00 what time will it be 25 minutes earlier
Answer:
8:35
Step-by-step explanation:
Answer:
8:35
Step-by-step explanation:
-25+60=35
9h-1h(60 above)=8h
=8:35
Solve the inequality and write the solution set using both set-builder notation and interval notation. -3a-15≤-2a+6
Answer:
[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex] --- set builder
[tex][-21,\infty)[/tex] --- interval notation
Step-by-step explanation:
Given
[tex]-3a - 15 \le -2a + 6[/tex]
Required
Solve
Collect like terms
[tex]-3a + 2a \le 15 + 6[/tex]
[tex]-a \le 21[/tex]
Divide by -1
[tex]a \ge - 21[/tex]
Rewrite as:
[tex]-21 \le a[/tex]
Using set builder
[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex]
Using interval notation, we have:
[tex][-21,\infty)[/tex]
math help plz
how to solve parabola and its vertex, how to understand easily and step by step with an example provided please
Answer:
The general equation for a parabola is:
y = f(x) = a*x^2 + b*x + c
And the vertex of the parabola will be a point (h, k)
Now, let's find the values of h and k in terms of a, b, and c.
First, we have that the vertex will be either at a critical point of the function.
Remember that the critical points are the zeros of the first derivate of the function.
So the critical points are when:
f'(x) = 2*a*x + b = 0
let's solve that for x:
2*a*x = -b
x = -b/(2*a)
this will be the x-value of the vertex, then we have:
h = -b/(2*a)
Now to find the y-value of the vertex, we just evaluate the function in this:
k = f(h) = a*(-b/(2*a))^2 + b*(-b/(2*a)) + c
k = -b/(4*a) - b^2/(2a) + c
So we just found the two components of the vertex in terms of the coefficients of the quadratic function.
Now an example, for:
f(x) = 2*x^2 + 3*x + 4
The values of the vertex are:
h = -b/(2*a) = -3/(2*2) = -3/4
k = -b/(4*a) - b^2/(2a) + c
= -3/(4*2) - (3)^2/(2*2) + 4 = -3/8 - 9/4 + 4 = (-3 - 18 + 32)/8 = 11/8
If a projectile is fired with an initial speed of vo ft/s at an angle α above the horizontal, then its position after t seconds is given by the parametric equations x=(v0cos(α))t andy=(v0sin(α))t−16t2
(where x and y are measured in feet).
Suppose a gun fires a bullet into the air with an Initial speed of 2048 ft/s at an angle of 30 o to the horizontal.
(a) After how many seconds will the bullet hit the ground?
(b) How far from the gun will the bullet hit the ground? (Round your answer to one decimal place.)
(c) What is the maximum height attained by the bullet? (Round your answer to one decimal place.)
Answer:
a) The bullet hits the ground after 64 seconds.
b) The bullet hits the ground 113,511.7 feet away.
c) The maximum height attained by the bullet is of 16,384 feet.
Step-by-step explanation:
Equations of motion:
The equations of motion for the bullet are:
[tex]x(t) = (v_0\cos{\alpha})t[/tex]
[tex]y(t) = (v_0\sin{\alpha})t - 16t^2[/tex]
In which [tex]v_0[/tex] is the initial speed and [tex]\alpha[/tex] is the angle.
Initial speed of 2048 ft/s at an angle of 30o to the horizontal.
This means that [tex]v_0 = 2048, \alpha = 30[/tex].
So
[tex]x(t) = (v_0\cos{\alpha})t = (2048\cos{30})t = 1773.62t[/tex]
[tex]y(t) = (v_0\sin{\alpha})t - 16t^2 = (2048\sin{30})t - 16t^2 = 1024t - 16t^2[/tex]
(a) After how many seconds will the bullet hit the ground?
It hits the ground when [tex]y(t) = 0[/tex]. So
[tex]1024t - 16t^2 = 0[/tex]
[tex]16t^2 - 1024t = 0[/tex]
[tex]16t(t - 64) = 0[/tex]
16t = 0 -> t = 0 or t - 64 = 0 -> t = 64
The bullet hits the ground after 64 seconds.
(b) How far from the gun will the bullet hit the ground?
This is the horizontal distance, that is, the x value, x(64).
[tex]x(64) = 1773.62(64) = 113511.7[/tex]
The bullet hits the ground 113,511.7 feet away.
(c) What is the maximum height attained by the bullet?
This is the value of y when it's derivative is 0.
We have that:
[tex]y^{\prime}(t) = 1024 - 32t[/tex]
[tex]1024 - 32t = 0[/tex]
[tex]32t = 1024[/tex]
[tex]t = \frac{1024}{32} = 32[/tex]
At this instant, the height is:
[tex]y(32) = 1024(32) - 16(32)^2 = 16384[/tex]
The maximum height attained by the bullet is of 16,384 feet.
HELP PLEASSSSSS I will give brainlyest!!!!!!!!!!!!!!!!!!
Answer:
1/2
Step-by-step explanation:
Convert 2/3 to 4/6
Subtract: 4/6 - 1/6
You get 3/6
Simplify: 1/2
Hope this helps!
Answer: The answer is 1/2
How can one estimate a car annual fuel expense
Answer:
determine the number of miles the car drives in a year.
divide that number by the cars average MPG (miles per gallon) then multiply that number by the average cost of a gallon of gas in your area.
Step-by-step explanation:
ab=6cm ac=12 calculate the length of cd
Answer:
is that the full question?
Answer:
Solution:-
Given,
ab =perpendicular (p)= 6cm
ac =hypotenuse (h)= 12cm
cd =base (b)= ?
using , Pythagoras theorem we have ,
b²=√h²-p²
or,cd²=√ac²-ab²
= √12²-6²
= √144-36
=√108
=√10.8²
=10.8cm
the length of cd is 10.8 cm
hope it is helpful to you
alvin is 5 years older than elga. the sum of their age is 85. what is elga age
Answer:
40 years old.
Step-by-step explanation:
We can let Elga's age equal [tex]x[/tex]. Alvin's age can be equal to [tex]y[/tex]. We can make several equations from the information we know. We know that Elga's age plus five equal's Alvin's age.
[tex]x+5=y[/tex]
We also know that the sum of their ages is 85.
[tex]x+y=85[/tex]
We can substitute [tex]x+5[/tex] for [tex]y[/tex] in the second equation since [tex]x+5=y[/tex], so we have the following equation:
[tex]x+(x+5)=85[/tex]
We can combine like terms to get
[tex]2x+5=85[/tex]
Subtracting 5 from both sides results in
[tex]2x=80[/tex]
After that, we can divide both sides by 2 to get
[tex]x=40[/tex]
Thus, Elga is 40 years old.
Answer:
e = 40
a=45
Step-by-step explanation:
a + e = 85
a = e+5
e + 5 + e = 85
2e = 80
e = 40
a=45
Which proportion resulted in the equation 3a = 7b?
Hello!
3a = 7b =>
=> 3 × a = 7 × b =>
=> a/b = 7/3
Good luck! :)
Which of the following represents the ratio of the hypotenuse to the given
side?
Answer:
D. √2 : 1
Step-by-step explanation:
The hypotenuse = 4√2 (longest side of a right triangle)
The given side = 4
Ratio of the hypotenuse to the given side = 4√2 : 4
Simplify by dividing both numbers by 4
√2 : 1
2(P +1) + 3(P + 2 ) > 2
Answer:
P>-6/5
Step-by-step explanation:
2(P+1)+3(P+2)>2
Use the distributive property to multiply 2 by P+1
2P+2+3(P+2)>2
Use the distributive property to multiply 3 by P+2
2P+2+3P+6>2
Combine 2P and 3P to get 5P
5P+2+6>2
Add 2 and 6 to get 8
5P+8>2
Subtract 8 from both sides
5P>2−8
Subtract 8 from 2 to get −6.
5P>−6
Divide both sides by 5. Since 5 is positive
P>−6/5
determine lcm and HCF of 24 and 26 using prime factors
Answer:
WHAT IS THE FACTOR?
Step-by-step explanation:
If the domain of a function that is translated down 3 is (0, 4), (-5, 8), (4, -2), what is the range?
A. (0, 1), (-5, 5), (4, -5)
B. (3, 4), (-2, 8), (7, -2)
C. (-3, 4), (-8, 8), (1, -2)
D. (0, 7), (-5, 11), (4, 1)
Given:
The domain of function that is translated down 3 is (0, 4), (-5, 8), (4, -2).
To find:
The range of the function.
Solution:
If a function is translated 3 units down, then
[tex](x,y)\to (x,y-3)[/tex]
Using this rule, we get
[tex](0,4)\to (0,4-3)[/tex]
[tex](0,4)\to (0,1)[/tex]
Similarly,
[tex](-5,8)\to (-5,5)[/tex]
[tex](4,-2)\to (4,-5)[/tex]
The range of the given function is (0, 1), (-5, 5), (4, -5).
Therefore, the correct option is A.
Which expression can be used to determine 50% of 42?
42-2 ,42÷2,42÷10,42-10
Answer:
42÷2
Step-by-step explanation:
SECTION B
Answer ALL questions. Write your answers in the spaces provided.
1 Data set A has a median value of 3.1
Here is data set B.
14
-9
28
-38
-13
-2
(a) Write a statement to compare the median values of the two sets of data.
(2)
Answer: The median value of data set B is -5.5, which is less than the median value of 3.1 in dataset A.
Step-by-step explanation:
Order the dataset from least to greatest:
-38 → -13 → -9 → -2 → 14 → 28
Then find the values that lies in the middle:
-38 → -13 → -9 → -2 → 14 → 28
Since there are 2 values, find the average of those 2 values:
[tex]\frac{-9+(-2)}{2} =\frac{-11}{2} =-5.5[/tex]
The median value = -5.5.
The median value of data set B is -5.5, which is less than the median value of 3.1 in dataset A.
A weight clinic recorded the weight lost (in pounds) by each client of a weight control clinic during the last year, and got the following data: 35, 26, 31, 17, 46, 30, 28, 21, 26, 34, 15, 27, 7, 18, 16, 57 Assume you created the frequency grouping in intervals of 10 starting at 1. What is the percentile in the next to highest group
Answer:
Class interval ____, Frequency _ C/frequency
1 - 10 ____________ 1 _________ 1
11 - 20 ___________ 4 _________ 5
20 - 30 __________ 6 _________ 11
31 - 40 ___________3 _________ 14
41 - 50 ___________ 1 _________ 15
51 - 60 ___________ 1 _________ 16
Step-by-step explanation:
Given the data :
35, 26, 31, 17, 46, 30, 28, 21, 26, 34, 15, 27, 7, 18, 16, 57
Class interval ____, Frequency _ C/frequency
1 - 10 ____________ 1 _________ 1
11 - 20 ___________ 4 _________ 5
20 - 30 __________ 6 _________ 11
31 - 40 ___________3 _________ 14
41 - 50 ___________ 1 _________ 15
51 - 60 ___________ 1 _________ 16
The next to highest frequency group has a frequency of 4 and the highest frequency of 6
Total frequency, n = (1 + 4 + 6 + 3 + 1 + 1) = 16
Please help
A stamp collection consists of 10 albums each containing 42 pages. How many stamps are in the total collection if 40 stamps fit on a page?
(1) 92
(2) 820
(3) 1,680
(4) 2,080
(5) 16,800
Step-by-step explanation:
Total number of albums = 10 albums[tex] \; [/tex]Number of pages in each album = 42 pages Stamps fit on 1 page = 40 stampsAs total number of pages in each album is 42 pages, so
➝ Total number of pages in 10 albums = (42 × 10) pages
➝ Total number of pages in 10 albums = 420 pages
Now, as the number of stamps fit on 1 page is 40 stamps, so
➝ Stamps fit on 420 pages = (420 × 40) stamps
➝ Stamps fit on 420 pages = 16,800 stamps
Therefore, 16,800 stamps are in the total collection.
(2x+3)(5x-8)
10x7€ 16x+158–24
10x2-x-24
Answer:
16X+134
Step-by-step explanation:
I need help with these questions
Answer:
1) 6m+8n
4) 21x+14y
7) 14c+16d
10) d+3e
Step-by-step explanation:
Suppose the sales tax rate in Idaho is 6%. If a computer sells for $589, how much is
the sales tax?
Solve the following equation or inequality for the unknown variable. Round answer to two decimal places if necessary.
(3x)2 - 10 = 56
4
x =
Answer:
x = 2.7
Step-by-step explanation:
The given equation is :
[tex](3x)^2-10=56[/tex]
We need to solve it for x.
It can be rewrite as follows:
[tex]9x^2-10=56[/tex]
Adding 10 to both sides,
[tex]9x^2-10+10=56+10\\\\9x^2=66\\\\x=\sqrt{\dfrac{66}{9}}\\\\x=2.70[/tex]
So, the value of x is equal to 2.7.
Work out the area of the shape,show working out
help me and I think I did the sides wrong
What transformation was not done to the linear parent function, f(x) = x, to
get the function g(x) = – } (x + 5) + 7?
A. Reflected over the x-axis
B. Vertically compressed by a factor of 2
O c. Shifted right 5 units
D. Shifted up 7 units
Answer:
C.
Step-by-step explanation:
The function shifted left five units instead of right five units.
There's no vertical compression in the equation provided, but that's probably just a typo since there's a random bracket that I assume was supposed to be a fraction.