Answer:
a) [tex]f(2) = 5[/tex], b) [tex]f^{-1} (x) = \frac{x-1}{2}[/tex], c) [tex]f^{-1} (7) = 3[/tex]
Step-by-step explanation:
a) We evaluate the function at [tex]x = 2[/tex]:
[tex]f(2) = 2\cdot (2) + 1[/tex]
[tex]f(2) = 4+1[/tex]
[tex]f(2) = 5[/tex]
b) First, we determine the inverse of the function by algebraic means:
1) [tex]y = 2\cdot x + 1[/tex] Given
2) [tex]y +(-1) = 2\cdot x + [1+(-1)][/tex] Compatibility with addition/Associative property
3) [tex]y + (-1) =2\cdot x[/tex] Existence of additive inverse/Modulative property
4) [tex]2^{-1}\cdot [y+(-1)] = (2\cdot 2^{-1})\cdot x[/tex] Compatibility with multiplication/Commutative and associative properties
5) [tex][y+(-1)]\cdot 2^{-1} = x[/tex] Existence of multiplicative inverse/Modulative and commutative properties
6) [tex]x = [y+(-1)]\cdot 2^{-1}[/tex] Symmetry property of equality
7) [tex]x = \frac{y-1}{2}[/tex] Definitions of subtraction and division
8) [tex]f^{-1} (x) = \frac{x-1}{2}[/tex] [tex]x = f_{-1} (x)[/tex]/[tex]y = x[/tex]/Result
c) Now we evaluate the expression obtained on b) at the given number:
[tex]f^{-1} (7) = \frac{7-1}{2}[/tex]
[tex]f^{-1} (7) = 3[/tex]
Write an equation and solve for x.
That's the final Answer, and don't worry about the answer in point form. I worked it out correctly. All steps followed;
angles in a triangle add up to 180°
An architect is making a floor plan for a rectangular gymnasium. If the gymnasium is 80 feet
long and 60 feet wide, what will the distance be between opposite corners?
feet
Answer:
160
Step-by-step explanation:
the length betwenn side to side woukd be 160
Answer:
The answer is 100
Step-by-step explanation:
a² + b² = c²
80²+60²=c²
6,400+1,200=c²
√6,400=√c²
subtract 1,200 - 6,400= 5,200
c2=72.1
Which of the following is not a right triangle?
Group of answer choices
3 in, 4 in, 5in
6 in, 11 in, 13 in
8 in, 15 in, 17 in
15 in, 20 in, 25 in
Can someone plz help!!!! :(
Answer:
60 degress
Step-by-step explanation:
How I got it:
1. Find out the angel of each side. 360 divded by 6 = 60
2. Get the answer of 60
Advice:
-Make an polygon using paper and rotate it. (Use protractor and ruler if your gonna do it)
(10) Find the values of x, y, and z. The diagram is not to scale.
Answer:
y = 67 degrees
x = 86 degrees
z = 94 degrees
Step-by-step explanation:
This is easy...
38 + 56 = x
94
180 - 94 = 86
86 + 38 + 56 = 180
so x = 86 degrees
___________________
180 - 86 = 94
z = 94
___________________
94 + 19 = 113
180 - 113 = 67
67 + 94 + 19 = 180
so y = 67 degrees
yall please help me with this math question :/
Mai skated x miles, and Clare skated ⅗ farther than that. Write an expression for the distance Clare skated.
Answer:
Its either 8x/5 or 5x/8
im not sure sorry.
What is the slope of the line?
Answer:
Step-by-step explanation:
by inspection.. ( looking at the graph) we can see that the slope is down hill. so it's going to be negative and also slope = rise / run [rise is negative in this question] soo ... i'm looking carefully to see where the line is crossing the grid marks exactly .. it looks like to me (-3,1) and (2,-3) you tell me if that looks right... if it does .. then the rise / run is 4/5 and this is a negative slope sooo
- 4/5
:)
Sonya had 20 dollars to spend on 3 gifts. She spent 8 1 4 dollars on gift A and 4 4 5 dollars on gift B. How much money did she have left for gift C?
Answer:
6 19/20 dollars
Step-by-step explanation:
Sonya had 20 dollars to spend on 3 gifts.
She spent 8 1 4 dollars on gift A and 4 4 5 dollars on gift B.
Gift A + Gift B + Gift C = $20
Gift C = $20 - (Gift A + Gift B)
Gift A = $8 1/4
Gift B = $4 4/5
Hence:
The amount she had left for gift C is :
Gift C = $20 - ($8 1/4 + $ 4 4/5)
Gift C = $20 - $13 1/20
Gift C = $ 6 19/20
Question Below please help
What does k represent in the equation y = kx?
Answer:
The constant of variation.
Ms. Petters has 36 red, blue, and green markers. She has an equal number of each color of marker. She arranges the red markers in 2 equal groups. How many red markers are in each group?
On a summer road trip, a family
traveled 3,263.04 miles
. The family
traveled 16 days by car and drove the
same distance each day
. How many
miles did the family travel each day?
Answer:
203.94
Step-by-step explanation:
just divide the number of miles by the days :DDDDD
Craig measured a length as 0.034 millimeters. What is the margin of error? 0.03 mm to 0.04 mm 0.033 mm to 0.034 mm 0.0335 mm to 0.0345 mm 0.0345 mm to 0.0350 mm
C. 0.0335 mm to 0.0345 mm
Step-by-step explanation:
The least significant digit of Craig's measurement is in the 0.001 mm place. The error in the measurement is presumed to fall within half that value either side of Craig's measurement. So, the actual value is expected to be in the range ...
0.034 - 0.0005 = 0.0335
to
0.034 + 0.0005 = 0.0345
The measurement is presumed to be in the range 0.0335 mm to 0.0345 mm.
Answer:
C
Step-by-step explanation:
cuz...just trust me
HELP ASAP!!!!
GIVING BRAINLIEST!
Find the value of x and y with the steps PLEASE.
Answer:
x=70
y= 40
Step-by-step explanation:
the triangle containing x is an isosceles triangle so two of the sides are 55.
55+55+x=180.
110+x=180
110-110+x=180-110
x=70
Triangle BAC is equilateral so 180/3=60. Now
x+60+c=180
70+60+c=180
130+c=180
130-130+c=180-130
c=50
That gives us one corner of triangle CBD. We know a second angle is 90 so
50+90+y=180
140+y=180
140-140+y=180-140
y=40
I think that is correct but you are free to check it yourself
A table titled Number of Dogs Adopted has entries 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9. The total is 132.
A shelter kept track of the number of dogs adopted each day for three weeks. Use the table to find the statistical measures.
Mean:
Median:
Mode:
Range:
Answer:
mean- 66
median- 7
mode- 8
range- 6
Step-by-step explanation:
to find the mode you line up all the numbers, add them all together and then divide that number by 2.
to find the median you line up all the numbers then one by one taking turns from left to right you cross of the numbers to find the number in the middle. (think of median as middle)
to find mode you just find the number that is used the most. (mode=most)
to find the range you find the highest number and the lowest number. and subtract the lowest from the highest to find the difference between the 2. in this case its 9-3 so the difference is 6.
Answer:
Hello!!! erz here ^^
Step-by-step explanation:
mean- 6.29
median- 7
mode- 8
range- 6
Hope this helps!! :D
WILL MARK BRAINLIEST TO THE BEST ANSWERS. The interior angles of a pentagon measure x°, (2x)°, (2.5x)° , (x + 10)° , and (2x + 20)°. Determine the value of x. PLEASE SHOW ALL SOLUTIONS NESSICARY. THANK YOU.......
Answer:
x=60
Step-by-step explanation:
The sum of interior angles of a regular Pentagon is 540°
x+2x+2.5x+x+10+2x+20=540
8.5x=540-30
8.5x=510
x=510/8.5=60
Answer:
x = 60°Step-by-step explanation:
Sum of interior angles of a regular polygon is:
180°(n-2)Pentagon has 5 sides, so sum of angles is:
180°(5-2) = 180°*3 = 540°For the given pentagon we have sum of angle measures as below, and solving for x:
x + 2x + 2.5x + (x +10) + (2x + 20) = 540°8.5x + 30° = 540°8.5x = 510°x = 510°/8.5x = 60°each unit cost 14p. How much do 942 units cost
Answer:
Answer: Cost of 1 unit = 14 p Cost of 942 unit = 14 × 942 == 13,188 p
Step-by-step explanation:
Enter an inequality that represents the graph in the box. Please help!!
Complete the ratio. 78 chairs in 6 rows : ______ chairs in 1 row.
Answer:
13 chairs in one row
Step-by-step explanation:
i don't know how to explain bi have given you the answer already goodbye
what is the 7th term of the geometric sequence for 400, 200,100,....
Step-by-step explanation:
400,200,100,50,25,12.5, ...... 0.78125
(2x - 9) (x + 4) = 0
What the answer
Answer:
x = 4.5 AND x = -4
Step-by-step explanation:
for the first answer
add 9 to 0 and divide by 2
for the second answer
subtract 4
Answer:
x = 9/2 and x = -4
Step-by-step explanation:
you can set each expression in the parenthesis' equal to zero. this is due to it being multiplication so if one parenthesis equals 0, the answer will be 0
2x - 9 = 0 and x + 4 = 0
starting with 2x-9=0
add 9 to both sides
2x = 9
divide by 2
x = 9/2
then do x + 4 = 0
subtract 4
x = -4
so your two answers are
x = 9/2 and x = -4
If you want to show an increase to the original quantity, how could you change the bar diagram?
Answer:
Write a situation in which positive and negative numbers are used to describe values that have opposite meaning. What does 0 represent in this situation you created?
Step-by-step explanation:
least common multiple of 9, 12, 18
Answer:
36
Step-by-step explanation:
Answer:
36
Step-by-step explanation:
Question 2 of 5
The side lengths of a triangle are 5, 8, and 12. Is this a right triangle?
A. Yes, because 52 + 82 < 122.
B. No, because 52 + 82 + 122.
C. No, because 5+ 8 + 12.
D. Yes, because 52 + 82 = 122
SUBM
Answer:
b
Step-by-step explanation:
5^2 + 8^2 = 12^2
25 + 64 = 144
89 does not equal 144
Please please help please please
Answer:
A. 4/ 3
Step-by-step explanation:
With reference angle X
perpendicular (p) = 24
base (b) = 18
Now
tan X = p / b = 24 / 18 = 4 / 3
can someone anyone please help me asap
Answer:
the answer is option : D
Step-by-step explanation:
multiply 9 with the given hrs to find the correct one
I'll give brainliest to correct answer.
Which statement best describes the area of the triangle shown below?
A. It is twice the area of a rectangle of length 4 units and width 3 units.
B. It is twice the area of a square of side length 3 units.
C. It is one-half the area of a rectangle of length 4 units and width 3 units.
D. It is one-half the area of a square of side length 3 units.
Answer:
C
Step-by-step explanation:
Can someone please help me? I need to get 10 of these right and I don’t understand them
9514 1404 393
Answer:
(x, y) = (1, 1)
Step-by-step explanation:
About Algebra
All of Algebra is based on a few simple rules:
adding 0 doesn't change anythingmultiplying by 1 doesn't change anythingdoing the same thing to both sides of an equation doesn't change the values of the variablesanything can be substituted for its equalWhen we solve equations by substitution, we make use of these facts.
__
About Substitution
Generally, substitution in equation solving is done for the purpose of eliminating a variable from the equation. That usually means you want to write an expression for one variable in terms of other variables.
Finding the Expression to Substitute
In this set of equations, the variables are x and y. We can substitute for y an expression involving x, or we can substitute for x an expression involving y. These equations are written in such a way that either method works as well as the other.
Let's choose to substitute for y. This means we need an equation of the form ...
y = <some expression involving x>
The first equation makes it easy to get that. If we add y (to both sides, see rule 3 above), we get ...
5x -y +y = 4 +y
5x = 4 + y . . . . . . . . . simplified
Subtracting 4 (from both sides) gets us the form we want.
5x -4 = 4 -4 + y
5x -4 = y . . . . . . by rule 4 above, we can use (5x-4) anyplace you see y
Using the Expression to Substitute
Now, we have an expression for y that we can use in the second equation. There, y is multiplied by 4, so we need to be sure to multiply the whole expression by 4:
-x + 4(5x -4) = 3 . . . . . . substituted for y in the second equation
-x +20x -16 = 3 . . . . . use the distributive property to eliminate parentheses
19x -16 = 3 . . . . . . collect terms
This has a constant (-16) where we don't want it, so we can add 16 (to both sides) to get rid of it.
19x -16 +16 = 3 +16
19x = 19 . . . . simplify
Now, we can divide by 19 (to both sides) to get x by itself.
(19x)/19 = 19/19
x = 1 . . . . almost done; we still need to find y
Finishing Up
Using the equation for y that we used for substitution, we can find y from our value of x.
y = 5x -4 = 5×1 -4 = 5-4
y = 1
So, the solution is x = 1, y = 1, or (x, y) = (1, 1).
_____
Additional comment
In this set of equations, both variables (x and y) appear with coefficients of 1 (actually, -1). This makes it easy to solve for an expression that can be substituted for the variable. In systems of equations that you want to solve by substitution, it usually works well to start by looking for a variable with a coefficient of 1 (or -1). Use that to write the substitution expression as we did here.
__
Alternate Solution
If you use a variable with a coefficient other than 1 to write the substitution expression, you end up with fractions. That's OK if you're comfortable with arithmetic using fractions. It generally requires more care.
For example, we could solve the first equation for x:
x = (4 +y)/5
Substituting that into the second equation gives ...
-(4 +y)/5 +4y = 3
-4/5 -y/5 +4y = 3
(3 4/5)y = 3 4/5 . . . . . add 4/5 (to both sides), collect terms
Now, you get to divide by 3 4/5 to get ...
y = (3 4/5)/(3 4/5) = 1
Fortunately, in this case, we can see the numerator and denominator are identical, so the division result is 1. If it weren't you'd be faced with dividing mixed numbers--not always a student's first choice of fun math operations.
x = (4 +1)/5 = 1 . . . . finishing up
Please help ASAP help please
Answer:
The ladder is 10 ft long...