A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent.
4. Which shows that these two rectangles are similar?
Given that f(x)=2x+1
a) find f(2)
b)find f^-1(x)
c)f^-1(7)
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]
For each year that a gift card goes unused, the value of the card decreases by 5%. What is the value of a $25.00 gift card after 1 year? Show your work.
Answer:
25*0.95 = 23.75
Step-by-step explanation:
i multiplied by 0.95 because the card is still worth 95% of it's original worth.
you could've done:
25*0.05= 1.75 and then subtract that from 25 to get 23.75, i just find the other way easier.
i hope this helped :)
Which of the following correctly uses absolute value to show the distance between -80 and 15? (5 points)
a
|-80 - 15| = |-95| = -95 units
b
|-80 + 15| = |-65| = 65 units
c
|-80 - 15| = |-95| = 95 units
d
|-80 + 15| = |-65| = -65 units
Answer:
it's answer is b
|-80+15| = |-65| = 65 units
Hope this helps :)
This question is about displacement. Displacement is a set of vectors. So the answer is - can't be + can't be.
so,answer-b
What is the solution to 2x-8<12?
x<2
x<8
x<10
x<40
Can someone please help me solve this??
Answer: X = - 12/5
Step-by-step explanation:
8+\left\{-2-10x\right\}=30
8+\left\{-2-10x\right\}=30
The scale on a map is 4 cm = 25 miles. Dave measures the distance to the next town at 9 cm. How many miles away is the next town?
Answer:
58.333....
Step-by-step explanation:
8cm=50
1cm so 25/3
8.3333333333
Answer:
56.25 or 56 1/4
Step-by-step explanation:
If 4 cm is equal to 25 miles then we can divide 25 by 4 to see how many miles is in 1 cm.
25 divided by 4 is 6.25 or 6 1/4
Therefor 1 cm is equal to 6.25 miles.
Now we multiply 9 by 6.25 to get 56.25
solve the equation:
3t²-3t+1=0
Answer:
There are no solutions
Step-by-step explanation:
Answer:
?? im not very good at math
Step-by-step explanation:
Which table shows a function that is decreasing only over the interval (-1, oo)?
х
-3
-2
-1
0
1
2
f(x)
-1
-3
-5
-2
-1
2
х
-3
-2
-1
0
1
2
f(x)
-3
-5
-7
-6
1
|--1
х
-3
-2
-1
0
1
2
f(x)
-4
-3
-1
2
1
-6
O
f(x)
х
-3
-2
-1
0
1
2.
-1
1
0
4
-8
Answer:
the thrid one
Step-by-step explanation:
The table that shows a function that is decreasing only over the interval (-1, oo) is table 3
For a table to show a decreasing interval, then the table values must reduce as the x value increase
The interval (-1, oo) means that, -1 is exclusive of the x values.
So, we start from x > -1
The first table shows an increasing function for x > -1
The second table shows an increasing and decreasing function for x > -1
The third table shows a decreasing function for x > -1
The last table shows a decreasing function for x > -1 but increases at other values
Hence, the table that shows a function that is decreasing only over the interval (-1, oo) is table 3
Read more about continuous functions at:
https://brainly.com/question/9412728
What is the probability of spinning an odd number
Answer:
If the spinner has an odd number of numbers on it, the probability of spinning an odd number will vary. For instance, if there are 3 spaces on the spinner, the probability of spinning an odd number will be 23 . However, if there are 11 spaces, the probability will be 611
Evaluate the function:
f(x)=x2−x, find f(−10)
6h + 24 = 0
What is h?
Answer:
h= -4
Step-by-step explanation:
6h + 24 = 0
subtract 24 on both sides
6h = -24
divide 6 on both sides
h= -4
please help me im so confused
Answer:
ijrrrrrrrrrrrrg to 19399
Step-by-step explanation:
Answer:
Its a because volume is equal to length times width time height and that answ choice is the only one that provides this correct statement
sea level = 0
A submarine is 120 ft below sea level. It climbs 50 ft towards sea level.
Where is the submarine compared to sea level now?
A. −170 ft
B. 70 ft
C. −70 ft
Answer:
c. -70
Step-by-step explanation:
subtract 50 from 120 you get 70, and since we are below sea level it is negative
There are 3 teachers to 125 pupils during the school program. How many teachers were
there if there were 2 500 pupils
Answer:
There were 60 teachers.
Step-by-step explanation:
☆We can use proportion to solve this!
[tex] \frac{3 \: teachers}{125 \: pupils} = \frac{x}{2500 \: pupils} \\ \\ \frac{125x}{125} = \frac{7500}{125} \\ \\ x = 60[/tex]
A line passes through the points (-3, -1) and (-5, 4). What is the slope of this line.
Answer:
-5/2
Step-by-step explanation:
4+1/-5+3 your welcome could you give me brainliest pls? thankss
Which equation js equivalent to 4(2x-3)-3(x-4)+7x=6?
4x³y²/4yx²•y⁴
I need to simplify that ^^
HELP ILL MARK YOU BRAINLIST write in y=mx+b form HELP ILL MARK YOU BRAINLIST write in y=mx+b form
Answer:
y=-0.25x +6
Step-by-step explanation:
3=(-0.25)12+c
3=-3+c
6=c
Tiffany spent 30 minutes on math homework and 15 minutes on science homework. What is the ratio of the minutes she spent on math homework compared to the minutes she spent on science homework?
Answer: The ratio would be 30/15, simplified as 2/1. So, she spent half as much time on science, or twice as much on math.
Step-by-step explanation:
Solve the following equation using the substitution method 2x - y = -2 y = 8
What is the slope of the line that passes through the points (–20, 18) and (30, 14)?
Negative StartFraction 25 Over 2 EndFraction
Negative five-halves
Negative two-fifths
Negative StartFraction 2 Over 25 EndFraction
Answer:
-2/25
Step-by-step explanation:
m= y2-y1/x2-x1
m=14-18/30 -(-20)
m=-4/50
m=-2/25
Answer:
-2 /25
Step-by-step explanation:
help me translate this into an expression!
" Four times the quotient of twice a number and eight "
thank you!
Answer:
[tex]4(\frac{2x}{8})[/tex]
Step-by-step explanation:
There you go! :)
Hhhjeeeeelllppppp pppplllllsss
Answer:
c= 89
Step-by-step explanation:
the angles of a triangle add up to 180
in this triangle, our angles are:
c-33
c-25
c-29
this means that
(c-33) + (c-25) + (c-29) = 180
3c - 87 = 180
add 87 to both sides
3c = 267
divide both sides by 3
c = 89
santiago drew a scale drawing of a community college. he used the scale 2 centimeters : 1 meter. The actual length of a building at the college is 76 meters. how long is the building on the drawing ?
Answer:
The building is 152 cm long.
Step-by-step explanation:
-We can solve using proportion!:
[tex]\frac{2 cm}{1 meter} = \frac{x}{76 meters} \\\\\frac{1x}{1} =\frac{152}{1} \\\\\\x = 152[/tex]
Jada had some dimes and quarters that had a total value of $12.50. The relationship between the number of dimes, d, and the number of quarters, q, can be expressed by the equation 01.d+0.25q= 12.5.
Question 1 - 1 pts
If Jada has 4 quarters, how many dimes does she have?
Question 2 - 1 pts
If Jada has 10 quarters, how many dimes does she have?
Question 3 - 1 pts
Is the number of dimes a function of the number of quarters? If yes, write a rule (that starts with d =...) that you can use to determine the output, d, from a given input, q. If no, explain why not.
Question 4 - 1 pts
If Jada has 25 dimes, how many quarters does she have?
Question 5 - 1 pts
If Jada has 30 dimes, how many quarters does she have?
Question 6 - 1 pts
Is the number of quarters a function of the number of dimes? If yes, write a rule (that starts with q =...) that you can use to determine the output, q, from a given input, d. If no, explain why not.
What is the slope of the line through (0,5) and (-2, -1)?
(0.5)
3
2
X
2
4
-4 -3
+(-2,-1)
-1
-2
-3
A. -3
O
B. -
o
C. 3
O
D.
10
PREVIOUS
Answer: 3
Step-by-step explanation:
*Slope formula*
Y2 - Y1 / X2 - X1
-1 - (5) / -2 - (0) = -6/-2 = 3
I NEED HELP ASAP PLEASEEE!!!! WILL GIVE BRAINLIEST !!
Hannah and Becky are learning to type on a cormputer keyboard. Hannatfs
typing speed is represented by the equation y = 11z vwhere y is the nurnber of
words she types and x is the nurmber of minutes, Becky's typing speed is
given by the graph.
60
36
1
2
Time (minutes)
4
Answer:
it's d credit to the people who said it
Hanna's typing speed is one word fewer than that of Becky's speed.
What is the general equation of a Straight line? What is equation modelling?The general equation of a straight line is -
y = mx + c[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.Other possible equations of lines are -
(y - y₁) = m(x - x₁) {Point - slope form}(y - y₁) = (y₂ - y₁) × (x - x₁)/(x₂ - x₁) {Two point - slope form}x/a + y/b = 1 {intercept form}x cos(β) + y sin(β) = L {Normal form}Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given are Hannah and Becky, who are learning to type on a computer keyboard. Hanna's typing speed is represented by the equation y = 11z. Becky's typing speed is given by the graph as shown in the question.
Now, for Hanna, her typing speed would be -
11 words per minute
For Becky, the slope of the graph will be -
m = (24 - 12)/(2 - 1)
m = 12
12 words per minute
It can be seen easily that Hanna's typing speed is one word fewer than that of Becky's speed.
Therefore, Hanna's typing speed is one word fewer than that of Becky's speed.
To solve more questions on equations, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
Is the following statement true or false?
The triangle proportionality theorem only applies to right triangles.
A.) False
B.) True
Answer:
A.) False
Step-by-step explanation:
The triangle proportionality theorem can apply to all triangles, because if a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally. This situation does not just apply to right triangles.
Answer:
I think it's actually True
Step-by-step explanation:
The triangle proportionality theorem can apply to all triangles, because if a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally. This situation does not just apply to right triangles.
-2x - (-18x + 126) = -18
Answer:
6.75 or 6and 3/4
Step-by-step explanation:
-2x - (-18x + 126) = -18
-2x + 18x - 126 = -18
16x = -18 + 126
16x = 108
x = 6.75 OR 6 3/4
Pls makr brainliest tysm