ANSWER
[tex]{f}^{ - 1}( f(x)) = f( {f}^{ - 1} ( x)) = x[/tex]
EXPLANATION
The given functions are;
[tex]f(x) = \frac{1}{2} x[/tex]
[tex] {f}^{ - 1} (x) = 2x[/tex]
[tex]f( {f}^{ - 1} (x)) = f(2x)[/tex]
[tex]f( {f}^{ - 1} (x)) = \frac{1}{2} \times 2x = x[/tex]
Also,
[tex] {f}^{ - 1}( f(x)) = {f}^{ - 1} ( \frac{1}{2} x)[/tex]
[tex]{f}^{ - 1}( f(x)) = 2 \times \frac{1}{2} x = x[/tex]
In general,
[tex]{f}^{ - 1}( f(x)) = f( {f}^{ - 1} ( x)) = x[/tex]
What is the opposite of 0?
What is the opposite of opposite of -3?
What is the opposite of -9
Answer:
0
3
9
Step-by-step explanation:
0 has no opposite
-3 = 3
-9 = 9
Mr Rodríguez drove 136 miles to main city .then he drove another 146 miles to rock town. How many miles did mr Rodríguez drive ?
Answer:
he drove 282 miles
Step-by-step explanation:
you add 136 and 146 to get 282
HELP ASAP! GIVING BRAINLIEST!!
Trapezoid RSTU is reflected over X and then over Z. What is the image of the rotation?
A) Trapezoid NOLM
B) Trapezoid BADC
C) Trapezoid RSTU
Answer:
A
Step-by-step explanation:
B C were already used in the graph
The answer is A) Trapezium NOLM. If you reflect RSTU over the X axis it produces the trapezium in the top left. Then flipping it over the Z axis is bottom right, NOLM.
Nadia bought 5 tickets to attend a spaghetti super fundraiser at her. school.The equation 5x equals 32.50 can be used to find x, the cost of each ticket in dollars.Which equation represents the cost of each ticket.
A: x equals 32.50/5
B: x equals 32.50(5)
C: x equals 32.50 - 5
D: x equals 32.50 + 5
Answer:
32.50 is the total cost, so you need to find the cost of each separate ticket.
First, you take the total, 32.50, and you divide it by the number of tickets, 5.
32.50/5
The answer is A.
Step-by-step explanation:
Final answer:
The correct equation that represents the cost of each ticket is A: x equals 32.50/5, which is obtained by dividing both sides of the original equation 5x = 32.50 by 5.
Explanation:
To determine the cost of each ticket that Nadia bought, we can use the given equation 5x = 32.50, where x represents the cost of each ticket. To solve for x, we need to isolate the variable on one side of the equation. This can be done by dividing both sides of the equation by 5, which leads us to x = 32.50 / 5. Therefore, the correct equation that represents the cost of each ticket is A: x equals 32.50/5.
You increase the size of a page by 50% then you decrease it by 50% what is the size of the page now
Answer:
75% of the original paper’s size.
Step-by-step explanation:
Let’s say that the original size was 10 inches.
You then increase it by 50%. It is now 15 inches.
Now, you decrease it by 50%. 50% of 15 is 7.5. So, the paper is now 7.5 inches.
7.5 inches is 75% of the original paper size.
I hope I helped!
Let me know if you need anything else!
~ Zoe
Answer:
Smaller than you started with.
Brew Ha Ha Coffee produces two types of coffee blends: Morning,x,and House,y. The Morning blend has 9oz of a Guatemalan coffee and 7oz of Brazilian coffee. The company makes $2 in profit from each bag of Morning Blend sold and $2.50 in profit from each bag of House Blend sold. The company has 400oz of both the Guatemalan and Brazilian coffees available.
This set of inequalities represent the constraints in this situation.
9x+6y<400
7x+10y<400
X>0
Y>0
The company wants to maximize its profits by using the objective function P = 2x + 2.5y
What is the maximum profit.
88
0
160
106
Answer:
Fourth option
Step-by-step explanation:
When graphing the given inequalities you will get a region like the one shown in the attached image. This region is delimited by 4 straight
[tex]x = 0\\\\y = 0\\\\9x + 6y = 400\\\\7x + 10y = 400[/tex]
The points indicated at the ends of the region are the maximum possible values of x and y.
We must test these points in the objective function [tex]P = 2x + 2.5y[/tex] and see which point maximizes the value of P.
Remember that the boundaries of the region are not included.
We can prove the point x = 0 and y = 39 because (0,4) is not included in the region.
[tex]P = 2(0) + 2.5(39) = 97.5[/tex]
Now we test the point x = 33 and y = 16
[tex]P = 2(33) + 2.5(16) = 106[/tex]
Now we test the point x = 44 and y = 0
[tex]P = 2(44) + 2.5(0) = 88[/tex]
Finally the optimal value is:
x = 33 oz
y = 16 oz
With a gain of $106
What is 0.95 rounded off to the nearest whole number
1.00 would be your answer because 95 rounded up is 100. So, 0.95 is closest to 1.00
Match the functions to their x-intercepts.
f(x) = log x – 1
f(x) = -(log x – 2)
f(x) = log(-x – 2)
f(x) = -log -(x – 1)
(0, 0)
arrowBoth
(-3, 0)
arrowBoth
(10, 0)
arrowBoth
(100, 0)
arrowBoth
Answer:
f(x) = log x – 1 ⇒ x-intercept = (10 , 0)
f(x) = -(log x – 2) ⇒ x-intercept = (100 , 0)
f(x) = log(-x – 2) ⇒ x-intercept = (-3 , 0)
f(x) = -log -(x – 1) ⇒ x-intercept = (0 , 0)
Step-by-step explanation:
* lets talk about the log
- If log a = b, that means the base of the log is 10
- To solve it we will change it to exponential function
∴ [tex]10^{b}=a[/tex]
* Now do that in each one of the problem
* ∵ f(x) = log x - 1
- To find the x-intercept put y = 0
∴ log x - 1 = 0 ⇒ add 1 to both sides
∴ log x = 1 ⇒ change it to exponential function
∴ [tex]10^{1}=x[/tex]
∴ x = 10
* The x-intercept = (10 , 0)
* ∵ f(x) = -(log x - 2)
- To find the x-intercept put y = 0
∴ -(log x - 2) = 0 ⇒ Multiply both sides by -1
∴ log x - 2 = 0 ⇒ add 2 to the both sides
∴ log x = 2 ⇒ change it to exponential function
∴ [tex]10^{2}=(x)[/tex]
∴ x = 100
* The x-intercept = (100 , 0)
* ∵ f(x) = log (-x - 2)
- To find the x-intercept put y = 0
∴ log (-x - 2) = 0 ⇒ change it to exponential function
∴ [tex]10^{0}=(-x-2)[/tex] ⇒ any number to the power of zero = 1 except 0
∴ -x - 2 = 1 ⇒ add 2 to the both sides
∴ -x = 3 ⇒ multiply both sides by -1
∴ x = -3
* The x-intercept = (-3 , 0)
* ∵ f(x) = -log -(x - 1)
- To find the x-intercept put y = 0
∴ -log -(x - 1) = 0 ⇒ multiply both sides by -1
∴ log -(x - 1) = 0 ⇒ change it to exponential function
∴ [tex]10^{0}=-(x-1)[/tex] ⇒ any number to the power of zero = 1 except 0
∴ -(x - 1) = 1 ⇒ multiply both sides by -1
∴ x - 1 = -1 ⇒ add 1 to both sides
∴ x = 0
* The x-intercept = (0 , 0)
Answer:
Please mark as Brainliest :)
Step-by-step explanation:
The age of a father is to less than seven times the age of his son in three years the sum oftheir ages will be 52 if the sons presents age is S years which equation models this situation
Answer:
The correct answer is:
(7s-2)+3+(s+3) = 52, or 8s+4 = 52.
Step-by-step explanation:
Since s is the son's age, "two less than seven times" the son's age would be represented by 7s-2. To represent this in 3 years, we would add 3: (7s-2)+3. In 3 years, the son's age, s, would be represented by s+3. We are told that the sum of these ages will be 52; this gives us (7s-2)+3+(s+3) = 52.
To simplify this, combine like terms. 7s+s = 8s; -2+3+3 = 4. This gives us 8s+4=52.
write a simplified expression that expression that shows thesum of three consecutive numbers where n is the last number. substitute n=5 to test the expression. what are the three consecutive numbers? what is their sum?
➷ The last number : n
The second number : n - 1
The third number : n - 2
n + n - 1 + n - 2
Simplify this:
3n - 3
Substitute 5 into it:
n = 5
n - 1 = (5) - 1 = 4
n - 2 = (5) - 2 = 3
3(5) - 3 = 12
Their sum is 12
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer: i dont know
Step-by-step explanation: hello im only here to complete a task, im receiving 50 points. I hope someone else can help you, cause I cant ;-;
Brahim completed 18 free throws and missed 12.
Using experimental probability, how many free throws is he predicted to complete in the next 100 tries?
A.
6
B.
36
C.
48
D.
60
Most likely I would pick B
Answer:
The answer is D. 60
Step-by-step explanation:
Step 1: 18 + 12 = 30
18 = 60% of 30, therefor with this knowledge we know that 60% of a hundred, or 60 will be the answer.
(I also have proof, as I have done this quiz before.)
I hope my answer is correct.
[Please give brainliest!]
Have a good day,
-johannelbekian
Consider circle O, in which arc XY measures 16π cm. The length of a radius of the circle is 32 cm.
What is the circumference of the circle?
π units
What is the ratio of the arc length to the circumference?
What is the measure of central angle XOY?
Answer:
Circumference: 64π
Ratio: 1 : 4
Measure of ∠xoy: π/2
Step-by-step explanation:
We are given an arc length of 16π. Since it's in terms of pi, we use the formula
S = rФ where r is the radius, and Ф is the measure of the angle in radians (in terms of pi)
We are given S = 16π and r = 32, plug those in and find Ф
16π = 32Ф
16π/32 = Ф
π/2 = Ф
This is the measure of the central angle.
The angle is π/2 radians. There are 2π radians in the circumference, so the circumference is 4 times the arc length created by the central angle. (There are 4 halves in 2) so the ratio of the arc length tothe circumference is 1 : 4
The formula for circumference is C = 2πr, where r is the radius, so we hace
C = 2π(32) = 64π
The answer is
64
1/4
90
Hope this helps.
The stones that make up Stonehenge in England are shaped roughly like rectangular prisms. The average stone in the outer circle has a height of 13 feet and a base area of 19 1/2 square feet. Explain how to find the volume of one of the stones and then calculate the volume.
The volume of an average stone in the outer circle of Stonehenge is calculated by multiplying the base area, 19.5 square feet, by the height, 13 feet, resulting in a volume of 253.5 cubic feet.
To calculate the volume of a stone from Stonehenge, which is shaped like a rectangular prism, we need to multiply the height of the stone by the base area. The height is given as 13 feet, and the base area is 19.5 square feet. The formula for volume V of a rectangular prism is
V = base area × height.
So, the volume V of one of the average stones in the outer circle of Stonehenge would be:
V = 19.5 sq ft × 13 ft
V = 253.5 cubic feet
Therefore, the volume of the stone is 253.5 cubic feet.
Chad poured a sidewalk that is 42 feet long.He is going to start at the beginning and make a cut every 20 inches.How many cuts will Chad make?
Answer:
26 cuts
Step-by-step explanation:
1. convert 42 feet into inches by multiplying by 12 (12 inches=1 foot)
42*12 = 504 inches
2. divide the total number of inches (504) by 20 (where Chad cuts)
504/20 = 25.2
Since Chad cannot make a partial cut (.2) round up to the next whole number - 26
What is the product? 2y/y-3 multiplied by 4y-12/2y+6
The answer is [tex]\frac{4y}{y+3}[/tex]
Step-by-step explanation:See the attached figure
Answer:
[tex] \frac { 4y } { y + 3 } [/tex]
Step-by-step explanation:
We are given the following terms and we are to find their product:
[tex] \frac { 2y } { y - 3 } \times \frac { 4y - 12 } { 2y + 6 } [/tex]
[tex] \frac { 8y^2 - 24y } { 2y^2 - 6y + 6y - 18 } [/tex]
Taking the common terms out and cancelling them to get:
[tex] \frac { 2 (4y^2 - 12y ) } { 2 (y^2 - 9 ) } [/tex]
[tex] \frac { 4y ( y - 3 ) } { ( y + 3 ) ( y - 3 ) } [/tex]
[tex] \frac { 4y } { y + 3 } [/tex]
3 3/4 * 2 1/2 can somebody help me
Answer:
9 3/8
Step-by-step explanation:
You have to turn them both into mixed numbers so:
15/4 x 5/2
Then you just multiply across:
15 x 5/4 x 2
That should equal
75/8
Simplify! You should end up with 9 3/8
The sum of 18 and twice a number use n to rep
Repesent unknown number
18+2n. For sure hope it helps
18+2n. Hope this helps!
can someone help me find this expression!! i don’t understand it at all, please comment only if you can help !!
Check the picture below.
Your science teacher recently gave a quiz to 28 students present in class. The class average was an 82.5. Five students that were absent made up the quiz after schoolamd their scores were a 78, 89,92,,99, & 63. Find the new class average with the newscores
Total students in the class who got the quiz = 28
The average of the class average was = 82.5
Five students that were absent made up the quiz after school and their scores were a 78, 89,92,99, & 63.
The formula for an average= (sum of values) / (count of values)
As the average is given as 82.5 and there were 28 students, so sum of the 28 values will be = [tex]28\times82.5=2310[/tex]
Total students of the class = 28+5(absent) = 33
For 33 students the total score was = 2310 +(78+89+92+99+63)
= 2731
So, average for 33 students will be = [tex]\frac{2731}{33} =82.757[/tex] or 82.76
So, the new class average is 82.76
A tree that is 100 feet tall casts a shadow that is 150 feet long. Determine the angle at which the rays of the sun hit the ground, to the nearest degree.
Answer:
34°
Step-by-step explanation:
Let θ = the angle of elevation from the ground to the top of the tree. Then
tanθ = 100/150 = 0.6667
θ = arctan0.6667
θ = 34°
The sin's rays hit the ground at an angle of 34°.
Albert buys a car for $12,000. The value of the car depreciates about 9% per year. After about how many years will the car be worth $7500?
Answer:
[tex]5\ years[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]D=P(1-r)^{t}[/tex]
where
D is the depreciated value
P is the original value
r is the rate of depreciation in decimal
t is Number of Time Periods
in this problem we have
[tex]P=\$12,000\\r=9\%=0.09\\D=\$7,500[/tex]
substitute in the formula above and solve for t
[tex]\$7,500=\$12,000(1-0.09)^{t}[/tex]
[tex](7,500/12,000)=(0.91)^{t}[/tex]
Apply log both sides
[tex]log(7,500/12,000)=t*log(0.91)[/tex]
[tex]t=log(7,500/12,000)/log(0.91)=5\ years[/tex]
What is the volume of a square pyramids
Answer:
[tex]\large\boxed{V=75\ in^3}[/tex]
Step-by-step explanation:
The formula ogf a volume of a pyramid:
[tex]V=\dfrac{1}{3}BH[/tex]
B - area of a base
H - height
We have a base length a = 5 in and a height H = 9 in.
In the base we have a square. The formula of an area of a square is:
[tex]B=a^2[/tex]
Substitute:
[tex]B=5^2=25\ in^2[/tex]
Calculate the volume:
[tex]V=\dfrac{1}{3}(25)(9)=(25)(3)=75\ in^3[/tex]
pls help!! this is #9 btw
Answer:
A, cus he has other markers in the box, we dont know how many, or how many blue markeys he has so it cant be A
Step-by-step explanation:
Mrs Cambell gave her algebra I students a list of teinomials to factor for homework. which of these can be factored into two binomials
a) x^2+3x+2
b) x^2+4x+5
c) x^2+5x+7
D) x^2+6x+10
Answer: option a.
Step-by-step explanation:
To factor a polynomial of degree 2, with the form [tex]ax^{2}+bx+c[/tex], you must find two number whose sum is a and whose product is c. Then:
a) [tex]x^2+3x+2\\(x+1)(x+2)[/tex]
(it can be factored into two binomials)
b) [tex]x^2+4x+5[/tex] cannot be factored into two binomials.
c) [tex]x^2+5x+7[/tex] cannot be factored into two binomials.
d) [tex]x^2+6x+10[/tex] cannot be factored into two binomials.
Therefore, the answer is the option a.
Divide: (4x10^5)/(5x10^2)
Answer:
800Step-by-step explanation:
[tex]\dfrac{4\cdot10^5}{5\cdot10^2}=\dfrac{4}{5}\cdot\dfrac{10^5}{10^2}=0.8\cdot10^{5-2}=0.8\cdot10^3=0.8\cdot1,000=800\\\\\\\text{Used}\ \dfrac{a^m}{a^n}=a^{m-n}[/tex]
40 POINTS AND BRAINLIEST IF FAST!!!!!!! Anwser the picture!!!!! Pls rn!!!!
Answer:
Length is your answer
Answer: The answer is COLOR
Step-by-step explanation:
Extensive means covering or affecting a large area and all other options are numerical values expect color. :)
what is the sum of the polynomials? (4x^5+3x^3-x-6)+(3x^3-9x-4)
Answer:
You only can to sum expressions with the same exponent, so:
Step-by-step explanation:
(4x^5+3x^3-x-6)+(3x^3-9x-4)
4x^5 + 6x^3 - 10x - 10Best regards
Answer:
4x^5+6x^3-10x-10
Step-by-step explanation:
you get rid of the parenthesis and combine like terms
Simplify:
(3xy^3)(2x^3y)
(Please show your work)
Answer:
6x^4y^4
Step-by-step explanation:
(3xy^3)(2x^3y)
= (3*2) x^(1+3) y^(3+1)
= 6x^4y^4
suppose you are in your last semester of college and have a 2.75 GPA after 105 credit hours if you are taking 15 credit hours in your last semester and get a perfect 4.0 GPA what will your overall GPA be is it possible to get your GPA up to 3.0 for the graduation
Answer:
The overall CGPA would be 2.90 so it is not possible for hum to secure a CGPA of 3 for graduation.
Step-by-step explanation:
Given,
CGPA = 2.75
Credit hours = 105
Last semester GPA = 4
Last semester credit hours = 15
CGPA = [tex]\frac{sum of (Credit hours of each subject * GPA of each subject)}{Total credit hours}[/tex]credit hours * gpa
in our case, it would be:
CGPA = [tex]\frac{(2.75*105)+(4*15}{105+15}[/tex]
=> [tex]\frac{(288.75)+(60)}{120}[/tex]
=> [tex]\frac{348.75}{120}[/tex]
=> 2.90
The overall CGPA would be 2.90 so it is not possible for hum to secure a CGPA of 3 for graduation.
Which balance accrued the most interest in a month?
A)$458.90
B)$2,249.80
C)$946.95
D)$1,500.00
your answer is A 458.90.
The answer would be A)$458.90