Answer:
The first two pairs of functions are inverse of each other
Step-by-step explanation:
Inverse functions?
1...................................
f(x) = {(-5, -9), (-3, -4), (0,1), (3,7), (6,13)}
g(x) = {(-9,-5), (-4, -3), (1,0), (7,3), (13,6)}
Yes, this pair is inverse as all points of the functions have inverse values2...................................
f(x) = x + 7 is given
Inverse of f(x) is
x = f'(x) + 7 ⇒ f'(x) = x - 7Since g(x) = x - 7 it is inverse with f(x)
Yes, this pair is inverse as described above3...................................
Data of f(x) and g(x)
x = {2, 3, 4, 5} f(x) = {3, 8, 15, 24}
x = {5, 4, 3, 2} g(x) = {24, 15, 8, 3}
No, as both functions have same domain and rangeexample is f(2) = 3 and g(2) = 3 as per tableA nurse mixes 50 cc of a 60% saline solution with a 10% saline solution to produce a 20% saline solution. How much of the 10% solution should he use?
Answer:
The nurse should use 200cc of the 10% saline solution in order to produce a 20% saline solution.
Step-by-step explanation:
to the given mix we add a quantity of a lower mix to generate another.
50cc at 60% + Xcc at 10% = (50 + X)cc at 20%
50 x 60% + X x 10% = (50 + X) x 20%
30 + 0.1X = 10 + 0.2X
30 - 10 = 0.2X - 0.1X
20 = 0.1X
20/0.1 = X
X = 200
Students are planning the backdrop for the school play. The backdrop is 15 feet wide and 10 feet high. Every 16 inches on the scale drawing represents 5 feet on the backdrop What is the area of the scale drawing?
Answer:6
Step-by-step explanation:
8. Joe walked 5 miles north, 9 miles east, then 9 miles north, and 7 miles east. If Joe decides to
walk straight back to where he started, how far must he walk?
Answer:
tim has an after school delivery service that he provides for several small retailers in town. he uses his bicycle and charges $1.25 for a delivery made within 1 1/2 miles, $1.70 for a delivery of at least 1 1/2 miles but less than 1 3/4 miles. $2.15 for a delivery of at least 1 3/4 miles but less than 2 miles, and so on. if tim raised his rates by 10%, what would he be paid to deliver a package 3 1/8 miles?
since the rate was 45 cents i multiplied 0.45 by 1.1 and got 0.495 and then i kept adding to the cost and 1/4 to the amount of miles until i got 3 1/8 miles. my answer was 4.715 so i rounded to 4.72, is that correct?Step-by-step explanation:
Proving the Congruent Supplements Theorem
Try
Statements Reasons
Given: 21 and 22 are supplements, 23
and 24 are supplements, and
2124
Prove. 22 23
m2 1 + m 2 = 180
m23+ m24 = 180
21 and 22 are supp.
23 and 24 are supp
21 24
m2 1 + m 2 = m 3 + m24
Statements
Reasons
3
2
Assemble the proof by dragging tiles to
the Statements and Reasons columns
Answer:
From
m∠1 = m∠4
m∠1 + m∠2 = m∠3 + m∠4
m∠2 = m∠3 [tex]{}[/tex] Identity property
∠2 ≅ ∠3 [tex]{}[/tex] [tex]{}[/tex] Equal angles are congruent
Step-by-step explanation:
Given [tex]{}[/tex] Reason
∠1 and ∠2 are supplementary [tex]{}[/tex] Given
Therefore;
m∠1 + m∠2 = 180° [tex]{}[/tex] Supplementary ∠s sum up to 180°
∠3 and ∠4 are supplementary [tex]{}[/tex] Given
Therefore;
m∠3 + m∠4 = 180° [tex]{}[/tex] Supplementary ∠s sum up to 180°
From which we have;
m∠1 + m∠2 = 180° = m∠3 + m∠4 [tex]{}[/tex] [tex]{}[/tex] Transitive property
m∠1 + m∠2 = m∠3 + m∠4
∠1 ≅ ∠4 [tex]{}[/tex] Given
m∠1 = m∠4 [tex]{}[/tex] Congruent ∠s have equal measure
Therefore;
m∠1 + m∠2 = m∠3 + m∠1 [tex]{}[/tex] [tex]{}[/tex] Transitive property
Therefore;
m∠1 + m∠2 - m∠1= m∠3 + m∠1 - m∠1 [tex]{}[/tex]Subtraction property
m∠1 - m∠1 + m∠2 = m∠3 + m∠1 - m∠1 [tex]{}[/tex]
0 + m∠2 = m∠3 + 0 [tex]{}[/tex] Inverse property
Therefore;
m∠2 = m∠3 [tex]{}[/tex] Identity property
∠2 ≅ ∠3 [tex]{}[/tex] [tex]{}[/tex] Equal angles are congruent.
Answer:
<1 and <2 are supp. givenm <1+ m<2 =180. def. of supplementary angles<1≅<4. given<3 and <4 are supp. givenm< 3 + m<4 = 180. def. of supplementary anglesm<1+m<2 = m< 3 + m<4. substitution propertym<1 = m<4. definition of ≅ anglesm<1+m<2 = m< 3 + m<1. Substitution propertym<2 = m< 3. subtraction property<2 ≅ < 3. definition of ≅ angle
Solve the equation,
3(b + 3) - 4(-2+b) = 19
Answer:
b= -2
Step-by-step explanation:
Answer:
b = -2
Step-by-step explanation:
The first thing we need to do to solve this equation is expand the brackets. To so this we need to multiply the outside term with each of the terms inside the bracket (distributive law).
This gives us:
3xb + 3x3 -4x-2 -4xb = 19
Which multiplies out to:
3b + 9 + 8 -4b = 19
Combine like terms:
-b +17 = 19
From here we move the 17 to the other side by subtracting 17 from both sides
-b +17 -17 = 19 - 17
-b = 2
Divide both sides by -1:
-b/-1 = 2/-1
Which gives us:
b = -2
Hope this helped!
Find the inverse function (find f^-1)
[tex]f(x)=\frac{x-2}{3x+3}[/tex]
I have the correct answer, I just don't know how to get to it.
answer is: [tex]f^{-1} =\frac{-2-3x}{3x-1}[/tex]
Step-by-step explanation:
f(x) = (x-2)/(3x+3). Let y = f(x).
Then y = (x-2)/(3x+3).
y(3x+3) = x - 2
3xy + 3y = x - 2
3xy - x = -3y - 2
x(3y-1) = -(3y+2)
x = -(3y+2)/(3y-1)
Hence, the inverse of f(x) is -(3x+2)/(3x-1).
SOMEONE HELP PLEASEEE !!!
Answer:
if im right its 13.09 miles since perimiter is just the total length of the outside lines.
Step-by-step explanation:
What is the sum of 9+10=???
Answer:
19 but if its is the joke version then 21
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
The greater of 2 consecutive odd integers is 8
more than 3 times the lesser. Find the integers.
Step-by-step explanation:
let the odd integers be a, a+2.
a+2=8+3a
collect like term
a-3a=8-2
-2a=6
a=-3
so the integers are -3, -1
While traveling to Europe, Phelan exchanged 250 US dollars for euros. He spent 150 euros on his trip. After returning to the United States he converts his money back to US dollars. How much of the original 250 US dollars does Phelan now have? Round to the nearest cent. 1 European euro = 1.3687 US dollars
Answer:$ 44.70
Step-by-step explanation: 250/1.3687 = 182.655-150 =32.655 times 1.3687
Answer:
He has 45 USD left.
Step-by-step explanation:
250 USD = 212 Euros. 250 - 212 = 38. 38 euros - about 45 USD, rounded.
hi! when finding a ratio, like teeth to no teeth, (pretend theres 9 faces with teeth and 10 with none), do you put the bigger number in front or follow the question and put the 9 faces with teeth first?
Answer:
it matters what word came first
Step-by-step explanation:
The order of the items in a ratio is very important, and must be respected; whichever word came first in the ratio (when expressed in words), its number must come first in the ratio.
4:3. The order of numbers in a ratio is important. ...
numerator / denominator. A fraction is another way of expressing one number divided by another. ...
24 / 56 = 0.42857.
Determine if the expression -5y^5-y^3−5y5−y3 is a polynomial or not. If it is a polynomial, state the type and degree of the polynomimal.
Answer:I think it y=73
Step-by-step explanation:
Answer: It is a polynomial, and the degree is 5.
I could be wrong on this but, i'm trying
Step-by-step explanation:
Polynomials in one variable are algebraic expressions that consist of terms in the form axn a x n where n is a non-negative (i.e. positive or zero) integer and a is a real number and is called the coefficient of the term. The degree of a polynomial in one variable is the largest exponent in the polynomial. Also, all exponents have to be positive in a polynomial. Another rule of thumb is if there are any variables in the denominator of a fraction then the algebraic expression isn’t a polynomial.Note that this doesn’t mean that radicals and fractions aren’t allowed in polynomials. They just can’t involve the variables.
The degree is 5 (since the largest exponent is 5)
Examples of Non- Polynomials
Example Polynomial Explanation
5x^-2 +1 Not a polynomial because a term has a negative exponent
3x^½ +2 Not a polynomial because a term has a fraction exponent
(5x +1) ÷ (3x) Not a polynomial because of the division
If I fall for 18 s what would my final velocity be, if I started from rest.
Answer:
176.58 m/s
Step-by-step explanation:
assume that the acceleration due to gravity, g = 9.81 m/s²
I also assume we neglect air resistance (hence we assume no terminal velocity)
recall that one of the equations of motions can be expressed as
v = u + at, where
u = initial velocity = 0 (because it says you started from rest)
v = final velocity (we are asked to find this)
a = acceleration due to gravity = 9.81 m/s²
t = time = given as 18s
simply substitute the above into the equation.
v = 0 + (9.81)(18)
v = 176.58 m/s
Jonathan was thrilled when his boss told him he was going to get a 5% raise. If Jonathan
is currently paid $10,000 per year, how much raise did he get?
Answer:10,500
Step-by-step explanation:
10,000*5%=500
How do I solve an absolute value question?
Answer:
absolute value is how many units it is away from 0. meaning that -6 and 6 both have an abosolute value of 6.
Step-by-step explanation:
Midpoint of the segment with endpoints (-8, 5) and (3, -6)
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{( - 2.5 \: , \: - 0.5)}}}}}[/tex]
Step-by-step explanation:
Let the given points be A and B
Let A( -8 , 5 ) be ( x₁ , y₁ ) and B ( 3 , -6 ) be ( x₂, y₂ )
Finding the midpoint
[tex] \boxed{ \sf{midpoint = (\frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )}}[/tex]
[tex] \dashrightarrow{ \sf{( \frac{ - 8 + 3}{2} , \: \frac{5 + ( - 6)}{2} )}}[/tex]
[tex] \dashrightarrow{ \sf{( \frac{ - 8 + 3}{2} \: , \: \frac{5 - 6}{2} )}}[/tex]
[tex] \dashrightarrow{ \sf{( \frac{ - 5}{2} \: , \: \frac{ - 1}{2} )}}[/tex]
[tex] \dashrightarrow{ \sf{( - 2.5 \: , \: - 0.5 \: )}}[/tex]
Hope I helped !
Best regards!
is 4 to 7 the same as 7 to 4? Explain why or why not.
Answer:
No, 4 to 7 is not the same as 7 to 4.
Order is important when writing a ratio.
The ratio compares the first quantity to the second.
The ratio 4 to 7 means there are more of the second quantity, but 7 to 4 means there are more of the first.
Step-by-step explanation:
Помогите пожалуйста!
i don't speak russian bro
solve for x. 7(x+2)=6(x+5)
Answer:
16
Step-by-step explanation:
7x+14=6x+30
Move x into one side and whole numbers to the other.
Solve like linear equation.
7x+14=6x+30
7x-6x=30-14
x=16
Answer:
x = 16
Step-by-step explanation:
7(x+2)=6(x+5) multiply
7x + 14 = 6x + 30 add like terms
7x - 6x = 30 - 14
x = 16
Factor 6x^2+28x+16 Thank you so much for your help!
Answer:
2(3x+2)(x+4)
Step-by-step explanation:
6x^2+28x+16
first : 2 as a common factor:
2(3x²+14x+8) then factorize
2(3x+2)(x+4)
4 more is twice a number is equal to 10 what is the number
The function f(x) is shown on the graph.
What is f(0)
Answer:
-6 only
Step-by-step explanation:
i just did the test
What is 2x=4????????????
Answer:
x = 2
Step-by-step explanation:
2× = 4
x = 2
2x = 4
4/2 = 2
so...
2(2) = 4
x = 2
2x+3y=12 complete the missing value in the solution to the equation
Answer:
(-6,8) is your answer.
Step-by-step explanation:
1. 2x + 3y = 12
2. 2x +3 * 8 = 12
3. 2x + 24 = 12
4. 2x = -12
5. x = -6
So, our final answer is (-6,8)
In the morning the temperature is 0 F. It is drop out rate of 3° perh what is the temperature after five hours
Answer:
-15 degrees
Step-by-step explanation:
3 times 5 is 15 and its negative because it says it DROPS every hour and its taking the temp every 5 hrs
What type of move takes Figure A to Figure B?*
Answer: Rotation
Step-by-step explanation:
From the figure , we can observe that both figure A and b are absolutely congruent.
To translate a figure to make congruent images , we use rigid motions (Translation, Reflection, Rotation)
It is Rotation because of we move Figure A 180 degrees clockwise about the fixed point O, we will get Figure B .
It cannot be reflection because both figures are not mirror images.
It cannot be translation because all points on Figure A is not moving , as point O remained at same position throughout this which is not possible in translation.
When the movie is half over, popcorn sells for half price. Which expression can be used to determine the new cost for 3 orders of popcorn and 3 drinks? 3 Left-bracket one-half (3.50) + 1.35 Right-bracket One-half (3.50) + 3 (1.35) One-half left-bracket 3 (3.50) + 3 (1.35) right-bracket (3.50) (3) divided by one-half + 1.35
Answer:
3[1/2(3.50)+1.35]Step-by-step explanation:
The expression for new cost is 3(3.50/2 + 1.35)
What is equations?A mathematical statement that consists of two expressions connected by an equal sign is called an equation.
Given the cost of popcorn is half when movie is half over,
according to question
original cost of popcorn = 3.50
cost at interval = 3.50/2
cost of drink = 1.35
cost of 3 drink = 3 x 1.35
cost of 3 popcorn = 3 x 3.50/2
expression for new cost for 3 orders of popcorn and 3 drinks
3 x 3.50/2 + 3 x 1.35
= 3(3.50/2 + 1.35)
Hence the expression is 3(3.50/2 + 1.35)
Learn more about equations;
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the slope of (-2,3) and (4,-5)
Answer:
-4/3
Step-by-step explanation:
Slope= - 5-3/4+2
Slope= - 8/6
Slope = - 4/3
answer:
0.75 i think i'm not really sure i hope it helps tho
Step-by-step explanation:
how many pennies fit in a 22-inch circle?
Answer :
663 Pennies can fit into a 22-inch circle
The required number of pennies fit in the circle is 13.
Area of the Circle:The formula of the area of the circle is [tex]A=\pi r^2[/tex]
As we know that the standard radius of a penny is 0.75 inch
So, the area of the one penny is,
[tex]A=\pi r^2\\A=3.14\times (0.75)^2\\A=1.77[/tex]
So, the total number of pennies fit in the 22-inch circle is,
[tex]n=\frac{22}{1.77} \\n=12.49\\n\approx 13[/tex]
Learn more about the topic of the area of the circle:
https://brainly.com/question/24119229
Solve the equation below for y.
8x+4y=20