Given:
Different functions in the ordered pairs.
To find:
The function which has an inverse that is also a function.
Solution:
A relation is a function, if there exist unique output for each input.
The inverse of a function is a function, if there exist unique input for each output in the function.
It means, the inverse of a function is a function if each y value has unique x-value.
In {(-1, -2), (0, 4), (1, 3), (5, 14), (7,4)},
For y=4 we have x=0 and x=7, therefore, the inverse of this function is not a function.
In {(-1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} ,
For y=4 we have x=0 and x=5, therefore, the inverse of this function is not a function.
In {(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} ,
For all y value we have unique x values, therefore, the inverse of this function is a function.
In {(-1, 4), (0, 4), (1, 2), (5, 3), (7, 1)},
For y=4 we have x=-1 and x=0, therefore, the inverse of this function is not a function.
Therefore, the correct option is C.
Answer:C
Step-by-step explanation:
A ream of a certain brand of paper weighs about 3.225 pounds. A ream contains 500 sheets of paper. How much does a sheet of paper weigh?
Answer:
A single sheet of paper should weigh: 0.00645 pound or [tex]6.45*10^{-3}[/tex] (in scientific notation)
Step-by-step explanation:
Divide 3.225 (the weight of the ream of paper) by 500 (the amount of paper in a ream).
If you need the scientific notation form, simply move the decimal point/place right or left until you end up with a whole number that is between 1 and 10 (in this case, 3 times to the right), then determine what power of 10 it should be, depending on the number of times you moved the decimal place (in this case, the power is -3).
The power/exponent is determined by the direction you have to move your decimal point, right=negative and left=positive. For example, if you started off with the number 6450, you would move the decimal point 3 times to the left and your power would be positive 3, which results in [tex]6.45*10^{3}[/tex].
Hope this helps!
First correct answer will get braniley
Answer:
The first one
Step-by-step explanation:
According to definition of proportion, the correct statement is,
⇒ AC / BC = DF / EF
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
⇒ Δ ABC ≅ Δ EFD
Now,
Since, We have;
⇒ Δ ABC ≅ Δ EFD,
Hence, By definition of congruency, the ratio of there corresponding sides are equal.
So, We get;
⇒ AC / BC = DF / EF
Thus, ''Option 3'' is true.
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Use fundamental identities and/or the complementary angle theorem to find the exact value of the given expression. Do not use a calculator. sec234°−tan234°
Answer:
1Step-by-step explanation:
Given the expression sec²34°−tan²34°, to get the exact value using the fundamental identities and/or the complementary angle theorem, we will apply the trigonometry identity
From sin²θ+cos²θ = 1
Divide both sides of the expression by cos²θ
sin²θ/cos²θ+cos²θ/cos²θ = 1/cos²θ
tan²θ+1 =sec²θ
Since sec²θ= tan²θ+1, hence sec²34°= tan²34°+1... 1
Substituting equation 1 into the expression given in question we will have;
sec²34°−tan²34°
= (tan²34°+1)-tan²34°
collect like terms
= tan²34°-tan²34°+1
= 1
Hence the exact value of the expression sec²34°−tan²34° is 1
Crab boats require 102 gallons of oil to run their
engines properly. How much oil does that equal in quarts?
Answer:
408 quarts
Step-by-step explanation:
Which scenario shows the best example of intrinsic motivation? O Zareem takes good notes in class to know the lesson better. O Yuto answers questions in class to impress the teacher. O Arthur prepares study sheets in class for other students. O Nikita shows up to class to avoid getting into more trouble.
Answer:
The first one. Zareem takes good notes in class to know the lesson better
The first one. is the answer
Can someone help me with this simple math problem, I’m a little confused on what’s the correct answer. I will mark you brainliest.
Answer:
Its irrational because pi is a repeating number with no pattern.
UwU hope this helps
the sum of 9 and 2 times the number d
Answer:
(9+2)d
Step-by-step explanation:
The sum of 9+2
Times the variable, d
Apply the distributive property to rewrite 3(2-b).
Answer:
3·2 - 3·b = 6 - 3b
Step-by-step explanation:
You "distribute" the 3 over the 2 and the -b.
Distribute the expression (u - 6) x 4.
Answer:
4u - 24
Step-by-step explanation:
(u-6)*4
Distribute
4*u - 4*6
4u - 24
Mr. and Mrs. Tournas know that their son will attend a college, in 14 years, that they estimate to cost approximately $250,000. How much should they deposit now if they assume that they can earn 8.5% compounded annually?
a) $72,083.41
b) $76,055.32
c) $75,450.20
d) $79,785.45
Answer: D
Step-by-step explanation:
We will try it to determine how much the need to save using the exponential function. In an exponential function,we need the start up amount and the common difference.
We know that the common difference is is 1.085 because if they will earn 8.5% interest plus 100% .
So 1.085 raised to the number of years times a number has to equal 250,000
x * 1.085^14 = 250,000 now solve for x
3.13340357495x = 250,000
x = 79785.44544 Rounded to the nearest cent is $79785.45
Tell me all the properties of algebra
Answer:
Commutative Property of Addition.- 2 + 3 = 3 + 2 Commutative Property of Multiplication.- ex. 5 × 7 = 7 × 5 Associative Property of Addition.- ex.(2 + 3) + 6 = 2 + (3 + 6) Associative Property of Multiplication.- ex. (7 × 3) × 10 = 7 × (3 × 10) Distributive Properties of Addition Over Multiplication- ex. 2 × (2 + 8) = 2 × 2 + 2 × 8 (2 + 8) × 10 = 2 × 10 + 8 × 10The reciprocal of a non zero real number a is 1/a.- ex. reciprocal of 5 is 1/5 and 5 × (1/5) = 1Step-by-step explanation:
A group of 6 students was asked, " How many hours did you watch television last week?" Here are their responses 17 , 15 , 5 , 8 , 20 Find the mean number of hours for these students. If necessary, round your answer to the nearest tenth.
Answer:
13 hours
Step-by-step explanation:
Mean=sum of observations/number of observations
=>17+15+5+8+20/5
=>65/5
=>13
Answer: 14.2
Step-by-step explanation:
The numbers are 17,15,5,8,20, and 20 and to find their mean you need to find their average which their sum divide by the number of values.
17 + 15 + 5 + 8 + 20 + 20 = 85
85 /6 = 14.1666... and rounded to the nearest tenth is 14.2
find the endpoint of the segment with endpoint (4, 12) and midpoint (-1, 13)
Answer:
(-6,14)
Step-by-step explanation:
We are given one endpoint and the midpoint, so we have to figure out how far apart these two points are:
(4,12) and (-1,13)
First, we take the x values because these two points are using the (x,y) pattern.
How far away are 4 and -1? The answer is 5.
How far away are 12 and 13? Only 1
If we start at the endpoint (4,12) and go to the midpoint at (-1,13), we go 5 to the left. That means we need to go 5 more spaces to the left to get to the other endpoint. The first part of our answer is -6, which is 5 to the left of -1.
Doing the same thing for the y values now, to get from 12 to 13 we go up 1. So we have to go up one more to find the y value of the other endpoint. If you are at 13 and you go up one, you are at 14.
what is the trick to solving any math word problem?
Answer:
by memories the formula and practice questions
Answer:
Break it down
Take it slow
Step-by-step explanation:
By taking apart the information given, you can decide what information is useful and what isn't.
Don't rush this process. If you try and rush through math, you will likely make a mistake.
3x – 7y=9; x= -1,0, 1
Solve the equation for y.
Answer:
Answers in the pic
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask =)
Please answer this it's confusing
Answer: Approximately 1336.50301206033 square cm
=======================================================
Explanation:
If we know the three side lengths of a triangle, then we can use Heron's formula to get the area
Heron's formula is
[tex]A = \sqrt{S(S-a)(S-b)(S-c)[/tex]
with S being the semiperimeter, or half the perimeter, so [tex]S = \frac{a+b+c}{2}[/tex]. We add up all three sides and divide by 2.
----------------
The smaller triangle has side lengths of a = 19, b = 40, c = 41. So we get a semiperimeter of S = (a+b+c)/2 = (19+40+41)/2 = 50
Plug this along with the a,b,c values to get an area of...
[tex]A = \sqrt{S(S-a)(S-b)(S-c)}\\\\A = \sqrt{50(50-19)(50-40)(50-41)}\\\\A = \sqrt{139500}\\\\A \approx 373.496987939661\\\\[/tex]
which is approximate
-----------------
Do the same for the larger triangle as well
S = (a+b+c)/2 = (19+180+181)/2 = 190
[tex]A = \sqrt{S(S-a)(S-b)(S-c)}\\\\A = \sqrt{190(190-19)(190-180)(190-181)}\\\\A = \sqrt{2924100}\\\\A = 1710\\\\[/tex]
Interestingly enough, we get an exact area value this time as opposed to some approximation.
-----------------
The difference between the two results is the area of the shaded region
1710 - 373.496987939661 = 1336.50301206033
This is approximate since the first result was approximate.
Answer:
K = 1710 cm^2 - K = 373.497 cm^2 = 1337 cm^2
Step-by-step explanation:
Why don't you just look for the whole area and deduct the non-shaded area?
Total
Sides:
a = 180 cm
b = 181 cm
c = 19 cm
Angles:
A = 83.9744 °
B = 90 °
C = 6.02558 °
Other:
P = 380 cm
s = 190 cm
K = 1710 cm^2
r = 9 cm
R = 90.5 cm
________________________
Non shaded area:
Answer:
Sides:
a = 40 cm
b = 41 cm
c = 19 cm
Angles:
A = 73.519 °
B = 79.3849 °
C = 27.0961 °
Other:
P = 100 cm
s = 50 cm
K = 373.497 cm^2
r = 7.46994 cm
R = 20.8569 cm
where:
A = angle A
B = angle B
C = angle C
a = side a
b = side b
c = side c
P = perimeter
s = semi-perimeter
K = area
r = radius of inscribed circle
R = radius of circumscribed circle
At a certain game at a school carnival, people won 42 small prizes and 18 large prizes. For every _____ small prizes won, there were _____ large prizes won.
Answer:
For every 7 small prizes won, there were 3 large prizes won.
ratio : 42:18 or 7:3
As 42/18 is the same as 7/3 For every 7 small prizes won, there were 3 large prizes won.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, At a certain game at a school carnival, people won 42 small prizes and 18 large prizes.
Now, 42/18 = 21/9 = 7/3.
∴ For every 7 small prizes won, there were 3 large prizes won.
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5(x−6+3x)2−6 where x=2 .
Answer:
14
Step-by-step explanation:
5(x−6+3x)2−6
10(4x-6)-6
40x-60-6
40x-66
x=2
40*2-66
80-66
14
2−(−4)+3+(−6)−(−2)2, minus, left parenthesis, minus, 4, right parenthesis, plus, 3, plus, left parenthesis, minus, 6, right parenthesis, minus, left parenthesis, minus, 2, right parenthesis.
Answer: 7
Step-by-step explanation:
2−(−4)+3+(−6)−(−2)2
solution:
– x – = +
– x + = –
= 2−(−4)+3+(−6)−(−2)2
= 6 + 3 + ( – 6) – ( 2 ) 2
= 9 + ( –6 ) – ( –2 ) 2
= 3 – (–2)2
= 3 – ( –4 )
= 7
To solve any expression the BODMAS priority rule is applicable. Thus, the solution of the expression is 7.
The given expression is [tex]2-(-4)+3+(-6)-(-2)2[/tex]
Apply the BODMAS priority rule to the above expression.
To set the priorities of mathematical operations, the BODMAS is applied. BODMAS rule can be explained below:
B stands for brackets.
O stands for of, and or terms.
D stands for divide.
M for multiply.
A for addition.
S for subtraction.
Therefore, apply the BODMAS and solve the expression further.
[tex]\begin{aligned}2-(-4)+3+(-6)-(-2)2&=2-(-4)+3+(-6)-(-4)\\&=2+4+3-6+4\\&=7\end{aligned}[/tex]
Thus, the solution of the expression is 7.
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what is the value of x in the equation 6(x+1)-5x=8+2(x+1)
Answer:
it is x=-4
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Factoring expressions 3x+ 12
Answer:
3(x + 4)
Step-by-step explanation:
Factor out a 3 from both terms, since 3 and 12 are both divisible by 3.
3x + 12
3(x + 4)
So, the factored expression is 3(x + 4)
Answer: 3(x+4)
Step-by-step explanation:
Hii! Do you need to factor the expression 3x+12? No problem! :)
Note that, both 3x and 12 have something in common. This "something" is known as the greatest common factor, or g.c.f.
The g.c.f. of 3x and 12 is 3, so we divide both 3x and 12 by 3
x+4; next we put parentheses around x+4.
(x+4)
Now we put 3 outside the parentheses.
3(x+4)
Voila! There's our solution, cheers!
--
Hope that this helped! Best wishes.
--
Write as a fraction and simplify. (use the symbol / for your answer)
0.23333...
I
Answer:
23/99
Step-by-step explanation:
0.23 is x.
Because x is recurring in two decimal places, we will multiply it by 100.
100x=23.23
Then we subtract.
100x-x=23.23-0.23
99x=23
x=23/99
If there are 2.54 cm in 1 inch how long is a 36 inch long measuring stick in cm
Answer: The answer is 91.44 centimeters/cm
Step-by-step explanation:
2.54*36= 91.44 centimeters/cm
A 36-inch long measuring stick is equivalent to 91.44 cm.
To convert inches to centimeters, we can use the conversion factor:
1 inch = 2.54 cm
To find out the length of a 36-inch measuring stick in centimeters,
we multiply the length in inches by the conversion factor:
36 inches x 2.54 cm/inch
= 91.44 cm
Therefore, a 36-inch long measuring stick is equivalent to 91.44 cm.
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There are 216 black sheep and 357 white sheep in a field. How many sheep are in
the field?
563
562
3
573
572
My Progress >
Answer:
The answer is 573 this is correct
help me with this question please
Answer:
the answer is 27
Step-by-step explanation:
Help me find the slopes of these please.
Slope formula: y2-y1/x2-x1
Part one:
-7-4/-7-(-7)
-11/0
Since the denominator is 0, the slope is undefined.
Part two:
-9-(-9)/2-(-5)
0/7
Since the numerator is 0, the slope is 0.
Best of Luck!
Problem 1
Use the slope formula to get
m = (y2 - y1)/(x2 - x1)
m = (-7 - 4)/(-7 - (-7))
m = (-7 - 4)/(-7 + 7)
m = -11/0
The result is undefined as we cannot divide by zero.
This line is vertical and all vertical lines have undefined slopes. This happens when both points have the same x coordinate.
Answer: Undefined=========================================================
Problem 2
Use the slope formula again, just with different values of course
m = (y2 - y1)/(x2 - x1)
m = (-9 - (-9))/(2 - (-5))
m = (-9 + 9)/(2 + 5)
m = 0/7
m = 0
In contrast to the previous problem, we can have 0 in the numerator. Dividing 0 over any nonzero value leads to 0.
This line is horizontal as both y coordinates are the same value. All horizontal lines have a slope of 0. You can think of it like
slope = rise/run = 0/1
rise = 0 means we don't move up or down
run = 1 means we move to the right 1 unit
Answer: 0Which of the following options have the same value as 25% of 64?
Please solve!!!!!!!!!!!
Micheal just moved here from Chicago. Micheal has red hair, therefore people from Chicago have red hair
Is this Inductive reasoning or Deductive reasoning?
Answer:
inductive
Step-by-step explanation:
Inductive reasoning is based on generalization, and making conclusions without hard evidence. If Micheal has red hair and is from Chicago, inductive reasoning draws the conclusion that everyone in Chicago has red hair. Deductive reasoning would be predicting that everyone in Chicago has red hair, and then testing it to see if you are right.
please help me I dont know how to find the domain and range of this one