The weight of the original sample from which all 14 batches in the task content is; 65.8 x 10-8 grams.
What is the fundamental principle of multiplication?If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
WE have been given that Eli broke a cell sample into 14 batches, each weighing 4.7 x 10-8 grams. which follows that the task content; the weight of the original sample from which the eight batches were obtained be determined.
Hence, since each of the 14 batches weighs;
[tex]4.7 \times 10^{-8}[/tex]
Therefore, the weight of the original sample can be obtained as;
[tex]4.7 \times 10^{-8} \times 14\\\\65.8 \times 10^{-8}[/tex]
However, when the weight is expressed in scientific notation, thus the weight of the original sample is;
[tex]65.8 \times 10^{-8}[/tex]
Hence, The weight of the original sample from which all 14 batches which each weighed 4.7 x 10-8 grams are obtained as required in the task content is; 65.8 x 10-8 grams.
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1/|2x - 9|≤5
How to solve the inequality
Answer:
5<x<7
Step-by-step explanation:
Hey there !
firstly, in inequality; we must know that we should put the x alone.
so, in order to put the x alone; we should do the following process,
1</2x-9/<5
here,
adding +9 in all sides, we get;
=1+9<2x-9+9<5+9
=10<2x<14
dividing it by 2;we get
=10/2<2x/2<14/2
=5<x<7
This is the following answer. hope it helps!
Thank you!
PLEASE HELP ME FIGURE THIS OUT
Cycling.
The graph below shows the ages of the top five male finishers in the Mt. Washington Auto Road Bicycle Hillclimb each year from 2017 through 2021.
1. Write the relation of this situation as a set of ordered pairs in terms of (age, finishing place).
2. Identify the domain and range of the relation.
3. Do the ordered pairs represent a function? Explain.
Answer:From the given table, we have that:
1. The relation of the situation is: (20,2), (22.5, 5), (25,4), (27.5, 4), (29,4), (29,5), (30,1), (30,2), (30,3), (30,4), (30,5), (32.5, 1), (32.5, 3), (35,4), (40,2), (42.5, 3).
2. The domain is {20, 22.5, 25, 27.5, 29, 30, 32.5, 35, 40, 42.5} and the range is {1, 2, 3, 4, 5}.
3. There are inputs such as 25, 29, 30 and 32.5 that are mapped to multiple outputs, hence the relation does not represent a function.
What is the relation of this situation?
To build the relation, we look at the graph, and write all pairs of (Age, Finishing Place), as follows:
(20,2), (22.5, 5), (25,4), (27.5, 4), (29,4), (29,5), (30,1), (30,2), (30,3), (30,4), (30,5), (32.5, 1), (32.5, 3), (35,4), (40,2), (42.5, 3).
What are the domain and the range?
The domain of a relation is the set that contains all possible input values for the values, that is, the values of x.
The range of a relation is the set that contains all possible output values for the values, that is, the values of y.
Hence, for the given relation:
The domain is {20, 22.5, 25, 27.5, 29, 30, 32.5, 35, 40, 42.5} and the range is {1, 2, 3, 4, 5}.
When does a relation represents a function?
A relation represents a function if each value of the input is mapped to only one value of the output.
For this problem, we have that:
There are inputs such as 25, 29, 30 and 32.5 that are mapped to multiple outputs, hence the relation does not represent a function.
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Step-by-step explanation:
Simplify to create an equivalent expression.
\qquad{2(3y+6)-3(-4-y)}2(3y+6)−3(−4−y)2, left parenthesis, 3, y, plus, 6, right parenthesis, minus, 3, left parenthesis, minus, 4, minus, y, right parenthesis
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
9y9y9, y
(Choice B)
B
5y+245y+245, y, plus, 24
(Choice C)
C
9y-249y−249, y, minus, 24
(Choice D)
D
9y+249y+24
The generated equivalent expression is 9y + 24. So, the correct answer is option D.
What is an expression?
An expression can be defined as the combination of variables and constants with two or more operations applied on it. The operation can be addition, subtraction, multiplication and division.
Simplifying to generate an equivalent expression
The given expression is 2(3y + 6) - 3(- 4 - y)
= 2(3y + 6) + 3(4 + y)
= 6y + 12 + 12 + 3y
= 6y + 3y + 24
= 9y + 24
Hence, the generated equivalent expression is 9y + 24.
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Can y’all help me please??
Answer: 29/21
Quotient: 1
Reminder: 8
Step-by-step explanation:
Add up the amount of 7th graders playing instruments (not including drums) total and put that number under the amount of 8th graders playing a instrument.
Use the 1st digit 2 from dividend 29
21 & 29 squared root
Since 2 is less than 21, use the next digit 9 from dividend 29 and add 0 to the quotient. Find the closest multiple of 21 to 29.
1×21=21 is the nearest. Now subtract 21 from 29 to get reminder 8. Add 1 to quotient.
Since 8 is less than 21, stop the division. The reminder is 8. The topmost line 01 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 1.
find the coordinates of pint P along the directed line segment AB so that AP to PB is the give ratio 2 to 6
Coordinates of P is 8
Since 3+2 = 5, we are dividing line segment AB into 5 congruent parts with point P 3/5 of the way from A to B.
x-coordinate of P = x-coordinate of A + (3/5)(change in x from A to B) = -4 + (3/5)(20) = 8
y-coordinate of P = y-coordinate of A + (3/5)(change in y from A to B) = 8 + (3/5)(-10) = 2
P = (8,2)
In each axis, find the distance from A to B, apply the ratio to get the distance from A to P, and add that value to A.
Note the ratio: We are given the ratio of AP to PB as 3/2. This means that the ratio of AP to AB is 3/5
Here is is for the X-axis:
AB = 20
AP = 20 *3/5 = 12
So P = -4 + 12 = 8
It is one of the branches of geometry where the position of a point is defined using coordinates.
Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.
A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
It is used to divide any line into two parts, in m:n ratio
The number line which is also known as a Cartesian plane is divided into four quadrants by two axes perpendicular to each other, labelled as the x-axis (horizontal line) and the y-axis(vertical line).
The four quadrants along with their respective values are represented in the graph below-
Quadrant 1 : (+x, +y)
Quadrant 2 : (-x, +y)
Quadrant 3 : (-x, -y)
Quadrant 4 : (+x, -y)
The point at which the axes intersect is known as the origin. The location of any point on a plane is expressed by a pair of values (x, y) and these pairs are known as the coordinates.
How To Find Coordinates of a Point on Graph With Examples
A set of values that shows the exact position of a point in a two-dimensional coordinate plane are called the coordinates. These represent the exact location of a point on a coordinate graph having both x, y axes. You can check the definition of coordinates, step by step detailed procedure to find the coordinates of a point with solved examples.
Coordinates Definition
A pair of numbers that describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines called the coordinates. Usually represented by (x, y) the x value and y value of the point on a graph. Every point or an ordered pair contains two coordinates. The first one is the x coordinate or abscissa and the second is the y coordinate or ordinate. The values of the coordinates of a point can be any positive or negative real number.
The other types of coordinates are map coordinates (north/south, east/west), three-dimensional coordinates, polar coordinates (distance, angle), etc. Detailed information about x coordinate, y coordinate of a point follows:
x‐coordinate (Abscissa): The first number or the number which is located to the left side of a comma in the point is the x coordinate of the ordered pair. It represents the amount of movement along the x-axis from the origin. The movement is to the right side if the number is positive and to the left side of the origin if the number is negative.
y‐coordinate (Ordinate): The number which is located to the right side of the comma in the ordered pair or the second number is known as the y coordinate of the ordered pair. This ordinate indicates the amount of movement along the y-axis. If the number is positive, then the movement is above the origin and the movement is below the origin if the number is negative.
Point on x-axis: A point on the x-axis means its movement along the horizontal line is always zero and the y-coordinate of all points on the x-axis is zero. Therefore, the coordinates of a point on the x-axis are of the form (x, 0).
Point on y-axis: A point on the y-axis means the distance from the y-axis is zero and the x coordinate of every point on the y-axis is zero. Hence, the coordinates of a point on the y-axis are (0, y).
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Simplify.
(y^5)^3
Write your answer without parentheses.
Answer:
[tex]\boxed{\sf y^{15}}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sf (\:y^5\:)^3[/tex]When any expression is given in the format [tex]\sf (\ a^b \ )^c[/tex] then [tex]\sf a^{bc}[/tex].
[tex]\sf \rightarrow y^{5(3)}[/tex]simplify
[tex]\sf \rightarrow y^{15}[/tex]What is the image of the point (-7,-6) after a rotation of 270° counterclockwise
about the origin?
Submit Answer
Drivsar Police Tormer Sondico
hp
attempt 2 out of 2
Answer:
(-6, 7)
Step-by-step explanation:
90 degrees counterclockwise / 270 degrees clockwise:
(x,y) -> (-y,x)
180 degrees counterclockwise / 180 degrees clockwise:
(x,y) -> (-x,-y)
270 degrees counterclockwise / 90 degrees clockwise:
(x,y) -> (y,-x)
() Which number is closest to √5?
1.7
2.2
3.4
3.1
Answer:
Step-by-step explanation:
Find x
A. 2.6
B 3.1
C 2.9
D 4
Answer:x=
Step-by-step explanation:
1. Which of the following is a linear inequality in two variables? A. 3a-2b = 6 C. 3x ≤ 10 B. 3c+16 < -10 D. 3x + 4y ≥ 10
Answer:
D
Step-by-step explanation:
a linear expression in two variables has the form ax + by
an inequality uses the symbols < , > , ≤ , ≥
the only expression in this form is
3x + 4y ≥ 10
Using company C’s phone plan, the cost of an overseas phone call is a $0.80 connection fee plus 23 cents per minute. If the total cost of the call is 7.93, how long is the phone call?
Answer: 31 Minutes
Step-by-step explanation:
Minus 0.80 from 7.93, and then divide 7.13 by 0.23 and you get 31
Simplify, if possible.
8ab² +3ab+2a-3b+5
A. The expression is in its simplest form.
B. -10ab² +5
2
C. 8ab² + 2ab +5
D.
8ab²-3ab+5
Please select the best answer from the choices provided
Answer:
A. The expression is in its simplest form.
Step-by-step explanation:
Answer:
i tried this i think the answer is 11a plus 2a subract3b ppus 5
Identify all the pairs of parallel sides of each figure.
Answer:
2 on the 1st, 1 on the second, 3 on the third, 1 on the fourth
Let D={12,15,17), E = {12,14,15,16) and F = {11,13,14,15,17).
List the elements in the set D UE.
DUE= (Use commas to separate answers.)
The elements that will be coming in the set D∪E will be {12, 14, 15, 16, 17}.
A set may be defined as a collection of letters or numbers that are written in order to depict a certain value or entity. A set is always represented by a capital letter symbol and is always written in curly brackets { }. Union of two sets may be defined as a new set which has the collection of all the elements of the two individual sets. Union of two sets is represented by the symbol '∪'. Union of two Indvidual sets, set A and set b is written as A∪B.
Now, according to the question set D is = {12, 15, 17} and set E is = {12, 14, 15, 16}.
The union of the two sets contains all the elements of the sets D and E.
Thus, D∪E will be given by {12, 14, 15, 16, 17}.
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11. Find the solution of the following system of equations using substitution:
2x + 7y = 5
y = x + 2
Answer:
(x,y) = (-1,1)
Step-by-step explanation:
step 1
subsitute the given value of y into the equation
2x+7(x+2)=5
step 2
solve for x
x= -1
step 3
subsitute the value of x in to the second equation
y= -1+2
step 4
solve for y
y=1
step 5
check if there true by putting the value of x and y back in to the equation.
then configure x and y into an ordered pair.
(x,y)=(-1,1)
I hope this helped!
please help simplify !
Answer:
B
Step-by-step explanation:
using the rule of exponents
[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]6^{9}[/tex] ÷ 6³ = [tex]6^{(9-3)}[/tex] = [tex]6^{6}[/tex]
Between what two integers does square root of -80 lies
Answer: 8 and 9
Step-by-step explanation:
square root of - 80 is 8.94427191 so 8 and 9 is the integers around it.
How many times larger is (1.064 x 101) than (7 x 10−1)?
0.152
15.2
6.58
7.448
Answer:
is 15.2
Step-by-step explanation:
Choose the estimate closest to the length of a woman's hand : 30 cm, 200mm, or 20 mm. Which is the correct answer?
Answer:
200mm
Step-by-step explanation:
200mm can be rewritten as 20 cm
a womans hand is on average 17.3 cm
this is the closest estimate out of the three
A jewelry maker incurs costs for a necklace according to the equation shown below.
C(x) = 30x + 1692
The revenue function for the necklaces is given below.
R(x) = 77x
How many necklaces must be sold to break even?
necklaces
What is the area of the polygon if the side length of the square is 4
Answer:
16
Step-by-step explanation: This is because when we look at the square we realize by definition it is a 4-sided shape with 4 equal side lengths this means that if one side is 4 all the 4 sides of a square are also 4 and in this case, we would do length times width and get an answer of an area of 16 units.
1. Let f be the function given by f(x)= X/ √x²-4 Find the domain of f.
A factory bottles 360 bottles of juice in 5 minutes. Find the factory’s unit rate of bottles per minute.
Answer:
72
Step-by-step explanation:
let's begin by restating what we already know,
360 bottles of juice in 5 minutes
for goodness's sake let's abbreviate this
360 boj in 5 mins
RATIO TIME!
360 : 5
pay attention how I put the BOJ (bottles of juice) first and the time last
now to find how many boj per min. we will say
[tex]\frac{1}{5} (360: 5)[/tex]
72:1
so, we now know that the factory of juice produces 72 bottles of juices per minute ( that's ALOT of juices per minute imo)
^_^ hope this helps, happy learning
what’s the answer to this question
Prove that:
( 1 - tan^4 A)cos^4 A = 1 - 2 sin^2 A
Here we go ~
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
[tex]\qquad \sf \dashrightarrow \: (1 - \tan {}^{4} (a) ) \cos {}^{4} (a) [/tex]
[tex]\qquad \sf \dashrightarrow \: (1 + \tan {}^{2} (a) )(1 - { \tan}^{2} (a)) \cos {}^{4}(a ) [/tex]
[ a² - b² = (a + b)(a - b) ]
[tex]\qquad \sf \dashrightarrow \: ( \sec {}^{2} (a) )(1 - ( \sec{}^{2} (a) - 1) )\cos {}^{4} (a) [/tex]
[ sec² a = 1 + tan² a, so : tan² a = sec²a - 1 ]
[tex]\qquad \sf \dashrightarrow \: \bigg( \dfrac{1}{{}cos^{2} (a)} \bigg)(2 - \sec{}^{2} (a) ) \cos {}^{4} (a) [/tex]
[tex]\qquad \sf \dashrightarrow \: \bigg(2 - \dfrac{1}{ \cos {}^{2} (a) } \bigg) \cos {}^{2} (a) [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{2 \cos {}^{2} (a) - 1}{ \cos {}^{2} (a) } \times \cos {}^{2} (a) [/tex]
[tex]\qquad \sf \dashrightarrow \: 2 \cos {}^{2} (a) - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 2(1 - \sin {}^{2} (a) ) - 1[/tex]
[ sin²a + cos² a = 1, hence sin²a = 1 - cos²a ]
[tex]\qquad \sf \dashrightarrow \: 2 - 2 \sin {}^{2} (a) - 1[/tex]
[tex]\qquad \sf \dashrightarrow \: 1 - 2 \sin {}^{2} (a) [/tex]
Answer:
See proof below
Step-by-step explanation:
Prove [tex]\left(\:1\:-\:tan^4A\right)cos^4A\:=\:1\:-\:2\:sin^2A[/tex]
[tex]\left(1-\tan ^4\left(A\right)\right)\cos ^4\left(A\right)[/tex] can be expressed in sin, cos terms
Use the trigonometric identity [tex]\tan \left(x\right)=\frac{\sin \left(x\right)}{\cos \left(x\right)}[/tex]
[tex]\left(1-\tan ^4\left(A\right)\right)\cos ^4\left(A\right) = \left(1-\left(\frac{\sin \left(A\right)}{\cos \left(A\right)}\right)^4\right)\cos ^4\left(A\right)[/tex]
[tex]\mathrm{Simplify}\:\left(1-\left(\frac{\sin \left(A\right)}{\cos \left(A\right)}\right)^4\right)\cos ^4\left(A\right)[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]
= [tex]\left(1-\frac{\sin ^4\left(A\right)}{\cos ^4\left(A\right)}\right)\cos ^4\left(A\right)[/tex]
Multiplying the expression in parentheses by [tex]\cos ^4\left(A\right)[/tex] we get
[tex]\frac{\cos ^4\left(A\right)-\sin ^4\left(A\right)}{\cos ^4\left(A\right)}\cos ^4\left(A\right)[/tex]
Cancel the common factor [tex]\cos ^4\left(A\right)[/tex]
This gives us
[tex]\cos ^4\left(A\right)-\sin ^4\left(A\right)[/tex]
Now,
[tex]\sin ^4\left(A\right)=\left(\sin ^2\left(A\right)\right)^2[/tex]
[tex]\cos ^4\left(A\right)=\left(\cos ^2\left(A\right)\right)^2[/tex]
[tex]\:\cos ^4\left(A\right)-\sin ^4\left(A\right)[/tex] = [tex]\left(\cos ^2\left(A\right)\right)^2-\left(\sin ^2\left(A\right)\right)^2[/tex]
[tex]\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)[/tex]
[tex]\left(\cos ^2\left(A\right)\right)^2-\left(\sin ^2\left(A\right)\right)^2=\left(\cos ^2\left(A\right)+\sin ^2\left(A\right)\right)\left(\cos ^2\left(A\right)-\sin ^2\left(A\right)\right)[/tex]
= [tex]\cos ^2\left(A\right)-\sin ^2\left(A\right)[/tex] [tex]\textrm{ since }\cos ^2\left(A\right)+\sin ^2\left(A\right)[/tex] = 1
Using the fact that [tex]\cos ^2\left(A\right)=1-\sin ^2\left(A\right)[/tex]
we get
[tex]\cos ^2\left(A\right)-\sin ^2\left(A\right) = 1-\sin ^2\left(A\right)-\sin ^2\left(A\right)\\\\= 1-2\sin ^2\left(A\right)[/tex]
Proved
The tax on a $30 item is $1.50.
Find the tax on a $50 item.
Answer: $2.50
Step-by-step explanation: To find the tax rate, you need to divide 1.50 by 30
1.5/30 = .05, which is the percent taxed. To find the tax amount for a $50 item, you just need to multiply $50 by the tax rate, which is .05, to get $2.50
11. Represent and Connect After a recycling
awareness program, the number of tons of
recyclable material taken to the landfill is
reduced by 13 tons per month. Represent
the total change in the tons of recyclable
material taken to the landfill after
10
7 months resulting from the awareness
program. Show your work.
The total change in the tons of recyclable material taken to the landfill after 10 7 months resulting from the awareness program = (x - 95.9) tons, where x is the initial amount.
In this question, we have been given after a recycling awareness program, the number of tons of recyclable material taken to the landfill is reduced by 13 tons per month.
We need to represent the total change in the tons of recyclable material taken to the landfill after 10 7 months resulting from the awareness program.
Given that reduction in materials = 13 7/10 tons per month
We rewrite the improper fraction 13 7/10 as a proper fraction.
13 7/10 = 137/10
Monthly reduction = 137/10 tons
After 7 months : (7 × 137/10)
= 959/10 tons
= 95.9 tons
Change in amount of material taken to the land fill:
Initial amount - amount after 7 months
If initial amount be x, then the change in amount = (x - 95.9) tons
So, we get an expression (x - 95.9)
Therefore, the total change in the tons of recyclable material taken to the landfill after 10 7 months resulting from the awareness program = (x - 95.9) tons, where x is the initial amount.
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A quadratic function has its vertex at the point
(
2
,
−
10
)
(
2
,
-
10
)
. The function passes through the point
(
−
6
,
−
5
)
(
-
6
,
-
5
)
. Find the quadratic and linear coefficients and the constant term of the function.
the standard form equation is y=ax²+bx+c where a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.
therefore, for y = 5/16x² - 5x/4 -35/4
Quadratic coefficient = 5/16, linear coefficient = 5/4, constant term = -35/4
What are zeros ?
zeros denotes the factors of the given equation in other words the zeros of the function are the values that make the factors zero. The factors need to multiply out to give the original standard-form equation.
Polynomial roots are the same as polynomial zeros, so they can be found by factoring the quadratic equation into two linear factors, after which they can be equating to zero.
Its easiest to first start out with a vertex form equation because it can then be converted to a standard quadratic equation.
given a vertex at (2,-10) , and point of intersection at (6,-5), the equation can be set up like this in the form of :
y = a(x-h)²+ k
y = a(x-2)^2-10, as we know h and k from the vertex.
We also know y and x from the given point of intersection so a can be solved by substituting the values of x and y to get value of a.
y = a(x-2)²-10
-5 = a(6-2)² - 10
16a = 10-5
a = 5/16
a = 5/16 which is also known as the quadratic coefficient because it is part of a second degree quantity and a Trinomial as a whole(quadratic).
since all the variables are known, you can expand the equation and set it to standard form :
y = 5/16(x-2)²-10
y = 5/16(x-2)² - 10
y = 5/16(x²+4-4x) -10
y = 5/16x² + 5/4 - 5x/4 - 10
y = 5/16x² - 5x/4 -35/4
For reference, the standard form equation is y=ax²+bx+c where a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.
In this instance, 5/16x² - 5x/4 -35/4 = ax²+bx+c
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Write the following in terms of sin x and cos x ; then simplify if possible. sec x csc x cot x =
The expression sec x csc x cot x in terms of sin x and cos x is
1/ (sin x)^2.
According to the given question.
We have an expression sec x csc x cot x.
Here, we have to write the above expression in terms of sinx and cosx.
As we know that,
sec x = 1/cos x
csc x = 1/sin x
cot x = cos x/ sin x
Thereofore, the expression sec x csc x cot x in terms of sin x and cos x is given by
sec x csc x cot x
= (1/cos x) (1/sinx) (cosx/ sinx)
= 1/ (sin x)^2
Hence, the expression sec x csc x cot x in terms of sin x and cos x is
1/ (sin x)^2.
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If f(x) is a decreasing function, which of the following statements must be true? Select all that apply.
(Assume that f(x) is always decreasing.)
a) f(5)−f(1) / 5−1 > 0
b) f(5)−f(1) / 5−1 < 0
c) For some value of x≠5, f(x)=f(5)
d) f(5) < f(1)
e) f(5) > f(1)
The two true statements are:
b) (f(5)−f(1)) / (5−1) < 0
d) f(5) < f(1)
Which of the following statements must be true?
We know that f(x) is a decreasing function, this means that, as x increases, the value of f(x) decreases.
So, if there are two values in the domain a and b, such that a < b, we will have that:
f(a) > f(b).
Then the statement:
[ f(5) - f(1)]/(5 - 1) < 0
Is true, because f(1) is larger than f(5).
Which means that statement d ( f(5) < f(1)) is also true.
Then the two correct options are b and d.
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