Function: A function is a mathematical relationship between two sets of values, where each element in the first set (called the domain) is related to exactly one element in the second set (called the range). A function can be represented by a formula, equation, or graph, and it describes how one set of values is related to another.
Domain: In a function, the domain is the set of all possible values that can be used as input for the function. It is the set of values that the function operates on.
Range: In a function, the range is the set of all possible values that can be produced as output by the function. It is the set of values that the function produces as a result of operating on the domain.
Vertical line test: The vertical line test is a method used to determine whether a graph represents a function.
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Directions: Find the sum for each of the following arithmetic series below. Use the summation
formula to find the sums.
1. A series with six terms, the first term is five, and the common difference is five.
2. A series with six terms, the first term is nine and the common difference is twelve.
3. A series with five terms, the first term is 5.7 and the common difference is 1.4.
Therefore , the solution to the given problem of arithmetic mean comes out to be 1. 105, 2. 234 and 3. 42.5
Arithmetic mean: What is it ?The combination of the amount of all of the values in a list and the number of items in the that list, split by both, is the arithmetic average or mean of the group. The mathematical progression is same to this. This mean of the digits 5, 7, and 9 is 4,
For example, as expression 5 + 7 + 9 is 21, and 21 divided by 3 [there are actually three numbers] equals 7.
Given:
1) There are six terms in AP, with terms a and d each being worth five points.
2) There are 6 terms in AP, with terms 9 and 12 respectively.
3) In AP, there are five terms, where an is 5.7 and d is 1.4.
4) In AP, = 20, t21 = 400
5) In AP, t100 = 99 and a = 0
Find the sum of the terms in the arithmetic series.
As is common knowledge, Sn in the AP equals n/2[2a+(n-1)d]
To determine: the total terms in the arithmetic series
The AP sum of n words is well known. Sn = (n-1)/2[2a+(n-1)d]
1) There are 6 terms in the case where a = 5 and d = 5, as shown by S6 = [2(5)+(61)5] = 3[10+5(5)] = 3[10 + 25] = 3(35) = 105
2) There are 6 terms in the case where a = 9 and d = 12, where S6 = [2(9)+(61)12] = 3[18+5(12)] = 3[18+60] = 3(78) = 234
3) There are 5 terms total, with terms a = 5.7 and d = 1.4.
S5= [2(5.7)+(5—1)1.4] = 2.5[11.4+4(1.4)] = 2.5[11.4+5.6] = 2.5(17) = 42.5
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the ratio of boys to girls in the sixth grade is 3 to 5 if there are 45 girls how many students are there in the 6th grade
Answer: 27 boys
Step-by-step explanation:
There is a rule in math, what you do to one side, you do to the other.
So in this case the ration is 3:5
?:45
As you can see, they multiplied 5 by 9 to get 45, remember the rule, so we do the same.
3 times 9 is 27, so 27 boys
Ross walked 7 miles in 2 hours. What is his unit rate of miles per hour?
Answer:
3.5 miles per hours
Step-by-step explanation:
7/2 =3.5
100 POINTS!!!!! PLEASE HELP!
Answer:
[tex]a^{12} b^{4}[/tex]
Step-by-step explanation:
To simplify we will have to use the negative exponent rule and the power rule along with some algebra.
Negative Exponent Rule
[tex]a^{-b} =\frac{1}{a^b}[/tex]
Power Rule
[tex](a^b)^{c} =a^{bc}[/tex]
Given
[tex](a^{-4}b^{-1}c )^{2} (a^2bc)^{2}[/tex]
Rewrite [tex]a^{-4}[/tex] using negative exponent rule.
[tex](\frac{1}{a^{4}}* b^{-1}c )^{2} (a^2bc)^{2}[/tex]
Rewrite [tex]b^{-1}[/tex] using negative exponent rule.
[tex](\frac{1}{a^{4}}* \frac{1}{b}*c )^{2} (a^2bc)^{2}[/tex]
Simplify
[tex](\frac{c}{a^4b} )^{2} (a^2bc)^{2}[/tex]
Rewrite the base as its reciprocal.
[tex](\frac{a^4b}{c} )^{2} (a^2bc)^{2}[/tex]
Apply the power rule.
[tex]\frac{a^8b^2}{c^2} *(a^2bc)^{2}[/tex]
Apply the power rule.
[tex]\frac{a^8b^2}{c^2} *a^4b^2c^2[/tex]
Cancel the common factor of [tex]c^2[/tex].
[tex]a^8b^2 a^4b^2[/tex]
Apply the power rule.
[tex]a^{12} b^{4}[/tex]
Answer:
[tex]a^{12}\:b^{4}[/tex]
Step-by-step explanation:
Given expression:
[tex]\left(a^{-4}\:b^{-1}\:c\right)^{-2}\left(a^2\:b\:c\right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies a^{(-4 \times -2)}\:b^{(-1 \times -2)}\:c^{-2}\:a^{(2 \times 2)}\:b^2\:c^2[/tex]
Simplify:
[tex]\implies a^{8}\:b^{2}\:c^{-2}\:a^{4}\:b^2\:c^2[/tex]
Collect like terms:
[tex]\implies a^{8}a^{4}\:b^{2}b^2\:c^{-2}c^2[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies a^{(8+4)}\:b^{(2+2)}\:c^{(-2+2)}[/tex]
Simplify:
[tex]\implies a^{12}\:b^{4}\:c^{0}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^0=1:[/tex]
[tex]\implies a^{12}\:b^{4}(1)[/tex]
[tex]\implies a^{12}\:b^{4}[/tex]
Education order reads: 24 hours after bone marrow transfusion give Neupogen 10 mcg/kg/d IV. Supply on hand. Neupogan 300 mcg/ml. Patient’s weight 115 lbs. Give __ mL
Education order reads: 24 hours after bone marrow transfusion give Neupogen 10 mcg/kg/d IV. Supply on hand. Neupogan 300 mcg/ml. Patient’s weight 115 lbs. Give 1.74 mL
What is the Neupogen calculations about?To calculate the appropriate dosage of Neupogen to give to the patient, we need to convert the patient's weight from pounds to kilograms and then use the dosage provided in the order (10 mcg/kg/d IV).
First, we have to convert the patient's weight from pounds to kilograms:
115 pounds = 52.16 kg
Now we can use the dosage provided in the order (10 mcg/kg/d IV) to calculate the appropriate dosage for the patient:
10 mcg/kg/d IV
= 10 mcg/kg/day * 52.16 kg
= 521.6 mcg/day
Then, since the Neupogen is available in a solution of 300 mcg/ml, we can use the following formula to calculate the required volume of solution to give to the patient:
Volume = Dosage / Concentration
= 521.6 mcg / 300 mcg/ml
= 1.74 ml
So, the education order reads 24 hours after bone marrow transfusion, give 1.74 mL of Neupogen at a concentration of 300 mcg/mL IV.
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in the past year, a veterinarian finds a 35% of animals she treats are cats. Assuming the pets are brought to the vet randomly, what is the probability that exactly 2 of the next 5 animals brought in will be cats?
ax + by = 6000 and a + 5 = b are two equations that might be used to calculate how many soup cans and frozen dinners were purchased.
What is an equation?There are several methods to define a formula. A mathematical statement that establishes the equivalence of two mathematical expressions is the definition of an equation in algebra. This is best shown by the formula 3x + 5 = 14. In this instance, the word equal comes between the phrases 3x + 5 and 14. Even the most basic algebraic equations include the usage of mathematical variables.
X now has 300 mg of sodium in it.
[tex]x = 300[/tex]
Y also has 450 mg of sodium in it.
[tex]y = 450[/tex]
Samuel reportedly buys five more frozen dinners than soup cans, and they all have a combined salt content of 6000 mg.
Let the number of frozen dinners be "b," and the number of soup cans be "a."
ax + by = 6000
a(300) + b(450) = 6000 .
Samuel bought 5 more frozen dinners than soup cans, according to the inquiry, which results in equation
[tex]a + 5 = b \\a(300) + (a + 5)(450) = 6000\\300a + 450a = 6000 - 2250\\ 750a = 3750\\ a = 3750/750\\ a = 5\\5 + 5 = b\\ b = 10[/tex]
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I need help because I don't understand and I need an explanation of how to do it, please.
Answer:
Step-by-step explanation:
a.we konw DC=2b and DO=OC, so the coordinate of D(-b, 0), C(b, 0)
b.we konw the height of rectangle is h, so the coordinate of A(-b, h), B(b, h).
One integer is 5 less than another. The sum of their squares is 277
The equation is x² + y² = 277 and the value of x and y is 9 and 14 respectively
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the two number be x and y
One integer is 5 less than another
So , x = y - 5
x - y = -5 be equation (1)
And , sum of their squares is 277
So , x² + y² = 277 be equation (2)
On simplifying the equation , we get
( x - y )² = x² + y² - 2xy
Substituting the values in the equation , we get
( -5 )² = 277 - 2xy
2xy = 277 - 25
2xy = 252
And , ( x + y )² = x² + y² + 2xy
Substituting the values in the equation , we get
( x + y )² = 277 + 252
( x + y )² = 529
( x + y ) = 23 be equation (3)
Adding equation (1) and equation (3) , we get
2x = 18
x = 9
So , y = 14
Therefore , the value of x and y is 9 and 14 respectively
Hence , the equations are solved
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if a tree is 105 metres tall in real life what would be the height of the diagram of the tree if the scale was 1: 1000
Answer:
1.05
Step-by-step explanation:
it is 105 divided by 1000
Answer:
0.105 metres
Step-by-step explanation:
105 divided by 1000
What is an equation for the linear function whose graph contains the points (9, 7) and (4, −8)?
Enter your answers in the boxes.
y−
=
(x−9)
The line that passes through these two points is y=x-2
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here function whose graph contains the points (9, 7) and (4, −8)
Thus using the two point formula for a line we get the equation as
y-7=(x-9)
y=x-2
Hence, The line that passes through these two points is y=x-2
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A conservative investor has $100,000 to invest. The investor has decided to use three vehicles for generating income: Municipal bonds, a certificate of deposit (CD), and a money market account. After reading a financial newsletter, the investor also has identified several additional restrictions on the investments:
a. No more than 40 percent of investment should be in bonds
b. The proportion allocated to the money market account will be at least double the amount in the CD
c. The annual return will be 8% for bonds, 9% for the CD and 7% for the money market account. Assume that the investor wants to maximize the total annual return
Then, formulate the LP model for this problem, ignoring any transaction costs and the potential for different investment
Answer: Here, let X,Y,ZX,Y,Z indicate the amount in dollars to be invested
Step-by-step explanation: Here, let X,Y,ZX,Y,Z indicate the amount in dollars to be invested
solue, giving all solutions between 0 and 360 degrees 8 (COS X)² - 10 COS X+3=0
Step-by-step explanation:
please refer to the sketch
Solve the differential equation dy/dx=(1+y²)e^x ?
This is a separable differential equation, which means we can separate the variables y and x on either side of the equation. To do this, we'll move all the terms involving y to one side and all the terms involving x to the other side.
dy/dx = (1+y²)e^x
We'll divide both sides by (1+y²)e^x:
dy/(1+y²)e^x = dx
Now we'll integrate both sides with respect to their respective variables. The integral of dy/(1+y²) with respect to y is the inverse tangent (tan^-1) function, so we'll use that on the left side:
∫ dy/(1+y²) = ∫dx + C
tan^-1(y) = x + C
On the right side, we'll integrate e^x with respect to x, which gives us e^x. So we have:
tan^-1(y) = e^x + C
We can solve for y by reversing the tan^-1 function:
y = tan(e^x + C)
Where C is an arbitrary constant of integration.
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Bridgette has drawn a representation of a sphere with a
radius of 3 units, using the graphs of a circle and an ellipse,
as shown in the picture below on the left.
She needs to determine the equations of the graphs that
will generate the representation of the 3D sphere, as
shown in the picture below on the right.
What are possible equations of the circle and ellipse that
Bridgette can use to create her 3D drawing?
Answer:
C
Step-by-step explanation:
You want the equations of the circle and ellipse in the given figure.
EquationsThe standard form equation for an ellipse is ...
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
where 'a' and 'b' are the semi-axes in the x-direction and y-direction, respectively.
You will notice that when a=b=r, the ellipse becomes a circle and the equation can be rewritten as ...
[tex]\dfrac{x^2}{r^2}+\dfrac{y^2}{r^2}=1\ \Longleftrightarrow\ x^2+y^2=r^2[/tex]
ApplicationHere, the radius is 3, the same as the semi-major axis in the x-direction (a=3). The ellipse axis in the y-direction appears to be about 1/3 that value, so b=1, and the equations of the circle and ellipse are ...
[tex]x^2+y^2=9\qquad\text{circle}\\\\\dfrac{x^2}{9}+\dfrac{y^2}{1}=1\qquad\text{ellipse}[/tex]
In a survey, 13 out of 20 teachers respond yesto a proposal for a new after-school club. In the same survey, 37 out of 50 students respond yes. a.Which group is more in favor of the new after-school club, teachersor students? Show your work
Answer: To compare the level of support for the new after-school club between teachers and students, we can calculate the percentage of individuals in each group that responded "yes" to the proposal.
For teachers: 13 out of 20 is equivalent to 13/20 = 0.65 or 65%
For students: 37 out of 50 is equivalent to 37/50 = 0.74 or 74%
Based on the percentage of individuals in each group that responded "yes," we can see that students are more in favor of the new after-school club than teachers. 74% of students responded "yes" to the proposal, while only 65% of teachers responded "yes."
It's worth mentioning that it's important to keep in mind that this comparison is based on the sample size of teachers and students that responded to the survey and not the whole population, also if the sample size isn't representative of the population and not randomly selected it can't be generalized.
Step-by-step explanation:
A two story building measures 21 ft from the ground. A scale model shows the building to be 3 inches taller. How many inches would an 84 foot building be in the model?
Answer:
The scale of the model is (21 ft / 3 in) = 7 ft / 1 in. So an 84 foot building would be (84 ft / 7 ft) * 1 in = 12 inches tall in the model.
Step-by-step explanation:
hope it helps
Answer:
588 inches
Step-by-step explanation:
First, find the scale factor of the model by dividing the height of the real building by the height of the model: 21 ft / 3 inches = 21/3 = 7
7 inches/ft
Then, multiply the scale factor by the height of the 84 foot building to find the height of the model: 7 inches/ft * 84 ft = 7*84 = 588
588 inches
5. Two Friends Kofi and tayo own a Store. The ratio of kofi Share to tayo's Share Is N120.00, Its 11:9 Of Tayo's Calculate the value of the Store
Answer:
Step-by-step explanation:
I need help on questions 9 and 12 pls help:(
The graphs as per the transformations are given below.
What are transformation of graphs?
There are four transformations that happens in a graph -
When a figure is translated, it is moved in any direction.
Flipping a figure over a line is called reflection.
Rotation is the process of turning a figure a specific amount around a point.
When we dilate a figure, we increase or decrease its size.
The triangle CHV have points C(-4,5), H(-3,3) and V(-3,5). When it is reflected across x=-3. The image gets mirrored in the negative y-axis with the points C(-4,-2), H(-3,0) and V(-3,-2).
The parallelogram CJWY have points C(-3,-1), J(-2,-1), W(-2,-4), Y(-1,-4). It needs to be translated by (x,y)->(x+2,y+0)
C=(-3+2,-1+0)=(-1,-1)
J=(-2+2,-1+0)=(0,-1)
W=(-2+2,-4+0)=(0,-4)
Y=(-1+2,-4+0)=(1,-4)
The parallelogram TSCH have points T(-1,3), S(1,4), C(1,-1), H(3,0). It needs to be translated by (x,y)->(x+0,y-1)
T=(-1+0,3-1)=(-1,2)
S=(1+0,4-1)=(1,3)
C=(1+0,-1-1)=(1,0)
H=(3+0,0-1)=(3,-1)
The triangle RDP have points R(0,0), D(-2,-2) and P(3,-3). On rotation of 180 degrees graph (x,y) becomes (-x,-y).
R=(0,0)
D=[-(-2),-(-2)]=(2,2)
P=[-(3).-(-3)]=(-3,3)
Therefore, the transformations are made.
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Need to find the x and y
Need to find the x and y: The Graph asking in question is attached below:
What is Graph?A graph is a type of data structure used to represent relationships between different objects. It consists of nodes, which are connected by edges. The nodes represent the objects, while the edges represent the relationships between them. Graphs can be used to represent many different types of information, such as road networks, social networks, and even computer networks. Graphs can be used to solve a variety of problems, such as finding the shortest path between two nodes, or finding the most efficient way to route data throughout a network. Graphs can be represented in a variety of ways, such as in the form of a table, a map, or a diagram. In addition, graphs can be used to represent abstract concepts such as relationships between individuals.
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-5b + 35 = 85
Help pls
Answer:
-10
Step-by-step explanation:
-5b + 35 = 85
-5b = 50
-5b/-5 = 50/-5
b = -10
Answer:
B = -10
Step-by-step explanation:
-5b + 35 = 85
work is shown in picture
Solve for p if L = 2 1/2 ft and W = 3 2/5 ft. P = 2L + 2W
Answer:
P = 59/5
Step-by-step explanation:
What is 2/3 plus 1/5 equal
Answer: 13/15
Step-by-step explanation: Hope this helps, please mark brainliest and give thanks!
2/3+1/5
15÷3*2+15÷5*1
10+3/15
13/15
Two alien spaceships start traveling toward each other from space stations that are 710,000 km apart. The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr. In how many hours will the two spaceships meet if the second spaceship is traveling at 90,000 km/hr?
The spaceship will meet in how many hours?
The time that it will take for the spaceships to meet is given as follows:
3 hours.
How to model the situation?Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
The slope m represents the velocity.The intercept b represents the initial position.The positive direction is considered from the first spaceship towards the second spaceship.
The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:
710,000 - 110,000 = 600,000 km.
Then the functions are given as follows:
x1(t) = 110t.x2(t) = 600 - 90t. (negative as they travel in opposite direction).They will meet when:
x1(t) = x2(t).
Hence:
110t = 600 - 90t
200t = 600
t = 600/200
t = 3 hours.
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The time that it will take for the spaceships to meet is given as follows:
3 hours.
How to model the situation?
Each of the spaceships is traveling at a constant rate, hence linear functions are used to model the situation.
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are given as follows:
The slope m represents the velocity.
The intercept b represents the initial position.
The positive direction is considered from the first spaceship towards the second spaceship.
The first spaceship started an hour before the second spaceship and is traveling at 110,000 km/hr, hence the difference when the second spaceship starts traveling is given as follows:
710,000 - 110,000 = 600,000 km.
Then the functions are given as follows:
x1(t) = 110t.
x2(t) = 600 - 90t. (negative as they travel in opposite direction).
They will meet when:
x1(t) = x2(t).
Hence:
110t = 600 - 90t
200t = 600
t = 600/200
t = 3 hours.
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Given A(0, a) and B(b, 0) , find coordinates of C so that the orthocenter of triangle ABC lies on the triangle.
The coordinate of the point C is (0, a)
How to determine the coordinates of point CFrom the question, we have the following parameters that can be used in our computation:
A = (0, a)
B = (b, 0)
As a general rule, the orthocenter of a triangle is a point located at the intersection of the lines containing the altitudes of the triangle.
This means that we start by calculating the equation of the altitude from B to line AC.
A linear equation is represented as
y = mx + c
Where
slope = m
y-intercept = c
Using the above as a guide, we have the following:
slope = (y₂ - y₁)/(x₂ - x₁)
This gives
m(BC) = (0 - 0)/(b - 0) = 0
y-intercept (c) = a
So the equation of the line BC is
y = 0 * x + a
y = a
For line AC, we have
m(AC) = (a - 0)/(0 - 0) = a/0 = undefined.
This means that the equation of the line AC is
x = 0
The equation x = 0 implies that the x-coordinate is always 0, irrespective of the y-coordinate e.g. (0, a)
At this stage, we have the coordinates of the points from lines AC and BC to be
(0, a) and (0, a)
Next, we calculate the C as follows
C = Midpoints of (0, a) and (0, a)
This gives
C = 1/2 * (0 + 0, a + a)
Evaluate
C = (0, a)
Hence, the coordinate of C is (0, a)
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Three angle measures of a triangle are given. Does the triangle exist in Euclidean geometry, Spherical geometry, or Neither?
65°, 82°, 100°
Answer:yesb
Step-by-step explanation:
because u
PLEASE HELP!!
The equation of a circle is (x+10)2+(y−4)2=100.
What is the center and radius of the circle?
Responses
center: (10, −4); radius: 10,000
center: , begin ordered pair 10 comma negative 4 end ordered pair, ; radius: 10,000
center: (−10, 4); radius: 10,000
center: , begin ordered pair negative 10 comma 4 end ordered pair, ; radius: 10,000
center: (10, −4); radius: 10
center: , begin ordered pair 10 comma negative 4 end ordered pair, ; radius: 10
center: (−10, 4); radius: 10
The center of the circle is (-10,4) and the radius is 10.
What is a circle?The circle is defined as the locus of the point traces around a fixed point called as the center and is equidistant from the outer trace.
All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
The equation of the circle is,
( x - h )² + ( y - k )² = r²
(x+10)² + (y−4)² = 100
(x+10)² + (y−4)² = 10²
Compare the equations and find the center and radius,
Center = ( h,k) = ( -10,4)
Radius = r = 10
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In ΔUVW, w = 1.4 cm, m m∠W=63° and m m∠U=29°. Find the length of v, to the nearest 10th of a centimeter.
In order to find the length of v in ΔUVW, we can use the Law of Sines.
The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all sides and angles in the triangle. This can be expressed as:
a/sin A = b/sin B = c/sin C
Where a, b, and c are the lengths of the sides of the triangle and A, B, and C are the angles opposite those sides.
In ΔUVW, we are given the lengths of two sides (w and v) and the measure of the angles opposite those sides (m∠W and m∠U). We can use the Law of Sines to find the length of v:
v/sin U = w/sin W
v = (w/sin W) * sin U
Substituting the given values, we get:
v = (1.4 cm / sin 63°) * sin 29°
Using a calculator, we find that v = 2.72 cm to the nearest hundredth of a centimeter. Rounding to the nearest 10th of a centimeter, we get v = 2.7 cm.
Therefore, the length of v in ΔUVW is approximately 2.7 cm to the nearest 10th of a centimeter.
Tyler’s brother earns 14 per hour. The store offers him a raise a 15% increase per hour. After the raise, how much will Tyler brother make per hour
Answer: 16.10
Step-by-step explanation:
$14 + 15% increase rate = 16.10
15% = 2.10
Draw a number line and put the following numbers in the correct location
2.5, -6, -3, 4, -2.2, 1/4, -1/2, 2 1/3
Therefore , the solution to the given problem of order comes out to be
-6< -3< -2.2 < -1/2 < 1/4 < 2[tex]\frac{1}{3}[/tex] < 2.5 < 4.
What is order?Numerical order can be used to organise a set of numbers. It is possible to use both increasing and decreasing ordering. Consider how a set of numbers would seem if they were organized in ascending order like 2, 55, 103, 256, and 802, for example. This can make sorting through a huge collection of numbers much easier.
Here,
Given : 2.5, -6, -3, 4, -2.2, 1/4, -1/2, 2 1/3
To put them according to ascending order :
So ,
negative terms are the smallest compare to positive terms as their values are lower than 0.
thus,
-6< -3< -2.2 < -1/2 < 1/4 < 2[tex]\frac{1}{3}[/tex] < 2.5 < 4
Therefore , the solution to the given problem of order comes out to be
-6< -3< -2.2 < -1/2 < 1/4 < 2[tex]\frac{1}{3}[/tex] < 2.5 < 4.
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8. Laurie graphed two lines, as shown on the right.
One line has a slope of -2 and the other has a slope of
1/2. Laurie noticed that although the slopes are
negative reciprocals of each other, the lines do not
appear to be perpendicular. Explain why this result
occurs, even though she graphed the lines correctly.
It's possible that the lines do not appear to be perpendicular, even though the slopes are negative reciprocals, because the lines may not be intersecting at 90 degrees angle,
What are the slopes of the two lines?
The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter m.
The slopes of the two lines that Laurie graphed, -2 and 1/2, are negative reciprocals of each other, which means that their product is -1.
In a Cartesian coordinate system, lines that are perpendicular to each other will have slopes that are negative reciprocals of each other, and the product of their slopes will be -1.
However, it's possible that the lines do not appear to be perpendicular, even though the slopes are negative reciprocals, because the lines may not be intersecting at 90 degrees angle.
The two lines could be skew lines that never intersect and thus cannot be perpendicular.
Another reason could be that the lines may not be in the same coordinate system or not graphed on the same set of axes.
When working with slope, we always assume that the lines are defined on a 2D Cartesian coordinate system, if that is not the case, it could cause the lines to not appear as perpendicular.
Hence, it's possible that the lines do not appear to be perpendicular, even though the slopes are negative reciprocals, because the lines may not be intersecting at 90 degrees angle, another reason could be that the lines may not be in the same coordinate system or not graphed on the same set of axes.
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