Given the statement 'whatever is done on one side of the equation must also be done on the other side of the equation”, the mathematical properties that described this statement is Property of equality.
For any equality operation, whatever is done on one sides must be carried out on the other side. For example, given the equation;
3x + 3 = 5
We can subtract 3 from both sides to have;
3x+3 - 3 = 5-3
3x = 2
Then we can divide both sides by 3;
3x/3 = 2/3
From the illustration above, you can see that what we did to the left hand side of the equation, we also did for the right. Hence the correct answer is Property of Equality
Emmet opened a savings account and deposited 1,000.00 as principal the account earns 8%interest compounded monthly what is the balance after 9 years
We have to use the compound interest formula to solve this problem.
The compound interest formula:
[tex]F=P(1+r)^n[/tex]Where
F is the future value [what we are solving for]
P is the principal, or initial, amount [It is $1000]
r is the rate of interest per period [It is given 8% annual interest, so 8/12 = 0.66% per month, in decimal that is r = 0.0066]
n is the time period [monthly compounding for 9 years is n = 12 * 9 = 108]
Now, we can substitute all the known information and solve for F:
[tex]\begin{gathered} F=P(1+r)^n^{} \\ F=1000(1+0.0066)^{108} \\ F=2048.06 \end{gathered}[/tex]After 9 years, the balance is:
$2048.06Please help!! slope-intercept form!!
Answer: y=1x+4
Step-by-step explanation: the b (y-intercept) is 4 and when you go up 1/1 (1) it crosses the lines
A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed.
Part A: Find the constant of proportionality. Show every step of your work. (4 points)
Part B: Write an equation that represents the relationship. Show every step of your work. (2 points)
Part C: Describe how you would graph the relationship. Use complete sentences. (4 points)
Part D: How many gallons of water are needed for 10 scoops of drink mix? (2 points)
please help asap its almost to late
All the answers to the given parts are mentioned below -
What is the general equation of a Straight line? How it represents a proportional relationship?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have a cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed.
We can write the proportional relationship as -
y = kx
Now, from the given information, we can write -
2 scoops need 0.5 gallon of water
6 scoops need 1.5 gallon of water
So -
k = 2/0.5
k = 2/(1/2)
k = 2 x 2 = 4
Equations that represents the relationship can be written as -
y = 4x + c
Now, 2 scoops need 0.5 gallon of water.
2 = 4 x 1/2 + c
2 = 2 + c
c = 0
So, the equation will be y = 4x.
Graph of y = 4x is attached at the end.
For 10 scoops of water -
10 = 4x
x = 2.5 gallons of water is needed.
Therefore, all the answers to the given parts are mentioned above.
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which of the following is equivalent to the expression below? In(e^7)
Answer: C. 7
Explanation
When the exponent of a natural logarithm has an exponent, we can do the following:
[tex]\ln(e^7)=7\ln(e)[/tex]Additionally, we are given a natural logarithm, and the base for the natural logarithm is the mathematical constant e. When the argument of the logarithm is equal to the base, then it is equal to 1:
[tex]7\ln(e)=7\cdot1[/tex][tex]=7[/tex]A bag contains 50 marbles. Marsha chooses a marble, records its color, and then puts the marble back into the bag. Marsha repeats this process and records 7 red marbles and 3 yellow marbles. What is the ratio of the number of red marbles to the number of yellow marbles she chooses
Probability is the chance that an event will occur and it's measured by the ratio of the favorable cases to the total number of cases possible.
The ratio for probability is given by:
[tex]\begin{gathered} \text{ratio of 3 marbles:ratio of yellow marbles} \\ 7\colon3 \end{gathered}[/tex]Algebraic models grade 12 math please write the answers without explaining thank you.
Explanation
let's remember this property of the exponent number
[tex]a^m\cdot a^n=a^{m+n}[/tex]Step 1
solve by applying the property. ( let the same base and add the exponents)
[tex]\begin{gathered} 6^4\cdot6^{-5} \\ 6^4\cdot6^{-5}=6^{4+(-5)} \\ 6^4\cdot6^{-5}=6^{-1} \\ \end{gathered}[/tex]hence, the answer is
[tex]d)6^{-1}[/tex]I hope this helps you
Use the drawing tools to form the correct answers on the graph Consider function f(x)= ( 1 2 )^ x ,x<=0\\ 2^ x ,&x>0 Complete the table of values for function and then plot the ordered pairs on the graph. - 2 -1 1 2 f(x)
See explanation and graph below
Explanation:For x less than or equal to zero, we would apply the function f(x) = (1/2)^x
For x greater than zero, we would apply the function f(x) = 2^x
when x = - 2 (less than 0)
This falls in the 1st function
[tex]\begin{gathered} f(-2)\text{ = (}\frac{1}{2})^{-2} \\ f(-2)=\frac{1}{(\frac{1}{2})^2}\text{ = 1}\times\frac{4}{1} \\ f(-2)=2^2\text{ = 4} \end{gathered}[/tex]when x = -1 (less than 0)
This falls in the 1st function
[tex]\begin{gathered} f(-1)\text{ = (}\frac{1}{2})^{-1} \\ f(-1)\text{ = }\frac{1}{(\frac{1}{2})^1}\text{ = 2} \end{gathered}[/tex]when x = 0 (equal to 0)
This falls in the 1st function
[tex]\begin{gathered} f(0)\text{ = (}\frac{1}{2})^0 \\ f(0)\text{ = 1} \end{gathered}[/tex]when x = 1 (greater than 0)
This falls in the 2nd function
[tex]\begin{gathered} f(1)=2^1 \\ f(1)\text{ = 2} \end{gathered}[/tex]when x = 2 (greater than 0)
THis falls in the 2nd function
[tex]\begin{gathered} f(2)\text{ = }2^2 \\ f(2)\text{ = 4} \end{gathered}[/tex]Plotting the graph:
The end with the shaded dot reresent the function with equal to sign attached to the inequality [f(x) = (1/2)^x].
The end with the open dot represent the function without the equal to sign [f(x) = 2^x)
101987006HR5SrOL4.3ON21.1 2 345 6 78 9 10Which of these statements are true for the scatter plot? Select all that apply.The scatter plot shows a negative association.The scatter plot shows a linear association.The scatter plot shows a positive association.The scatter plot shows no association.
The scatter plot shows a linear association.
The scatter plot shows a positive association.
Campsite A and campsite B are located directlyopposite each other on the shores of Lake Omega,as shown in the diagram below. The two campsitesform a right triangle with Sam's position, S. Thedistance from campsite B to Sam's position is1,300 yards, and campsite A is 1,700 yards from hisposition1,700 yardsLake OmegaB1,300 yardsSWhat is the distance from campsite A to campsiteB, to the nearest yard?
Answer:
The distance from campsite A to campsite B is;
[tex]1095\text{ yards}[/tex]Explanation:
Given that The two campsites A and B form a right triangle with Sam's position, S.
The distance from campsite B to Sam's position is 1,300 yards, and campsite A is 1,700 yards from his position;
[tex]\begin{gathered} AS=1700\text{ yards} \\ BS=1300\text{ yards} \end{gathered}[/tex]Applying pythagorean theorem, to solve for the third side AB;
[tex]\begin{gathered} AS^2=AB^2+BS^2 \\ \text{making AB the subject of formula;} \\ AB^2=AS^2-BS^2 \\ AB=\sqrt[]{AS^2-BS^2} \end{gathered}[/tex]Substituting the given values;
[tex]\begin{gathered} AB=\sqrt[]{1700^2-1300^2} \\ AB=\sqrt[]{1200000} \\ AB=1095\text{ yards} \end{gathered}[/tex]Therefore, the distance from campsite A to campsite B is;
[tex]1095\text{ yards}[/tex]How do you write this as a power? 8x8x8x8x8x8 A) 86 B) 86 C) 68 D) 87
8 x 8 x8 x8 x8 x8 can be written as;
[tex]8^6[/tex]The correct option is A) [tex]8^6[/tex] . In the expression 8x8x8x8x8x8 can be written in the exponentiation as [tex]8^6[/tex].
.
To write the expression 8x8x8x8x8x8 as a power, we can use exponentiation to represent the repeated multiplication.
Step by step, we can simplify the expression as follows:
Start with the given expression: 8x8x8x8x8x8.
Since all the factors are the same (8), we can rewrite the expression using the base (8) and the exponent representing the number of times it is multiplied (6 times).
Therefore, we can write 8x8x8x8x8x8 as [tex]8^6[/tex].
Hence, the expression 8x8x8x8x8x8 can be written in the exponentiation as [tex]8^6[/tex]. The correct option is A) [tex]8^6[/tex]
.
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1.Given the graph, find the following:A: Identify the slope of the lineB.Identify the y-intercept of the lineC.Identify the x-intercept of the lineD. Write the equation of the line in slope-intercept form (y = mx+b)
A.
The slope of a line is the rate of change of the dependent variable (y) with respect to the independent variable (x).
Notice that for each increase of 3 units in the variable x, the variable y decreases 2 units. Then, the change in y is -2 when the change in x is 3. Then, the rate of change is:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{-2}{3}[/tex]B.
The y-intercept of a line is the value of y in which the line crosses the Y-axis. In this case, the line crosses the Y-axis at y=4. Then, the y intercept is:
[tex]4[/tex]C.
Similarly, the x-intercept is the value of x in which the line crosses the X-axis. In this case, we can see that the x-intercept is:
[tex]6[/tex]D.
Since the slope m is equal to -2/3 and the y-intercept b is equal to 4, then the equation of the line is:
[tex]y=-\frac{2}{3}x+4[/tex]Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 16 gallons of fuel, the airplane 2104. When carrying 48 gallons of fuel, it weighs 2312. How much does the airplane weigh if it is carrying 66 gallons of fuel?
Let 'y' be the weight of the airplane corresponding to when the amount of fuel is 'x'.
Given that the airplane weighs 2104 when fuel is 16 gallons, this can be represented as the ordered pair,
[tex](16,2104)[/tex]Also, given that the airplane weighs 2312 when fuel is 48 gallons.The corresponding ordered pair will be,
[tex](48,2312)[/tex]It is mentioned that there is a linear relationship between the amount of fuel (x), and the weight of airplane (y).
Consider that the equation of a straight line passing through two given points is given by,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\cdot(x_2-x_1)[/tex]As per the given problem,
[tex]\begin{gathered} (x_1,y_1)=(16,2104) \\ (x_2,y_2)=(48,2312) \end{gathered}[/tex]Substitute the values,
[tex]\begin{gathered} y-2104_{}=\frac{2312-2104}{48-16}\cdot(x-16) \\ y-2104_{}=\frac{13}{2}\cdot(x-16) \\ y-2104=\frac{13}{2}x-104 \\ y=\frac{13}{2}x-104+2104 \\ y=\frac{13}{2}x+2000 \end{gathered}[/tex]At the instant when the fuel is 66 gallons,
[tex]x=66[/tex]The corresponding weight of airplane is calculated as,
[tex]\begin{gathered} y=\frac{13}{2}(66)+2000 \\ y=429+2000 \\ y=2429 \end{gathered}[/tex]Thus, the airplane weighs 2429 if it is carrying 66 gallons of fuel.
write an equation of the circle that passes through (2, 8) with center (-3 4)
we have, the equation is of the form
[tex](x-h)^2+(y-k)^2=r^2[/tex]then, first calculate the radius of the circle
[tex]\begin{gathered} r=\sqrt[]{(x2-x1)^2+(y2-y1)} \\ r=\sqrt[]{(14-14)^2+(-8-1)^2} \\ r=\sqrt[]{0+(-9)^2} \\ r=\sqrt[]{81} \\ r=9 \end{gathered}[/tex]so, (h,k) is the center and the equation is
[tex]\begin{gathered} (x-14)^2+(y-(-8))^2=9^2 \\ (x-14)^2+(y+8)^2=81 \end{gathered}[/tex]factor they expression completely 9x−21
Answer:
3(3x - 7)
Step-by-step explanation:
9x - 21
GCF of 9 and 21 is 3
3(3x - 7)
I hope this helps!
What is the end behavior of f(x) =2^–x− 5 as x goes to infinity?
Given the function:
[tex]f(x)=2^{-x}-5[/tex]As x goes to infinity, the term (2^-x) will go to zero
And the overall value of the function will be -5
So, the end behavior of f(x) as x goes to infinity = -5
1. According to the story of Pythagoras's discoveries and your own exploration during the lesson,
when does the relationship a² + b² = c² hold true?
The given relationship using the Pythagorean theorem holds true for a right-angled triangle.
We are given a mathematical relationship using the Pythagorean theorem. The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relationship between the three sides of a right triangle in Euclidean geometry. The equation is given below.
a² + b² = c²
We need to describe the situation when this relationship holds true. The variables "a", "b", and "c" represent the sides of a triangle. The Pythagorean theorem is applicable to a right-angled triangle. It states that the sum of the squares of the base and the perpendicular is equal to the square of the hypotenuse.
Here a, b, and c denote the lengths of the base, the perpendicular, and the hypotenuse of the triangle, respectively.
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Find the zeros of the function. You may want to view the graph of the function to help you identifythe real root, then use it to depress the polynomial & find the remaining roots.I
We must find the zeros of the following function:
[tex]f(x)=x^3-x^2-11x+15.[/tex]1) First, we plot a graph of the function:
From the graph, we see that the function crosses the x-axis at x = 3, so x = 3 is one of the zeros of the function.
2) Because x = 3 is a zero of the function, we can factorize the function in the following way:
[tex]f(x)=x^3-x^2-11x+15=(x^2+b\cdot x+c)\cdot(x-3)\text{.}[/tex]To find the coefficients b and c, we compute the product of the parenthesis and then we compare the different terms:
[tex]f(x)=x^3-x^2-11x+15=x^3+(b-3)\cdot x^2+(c-3b)\cdot x-3c.[/tex]To have the same expressions at both sides of the equality we must have:
[tex]\begin{gathered} -3c=15\Rightarrow c=-\frac{15}{3}=-5, \\ b-3=-1\Rightarrow b=3-1=2. \end{gathered}[/tex]So we have the following factorization for the function f(x):
[tex]f(x)=(x^2+2x-5)\cdot(x-3)\text{.}[/tex]3) To find the remaining zeros, we compute the zeros of:
[tex](x^2+2x-5)\text{.}[/tex]The zeros of this 2nd order polynomial are given by:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2a},[/tex]where a, b and c are the coefficients of the polynomial. In this case we have a = 1, b = 2 and c = -5. Replacing these values in the formula above, we get:
[tex]undefined[/tex]s
1. ABC Bank offers a certificate of deposit (CD), where you deposit money and are required to leaveit in the account for a set amount of time. You will be penalized if you withdraw your money fromit early. Suppose you want to deposit $6,000 in a 5-year CD where interest is accrued daily (1 year= 365 days).(a) How much money will you have in the account after 5 years if the APR is 2.12%? Round yourfinal answer to 2 decimals.(b) What is the annual percentage yield (APY) on this account? Round your final answer to 2decimals.
To calculate the ampount of money in the account after 5 years, we will use the formula:
[tex]A=p(1+\frac{r}{n})^{nt}[/tex]where A is the final amount
P is the initial amount or principal
r is the rate
n is the number of times the interest is applied
t is the time in years
From the question,
P = $6000 r = 2.12/100 = 0.0212 t= 5 n=365
substitute the values ibto the formula and evaluate
[tex]A=6000(1+\frac{0.0212}{365})^{365\times5}_{}[/tex][tex]A=6000(1+\frac{0.0212}{365})^{1825}[/tex][tex]A=6670.91[/tex]The amount is $6670.91
b)
To find the annual percentage yield (APY) on this account, we will use the formula:
[tex]APY=(1+\frac{r}{n})^n-1[/tex]solve using elimination-10x - 10y = 10 -2x - 5y = -19(_ , _)
The given system of equations is expressed as
-10x - 10y = 10
-2x - 5y = -19
The first step is to make the coefficients of one of the variables in each equation equal. To make the coefficient of x equal, we would multiply the first equation by 2 and the second equation by 10. It becomes
- 20x - 20y = 20 equation 3
- 20x - 50y = - 190 equation 4
We would eliminate x by subtracting equation 4 from equation 3. It becomes
- 20x - - 20x - 20y - - 50y = 20 - - 190
- 20x + 20x - 20y + 50y = 210
30y = 210
y = 210/30
y = 7
Substituting y = 7 into the second equation, it becomes
- 2x - 5 * 7 = - 19
- 2x - 35 = - 19
- 2x = - 19 + 35 = 16
x = 16/- 2
x = - 8
The solution is
(- 8, - 7)
ty-qy+p=r solve for y
Help fast plssssss!!
A rectangular pyramid has a volume of 90 cubic feet. What is the volume of a rectangular prism with the same size base and same height?choice;45 cubic feet90 cubic feet270 cubic feet30 cubic feet
Solution
Step-by-step explanation:
Here we are given the volume of rectangular pyramid as 90 cubic feet as we are required to find the volume of rectangular prism.
For that we need to use the theorem which says that
the volume prism is always one third of the volume of the pyramid . Whether it is rectangular of triangular base. Hence in this case also the volume of the rectangular prism will be one third of the volume of the rectangular pyramid.
Volume of Rectangular prism = 1/3 x Volume of rectangular pyramid
[tex]\begin{gathered} \frac{1}{3}\times90 \\ =30\text{ cubic feet} \end{gathered}[/tex]Therefore the volume of the rectangular pyramid = 30 cubic feet
Find the length of the leg x. enter the exact value, not a decimal approximation x1210x=
We can solve for the value of x using pythagorean theorem
[tex]c^2=a^2+b^2[/tex]where c is the hypotenuse ( in this case is 15) and a, b are the other legs of the triangle ( in this case is 8 and x).
Let's substitute the given values to the formula
[tex]\begin{gathered} c^2=a^2+b^2 \\ 15^2=8^2+x^2 \\ 225=64+x^2 \\ x^2=225-64 \\ x^2=161 \\ x=12.69 \end{gathered}[/tex]Now please follow this solution to solve for x in:
Write 6.546 x 10 ^-6 in standard notation
The given number in scientific notation is:
[tex]6.546\times10^{-6}[/tex]In order to write it in standard notation, first take a look at the power: -6.
As it is a negative number, it means we need to move the dot to the left 6 units.
Therefore, we need to fill the blank places with zeros:
[tex]6.546\times10^{-6}=0.000006546[/tex]2. Given the degree and zero of a polynomial function, identify the missing zero and then find the standard form of the polynomial
Degree: 2; zero: -7 + 2i
The missing zero is:
+
i
The expanded polynomial is:
The expanded quadratic equation with real coefficients is y = x² + 14 · x + 45.
How to determine the least polynomial that contains a given root
In this problem we need to determine the expanded quadratic equation with real coefficients such that one of its roots is - 7 + i 2. According with the quadratic formula, quadratic equations can have two conjugated complex roots, that is:
r₁ = α + β, r₂ = α - β
Then, the complete set of roots of the quadratic equation are r₁ = - 7 + i 2 and r₂ = - 7 - i 2. Then, the factor form of the polynomial is:
y = (x + 7 - i 2) · (x + 7 + i 2)
y = x · (x + 7 + i 2) + (7 - i 2) · (x + 7 + i 2)
y = x² + 7 · x + i 2 · x + (7 - i 2) · x + 7 · (7 - i 2) + i 2 · (7 - i 2)
y = x² + 7 · x + i 2 · x + 7 · x - i 2 · x + 49 - i 14 + i 14 - i² 4
y = x² + 14 · x + 45
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Which of the following is the closet approximation to 3√20?A) 3B) 5C) 2D) 4
The given expression is:
[tex]\sqrt[3]{20}[/tex]This can also be written as:
[tex]20^{(\frac{1}{3})}[/tex]The result = 2.71
Since 7 is greater than 5, it will become 0 and add 1 to 2 to become 3
Therefore, the closest approximation is 3
Hi i need help with unit rate fractions and ill show an example i need to have this figured out by thurday for a test and i have no clue so pls help
To find the rate in teaspoons per cup we divide the number of teaspoons by the cups:
[tex]\frac{4}{\frac{2}{3}}=\frac{12}{2}=6[/tex]Therefore, the unit rate is 6 teaspoons per cup.
A robot can complete 10 tasks in hour. Answer in fraction form.How many tasks can the robot complete in 1 hour?How long does it take the robot to complete one task?hoursIf you have a mixed number put a space between the whole number and fraction. Ex 7=7 1/2tasks
Hello!
We know that the robot can complete 10 tasks in 3/4 hour.
To solve this exercise, we can use the rule of three, look:
How many tasks can the robot complete in 1 hour?[tex]\frac{\frac{3}{4}h\rightarrow10\text{ tasks}}{1h\rightarrow x\text{ tasks}}[/tex]So, we have:
[tex]\begin{gathered} \frac{3}{4}x=10 \\ \\ x=\frac{10}{1}\div\frac{3}{4}\rightarrow\frac{10}{1}\times\frac{4}{3}=\frac{40}{3} \\ \\ \end{gathered}[/tex]Let's write it as a mixed number:
Answer:
[tex]13\text{ }\frac{1}{3}\text{ tasks}[/tex]How long does it take the robot to complete one task?We'll solve it in a similar way, look:
[tex]\frac{\frac{3}{4}h\operatorname{\rightarrow}10\text{ tasks}}{x\text{ }h\operatorname{\rightarrow}1\text{ task}}[/tex][tex]\begin{gathered} 10x=\frac{3}{4} \\ \\ x=\frac{3}{4}\div\frac{10}{1}\rightarrow\frac{3}{4}\times\frac{1}{10}=\frac{3}{40}\text{ hours} \end{gathered}[/tex]Answer:
[tex]\frac{3}{40}\text{ hours}[/tex]can someone please help me find the answer to the following?
Answer:
1077.19 ft
Explanation:
Using the depression angle, we get that one of the angles of the formed triangle is also 18° because they are alternate interior angles, so we get:
Now, we can relate the distance x, the angle of 18°, and the height of the tower using the trigonometric function tangent, so:
[tex]\begin{gathered} \tan 18=\frac{Opposite}{Adjacent} \\ \tan 18=\frac{350}{x} \end{gathered}[/tex]Now, solving for x, we get:
[tex]\begin{gathered} x\cdot\tan 18=x\cdot\frac{350}{x} \\ x\cdot\tan 18=350 \\ \frac{x\cdot\tan18}{\tan18}=\frac{350}{\tan 18} \\ x=\frac{350}{\tan 18} \end{gathered}[/tex]Using the calculator, we get that tan(18) = 0.325, so x is equal to:
[tex]x=\frac{350}{0.325}=1077.19\text{ }ft[/tex]Therefore, the forest ranger is at 1077.19 ft from the fire.
Select ALL the pairs of points so that the line between these points has a slope of 2/3?(0,0) and (3, 2)(1,5) and (4,7)(-2,-2) and (4,2)0 (0,0) and (2,3)(20, 30) and (-20, -30)
Answer:
• (0,0) and (3, 2)
,• (1,5) and (4,7)
,• (-2,-2) and (4,2)
Explanation:
Points (0,0) and (3, 2)
[tex]m=\frac{2-0}{3-0}=\frac{2}{3}[/tex]Points (1,5) and (4,7)
[tex]m=\frac{7-5}{4-1}=\frac{2}{3}[/tex]Points (-2,-2) and (4,2)
[tex]m=\frac{2-(-2)}{4-(-2)}=\frac{2+2}{4+2}=\frac{4}{6}=\frac{2}{3}[/tex]Points (0,0) and (2,3)
[tex]m=\frac{3-0}{2-0}=\frac{3}{2}[/tex]Points (20, 30) and (-20, -30)
[tex]m=\frac{30-(-30)}{20-(-20)}=\frac{60}{40}=\frac{3}{2}[/tex]The first three options are correct.