Answer: options C and D
Step-by-step explanation:
An Irrational Number is a real number that cannot be written as a simple fraction.
A . 2/3 is a rational number because it is a fraction
B . -[tex]\sqrt{81}[/tex] = -9 which could be written as -9/1 , so it is a rational number
C. 5.76262... is irrational because the decimal has no end point
D. [tex]\sqrt{2}[/tex] is a common example of irrational number , because finding the square root of 2 is also continuous .
Therefore , options C and D are irrational
A store sells notebooks with each of the combinations of color, binding, and dividers shown in the table.
Which statements are true about the variety of notebooks that the store sells? Check all that apply.
-There is a greater number of combinations with pocketed dividers than with no pockets.
-There are more than 18 different combinations of features for sale.
- The number of combinations of red notebooks is the same as the number of combinations that are yellow.
- The number of combinations of black notebooks is the same as the number of combinations that have dividers with no
pockets.
-Adding one more color option would increase the number of different combinations by 4.
Answer:
These are the true statements:
1) There are more than 18 different combinations of features for sale.
2)The number of combinations of red notebooks is the same as the number of combinations that are yellow.
3)Adding one more color option would increase the number of different combinations by 4.
Step-by-step explanation:
Here, we need combination of three different things color, binding and divider.
Firstly, from color we have 5 options, so there are 5 different ways of choosing color.
Next, 2 options for binding, so 2 ways to choose the binding.
Thirdly, 2 more ways to choose divider.
So, total number of ways = 5×2×2 = 20 ways.
This is because when we fix one of the things, say color to be red, then there are 2 ways for binding and 2 ways for divider. so, we get a total of 4 different combinations.
Now, as we are having 5 different colors, total ways = 5×4 = 20.
Here, it is obvious that combinations of notebooks of any color are same(4 red, 4 blue, 4 green, 4 yellow, 4 black)
Suppose, we have one more color option then total ways = 6 ×4 =24 ways.
⇒Adding one more color option would increase the number of different combinations by 4.
Answer:
B,C,E
Step-by-step explanation:
I got it right on the test
hope this helps
i have three fractions (9/10, 2/3, 2/4), i know that the order from largest to smallest is 9/10, 2/3, 2/4, but how do i actually go about figuring out WHY its in that order without just looking at it or using graphs?
Step-by-step explanation:
To compare fractions, they need to have the same denominator. So you need to find the least common multiple (LCM) of 10, 3, and 4.
To find the LCM, first write the prime factorizations.
3 = 3
4 = 2²
10 = 2×5
The LCM is the product of each factor raised to its highest exponent.
LCM = 2²×3×5
LCM = 60
Now we rewrite each fraction with this new denominator.
9/10 = 54/60
2/3 = 40/60
2/4 = 30/60
Answer:
You need to convert the numbers into the same format.
Step-by-step explanation:
If you want to keep them in fraction form, you need to find the least common multiple. This means the smallest number that can be divided by all of the denominators. For this example, the number would be 60, because 60/10 is 6, 60/3 is 2, and 60/4 is 15. Now that we know this, you need to make every denominator 60. You do this by multiplying the numerator by whatever you needed to multiply the denominator by to get 60. For example, you need to multiply 10 by 6 to get sixty, so you would multiply 9 by 6 as well. You would repeat this pattern with all of the numbers, getting 54/60 (9/10), 40/60 (2/3), and 30/60 (2/4). This makes it very easy to tell which is the larger number.
If you don't want to do all of that, you can use decimal form. To find what each number would be in decimal form, divide the numerator by the denominator. For example, 9 divided by ten is .9, 2 divided by 3 is .66..., and 2/4 is .5.
5% tax on $1.50 What us total cost
Answer:
Step-by-step explanation:
In order to obtain the total amount that Monica was charged you should follow some steps.
How much was the net price? You can obtain this value either by clearing the x:
X * 5% = $1.50
X = $1.50 / 5%
Or by using simple rule of three:
If 5% is $1.50
Then 100% is X
So you obtain = $30
Now you just need to sum The net prices and the taxes
Net + tax = Total Charge
$30 + $1.5 = $31.5
Answer:
.08 cents rounded
Step-by-step explanation:
1.50x.05%=.075
As a laboratory assistant, you measure chemicals using the metric system. For your current research, you need to measure out 45 grams of sodium chloride. The bottle you are using lists the amount in ounces. About how many ounces of sodium chloride will you need?
Answer:
About 1.5873 ounces of sodium chloride is needed.
Step-by-step explanation:
Here, the amount of sodium chloride needed = 45 grams
Now, by the conversion of units, we know
1 gram = 0.0352739619 ounce
⇒ 45 grams = 45 x 0.0352739619 ounce = 1.5873 ounces
Hence, about 1.5873 ounces of sodium chloride is needed.
Please help me with these five problems dont understand them
Answer:
22. 150 minutes
23. ½ day
24. 0,045 minutes
25. 1,5 weeks
26. 1 year
if the relationship between distance y in feet and time x in seconds is proportional, which rate is represented by y/x=0.6
Answer:
3 feet in 5s
Step-by-step explanation:
Consider the complete question is,
'If the relationship between distance y in feet and time x in seconds is proportional, which rate is represented by y/x=0.6?
a. 3 feet in 5s
b. 3 feet in 9s
c. 10 feet in 6s
d. 18 feet in 3s'
If y = 3 ft, x = 5 sec
[tex]\frac{y}{x}=\frac{3}{5}=0.6[/tex]
If y = 3 ft, x = 9 sec
[tex]\frac{y}{x}=\frac{3}{9}=0.33...[/tex]
If y = 10 ft, x = 6 sec
[tex]\frac{y}{x}=\frac{10}{6}=1.66666...[/tex]
If y = 18 ft, x = 3 sec
[tex]\frac{y}{x}=\frac{18}{3}=6[/tex]
Hence, the required rate would be 3 feet in 5s
Order each group from least to greatest.
Answer:
(1) 5 , PI + 2, 17/3
(2) 3/2, sqrt (5), 2.5
(3) Sqrt(5)/2, PI – 2, 5/4
Step-by-step explanation:
For each number, begin by comparing the whole numbers. The one with the least whole number is the smallest while the one with the largest is the biggest number.
If the numbers being compared have the same whole numbers, check the decimal places. Begin with tenths. The one with the lowest number is the smallest number. If they are the same compare the hundredths, if they are the same compare thousandths...until you find a decimal that is different and can differentiate the numbers.
Learn More:
https://brainly.com/question/11506796
https://brainly.com/question/11410123
#LearnWithBrainly
Find the median of 46 43 39 48 52 40 42 98 20 38. If the observation 42 is replaced by 92. Find the nest median
The median of given data is 42.5
And
The median after replacing 42 with 92 is 44.5
Step-by-step explanation:
A median is the middle value of the data that divided the data in two equal parts
Given data is:
46 43 39 48 52 40 42 98 20 38
First of all, the data has to arranged in ascending order
20, 38, 39, 40, 42, 43, 46, 48, 52, 98
As the number of values is even, n=10, the median will be the average of middle two numbers
20, 38, 39, 40, 42, 43, 46, 48, 52, 98
[tex]Median = \frac{42+43}{2}\\=\frac{85}{2}\\=42.5[/tex]
The median is 42.5
Now,
Replacing 42 with 92
20, 38, 39, 40, 92, 43, 46, 48, 52, 98
The data has to be re-arranged
So,
20, 38, 39, 40, 43, 46, 48, 52, 92, 98
As the number of values is same,
[tex]New\ median = \frac{43+46}{2}\\=\frac{89}{2}\\= 44.5[/tex]
Hence,
The median of given data is 42.5
And
The median after replacing 42 with 92 is 44.5
Keywords: Median, mode
Learn more about median at:
brainly.com/question/788903brainly.com/question/774670#LearnwithBrainly
1. In which quadrant or on which axis do each of the points (-2,4) , (3,-1) ,(-1,0), (1,2) and (-3,-5) lie? Verify your answer by locating them on the cartesian plane
Point (-2 , 4) lies in the 2nd quadrant
Point (3 , -1) lies in the 4th quadrant
Point (-1 , 0) lies on the negative part of the x-axis
Point (1 , 2) lies in the 1st quadrant
Point (-3 , -5) lies in the 3rd quadrant
Step-by-step explanation:
Let us revise the signs of the coordinates in each quadrant
x and y coordinates are positive in the 1st quadrantx-coordinate is negative and y-coordinate is positive in the 2nd quadrantx and y coordinates are negative in the 3rd quadrantx-coordinate is positive and y-coordinate is negative in the 4th quadrantThe general point on the positive part of x-axis is (x , 0), and on the negative part of x-axis is (-x , 0)The general point on the positive part of y-axis is (0 , y), and on the negative part of y-axis is (0 , -y)Now let us check the points
Point (-2 , 4) ⇒ red point
∵ x = -2 and y = 4
∵ x-coordinate is negative and y-coordinate is positive
∴ Point (-2 , 4) lies in the 2nd quadrant
Point (3 , -1) ⇒ blue point
∵ x = 3 and y = -1
∵ x-coordinate is positive and y-coordinate is negative
∴ Point (3 , -1) lies in the 4th quadrant
Point (-1 , 0) ⇒ green point
∵ x = -1 and y = 0
∵ x-coordinate is negative and y-coordinate is zero
∴ Point (-1 , 0) lies on the negative part of the x-axis
Point (1 , 2) ⇒ purple point
∵ x = 1 and y =2
∵ x and y coordinates are positive
∴ Point (1 , 2) lies in the 1st quadrant
Point (-3 , -5) ⇒ black point
∵ x = -3 and y = -5
∵ x and y coordinates are negative
∴ Point (-3 , -5) lies in the 3rd quadrant
Look to the attached graph for more understand
Learn more:
You can learn more about the four quadrant in brainly.com/question/9381523
#LearnwithBrainly
Use the quadratic formula to find the solutions to the equation.
7- 3x+1=0
Answer:
B
Step-by-step explanation:
quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
1. find a, b, and c
a = 1
b = -3
c = 1
2. plug values into formula
x = [3 ± sqrt(9-4•1•1)] / 2
3. simplify
x = [3 ± sqrt(5)] / 2
This is B.
Answer:
Option b) is correct
ie., [tex]x=\frac{3\pm \sqrt{5}}{2}[/tex]
Step-by-step explanation:
Given quadratic equation is [tex]x^{2}-3x+1=0[/tex]
To find the solutions of given equation:
Solution of quadratic equation [tex]ax^{2}+bx+c=0[/tex]
[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex] where a,b, are coefficients of [tex]x^{2}[/tex] and x respectively and c is constant.
From the given quadratic equation a=1, b=-3 and c=1
[tex]x=\frac{-(-3)\pm \sqrt{(-3)^{2}-4(1)(1)}}{2(1)}[/tex]
[tex]x=\frac{3\pm \sqrt{9-4}}{2}[/tex]
[tex]x=\frac{3\pm \sqrt{5}}{2}[/tex]
Therefore Option b) is correct
ie., [tex]x=\frac{3\pm \sqrt{5}}{2}[/tex]
If A={3,5,7,9} and
B = {1, 2, 4, 6,7,9)
Find the intersection: A B.
A. {7,9}
B. {2,4}
C. {1,3,5}
D. {1,2,3,4,5,6,7,9}
Answer:
a. (7,9) this both includes in both sets hence the right answer is a.
which of the following is an even function
f(x) = 7 is a even function
Solution:
Given that we have to find the even function
A function is even if and only if f(–x) = f(x)
Steps to follow:
Replace x with -x and compare the result to f(x). If f(-x) = f(x), the function is even.
If f(-x) = - f(x), the function is odd.
If f(-x) ≠ f(x) and f(-x) ≠ -f(x), the function is neither even nor odd.
Option 1[tex]f(x) = (x - 1)^2[/tex]
Substitute x = -x in above function
[tex]f(-x) = (-x - 1)^2[/tex]
Thus [tex]f(-x) \neq f(x)[/tex]
So this is not a even function
Option 2f(x) = 8x
Substitute x = -x in above function
f(-x) = 8(-x) = -8x
Thus [tex]f(-x) \neq f(x)[/tex]
So this is not a even function
Option 3[tex]f(x) = x^2 - x[/tex]
Substitute x = -x in above function
[tex]f(-x) = (-x)^2 - (-x) = x^2 + x[/tex]
Thus [tex]f(-x) \neq f(x)[/tex]
So this is not a even function
Option 4f(x) = 7
f(-x) = 7
Thus f(-x) = f(x)
Thus it is a even function
Answer:
A
Step-by-step explanation:
edg verified
Find the vertical asymptote(s) of f of x equals quantity 5 x squared plus 3x plus 6 end quantity over quantity x squared minus 100.
x = −5, 10
x = −10, 10
x = 5, −10
x = −5, 5
Answer:
x = 10 and x = -10
Step-by-step explanation:
Given the function
[tex]f(x)=\dfrac{5x^2+3x+6}{x^2-100}[/tex]
This function is undefied when the denominator equals to 0. Find these values for x:
[tex]x^2-100=0\\ \\(x-10)(x+10)=0\\ \\x-10=0\ \ \text{or}\ \ x+10=0\\ \\x=10\ \ \text{or}\ \ x=-10[/tex]
This means that vertical lines x = 10 and x = -10 are vertical asymptotes (the graph of the function f(x) cannot meet these lines because this function is undefined at x = 10 and x = -10)
Write a two column proof.
Can someone please help me I posted this yesterday and nobody helped if you can also help me with the other that’ll be great. Happy New Years from my family’s to yours.
Step-by-step explanation:
HJ ≅ JH, by symmetric property of equality.
ΔGHJ ≅ ΔIJH, by SAS congruence.
GJ ≅ IH, corresponding parts of congruent triangles are congruent.
Which expression is equivalent to (4x^3y^5)(3x^5y)^2 ?
(3x^5y)^2=
3^2=9
(x^5)^2=x^10
y^2=y^2
(3x^5y)^2=9x^10y^2
9x^10y^2(4x^3y^5)=
9*4=36
x^10*x^3=x^13
y^2*y^5=y^7
9x^19y^2(4x^3y^5)= 36x^13y^7
Final answer: 36x^13y^7
Answer:
BBBBB!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
What are the solutions to the equation
[tex]2 |x - 2| - 8 = 20[/tex]
The solutions of the equation are -12 and 16
Step-by-step explanation:
Absolute value describes the distance of a number on the number line from 0 without considering which direction from zero the number lies. The absolute value of a number is never negative, if IxI = a, where a > 0, then
x = ax = -a∵ 2Ix - 2I - 8 = 20
- At first add 8 to both sides
∴ 2Ix - 2I = 28
- Then divide both sides by 2
∴ Ix - 2I = 14
Now By using the notes above equate x - 2 by 14 and -14
∵ x - 2 = 14
- Add 2 to both sides
∴ x = 16
∵ x - 2 = -14
- Add 2 to both sides
∴ x = -12
The solutions of the equation are -12 and 16
Learn more:
You can learn more about solving equations in brainly.com/question/2386054
#LearnwithBrainly
Which shows the ratio 12 : 400 as a fraction in simplified form?
Answer:
3:100, 3/100
Step-by-step explanation:
Answer:
3:100
Step-by-step explanation:
well 3 can go into both equally so it be 3: 100 and that cant be reduce anymore
Solve the following absolute value inequality graphically: |x|-3>1.
Answer:
x < -4 ∪ x > 4
Step-by-step explanation:
The absolute value function is shifted down 3 units. The solution space is values of x where y = |x|-3 is greater than 1. The solution is shown in red in the attachments, and the left and right (dashed) sides of the inequality are shown in blue.
__
I personally prefer to rewrite the inequality so the comparison is to zero. That is done in the second attachment, which rewrites it to ...
|x| -4 > 0
by subtracting 1 from both sides. It is often easier to read the values of x-intercepts than it is to read the coordinate values where lines cross each other.
Solve each compound inequality and graph its solution.
Good evening ,
Answer:
Look at the photo below for the answer.
:)
Will mark brainlest please help
Which of the following systems of inequalities has point C as a solution?
f(x) ≤ 3x + 4
g of x is less than or equal to negative one half times x minus 5
f(x) ≥ 3x + 4
g of x is less than or equal to negative one half times x minus 5
f(x) ≤ 3x + 4
g of x is greater than or equal to negative one half times x minus 5
f(x) ≥ 3x + 4
g of x is greater than or equal to negative one half times x minus 5
Answer:
B) f(x) ≥ 3x + 4
g of x is less than or equal to negative one half times x minus 5
Step-by-step explanation:
hope it helps
Answer:
The Answer is B.
f(x) ≥ 3x + 4
g(x) ≤ -1/2x - 5
Hope This Helps!
Find the slope of the line that passes through (2, 1) and (7, 10).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answer: Slope = [tex]\frac{9}{5}[/tex]
Step-by-step explanation:
Slope = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
[tex]x_{1}[/tex] = 2
[tex]x_{2}[/tex] = 7
[tex]y_{1}[/tex] = 1
[tex]y_{2}[/tex] = 10
Substituting into the formula , we have :
Slope = [tex]\frac{10 - 1}{7 - 2}[/tex]
Slope = [tex]\frac{9}{5}[/tex]
Help with the step by step
Step-by-step explanation:
First, distribute the -4 to the parenthesis:
24a-22=-4+24a
Add 22 to both sides:
24a-22+22=-4+22+24a
Simplify:
24a=18+24a
Subtract 24a from both sides:
24a-24a=18+24a-24a
Simplify:
0=18
hope this helps :)
-x^4y^2+7x^3y^3-3xy^5+2x^2y^4 in descending powers of x
Answer:
-x^4y^2 +7x^3y^3 +2x^2y^4 -3xy^5
Step-by-step explanation:
The powers of x in the terms of the given expression are ...
4, 3, 1, 2
so, we want to swap the last two terms to put them in the desired order:
-x^4y^2 +7x^3y^3 +2x^2y^4 -3xy^5
The volume of a large can of tuna fish can be calculated using the formula V= πr(r)h. Write an equation to find the radius, r, in the terms of V and h.
The equation [tex]r=\sqrt\frac{V}{3.14h}[/tex] can be used to find the radius.
Step-by-step explanation:
Given,
Volume of large can;
V=πr(r)h
V=πr²h
Dividing both sides by πh
[tex]\frac{V}{\pi h}=\frac{r^2\pi h}{\pi h}\\\\\frac{V}{\pi h}=r^2\\\\r^2=\frac{V}{\pi h}[/tex]
Taking square root on both sides
[tex]\sqrt{r^2}=\sqrt{\frac{V}{\pi h}}\\r=\sqrt\frac{V}{\pi h}[/tex]
Putting π=3.14
[tex]r=\sqrt\frac{V}{3.14h}[/tex]
The equation [tex]r=\sqrt\frac{V}{3.14h}[/tex] can be used to find the radius.
Keywords: volume, square root
Learn more about square root at:
brainly.com/question/10978510brainly.com/question/11007026#LearnwithBrainly
7. Which coordinate lies in the solution set for
graph of the system of inequalities shown
below?
Select one:
A. (0,5)
B.(3,0)
C. (0,0)
D -3.0
Answer:
The only point (0,0) lies inside the shaded region and hence it gives a solution for the set of inequalities.
Step-by-step explanation:
See the graph attached to this question.
The solution of the set of inequalities is given by the shaded region on the graph.
Now, the point (0,5) is outside this shaded region, hence it can not be the solution.
The point (3,0) also is outside this shaded region, hence it can not be the solution.
The point (-3,0) also is outside this shaded region, hence it can not be the solution.
Now, the only point (0,0) lies inside the shaded region and hence it gives a solution for the set of inequalities. (Answer)
f(x) = 4x - 1
g(x) = x2 - 2
(f + g)(9) = ?
A. 118
B. 112
C. 119
D. 114
E. 116
F. 111
G. 110
H. 115
I. 113
J. 117
Answer:
D
Step-by-step explanation:
Find (f + g)(x) then evaluate (f + g)(9)
(f + g)(x) = f(x) + g(x)
= 4x - 1 + x² - 2 = x² + 4x - 3
Now substitute x = 9 into the expression
(f + g)(9) = 9² + 4(9) - 3 = 81 + 36 - 3 = 114 → D
Answer:
J.117
Step-by-step explanation:
f(x) =4x-1
if f(2)= 4(2)-1
f(2)= 8-1 = 7
f(2) = 7 equation 1
g(x) =x2-2
if g(4)= (4)2-2
g(4) = 8-2 = 6 equation 2
Now,
(f+g)(9) =?
subtitute equation 1 and 2
(7+6)(9)=?
(13)(9)=?
13×9= 117
Hence, the answer is 117
If age is an explanatory variable and height is the corresponding response variable, which of these would be represented by the y - axis on a scatterplot?
Answer:
The height variable should be represented by the y-axis on a scatterplot.
Step-by-step explanation:
The explanatory variable and independent variable are similar terms. When a variable is not at all dependent on any factor then it is called an explanatory variable. So, it must be plotted along the independent axis i.e. x-axis.
On the other hand, a response variable is an alternate term of the dependent variable and in our case height is a corresponding dependent variable of explanatory variable age.
Therefore, the height variable should be represented by the y-axis on a scatterplot. (Answer)
Answer:Height
Step-by-step explanation:
Iridium-192 is an isotope of iridium and has a half life of 73.83 days. If a laboratory experiment begins with 100 grams of iridium-192, the number of grams, A, of iridium-192 present after t days would be A= 100(1/2)^t/73.83. Which equation approximates the amount of iridium-192 present after t days?
Answer:
[tex]A=100(0.990655512)^t[/tex]
Step-by-step explanation:
[tex]A=100(\frac{1}{2})^{\frac{t}{73.83}}[/tex]
It does say an approximate equation so we could play with law of exponents a little especially if you don't like that fraction in the exponent.
[tex]A=100(\frac{1}{2})^{\frac{1 \cdot t}{73.83}}[/tex]
[tex]A=100(\frac{1}{2})^{\frac{1}{73.83}t}[/tex]
[tex]A=100((\frac{1}{2})^{\frac{1}{73.83}})^t[/tex]
I'm going to put (1/2)^(1/73.83) into my calculator.
This gives me approximately: 0.990655512.
[tex]A=100(0.990655512)^t[/tex]
So maybe that is what you are looking for.
Please let me know.
A gram of the isotope of iridium is present. Then after t day, the equation is [tex]\rm A = 100*(0.990655)^t[/tex].
What is half-life?Half-Life is defined as the time required by a radioactive substance to disintegrate into a different substance. This was discovered in 1907 by Ernest Rutherford.
Given
Iridium-192 is an isotope of iridium and has a half-life of 73.83 days.
[tex]\rm A= 100(0.5)^\frac{t}{73.83}[/tex]
If A gram of the isotope of iridium is present. Then after t day, the amount will be
[tex]\rm A= 100(0.5)^{\frac{t}{73.83}}\\[/tex]
On simplifying, we have
[tex]\rm A = 100((0.5)^{\frac{1}{73.83}})^{t} \\\\A = 100*(0.990655)^t[/tex]
Thus, the required equation is [tex]\rm A = 100*(0.990655)^t[/tex].
More about the half-life link is given below.
https://brainly.com/question/24710827
Find the slope and y intercept, convert to slope intercept form
3x + 12y = 12
Answer:
16=53
Step-by-step explanation:
12.9 x 14 .9 + 6= 12
Consider the line y=-3/2x - 3
Find the equation of the line that is perpendicular to this line and passes through the point (3, 6).
Find the equation of the line that is parallel to this line and passes through the point (3, 6).
Answer:
Part 1) Equation of a perpendicular line is [tex]y=\frac{2}{3}x+4[/tex]
Part 2) Equation of a parallel line is [tex]y=-\frac{3}{2}x+\frac{21}{2}[/tex]
Step-by-step explanation:
Part 1) Find the equation of the line that is perpendicular to the given line and passes through the point (3, 6).
we have
[tex]y=-\frac{3}{2}x-3[/tex]
The slope of the given line is [tex]m=-\frac{3}{2}[/tex]
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)
so
The slope of the perpendicular line to the given line is equal to
[tex]m=\frac{2}{3}[/tex]
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{3}[/tex]
[tex]point\ (3,6)[/tex]
substitute
[tex]y-6=\frac{2}{3}(x-3)[/tex]
Convert to slope intercept form
[tex]y=mx+b[/tex]
Isolate the variable y
[tex]y-6=\frac{2}{3}x-2[/tex]
[tex]y=\frac{2}{3}x-2+6[/tex]
[tex]y=\frac{2}{3}x+4[/tex]
Part 2) Find the equation of the line that is parallel to the given line and passes through the point (3, 6).
we have
[tex]y=-\frac{3}{2}x-3[/tex]
The slope of the given line is [tex]m=-\frac{3}{2}[/tex]
Remember that
If two lines are parallel, then their slopes are the same
so
The slope of the parallel line to the given line is equal to
[tex]m=-\frac{3}{2}[/tex]
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{3}{2}[/tex]
[tex]point\ (3,6)[/tex]
substitute
[tex]y-6=-\frac{3}{2}(x-3)[/tex]
Convert to slope intercept form
[tex]y=mx+b[/tex]
Isolate the variable y
[tex]y-6=-\frac{3}{2}x+\frac{9}{2}[/tex]
[tex]y=-\frac{3}{2}x+\frac{9}{2}+6[/tex]
[tex]y=-\frac{3}{2}x+\frac{21}{2}[/tex]