Answers
Explanation: Here we will use two rules to be able to solve our question
First rule (complex numbers):
[tex]\sqrt[]{-1}=i[/tex]Second rule:
[tex]\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}[/tex]Step 1: Now we can solve our expression as follows
Final answer: So the final answer is
[tex]i\cdot8\cdot\sqrt[]{3}[/tex]
Related Questions
You have two spinners each with three sections of equal size, one labeled with the numbers 1,2,3 and the others 2,4,6. You spin both and observe the numbers. Let X be the sum of the two numbers. In the game you are playing, you win if you get a sum of at least a 600 in 100 spins. If not you lose, should I play?
Answers
From the table
[tex]\text{Total possible outcomes = 9}[/tex]we are to find the probability of getting a sum of at least 600 in 100 spins
This means, we need to get a sum of at least 6 in 1 spin
Hence
[tex]\begin{gathered} P(\text{getting a sum of at least }6\text{ in one spin)} \\ =\text{ }\frac{number\text{ of possible outcome}}{total\text{ possible outcome}} \end{gathered}[/tex]From the table
number of the possible outcome of getting a sum of at least 6 = 5
Therefore
[tex]\begin{gathered} P(\text{getting sum of at least 6 in one spin)} \\ =\text{ }\frac{5}{9} \\ \cong\text{ 0.56} \end{gathered}[/tex]Since the probability is more than 0.5 then
I can play the game
how do you think you can represent the number 2300 as a number times a multiple of 10? How do you think you can represent the number 2300 as a number x 10 to some exponents? How could you describe the relationship between the two representations?
Answers
Answer
23 × 10 = 2300
2.17¹⁰ = 2300
Explanation
The first parts us to represent 2300 as a number (let that number be x) multiplied by 10
x × 10 = 2300
10x = 2300
Divide both sides by 10
(10x/10) = (2300/10)
x = 230
The second part asks us to represent 2300 as a number (let that number be y) raised to power 10
y¹⁰ = 2300
To solve for y, we will take the logartihms of both sides
Log (y¹⁰) = Log 2300
10 log y = log 2300
Divide both sides by 10
(10 log y)/10 = (log 2300)/10
Log y = (3.362/10)
Log y = 0.3362
We will now take the Antilog of both sides
y = 2.17
Hope this Helps!!!
4
Ellie goes to tutoring every 4 days for math
and every 12 days for Science. If Ellie
attended tutoring for both Math and Science
today, when is the next time she will attend
both sessions on the same day?
Answers
Answer:
gcm conditions
1. all numbers are entered (in the picture, enter numbers 2 and 3)
2. if there are the same number, take the number that has the largest power
ahe Will attend both sessions 12 days after today
у = 3х – 7у = 3х + 1Are these equations, parallel, perpendicular or neither
Answers
A line equation can be written in slope-intercept form, which is
[tex]y=mx+b[/tex]Where m represents the slope and b represents the y-intercept.
If the slopes of two lines are equal they are parallel, if one slope is minus the inverse of the other they are perpendicular, otherwise they are neither.
Comparing our lines to the slope-intercept form, we can find their slopes.
[tex]\begin{gathered} y=3x-7\Rightarrow m=3 \\ y=3x+1\Rightarrow m=3 \end{gathered}[/tex]Since their slopes are equal, those lines are parallel to each other.
Finding the Midpoint of a line SegmentUse this formula to find the Midpoint (mean) of the line segment (-5, -3) and (9,3)
Answers
The formula for determining the midpoint of a line is expressed as
[tex]\begin{gathered} \text{Midpoint = }\lbrack\frac{(x1\text{ + x2)}}{2},\text{ }\frac{(y1\text{ + y2)}}{2}\rbrack \\ \text{From the information given,} \\ x1\text{ = - 5, x2 = 9} \\ y1\text{ = - 3, y2 = 3} \\ \text{Midpoint = }\lbrack\frac{(-\text{ 5 + 9)}}{2},\text{ }\frac{(-\text{ 3 + 3)}}{2}\rbrack \\ \text{Midpoint = (- 2, 0)} \end{gathered}[/tex]You invest $275 to start a sandwich stand and decide to charge $5.15 per sandwich.Set up a Linear Model that determines your profit or loss based on the number of sandwiches.How much money will you make if you sell 75 sandwiches?How many sandwiches must you sell to make a $100 profit?
Answers
Let the number of sandwichs sold be "x"
If you charge $5.15 per sandwich then the total sales of the sandwich will be 5.15x
Cost price = $275
The Linear Model that determines your profit or loss based on the number of sandwiches will be expressed as:
[tex]\text{Profit}=\text{Selling price - Cost price}[/tex]Substitute the given parameters;
[tex]\begin{gathered} \text{Profit/Loss}=5.15x\pm275 \\ p(x)=5.15x\pm275 \end{gathered}[/tex]If 75 sandwiches were sold, the amount of money made will be expressed as:
[tex]\begin{gathered} p(75)=5.15(75)-275 \\ p(75)=386.25-275 \\ p(75)=\$111.25 \end{gathered}[/tex]Hence the amount of money made if you sell 75 sandwiches is $111.25
To make $100 profit, the amount of sandwiches must you sell is given as:
[tex]\begin{gathered} 100=5.15x-275 \\ 5.15x=100+275 \\ 5.15x=375 \\ x=\frac{375}{5.15} \\ x\approx72\text{sandwiches} \end{gathered}[/tex]Hence 72 sandwiches must be sold to make a profit of $100
2. For each of the next dot plots, guess the approximate location of the mean by thinking aboutwhere the balance point for the data would be. Then check how close your guess was bycalculating the mean.0 1 2 3 4 5 6 7 8 9 1001235 6 7 89 10012569 10
Answers
ANSWER
1) The plot looks like the fulcrum would balance at point 4
After calculation, the mean is 4.
2) The plot looks like the fulcrum would balance at point 3;
After calculation, the mean is 3.8.
3) The plot looks like the fulcrum would balance at point 8;
After calculation, the mean is 7.2
EXPLANATION
From the given data;
1) The plot looks like the fulcrum would balance at point 4.
the mean
[tex]\begin{gathered} mean(x)=\frac{(2+2+2)+(7+7)}{5} \\ =\frac{20}{5} \\ =4 \end{gathered}[/tex]2) The plot looks like the fulcrum would balance at point 2;
The mean;
[tex]\begin{gathered} x=\frac{0+1+1+2+2+2+3+3+4+10}{10} \\ =\frac{38}{10} \\ =3.8 \end{gathered}[/tex]3) The plot looks like the fulcrum would balance at point 8;
[tex]\begin{gathered} x=\frac{0+6+7+7+8+8+8+9+9+10}{10} \\ =\frac{72}{10} \\ =7.2 \end{gathered}[/tex]A translation 5 units right and 6 units down maps A onto A'. Write thetranslation as a vector.
Answers
A translation 5 units right and 6 units down maps A onto A'. Write the
translation as a vector.
we have that
the rule for the translation is
A(x,y) -------> A'(x+5, y-6)4. Principal Sanders wants to know if wearing school uniforms will help students improve theirmath test scores. She decides to conduct an experiment to find out She chooses two groups ofstudents to test One group will wear uniforms, the other will not.Part A. Define the variables and treatment for the experiment. (3 points)I1 What is the control variable? Why?
Answers
Note that:
The control variable is the variable that does not change (that is, constant ) in an experiment. It does not take part in the experiment
The response variable is the dependent variable that determines the outcome of the experiment.
The treatment of an experiment is the independent variable, and it determines the outcome of the experiment.
From the illustration given in this exercise, the control variable, the response variable, and the treatments are identified below with reasons.
1) The control variable = The mathematical abilities of the students
Reason: The students chosen for the experiment must have the same mathematical abilities to prevent bias in the results of the experiment.
2) The response variable = Math test scores
Reason: The maths test scores of the two groups of students are the outcomes of the experiment, hence the response variable.
3) The treatment for the experiment = Wearing of school uniforms
Reason: Wearing of school uniforms is the treatment that the two groups of students were subjected to in order to confirm if their will be any effects on their Maths test scores.
Help me please so i can see if i’m on the rights track. if csc (θ) = 13/12 and 0° < θ < 90°, what is cos (θ)? write the answer in simplified, rationalized form.
Answers
Given in the question is:
[tex]\csc (\theta)=\frac{13}{12}[/tex]Recall the trigonometric identity:
[tex]\csc (\theta)=\frac{1}{\sin (\theta)}[/tex]Therefore, we have that
[tex]\sin (\theta)=\frac{12}{13}[/tex]Recall the trigonometric ratio:
[tex]\begin{gathered} \sin (\theta)=\frac{\text{opp}}{\text{hyp}} \\ \cos (\theta)=\frac{\text{adj}}{\text{hyp}} \end{gathered}[/tex]and, using the Pythagorean Theorem:
[tex]hyp^2=opp^2+adj^2[/tex]From the sin value, we have:
[tex]\begin{gathered} opp=12 \\ hyp=13 \\ \therefore \\ 13^2=12^2+adj^2 \\ 169=144+adj^2 \\ adj^2=169-144=25 \\ adj=\sqrt[]{25} \\ adj=5 \end{gathered}[/tex]Therefore, the value of cos(θ) is:
[tex]\sin (\theta)=\frac{5}{13}[/tex]Find the z-score for 67.4% of the distribution area to the right
Answers
Usually, the tables for z-scores report the value at the left of given z-values. Then we can rewrite the question.
When the z-value has 67.4% of the area distribution it means that at its left we have: 100% - 67.4% = 32.6% of the area.
Now we just need to read the z-value table and find the z-score associated with a probability of 0.326. Reading from the table, the z value is approximately -0.45.
Find the next number 7.14.28.56, ?*
Answers
Answer: 112
Explanation:
The sequence we have is:
[tex]7,14,28,56[/tex]We can see that the numbers are all multiples of 7:
[tex]\begin{gathered} 7\times1=7 \\ 7\times2=14 \\ 7\times4=28 \\ 7\times8=56 \end{gathered}[/tex]In each step, the number we multiply 7 by, doubles.
So the next number must be 7 multiplied by double of 8 which is 16:
[tex]7\times16=112[/tex]Another way to see this sequence is that each number is twice the previous number:
14 is twice 7
28 is twice 14
56 is twice 28
So the next number must be twice 56:
[tex]56\times2=112[/tex]In any case, the next number is 112
I NEED HELPPP Which expression is equivalent to 34.3-97
Answers
-62.7
1) Solving that expression we'll find an equivalent number or expression.
34.3 -97=
2) Rewriting 97 as 97.0 to proceed with the subtraction:
Since -97 is the number whose absolute value is greater than 34.3 than the result is : -62.7
A road crew Musri pave a road that is 7/8 miles long they can repave 1/56 miles each hour how long will it take the crew to repave the road
Answers
Given data :
[tex]1\text{ hour = }\frac{1}{56}miles[/tex]distance required to cover =
[tex]\frac{7}{8}[/tex]thus, the time taken is,
[tex]\begin{gathered} =\frac{\frac{7}{8}}{\frac{1}{56}} \\ =\frac{7}{8}\times56 \\ =\frac{7}{1}\times7 \\ =7\times7 \\ =49 \end{gathered}[/tex]thus the time taken is 49 hours.
The owner of a small store buys coats for 40.00 each. She sells the coats for 72.00 each. What percent of the purchase price is the sales price?
Answers
In order to calculathe the percent, we just need to divide the sales price by the purchase price.
So we have:
[tex]\frac{72}{40}=\frac{36}{20}=\frac{18}{10}=1.8=180\text{\%}[/tex]Therefore the sales price represents 180% of the purchase price.
The weighted voting systems for the voters A, B, C, ... are given in the form q: w1, w2, w3, w4, ..., wn. The weight of voter A is w1, the weight of voter B is w2, the weight of voter C is w3, and so on.Calculate, if possible, the Banzhaf power index for each voter. Round to the nearest hundredth. (If not possible, enter IMPOSSIBLE.){72: 46, 35, 22, 14}
Answers
I would not be able to continue this session, because the information is incomplete. Thank you.
A) If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is: B) If half of the passengers are men, find the probability that the mean height of the men is less than 74 in. C) When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why? D) When considering the comfort and safety of passengers, why are women ignored in this case?
Answers
Hello there. To solve this question, we'll have to remember some properties about probabilities.
Selecting male passengers randomly from the 400 passengers set, we want to find the probability that he can fit through the 74 in doorway without bending.
First, calling x the height of the random selected man, the probability of him fitting is P(x <= 74), and of him not fitting is P(x > 74)
To find P(x <= 74), we calculate the z-score by the formula:
[tex]z=\frac{x-\mu}{\sigma}=\frac{74-69}{2.8}=\frac{5}{2.8}\approx1.78[/tex]Looking for a table of z-scores for a normally distributed set, we say that the probability is around 95 or 96%. Using the under 8 approximation, P(x <= 74) = 0.96246 or 96.25%.
part (b)
We now have that the sample size is 200, since we had 400 passengers on the flight.
Making the new standard deviation as:
[tex]s=\frac{\sigma}{\sqrt[]{\text{sample}}}=\frac{2.8}{\sqrt[]{200}}=0.198[/tex]From the Central limit theorem, the z-score will then be:
z = (74 - 69)/0.198 = 25.25
How do you determine the domain and range of a relation• when the relation is presented as a set of ordered pairs?• when the relation is presented in a mapping diagram?• when the relation is presented as a graph?B./UType your response here.
Answers
First item:
When a relation is presented as a set of ordered pairs (a,b) its domain is given by all the different values that appear in the first coordinate of the pairs. Analogously its range is given by all the different values that appear in the second coordinate. For example, if we have the following relation:
[tex]\mleft\lbrace(1,2\mright),(2,3),(2,4)\}[/tex]There are only two different values in the first coordinate of the pairs: 1 and 2. Then its domain is {1,2}.
There are three different values in the second coordinate of the pairs: 2, 3 and 4. Then its range is {2,3,4}.
Second item:
When the relation is presented in a mapping diagram we have something like this:
Each ellipse represents a set. The set from which the arrows come from is the domain and that at which the arrows arrive is the range. So for the relation shown in the picture its domain is {a,b,c,d} and its range is {x,y,z}
Third item:
When the relation is presented as a graph in a grid the domain will be given for all the values in the horizontal axis for which there's a corresponding value in the graph. If you draw a vertical line that passes through a value A in the horizontal axis you can find two cases:
- The line meets the graph at least once. Then A is part of the domain.
- The line never meets the graph. Then A is not part of the domain.
Something very similar happens with the range. The values that are part of the range are values in the vertical axis for which there's at least one corresponding value in the graph. If you draw a horizontal line that passes through a value B in the vertical axis you have:
- The line meets the graph at least once. Then B is part of the range.
- The line never meets the graph. Then B is not part of the range.
Find the population mean or sample mean as indicated.Sample: 24, 8, 9, 5, 19
Answers
The mean of a population set can be calculated through the formula:
[tex]\bar{x}=\frac{\sum ^n_{i\mathop=1}(x_i)}{n}[/tex]in which, n is the total number of data points that are in the set
then, with the sample given the mean can be found as,
[tex]\begin{gathered} \bar{x}=\frac{24+8+9+5+19}{5} \\ \bar{x}=\frac{65}{5} \\ \bar{x}=13 \end{gathered}[/tex]Answer:
The sample mean is 13.
What is the equation of the horizontal line that passes through the point (5,-1).X= 5Y=-1Y+1=2(x-5)Y=5x-1
Answers
We have the next point (5,-1) and we need to find the horizontal line that passes through this point.
The equation of a horizontal line with y-intercept b is y = b
Where the point (a,b) = (5,-1)
Hence, the equation of the line is y=-1
The correct answer is the second option.
how does h (x) =-0.1x-5 change over the interval from x=2 to x=4
Answers
The given expression is,
[tex]h(x)==0.1x-5[/tex]Let us first consider, x = 2. We have,
[tex]h(2)=0.1\times2-5=-4.98[/tex]Now, let us take x = 4, we have,
[tex]h(4)=0.1\times4-5=-4.6[/tex]So the range is, -4.98 to -4.6. So, h (x) decreases by 0.3
Solve the equation 2(8+4c)=32
Answers
c = 2
Explanation:
2(8+4c)=32
we open the bracket:
2×8 + 2×4c = 32
16 + 8c = 32
collect like terms:
8c = 32 - 16
8c = 16
Divide through by 8:
8c/8 = 16/8
c = 2
The length of a rectangle is 2ft more than twice the width. The area is 144 ft squared. Find the length and width of the rectangle.
Answers
The formula for the area of a rectangle (A) is given as
[tex]A=\text{length}\times breadth[/tex]Given that
The length of a rectangle is 2ft more than twice the width,
Therefore,
length = 2 + 2width
where,
[tex]\begin{gathered} w=\text{width} \\ l=2+2w \\ A=144ft^2 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} 144=(2+2w)\times w \\ 144=2w+2w^2 \\ 144=2(w+w^2) \\ \frac{144}{2}=\frac{2(w+w^2)}{2} \\ 72=w+w^2 \\ w^2+w-72=0 \end{gathered}[/tex]Factorizing the equation above
[tex]\begin{gathered} w^2+9w-8w-72=0 \\ w(w+9)-8(w+9)=0 \\ (w-8)(w+9)=0 \\ w-8=0\text{ or }w+9=0 \\ w=8\text{ or w=-9} \\ \therefore w=8or-9 \end{gathered}[/tex]Note that the width can never be negative, therefore the width of the rectangle is 8.
Recall that:
[tex]\begin{gathered} l=2_{}+2w=2+2(8)=2+16=18 \\ l=18 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \text{length = 18ft} \\ \text{width = 8ft} \end{gathered}[/tex]
A cyclist pedals at a rate of 300 m min(exponent of -1) for 20 minutes. Then she slows down to 150 m min (exponent of -1) for 16 minutes, then races at 400 m min (exponent -1) for four minutes. find the distance traveled after20 minutes36 minutes40 minutesWrite a piecewise linear function for the distance of D(t) in terms of time (T) in minutes. find the distance traveled after 30 minutes38 minutesbonus - when has the cyclist traveled? 8km9 km
Answers
Given:
A cyclist pedals at a rate of 300 m min(exponent of -1) for 20 minutes. Then she slows down to 150 m min (exponent of -1) for 16 minutes, then races at 400 m min (exponent -1) for four minutes.
We will draw the diagram between the rate (speed of the cyclist) and the time (t) in minutes, the graph will be as follows:
For the first 20 minutes, the rate increased from 0 to 300 m/min
Then the next 16 minutes, the rate decreased to 150 m/min
And in the last 4 minutes, the rate increased to 400 m/min.
To find the distance traveled, we will find the area under the lines according to a specific time.
So, first, we will find the distance traveled after 20 minutes
It will be as follows = d(20)
[tex]d(20)=\frac{1}{2}*300*20=3000\text{ }m=3\text{ }km[/tex]And the distance traveled from 20 min to 36 min is the area of a trapezoid with a height = 16 min. and the parallel base are 150 and 300
So, the area will be =
[tex]\frac{1}{2}(300+150)*16=3600\text{ }m=3.6\text{ }km[/tex]So, the distance traveled after 36 minutes = 3 + 3.6 = 6.6 km
And the distance traveled from 36 min to 40 min is the area of a trapezoid with a height = 4 min. and the parallel bases are 150 and 400
So, the area =
[tex]\frac{1}{2}(150+400)*4=1100\text{ }m=1.1\text{ }km[/tex]So, the total distance after 40 minutes = 6.6 + 1.1 = 7.7 km.
=========================================================
To find the piecewise linear function for the distance of D(t) in terms of time (T) in minutes.
First, we will write the function v(t) that represents the rate from the graph.
[tex]v(t)=\begin{cases}{15t\rightarrow0\leq t\leq20} \\ -9.375t+487.5\rightarrow20\leq t\leq36 \\ {62.5t-2100\rightarrow t\ge36}\end{cases}[/tex]To find the function of the distance integrate each function with respect to the time t:
[tex]D(t)=\begin{cases}{7.5t^2}\rightarrow0\leq t\leq20 \\ {-4.6875t^2+487.5t-4875\rightarrow20\leq t\leq36} \\ {31.25t^2-2100t+41700\rightarrow t\ge36}\end{cases}[/tex]it says, "or use prime factorization" #1-3, and 5 pls!!
Answers
The LCM (lowest common multiple) of the following;
(1) 5 and 7
5 = 1 x 5
7 = 1 x 7
LCM = 1 x 5 x 7
LCM = 35
(2) 4, 5 and 10
4 = 2 x 2
5 = 1 x 5
10 = 2 x 5
LCM = 2 x 2 x 5
LCM = 20
(3) 6, 9 and 12
6 = 2 x 3
9 = 3 x 3
12 = 2 x 2 x 3
LCM = 2 x 2 x 3 x 3
LCM = 36
Find the LCD (lowest common denominator) of the fractions,
[tex]\begin{gathered} \frac{3}{8},\frac{3}{5} \\ We\text{ take the LCM of the denominators, that is 8 and 5} \\ \text{The LCM is,} \\ 5=1\times5 \\ 8=2\times2\times2 \\ \text{LCM}=2\times2\times2\times5 \\ \text{LCM}=40 \\ \text{The fractions can now be re-written as } \\ \frac{15}{40}\text{ and }\frac{24}{40} \end{gathered}[/tex]Let s be an Integer. Alonso claims that -s must always be less than zero. Iliana claims that -s is only sometimes less than zero. Whose statement is correct? Explain, support your reasoning with an example
Answers
Answer:
Iliana's claim is correct
Explanation:
If s is an integer.
Integers are positive or negative whole numbers.
• Illiana's claim is correct.
This is as a result of the fact that when s is negative: e,g s=-5
[tex]\begin{gathered} s=-5 \\ -s=-(-5)=5 \\ 5\text{ is greater than 0} \end{gathered}[/tex]However, when s is a positive integer:
[tex]\begin{gathered} s=5 \\ -s=-5 \\ -5\text{ is less than 0} \end{gathered}[/tex]Therefore, for an integer s, -s is only sometimes less than zero.
Illiana's claim is correct.
Slope What is the slope of the line through (-4, 2) and (3,-3)?
Answers
We have the next formula in order to obtain the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
(-4, 2)=(x1,y1)
(3,-3)=(x2,y2)
we substitute the values
[tex]m=\frac{-3-2}{3+4}=\frac{-5}{7}=-\frac{5}{7}[/tex]the slope is -5/7
I have a question on area of a triangle an area of a circle. See picture of my problem
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
equilateral triangle:
side = 7x
circle:
radius = 4r
Step 02:
area:
a = circle area - triangle area
triagle area:
triagle area = (b * h) / 2
b = 7x
h:
[tex]\begin{gathered} (7x)^2=h^2+(\frac{7x}{2})^2 \\ 49x^2=h^2+\frac{49x^2}{4} \\ h^2=49x^2-\frac{49x^2}{4}=\frac{147x^2}{4} \\ h\text{ = }\sqrt[]{\frac{147x^2}{4}\text{ }}=6.06x=6.1x \end{gathered}[/tex]h = 6.1x
[tex]\text{triangle area = }\frac{7x\cdot6.1x}{2}=\frac{42.7x^2}{2}=21.35x^2[/tex]circle area:
circle area (r) = π r² = π (4r)² = 16 π r²
a = circle area - triangle area
a = 16 π r² - 21.35x²
The answer is:
a = 16 π r² - 21.35x²
I need help with this. can you help me find the answer please?
Answers
ANSWER
15 degrees Celcius
STEP-BY-STEP EXPLANATION:
From the graph provided in the question tab, you will see that the outdoor temperature is plotted against the number of chips made per 25 seconds by the cricket.
On the x-axis, one box represents 10 units, on the y-axis, one box represents 4 units
At 33 cricket chirps in 25 seconds on the x-axis, we can trace the point to the y-axis, and this will give us 15 degrees Celcius.
Hence, the predicted outdoor temperature is 15 degrees Celcius
How do you turn 2x+3y=12 into slope intercept form?
Answers
Answer:
y = -2x/3 + 4
Explanation:
The equation of a line in slope-intercept form is expressed as y = mx+c
Given the equation 2x+3y=12, you will have to make y the subject of the formula as shown:
Given
2x+3y=12
3y = 12 - 2x
3y = -2x + 12
Divide through by 3
3y/3 = -2x/3 + 12/3
y = -2x/3 + 4
Hence the expression in slope intercept form is y = -2x/3 + 4