Answer:
[tex]\large\boxed{x=-8\pm5\sqrt2}[/tex]
Step-by-step explanation:
[tex](x-2)^2+12(x+2)-14=0\\\\\text{Substitute}\ (x+2)=t:\\\\t^2+12t-14=0\qquad\text{add 14 to both sides}\\\\t^2+2(t)(6)=14\qquad\text{add}\ 6^2=36\ \text{to both sides}\\\\\underbrace{t^2+2(t)(6)+6^2}=14+36\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(t+6)^2=50\Rightarrow t+6=\pm\sqrt{50}\qquad\text{subtract 6 from both sides}\\\\t=-6\pm\sqrt{25\cdot2}\\\\t=-6\pm5\sqrt2[/tex]
[tex]\text{we're going back to substitution}\\\\x+2=-6\pm5\sqrt2\qquad\text{subtract 2 from both sides}\\\\x=-8\pm5\sqrt2[/tex]
What is the measure of angle RST?
Options
A) 15°
B) 75°
C) 105°
D) 165°
The measurement of angle RST is 105
Answer:
Option C). 105°
Step-by-step explanation:
From the figure we can see a cyclic quadrilateral QRST
To find the measure of <RST
From the figure we can see that, angle RST is an obtuse angle.
The measure of angle RST is nearer to a right angle that is nearer to 90°
From the options we get the measure of angle RST = 105°
Over Thanksgiving break, the Heywards collected 980 cans for a food drive. The Ballards collected 200 fewer cans than the Heywards. How many cans did the Ballards collect?
Answer:
1180 cans
Step-by-step explanation:
Heywards collected = 980 cans
Ballards collected 200 fewer cans than Heywards.
Total cans collected by Ballard = ?
Therefore the sum of Heywards collected cans and Ballards fewer cans will give us the total cans collected by Ballard.
=980+200
=1180
Ballard collected 1180 cans....
Is the spinner below , what is the probability of lading on 2 ? Help me !!!!
Answer: C
Step-by-step explanation:
Probability: the outcome you want (2) over the total number of outcomes (6).
Probability= 2/6= 1/3.
The probability of landing on 2 is 1/6 if the total number of outcomes is 6 and favorable outcomes are 1 option (C) is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have a spinner shown in the picture.
Total number of outcomes = 6
{1, 2, 3, 4, 5, 6}
Total number of favorable outcomes = 1
{2}
P(landing on 2) = 1/6
Thus, the probability of landing on 2 is 1/6 if the total number of outcomes is 6 and favorable outcomes are 1 option (C) is correct.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ1
21
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
The solution set of n2 - 14n = -45 is {
(Separate the solutions with a comma)
Answer:
the solution set of n2 - 14n = -45 is {5, 9}
Step-by-step explanation:
We have the following equation: n^2 - 14n = -45
Rearrange:
n^2 - 14n +45 = 0
Factorizing:
(n-9)(n-5) = 0
Therefore, the solution set of n2 - 14n = -45 is {5, 9}
What is the solution of (4x-16)1/2=36^
Answer:
Answer is x=328 .
Step-by-step explanation:
solution= (4x-16)^1/2=36
squaring both sides we get
4x-16=129
4x=1296+16
x=(1296+16)/4
x=328 .
Answer:
x = 328
Step-by-step explanation:
The given equation is
[tex](4x-16)^{\frac{1}{2}}=36[/tex]
We need to find the solution of the given equation.
Taking square on both sides.
[tex]((4x-16)^{\frac{1}{2}})^2=(36)^2[/tex]
[tex](4x-16)^{\frac{2}{2}}=1296[/tex]
[tex]4x-16=1296[/tex]
Add 16 on both sides.
[tex]4x-16+16=1296+16[/tex]
[tex]4x=1312[/tex]
Divide both sides by 4.
[tex]x=\dfrac{1312}{4}[/tex]
[tex]x=328[/tex]
Therefore, the value of x is 328.
Which of the following equations is equivalent to 1/4x - 1/2y = 8?
(A) 2x - 4y = 8
(B) 2x - 4y = 64
(C) 4x - 2y = 64
Answer:C
Step-by-step explanation:4x _2y =64 because 8×8= 64
For this case we must find an equation equivalent to:
[tex]\frac {1} {4} x- \frac {1} {2} y = 8[/tex]
We add [tex]\frac {1} {2}[/tex] and on both sides of the equation:
[tex]\frac {1} {4} x = 8 + \frac {1} {2}y[/tex]
We multiply by 4 on both sides of the equation:
[tex]x = 32 + \frac {4} {2}y\\x = 32 + 2y[/tex]
Multiplying by 2 on both sides of the equation:
[tex]2x = 64 + 4y\\2x-4y = 64[/tex]
Answer:
Option B
Which of the following expresses 2.4 as a fraction in simplest form ?
Answer:
its 2 4/9
Step-by-step explanation:
because i did trial and error, i converted all the fractions into decimals until one of the conversions was equal to 2.444444444444...infinite
[tex]2 \frac{4}{9}[/tex] would be the correct answer.
This is not 2.4. This is "2.44444..." because of the line over the 4 after the decimal place (this applies for any decimal such as [tex]2.48\overline{47} = 2.484747474747...[/tex]).
In general, the over-lined part can be written as a fraction of 9 (99, 999, 9999, etc. if the over-lined part has more than one digit, in increasing order of digits), which is why [tex]2 \frac{4}{9}[/tex] is the correct answer.
Find the number of pages when the minutes equals 72 according to the table below. To help, write a rule relating the minutes, x, to the number of pages.
minutes: 6 15 27 72
pages: 20 50 90 ?
Answer:
240
Step-by-step explanation:
Where P = pages and x = minutes, your rule is as follows:
[tex]P=\frac{10}{3} x[/tex]
Simply plug in your last minute value to find your last page value.
[tex]P=\frac{10}{3} (72)\\P=240[/tex]
Write an expression to represent:
One minus the product of four and a number x
Answer:
1-4x
Step-by-step explanation:
Answer:
1 - 4xStep-by-step explanation:
The product of four and a number x: 4 · x = 4x
One minus the product of four and a number x: 1 - 4x
Consider the equation and its solution.
8(x-2)=64
8x-16=64
8x=80
x=10
Which property is used in the last step to find that X=10?
A. distributive property
B. addition property of equality
C. subtraction property of equality
D. division property of equality
Answer:
D. division property of equalityStep-by-step explanation:
[tex]8(x-2)=64\qquad\text{distributive property}\\8x-(8)(2)=64\\8x-16=64\qquad\text{add 16 to both sides}\\8x-16+16=64+16\qquad\text{addition property of equality}\\8x=80\qquad\text{divide both sides by 8}\\\dfrac{8x}{8}=\dfrac{80}{8}\qquad\text{division property of equality}\\x=10[/tex]
Answer:
ANSWER WOULD BE D . division property of equality
Step-by-step explanation:
Took the test the math is quite simple
TW¯¯¯¯¯¯¯¯¯=14.6, CW¯¯¯¯¯¯¯¯¯=6, TU¯¯¯¯¯¯¯=21.2. Find the value of VW¯¯¯¯¯¯¯¯¯.
A. 6.9
B. 8.2
C. 7.5
D. 16.1
TW x WU = CW x VW
Fill in the known values:
WU = TU - TW = 21.2 - 14.6 = 6.6
14.6 x 6.6 = 6 x VW
Simplify:
96.36 = 6VW
Divide both sides by 6:
VW = 96.36 / 6
VW = 16.06
Round to one decimal place:
VW = 16.1
The answer is D>
Answer:
D.) 16.1
Step-by-step explanation:
I got it correct on founders edtell
What is this in simplest rational exponent form
Answer:
[tex]4x[/tex]
Step-by-step explanation:
We want to find the simplest rational exponent form of
[tex]\sqrt{x} \cdot 4\sqrt{x}[/tex]
Recall that: [tex]\sqrt{a}=a^{\frac{1}{2} }[/tex]
We rewrite the expression in the exponent form to get:
[tex]x^{\frac{1}{2}}\cdot 4x^{\frac{1}{2}[/tex]
We can regroup the product to get:
[tex]4 x^{\frac{1}{2}\cdot x^{\frac{1}{2}[/tex]
We apply the rule: [tex]a^m\cdot a^n=a6{m+n}[/tex] to get:
[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4 x^{\frac{1}{2}+\frac{1}{2}}[/tex]
[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4 x^{1}[/tex]
[tex]4 x^{\frac{1}{2}}\cdot x^{\frac{1}{2}=4x[/tex]
(polynomials) multiply. (x^2-5x)(2x^2+x-3)
A. 2x^4 - 9x^3 - 9x^2 - 15x
B. 2x^4 + 9x^3 - 8x^2 + 15x
C. 4x^4 + 9x^3 - 8x^2 + 15x
D. 2x^4 - 9x^3 - 8x^2 + 15x
Answer:
2x^4 - 9x^3 -8x^2 + 15x
Step-by-step explanation:
(x^2-5x)(2x^2+x-3) distribute first
2x^4
x^2 + x = x^3
5 * 2x^2 x= 10x^3
5x^1+1 = 5x^2
5 * 3x = 15x Put them all together
2x^4 + x^3 - 3x^2 - 10x^3 - 5x^2 + 15x Like terms
2x^4 + x^3 -10x^3 - 3x^2- 5x^2 + 15x Add similar terms
= 2x^4 + x^3 - 10x^3 - 8x^2 + 15x more adding terms
2x^4 - 9x^3 -8x^2 + 15x
Hope my answer has helped you, if not i'm sorry.
For this case we must multiply the following expression:
[tex](x ^ 2-5x) (2x ^ 2 + x-3)[/tex]
We apply distributive property term to term taking into account that:
[tex]+ * - = -\\- * - = +\\x ^ 2 * 2x ^ 2 + x ^ 2 * x-x ^ 2 * 3-5x * 2x ^ 2-5x * x + 5x * 3 =[/tex]
For powers of the same base, we place the same base and add the exponents:
[tex]2x ^ 4 + x ^ 3-3x ^ 2-10x ^ 3-5x ^ 2 + 15x =[/tex]
We add similar terms:
[tex]2x ^ 4-9x ^ 3-8x ^ 2 + 15x[/tex]
Answer:
OPTION D
[tex]2x ^ 4-9x ^ 3-8x ^ 2 + 15x[/tex]
Complete these ordered pairs for this equation. (0, ), (-2, ), (4, ) y=2x
Answer:
Part 1) The ordered pair is (0,0)
Part 2) The ordered pair is (-2,-4)
Part 3) The ordered pair is (4,8)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem we have a direct variation
[tex]y=2x[/tex]
Complete the ordered pairs
Part 1) we have (0,?)
For x=0
Substitute in the equation and solve for y
[tex]y=2(0)=0[/tex]
therefore
The ordered pair is (0,0)
Part 2) we have (-2,?)
For x=-2
Substitute in the equation and solve for y
[tex]y=2(-2)=-4[/tex]
therefore
The ordered pair is (-2,-4)
Part 3) we have (4,?)
For x=4
Substitute in the equation and solve for y
[tex]y=2(4)=8[/tex]
therefore
The ordered pair is (4,8)
For this sequence, write an explicit formula. Then determine the 15th term in the sequence.
1/2, 1, 3/2, 2 5/2, 3 7/2
((help ;;-;;))
Answer:
Step-by-step explanation:
[tex]S = 1/2, 1, 3/2, 4, 5/2, 3, 7/2...\\a_n = \frac{n}{2}\\a_{15} = \frac{15}{2}[/tex]
Determine if the relation represented in table form represents y as a function of x.
Answer:
Yes, it is a function.
Step-by-step explanation:
Since each x-value is used only once, the relation is a function.
Yes, The relation represented in table is a function.
What is Function?A relation between a set of inputs having one output each is called a function.
Given that;
The table is,
x | 5 10 15
y | 3 8 8
Now,
Clearly, Each inputs having one output in the table as;
⇒ f (5) = 3
⇒ f (10) = 8
⇒ f (15) = 8
So, The table represent the function.
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ2
What are the dimensions of a rectangular box with a volume of 50b 3 + 75b2 - 2b - 3?
Answer:
[tex]\large\boxed{(2b+3)\times(5b-1)\times(5b+1)}[/tex]
Step-by-step explanation:
The formula of a volume of a rectangular box:
[tex]V=lwh[/tex]
l - lenght
w - width
h - height
[tex]V=50b^3+75b^2-2b-3=25b^2(2b+3)-1(2b+3)\\\\=(2b+3)(25b^2-1)=(2b+3)(5^2b^2-1^2)\\\\=(2b+3)\bigg((5b)^2-1^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(2b+3)(5b-1)(5b+1)[/tex]
Therefore the dinemsions of thisp prism are:
[tex](2b+3)\times(5b-1)\times(5b+1)[/tex]
Answer:
the one with ++-
Step-by-step explanation:
If z is a standard normal variable, find the probability.
P(–0.73 < z < 2.27)
0.2211
0.4884
1.54
0.7557
Answer:
0.7557
Step-by-step explanation:
In this question use the Table of Standard Normal Probabilities for Negative z-scores and the Table of Standard Normal Probabilities for Positive z-scores
Where z=2.27 NORMDIST(2.27)=0.9884 (read from table for positive z-scores)
Where z=-0.73 NORMDIST(-0.73)=0.2327 (read from table for negative z-scores)
You know P(-0.73<z<2.27)= 0.9884-0.2327=0.7557
The probability that P(–0.73 < z < 2.27) is 0.7557.
The z score is used to determine by how many standard deviations, the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where\ x=raw\ score,\mu=mean, \sigma=standard\ deviation,n= sample\ size\\\\\\[/tex]
From the normal distribution table, P(-0.73 ≤ z ≤ 2.27) = P(z < 2.27) - P(z<-0.73) = 0.9884 - 0.2327 = 0.7557
Find out more at: https://brainly.com/question/7449180
Pleaseeeeeeee helppppp ASAP help....
Answer:
42.5 %
Step-by-step explanation:
You would multiply the probability of the couple having a girl and the test predicting it’s a girl.
0.85 x 0.5= 0.425 = 42.5%
In △ABC, m∠A=15°, a=9, and b=12. Find c to the nearest tenth.
Answer:
=20.0
Step-by-step explanation:
We can first find the value of the angle at B using the sine formula.
a/sine A=b/Sin B
9/sin 15=12/sin B
Sin B=(12 sin 15)/9
Sin B=0.345
B=20.18°
Therefore angle C =180-(15+20.18)
=144.82°
a/Sin A=c/Sin C
9/Sin 15=c/Sin 144.82
c=(9 sin 144.82)/sin15
=20.0
El costo variable de fabricar una calculadora es de $2 y los costos fijos son de $105.
a. Determina la función lineal del costo total por fabricar x calculadora al día.
b. ¿Cuál es el costo por fabricar 50 calculadoras al día?
Answer:
a. [tex]c(x) = 2x + 105[/tex]
b. [tex]c(50) =\$205[/tex]
Step-by-step explanation:
The variable cost of $ 2 implies that for each manufactured calculator the total cost increases $ 2.
The fixed cost of $ 105 implies that regardless of the number of manufactured calculators there will always be a cost of $ 105.
If we call x the number of manufactured calculators then the total cost c(x) will be:
[tex]c(x) = 2x + 105[/tex]
Then, the cost of manufactured 50 calculators a day is:
[tex]c(50) = 2(50) + 105[/tex]
[tex]c(50) = 100 + 105[/tex]
[tex]c(50) =\$205[/tex]
Two angles are complementary, and Angle A is 6° more than Angle B. What is the measure of Angle A?
6°
42°
45°
48°
Complementary angle add up to 90 degrees.
Angle A = x + 6
Angle B = x
They both add up to 90.
x + 6 + x = 90
2x + 6 = 90
2x = 90 - 6
2x = 84
x = 84/2
x = 42
Angle A = x + 6
Angle A = 42 + 6
Angle A = 48 degrees
Perform the indicated operation. Be sure the answer is reduced.
[tex] \frac{m}{n} . \frac{n}{p} \div \frac{p}{q} \\ = \frac{m}{p} \div \frac{p}{q} \\ = \frac{m}{p} . \frac{q}{p} \\ = \frac{mq}{ {p}^{2} } [/tex]
Hope it helps...
Regards;
Leukonov/Olegion.
Answer:
The correct answer is first option
mq/p²
Step-by-step explanation:
It is given that, (m/n) * (n/p) ÷ (p/q)
To find the simplified form of given expression
Let (m/n) * (n/p) ÷ (p/q) can be written as,
(m/n) * (n/p) ÷ (p/q) = (m/n) * (n/p) * (q/p)
= (m * n * q)/(n * p * q)
= (m * q)/(p * p)
= mq/p²
Therefore the correct answer is mq/p²
The smiths have saved $25,000 toward the purchase of a new car. If the sales tax is 5%, the purchase price of smiths new car before taxes cannot exceed what
Answer:
26,250
Step-by-step explanation:
25,000 + 5% = 26,250
:) please mark Brainliest
The Smiths' new car purchase price before taxes cannot exceed $23,809.52 considering they have $25,000 and need to pay a 5% sales tax on the purchase.
To calculate the maximum purchase price of the new car before taxes that the Smiths can afford, we need to account for the 5% sales tax they will have to pay on top of the purchase price. Since the Smiths have saved $25,000, this is the total amount they have available to pay for the car including the sales tax.
To find the purchase price before tax, call this price 'P'. The total cost including the sales tax will be P + 0.05P (which is the sales tax). This total cost must not exceed $25,000. Therefore, we can set up the following equation:
1.05P <= $25,000
Divide both sides of the equation by 1.05 to isolate P:
P <= $25,000 / 1.05
P <= $23,809.52
So, the purchase price of the Smiths' new car before taxes cannot exceed $23,809.52.
What is the location of the point on the number line that is 2/9 of the way from A=5 to B=23
Answer:
9 is (2/9) of the way from A = 5 to B = 23.
Step-by-step explanation:
Note that there are 23-5, or 18, units separating 5 and 23.
2/9 of that distance is (2/9)(18), or 4.
Adding 4 to 5, we get 9.
9 is (2/9) of the way from A = 5 to B = 23.
If this is not clear, I'd suggest you draw this situation and prove to yourself that 9 is (2/9) of the way from A = 5 to B = 23.
Answer:
9
Step-by-step explanation:
The equation is A+K (B-A). So 5+ 2/9 (23-5) = 9
which inequality represents all values of x for which the quotient below is defined?√8x^2 divided by √2x
Answer:
The function is defined when x > 0
Step-by-step explanation:
Functions with radicals are only undefined when the value in the radical is negative, because the root of a negative number is imaginary.
We know the function is undefined when the denominator is equal to zero. [tex]\sqrt{2x}[/tex] is equal to zero when x=0.
We also know that functions with radicals are undefined when the value in the radicals are negative, because the root of a negative number is imaginary. . [tex]8x^{2}[/tex] will always be positive, but [tex]2x[/tex] is negative when x < 0.
So the function is undefined when x = 0, and when x < 0.
Therefore it is defined when x > 0
Using the distance formula , find the distance from the center of your habitat to the point (x, y). Write this equation. Your answer will contain x- and y-terms.
Answer:
See explanation
Step-by-step explanation:
The distance formula is given by:
[tex]d = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} } [/tex]
We want to find the distance between (a,b) and (x,y).
The center of the habitat is missing in the question.
Assuming the center is (a,b) where a and b are real numbers, then we can use the distance formula to obtain:
[tex] d = \sqrt{(x - a)^{2} + {(y - b)}^{2} } [/tex]
For instance if the center of your habitat us (2,-1), then
[tex]d = \sqrt{(x - 2)^{2} + {(y + 1)}^{2} } [/tex]
For Sophia’s graduation party, several tables of the same width will be arranged end to end to form a serving table with a total area of 75 ft 2 . The total length of the tables will be two more than three times the width. Find the length and width of the serving table so that Sophia can purchase the correct table cloth. Round your answers to the nearest tenth
Answer:
The length is 16.1 ft and the width is 4.7 ft
Step-by-step explanation:
Let
x -----> the total length of the tables
y -----> the width of the tables
we know that
The area is equal to
[tex]A=xy[/tex]
[tex]A=75\ ft^{2}[/tex]
so
[tex]75=xy[/tex] -----> equation A
[tex]x=3y+2[/tex] -----> equation B
substitute equation B in equation A
[tex]75=(3y+2)y[/tex]
[tex]3y^{2} +2y-75=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]y=4.7\ ft[/tex]
Find the value of x
[tex]x=3(4.7)+2=16.1\ ft[/tex]
therefore
The length is 16.1 ft and the width is 4.7 ft
Answer:
The length and width of the serving table is 16.1 ft and 4.7 ft respectively.
Step-by-step explanation:
Consider the provided information.
Let the width of the table is x and length of the table is y.
The total length of the tables will be two more than three times the width.
This can be written as:
y = 2+3x
The area of the table is 75 ²ft
The area of rectangle is:
length × width = Area
Substitute width = x and length = 2+3x in above formula.
(x)(2+3x) = 75
2x+3x²-75 = 0
3x²+2x-75 = 0
The above equation is in the form of ax²+bx+c=0. Now use the quadratic formula to find the root of the equation.
[tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Substitute a=3, b=2 and c=-75 in above formula.
[tex]x_{1,2}=\frac{-2\pm\sqrt{2^2-4(3)(-75)}}{2(3)}[/tex]
[tex]x_{1,2}=\frac{-2\pm\sqrt{904}}{6}[/tex]
[tex]x_{1,2}=\frac{-2\pm30.07}{6}[/tex]
[tex]x_{1}=\frac{-2+30.07}{6}[/tex]
Ignore the negative value of x as width should be a positive number.
[tex]x=4.7\ ft[/tex]
Now substitute the value of x in y = 2+3x.
y = 2+3(4.7)
y = 16.1 ft
Hence, the length and width of the serving table is 16.1 ft and 4.7 ft respectively.
Which of the x values are solutions to the inequality 4(2 – x) > –2x – 3(4x + 1)? Check all that apply.
A x= -1.1
B x= -2.2
C x= 0
D x=-10
E x= 10
Answer:
C x= 0 greater than
E x= 10 greater than
Step-by-step explanation:
4(2 – x) > –2x – 3(4x + 1)
Distribute
8 –4x > –2x – 12x -3
Combine like terms
8 –4x > – 14x -3
Add 14x to each side
8 –4x+14x > – 14x+14x -3
8 +10x > -3
Subtract 8 from each side
8-8+10x>-3-8
10x > -11
Divide each side by 10
10x/10 >-11/10
x >-1.1
Any number greater than -1.1 is a solution
A x= -1.1 not greater than
B x= -2.2 not greater than
C x= 0 greater than
D x=-10 not greater than
E x= 10 greater than
Answer:
C & E
Step-by-step explanation:
What is the equation?
to get the equation of a straight line, all we need is two points, hmmm say this line runs over (0 , -2) and (3 , 0), so let's use those.
[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-2-0}{0-3}\implies \cfrac{-2}{-3}\implies \cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-0=\cfrac{2}{3}(x-3)\implies y=\cfrac{2}{3}x-2[/tex]