The equation in point-slope form is y=4x-25.
A line passing through the point (x 1, y1) has a slope of "m," and its point slope form is given by the equation y - y1=m (x - x1).
A horizontal line's equation is of the form y=b when it passes through the points (a, b).
Step 1: Write down the line's slope, "m," and the coordinates (x 1, y 1) of the point that is given and is on the line.
Step 2: Replace the given values in the calculation for the point slope: y - y1 = m. (x - x1).
Point-slope form is y=mx+b.
To get the equation of the line in standard form, simplify in step three.
Given, m(slope)= 4.
The point is (8,7)= (x1,y1)
y-7=4(x-8)
y-7=4x-32
y=4x-32+7
y=4x-25
Hence, the equation in point-slope form is y=4x-25.
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Solve the system of equations. 8x-3y = 3 3x - 2y = -5
The solution of the system of equations is x = 1 and y = -1.
What is a two-variable linear equation?
If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equivalent to zero, it then is said to be a linear equation in 2 factors. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.
SOLUTION TO WORK OUT
the equations are resolved
8x + 3y = 5 & 3x − 2y = 5
EVALUATION
The equations in the given system are
8x + 3y = 5 - - - - - - - (1) (1)
3x − 2y = 5 - - - - - - - (2) (2)
Equation 1's two sides multiplied by two gives us
16x + 6y = 10 - - - - - - (3) (3)
Equation 2's two sides are multiplied by three to get
9x - 6y = 15 - - - - - - (4) (4)
Equation 3 and Equation 4 together give us
25x = 25
⇒ x = 1
Equation 1 is completed when x = 1.
8 + 3y = 5
⇒ 3y = 5 - 8
⇒ 3y = - 3
⇒ y = - 1
FINAL RESPONSE
Consequently, the needed answer is x = 1 and y = - 1.
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Solve for X
HELP PLS
Based on the graph, can this be a proportional relationship? Why or why not?
Proportional relationships are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."
What is a proportional relationship?A proportional relationship exists when each pair of data values is related in the same way, by multiplying by a factor. A proportional relationship can be identified by looking at data, an equation, or a graph. A proportional relationship with a constant of proportionality k between two quantities y and x is represented by the equation y = kx.
They pass through the source. They are linear (straight lines) and pass through the origin as well. The x to y ratio is a proportionality constant. For example, consider the following number pairs with a ratio of 2.5: 5 and 2; 10 and 4; 100 and 40; 2.5 and 1. These number pairs are all proportional to one another.
Note that an overview was his as the information is incomplete.
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what is the probability that, of 6 such types of devices, at least 3 will function for at least 15 hours? what assumptions are you making?
The probability that one such device will work at least 15 hours at least 3 among 6 devices is 0.33 approximately.
The cumulative distribution function of X is:[tex]F(x)= 1- 10/x[/tex] ( for x > 10)
X = the entire lifespan of a definite type of electronic device in hours, then the probability function of X,
here we use the cumulative distribution function, which is used to specify random variables,
F(X)= 1 - 10/X is cumulative distribution function,
then the probability that at least 3 devices will work for 15 hours
P(X[tex]\geq[/tex]15)= 1- P(X<15)
= F(15)
= 1- 10/15
=5/15
=0.333
Hence, the probability that one such device will work at least 15 hours at least 3 among 6 devices is 0.33 approximately.
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write the expression in algebraic form. [hint: sketch a right triangle, as demonstrated in example 3.] cos arcsin x - h r
Given trigonometric expression in algebraic form would be,
cos(arcsin(x - h/r)) = ± [√(r² - (x - h)²)]/r
In this question, we need write the expression in algebraic form.
Given trigonometric expression is cos(arcsin(x - h/r))
Let y = arcsin(x - h/r)
so, sin(y) = (x - h)/r
By trigonometric identity,
sin^2(y) + cos^2(y) = 1
we have cos(y) = ±√(1 - sin²y)
cos(arcsin(x - h/r)) = ±√[1 - ((x - h)/r)^2]
= ± [√(r² - (x - h)²)]/r
Therefore, given trigonometric expression in algebraic form would be,
cos(arcsin(x - h/r)) = ± [√(r² - (x - h)²)]/r
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PLS HELP!!!
(Order of Operations with Radicals MC)
Simplify the expression.
-5 (3 - CUBE ROOT of 27 times 2) divide by 3 (or over 3 because it's a fraction)
A. six fifths
B. 5
C. negative six fifths
D. −5
The Simplify the expression is -10, when we use fraction.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
=-5(∛27 *2)/3
=-5(3*2)/3
=-5(6)/3
=-10
Hence the answer will be -10 simplify the expression.
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A cylindrical can without a top is made out of metal material with a total area of 1500π cm2. Find the dimensions that will maximize the volume held by the can.
The dimensions of the cylinder will be r = 8.92 cm and h = 17.86 cm.
What is dimensions ?
Dimensions refer to the length or width of an area, region, or space in one direction.
Main Body:
Volume of cylinder = πr²h
Surface area = 2πr² + 2πrh
Given surface area = 1500 cm²
1500 = 2πr²+2πrh
h= (750/πr)-r ----(1)
V= πr²{(750/πr)-h}
V =750r - πr³
V' = 750- 3πr²
Put V' =0
0 = 750 - 3πr²
r≈ 8.92 cm
substituting the value of r in equation (1)
we get h= 17.86 cm
Hence the dimension of cylinder are r = 8.92 cm and h = 17.86 cm
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Determine the degree measure of one angle of a 30-sided regular polygon. 5,400° 5,040° 180° 168°
To determine the degree measure of one angle of a 30-sided regular polygon.
The degree measure of one angle of a 30 sided regular polygon is 168°.
What is a regular polygon?
A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides or edges are made up of segments of straight lines that are joined end to end to create a closed shape.
The intersection of two lines is referred to as a vertex or corner, and an angle is created as a result. Regular polygons are those that have sides that are congruent.
We will use the side-angle relation of a regular polygon with any no. of sides to find total sum of interior angles that is
(Side - 2) × 180°
(30 - 2) × 180°
= 5040°
Measure of each angle of 30-gon
= 5040°/30
= 168°
Thus, the degree measure of One angle of a 30 sided regular polygon is 168°
Hence the answer is, The degree measure of one angle of a 30 sided regular polygon is 168°.
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Kristen lost 30 pounds in
12 weeks. She lost the same
amount of weight per week.
What is the unit rate of weeks to
pounds?
The unit rate of weeks to pounds is 2.5 pounds in just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.
Given that,
In just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.
We have to find how many weeks are there in a pound.
What is unit rate?A rate is a ratio that is utilized to compare the quantities of several commodities. A unit rate is a rate with one as the denominator. Whenever a rate's denominator, such as the price per unit of a certain number of items, is not 1.
So, we can write has
This is the fraction of the number of pounds and number of weeks.
=30pounds / 12 weeks
=2.5 pounds
Therefore, The unit rate of weeks to pounds is 2.5 pounds in just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.
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(03.05 HC)
Belinda is thinking about buying a car for $18,500. The table below shows the projected value of two different cars for three years:
Number of years 1 2 3
Car 1 (value in dollars) 17,390 16,346.60 15,365.80
Car 2 (value in dollars) 17,500 16,500 15,500
Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)
Part B: Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)
Part C: Belinda wants to purchase a car that would have the greatest value in nine years. Will there be any significant difference in the value of either car after nine years? Explain your answer, and show the value of each car after nine years. (4 points)
HELP!!!!!!!
a. The functions are classified as follows:
Car 1: Exponential.Car 2: Linear.b. The functions are given as follows:
Car 1: c(t) = 17390(0.94)^t.Car 2: c(t) = 17500 - 1000t.c. She should purchase Car 1, as it will have a higher value in nine years.
How to classify the functions?The functions are classified depending if there is an equal factor or an equal difference between consecutive terms, as follows:
Equal factor: exponential.Equal difference: linear.Hence the functions in this problem are classified as follows:
Car 1: Exponential, as there is an equal factor of 16346.6/17390 = 0.94.Car 2: Linear, as there is an equal difference of 1000.Hence the functions are given as follows:
Car 1: c(t) = 17390(0.94)^t. -> initial value multiplied by the equal factor elevated to time.Car 2: c(t) = 17500 - 1000t. -> Initial value subtracted by the equal difference multiplied by time.After nine years, the values are as follows:
Car 1: 17390(0.94)^9 = $9,964.Car 2: 17500 - 9(1000) = $8,500.More can be learned about exponential functions at https://brainly.com/question/25537936
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Answer:
That's right
Step-by-step explanation:
Write an exponential function y=ab^x whose graph passes through the points (2,6.4) and (5,409.6)
[tex]{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=2\\ y=6.4 \end{cases}\implies 6.4=ab^2\implies \cfrac{6.4}{b^2}=a \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} x=5\\ y=409.6 \end{cases}\implies 409.6=ab^5\implies \stackrel{\textit{substituting from the 1st equation}}{409.6=\left( \cfrac{6.4}{b^2} \right)b^5} \\\\\\ 409.6=6.4b^3\implies \cfrac{409.6}{6.4}=b^3\implies 64=b^3\implies \sqrt[3]{64}=b\implies \boxed{4=b} \\\\\\ \cfrac{6.4}{b^2}=a\implies \cfrac{6.4}{4^2}=a\implies \boxed{0.4=a}~\hfill {\Large \begin{array}{llll} y=0.4(4)^x \end{array}}[/tex]
briefly explain the goal for defining and measuring variability. a measure of variability describes the degree to which the scores in a distribution are . variability also measures the .
Variability provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out to clustered together. The purpose for measuring variability is to obtain an objective measure of how the scores are spread out in a distribution
What is variability ?Variability also measure how accurately individual score or sample represent the entire population
When the standard deviation is 0 , the scores have no variability.
Variability describes how far the data points are from each other and from the center of the distribution. In addition to measures of central tendency, measures of variability provide descriptive statistics that summarize the data.
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What is the slope of the line that passes through the points
(
−
9
,
−
7
)
(−9,−7) and
(
−
11
,
−
6
)
(−11,−6)? Write your answer in simplest for
Considering the expression of a line, the equation of the line that passes through the points (-9,-7) and (-11,-6) is the equation of the line is y= -1/2x -23/2.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of a line can be calculated as:
m= (y₂ - y₁)÷ (x₂ -x₁)
Substituting the value of the slope m and the value of one of the points in y=mx +b, the value of the "b" can be obtained.
Equation of the line in this case
Being (x₁, y₁)= (-9, -7) and (x₂, y₂)= (-11, -6), the slope m can be calculated as:
m= (-6 - (-7))÷ (-11 -(-9))
m= (-6 +7)÷ (-11 +9)
m= (1)÷ (-2)
m= -1/2
Considering point 1 and the slope m, you obtain:
-7= (-1/2)×(-9) + b
-7= 9/2 +b
-7 -9/2= b
-23/2= b
Finally, the equation of the line is y= -1/2x -23/2.
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the length of a rectangle is 11 less than three times the width, and the area of the rectangle is 42. find the dimensions of the rectangle.
The dimensions of the rectangle are length and width are 6 and 11.6 respectively.
L = 3w - 11 ,
where,
L = length of the rectangle and
W =width of the rectangle
A=LW
Here A is Area of the Rectangle which is product of its dimensions i.e., length and breadth.
LW = 42
substituting for l:-
(3W-11)W= 42
3W^2 - 11W - 42 = 0
(3W + 10)(W - 6) = 0
W = 6 or -10/3 (ignore the negative root)
So the width is 6 and the length is 70/6= 11.6
The rectangle's length and width are therefore 6 and 11.6, respectively.
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How would the median change for this set of data, if the 6 was swapped for a 10?
Thank you for helping.
Answer:
it will increase
Step-by-step explanation:
6 is bigger than 10
Graph the line: 6 - 3y = 2x
6-3y=2x
-3y=2x-6
y=(2x-6)/-3
y=-(2/3)x+2
No me deja adjuntar la imagen de la gráfica, te recomiendo una página de internet llamada Desmos
X=0
y=-(2/3)(0)+2=2
(0,2)esmos
x=3
y=-(2/3)(3)+2=-2+2=0
(3,0)
x=-3
y=-(2/3)(-3)+2=2+2=4
(-3,4)
Find - 18 + 27 +13 + (− 8)
Answer:
14
Step-by-step explanation:
Correct me if I'm wrong
Answer:answer is 14
Step-by-step explanation:
hope this helps
How do i find the area if the x is 25. i broke the shape into a rectangle and a triangle, the area of the smaller rectangle is 40 and the area of the bigger rectangle is 250. I am trying to find the area of the whole complex figure
Answer:
See the picture below
Step-by-step explanation:
a prism is made up of 120 equal cubes. if the volume of the prism is 25, 920 cm3, what is the length of each cube?
The side of the cube is 6 cm.
What is the Volume of a prism?
The area that a prism takes up is referred to as its volume. A prism is a solid, three-dimensional structure with two identical faces and additional faces that resemble parallelograms. It is a polyhedron whose nomenclature is influenced by the various basic forms. Every prism has a particular base, whether it be a triangular prism (triangular base), square prism (square base), rectangular prism (rectangular base), pentagonal prism (pentagonal base), hexagonal prism (hexagonal base), or an octagonal prism (octagonal base). Consequently, because a prism is a three-dimensional form, its volume likewise exists in a three-dimensional plane. Prisms are measured in terms of their volume in cubic meters, cubic millimeters, cubic inches, or cubic feet. Following are the steps to calculate the prism's volume:
Write down the prism's dimensions as specified in step one.
Step 2: Use the formula V = B H to calculate the prism's volume. V, B, and H stand for the prism's volume, base area, and height, respectively.
Step 3: After obtaining the volume of the prism's value, add the unit of prism volume at the conclusion (in terms of cubic units).
In the question, we have given that:
Prism is made up of 120 equal cubes;
The volume of the prism is 25, 920[tex]cm^{3}[/tex];
So, we can equate the volume of 120 equal cubes with the prism's volume;
⇒ 120 × [tex](a)^{3}[/tex] = 25, 920;
⇒[tex](a)^{3}[/tex] = [tex]\frac{25920}{120}[/tex]
⇒[tex](a)^{3}[/tex] = 216;
So, the value of a is 6 cm;
That is the side of the cube is 6 cm;
Hence, The side of the cube is 6 cm.
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a prism is made up of 120 equal cubes. if the volume of the prism is 25, 920cm3, then what is the length of each cube?
The side length of a single cube will be 6 centimeters.
What is the formula to calculate the volume of a cube of side length 'a' units?The volume of the cube will be -
V = (a x a x a) cubic units
We have the volume of Prism as V[P] = 25920 cm³ which is made up of [n] = 120 cubes of the same volume.
The volume of a single cube will be -
V[c] = V[P]/n
V[c] = 25920/120
V[c] = 216 cm³
Volume of a cube = V[c] = (a x a x a)
Equating volume, we get -
a³ = 216
a = 6 cm
Therefore, the side length of a single cube will be 6 centimeters.
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I need help ASAP!!!!!!!!!!!!!
It’s due today!
Answer:
Step-by-step explanation:
What is the slope intercept form equation of the line that passes through 3 4 and 5/16 )? Y 6x − 14 y − 6x 14 y − 6x − 14 y 6x 14?.
The correct option is (a) i.e. the slope intercept form of the given line is y = 6x-14.
What is the slope and slope-intercept form?The slope of the line through two points (x₁ ,y₁) and (x₁ ,y₂) can be found by using the formula below.
m = (y₂ - y₁) / (x₂ - x₁).
The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).
The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as y = mx + b.
Here we have a line that passes through two points (x₁ ,y₁) = (3 ,4) and (x₁ ,y₂) =(5 ,16).
The slope of the line m = (y₂ - y₁) / (x₂ - x₁) = (16 -4) /(5 -3) = 12/2 = 6.
⇒ slope m = 6.
And we know the slope intercept form is
y = mx + b
⇒ 4 = 6*3 + b {with points (3 ,4)}
⇒ b =4 - 18 = -14 ⇒ b = -14.
So the slope intercept form is y = 6x-14.
The slope-intercept form of the equation with m =6 and y-intercept as -14 was found to be
y = 6x -14.
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NOTE : The question given here is not complete. The complete question is given below.
Question: What is the slope intercept form equation of the line that passes through (3 ,4)and (5,16)?
(a) y = 6x − 14
(b) y = −6x +14
(c) y = −6x − 14
(d) y = 6x + 14?
Find the slope and the y-intercept of the line. y = - 4x + 3 Select the correct choice below and fill in any answer boxes within your choice. A. The slope is (Simplify your answer. Type an integer or a fraction.) B. The slope is undefined.
with simple explanation, please!!
Answer:
A- the slope is -4 and y-intercept is 3
Step-by-step explanation:
The standard form is y=mx+c (for straight line graph) while m is slope(gradient) and c is y-intercept.
So, slope is -4 and y-intercept is 3
The perimeter of the parallelogram is 102 feet. Find m. Write your answer as a decimal or mixed number.
If the perimeter of the parallelogram is 102 feet, then the value of m is 12.75
The perimeter of the parallelogram = 102 feet
The perimeter of the parallelogram = 2(l + w)
Where l is the length and w is the width of the parallelogram
The length of the parallelogram = 3m
The width of the parallelogram = m
Substitute the values in the equation of the perimeter
102 = 2(3m + m)
102 = 2(4m)
102 = 8m
m = 102 / 8
Divide the terms
m = 12.75
Hence, if the perimeter of the parallelogram is 102 feet, then the value of m is 12.75
The complete question is:
The perimeter of the parallelogram is 102 feet. Find m. Write your answer as a decimal or mixed number.
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A cout mater bough 45 meter of rope he ued two nine of the rope for knot tying. How many meter of rope were ued for knot tying
The meters of rope used for knot tying is 10 meters.
According to the question,
We have the following information:
A cout mater bough 45 meter of rope he used two-ninth of the rope for knot tying.
So, we have the following expression for the rope used for knot tying:
45 of 2/9
We know that the word of is replaced by multiplication.
45*2/9
Now, we will first multiply the numbers in the numerator and then we will divide the obtained result by denominator.
90/9
Dividing 90 by 9:
10 meters
Hence, the meters of rope used for knot tying is 10 meters.
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What is the answer of this question
The number of shelves is x/20.
From the question, we have
You collect miniature cars and display them on shelves that hold 20 cars each.
Number of shelves = x/20
Divide:
Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.
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PLS HELP
Angel is renting a meeting room at a college. There is a reservation fee of $41 and an additional fee of $4 per hour. She needs to spend no more than $65. What is the possible number of hours for which Angel can rent the meeting room? Use h for the number of hours.
pls explain
Answer:
She can rent the room for 6 hours.
Step-by-step explanation:
65 - 41 = 24
So she has left 24$ to use
24 divided by 4 = 6
She can rent the room for 6 hours.
What is the answer of 3 power 5?.
Jim began a 182-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 5 hours. If Jim walks at a rate of 4 miles per hour and rides at 40 miles per hour, find the amount of time he spent on the bicycle.
Based on the concept of unitary method, the amount of time he spent on the bicycle is 5.6 hours.
Unitary method:
Unitary method is used for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given,
Jim began a 182-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip walking. The whole trip took 5 hours.
Here we need to find the amount of time he spent on the bicycle if Jim walks at a rate of 4 miles per hour and rides at 40 miles per hour.
Let us consider x be the hours on the bike for distance 40x miles.
We know that, he spent 5 - x hours walking for distance 4(5 - x) miles or it can be written as
=> 20 - 4x
And we also know that those two, 40x and 20 - 4x, add to 182 miles
=> 40x + 20 - 4x + 182
=> 36x + 202
=> 36x = 202
=> x = 5.6
And the units calculation is m/h*h=m
If the value of x = 5.6 hours on the bike for 139.5 miles, then 5 - x =0.6 hours walking for 4 miles.
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Determine which quadratic equation has complex solutions
a) 15x² - 10 = 0
b) 1/2x² + 12 = 4
15x² - 10 = 0 is a quadratic equation which has complex solutions.
Define quadratic equation.The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. There should be two solutions to quadratic equations. If you think about the discriminant formula, two roots can be real, equal, or imaginary.
Given,
Quadratic equation:
15x² - 10 = 0
15x² = 10
x² = 10/15
Roots:
x = ±√10/15
15x² - 10 = 0 is a quadratic equation which has complex solutions.
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