The descriptors that are applicable for factor by grouping is 4 terms and 3 terms.
What is group factorization?
Factorization by grouping requires that we first group the terms according to their common factors. Method of factorization by term grouping:
(i) A factor can be extracted from each group of the supplied expression's groupings.
(ii) Factorize each group.
(iii) Next, eliminate the factor shared by the newly created group.
To factorize 4 terms use the method -
The first step is to group the first and last two terms together.
Then create a GCF by factoring each individual binomial.
Factor out the common binomial in step three.
To factorize 3 terms use the method -
Factoring out the GCF of the full phrase is the first step (from all 3 terms). There might not always be a GCF to account for (that is, the GCF is 1).
Next, select two terms to think about jointly (we may need to split a term into two parts). Subtract the two terms' GCFs.
Consider the remaining terms along with the factored pair and determine if there is any additional factoring that can be done (if anything).
A binomial cannot be factored by factor by grouping method as it contain only two terms which doesn't require further factoring using grouping method.
Both terms are not always perfect squares, there can be times when the factors are written as roots.
Therefore, descriptors are 4 terms and 3 terms.
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How do you simplify a binomial by a binomial?.
One binomial's terms are multiplied by the other binomial's terms. The algebraic total of these products is then calculated after this step. We employ a technique called the FOIL method to multiply binomials.
Therefore, the order in which the terms are multiplied in this order is FOIL (First Outer Inner Last).
An algebraic expression with two terms joined by a plus or minus sign is known as a binomial. Binomial multiplication is comparable to multiplying two whole numbers or fractions. Utilising the distributive property of multiplication twice is one way to multiply binomials.
The letters in the acronym FOIL stand for First, Outer, Inner, and Last. Since only binomials may be multiplied using this approach, it cannot be used to multiply all polynomials. The FOIL formula has the following general form: (a + b) (c + d) = ac + ad + bc + bd.
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tanik turns in his third report. his teacher says 20% of his reports for the year are done. How many research reports will Tanik complete during the school year? Show your work
The total reports during the year is 15.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that tanik turns in his third report. his teacher says 20% of his reports for the year are done.
We have to find the number of research reports will Tanik complete during the school year.
Let the number of reports be = x
As mentioned, when Tanik submitted his 3rd report, he had completed 20% of the reports so
20/100×x=3
0.2x=3
Divide both sides by 0.2
x=15
Hence, the total reports during the year is 15.
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I think I'm slow. Like FrFr
The slope of the given graph is m = -1, and the y-intercept is y = 1.
Define slope.A line's slope reveals its inclination and direction. Without actually using a compass, determining the slope of lines in a coordinate plane can aid in determining whether the lines are parallel, perpendicular, or have no relation at all.
Any two different points on a line may be used to derive the slope of that line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line equation.
Consider each box of the graph as 1 unit.
So, from the graph, at x = 0
y = 1
So, this is the y-intercept of the line.
Consider any two points
(x₁, y₁) = (0, 1)
(x₂, y₂) = (1, 0)
The slope is given by the slope formula as
m = (y₂ - y₁)/(x₂ - x₁)
= (0 - 1)/(1 - 0)
= -1
The slope of the graph is m = -1.
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A baseball team has three different pitchers. Randy allowed two runs and pitched three innings. Felix allowed four runs and pitched five innings. Johan allowed five runs and pitched seven innings. Which pitcher has the lowest number of runs allowed per inning
Answer:
Randy
Step-by-step explanation:
Randy: 2 runs / 3 innings = 0.67
Felix: 4 runs / 5 innings = 0.80
Johan: 5 runs / 7 innings = 0.71
Which graph represents the equation y equals one half times x minus 2?
graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1
graph of a line passing through the points negative 2 comma 0 and 0 comma 1
graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2
graph of a line passing through the points negative 4 comma 0 and 0 comma 2
Step-by-step explanation:
graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2
Answer:
it's c if you are taking pre algerbra 8th on question 5 if ur on flvs
Step-by-step explanation:
line passing through the points (-2,-3) (0,-2)
How do I find the domain and range in this? Please help!!
Answer:
Step-by-step explanation:
p
How do you find the standard deviation of a sample mean and n value?.
Divide the population standard deviation () by the square root of the sample size (n) to obtain the standard deviation of the sample mean (X).
How can the distribution of sample means' mean and standard deviation be determined?The sample mean is normally distributed, with mean X= and standard deviation X=/n, where n is the sample size, for samples of any size taken from a population that is normally distributed.
How is the sampling distribution's SD determined?The standard deviation of the population divided by the square root of the sample size is equal to the standard deviation of the sampling distribution of means.
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B
Which answer completes the sentence?
0.5 is equivalent to the fraction
0.5 is equivalent to the fraction 1/2.
What is a fraction?
In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
We are given 0.5 which is to be converted into a fraction.
So, for this we will take 0.5 as the numerator and 1 as the denominator because anything divided by 1 is the number itself.
Thus, we get
⇒0.5/1
Now, we will multiply both numerator and denominator by 10.
From this, we get
⇒(0.5*10)/(1*10)
⇒5/10
Now, we will reduce the fraction to the lowest form by dividing both numerator and denominator by 5.
From this, we get the fraction as 1/2.
Hence, 0.5 is equivalent to the fraction 1/2.
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array indices must be positive integers or logical values.
You get the "Array indices must be positive integers or logical values" error when using the "angle" function because you are trying to use a non-numeric or non-logical value as an index.
The "angle" function in MATLAB is used to find the phase angle of a complex number. When you are trying to use the function, you are probably passing in a variable or expression that is not a numeric or logical value.
In MATLAB, array indices must be positive integers or logical values. When you try to use a non-numeric or non-logical value as an index, you will get the "Array indices must be positive integers or logical values" error.
This means that you need to make sure that the variable or expression you are passing into the "angle" function is a numeric or logical value before using it as an index.
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Complete question:
Why do I get "Array indices must be positive integers or logical values" error when using "angle" function?
Any help please? I’m stuck at this question.
The simplification of the expression is [tex]\frac{7}{5}[/tex].
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Here the given expression is
=> 1 + [tex]\frac{1}{1+\frac{1}{1+\frac{1}{2} } }[/tex]
=> 1 + [tex]\frac{1}{1+\frac{1}{\frac{2+1}{2} } }[/tex]
=> 1 + [tex]\frac{1}{1+\frac{1}{\frac{3}{2} } }[/tex]
=> 1 + [tex]\frac{1}{1+\frac{3}{2} }[/tex]
=> 1 + [tex]\frac{1}{\frac{2+3}{2} }[/tex]
=> 1 + [tex]\frac{1}{\frac{5}{2} }[/tex]
=> [tex]1+\frac{2}{5}[/tex]
=> [tex]\frac{5+2}{5}[/tex]
=> [tex]\frac{7}{5}[/tex]
Hence the simplification of the expression is [tex]\frac{7}{5}[/tex].
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In a pond, 7 fish are known to have a birth rate of 2.9 every month. How many fish are
in the pond (if the growth follows an exponential model) after 6 months? (Round up to
nearest whole fish).
By using exponential growth formula we get 5531 fish in the pond after 6 months.
What is exponential growth formula and calculate it?To find the number of fish in the pond after 6 months, we can use the formula for exponential growth:
N(t) = N0 * [tex](1 + r)^{t}[/tex]
where N(t) is the number of fish at time t (in this case, after 6 months), N0 is the initial number of fish (7), and r is the growth rate (2.9 fish per month).
We can substitute these values into the formula and solve for N(6):
N(6) = 7 * [tex](1 + 2.9)^{6}[/tex]
N(6) = 7 * [tex](3.9)^{6}[/tex]
Using the calculator, we get N(6) = 7 * 791.64 = 5530.5
Rounding up to the nearest whole fish, we get 5531 fish in the pond after 6 months.
Note: The exponential model assumes that the growth rate is constant over time and that the pond has unlimited resources to sustain the fish population.
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What quadrant will the point (- 4 2 be located in?.
The point (-4, 2) be located in second quadrant. Due to the fact that x is negative and y is positive.
The coordinate system's two axes, the x-axis and the y-axis, define a region is called a quadrant. The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle.
These areas include coordinates, or positive and negative values of the x- and y-axes. The position of a point in a quadrant is indicated by the coordinates.
The first quadrant is located in the graph's upper right-hand corner. Both the x and y values in this quadrant are positive.
The second quadrant is located in the graph's upper left corner. The value of y is positive in this quadrant while the value of x is negative.
The third quadrant is located in the graph's lower left-hand corner. It includes both the negative values of x and y.
Fourth Quadrant, the final quadrant has a positive x value and a negative y value, and it is located in the lower right corner.
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The complete question is:
What quadrant will the point (-4, 2) be located in?
I need help on this question. What is 4/7 x 3/8?
Answer choices:
Answer:
C
Step-by-step explanation:
multipled is 12/56 but simplified is 3/14
URGENT PLEASE I NEED IT RN!! THANKS
8. Prove the triangles are congruent
Step-by-step explanation:
Angle BAD = Angle CDA (Alternative angle)
AD=AD (Common side)
AB=CD (Given)
Thus, the given triangles are congruent by SAS.
In a continuous series, the mean is 5. If efx= p and ef= 10 than find the of p
In a continuous series, the mean is 5, If efx= p and ef= 10 than the value of p = 50
How to find p value?Instead of being presented as a single number in a continuous series, the observations are presented in different class intervals, and the frequency represents the percentage of observations that fall into each class interval.
Continuous series are those in which frequencies are provided along with the variable's value as class intervals. an example: Their respective frequencies are 3, 7, 11, 9, and 6.
step1:
here mean(x)=5
and e f x=10
then as given
p=e f x
step2;
p=10*5=50
p=50
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Samantha constructs a scatter plot. She realizes that she needs to add one more point, which will be an outlier. Which of the ordered pairs does she still need to plot?
Responses
(8,6)
(10,14)
(19,9)
(4,15)
Answer:(8,6)
Step-by-step explanation:
Keshawn is asked to compare and contrast the domain and range for the two functions f(x)= 5x
G(x)=5x
The correct option is 'The domain of both functions is all real numbers'.Option A
What is a domain?Generally, functions are f(x) = 5x and g(x) =5x
Since the domain of f(x) is, D= { x : x belongs to all real numbers.}
Therefore, the set of all real numbers constitutes the domain of f(x).
Due to the fact that f(x) and g(x) both return the same result,
Therefore, the set of real numbers is likewise included in the domain of g(x).
Now, the range of f(x) is , R= { 5x : x belongs to all real numbers.}
As a result, the set of possible values for f(x) includes only real numbers.
In addition, the range of g(x) includes all real values.
Given what has been said so far, it is clear that only choice (1) should be considered accurate.
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CQ
Keshawn is asked to compare and contrast the domain and range for the two functions.
f(x) = 5x
g(x) = 5x
Which statements could he include in his explanation? Check all that apply.
1. The domain of both functions is all real numbers.
2. The domain of f(x) is x > 5.
3. The domain of g(x) is x > 5.
4. The range of both functions is y > 5.
5. The range of f(x) is y > 0.
6. The range of g(x) is y > 0.
Aume that the box contain 6 ball: 1 blue, 3 red, and 2 green. Ball are drawn in ucceion without replacement, and their color are noted until a blue ball i drawn
If a box contains 6 balls, 1 of which is blue, 3 of which are red, and 2 of which are green, and balls are drawn in succession without replacement until a blue ball is drawn, the probability of drawing a blue ball on the first draw is 1/6, or approximately 0.17.
On the second draw, the probability of drawing a blue ball is 0, since there is only one blue ball in the box and it has already been drawn.
On the third draw, the probability of drawing a blue ball is 0 as well, for the same reason as above.
In general, the probability of drawing a blue ball on any draw after the first one is 0, since a blue ball has already been drawn and removed from the box and there are no more blue balls left in the box.
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Since there is only one blue ball in the box and it has already been drawn, the chance of drawing a blue ball on the second draw is zero.
For the same reason as above, the likelihood of getting a blue ball on the third draw is also zero.
Since a blue ball has already been drawn and taken out of the box and there are no more blue balls in the box, the chance of drawing a blue ball on any draw following the first one is typically zero.
The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
-5
5
Y
G(X) = x²
+++
F(x) = ? 5
The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has been changed.
[tex]y=a(x-hx)^{2} + k[/tex] the answer is F(x) = [tex]4x^{2} -1[/tex]
What is meant by graph?
A visual representation of the variation of one variable with relation to one or more other variables, such as a collection of dots, lines, line segments, curves, or regions.In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.The relationships between two or more items are frequently represented by the points on a graph.A graph is a type of non-linear data structure composed of nodes, also known as vertices and edges.Any two nodes, often referred to as vertices, in a network are connected by edges.Graphs and charts are useful visual aids because they make information accessible and quick to understand.We are given a function:
G(x)=[tex]x^{2}[/tex]
The graph of G([tex]x[/tex]) is also shown in the given question figure.
It is a parabola with vertex at (0,0).
Sign of [tex]x^{2}[/tex] is positive, that is why the parabola opens up.
General equation of parabola is given as:
[tex]y=a(x-hx)^{2} + k[/tex]
Here, in G(x), a = 1
Vertex (h,k) is (0,0).
As seen from the question figure,
The graph of F(x) opens down that is why it will have:
Sign of [tex]x^{2}[/tex] as negative. i.e. a = -1
And vertex is at (0,-5)
Putting the values of a and vertex coordinates,
[tex]y= -1 (x-0x)^{2} + (-5)[/tex]
Hence, the equation of parabola will become:
[tex]y=-x^{2} -5x[/tex]
The correct answer is:
F(x) =[tex]y=4x^{2} -1[/tex]
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How do you graph y =- 2x?.
The slope is 2 when expressed in the slope-intercept form. Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.
How should the slope intercept form be written?When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.
What causes the slope intercept form?Writing an equation for a line in the form y = mx + b is known as slope intercept form in mathematics. The m indicates the line's slope, while the b indicates the y-intercept. When attempting to locate a point on a line or determine y given x, the slope intercept form is utilized.
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How do you use the substitution method with three variables?.
The substitution method is a powerful tool used to solve systems of linear equations with three variables. Beginning with one of the equations for one of the variables, utilise the substitution method.
This will give you an expression for that variable in terms of the other two. Then, substitute this expression into the other equations and solve for the remaining variables.
Consider, for example, a set of linear equations involving the variables x, y, and z:
x + y + z = 13
2x + 4y - z = 6
3x - 2y + 3z = 11
Start by solving the first equation for x in order to apply the substitution method here:
x = 13 - y - z
Now solve for y and z by substituting this expression into the previous two equations:
2(13 - y - z) + 4y - z = 6
39 - 2y + 3z = 6
3(13 - y - z) - 2y + 3z = 11
39 - 5y + 6z = 11
Subtract 39 from both sides of each equation, then solve for y and z using elimination or another method. Once you have found values for both variables, plug them into the original expression for x to find its value.
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I’m stuck on this question too, I need some assistance
Equation for m< 1 (x - 9)° and m <2 =(8x)° is <1 = 168 <2 = 12
Explain about the Equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
When one side of an equation equals the other, it is said to be an equation. For instance, in this case, we know that 4 + 4 = 8 and 10 - 2 = 8, which means that this equation is correct.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10.
To start, you must find x.
8x + x -9 = 180
9x -9 = 180
9x = 189
x = 21
Now, change both angles' x values to 21.
8(21) = 168
(21) - 9 = 12
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A recipe for 48 chocolate chip cookies calls for 3 cups of flour. The number of cookies varies directly with the amount of flour you use.
Answer:
answer is 114 I have confirmed it
A rectangle field ha meaurement of 2t and 50m Kim walk around the edge of the field. She walk le than 1km a) form and olve an inequality to find the value of t
The inequality equation for the measurements of the rectangular field must satisfy t<225.
If two real numbers or algebraic expressions are related by the symbols “>”, “<”, “≥”, “≤”, then the relation is called an inequality.
Given that,
The length of the rectangle is 2t meters
the breadth of the rectangle is 50 meters
The perimeter of the rectangle is given by 2×(length+breadth)
Here the perimeter of the rectangle is less than 1km=1000meter
Forming an equation with the given data
2×(2t+50)<1000
2t+50< 1000/2
2t+50<500
2t<500-50
2t<450
t<450/2
t<225
Thus, The inequality equation for the measurements of the rectangular field must satisfy t<225.
Complete question: A rectangular field has these measurements kim walks around the edge of the field. she walks less than 1km. form and solve an equality to find the possible values of t when length of the field is 2t meters and breadth is 50 meters
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Pt 2
Please answer with a good reasoning with EXPLANATION!!
A perimeter is the length of a two-dimensional shape's boundary. It is sometimes described as the total length of the object's sides. The perimeter of that shape is equal to the algebraic sum of the lengths of its sides.
What is Perimeter?The term "two-dimensional shape" refers to any shape that is flat and has only two dimensions, i.e. length and breadth. Each polygon is a flat, 2-D figure that rests on a plane. Polygons, such as triangles, rectangles, and squares, are closed figures that are enclosed by a series of lines. The length or linear measure of these confined line segments is known as the polygon's perimeter (peri: around; metre: measure). Or to put it another way, it is the length of its borders. The centimetre (cm) or metre is its unit (m).
Perimeter of RectangleThe whole distance that a rectangle's boundaries, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the sum of its four sides. Since a rectangle's perimeter is a linear measurement, the unit will be in metres, centimetres, inches, feet, etc.
Perimeter of a rectangle = sum of four sides
= AB + BC + CD + AD
= length + breadth + length + breadth
= 2 length + 2 breadth
Perimeter of a rectangle = 2 × (length + breadth)
Perimeter of CircleThe radius of the circle serves as one of the three variables in the perimeter of a circle formula, along with two constants. The formula for calculating a circle's circumference or perimeter is as follows:
Circumference of a circle is equal to 2πr.
where,
r = radius of the circle
D = diameter of the circle
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CIn a group of 20 children, 25% are
girls. How many boys are there in the
class?
9
Answer:
15 boys
Step-by-step explanation:
We know
A group has 20 children
25% girls
25% = 0.25
20 times 0.25 = 5 girls
20 - 5 = 15 boys
So, there are 15 boys
A phone company offers two monthly plans. Plan A costs $40 plus an additional $0.02 for each minute of calls. Plan B has no initial fee but costs $0.18 for each minute of calls. What is the cost when the two plans cost the same for a set number of minutes?
The cost of plan A is represented by the equation:
Cost A = 40 + 0.02x
where x is the number of minutes of calls.
The cost of plan B is represented by the equation:
Cost B = 0.18x
To find the point where the two plans cost the same, we can set the two equations equal to each other and solve for x:
40 + 0.02x = 0.18x
40 = 0.16x
x = 250
So when the customer makes 250 minutes of calls, the cost of the two plans will be the same.
The cost of plan A will be 40 + 0.02250 = $50 and the cost of plan B will be 0.18250 = $45
So when the customer makes 250 minutes of calls, Plan A and Plan B cost the same amount of money.
How do I tell how many solutions an equation has?.
To find the number of solutions to given equation by comparing the coefficients of the variables of the equations.
We know that a solution of an equation is a value that satisfies given equation.
We can find the number of solutions to given equation by comparing the coefficients of the variables of the equations.
There are three types of solutions to the set of linear equations: Unique Solution: The linear equation in one variable (equation of the form ax + b = 0) always has a unique solution.
No Solution: When the graphs of the linear equations represents parallel lines, then the system of linear equations has no solution.
Infinitely Many Solution: if the system of equations represent coincident lines, and they have the same y-intercept, then the system of equations has infinitely many solutions.
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Need help with this
There is a loss of $14500 and 30 units are required to be made to break- even. The solution has been obtained using profit function.
What is profit function?
A relationship that depicts the difference created by subtracting the cost function from the revenue function is called a profit function. The ideal pairing of revenues and expenses to generate the greatest possible profit can be seen on the graph of a profit function.
a. The fixed cost of the factory is $5000 + $10000 = $15000
The variable cost of the factory is $700 + $800 = $1500
The revenue of the factory is $2000x.
We need to find profit after 1 unit is made i.e. x = 1
So, TC= FC + VC(x)
⇒ TC = $15000 + $1500(1)
⇒ TC = $16500
Therefore, the profit will be
⇒Profit = R(x) - TC
⇒Profit = $2000(1) - $16500
⇒Profit = -$14500
Hence, there is a loss of $14500.
b. For break even, the total cost must be equal to the revenue
So, TC = R(x)
⇒ FC + VC(x) = R(x)
⇒ $15000 + $1500(x) = $2000(x)
⇒ $15000 = $500(x)
⇒ x=30
Hence, 30 units are required to be made to break- even.
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What is the formula of area of acute angle triangle?.
The formula for area of an acute angle triangle is (½) × b × h
a triangular shape with three acute angles. It indicates that none of the angles are precisely 90 degrees. Any triangle with all interior angles being acute angles is said to have an acute angle triangle. The line traced from the base of the triangle to the opposite vertex of an acute triangle is always perpendicular. The formula for the area of an acute angle triangle is (½) × b × h
Based on the side dimensions and angles of the triangles, one can classify acute triangles into distinct categories. One of them is an equilateral triangle with equal-length sides and interior angles, every sixty degrees in length. A triangle that is equilateral is always sharp. An acute isosceles triangle has two equal sides, and its opposing angles are also of equal length. A scalene acute triangle has uneven sides and internal angles on each of its three dimensions. The sum of all angles is less than 90 degrees.
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