Figure 1 and figure 2 are right triangles.
two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 5 units long
What scale factor was used to produce Figure 2 from Figure 1?
3 over 5
5 over 3
3
5
The scale factor used to produce the second triangle is 5/3.
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size. For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.
Given that, a triangle with base length of 3 units is transformed into a second triangle with a base length of 5 units,
Therefore, the scale factor = 3/5
Therefore, to produce Figure 2 from Figure 1 we will multiply it by 5/3
Hence, the scale factor used to produce the second triangle is 5/3.
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Answer:
If ur options are one sixth
6
one half
2
then the correct answer is 2
Step-by-step explanation:
I took the quiz and got it right.
How do you graph x+y= -1
Answer:
See the image attached.
Step-by-step explanation:
x y
0 -1
1 -2
Help someone tell me what’s x??
The length of the rectangle side x is equal to 35.33 cm approximately to 2 decimal place using the trigonometric ratio of tangent.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
We shall represent the intercept of the diagonal lines in the rectangle with O so that we consider the right triangle ∆AOx, then we solve for the length of Ax and multiply the result by 2 to derive the value of x as follows:
angle 54 and m∠AOD are supplementary so;
m∠AOx = (180 - 54)/2 {m∠AOD/2}
m∠AOx = 63°
tan 63° = (x/2) ÷ 9
tan 63° = x/2 × 1/9 {change division to multiplication}
tan 63° = x/18
x = 18 × tan 63° {cross multiplication}
x = 35.3270
Therefore, 35.33 cm approximately to 2 decimal place is the length of the rectangle side x using the trigonometric ratio of tangent.
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An architect is designing a water fountain for a park. She uses the given function to model the water jets flowing from the fountain's nozzles,
where h(x) gives the height of the water jet, in feet, x feet from its starting point.
The two adjacent columns that show an interval with an average rate of change of -0.3 are column 7ᵗʰ and 8ᵗʰ.
We have a function used by an architect is designing a water fountain for a park. The function is defined as h(x) = - x²/20 + x + 15
where h(x) --> height of the water jet, in feet,
x --> distance from its starting point in feet.Also , the average rate of change = - 0.3
Average rate of change is used to measure the change in value of function per unit, on average over an interval. It is derived from the slope line which is formed bu joining the end points of graph. Formula is represented as
A(x) = {F(b) - F(a)}/(b - a)
where b and a are end points of interval.
In this case, this formula is used as
A(x) = {H(x₂) - H(x₁)}/(x₂ - x₁ )
=> -0.3 = {H(x₂) - H(x₁)}/(x₂ - x₁ )
As we see in above figure the difference between the any two values of x is equals to 2 i.e., the final value - initial value = 2 in an interval.
So, x₂ - x₁ = 2
=> -0.3 = {H(x₂) - H(x₁)}/2
=> -0.3× 2 = H(x₂) - H(x₁)
=> -0.6 = H(x₂) - H(x₁)
=> H(x₂) = H(x₁) - 0.6
so, the columns which follows this relationship are the following
distance , x 12 14
Height of jet , h(x) 19.8 19.2
Hence, the required relationship is H(x₂) = H(x₁) - 0.6.
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Complete question:
An architect is designing a water fountain for a park. She uses the given function to model the water jets flowing from the fountain's nozzles,
where h(x) gives the height of the water jet, in feet, x feet from its starting point. select two adjacent columns that show an interval with an average rate of change of -0.3
Anybody know how to solve this??? Plsss
Answer:
12,34
Step-by-step explanation:
For 'a'
8x=(2x+72) [vertically opposite angle]
8x-2x=72
6x=72
x=72/6
x=12
For 'b'
4x+20+x-10=180° [ being straight angle ]
4x+x+20-10=180°
5x+10=180°
5x=180-10
x=170/5
x=34
A5=768 and a2=12; given two term in a geometric equence find the 8th term and the recurive formula
The recursive formula for this geometric sequence is , an = a(n-1) * 64, where a(n-1) is the previous term of the sequence.
What is geometric ?
A geometric sequence is a sequence of numbers such that the quotient between any two consecutive terms is always the same, this common ratio is denoted by "r" and the first term of the sequence is denoted by "a1". A geometric sequence can be represented by the following formula
a_n = a_1 * r^(n-1)
Given a5=768 and a2=12, we can find the value of the common ratio (r) by dividing the two terms:
r = a5 / a2 = 768 / 12 = 64
To find the 8th term of the geometric sequence, we can use the formula:
an = a1 * r^(n-1)
where a1 is the first term, r is the common ratio, and n is the position of the term.
Given the 8th term, we can substitute the values
a8 = a1 * r^(8-1) = a1 * 64^7 = a1 * 64^7
To find the recursive formula, we can use the formula:
an = a(n-1) * r, where a(n-1) is the previous term of the sequence
So the recursive formula for this geometric sequence is , an = a(n-1) * 64, where a(n-1) is the previous term of the sequence.
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A geometric sequence is a set of numbers where any two consecutive terms' quotients are always the same. The first term in the series is indicated by the letter "a1," and the common ratio is indicated by the letter "r". The following formula can be used to describe a geometric sequence.
Given a5=768 and a2=12, we can find the value of the common ratio (r) by dividing the two terms:
r = a5 / a2 = 768 / 12 = 64
To find the 8th term of the geometric sequence, we can use the formula:
an = a1 * r^(n-1)
where a1 is the first term, r is the common ratio, and n is the position of the term.
Given the 8th term, we can substitute the values
a8 = a1 * r^(8-1) = a1 * 64^7 = a1 * 64^7
why is paying back along with a nominal interest rate of 13.62% if the interest is compounded quarterly, how much greater is white effective interest rate than his nominal interest rate
The required white effective interest rate is 0.71% more than his nominal interest rate.
What is compound interest?Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
Here,
White Effective interest R,
[tex]R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=[/tex]
R = 14.33 percent
So
Difference in interest = 14.33%-13.62%
=0.71%
Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.
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simplify the expression
6(6- 2s)=
Answer:
36-12s=y
s=3
thats with it all the way simplified
How do you find the properties of a 30 60 90 triangle?.
A 30-60-90 triangle has one right angle, with the other two angles measuring 30 and 60 degrees. The shortest side is half as long as the hypotenuse, while the middle side is equal to the shortest side multiplied by the square root of 3. The area can be found using (1/2) x base x height, with the perimeter equal to the sum of all three sides.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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I seriously need help on this question, can someone help?
Answer:
a. A + C < B + C
Step-by-step explanation:
when we know that A < B, then adding the same amount to both sides did not change the relationship between both sides.
this is like having a balance with 2 cups. one side is heavier than the other, so the heavier cup is down.
if we add the same weight to both cups, the situation will not change.
that is why a. is the right answer.
b. would only be right, if C is negative.
for positive C the same argument as for A applies. a smaller amount (or weight) stays smaller also after multiplying both sides by the same number.
but because this option would only be right for a subset of the possible values, this is not true in general.
c.
this is not true at all.
if we multiply the expression by -1, then the inequality sign has to flip. < becomes >, > becomes <.
which did not happen here.
MCD y mcm de 420,630,330
The GCD is 30 and the LCM is 13860 for the numbers 420, 630, and 330 .
What are LCM and GCD?The highest factor among two or more numbers is the greatest common denominator (GCD).
The lowest common multiple (LCM) is another name for the least common multiple in mathematics. The least common multiple of two or more numbers is the smallest of all the common multiples of the numbers provided.
Take all three numbers and their factors to determine the greatest common divisor.
1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420 are the factors for 420.
The factors for 630 are as follows: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630, and 330 are as follows: 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330.
Of the three, 30 is the common factor with the highest value.
Take all three numbers and their prime factors to determine the lowest common multiple.
The prime factors for 420 = 2 × 2 × 3 × 5 × 7
The prime factors for 630 = 2 × 3 × 3 × 5 × 7
The prime factors for 330 = 2 × 3 × 5 × 11
The LCM of 420,630,330 = 2 × 2 × 3 × 3 × 5 × 7 × 11 = 13860.
Therefore, the GCD and LCM is 30 and 13860 respectively.
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2. *
5
A map is represented on a coordinate grid. Town A is located at (-8, 2) and Town B is located
at (10, 8). Town C is the midpoint between Town A and Town B.
If each unit represents 1 mile, the approximate distance from Town A to Town C is
1 point
miles.
The approximate distance from Town A to Town C is 12.5 miles.
What is the midpoint?
The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.
To find the midpoint of Town A and Town B, you need to find the average of the x-coordinates and the average of the y-coordinates.
The x-coordinate of Town A is -8 and the x-coordinate of Town B is 10, so the average is (10 - (-8))/2 = 9/2 = 4.5.
The y-coordinate of Town A is 2 and the y-coordinate of Town B is 8, so the average is (8 - 2)/2 = 6/2 = 3.
Therefore, Town C is located at (4.5, 3).
To find the distance from Town A to Town C, you can use the distance formula, which is the square root of the difference in x-coordinates squared plus the difference in y-coordinates squared.
The distance from Town A to Town C = √((4.5 - (-8))^2 + (3 - 2)^2) = √(12.5^2 + 1^2) = √(156.25 + 1) = √(157.25) = 12.5 miles
Hence, the approximate distance from Town A to Town C is 12.5 miles.
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Answer the following question in the picture
Somebody please help
The algebraic expression y = $2x + $10 represent the cost of each ATM transaction for the month where x is the cost of transaction during the month. And $20 is the total cost of 5 ATM transactions with the expression y = $2(5) + $10.
How to evaluate the total cost of 5 ATM transactionWe shall represent the total cost of ATM transaction in a the month with the letter y and the cost of a transaction with the letter x so that we have an algebraic expression as follows:
y = $2x + $10
using the algebraic expression to evaluate for the total cost of 5 ATM transaction, we have;
y = $2(5) + $10
y = $10 + $10
y = $20
Therefore, the algebraic expression y = $2x + $10 can be used to represent the cost of each ATM transaction for the month. And the expression y = $2(5) + $10 with the result $20 represent the total cost of 5 ATM transaction during the month.
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Suppose you through a ball horizontally. How is the way the ball moves similar to the motion of the planets around the sun?
The forces acting on a horizontally moving ball in the air are gravity or the force of its own weight, and the force that displaces the ball in the horizontal direction.
What is force?Force is an external agent that acts on a body to cause it to move or stop. There are various types of forces, such as magnetic forces, nuclear forces, frictional forces, and so on.
The product of a moving body's mass and acceleration yields force, which is derived from Newton's second law of motion. As a result, as the mass of the object increases, the force required to change its state increases.
The forces acting on a moving ball horizontally are the normal force that displaces it in that direction and the downward force of gravitation equal to its weight. Air resistance acting on the ball can also be considered.
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What is a 45 degree triangle called?.
A 45-degree triangle is called a right-angle triangle.
A 45-degree angle is exactly half of a 90-degree angle formed between two rays.
It is equal to half of a straight angle or a 90-degree angle. An angle bisector of a 90-degree angle creates two equal 45-degree angles. The 45-degree angle can be found in many everyday objects, such as scissors, doors, and windows. It is also known as the angle created by a square's diagonal and its sides.
It is an acute angle and two angles measuring 45 degrees form a right angle or a 90-degree angle. We know that an angle is formed when two rays meet at a vertex.
Thus, A 45-degree triangle is called a right-angle triangle.
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What is the product of A & B?.
The cross product of A & B (A × B) is |A| |B| Sin θ, where θ is the angle between A and B.
The vector product or cross product of two vectors, A and B, is denoted by A × B, and its resultant vector is perpendicular to the vectors A and B.
The cross product is mostly used to determine the vector, which is perpendicular to the plane surface spanned by two vectors, whereas the dot product is used to find the angle between two vectors or the length of the vector.
The cross product of two vectors, say A × B, is equal to another vector at right angles to both, and it happens in the three dimensions.
If θ is the angle between the given two vectors A and B, then the formula for the cross product of vectors is given by:
|A| |B| Sin θ
--The given question is incorrect; the correct question is
"What is the cross product of A & B?"--
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please help me
[tex] \sqrt[4]{ - 81} [/tex]
Answer:
3 ⁴√-1
Step-by-step explanation:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
What are the slope and the y-intercept of the linear function that is represented by the equation y?.
The slope of the line is -10, and the y-intercept is 1.
Linear equations can be written in the form y=mx+b, where:y is a y coordinate on the line m is the slope of the line.A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
x is the x coordinate on the line that corresponds with the y coordinate in the equation,b is the y-intercept of the line
So for the equation y=-10x+1:
comparing the above equation with y=mx+b we get,
m=-10 and b=1 so the slope of the line is -10, and the y-intercept is 1.
Thus, The slope of the line is -10, and the y-intercept is 1.
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What is the scale factor in the dilation if the coordinates of A are (-7, 6) and the coordinates of Care (-4, 3)?
D
B
d
21
OLE
18-
45-
42-
9-
B'6
Dº 6'3-
-24-21-18-15-12-9-6-33- 3 6 9 12 15 18 x
-6-
60325
-9
42
►
The scale factor in the dilation can be found by comparing the coordinates of the original image (A) and the new image (B). The coordinates of A and B must be provided in order to determine the scale factor.
What is the scale factor in the dilation if the coordinates?The scale factor in the dilation can be found by comparing the coordinates of A and B. The x-coordinate of A is -7 and the x-coordinate of B is -4, which means that the x-coordinate of B is 3 units closer to the origin than the x-coordinate of A. Similarly, the y-coordinate of B is 3 units closer to the origin than the y-coordinate of A. Therefore, the scale factor in the dilation is 3. This means that the image of A is 3 times larger than the preimage, and the image of B is 3 times closer to the origin than the preimage of A. The scale factor can be found by dividing the distance between the coordinates of A by the distance between the coordinates of B. For example, if the coordinates of A are (4,5) and the coordinates of B are (8,10), the scale factor would be 2, as the distance between the coordinates of B is twice the distance between the coordinates of A. It is important to note that the scale factor applies to both the x and y coordinates and is the same value for both.To learn more about coordinates of Care refer to:
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What is a 120 degree angle called?.
Answer:
Obtuse angle
Step-by-step explanation:
Angles greater than 90 degrees are obtuse angles, angles less than 90 degrees are acute angles, and angles at 90 degrees are right angles.
find the value of f(3) + f(6)
Answer: The answer Is 9f
Step-by-step explanation:
Which relation is a function?
Responses
{(1, 2), (2, 3), (3, 4), (4, 5)}
{(1, 2), (3, 4), (5, 6), (1, 8)}
{(1, 2), (2, 1), (1, 3), (3, 1)}
{(0, 2), (0, 4), (0, 6), (0, 8)}
The relation that is a function is
{(1, 2), (2, 3), (3, 4), (4, 5)}
Option A is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
A function can have different inputs but the same output.
i.e many to one.
But a function can not same input and different output.
i.e one to many.
Now,
{(1, 2), (2, 3), (3, 4), (4, 5)}
This is a function because each input has a different output.
This is a one-to-one function.
{(1, 2), (3, 4), (5, 6), (1, 8)}
This is not a function because 1 has different outputs 2 and 8.
{(1, 2), (2, 1), (1, 3), (3, 1)}
This is not a function because 1 has different outputs 2 and 3.
{(0, 2), (0, 4), (0, 6), (0, 8)
This is not a function because 0 has different outputs 2, 4, 6, and 8.
Thus,
{(1, 2), (2, 3), (3, 4), (4, 5)} is a function.
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Noah earn 37 for 4 hr of babyitting. At thi rate how much more would he earn for 9 hr
The rate he would he earn for 9 h will be 83.25
Your pay for each hour of labor is expressed as an hourly rate. You might need to estimate your income for other applications or change your own budget after comparing the hourly and salaried pay rates.
The sum of money charged, received, or earned for each hour of work: Instead of paying for the things the advisers try to sell you, you pay a set or hourly charge for their time.
Noah earns 37 for 4 hr of babysitting.
so if you divide 37 by 4 you get the rate per hour
which is 9.25 so if you multiply 9 times 9.25
The rate he would earn for 9 h will be
you would get 83.25.
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Alex ran 4 1/2 kilometers in 3/4 of an hour. How many kilometers he ran per hour?
First convert the distance she ran from a mixed number to a improper fraction:
• 4-1/2 equals 9/2.
Since this a unit rate problem divide the km by the time traveled.
• 9/2 (km) ÷ 3/4 (hour). When you divide a number by a fraction use (Keep-Change-Flip).
• 9/2 × 4/3 = 36/6 miles/hour.
That's means 36/6 = 18/3 = 6 km/ hour.
What is the value of K if ½ is a root of equation x² KX 5 4 0?.
So, the value of k that makes 1/2 a root of the equation x^2 - kx - 5 = 0 is 11.
A root of an equation is a value that satisfies the equation when it is set equal to zero. In other words, a root of an equation is a solution to the equation of the form x = constant.
The equation x^2 - kx - 5 = 0 is a quadratic equation, which can be factored into (x - r1)(x - r2) = 0 where r1 and r2 are the roots of the equation.
In this case, we can use the fact that 1/2 is a root of the equation x^2 - kx - 5 = 0
We can use the factored form of the equation and substitute x = 1/2
(x-1/2) (x-r2) = 0
Then, we can set each factor equal to zero and solve for r1 and r2:
x - 1/2 = 0 and x - r2 = 0
x = 1/2 and x = r2
We can use the quadratic formula to find the value of r2:
x = (-b ± √(b^2 -4ac) ) / 2a
We can substitute the values in the equation x^2 - kx - 5 = 0
x = (-(-k) ± √((-k)^2 - 41(-5)) ) / 2*1
x = (k ± √(k^2 + 20) ) / 2
x = (k ± √(k^2 + 20) ) / 2
r2 = (k + √(k^2 + 20) ) / 2
Now we have two values of x that satisfies the equation x^2 - kx - 5 = 0
x = 1/2 and x = (k + √(k^2 + 20) ) / 2
We can use the first value x = 1/2 and substitute it back into the original equation:
(1/2)^2 - k(1/2) - 5 = 0
1/4 - k/2 - 5 = 0
k/2 = 6 - 1/4
k = 12 - 1
k = 11
Therefore, the value of k that makes 1/2 a root of the equation x^2 - kx - 5 = 0 is 11.
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When using substitution to solve a linear system how do you know if the system is inconsistent?.
The first step in determining whether a linear system is inconsistent is to identify whether the lines are parallel. Check to see if the lines have a y-intercept in common, if so.
This result establishes an inconsistent system due to the fact that two parallel lines with distinct y-intercepts will never intersect.
If there is at least one solution to a linear equations system, it is said to be a consistent system. The system is regarded as inconsistent if there is no solution.
When the lines are parallel to one another, a system of linear equations cannot become inconsistent in any other way. The slope of parallel lines is the same. Therefore, comparing the slopes is a good way to ascertain whether the system is inconsistent. The comparison is simple if the linear equations are written in the point-slope or slope-intercept form. In order to determine the coefficient of x and compare slopes, it is a good idea to solve for y on all equations that are in a different form and express them in the slope-intercept form. The equation system is inconsistent if the slopes are equal to one another.
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Bowling Green middle school has 600 students. in Aiko’s class, 6 10 students prefer summer to spring. based on these results, how many students prefer summer
The number of students who prefer summer is equal to 60 students.
How to determine the number of students who prefer summer?In order to determine the number of students who prefer summer, we would multiply the total number of students in Bowling Green middle school by the number of students in Aiko’s class who prefer summer to spring.
Mathematically, an expression which models the number of students who prefer summer is given by;
Number of students who prefer summer = 6/10 × 600
Number of students who prefer summer = 0.6 × 600
Number of students who prefer summer = 60 students.
Based on these results, we can logically conclude that 60 students in Aiko’s class who prefer summer to spring.
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Complete Question:
Bowling Green middle school has 600 students. in Aiko’s class, 6 out of 10 students prefer summer to spring. Based on these results, how many students prefer summer?
How do you find the sum of the given polynomial?.
The sum of the polynomial is obtained by adding the terms with the same power and variable together.
The steps to determine the sum of the polynomial :
Step 1: Arrange each polynomial with the term with the highest degree first then
in decreasing order of degree.
Step 2: Group the like terms : Like terms are defined as the terms whose variables and exponents are the same. For example 2x² and 3x² are like terms.
Step 3: Simplify by combining like terms.
For example, (2x² + 6x +5) +(-2x + 3x²- 1)
and we have determine sum of polynomial. Follows the above steps :
Arrange the polynomials are in decreasing order of degree.=> (2x² + 6x +5) + ( 3x²– 2x – 1)
Group the like terms.2x² + 3x² + 6x – 2x + 5 -1
Simplify by combining the like terms= 2x² + 3x² + 6x – 2x + 5 -1
= 5x² + 4x + 4
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Can a 9 12 15 form a triangle?.
Yes, it is possible to draw a triangle.
This will be done by the property: the sum of two sides of a triangle should be more than the third side.
(9cm + 12cm) =15cm
21cm = 15cm
LHS>RHS
A triangle is possible.
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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