Dilation is the process by which rectangle ABCD becomes another rectangle ABCD.
What is invariant transformations?When the predictions of physical laws remain unaltered, they are considered to be invariant under transformations.This typically means that no new or different solutions are discovered since the law's form (such as the kind of differential equations used to represent it) remains unchanged via modifications.An altered rectangle's dimensions and orientation are called transformation.Dilation is the process by which rectangle ABCD becomes another rectangle ABCD.We infer from the question that the sizes of the two figures are proportionate rather than equal.The transition is a dilation since the sizes are proportionate but not equal.Consequently, (a) dilation is the best choice.To learn more about invariant transformations refer
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The person is 8 feet tall and casts a shadow of 4 feet. The building casts a shadow of 15 feet. Which ratio can be used to calculate the height of the
building?
||
11
APR
||
15
E-LED
15
M
R
S
The ratio which can be used to calculate the height of the building would be [tex]\frac{8}{4}=\frac{x}{15}[/tex].
Option (B) is correct.
What is the triangle similarity test?
The triangle similarity test is a method used to determine whether two triangles are similar or not. Similar triangles are triangles that have the same shape but different sizes. They are similar if their corresponding angles are congruent and their corresponding sides are in proportion. There are several ways to test for similarities, such as the side-side-side (SSS) test, the angle-angle-side (AAS) test, and the side-angle-side (SAS) test.
In the given figure, triangle KLM is similar to Triangle ORS.
and by the property of similar triangles, sides of similar triangles are in proportion:
so we can write:
LM/RS = KL/OR
15/4 = x/8
[tex]\frac{15}{4}=\frac{x}{8}\\\\\frac{8}{4}=\frac{x}{15}[/tex]
Hence, the ratio which can be used to calculate the height of the building would be [tex]\frac{8}{4}=\frac{x}{15}[/tex].
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U partly varies directly as S and partly inversely as the square root of M. When U=86.75, S=16, M=25 and when U=124.6, S=24, M=36. Find the equation connecting U,S and M. Find the value of 19 when U=110.5 and S=32
The equation connecting U,S and M is K = U√M/S
The value of M when U=110.5 and S=32 is 4.32
How to determine the valueFrom the information given, we have that U partly varies directly as S and partly inversely as the square root of M.
This is represented mathematically as;
U ∝S/√M
To determine the constant of the variation, we have;
U = KS√M
Now, make 'K' the subject of formula;
K = U√M/S
Substitute the values
K = 124.6 √25/86.75
Find the square root
K = 7. 18
To determine the value of M, we have;
KS/U = √M
substitute the values
√M = 7.18(32)/110. 5
√M = 2. 08
find the square of both sides
M = 4. 32
Hence, the value is 4.32
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Solve for x !
[tex] \large\pmb{\sf{2x + 3 = 4 - 8x}}[/tex]
Answer:
x=1/10
Step-by-step explanation:
2x+3 = 4-8x
2x+8x=4-3
10x=1
x=1/10
(Continuouly Compounded Interet LC)
A cutomer ue a tore credit card to purchae a boat for $10,500. The tore credit card offer an annual interet rate, compounded continuouly, of 18. 99% with no payment due for the firt two year. If no payment are made for the two year, what will be the balance on the card, rounded to the nearet penny?
a ) $12,679. 59
b ) $12,695. 85
c ) $15,311. 62
d ) $15,350. 92
The balance on the card, rounded to the nearest penny $15350.92..
The correct option is D.
Interest that compounded continuously to the principal amount. This interest rate provides exponential growth to a period of time.
Formula of continuous compound interest rate;
P(t) = P₀[tex]e^{rt}[/tex]
where P₀ is the principal amount, r is the interest rate and t is the time period.
A customer uses a store credit card to purchase a boat for $10,500.
The store credit card offers an annual interest rate, compounded continuously, of 18.99% with no payments due for the first two years.
That means,
P₀ = $10500, r = 18.99 and t = 2.
So,
P(t) = P₀[tex]e^{rt}[/tex]
Substituting the values,
P(t) = (10500)
P(t) = (10500)(1.46199)
P(t) = 15350.917
P(t) = $15350.92
Therefore, the final amount is $15350.92.
The balance on the card, rounded to the nearest penny $15350.92.
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Find the percent equivalent to 66 over 165.
Answer:
40%
Step-by-step explanation:
65/165 = 65 divided by 165 = 0.4 = 40%
A rectangular pool has an area of 640 square feet. The length is 12 feet shorter than the width.
The rectangular pool has a width of 80 feet and a length of 68 feet. The area is 640 square feet and the length is 12 feet shorter than the width.
1. 640 divided by 12 = 53.33
2. 53.33 + 12 = 65.33
3. Width = 65.33 feet
4. Length = Width - 12 = 65.33 - 12 = 53.33 feet
The area of the rectangular pool is 640 square feet. To find the width, we divide 640 by 12 because the length is 12 feet shorter than the width. 640 divided by 12 gives us 53.33. We add 12 to this number to get the width of the pool, which is 65.33 feet. To find the length, we subtract 12 from the width, which gives us 53.33 feet. Therefore, the width of the pool is 65.33 feet and the length is 53.33 feet. The area of the pool is 640 square feet and the length is 12 feet shorter than the width.
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The table shows the depths of four plants. Order the numbers form least to greatest
Answer:
sea grass red algae green seaweed mangrove or -20 3/4, -15 1/2, -14 3/4, -1/4
Step-by-step explanation:
negatives switch around the rules of positive so the one with the number tat is bigger when not negative is the lowest when negative
How do you find the bisector of an equilateral triangle?.
An angle bisector of a triangle is a line segment that divides an angle into two congruent angles. In an equilateral triangle, all angles are congruent (60 degrees), so any line segment that divides an angle into two congruent angles is also an angle bisector.
To find the angle bisector of an equilateral triangle, you can use the following method:
Draw an equilateral triangle.
Choose an angle and draw the angle bisector from the vertex of the angle to the midpoint of the opposite side.
Since all the angles of an equilateral triangle are congruent, the angle bisector that you drew bisects any angle of the triangle.
Alternatively, you can use the following method:
Draw an equilateral triangle.
Connect the midpoint of one side of the triangle to the opposite vertex.
The segment that you drew bisects the angle of the triangle.
It is important to note that in an equilateral triangle, all medians, altitudes, angle bisectors, and perpendicular bisectors are congruent, they all divide the triangle in the same ratio, so they all meet at the same point, called the centroid, which is 2/3 of the distance from each vertex to the midpoint of the opposite side.
Which values are within the range of the piecewise-defined function?
The values within the range of the piecewise-defined function are
y = -6, y = -4, y = 1 and y = 3.
What is a piecewise function?A piecewise function, or f(x), is a function with various definitions at various intervals of x. A piecewise function's graph is divided into sections that each correspond to one of its definitions. A very good illustration of a piecewise function is the absolute value function.
Given f(x) = 2x + 3, if x < -3
f(x) = x, if x = -3
f(x) = -x - 2, if x > -3
the function will be at x ≤ -3 and x ≥ -3
We now wish to determine which values fall within this function's range. Keep in mind that the set of possible outputs from a function constitutes its range.
The range of the first part of the function f(x) = 2*x + 2 has an upper bound at x = -3
f(-3) = 2*-3 + 2 = -6 + 2 = -4
Then the range of the first part is (-∞, -4)
Notice that the actual value -4 belongs to the range because x is smaller than and equal to -3.
The range of the second part has a lower bound for x = -3, the lower bound is:
f(-3) = -(-3) - 2 = 1
Then the range of this part is (1, ∞)
Then the range of the piecewise function is:
(-∞, -4) U (1, ∞)
and including -4 and 1
y = -6, y = -4
y = 1, y = 1
Hence values in the range are y = -6, y = -4, y = 1, and y = 3.
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Decribe two detail from Wahington' narrative that upport thi purpoe: to inform reader about the importance of hard work. Explain how the detail upport that purpoe
The first detail is Washington's description of how he rose to the top of his class through hard work and dedication.
The first detail from Washington's narrative that supports the purpose of informing readers about the importance of hard work is how he rose to the top of his class through hard work and dedication. This is an example of how Washington himself was successful because of his hard work, and this encourages readers to follow in his footsteps. The second detail is Washington's emphasis on the importance of setting goals and working hard to them. This encourages readers to take initiative and work hard to reach their goals, which is a key part of any successful endeavor. Both of these details demonstrate the importance of hard work and the benefits it can bring, thereby supporting the purpose of informing readers about the importance of hard work.
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What is co-prime numbers for Class 6?.
Co-prime numbers are those numbers that have only one common factor, namely 1.
Coprimes are pair of numbers that have no common factor other than 1. There should be at least two numbers to form a set of coprimes. Such numbers have only 1 as their highest common factor, for example (4 and 7), (5, 7, 9) are co-prime numbers. It should be noted that concurrent primes need not always be primes. If the only common factor of two numbers a and b is 1, then a and b are coprimes. In this case, (a, b) is considered a prime pair. Minor primes are also referred to as relatively primes. To determine whether any two numbers are co-prime, we first find their greatest common factor (GCF). If their GCF is 1, we can say they are co-prime. Consider the two numbers 5 and 9. The factors of 5 are 1 and 5. The factors of 9 are 1, 3, and 9. The factor that is common to both 5 and 9 is 1. The GCF of (5, 9) = 1. Thus, (5 , 9) is a co-prime pair.
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If you volunteer to ell or erve alcohol at an event and are not being paid, you cannot be held criminally or civilly liable for elling/erving alcohol to an intoxicated peron a long a you’re TABC certified. True Fale
The given statement that "unpaid volunteer selling or serving alcohol at an event does not hold the volunteer to be civilly or criminally liable for selling/serving alcohol to an intoxicated person as far as the volunteer is TABC certified" is false because, under the TABC program, alcohol is prohibited to be served or sold to the intoxicated person.
The Texas Alcoholic Beverage Commission (TABC) does not prohibit alcohol to be served at private, invitation-only events in private residences, where there is no direct or indirect charge for that alcohol. However, TABC certification disallows to serve of alcohol to already dru-nk persons.
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what are the terms in the expresion 5b+3.79
Answer: 1240
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How many times more ground shaking is an earthquake that measures 8 on the Richter scale than one that measures 6 on the Richter scale?.
A magnitude 8 on the Richter scale is 100 times more ground shaking than one that measures 6 on the Richter scale.
The magnitude of an earthquake is determined using the logarithm of the amplitude (height) of the largest seismic wave, calibrated to a scale by the seismometer. The Richter scale was originally developed to measure the magnitude of moderate earthquakes (magnitude 3 to magnitude 7) by assigning numbers so that the magnitude of one earthquake can be compared to another. We have, maganitude of two earthquakes, 8 and 6 Let the magnitude of first earthquake be A and second be B . So, A = 8 , B = 6 , to compare two earthquakes in terms of shaking, you subtract one magnitude from the other and raise 10 to that power, 10⁽ᴹ ⁻ ᴹ´⁾
=> 10ᴬ⁻ᴮ = 10⁸⁻⁶ = 10² = 100
Hence, the magnitude 8 of one quakehas has shake the ground 100 times than the other with magnitude 6.
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what are the coordinates of point M after a 90° clockwise rotation about p
The coordinates of point M after a 90° clockwise rotation about P is (0, -3).
Define the 90° clockwise rotation?Our point A(x,y) becomes A' when a point is rotated 90 degrees anticlockwise about the origin (-y,x). To put it another way, flip x and y, and give y negative.When position M (h, k) is rotated through 90 degrees in a clockwise direction around the origin O, the rotation of the point occurs. M' will represent the updated location of position M' (k, -h).Thus, by applying the rule of 90° clockwise rotation-
M = (3,0) taking P as reference point .
M' = (0, -3) after 90° clockwise rotation.
Thus, the coordinates of point M after a 90° clockwise rotation about P is (0, -3).
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The scatter plot shows the systolic blood pressure of people of several different ages. The equation represents the linear model for this data. Y = x + 95 according to the model, how much does the systolic blood pressure increase for each year of age? responses 1 mm hg per year 1 mm hg per year 5 mm hg per year 5 mm hg per year 15 mm hg per year 15 mm hg per year 95 mm hg per year 95 mm hg per year 110 mm hg per year.
The equation Y = x + 95 shows that for each year increase in age, the systolic blood pressure increases by 15 mm hg.
1. Plot the data points on a scatter plot.
2. Draw a line of best fit that passes through as many data points as possible.
3. Calculate the slope of the line of best fit using the formula
m = (y2-y1) / (x2-x1).
4. For example, if the line of best fit passes through two points with coordinates (x1, y1) and (x2, y2), calculate the slope as:
m = (y2-y1) / (x2-x1).
5. The slope represents the increase in systolic blood pressure for each year of age.
The equation Y = x + 95 is a linear model that represents the relationship between age and systolic blood pressure. To calculate the increase in systolic blood pressure for each year of age, we can plot the data points on a scatter plot and draw a line of best fit that passes through as many data points as possible. The slope of this line of best fit is then used to calculate the increase in systolic blood pressure for each year of age. For example, if the line of best fit passes through two points with coordinates (x1, y1) and (x2, y2),
the slope can be calculated as
m = (y2-y1) / (x2-x1).
This slope represents the increase in systolic blood pressure for each year of age.
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72/10 is equal to which decimal?
Answer:
7.2 because 72 / 10 = 7.2
hope this helps!!!
26. Extended Problem Solving A
signal from a walkie-talkie can be
received up to 1 mile away. A signal
from a CB radio can be received up
to 5 miles away.
a. Calculate. Over how great an area
can a walkie-talkie transmit a
signal? Express your answer in
terms of Pi.
b. Calculate. Over how great an area can a CB radio transmit a signal?
Express your answer in terms of Pi.
c. Compare. Write a ratio to compare the area of CB radio reception to
the area of walkie-talkie reception.
The area over which the signal is transmitted are: a.[tex]\pi[/tex] b. [tex]25\pi[/tex] c. CB transmits 25 times more signal to walkie talkie.
What is ratio?When two quantities of the same units are compared, the ratio shows how much of one quantity is included in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, while part to part ratio is the other.
The area of the circle is given by the formula:
[tex]A = \pi r^2[/tex]
For the walkie-talkie the signal is received up until 1 mile. Substitute the value of r = 1.
[tex]A _1= \pi (1)^2\\\\A_1 =\pi[/tex]
For the CB radio the signal is received up until 5 miles. Substitute the value of r = 5.
[tex]A_2 = \pi (5)^2\\\\A_2= 25 \pi[/tex]
a. The area over which a walkie-talkie can transmit its signal is [tex]\pi[/tex] miles.
b. The area over which a CB radio signal can transmit its signal is [tex]25\pi[/tex] miles.
c. The ratio of the transmitted signals are:
[tex]\frac{CB}{WT} = \frac{25\pi}{\pi} \\\\CB = 25 (WT)[/tex]
Hence, the CB signal transmits 25 times more than the signal transmitted by the walkie-talkie.
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The perimeter of a rectangular field i 274 yard. If the width of the field i 63 yard, what i it length?
The length of the rectangle is 74 yard.
What is perimeter of rectangle?The perimeter of a rectangle is the sum of the lengths of all four sides of the rectangle. It is calculated by adding twice the length and twice the width. The formula to calculate the perimeter of a rectangle is
P = 2(L + W), where P is the perimeter, L is the length and W is the width of the rectangle. In simpler terms, it is the total distance around the rectangle.
The perimeter of rectangle is given by 2 ( l + b)
where l is length of rectangle and b is width of the rectangle
given that perimeter of rectangle is 274
so 2 (l+b)= 274
=> l+b= 137 ---(i)
so l = 137 -b
=> l = 137 - 63
=> 74
so the lenth of rectangle is 74 yard.
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Help Me Please :<
In Which Of These Situations Do The Quantities Combine To Make 0?
The situation in which the quantities combine to make 0 is "On Monday, Huang withdraws $30 from a bank account. On Friday, she deposits $30 into the account".
In which case the quantities combine to make 0?For two quantities two make 0, it is necessary to add two numbers with the same value but different sign (positive or negative). Here is an example:
+15-15 = 0For example if you buy 10 apples but use 10 apples to make a pie.
Based on this, the correct situation is "On Monday, Huang withdraws $30 from a bank account..." as -30 + 30 = 0.
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A square floor is covered by a number of whole rectangular tiles of sides 54 cm by 30 cm such that a uniform margin of width 6 cm is left on a round the floor. calculate the least possible area of the floor giving me answer in square metres.
Answer: 7.9524 m^
Step-by-step explanation:
The square with the least area can only be formed when we take LCM of the dimensions of the rectangular tile I.e. 54 CM × 30 CM
LCM = 270
This means that a square of length 270 CM will be formed when we take least no. of tiles.
Also given in question, 6cm is left around the square that means 12cm is added on every side to make the floor with minimum area = 282 × 282 cm^2
minimum area = 79524 cm^
in m^2 = 79524/10000 = 7.9524 m^
how would i simplify this? explain please
The simplified form of the given expression is [tex]4x^2y^3[/tex].
What are exponents?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
Depending on the abilities they possess, many rules of exponents are given.
Adding exponents while maintaining the same base is the rule for multiplying similar bases.
Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.
Division Rule: When dividing similar bases, maintain the base constant and deduct the exponential of the denominator from the exponential of the numerator.
The given expression is:
[tex]\sqrt[4]{256x^8} * \sqrt[4]{y^{12}}[/tex]
The first term can be separated and written as follows:
[tex]\sqrt[4]{256} * \sqrt[4]{x^8} * \sqrt[4]{y^{12}}[/tex]
Using the identity [tex]\sqrt[n]{x^a} = x ^{\frac{a}{n} }[/tex] we can write the expression as:
[tex]4 * x ^{\frac{8}{4} } * y^{\frac{12}{4} }\\\\4x^2y^3[/tex]
Hence, the simplified form of the given expression is [tex]4x^2y^3[/tex].
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What are m<1 and m<2?
1. <1 is an exterior angle of the triangle. What are the measures of its remote interior angles?
2. Add the measures of the remote interior angles you identified in Exercise 1 to find m<1.
3. Complete the equation.
M<1+m<2=
4. Use your answer to Exercise 2 and the equation in Exercise 3 to find M<2
5. What are m<1 and m<2?
(photo attached)
please answer i’ll give brainliest
The remote interior angles of ∠1 are 34° and the right angle. The amount of m∠2 is 56°.
∠1 is an exterior angle because it is located outside the triangle. It has 2 remote interior angles. Remote interior angles are the angles with no shared vertex with the exterior angle. In this case, the remote interior angle of ∠1 is angle 34° and the right angle.
m∠1 can be measured by adding the remote interior angles:
m∠1 = 34° + 90°
m∠1 = 124°
Since m∠1 share a vertex with m∠2, then the total of both angles should be equal to 180° (a straight line). Hence:
m∠1 + m∠2 = 180°
Using the value of m∠1 known above, we can find the value of m∠2:
m∠1 + m∠2 = 180°
124° + m∠2 = 180°
m∠2 = 56°
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If x and y vary directly and y is 44 when x is 11, find y when x is 9.
The value of y when x is 9 and the constant of proportionality(k) is 4 is 36.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, x and y vary directly and y is 44 when x is 11.
Let, y ∝ x.
y = kx.
44 = 11k.
k = 44/11.
k = 4.
Now x = 9.
y = 4×9.
y = 36.
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How doe the location of the negative make value of 5. 3 x 10^-4 different from -5. 3 x 10^4
Location of the negative make value different from each other that is 5.3/10^4 and -(5.3 * [tex]10^{4}[/tex])
According to this rule, if the exponent is negative, we can change the exponent into positive by writing the same value in the denominator and the numerator holds the value 1.
The negative exponent rule is given as:
5. 3 x 10^-4
= 5.3/10^4 (1)
-5. 3 x 10^4
-(5.3 * [tex]10^{4}[/tex]) (2)
from equation 1 and 2 these two equations are different from each other.
location of the negative make value different from each other that is 5.3/10^4 and -(5.3 * [tex]10^{4}[/tex])
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which property is not a characteristic of a parallelogram
A parallelogram does not comprise the characteristics of having all congruent angles, Therefore, option B: "All angles are congruent." is the correct answer.
A parallelogram is a quadrilateral with opposite sides parallel and therefore opposite angles equal. Examples of parallelograms include rhombuses, rectangles, and squares.
So common characteristics of a parallelogram are:
Containing congruent opposite sidesHaving parallel opposite sides Consisting of congruent opposite anglesWhile all angles in parallelogram are not congruent, so this is not a property of a parallelogram.
"
Complete question
Which property is not a characteristic of a parallelogram?
O A. Opposite sides are congruent.
B. All angles are congruent.
O C. Opposite sides are parallel.
D. Opposite angles are congruent.
"
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PLEASE HELP ASAP!!!! ILL MARK BRAINLIEST
A graph of the solution of the inequality is: graph F.
What is an inequality?In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Greater than (>).Greater than or equal to (≥).Less than (<).Less than or equal to (≤).Next, we would solve the given inequality by making x the subject of formula as follows;
x - 5 < 14
By adding 5 to both sides of the inequality, we have the following:
x - 5 + 5 < 14 + 5
x < 19
Note: The line on a number line should be open when the inequality symbol is greater than (>) or less than (<).
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A wheel of radius 14 in. is rotating 0.5 rad/sec. What is the angular speed in RPM (revolutions per minute)? What is the linear speed in in/sec?
Round to three decimal places.
Answer:
The linear speed (V) is equal to 7 in/s.
The angular speed in rpm is equal to 4.77 rpm.
The angular speed in deg/s is equal to 28.65 deg/s.
Step-by-step explanation:
What is a perfect square trinomial formula?.
The general form of a perfect square trinomial is (x + y)², where x and y are the roots of the trinomial. It can also be written as x² + 2xy + y² or x² + (2xy)x + y².
The general form of a perfect square trinomial is (x + y)^2, where x and y are the roots of the trinomial. To check if a trinomial is a perfect square, we can try to factor it into the square of a binomial. We can also complete the square method, which involves adding and subtracting the square of half of the x-coefficient of the linear term and then grouping the resulting terms.
It is important to note that for a trinomial to be a perfect square trinomial, the constant term must be a square of an integer and the linear term must be an even number.
Perfect square trinomials are used in solving quadratic equations and understanding their solutions, they also have applications in algebra, geometry, and trigonometry. Factoring them is a fundamental skill in algebra and is used in solving different types of mathematical problems.
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What is the extended ratio relating the side lengths of a 30 60 90 triangle?.
Answer:
Remembering the 30-60-90 triangle rules is a matter of remembering the ratio of 1: √3 : 2, and knowing that the shortest side length is always opposite the shortest angle (30°) and the longest side length is always opposite the largest angle (90°).
