A 45-45-90 triangle is an isosceles right triangle, meaning that it has two congruent sides and one right angle. To find the area and perimeter of a 45-45-90 triangle, use the following formulas:
Area:
(1/2) * (side length)^2
Perimeter:
2 * (side length) + (side length) * √2
Note that the perimeter of a 45-45-90 triangle is equal to twice the length of one of its sides plus the length of the hypotenuse.
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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In the diagram below, the length of segment XY can be written as √
N for some positive integer N. Find N.
The value of √N is 3.16159
What is the Pythagoras theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².
Given here: A quadrilateral WXYZ with ∠Z=75 and ∠X=105
Let P be a point on ZW such that ZP=x and WP=4-x, then we form a right-angled triangle ΔZPY with tan 15°=x/PY
∴ PY=x/tan 15
=3.732x
Now using Pythagoras' theorem we get ZY as
[tex]\sqrt{13.927x^2+x^2} \\=\sqrt{14.92x^2}\\ =3.862641x[/tex]
Now let's connect the diagonal ZX we get the right triangle ZWX
Thus using Pythagoras' theorem we get
ZX=[tex]\sqrt{4^2+4^2}[/tex]
=4√2
Again let Q be an extension such that YQ=4-x & ∠YXQ=75°
Thus Sin 75=4-x/√N
√N=4-x/0.965923
squaring both sides we get N=(4-x)²/0.9330127........(1
Now using the Pythagoras theorem in ΔZYX we get
√N=
[tex]\sqrt{ZX^2-ZY^2} \\=\sqrt{32-14.92x^2} \\[/tex]
⇒N=32-14.92x²..,.......2)
Thus equation two values of N we get
(4-x)²/0.9330127=32-14.92x²
16-8x+x²=29.8564-13.920549x²
14.921x²-8x-13.856=0
Thus using the quadratic formula we get the value of x as
x= 8±29.85 /29.84
x=1.2684 (∵ Distance cannot be negative)
∴ Value of N=32-14.92×1.2684
N=13.075
√N=3.6159
Hence, The value of √N is 3.16159
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What is a linear and nonlinear equation?.
A linear equation is an equation in which the highest power of the variable is 1 and a nonlinear equation is an equation in which the highest power of the variable is greater than 1.
A linear equation example:
y = 2x + 3
This is a linear equation in one variable, x. The highest power of x is 1 and the coefficient of x is 2.
A nonlinear equation example:
y = x^2 + 3x + 2
This is a nonlinear equation in one variable, x. The highest power of x is 2 and the coefficient of x is 1.
Another example of nonlinear equation is:
y = x^3+3x^2-5x+1
This is a nonlinear equation in one variable, x. The highest power of x is 3 and the coefficient of x is 1.
Note that the linear equation can be in any number of variables, and the nonlinear equation can also be in any number of variables, but the degree of the polynomial should be greater than 1.
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How do you write greater than 35?.
The correct way to write greater than 35 is A > 35 where it tells that A having greater value than 35.
In mathematics,
→The greater than symbol (>) is used to indicate that one value is larger than another. For example, if we say "A > B," this means that the value of A is greater than the value of B.
→The less than symbol (<) is the opposite, it indicates that one value is smaller than another. For example, if we say "A < B," this means that the value of A is less than the value of B.
→The greater than or equal to symbol (≥) indicate that one value is larger than or equal to another. For example, if we say "A ≥ B," this means that the value of A is greater than or equal to the value of B.
→The less than or equal to symbol (≤) indicate that one value is smaller than or equal to another. For example, if we say "A ≤ B," this means that the value of A is less than or equal to the value of B.
These symbols are commonly used in mathematical expressions, equations, and inequalities.
To write "greater than 35" in mathematical notation, you would use the greater than symbol (>) followed by the letter 35. For example:
A > 35
This means that A is greater than 35.
Therefore, the correct way to write greater than 35 is A > 35 where it tells that A having greater value than 35.
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Write the equation of the tangent line to the graph of y = x^2 at the point x = -0.3
Answer:
9854+w8r++0.3
Step-by-step explanation:
32927372737347599939
help simplify:px-1 .px+1
Answer:
Answer is 1
Step-by-step explanation:
what is the answer for this???
The solution set for the given inequality w + 43 ≤ 51 is; w ≤ 8. Hence,
11 ....NO.14 ......NO.7 ........YES.10 .......NO.What is the solution set for the inequality w + 43 ≤ 51?It follows from the task content that the solution set for the given inequality w + 43 ≤ 51 is to be determined and it's solutions be identified among the answer choices.
Given; w + 43 ≤ 51
w ≤ 51 - 43
w ≤ 8.
On this note, the only number which is a solution among the given answer choices is 7 as it is less than 8.
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Find each product mentally show the steps you used 3 x 3.9
What is mixed fraction in Maths for Class 7?.
A mixed number is a whole number, and a proper fraction represented together.
Now, According to the question:
A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
A fraction denotes a portion of a whole. Therefore, if we have to read a fraction say ¾, then it read as three-fourth of a whole. In the same way, we read the other fractions such as:
½ – half of a whole
¼ – one-fourth of a whole
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What is the ration of corresponding side lengths of 20:36
Answer:
5/9
Step-by-step explanation:
Which polynomial correctly combines the like terms and puts the given polynomial in standard form?.
The polynomial 8x⁴ - (2/3)x² - (2/3)x correctly combines the like terms and puts the polynomial (1/3)x + 8x⁴ - (2/3)x² - x in the standard form option (C) is correct.
What is polynomial?
Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
It is given that:
The polynomial:
(1/3)x + 8x⁴ - (2/3)x² - x
Adding combine like terms:
= 8x⁴ - (2/3)x² + (1/3)x - x
= 8x⁴ - (2/3)x² - (2/3)x
Thus, the polynomial 8x⁴ - (2/3)x² - (2/3)x correctly combines the like terms and puts the polynomial (1/3)x + 8x⁴ - (2/3)x² - x in the standard form option (C) is correct.
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13) Honeybee produce about 50 pound of honey per hive each eaon. The amount of honey can be
repreented by 50(x) = y. The x i the number of hive and y i the amount of honey in pound. Give three
number which would NOT be appropriate for the input (x) on a function table. Explain
Three numbers that would not be appropriate for the input (x) on a function table for this equation would be:
1. A negative number, such as -5. This is because the number of hives cannot be negative, it is a physical quantity.
2. A non-integer, such as 3.5. This is because the number of hives cannot be a fraction or decimal, it is a whole number.
3. A number greater than 1, such as 2. This is because in the context of the problem, one hive is assumed, and the function is describing the production of one hive.
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What is the value of Cosec²a Cot²a?.
The value of Cosec2a 1 and the value of Cot2a is also Cot A.
cosec 2A + cot 2A
1/sin2a + cos2a/sin2A
= (1+cos2A)/sin2a
=(1 + 2cos²a -1)/sin2A
=(2cos²A)/sin2A
= (2.cosA.cosA)/2.sinA.cosA
=cosA/sinA
=cotA
A right-angled triangle's hypotenuse to opposite side ratio is a right-angle triangle's trigonometric function known as the reciprocal of sine.
The cosecant of an angle in a right triangle is obtained by dividing the length of the hypotenuse by the length of the other side.
It is written as Cosec and csc on occasion. In trigonometry, it is one of the trigonometric functions.
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What is one fifth of 13.7?
Answer:
2.74
Step-by-step explanation:
Answer: 2.74
Step-by-step explanation: When it says 1/5 of this number, you just divide it by the denominator (5) So, 13.7 / 5 = 2.74. To check, we multiply 2.74 by the denominator. (5) We get 13.7. This makes the statement true. I hope this helped!
How do you solve a linear system using multiplication?.
The elimination method is used to solve a linear system using multiplication.
Another strategy for resolving a set of linear equations is the elimination method. Here, we attempt to multiply either the "x" variable term or the "y" variable term by a constant amount in order to obtain the value of the other variable by having the "x" variable term or the "y" variable term cancel out.A linear equation is one in which the variable has the highest power of 1 in it.A linear equation has the formula Ax + B = 0, which is its standard form.where the slope is m and the y-intercept is c.To learn more about linear equations here
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What is the factor of the polynomial a2 2ab b2?.
The factors of polynomial a² - 2ab + b² is equals to the (a - b)², that is (a -b) and (a-b).
To determine the factors we can use the concept of splitting the middle terms and first making the pair of two terms and then finding the common factors from the paired terms and finally the factors for the expression. We have an expression, a² - 2ab + b². Using the concept of to split the middle term. As we see there is three terms in the expression.
Now, multiply the coefficient of first term with the cofficient of last term, i.e., 1 × 1 = 1 Split the middle term cofficient, that is -2 such that sum or difference of spliting terms is -2 and multiplication become 1. Use the basic concept of the product of two negative values results positive value and addition of two negative values provide negative sign, so (-1)(-1) = 1 and -1 + (-1) = -2.Thus, we can rewrite the expression as
=> a² - ab - ab + b²
Make the pair of two terms in the above expression, (a² - ab) - ( ab - b²).
Take common factors from the paired terms,
=> a(a - b) - b(a - b).
Take the common factors in the above equation => (a - b) (a - b)
=> (a - b)¹⁺¹ = (a + b)²
Hence, factor of a² - 2ab + b² is (a-b)² i.e., (a - b) and (a - b).
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complete question:
What is the factor of the polynomial a² - 2ab + b²?.
hey I need help with this two step equation!! m/3-7=1
Answer:
m = 24
Step-by-step explanation:
To solve the equation m/3-7 =1, we can start by isolating m on one side of the equation. To do this, we will add 7 to both sides of the equation:
m/3 - 7 + 7 = 1 + 7
m/3 = 8
The next step is to multiply both sides of the equation by 3 to get rid of the fraction:
m/3 * 3 = 8*3
m = 24
So the solution to the equation is m=24
Ginger want to join a gym he goe to the local gym and i told that there i a one time fee of 100$ to join and then a monthly fee of 30$ write an agebraic expreion to repreent the total cot of joining the gym uing "m" a a variable
The algebraic expression to represent the total cost of joining the gym using "m" as a variable would be: 100 + (30m)
An equation is a mathematical statement that asserts the equality of two expressions. It is written in the form of "left-hand side = right-hand side," where both sides are expressions that are made up of numbers, variables, and mathematical operations.
The algebraic expression to represent the total cost of joining the gym using "m" as a variable would be:
100 + (30m)
This represents the one-time fee of $100 to join plus the monthly fee of $30 multiplied by the number of months, represented by the variable "m".
Thus, The algebraic expression to represent the total cost of joining the gym using "m" as a variable would be: 100 + (30m)
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Using "m" as a variable, the algebraic expression for the total expense of joining the gym would be: 100 + (30m)
This is the sum of the $100 one-time joining fee and the $30 per month price, multiplied by the variable "m," which stands for the number of months.
Therefore, using "m" as a variable, the algebraic expression to represent the overall expense of joining the gym would be: 100 + (30m)
If the fifth of the month comes two days after Monday, what day of the week comes before the 19th of the month
If the fifth day of the month is two days after Monday, then the fifth day would be Wednesday. Additionally, the 19th would be a Wednesday, that is, the day before the 19th would be Tuesday the 18th.
How to identify what day is the date 19 and 5 of the month?To identify the day of the week that coincides with the date 19 and 5 we must have the information as a reference:
The fifth day is two days after Monday.
According to the information above, the fifth day would be a Wednesday. Additionally, we must use this information to organize the rest of the days of the month as shown below:
Wednesday 5Thursday 6Friday 7Saturday 8Sunday 9Monday 10 Tuesday 11Wednesday 12Thursday 13Friday 14Saturday 15Sunday 16Monday 17Tuesday 18Wednesday 19According to the above, the 19th would be Wednesday and the day before this would be Tuesday the 18th.
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A carpenter manufactures chairs and tables. It takes them 3 hours to make a table and 3.5 hours to make a chair. In a month, they do not work for more than 180 hours. On each table, they earn $30, and on each chair, they earn $38. In a month, they want to earn at least $1500. If they manufacture t tables and c chairs in a month, which pair of inequalities represent the correct relationship?
A. 3t+3.5c< 180
30t+38c 1500
B. 3t+3.5c 180
30t+38c≥ 1500
C. 3t+3.5c 180
30t+38c 1500
D. 3t+3.5c 180
30t+38c> 1500
The two expressions that make up an equation or an inequality are connected in a mathematical statement.
How do you identify inequalities?
The equals sign in the equation-like statement 5x 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 5x 4, is larger than the right part, 2x + 3, in the equation.
A mathematical inequality is a comparison made between two algebraic expressions using the larger than (>), less than (), and other inequality symbols. An inequality pair connected by and or or is referred to as a compound inequality.
B. 3t + 3.5c <= 180 and 30t + 38c >= 1500.
The first inequality represents the constraint that the carpenter cannot work more than 180 hours in a month. The second inequality represents the requirement that they earn at least $1500 in a month.
These two inequalities, combined, describe the conditions that the carpenter must satisfy in order to manufacture tables and chairs in a way that meets both the time constraint and the income requirement.
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35 POINTS PLEASEEE HELPP I NEED THIS DONE
Answer: what do you have to do
Step-by-step explanation:
How much is all 3 angles of a triangle?.
All 3 angles of a triangle always add up to 180 degrees.
This is because a triangle is a three-sided polygon and the sum of the angles in any polygon is always 180 degrees multiplied by the number of sides minus 2. Therefore, in a triangle, which has three sides, the sum of the angles is 180 x (3-2) = 180 degrees. This rule is known as the "triangle angle sum theorem" and is a fundamental property of triangles. It is important to note that this rule applies to all types of triangles, whether they are right triangles, acute triangles, or obtuse triangles. Understanding this theorem is crucial in solving geometric problems related to triangles.
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PLEASE HELP ME WITH THIS ASAP!!!
Answer: F
the inequality is x<3
Step-by-step explanation:
plEASE HELP I WILL GIVE 50 POINTS
Answer:r=175 this is for IXL I hope this helps
Step-by-step explanation:
r/-25 =-7
Multiply both sides of the equation by -25
-25 times r/-25=-25 time (-7)
Multiplying two negatives equals a positive: (-) times (-) =(+)
25•r/25=-25•(-7)
then
Cancel out the greatest common factor 25
R=-25 times (-7)
Also Multiplying two negatives equals a positive: (-) times (-) =(+)
r=25 times 7
Multiply the numbers 25•7
Then you get
R=175
Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
B. 66 degree
Step-by-step explanation:
We know
A triangle is 180 degrees. Angle B is 27 degrees, and angle C is 87 degrees. To find angle A, we take
27 + 87 = 114 degree
180 - 114 = 66 degree
So, the answer is B. 66 degree
Is addition distributive?.
Yes, the distributive law is followed by the addition arithmetic operation.
Distributive Property of Multiplication Over Addition: This implies that the operation involves dividing or distributing the things. The distributive law applies to addition and subtraction arithmetic operation.
Distributive Property of Multiplication Over Addition : If we need to multiply a number by the sum of two numbers, we are using the distribution properties of multiplication and addition. The expresion for distributive property is: p( q+ r) = pq + pr ; p,q,r are three whole numbers.For example, let us multiply 8 by the sum of (20 + 3). Mathematically, we can represent this as 8 (20 + 3). First, use the distributive property to multiply each addend by 8. This is called distributing the number 8 over two addenda and then adding their products. That is, multiplication of 8(20) and 8(3) will be performed first, then addition. The result is 8 (20) + 8 (3) = 160 + 24 = 184.
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How do you describe the end of the behavior of the graph if the degree is odd and the leading coefficient is negative?.
If the degree is odd and and the leading coefficient is negative then the right end of the graph will point down and the left end will point up .
The End Behaviour of the graph of polynomial is said to be defined by the degree and leading coefficient of polynomial .
the end behaviour for the Odd degree polynomial is given as :
(i) If the degree of polynomial is odd and lead coefficient is positive, then the right end of graph will point up and the left end will point down.
(ii) If the degree of polynomial is odd and the lead coefficient is negative, then right end of graph will point down and left end will point up .
So , according to the question , for the given condition , the right end will point down and left end will point up .
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If CAT ~ MUD and the sides of the triangle are the lengths 9 18 21 and 3 6 7 respectively what is the scale factor of triangle CAT to triangle MUD
Answer: The scale factor of triangle CAT to triangle MUD is the ratio of the corresponding side lengths of the two triangles. In this case, we are told that the sides of triangle CAT are 9, 18, and 21 units long, and the sides of triangle MUD are 3, 6, and 7 units long.
To find the scale factor, we divide the length of each side of triangle CAT by the length of the corresponding side of triangle MUD:
Scale factor = (9/3), (18/6), (21/7) =3,3,3
So the scale factor of triangle CAT to triangle MUD is 3. This means that triangle CAT is 3 times larger than triangle MUD.
It's worth noting that the scale factor is the same for all three sides, this means that the two triangles are similar.
Step-by-step explanation:
What is the molar mass of nh3?.
Answer:
17.031g/mol
Step-by-step explanation:
pay attention in class
solve the inequality |y -8 | + 11 > 19 and please show all work
The inequality |y -8 | + 11 > 19 can be solved to get the compound inequality:
y > 16
y < 0
How to solve the inequality?Here we want to solve the inequality:
|y - 8| + 11 > 19
To solve the inquality, we need to isolate the variable, we can start by subtracting 11 in both sides, then we will get:
|y - 8| + 11 - 11 > 19 - 11
|y - 8| > 8
Now we can decompose that into two inequalities so we get:
y - 8 > 8
y - 8 < -8
Solving these two we will get:
y > 8 + 8 = 16
y < -8 + 8 = 0
The the solution is the compound inequality:
y > 16
y < 0
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The sum of three consecutive numbers is eighty seven. What is the smallest of the three numbers?
well, consecutive numbers, we're assuming integers btw, so hmmm since they're consecutive, if the smallest is "a", the next is either "a-1" or "a+1", let's use
a = small
a+1 = larger
a+2 = largest
[tex]\stackrel{\textit{their sum}}{a+(a+1)+(a+2)}=87\implies 3a+3=87 \\\\\\ 3a=84\implies a=\cfrac{84}{3}\implies a=28[/tex]
