To find the sine of an angle in a right triangle, we can use the following relationship:
[tex]sin(angle) = opposite side / hypotenuse\\[/tex]
What is right triangle?
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (also known as a right angle). This angle is formed by the intersection of two legs of the triangle, which are not the hypotenuse of the triangle. The side opposite the right angle is called the hypotenuse and it is always the longest side of the triangle.
To find the sine of an angle in a right triangle, you can use the following relationship:
[tex]sin(angle) = opposite side / hypotenuse\\[/tex]
This relationship holds true for any angle in a right triangle, not just the acute angles.
For example, if you have a right triangle with an angle of 30 degrees and the opposite side is 5 units and the hypotenuse is 12 units, you can find the sine of the angle by dividing the opposite side by the hypotenuse:
[tex]sin(30) = 5/12 = 0.4166\\[/tex]
It's also important to note that the sine of an angle is always between -1 and 1, and the sine of an acute angle is always positive.
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To find the sine of an angle in a right triangle, we can use the following relationship:
sine = opposite side / hypotenuse side
What is right triangle?
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (also known as a right angle). This angle is formed by the intersection of two legs of the triangle, which are not the hypotenuse of the triangle. The side opposite the right angle is called the hypotenuse and it is always the longest side of the triangle.
To find the sine of an angle in a right triangle, you can use the following relationship:
sine = opposite side / hypotenuse side
This relationship holds true for any angle in a right triangle, not just the acute angles.
For example, if you have a right triangle with an angle of 30 degrees and the opposite side is 5 units and the hypotenuse is 12 units, you can find the sine of the angle by dividing the opposite side by the hypotenuse:
sin(30) = 5/12 = 0.4166
It's also important to note that the sine of an angle is always between -1 and 1, and the sine of an acute angle is always positive.
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How old is the king, how many children has he, and how long is his boat? Given that the product of three positive integers gives 32118 which answers these questions. The length of his boat is given in metres, the king has sons and daughters, he has more years than his children, but he is not yet one hundred years old. please help fast please
If the product is positive integers is 32118, then the king's age is 53, his number of children is 6 and is length of boat is 101m.
What is integer?
The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
The puzzle demands for three numbers - x, y, z which represent the king's number of children, age and length of boat respectively.
It will be advantageous to conceive the problem thus: We have but one unknown; this unknown, however, is not a number but a tripartite unknown, a triplet (x, y, z) of numbers.
It is very important to split the condition that is expressed by the statement of the problem into appropriate clauses. This needs careful con-sideration of details and considerable regrouping. After several trials (which we skip to save space) we may arrive at the following two clauses:
(r1), x, y, and z are positive integers different from 1 and such that -
xyz = 32118
(r2) 4 ≤ x < y < 100
Begin with (r1) which leaves only a finite number of possibilities, whereas (r2), which does not restrict z at all, leaves an infinite number.
Therefore, we examine (r1). Now, 32118 is divisible by 6, and so we easily decompose it into prime factors:
32118 = 2 × 3 × 53 × 101
For a decomposition into three factors we have to combine two of the four primes. Therefore, there are only six different ways to decompose the number 32118 into a product of three factors all different from 1:
6 × 53 × 101
3 × 101 × 106
3 × 53 × 202
2 × 101 × 159
2 × 53 × 303
2 × 3 × 5353
Of these six possibilities, the remaining requirement (r2) rejects all except the first one, and so we obtain -
x = 6 , y = 53 and z = 101.
Therefore, the values of x, y and z are 6, 53 and 101 respectively.
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What is the answer to this
The expression that represents the shaded length of the number line would be = 3/20 × 9/20. That is option C.
What is a number line?A number line is defined as the graduates line that is used to represent the position of both positive and negative real numbers.
The shaded length of the number line contains 20 bars with a total of 9 shaded bars.
There are a total number of 3 per each bar of the number line, therefore, the shaded length of the number line would be = 3/20 × 9/20.
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What must be known to use the law of sines to find a missing measurement in a triangle?.
If two of the angles and one of the sides of an oblique triangle are known, the Law of Sines can be used to find the missing lengths or angle measurements.
We cannot utilize the formulas specified for right triangles to solve oblique triangles; instead, new formulas must be used. We'll look at how the Law of Sines can be applied to resolve oblique triangles.
The Sine Rule:
The ratios of the length of a side to the sine of the angle opposite the side must all be the same if A, B, and C are the measurements of the angles of an oblique triangle and a, b, and c are the lengths of the corresponding sides.
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
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What is the sum of in the interior angles of a 21-gon (21 sides)? S=180 (n -2)
The sum of the interior angles of a 21-gon (21 sides) is 3420°.
What are Interior angles?
Any angle that is created between two of a polygon's adjacent sides is said to be its internal angle. The internal angle of a polygon is what we might refer to as the angle measured at the interior portion of a polygon.
The polygon has 21 sides.
we can find the sum of all interior angles of the polygon by using this formula :
S = 180 ( n - 2)
So, S = 180 (21 - 2)
= 180 × 19
= 3420°.
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Is the solution of the equation 2x y 5 and 3x 2y 11 *?.
The value of x = 3 and y = 1 is the solution.
Two or more algebraic equations that have a common variable and are solved simultaneously are referred to as simultaneous equations (that is, simultaneously). For instance, the simultaneous equations x + y = 5 and x - y = 6 are created by concurrently solving two equations that have the same unknown variables, x and y. Multiple techniques, including the substitution method, elimination approach, and visual methods, can be used to solve simultaneous equations.
We have 2 equations,
2x - y = 5 (equation 1)
3x + 2y = 11 (equation 2)
We can solve the given equations simultaneosuly.
Multiplying equation 1 by 2,
4x - 2y = 10
Adding the 2 equations,
4x - 2y = 10
3x + 2y = 11
⇒ 7x = 21
⇒x = 3
Substituting the value of x = 3 in equation 1,
2x - y = 5
⇒ 6 - y = 5
⇒ y = 1
Hence, the values of x and y are 3 and 1 respectively; this is the solution of the equation.
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A die ha ix face numbered 1 to 6. On a ingle roll of the die,find the probability of:
a Getting the number 6
b Getting the number 10
c Not getting the number 6
d Getting one of the number 1,2,3,4,5 or 6
PLS WITH EXPLANATION <3
The probability of getting number 6 on a single roll of the fair die is 1/6; not getting 6 is 5/6; getting number 10 is 0 and getting any number of 1-6 is 1.
a) The probability of getting the number 6 on a single roll of a fair die numbered 1 to 6 is 1/6, or approximately 0.17. This is because there is a single outcome (rolling a 6) out of a total of 6 possible outcomes (rolling any number from 1 to 6) that will result in rolling a 6.
b) The probability of getting the number 10 on a single roll of a fair die numbered 1 to 6 is 0, because the die only goes up to 6.
c) The probability of not getting the number 6 on a single roll of a fair die numbered 1 to 6 is 5/6, or approximately 0.83. This is because there are five outcomes (rolling any number from 1 to 5) out of a total of 6 possible outcomes (rolling any number from 1 to 6) that will not result in rolling a 6.
d) The probability of getting one of the numbers 1, 2, 3, 4, 5, or 6 on a single roll of a fair die numbered 1 to 6 is 1 because there is only one outcome out of one possible outcome that is not getting one of the numbers 1, 2, 3, 4, 5 or 6.
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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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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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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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3. Rule: output = input +29. Additional practice 7-4 use tables to represent input/output relationships
output of the given input/output relationships is 36 and 25.
What is the input-output table's rule?To illustrate a function, an input-output table can be used, as in the example below. The same function rule connects every pair of numbers in the table. To find each output number, multiply each input number (-value) by 3. ( -value).
Input-output analysis table: what is it?
The table of input-output analysis measures the flows of outputs from one industry as inputs into another (in rows) (in columns). In the input-output analysis paradigm, the original demand shift and its direct, indirect, and induced implications can be used to examine the overall economic impact of an event.
output = input +29
input= 7
output = input +29=7+29=36
input= -4
output = input +29= -4+29=25.
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Help me answer all 4 of these please!!!
Step-by-step explanation:
for first image →
Option B ) 8n + 4
for second image →
Option A ) The number of minutes Dylan practises each weekdays
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
[tex]1/2 (x-5)=9[/tex]
Find the value of k. Then find the angle measures of the polygon.
2kº
45°
к
Sum of angle
measures: 180°
Answer:
67.5°
Step-by-step explanation:
180 -45 = 135
135 / 2
k= 67.5
What is the molar mass of nh3?.
Answer:
17.031g/mol
Step-by-step explanation:
pay attention in class
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?.
what is a devided by a% of a
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE x}\% of \textit{\LARGE y}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE x}}{100} \right)\cdot \textit{\LARGE y} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{a\% of a}}{\left( \cfrac{a}{100} \right)a}\implies \cfrac{a^2}{100} \\\\[-0.35em] ~\dotfill[/tex]
[tex]a\div \cfrac{a^2}{100}\implies \cfrac{a}{1}\div \cfrac{a^2}{100}\implies \cfrac{a}{1}\cdot \cfrac{100}{a^2}\implies \cfrac{a}{a^2}\cdot \cfrac{100}{1}\implies \cfrac{1}{a}\cdot 100\implies \cfrac{100}{a}[/tex]
make me brainalist
I'm in need of it
If you would like to know what is a divided by a% of a, you can write it as follows:
a divided by a% of a:
a/ (a% of a) = a/ (a% a) = a/ (a/100* a) = a/(a^2/100) = a * (100/a^2) = 100 / a
The correct result would be 100/a.
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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What is the standard form of the polynomial function in number 3 *?.
The correct option is A. The standard form of the polynomial function in number 3 is f(x) = 5[tex]x^{7}[/tex] +[tex]x^{4}[/tex] + 3x.
A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).
In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.
Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.
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Complete Question:
What is the standard form of the polynomial function in number 3?
A. f(x) = 5[tex]x^{7}[/tex] +[tex]x^{4}[/tex] + 3x
B. f(x) = 5[tex]x^{7}[/tex] + 3x + [tex]x^{4}[/tex]
C. f(x) = [tex]x^{4}[/tex] + 5[tex]x^{7}[/tex] + 3x
D. f(x) = 3x + 5[tex]x^{7}[/tex] + [tex]x^{4}[/tex]
The city of Rock Hill has an approximate population of 70,000. An average of 100 people move in to Rock Hill every month and 150 people move out of Rock Hill each month. The City of Greenville has an approximate population of 61,000. An average of 200 people move into Greenville every month. In how many months will the populations of the 2 cities be the same?
In 36 months the populations of the 2 cities be the same .
What is additive comparison?
In an additive comparison, we question or state how much more (or less) one amount is in contrast to the other to determine the relationship between the two numbers. Additive comparison issues are typically word problems that can be resolved by creating an equation.
The comparison approach is a technique for rewriting each equation with the same variable as the subject in order to solve systems of independent equations. The initial variable to isolate can be any of the variables. Every equation is now an isolated-subject equation with an isolated variable.
Let,
if in about x month, the population of the towns will be equal .
the equation will be;
70,000 + (150-100)x = 61,000 - 200x
⇒ 70,000 + 50x = 61,000 - 200x
⇒ 250x = 9000
⇒ x = 9000/250
⇒ x = 36
So, in 36 months the populations of the 2 cities be the same .
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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
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]
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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The diagonal PR of a cyclic quadrilateral PQRS bisect ZOPS and ZQRS. Show that PR is a diameter of the circum-circle PQRS.
Let the circum-circle of the cyclic quadrilateral PQRS be O.
The circum-circle of the cyclic quadrilateral PQRSSince PQRS is a cyclic quadrilateral, the four points P, Q, R, S are concyclic. Thus, the line joining any two points among them will pass through the center O of the circum-circle. Since PR bisects ZOPS and ZQRS, it follows that PR passes through the center O of the circum-circle.Therefore, PR is a diameter of the circum-circle PQRS.Let PQRS be a cyclic quadrilateral with PQ bisected at Z, QS bisected at O, RS bisected at P and PS bisected at S. Let PR be the diagonal of the quadrilateral.We have to prove that PR is a diameter of the circumcircle of PQRS.Since the quadrilateral is cyclic, the four angle bisectors all intersect at one point, which is the centre of the circumcircle of the quadrilateral, let us call it O. We know that the angle bisectors divide the angles of the quadrilateral into two equal parts. Therefore, the angles QOP, ROP, POR and QOS are all right angles. This implies that PQRS is a rectangle with the diagonal PR as its diameter.Moreover, the Euler’s theorem states that the sum of the angles of a cyclic quadrilateral is equal to two right angles. This implies that the angles POQ and RQS are equal. So, the line PR bisects the angles POQ and RQS.Thus, we have proved that the diagonal PR of a cyclic quadrilateral PQRS bisects ZOPS and ZQRS, and is a diameter of the circumcircle PQRS.To learn more about the circum-circle of the cyclic quadrilateral PQRS refer to:
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In a certain examination 52 candidate offered biology 60 offered hitory 96 offered mathematic 21 offered biology and hitory 22 offered mathematic and biology 16 offered mathematic and hitory if 7 candidate offered all the three ubject
Satisfying all the given situations, there were 156 candidates in the examination.
We can use the principle of inclusion-exclusion to solve the problem.
The principle of inclusion-exclusion states that the total number of elements in the union of two or more sets is equal to the sum of the number of elements in each set, minus the number of elements in their intersection.
Here, let A be the set of candidates who offered biology, B be the set of candidates who offered history, and C be the set of candidates who offered mathematics.
Using the principle of inclusion-exclusion, the total number of candidates, N, can be found as follows:
N = (A U B U C) = (A + B + C) - (A ∩ B + B ∩ C + A ∩ C) + (A ∩ B ∩ C)
where A U B U C is the union of the three sets, A ∩ B is the intersection of A and B, and so on.
Given that:
|A| = 52, |B| = 60, |C| = 96
|A ∩ B| = 21, |A ∩ C| = 22, |B ∩ C| = 16
|A ∩ B ∩ C| = 7
Therefore,
N = (52 + 60 + 96) - (21 + 22 + 16) + 7
N = 156
Hence, there were 156 candidates in the examination.
The problem seems incomplete, it must have been
"In a certain examination, 52 candidates offers biology,60 offers history,96 offers mathematics, if 21 offered both biology and history,22 offered mathematics and biology, and 16 offered mathematics and history. If 7 candidates offered all the subject. how many candidates were there for the examination?"
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Eliud wa running 125 mile per week. Now, he’ running 20% more mile per week. How many mile i Eliud running per week? Write and olve an equation to determine how many mile Eliud i now running per week, r. A- 25 mile per week
B- 15 mile per week
C-150 mile per week
D- 250 mile per week
Eliud was running 125 miles per week, and now he is running 20% more. To determine how many miles Eliud is now running per week, the equation is 125 plus 125 times 0.2, which equals 150 miles per week.
125 + (125 x 0.2)
=125 + 25
= 150
Eliud was previously running 125 miles per week. To determine how many miles he is now running per week, an equation needs to be solved. The equation is 125 plus 125 times 0.2, which equals 150 miles per week. This is because 20% of 125 is 25, so 125 plus 25 is 150. Therefore, Eliud is now running 150 miles per week, which is an increase of 25 miles per week from his previous running amount. This increase of 25 miles per week is equivalent to 20% more than he was previously running. Solving this equation reveals that Eliud is now running 150 miles per week, which is an increase of 20% from his previous mileage.
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help simplify:px-1 .px+1
Answer:
Answer is 1
Step-by-step explanation:
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:
Can you please help me?
9x² + 24x + 16 is equal to (3x + 4)².
This is a perfect square trinomial equation.
Option B is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
9x² + 24x + 16
This can be written as,
(3x)² + 2 x (3x) x 4 + 4²
This is the perfect square trinomial of (3x + 4)².
[ (a + b)² = a² + 2ab + b² ]
Thus,
9x² + 24x + 16 is a perfect square trinomial equation.
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PLEASE HELP ME WITH THIS ASAP!!!
Answer: F
the inequality is x<3
Step-by-step explanation:
