The side MN have the value of x = 4, and for the side LM have the value x = 5 for the similar polygons ABCD and LMNP.
How to evaluate for the value of x for the sides of the polygonThe polygons ABCD and LMNP are similar so:
angle A is equal to angle L
angle B is equal to angle M
angle C is equal to angle N
angle D is equal to angle P
side MN = side BC
x + 6 = 10
x = 10 - 6 {subtract 6 from both sides}
x = 4
side LM = side AB
x + 9 = 14
x = 14 - 9 {subtract 9 from both sides}
x = 5
Therefore, the x = 4 for the side MN and x = 5 for the side LM for the similar polygons ABCD and LMNP.
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Hi, could someone please help me with this shape I have to find the perimeter and the area of that shape But I have no clue Where to start from, so could anybody help me figure this out this is very important to me, and please do not Try to give me the wrong answer because I really need the right answer!!
Answer: The answer is 16
Step-by-step explanation:
Find the value of x-
1250=1/2×50×(2x+3x)
The value of x in the expression is 10
How to find x?You should understand that an equation is a mathematical statement showing the equality of two things
The given equation is 1250=1/2×50×(2x+3x)
To find the value of x, we have to simplify the right hand side of the equation
This is = 1250 = 50(5x)/2
This will give us 2500 250x after cross multiplication
Then make x the subject of the relation by dividing by 250
This implies that x = 10
The expression leaves the value of x at 10
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What is the final step with the McCandless method?
The final step with the McCandless method is step 5: Close.
Moving on to the presentation's next topic is crucial.
The McCandless Method will set you up for a successful presentation. It will ensure you present data in the right way. It’s important for you to build that method into your practice. You should also build other critical habits into your practice of presenting graphics, but the basic guidelines presented here will help ensure your presentation is successful.
In a method that meets your needs, conclude your visual presentation before moving on to the next subject of conversation.
Thus, The final step with the McCandless method is step 5: Close.
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The final step with the McCandless method is the process of telling the audience why your graphic matters.
Here we have know that according to the theory of "Into the Wild" said that the following process are included in it:
Here the first process is to introduce the graphic by name
And then we have to answer obvious questions before they're asked
Then the next step is to state the insight of your graphic
Then we have to move to the step that is to Call out data to support that insight
And the final steps is to tell your audience why it matters
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someone please help me I need to return this tomorrow ;(
Finnd the missing dimension. Show how you found the answer.
Answer: 15
Step-by-step explanation:
Area = bh
Area = 120
Height = 8
Since you have the area and the height you need to divide:
120/8
=
15
__________________________________________________________
You can also check your answer by doing bh
15 x 8
=
120
Imogen is organising a barbecue.
She needs bread rolls and burgers.
Bread rolls are sold in packs of 20.
Burgers are sold in packs of 12.
Imogen buys exactly the same number
of bread rolls as burgers.
What is the least number of each pack
that Imogen buys?
packs of bread rolls
............... packs of burgers
Imogen need to buy 3 packs of bread rolls for every 5 packs of Burgers packs that are sold.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
X= Number of Bread Roll Packs
Y= Number of Burger Packs
Therefor we can say
20X=12Y
X/Y=12/20=3/5
Therefore Imogen need to buy 3 packs of bread rolls for every 5 packs of Burgers packs that are sold.
Hence, Imogen need to buy 3 packs of bread rolls for every 5 packs of Burgers packs that are sold.
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Work out the volume of each of this prisms:
The volumes of right prisms are listed below:
Case A: 150 cm³
Case B: 525 m³
Case C: 429 m³
How to determine the volume of a right prism
The volume of right prism (V), in cubic length units, is always equal to the product of the base area (A), in square length units, and height (h), in length units:
V = A · h
There are three right prisms, whose areas are combinations of right triangles and rectangles. The area formulas are shown below:
Rectangle
A = w · l
Right triangle
A = 0.5 · w · l
Where:
w - Width, in length units.l - Length, in length units.The complete procedure is listed below:
Determine the base area.Calculate the volume of prism.Case A
A = 0.5 · (4 cm) · (5 cm) + (3 cm) · (5 cm)
A = 25 cm²
V = (25 cm²) · (6 cm)
V = 150 cm³
Case B
A = (5 m) · (8 m) + (5 m) · (7 m)
A = 75 m²
V = (75 m²) · (7 m)
V = 525 m³
Case C
A = (8 m) · (4 m) + (3 m) · (9 m) + 0.5 · (5 m) · (5 m)
A = 71.5 m²
V = (71.5 m²) · (6 m)
V = 429 m³
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PLEASE HELP ASAP!!!!!!!!
what is the total dose required for a 140 lb patient if the amount required is 28 mg/kg bodyweight?
The total dose required for a 140 lb patient is 3,920 mg, as it is calculated by multiplying 28 mg/kg bodyweight.
1. Calculate the patient's bodyweight in kilograms by dividing their weight in pounds (140) by
2.2: 140 ÷ 2.2
= 63.63 kg
2. Multiply the patient's bodyweight in kilograms (63.63) by the required dose per kilogram (28):
63.63 x 28
= 1,780.84 mg
3. Round this number up to the nearest whole number: 1,780.84 rounded up = 3,920 mg
The total dose required for a 140 lb patient is calculated by multiplying the amount required per kilogram of bodyweight by the patient's bodyweight in kilograms. To calculate the patient's bodyweight in kilograms, you need to divide their weight in pounds (140) by 2.2. This gives you 63.63 kg. Then, multiply the patient's bodyweight in kilograms (63.63) by the required dose per kilogram (28): 63.63 x 28 = 1,780.84 mg. Finally, round this number up to the nearest whole number: 1,780.84 rounded up = 3,920 mg. Therefore, the total dose required for a 140 lb patient is 3,920 mg.
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If the lease factor is given as 0. 00045 what interest rate is that equivalent to.
If the lease factor is given as 0. 00045 then the interest rate is that equivalent to 4.5%
The lease factor of 0.00045 is equivalent to an interest rate of 4.5%. This is because the lease factor is a measure of the interest rate a lessee pays on a lease.
It is calculated by dividing the interest rate by 2400. This means that the higher the lease factor, the higher the interest rate that the lessee pays.
For example, if the interest rate is 12%, then the lease factor would be 0.005.
In this case, the lessee would be paying an interest rate of 12%, or 0.005 as a lease factor.
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A fruit juice company includes 1.751 ounces of juice in a 6.45
-ounce bottle of a mixed fruit juice. How much of the bottle of mixed fruit juice is NOT juice?
Answer: 4.699 ounces (72.85 %)
Step-by-step explanation: Total Quantity in bottle = 6.45
Total quantity = quantity of fruit juice + quantity of not fruit juice.
ATQ.
6.45 = 1.751 + quantity of not fruit juice
quantity of not fruit juice = 4.699 ounces
in percentage it will be 4.699/6.45 × 100 = 72.85%
A hyperbola centered at (5, 0) has a focus at (5, 10) and vertex at (5, 6). Which is the equation of the hyperbola in standard form?
The equation of the hyperbola in standard form is y²/8² - (x-5)²/6² = 1
Given that the center of the hyperbola is (5,0) and the vertex is (5,6), we can see that the center is on the x-axis, so the y-coordinate of the center, k, is 0. The x-coordinate of the center, h, is 5.
We know that equation of Hyperbola is
(y-k)²/a² - (x-h)²/b² = 1
Where (h,k) is the center and given (h, k) = (5, 0) and b is the transverse axis and a is the conjugate axis.
Now b is the y-coordinate of vertex (5,6) ⇒b=±6
and c is the y-coordinate of focus (5,10)c=±10
And also c² = a²+b²
(±10)²=a²+(±6)²
⇒a²=100−36=64
Hence a=±8
Thus, the equation of the hyperbola is y²/8² - (x-5)²/6² = 1
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You must be more than 3.5 feet tall to ride this ride. Write an inequality to represent
this. Use x as your variable.
Inequality compares two variables, to show if one is less than, equal to or greater than the other variable being compared.
How to calculate inequality?inequality becomes h>3.5When solving an inequality: • you can add the same quantity to each side • you can subtract the same quantity from each side • you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.Subtract the same number from both sides. Multiply both sides by the same positive number. Divide both sides by the same positive number. Multiply both sides by the same negative number and reverse the sign.Rule 1. Adding or subtracting the same quantity from both sides of an inequality leaves the inequality symbol unchanged. Rule 2. Multiplying or dividing both sides by a positive number leaves the inequality symbol unchanged.To learn more about inequality refers to:
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In a hypothesis test, if the computed p-value is less than 0.001,there is very strong evidence to a).fail to reject the null hypothesis. b).retest with a different sample. c). reject the null hypothesis.
The p-value of the hypothesis test is a measure of the strength of the evidence. There is significant evidence to reject the null hypothesis if it is less than 0.001.
A hypothesis test is a statistical procedure used to make a decision about an underlying population based on sample data. The hypothesis test involves two hypotheses. The null hypothesis, which states that the population parameter is equal to a given value, and the alternative hypothesis, which states that the population parameter is not equal to the given value. The strength of the evidence is gauged by the p-value. A p-value of less than 0.001 indicates that the evidence is very strong, and that the null hypothesis should be rejected. This means that the data is not consistent with the null hypothesis, and the alternative hypothesis should be accepted. In other words, the population parameter is not equal to the given value.
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The mean of a set of five different positive integers is 15 and the median is 18. What is the maximum possible value of the largest of these five integers?.
The maximum possible value of the largest of these five integers is 35.
Integer:
An integer is a number with or without a fractional part, including negative and positive numbers, including zero. Examples of integers are -5, 0, 1, 5, 8, 97, and 3,043. The set of integers represented as Z includes:
Positive number: A number is positive if it is greater than zero. For example: 1, 2, 3. .
Negative number: A number is negative if it is less than zero. For example: -1, -2, -3. . .
Zero: Zero is not defined as negative or positive is an integer.
According to the question:
Since the average of 5 different positive integers is 15, we can assume that all sum to 5 * 15 = 75. Median is 18. So the sum of the remaining 4 numbers is 75 − 18 = 57, meaning 2 numbers are greater than 18 and 2 numbers are less than 18.
Find : the highest possible maximum, and I want the minimum to be very low.
The fourth number is 19 because we want the largest integer maximum. This is because it is the lowest value that can be obtained and is higher than the median value. Then we have 1, 2, 18, 19 in the dataset for a total of 40.
The sum of the five numbers is 75.
Therefore, the maximum possible value of the largest five integer is
75 - 40 = 35.
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The United States House of Representatives has 35 more members than four times the number of members in the United States Senate. Define a variable and write an expression to represent the number of members in the House of Representatives.
The expression to represent the number of members in the House of Representatives is 4x + 35.
How to calculate the expression?Based on the information, the question has to do with an expression. An expression shows the relationship between the variables.
In this situation, the United States House of Representatives has 35 more members than four times the number of members in the United States Senate
Let the number of members in Senate be x.
The expression will be:
(4 × x) + 35
= 4x + 35
The expression is 4x + 35.
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PLEASE HELP ASAP!!!!!!!!
please answer.........................
The proof of <BED = <BAC is shown below.
What is Similarity?If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.
Given:
AE ⊥ BC
and, CD ⊥ AB
As, AE is perpendicular to BC then BE = EC = 1/2 BC
and, BD = AD = 1/2 AB
Now, In ΔBED and ΔBCA
<EBD = <ABC {common}
BD/AB = BE/ BC = 1/2
By ASA similarity Criteria ΔBED ~ ΔBCA
So, <BED = <BAC
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exponent rules: (6m⁸n⁹) (4mn⁷) = ?
please help
The value of the given equation is, (6m⁸n⁹) (4mn⁷) =[tex]$$=24 m^9 n^{16}$$[/tex]
What is exponent rules?(am)n = am*n is the exponent power rule. Exponent times power is how you raise a number with an exponent to a power. The x-n = 1/xn Negative Exponent Rule. A negative exponent can become positive by inverting the base. According to the first law, adding the exponents will multiply two exponential functions with the same base. According to the second law, we must subtract the exponents when dividing two exponential functions with the same base. The third law indicates that we must multiply the exponents in order to increase a power to a new power.Simplify[tex]$\left(6 m^8 n^9\right)\left(4 m n^7\right): \quad 24 m^9 n^{16}$[/tex]
steps
[tex]$$\left(6 m^8 n^9\right)\left(4 m n^7\right)$$[/tex]
Apply exponent rule: [tex]$a^b \cdot a^c=a^{b+c}=0^{\prime}=$[/tex]
[tex]& m^8 m=m^{8+1} \\[/tex]
[tex]& =6 n^9 \cdot 4 m^{8+1} n^7[/tex]
\end{aligned}
Add the numbers: [tex]$8+1=9$[/tex]
[tex]=6 n^9 \cdot 4 m^9 n^7[/tex]
Apply exponent rule: [tex]$a^b \cdot a^c=a^{b+c}$[/tex]
[tex]& n^9 n^7=n^{9+7} \\[/tex]
[tex]& =6 \cdot 4 m^9 n^{9+7}[/tex]
Add the numbers: [tex]$9+7=16$[/tex]
[tex]$$=6 \cdot 4 m^9 n^{16}$$[/tex]
Multiply the numbers: 6 - [tex]$4=24$[/tex]
[tex]$$=24 m^9 n^{16}$$[/tex]
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use the ALEKS calculator to write 31/24 as a decimal rounded to the nearest hundredth.
The decimal form of the value, 31/24 is 1.29166... The nearest hundredth form of this expression will be 1.29.
What is the nearest hundredth?To calculate the nearest hundredth you have to examine the second number that comes after the decimal point. To get the nearest hundredth, leave the hundredth value as it is if the value after it is not up to five. If the value after the hundredth value is more than 5, then we have to add 1 to the figure that constitutes the hundredth value.
In the question given above, 9 is the hundredth value. The value after 9 is 1 and since it is less than 5, it will not be changed. Therefore, the figure when rounded off to the nearest hundredth form is 1.29.
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how many different permutations are there of the set {a, b, c, d, e, f, g}?
There are 5040 different permutations of the set {a, b, c, d, e, f, g}.
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040
The set {a, b, c, d, e, f, g} has seven elements, so there are 7! (7 factorial) permutations possible. The factorial of a number is the product of all the numbers up to and including that number. In this case,
7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.
This means that there are 5040 different permutations of the set
{a, b, c, d, e, f, g}.
A permutation is defined as an arrangement of elements in a specific order. In this case, the elements are {a, b, c, d, e, f, g} and the order can be changed in any way, as long as all elements are included. For example, one possible permutation is bfgdeca.
This is one of the 5040 possible permutations of the set.
As the set contains seven elements, there are 7! (7 factorial) possible permutations. This means that there are 5040 different permutations of the set {a, b, c, d, e, f, g}.
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2) what is the domain of f(x) = x³ + 6x² + 5
Answer:
[tex]-\infty \: < x < \infty[/tex]
or, in interval notation as
[tex]\left(-\infty \:,\:\infty \:\right)[/tex]
Step-by-step explanation:
The domain of a function [tex]f(x)[/tex] is the set of all values of [tex]x[/tex] for which [tex]f(x)[/tex] is real and defined
The given function is f(x) = x³ + 6x² + 5
There are no undefined points. So the domain is the set of all real numbers that can be expresses as
[tex]-\infty \: < x < \infty[/tex]
or, in interval notation
[tex]\left(-\infty \:,\:\infty \:\right)[/tex]
evaluate the integral. (use c for the constant of integration.) dx (ax)2 − b2 3/2
The integral evaluates the area under a curve by taking the antiderivative of the given function and evaluating the limits of the integral. The final result is (1/3) ax3 - (1/2) b2 ax + c.
∫ (ax)2 − b2 3/2 dx = (1/3) ax3 - (1/2)b2 ax + c
The integral evaluates the area under a curve. It is calculated by taking the antiderivative of the given function and then evaluating the limits of the integral. To find the antiderivative, we use the power rule to calculate the derivative of the function and then integrate the result. In this case, the function is (ax)2 - b2 3/2. Using the power rule, we find that the derivative of this function is (3/2) ax2 - (1/2) b2 ax. We then integrate this result and add the constant of integration (c) to obtain the integral. The final result for this integral is (1/3) ax3 - (1/2) b2 ax + c.
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How many terms are in the expression shown to en +5 minus 3p plus 4q?
The number of terms in the given algebraic expression "2n + 5 - 3p + 4q" are four terms .
An Algebraic Expressions are defined an expression that consists of numbers, variables and joined by mathematical operator .
For example, 3x + 6 is an expression where 3x and 6 are the terms and x is the variable that is separated by the arithmetic sign "+".
The given expression is 2n + 5 - 3p + 4q ,
as we can see that the mathematical operators used are + and - .
This expression cannot be simplified further ,
So , the first term is 2n , the second term is 5 , third term is 3p and fourth term is 4q .
Therefore , the given expression has four terms .
The given question is incomplete , the complete question is
How many terms are in the expression shown to n +5 - 3p + 4q ?
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The expression consists of 3 terms: en, minus 3p, plus 4q. It can be expanded by multiplying the first term, en, by the coefficients of the other two terms. The resulting expression is en - 3pen + 4qen. The final result is en - 3pen + 4qen, which can also be written as en + 4qen - 3pen.
Step 1: Expand the expression by multiplying the first term, en, by the coefficients of the other two terms.
Step 2: The resulting expression is en - 3pen + 4qen.
Step 3: Simplify the expression to get the final result: en + 4qen - 3pen.
The expression to en +5 minus 3p plus 4q consists of 3 terms. To expand it, we need to multiply the first term, en, by the coefficients of the other two terms. This means that en needs to be multiplied by -3p and +4q to get the expanded expression.
This is the final result of the expansion. By multiplying the first term by the coefficients of the other two terms, we have been able to expand the expression to en +5 minus 3p plus 4q. This expression can now be used in calculations to solve problems.
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Help it is due tomorrow
Answer:
s
Step-by-step explanation:
your welcome!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The following table shows the total number of quizzes taken in a high school.
4 quizzes are taken per week.
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
A linear equation is given by: y = mx + b;
where y, x are variables, m is the rate of change and b is the y intercept.
Let y represent the total number of quizzes after x weeks.
From the table we can see that when y = 12, x = 3 and when y = 20, x = 5. Hence:
Number of quizzes per week = 12/3 = 20/5 = 4
Hence, 4 quizzes are taken per week.
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Find the exact length of the curve y=ln[(e^x+1)/(e^x-1)], a < x < b,
a > 0 (">"= greater than or equal to and "<" = less than or equal to)
The exact length of the curve y=ln[(e^x+1)/(e^x-1)], a ≤ x ≤ b, is equals to the ln[( eᵇ - e⁻ᵇ )/ ( eᵃ - e⁻ᵃ)].
The exact length of curves implies the length of arc of curve. Arc length is the distance between two points along a section of a curve, formula
Arc length = ₕ∫ᵏ√( 1 + ( y')² dx , h≤x≤k
We have a curve , y = ln[ (eˣ + 1) /(eˣ - 1) ] , a≤x≤b , a> 0
firstly, determine the first derivative of y with respect to x ..
dy/dx = y' = [ 1/(eˣ +1) /(eˣ -1)] d/dx (( eˣ + 1) /(eˣ -1) )
( apply chain rule )
= (eˣ -1 )/(eˣ +1 )[{(eˣ -1) eˣ - ( eˣ +1)eˣ}/(eˣ - 1)²]
( using quotient rule)
= (eˣ -1 )/(eˣ +1 )[(e²ˣ - eˣ - e²ˣ - eˣ)/(eˣ - 1)²]
= (eˣ -1 )/(eˣ +1 )[(- 2eˣ)/(eˣ - 1)²]
= -2eˣ /(eˣ -1 )(eˣ +1 )
dy/dx = - 2eˣ /e²ˣ -1
so, (dy/dx)² = (- 2eˣ /(e²ˣ -1) )²
= 4e²ˣ /(e²ˣ -1 )²
and 1 + (dy/dx)² = 1 + {4e²ˣ /(e²ˣ -1 )² }
= {(e²ˣ -1 )² + 4e²ˣ}/(e²ˣ -1 )²
= (e⁴ˣ + 1 - 2e²ˣ + 4e²ˣ)/(e²ˣ -1 )²
= ( e⁴ˣ + 1 + 2e²ˣ )/(e²ˣ -1 )²
1 + (dy/dx)² = (e²ˣ + 1)²/(e²ˣ -1 )²
Now plugging the value in arc length formula,
Arc length = ₐ∫ᵇ √{1 + (dy/dx)²} dx
= ₐ∫ᵇ √{(e²ˣ + 1)²/(e²ˣ -1 )²} dx
= ₐ∫ᵇ√{(e²ˣ + 1)/(e²ˣ -1 )}² dx
= ₐ∫ᵇ {(e²ˣ + 1)/(e²ˣ -1 )} dx
= ₐ∫ᵇ[eˣ(eˣ + e⁻ˣ)/eˣ(eˣ - e⁻ˣ )] dx
= ₐ∫ᵇ[(eˣ + e⁻ˣ)/(eˣ - e⁻ˣ )] dx
Arc length= ₐ∫ᵇ(cosh x)/(sinh x)dx ( using hyperbolic functions formulas )
let sinh x = t => cosh xdx = dt
and when x = a => t = sinh a
when x = b => t = sinh b
so, arc length = ₛᵢₙₕ ₐ∫ˢᶦⁿʰ ᵇ (1/t) dt
= [ ln( sinh b ) - ln(sinh a) ]
= ln( sinh b/ sinh a)
Arc length= [( eᵇ - e⁻ᵇ )/ ( eᵃ - e⁻ᵃ)]
Hence, length of curve is ln[( eᵇ - e⁻ᵇ )/ ( eᵃ - e⁻ᵃ)].
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What is quadratic equation examples with answers?
A quadratic equation is an equation of degree 2 and has the standard form: ax² + bx + c = 0, with a ≠ 0. Example: 2x² - 3x - 2 = 0, the solution is {-1/2, 2}.
A quadratic equation is an equation of degree 2. The standard form of a quadratic equation is:
ax² + bx + c = 0, with a ≠ 0
The quadratic equations can be solved using:
- factorization
- completing the square
- abc formula
Example 1:
2x² - 3x - 2 = 0
Using factorization:
2x² - 3x - 2 = (2x +1) (x-2)
Hence,
(2x +1) (x-2) = 0
Solution:
x = -1/2 and x = 2
x = {-1/2, 2}
Example 2:
x² - 6x + 4 = 0
By completing the square:
x² - 6x + 5 = (x - 3)² - 4
Hence,
x² - 6x + 5 = 0
(x - 3)² - 4 = 0
(x - 3)² = 4
x - 3 = ± 2
The solutions are
x = 3 - 2 = 1 or
x = 3 + 2 = 5
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8.4, 3, 1.2, 0.2, 6.4, 7.1, 8, 1.4, 7, 9 State the median. Give your answer as a decimal.
Answer:
6.7 is the answer
Step-by-step explanation:
the two middles numbers are 6.4 and 7
subtract 7 and 6.4 you get .6
split .6 in half and add it to 6.4 to get 6.7
hope this helps:)
Answer: 6.4
Step-by-step explanation: First, let's list out the data set:
0.2, 1.2, 1.4, 3, 6.4, 7.1, 8, 8.4, 9
Okay, so to find the median, we need to find the exact middle of the data set. If it was a data set with 2 numbers in the middle, we would add them up and divide by 2. Fortunately, we have a data set with an exact number in the middle. We have to do nothing more, so therefore 6.4 would be your answer.
The salary of 157 employees in an office for a month is Rs. 7,10582.What is the annual salary of 1 employee, assuming all are paid equally?
Show division step-by-step
Answer:
To find the annual salary of one employee, you need to divide the total monthly salary by the number of employees and then multiply by 12 to get the annual salary.
Here's the step-by-step process:
Divide the total monthly salary by the number of employees: 710582 / 157 = 4550.85
Multiply the result by 12 to get the annual salary: 4550.85 * 12 = Rs. 54610.20
So, the annual salary of one employee is Rs. 54610.20.
Step-by-step explanation:
I need help with this assignment and finding the measures and equations
Answer:
(4x-9)° +(6x+2)° +x° = 180°∠P = 59°∠Q = 104°∠R = 17°Step-by-step explanation:
Given ∆PQR with ∠P = (4x-9)°, ∠Q = (6x+2)°, and ∠R = x°, you want an equation to find x, and the measures of the angles.
EquationThe equation expresses the fact that the sum of angles in a triangle is 180°.
∠P +∠Q +∠R = 180°
(4x -9)° +(6x +2)° +x° = 180°
Solution11x -7 = 180 . . . . . . . . . . . . divide by °, collect terms
11x = 187 . . . . . . . . . add 7
x = 17 . . . . . . . . divide by 11
AnglesThe angle measures are found by substituting for x in the angle expressions:
∠P = (4·17 -9)° = 59°
∠Q = (6·17 +2)° = 104°
∠R = 17°