The subtraction of fraction numbers 4(2/3) and 3(2/5) is, 19/15
What is subtraction?In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.
For example, if we take 4 pencils out of 10 then remaining pencils are 6
so this process is called subtraction.
Given that,
Two fraction numbers,
4(2/3)
And 3(2/5)
Subtraction of both the terms = ?
⇒ 4(2/3) - 3(2/5)
Both the numbers can be written in the simplified form as,
⇒ (12 + 2)/3 = 14/3
⇒ (15 + 2)/5 = 17/5
Now, subtracting both the terms,
⇒ 14/3 - 17/5
Taking LCM of 3 & 5
LCM(3,5) = 15
⇒ Now, for making denominator same we multiply and divide each term 14/3 & 17/5 by 5 and 3 respectively,
⇒ (14/3)x(5/5) - (17/5)x(3/3)
⇒ (14x5)/(3x5) - (17x3)/(5x3)
⇒ 70/15 - 51/15
Now, denominators are same,
So, it can be written as,
⇒ (70 - 51)/15
⇒ 19/15
Hence, the result is 19/15
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Using the region names in the image below, select all regions that represent:
(A ∪ B)' ∪ A'
3 group Venn Diagram with Roman numeral labeled regions
Not, parentheses A union B, close parentheses, union not A. Region I: Items only in group A, not in B or C. Region II: Items in A and B, but not C. Region III: Items only in B, not in A or C. Region IV: Items in A and C, but not B. Region V: Items in A, B, and C. Region VI: Items in B and C, but not A. Region VII: Items only in C, not in A or B. Region VIII: Items not in any of the groups.
The Venn diagram shown to Region II: Items in A and B, but not C are (A ∪ B)' ∪ A'
We have been given that the diagram we need to find the regions represent the set.
What do you mean by Venn diagram?A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits. Venn diagrams help to visually represent the similarities and differences between two concepts.
The Venn diagram, item represents the regions four, five, six and seven.
Therefore, it can be written us for Union Fight,...., we concluded that the regions represent see R. C.
This is equal to for Union Fighting Union Six, Seven.
We have, region represent (A ∪ B)' ∪ A'
Therefore, the Venn diagram shown to regions represent
(A ∪ B)' ∪ A' is Region II
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Calculate the angle of elevation from the
base of this leaning tower, B, to the point P.
Give your answer to 1 d.p.
Answer:
[tex]43.78^\circ[/tex]
Step-by-step explanation:
Let θ be the angle that the base of the leaning tower makes with the tower i.e. the angle of elevation
Since this is a right triangle we have the relationship
[tex]\tan\theta = \dfrac{height}{base} = \dfrac{46}{48} \approx 0.95833\\\\[/tex]
[tex]\theta = tan^{-1} (0.95833) = 43.78^\circ[/tex]
Answer
[tex]= 43.78^\circ[/tex]
The angle of elevation is given by the trigonometric relation and θ = 73.40°
What are trigonometric relations?
Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the angle of elevation be represented as E = θ
Now , the measure of the altitude = 46 m
The measure of the hypotenuse = 48 m
And , the angle of elevation is given by the trigonometric relation ,
sin θ = opposite / hypotenuse
On simplifying , we get
sin θ = 46 / 48
sin θ = 0.958333
Taking inverse on both sides , we get
θ = sin ⁻¹ ( 0.958333 )
θ = 73.40°
Hence , the angle of elevation is 73.40°
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Sadie earns a 20 percent commission on sales at a hair salon. If her weekly sales commission check was $125, what was her sales total for the week
can you guys please show step by step
Sadie's total weekly sales in the last week were $625.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Sadie earns a 20 percent commission on sales at a hair salon.
Let, 'x' be her total weekly sales.
Therefore, $125 is 20% of 'x' which can be numerically expressed as,
(20/100)×x = 125.
0.2x = 125.
x = 125/0.2.
x = 625.
So, her weekly sale was $625.
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What is the slope-intercept form of the following equation?
6y-18x=24
y = 3x+4
y = 3x + 24
6y = 18x+24
y= 3x-4
Answer:
6y=18x+24
Step-by-step explanation:
x come first cuz of pemdas
Ellen walks 0.75 mile to school each day. She stops
to get breakfast after completing 60% of her walk
How far has Ellen walked when she stops for
breakfast?
The manager of a nationwide department store wants to compare average store sales by region to identify which region has the lowest store sales. Which of the following numerical descriptive measures is best for this purpose?
The best numerical descriptive measure for comparing average store sales by region would be the mean or average.
This measure would provide an accurate representation of the overall store sales across the entire region and would allow the manager to easily identify which region has the lowest store sales.
Additionally, the median and mode could also be used as descriptive measures to compare the store sales by region.
For example, if there is a single store with particularly high sales, the mean will be heavily influenced by this one store. The median and mode would be more likely to provide a better representation of the overall sales across the region, as they are not as heavily influenced by extreme values.
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e of x.
2x-4
39
parate answers as needed.)
x+6
24
▪▪▪
The solution to the proportional relationship (2x - 4)/39 = (x + 6)/24 is given as follows:
x = 36.67.
How to solve the proportional relationship?The proportional relationship for this problem is defined as follows:
(2x - 4)/39 = (x + 6)/24
As the measures are proportional, we can apply cross multiplication, hence:
24(2x - 4) = 39(x + 6).
Applying the distributive property to each side of the equality, we have that:
48x - 96 = 39x + 234
Hence, isolating x, the solution is obtained as follows:
48x - 39x = 234 + 96
9x = 330
x = 330/9
x = 36.67.
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please help!!
very detailed explanation and answer please!
Answer:
20 Stickers
Step-by-step explanation:
You cross multiply
[tex] \frac{70 \times 4}{14} [/tex]
[tex] \frac{280}{14} = 20[/tex]
Which statements are true about a perfect cube monomial and its roots? Check all that apply.
A perfect cube monomial must have exponents on the variables.
A perfect cube monomial must have three identical roots, such that the product of the roots equal the perfect square monomial.
The coefficient of the monomial must be divisible by 3.
Any monomial can be a perfect cube root.
The least common multiple of all the exponents on variables of a perfect cube monomial must be 3.
It must be possible for the coefficient of a perfect cube monomial to be written in the form n3, where n equals the cube root of the coefficient.
Answer:
Step-by-step explanation:
A perfect cube monomial is a monomial with a cube root that is a monomial. In other words, it is a monomial, A, such that there exists a monomial, B, where B × B × B = A.
A car is traveling at a speed of 60 miles per hour. What's the dependent variable in this situation?
Question 1 options:
A)
The number of hours the car has traveled
B)
The age of the car
C)
The distance the car has traveled
D)
The speed at which the car travels
Answer:
C
Step-by-step explanation:
distance depends on the speed & the time traveled.
frank collected somewhere between 267 and 340 cans per day that he is going to recycle and give the money to charity if he did this for 21 days about how many cans did he collect A. 5,600 cans B.6,600 cans C.7,100 cans D. 12,750 cans
Answer:
somewhere between B & C
Step-by-step explanation:
267 *21 =5607
340*21 = 7140
the random variable x is the number of occurrences of an event over an interval of 10 minutes. it can be assumed the probability of an occurrence is the same in any two time periods of an equal length. it is known that the mean number of occurrences in 10 minutes is 5.3.
the random variable x is the number of occurrences of an event over an interval of 10 minutes. it can be assumed the probability of an occurrence is the same in any two time periods of an equal length. it is known that the mean number of occurrences in 10 minutes is 5.3.
A Poisson process is a statistical model used to describe the number of occurrences of an event over a fixed interval of time or space. It has the following properties:
The events are independent, meaning that the occurrence of one event does not affect the probability of another event happening.
The average rate of occurrences is constant over time and is equal to the rate parameter of the Poisson distribution.
The probability of having n events in a fixed interval of time is given by the Poisson probability formula:
P(n) = (λ^n * e^-λ) / n!
where λ is the rate parameter and n! is the factorial of n.
Given the mean number of occurrences in 10 minutes is 5.3, it can be assumed that the rate parameter is 0.53 occurrences per minute. This means that, on average, 0.53 events are expected to occur in each minute. Since the Poisson process is memoryless, this rate is constant over time and the mean number of occurrences in any 10-minute interval will be 5.3.
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consider the following recursive method, which is intended to display the binary equivalent of a decimal number. for example, tobinary(100) should display 1100100.
The resulting binary representation of 100 is 1100100.
The recursive method for displaying the binary equivalent of a decimal number is based on the binary representation of integers, which is expressed by the formula:
Decimal number = [tex](2^n * bn) + (2^n-1 * bn-1) + ... + (2^0 * b0)[/tex]
where n is the number of bits in the binary representation, and bn is the value at each bit position (either 0 or 1).
To calculate the binary equivalent of a decimal number, the method works by first calculating the largest power of two (2^n) that is less than or equal to the decimal number. The remainder of the decimal number is then calculated (Remainder = Decimal number - 2^n). This remainder is then recursively used to calculate the binary equivalent of the remainder. This process is repeated until the remainder is less than or equal to 2^0, at which point the binary representation can be determined.
For example, to calculate the binary equivalent of 100, the largest power of two that is less than or equal to 100 is 2^6 (64), so the remainder is 100 - 64 = 36. The binary equivalent of 36 is then calculated recursively, and the resulting binary representation of 100 is 1100100.
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The cost of 3 pounds of grapes is 6.57$. What is the cost of 2 pounds of grapes? Please help! I’ll give brainly.
need help, So the question is "write the equation of a line that is perpendicular to the graph y=-4x-9 that passes through the point (16,9) anybody please??
Answer:
Step-by-step explanation:
[tex]m_{2}=\frac{-1}{m_{1} }[/tex]
m2=4
y=mx+c
9=4(16)+c
9=64 +c
c=9-64
c=-55
∴y=4x-55
The measures of two supplementary angles are in the ratio 5:7 what is the measure of the larger angle
In a game of darts, there are 20 sectors on a target, and a smaller circular "bullseye" in the center. In this particular game, a player must correctly call "low,” consisting of the sectors numbered 1–10; "high,” consisting of the sectors numbered 11–20; or "bullseye,” depending on what they are trying to hit. If they hit the section they call, they are a winner. A player will attempt to hit "low" on the first throw, then will attempt to hit "high" on the second throw, then will attempt to hit "bullseye" on the third throw, and so on until hitting the section they called.
Is it appropriate to use the geometric distribution to calculate probabilities in this situation?
Answer: This game of darts involves the player calling the target they aim to hit and the winner is determined by hitting the section they called. The player starts by attempting to hit "low" (sectors 1-10), followed by "high" (sectors 11-20), then "bullseye", and this pattern continues until the player successfully hits the section they called.
Step-by-step explanation:
Hayley is surveying a piece of land. The land is shaped like a right triangle. The smallest angle
is one-fifth the measure of the medium-size angle. Sketch a diagram to represent the piece of
land. Then, find the measure of each angle.
The angle measures are given as follows:
90º.15º.75º.The sketch is given by the image presented at the end of the answer.
How to obtain the angle measures?We have a right triangle, hence one of the angle measures is given as follows:
90º.
The sum of the measures of the internal angles of a triangle is of 180º, hence the sum of the remaining measures is given as follows:
90º, as 180 - 90 = 90.
The smallest angle is one fifth the medium size angle, hence:
x + 5x = 90
x = 15.
The measures are:
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two socks are drawn from a drawer which tontains one red sock, three blue socks, and two green socks. once a sock is selected it is not replaced. detemine each probabily
The probability of drawing two socks of the same color depends on the color chosen, with 0 probability of drawing two red socks and non-zero probabilities of drawing two blue or two green socks.
The probability of drawing a red sock is 1/6.
The probability of drawing a blue sock is 3/6 or 1/2.
The probability of drawing a green sock is 2/6 or 1/3.
The probability of drawing a red and a blue sock in either order is (1/6) * (3/5) = 1/30.
The probability of drawing a blue and a green sock in either order is (3/6) * (2/5) = 4/15.
The probability of drawing two red socks is (1/6) * (0/5) = 0.
The probability of drawing two blue socks is (3/6) * (2/5) = 4/15.
The probability of drawing two green socks is (2/6) * (1/5) = 2/30.
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i really need help i have till 11:00
The expression that represents the combined inventory of these two stores is given as follows:
A. 7g²/2 - 4g/5 + 15/4.
How to obtain the combined inventory?The combined inventory is obtained adding the inventories for each store, combining the like terms.
The addition of the like terms for g² is given as follows:
1/2 + 3 = 0.5 + 3 = 3.5 = 7/2g².
The term with g is given as follows:
-4g/5.
The constant like terms are combined as follows:
7/2 + 1/4 = 14/4 + 1/4 = 15/4.
Hence the simplified expression is given as follows:
7g²/2 - 4g/5 + 15/4.
Meaning that the correct option is given by option A.
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PLEASE BE FAST :')
Determine whether the ordered pair is a solution to the given system of equations.
1) (1,5); -5m + 6n = 25 -7m +8n=33
2) (-2, 0); 8x-3y=-16 50= -9x - 2y
The solution to the equations -5m + 6n = 25 and -7m + 8n = 33 is (1, 5)
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic
a) Given the equations:
-5m + 6n = 25 (1)
And:
-7m + 8n = 33 (2)
From both equations simultaneously:
m = 1, n = 5
The solution is (1, 5)
b) Given the equations:
8x - 3y = -16 (1)
And:
50 = -9x - 2y (2)
From both equations simultaneously:
x = -4.23, y = -5.95
The solution is (-4.23, -5.95)
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Simplify
9x^2 -4x-3= [?]
x= -2
Step-by-step explanation:
Simplify: [tex]9x^2 -4x-3=[/tex] [?] when x= -2
Substitute in -2 for x:
[tex]9(-2)^2 -4(-2)-3\\= 9(-2)^2 -4(-2)-3\\=9(4) +8 -3\\= 36 + 8 - 3\\[/tex]
x = 41
Answer: = 41
What point divides the directed line segment AB¯¯¯¯¯ into a 2:3 ratio?
Responses
(6, 1)
begin ordered pair 6 comma 1 end ordered pair
(8, 1)
begin ordered pair 8 comma 1 end ordered pair
(10, 1)
begin ordered pair 10 comma 1 end ordered pair
(12, 1)
Answer:
(8, 1)
Option 2
Step-by-step explanation:
Let C be the point that divides AB in the ratio 2:3
The technique to find individual segments is to note that if a line is 2+3 = 5 units long then one segment will be 2/5 and the other segment will be 3/5
2/5 : 3/5 = 2 : 3
Length of segment AB = 14 - 4 = 10 since the y values are the same and it is a horizontal line
So length of segment AC = 2/5 + 10 = 4
TO find the absolute x-value we add this length to the x-coordinate of A: 4 + 4 = 8
The y-coordinate of C = y-coordinate of A = y-coordinate of B = 1
So the point that divides the line segment AB in the ration 2:3 is (8, 1)
This would correspond to the second option
Catniss is saving money to take a trip to the Capitol with her sister. Every week, after taking out the $292 she nees for her weekely expenses, she sets aside the same portion of her paycheck. After 10 wekks , Catniss has $405.
Which equation can be used to represent the sitation?
The relation between total salary and saving can be represent by the equation, Y = X + 292
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
Given that,
Catniss is saving money to take a trip to the Capitol with her sister
Every week,
After taking out the $292, which she needs for her weekly expenses
And that amount she sets aside the same portion of her paycheck
After 10 weeks ,
Catniss has $405
Suppose, she is saving X amount every week,
And her total salary is, Y
Total salary = saving + weekly expenses
Y = X + 292
So, she saved money after 10 week,
⇒ 10X
Given saving after weeks, $405
⇒ 10X = 405
⇒ X = 40.5
Y = X + 292
= 40.5 + 405
= $445.5
Hence, the equation is Y = X + 292
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What is the equation of a line that passes through (.5,4.25) and (2,18.5) and has a y-intercept of -.5
The equation of a line that passes through (0.5, 4.25) and (2, 18.5) and has a y-intercept of -0.5 is y = 9.5x - 0.5
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line that passes through (0.5, 4.25) and (2, 18.5).
y-intercept = -5
Now,
The equation of a line is y = mx + c
c = y-intercept
c = -0.5 ______(1)
Now,
(0.5, 4.25) and (2, 18.5)
m = (18.5 - 4.25) / (2 - 0.5)
m = 14.25 / 1.5
m = 9.5 ______(2)
Now,
The equation of a line.
y = mx + c
From (1) and (2).
y = 9.5x - 0.5
Thus,
y = 9.5x - 0.5 is the equation of the line.
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Solve the differential equations in Problems 26 through 28 by regarding y as the independent variable rather than x
The solution to the differential equation is:
26. y - 2xy^3 = (1/4)y^4 + C.
27. (1/2)x^2 + (1/2)e^(2y) = x + C.
28. y + x^2 + xy^2 = (1/3)y^3 + x^2 + C.
To solve this differential equation with y as the independent variable, we can first separate the variables:
26. (1 - 4xy^2)dy = y^3 dx
Integrating both sides, we have:
∫(1 - 4xy^2)dy = ∫y^3 dx
y - 2xy^3 = (1/4)y^4 + C, where C is an arbitrary constant of integration.
So, the solution to the differential equation is:
y - 2xy^3 = (1/4)y^4 + C.
27. (x + ye^y)dy = dx
Integrating both sides, we have:
∫(x + ye^y)dy = ∫dx
(1/2)x^2 + (1/2)e^(2y) = x + C, where C is an arbitrary constant of integration.
So, the solution to the differential equation is:
(1/2)x^2 + (1/2)e^(2y) = x + C.
28. (1 + 2xy)dy = (1 + y^2)dx
Integrating both sides, we have:
∫(1 + 2xy)dy = ∫(1 + y^2)dx
y + x^2 + xy^2 = (1/3)y^3 + x^2 + C, where C is an arbitrary constant of integration.
So, the solution to the differential equation is:
y + x^2 + xy^2 = (1/3)y^3 + x^2 + C.
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A total of 444 tickets were sold for a school play. They were either adult tickets or student tickets. There were 56 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer:
250 adult tickets were sold
Step-by-step explanation:
Let A represent the number of adult tickets sold and S the number of student tickets sold
Total tickets sold = A + S = 444
56 fewer student tickets than adult tickets means
S = A - 56
Substituting for s in the first equation,
A + S = 444
A + (A - 56) = 444
2A - 56 = 444
Add 56 to both sides:
2A - 56 + 56 = 444 + 56
2A = 500
A = 250
So 250 adult tickets were sold
You are the manager of a rental car company. A customer, Sandy Furrow, has asked you for an estimate of charges for a nine day rental of an SUV. She expects to drive 670 miles. If the company charges $54.50 per day plus 15 1/ 2 cents per mile for this category of vehicle, what would be the total rental charge (in $) for Sandy's trip?
Answer The total rental charge for Sandy's trip will be $601.05 (six hundrend one dollars and five cents)
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Step-by-step explanation:
Express each of the following natural numbers as a sum of distinct, nonconsecutive Fibonaccit Numbers...
A) 52, 143, 13, 88
B) 43, 90, 2000, 609
The sums of distinct, nonconsecutive Fibonacci numbers for each of the given natural numbers are 52 = 13 + 34, 143 = 89 + 34 + 13 + 8, 13 = 8 + 5, 88 = 55 + 34, 43 = 21 + 8 + 13 + 1, 90 = 55 + 34, 2000 = 1597 + 377 + 21 + 5, 609 = 377 + 233.
A) The Fibonacci sequence is a set of numbers that starts with a one or a zero, followed by a one, and proceeds based on the rule that each number (called a Fibonacci number) is equal to the sum of the preceding two numbers. The Fibonacci numbers are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, and so on. To express 52, 143, 13 and 88 as a sum of distinct, nonconsecutive Fibonacci numbers, we can use the following calculations.
For 52, the sum is 13 + 34. 13 is the 8th Fibonacci number and 34 is the 9th Fibonacci number. By adding these two numbers, we get 52.
For 143, the sum is 89 + 34 + 13 + 8. 89 is the 11th Fibonacci number, 34 is the 9th Fibonacci number, 13 is the 8th Fibonacci number and 8 is the 7th Fibonacci number. By adding these four numbers, we get 143.
For 13, the sum is 8 + 5. 8 is the 7th Fibonacci number and 5 is the 6th Fibonacci number. By adding these two numbers, we get 13.
For 88, the sum is 55 + 34. 55 is the 10th Fibonacci number and 34 is the 9th Fibonacci number. By adding these two numbers, we get 88.
B) To express 43, 90, 2000, 609 as a sum of distinct, nonconsecutive Fibonacci numbers, we can use the following calculations.
For 43, the sum is 21 + 8 + 13 + 1. 21 is the 6th Fibonacci number, 8 is the 7th Fibonacci number, 13 is the 8th Fibonacci number and 1 is the 5th Fibonacci number. By adding these four numbers, we get 43.
For 90, the sum is 55 + 34. 55 is the 10th Fibonacci number and 34 is the 9th Fibonacci number. By adding these two numbers, we get 90.
For 2000, the sum is 1597 + 377 + 21 + 5. 1597 is the 16th Fibonacci number, 377 is the 14th Fibonacci number, 21 is the 6th Fibonacci number and 5 is the 6th Fibonacci number. By adding these four numbers, we get 2000.
For 609, the sum is 377 + 233. 377 is the 14th Fibonacci number and 233 is the 13th Fibonacci number. By adding these two numbers, we get 609.
The sums of distinct, nonconsecutive Fibonacci numbers for each of the given natural numbers are 52 = 13 + 34, 143 = 89 + 34 + 13 + 8, 13 = 8 + 5, 88 = 55 + 34, 43 = 21 + 8 + 13 + 1, 90 = 55 + 34, 2000 = 1597 + 377 + 21 + 5, 609 = 377 + 233.
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Please help measure the angles
(picture included)
please show work
The value of the variable x is 53.
The measures of the angles include the following:
m∠P = 96°.
m∠Q = 95°.
m∠R = 53°.
What is a triangle?In Mathematics, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
Furthermore, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;
m∠P + m∠Q + m∠R = 180
Substituting the given parameters into the mathematical expression, we have the following;
(2x - 10)° + (x + 42)° + x° = 180°
4x - 32° = 180°
4x = 180° + 32°
x = 53.
For the measure of the angles, we have:
m∠P = (2(53) - 10)° = 96°.
m∠Q = (53 + 42)° = 95°.
m∠R = 53°.
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