Se desea construir una letra "ene" mayúscula de tal manera que sus segmentos paralelos midan 25 cm y el
segmento oblicuo que une ambos mida 65 cm. ¿Qué distancia en línea recta separará los segmentos paralelos?
Answers
Answer:
La distancia en línea recta que separa los segmentos paralelos es 60cm.
Step-by-step explanation:
Esta pregunta se puede resolver usando el teorema de Pitágoras:
\( \\ c^2 = a^2 + b^2\) [1]
Es decir, en triángulos rectágulos, el cuadrado de la hipotenusa es igual a la suma de los cuadrados de los catetos de dicho triángulo. Un triángulo es rectángulo cuando el ángulo que forman sus dos catetos es recto o de 90 grados sexagesimales.
Es importante notar que la letra N tiene dos lados paralelos y el lado oblicuo (o inclinado) une ambos lados paralelos. Pues bien, la letra N puede formar dos triángulos iguales. Escojamos uno de ellos para obtener la respuesta, es decir, la distancia en línea recta que separa los segmentos paralelos (segmentos verticales de la N)
El lado oblicuo (inclinado) es la hipotenusa de ese triángulo (es decir, c). De los catetos, uno está representado por uno de los segmentos paralelos (verticales) de la N (digamos que es b), y, el otro cateto, es la distancia horizontal que une ambos segmentos verticales (digamos que es a).
Si unimos el segmento inferior del cateto b con el extremo inferior de la hipotenusa, se forma el cateto a. Este cateto a forma un ángulo recto con el cateto b y, por lo tanto, forma un triángulo recto. Los lados de un triángulo recto pueden resolverse usando el teorema de Pitágoras, descrito en [1].
Usando [1] y despejando a, tenemos:
\( \\ c^2 = a^2 + b^2\)
Restamos \( \\ b^2\) de ambos lados de la igualdad:
\( \\ c^2 - b^2 = a^2 + b^2 - b^2\)
\( \\ c^2 - b^2 = a^2 + 0\)
\( \\ c^2 - b^2 = a^2\)
Luego
\( \\ a^2 = c^2 - b^2\)
Extrayendo la raíz cuadrada en cada lado de la igualdad:
\( \\ \sqrt{a^2} = \sqrt{c^2 - b^2}\)
Entonces
\( \\ a = \sqrt{c^2 - b^2}\)
Asimismo, tenemos que \( \\ c = 65\)cm y \( \\ b = 25\)cm
Entonces,
\( \\ a = \sqrt{65^2 - 25^2}\)
\( \\ a = \sqrt{4225 - 625}\)
\( \\ a = \sqrt{3600}\)
\( \\ a = 60\)cm
De esta manera, el valor de a, o la distancia en línea recta que separa los segmentos paralelos, es 60cm.
Podemos comprobar el resultado anterior haciendo uso del mismo teorema de Pitágoras:
\( \\ 65^2 = 60^2 + 25^2\)
\( \\ 4225 = 3600 + 625\)
\( \\ 4225 = 4225\)
En la figura anexa se aprecia gráficamente lo anteriormente explicado.
Related Questions
Consider this function.
f(x) = |x – 4| + 6
If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and its inverse related?
Answers
The domain of the inverse function will be y ≥ 6, and the range of the inverse function will be x > 4.
When the domain is restricted to the portion of the graph with a positive slope, it means that only the values of x that result in a positive slope will be considered.
In the given function, f(x) = |x – 4| + 6, the portion of the graph with a positive slope occurs when x > 4. Therefore, the domain of the function is x > 4.
The range of the function can be determined by analyzing the behavior of the absolute value function. Since the expression inside the absolute value is x - 4, the minimum value the absolute value can be is 0 when x = 4.
As x increases, the value of the absolute value function increases as well. Thus, the range of the function is y ≥ 6, because the lowest value the function can take is 6 when x = 4.
Now, let's consider the inverse function. The inverse of the function swaps the roles of x and y. Therefore, the domain and range of the inverse function will be the range and domain of the original function, respectively.
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Exactly 50% of the area under the normal curve lies to the left of the mean.
True or False
Answers
The statement "Exactly 50% of the area under the normal curve lies to the left of the mean" is a true statement.
In a normal distribution, the mean, median, and mode all coincide, and the distribution is symmetrical.
The mean is the balance point of the distribution, with 50% of the area to the left and 50% to the right of it. Exactly 50% of the area under the normal curve lies to the left of the mean.
This implies that the distribution is symmetrical, and the mean, mode, and median are the same.
Therefore, the statement "Exactly 50% of the area under the normal curve lies to the left of the mean" is a true statement.
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What is the slope of this linear relationship?
O (0,0)
O 4/1 or 4
O 3/1 or 3
O -2/1 or -2
Pls help me
Answers
The conditions for a sampling distribution of a sample mean, when you know the true mean, are?
Answers
The conditions for a sampling distribution of a sample mean, when you know the true involve random sampling, independence, and a large enough sample size.
The conditions for a sampling distribution of a sample mean, when you know the true mean, are as follows:
1. Random Sampling:
The samples should be selected randomly from the population to ensure that they are representative of the entire population.
2. Independence:
Each sample should be independent of the others.
This means that the outcome of one sample should not influence the outcome of another sample.
3. Sample Size:
The sample size should be large enough to ensure that the sampling distribution approximates a normal distribution.
In general, a sample size greater than 30 is considered sufficient.
Random sampling is important because it helps to minimize bias and ensure that the sample is representative of the population.
Independence is necessary to avoid any potential confounding factors that may influence the results.
Lastly, a sufficiently large sample size is needed to satisfy the central limit theorem, which states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution.
These conditions are important to ensure the validity and reliability of the statistical analysis.
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In this exercise we consider sequences defined over the positive natural numbers 1, 2, 3, ... The n-th element in the sequence is denoted as an and therefore the elements in the sequence are a1, 22, 23, ... Each of the following sequences is defined using a closed formula that directly gives an for any positive natural number n. For each sequence, give an equivalent recursive definition, i.e., a basis step and an inductive step defining the n-th element in the sequence as a function of elements already in the sequence (either the previous one or some other element preceding an.) a) an = 4n - 2 b) an = 1+(-1)" c) an = n(n-1) d) an = n2 Suggestion: it may be convenient to first tabulate the values of the sequence for a few values of n, observe the pattern, and then guess the basis and inductive steps. Then, make sure that the basis and inductive steps give the same elements you tabulated. Note: to be fully correct, one should formally prove that the inductive definition of the sequences generate all and only the elements in the sequence. This would require some additional steps, but we omit them for brevity.
Answers
Recursive definition:
a) a1 = 2, an+1 = an + 4
b) a1 = 0, an+1 = 2 if n is odd, 0 if n is even
c) a1 = 0, an+1 = an + (2n+1)
d) a1 = 1, an+1 = an + 2n + 1
Sequence defined by an = 4n - 2:
Basis step:
a1 = 4(1) - 2 = 2
Inductive step:
an+1 = 4(n+1) - 2 = 4n + 2 = (4n - 2) + 4 = an + 4
Recursive definition:
a1 = 2, an+1 = an + 4
Sequence defined by an = \(1 + (-1)^n\):
Basis step:
a1 = \(1 + (-1)^1\) = 0
Inductive step:
If n is odd, an+1 = \(1 + (-1)^{(n+1)\)= 2;
If n is even, an+1 = \(1 + (-1)^{(n+1)\) = 0
Recursive definition:
a1 = 0, an+1 = 2 if n is odd, 0 if n is even
Sequence defined by an = n(n-1):
Basis step:
a1 = 0
Inductive step:
an+1 = (n+1)n = \(n^2 + n\) = an + (2n+1)
Recursive definition:
a1 = 0, an+1 = an + (2n+1)
Sequence defined by an = \(n^2\):
Basis step:
a1 = \(1^2\) = 1
Inductive step:
\(an+1 = (n+1)^2 = n^2 + 2n + 1 = an + 2n + 1\)
Recursive definition:
a1 = 1, an+1 = an + 2n + 1
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How many ways are there to split a dozen people into three teams, where one team has two people, and the other two teams have five people each?
Answers
There are 16,632 ways to split a dozen people into three teams, where one team has two people and the other two teams have five people each.
To split a dozen people into three teams, where one team has two people and the other two teams have five people each, we can use the concept of combinations.
First, we choose the two people for the team with two members. This can be done in C(12, 2) ways, where C(n, k) represents the number of combinations of n items taken k at a time..
After selecting the two people for the first team, we are left with 10 people. We then divide them into two groups of five for the other two teams. Since the order of the teams doesn't matter, we don't need to consider permutations.
Thus, we can calculate the total number of ways as:
C(12, 2) * C(10, 5) = 66 * 252 = 16,632
Therefore, there are 16,632 ways to split a dozen people into three teams, where one team has two people and the other two teams have five people each.
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What is the greatest common factor of 42, 30, and 45
Answers
Answer:
3
Step-by-step explanation:
Express the numbers as a product of their primes.
42 = 2 × 3 + 7
30 = 2 × 3 × 5
45 = 3 × 3 × 5
Identify the prime factors common to all 3 numbers.
common prime factor = 3 , thus
GCF = 3
Answer: 3
Step-by-step explanation: The factors of 30 are 1. 2. 3. 5. 6. 10, 15, 30
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 45 are 1, 3, 5, 9, 15, 45
As you can see they all share the factors of 1 and 3. Since 3 is the greatest number of the factors all of them share it is the greatest common factor.
From a point at the waters edge, a bridge arch 53 m away has an angle of elevation of 30, and the top of a yacht mast 14 m away has an angle of elevation of 12°. Can the yacht pass under the bridge?
Answers
Answer:
Yes
Step-by-step explanation:
We don't even have to do a calculation.
The arch of the bridge is at point C.
The top of the yacht's mast is at E.
Even though the yacht is much closer to the water's edge, its mast has a much smaller angle of elevation.
The yacht can easily pass under the bridge.
(a) A pyramid is made above a cuboid with measure 90 cm x 50 cm × 225 cm. If the height of the pyramid including cuboid is 240 cm, find the total volume.
Answers
The total volume of the solid = 1,035,000 cm³
What is the Volume of a Pyramid and a Cuboid?Volume of a Pyramid = 1/3(length)(width)(height).
Volume of a cuboid = (length)(width)(height).
Volume of the Pyramid = 1/3(length)(width)(height)
Volume of the Pyramid = 1/3(90)(50)(240 - 225)
Volume of the Pyramid = 1/3(90)(50)(15)
Volume of the Pyramid = 22,500 cm³
Volume of the cuboid = (length)(width)(height)
Volume of the cuboid = (90)(50)(225)
Volume of the cuboid = 1,012,500 cm³
The total volume of the solid = 22,500 + 1,012,500
The total volume of the solid = 1,035,000 cm³
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Simplify this expression
.
22z - 11z + 13
[?]z + [ ]
Answers
collect your like terms so 22-11=11
11+13
11z+13
Answer:
11z+ 13
Step-by-step explanation:
22z - 11z = 11z
11z+ 13
If 4a² + 9b² = 25 and ab = 8, find the value of (2a + 3b)²
Answers
Answer:
(2a + 3b)² = 121
Step-by-step explanation:
given 4a² + 9b² = 25 and ab = 8
(2a + 3b)² ← expand using FOIL
= 4a² + 6ab + 6ab + 9b²
= 4a² + 9b² + 12ab ← substitute given values from above
= 25 + 12(8)
= 25 + 96
= 121
If Radhika adds these two numbers and represents the sum on an abacus, and if the beads on the ten's place are 2 and the beads on the one's place are 5, how many beads will be there on the hundreds place?
Answers
Answer:
Explained below.
Step-by-step explanation:
A standard abacus is a traditional method used to perform basic mathematical calculations, such as addition, subtraction, multiplication and division.
There are 5 rods on a standard abacus.
The shape of the abacus has a series of vertical rods on which a number of beads are placed.
Each bead on a particular rod is considered as 1 unit, i.e. if there are three beads on a rod, the value of that rod is 3.
The last rod on an abacus is for the unit's place, the second last rod is for the ten's place, the third last rod is for the hundredth's place, the fourth last rod is for the thousandth's place and the fifth rod is for the ten thousandth's place.
1) 9 + 2h - 16
-7 + 2h
Answers
I need HELPPPPplsssssssssss
Answers
Answer:
I have attached a picture of the completed graph.
The equation is k = r + 7
Kyle will be 59 when Ryan is 52.
Explanation:
Kyle's age is always seven years higher than Ryan's age.
Therefore, k (Kyle's age) = r (Ryan's age) + 7 (Number of years different)
Scarlet and paula are on a vacation. They went to a store to buy some souvenirs for their friends back home. Scarlet bought three pairs of sunglasses and two shirts for $81 and paula bought one pair of sunglasses and five shirts for $105. What is the cost of one pair of sunglasses and one shirt?.
Answers
Cost of one pair of sunglasses and one shirt is $15 and $18.
How to solve word problems?
Understand the ProblemPlan the solutionSolve the Problem Check the solutionLet x be the sunglasses
y be the shirts
3x + 2y = $81 → 1
1x + 5y = $105 → 2
By solving this equations
eq 1 * 5 → 15x + 10y = $405
eq 2 * 2 → 2x + 10y = $210
13x = 195
x = 15
Substitute x=15 in eq 1
3(15) + 2y = $81
45 + 2y = $81
2y = 36
y = 18
If x= 15 then y =18
Cost of one pair of sunglasses and one shirt is $15 and $18.
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Find the circumference of the circle using C = pi•D
Answers
Answer:
The correct answer is the third choice, 14 pi.
The choice you selected is wrong.
Circumference = πD
= diameter is 14, so its 14π
12. When 3a2-7a+6 is subtracted from 4a²-3a +4, the result is
(1) a² +4a-2
(2) a²-10a-2
(3)-a²-4a+2
(4) 7a²-10a+10
Answers
Answer:
(1) a² +4a-2
Step-by-step explanation:
\(4a^2-3a\:+4\:-\:\left(3a^2-7a+6\right)\\\\= 4a^2-3a\:+4\:- 3a^2 + 7a -6\)
Grouping like terms
\((4a^2 -3a^2) +(-3a + 7a) +(4 - 6)\\\\= a^2 +4a - 2\)
what is the factored form of x^3 + 125?
Answers
Answer:
(X+5)(x^2-5x+25)
Step-by-step explanation:
brandon rolls a six sided die twenty times, and records the result in the table below. how many times did brandon roll above the average?
Answers
The expected value for each roll is \((1+2+3+4+5+6)/6 = 3.5.\)
The average of Brandon's rolls, we simply add up all the results and divide by the number of rolls:
\((1+2+2+3+4+6+2+1+5+6+1+6+2+6+4+6+2+6+4+6)/20 = 3.6\)
So the average of Brandon's rolls is 3.6.
Now we need to count how many times he rolled above the average. To do this, we simply count how many rolls were greater than 3.6:
4, 6, 5, 6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 4, 6
There were 18 rolls that were greater than 3.6, so Brandon rolled above the average 18 times.
In summary, Brandon rolled a six-sided die 20 times and recorded the results in a table. To find out how many times he rolled above the average, we first calculated the average roll to be 3.6. We then counted how many times he rolled above this value and found that he did so 18 times.
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The average age of a university student was found to be 24 with a standard
deviation of 2. What age group is within 2 standard deviations of the mean?
Answers
The age group that falls between two standard deviations is 20 to 28.
What is the standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the mean.
Given, The average age of a university student was found to be 24 with a standard deviation of 2.
Therefore, age group is within 2 standard deviations of the mean is,
24 + 2×2 = 24 + 4 = 28,
And 24 - 2×2 = 24 - 4 = 20.
So, The age group between 20 to 28 falls within 2 standard deviations of the mean.
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which set of integers is a pythagorean triple? question 1 options: 10, 24, 25 9, 12, 21 8, 15, 23 6, 8, 10
Answers
The set of integers is a Pythagorean triple are option (A) 10, 24, 25 and (D) 6, 8, 10
A Pythagorean triple is a set of three positive integers a, b, and c, such that a^2 + b^2 = c^2, which represents the sides of a right triangle.
Let's check each set of integers
A. 10^2 + 24^2 = 100 + 576 = 676 = 25^2. Therefore, (10, 24, 25) is a Pythagorean triple.
B. 9^2 + 12^2 = 81 + 144 = 225 = 15^2. Therefore, (9, 12, 15) is a Pythagorean triple. However, the set given is (9, 12, 21), which is not a Pythagorean triple.
C. 8^2 + 15^2 = 64 + 225 = 289 = 17^2. Therefore, (8, 15, 17) is a Pythagorean triple. However, the set given is (8, 15, 23), which is not a Pythagorean triple.
D. 6^2 + 8^2 = 36 + 64 = 100 = 10^2. Therefore, the set of integers (6, 8, 10) is a Pythagorean triple.
Therefore, the correct options are (A) 10, 24, 25 and (D) 6, 8, 10
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The given question is incomplete, the complete question is:
Which set of integers is a Pythagorean triple?
A.
10, 24, 25
B.
9, 12, 21
C.
8, 15, 23
D.
6, 8, 10
f(x) = -424 x + 4Find f(-7)
Answers
is 4.16 equal or less than 4.266
Answers
Answer:
less
Step-by-step explanation:
4.26 is .006 less then 4.266
a box with a square base and open top must have a volume of . we wish to find the dimensions of the box that minimize the amount of material used. first, find a formula for the surface area of the box in terms of only , the length of one side of the square base. simplify your formula as much as possible. next, find the derivative, .
Answers
The formula for the surface area of the box, in terms of the length of one side of the square base (s), is A = s^2 + 4s^2 = 5s^2.
The derivative of the surface area function with respect to s, denoted as dA/ds, gives us the rate of change of the surface area with respect to the length of one side of the base.
1. The surface area of the box consists of the area of the square base and the four equal sides. The area of the square base is s^2, and each side has a length of s. Therefore, the total surface area is given by A = s^2 + 4s^2 = 5s^2.
2. To find the derivative of the surface area function, we differentiate 5s^2 with respect to s using the power rule of differentiation. The power rule states that if we have a function f(x) = cx^n, then the derivative is f'(x) = cnx^(n-1).
Applying the power rule, we have dA/ds = d(5s^2)/ds = 10s.
3. The derivative, dA/ds = 10s, represents the rate of change of the surface area with respect to the length of one side of the square base. This means that for every unit increase in s, the surface area increases by 10s units.
The derivative does not provide information about minimizing the amount of material used. To find the dimensions of the box that minimize the amount of material used, we need to set up an optimization problem and solve for the critical points. This involves setting the derivative equal to zero and finding the values of s that satisfy this equation. However, since the problem statement does not provide a specific volume constraint or objective function, we cannot proceed with the optimization process.
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The function f(x)=−0697x 3
+16642x 2
−102407x+650015 approximates the number of canstrucion workers employed ha a certan state Find the locabion of all focel exiframai. Seled the conect answrer below and, if necessary in in any answer box(es) within your answer. A. The function tas no local minimums. and has local mavimums (has a local mavimurie) at upproximaley x a (Rownd is the neaseur ienth as needed Use a comma to separatu arrowers as needed) B. The funcion has no local maximums, and has focal minimums (thes a locial mhinum) at appecodimately x= (Round lo the nearest tenth as needed Use a camna le separale anwers as heeded) (Round io the nearest tenth ss needed Use a easmema to separale answers as needed) 0. The funcilan has no focal extremum
Previous question
Answers
The correct answer is: B. The function has no local maximums and has local minimums at approximately x = 5.8 and x = 28.8 (rounded to the nearest tenth).
To determine the location of the local extrema (maxima and minima) of the function f(x) = -0.697x^3 + 16642x^2 - 102407x + 650015, we need to find the critical points where the derivative of the function is equal to zero or does not exist. First, let's find the derivative of f(x) with respect to x: f'(x) = -2.091x^2 + 33284x - 102407. To find the critical points, we set f'(x) = 0 and solve for x: -2.091x^2 + 33284x - 102407 = 0. Using the quadratic formula, we can solve for x: x = (-b ± √(b^2 - 4ac)) / (2a). Plugging in the values a = -2.091, b = 33284, and c = -102407, we can calculate the values of x: x ≈ 5.779 or x ≈ 28.755. These are the potential locations of the local extrema.
To determine whether these points are maxima or minima, we can analyze the concavity of the function. Taking the second derivative, we have: f''(x) = -4.182x + 33284. Setting f''(x) = 0 and solving for x: -4.182x + 33284 = 0; x ≈ 7963.28. Since the second derivative is negative for x < 7963.28, we can conclude that x ≈ 5.779 corresponds to a local maximum, and x ≈ 28.755 corresponds to a local minimum. Therefore, the correct answer is: B. The function has no local maximums and has local minimums at approximately x = 5.8 and x = 28.8 (rounded to the nearest tenth).
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Zhen borrows $1,200. She borrows the money for 2 years and owes $180 in simple interest. What is the yearly
simple interest rate on Zhen's loan?
Answers
Zhen's yearly simple interest rate on the loan is 7.5%. She borrowed $1,200 and owes $180 in simple interest over 2 years.
We can use the formula for simple interest to find the yearly interest rate:
Simple Interest = Principal × Rate × Time
where Principal is the amount borrowed, Rate is the interest rate, and Time is the time period for which the interest is calculated.
In this problem, Zhen borrowed $1,200 and owes $180 in simple interest for a period of 2 years. We can plug in these values and solve for the interest rate:
$180 = $1,200 × Rate × 2
Dividing both sides by $2, we get:
$90 = $1,200 × Rate
Dividing both sides by $1,200, we get:
Rate = $90 / $1,200
Rate = 0.075
Therefore, the yearly simple interest rate on Zhen's loan is 0.075 or 7.5%.
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Pls help me on this
Answers
The angle-side connection theorem states that angle E in triangle DEF is equal to angle F.
what is triangle ?Since a triangle has three sides and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to a triangle that has vertices A, B, and C. When the three points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sides and three corners. The points where the three sides meet are known as the triangle's corners.
given
The length of every triangle side is proportional to the size of the angles that are directly across from them, according to the angle-side relationship theorem.
Thus,
Angle F = (61 + 58)/180 (sum of triangle)
F = 61 degree angle
Since mE = 61 degrees, F and E are therefore congruent to one another.
It follows that the sides that are perpendicular to each angle will also be parallel to one another.
The angle-side connection theorem states that angle E in triangle DEF is equal to angle F, which also implies that the sides that are opposite one other are congruent.
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Rounding to the nearest ten, which two
numbers round to 40?
48
36
41
32
49
Answers
Answer:
48 and 32
Step-by-step explanation:
both numbers get rounded by 8 going up and down rounding it to 40
On October 23, 2011, one U.S. dollar was worth 49.84 Indian rupees.
(a) On that date, how many rupees was 77.65 dollars worth?
Round your answer to the nearest hundredth of a rupee.
rupees
(b) On that date, how many dollars was 82.12 rupees worth?
Round your answer to the nearest hundredth of a dollar.
dollars
Answers
On that date, 77.65 dollars is worth 3,870.08 rupees.
On that date, 82.12 rupees is worth $1.65.
What is the worth of the currencies?Exchange rate is the rate at which one currency is exchanged for another currency.
In order to convert rupees to dollars, multiply the value of the rupees by the exchange rate:
value of the rupees x exchange rate
77.65 to rupees = 77.65 x 49.84 = 3,870.08 rupees
In order to convert dollars to rupees, divide the value o the dollars by the exchange rate:
value of the dollars / exchange rate
82.12 to dollars = 82.12 / 49.84 = $1.65
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10. m/FGH = -6 +26x, m/FGW = 3x + 5,
and m/WGH = 150°. Find x.
F
G
H
W
X = ?
Answers
Answer:
x = 7°
Step-by-step explanation:
Hello!
The sum of Angle FGW and Angle WGH is equal to Angle FGH.
Given the values provided, this means that: 3x + 5 + 150 = -6 + 26x
Solve for x3x + 5 + 150 = -6 + 26x3x + 155 = -6 + 26x155 = - 6 + 23x161 = 23x7 = xThe value of x is 7°.