To solve triangle ABC, we can use the Law of Cosines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C, respectively:
c^2 = a^2 + b^2 - 2ab*cos(C)
We are given B, a, and b, so we can solve for c as follows:
c^2 = 25^2 + 41^2 - 2(25)(41)cos(64)
c^2 = 625 + 1681 - 2135cos(64)
c^2 = 1829 - 2135*cos(64)
c^2 = 311.90
Taking the square root of both sides, we get:
c ≈ 17.7
So the length of side c is approximately 17.7 units.
To find the measures of angles A and C, we can use the Law of Sines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C, respectively:
a/sin(A) = b/sin(B) = c/sin(C)
We know a, b, and c, and we just solved for c, so we can use the Law of Sines to solve for angles A and C:
a/sin(A) = c/sin(C)
sin(A) = asin(C)/c
A = sin^{-1}(asin(C)/c)
A = sin^{-1}(25*sin(C)/17.7)
Similarly,
b/sin(B) = c/sin(C)
sin(B) = bsin(C)/c
B = sin^{-1}(bsin(C)/c)
B = sin^{-1}(41*sin(C)/17.7)
To find angle C, we can use the fact that the sum of the angles in a triangle is 180 degrees:
C = 180 - A - B
Using a calculator, we get:
A ≈ 41.6 degrees
B ≈ 74.1 degrees
C ≈ 64.3 degrees
Therefore, the measures of the angles in triangle ABC are approximately:
A ≈ 41.6 degrees
B = 64 degrees
C ≈ 64.3 degrees
And the lengths of the sides are approximately:
a = 25
b = 41
c ≈ 17.7
as a television executive, you have been given 24 shows to choose from to run during your prime time slots each week. if you have to choose 16 shows to run on your network, how many ways can you choose which shows to pick up?
As per the combination concept, there are 735,471 ways to choose 16 shows from a set of 24.
To find the number of ways to choose 16 shows from a set of 24, we can use the formula for combinations, which is:
ⁿCₓ = n! / x!(n-x)!
Where n is the total number of objects in the set (in this case, 24), and x is the number of objects we want to choose (in this case, 16). The exclamation mark (!) denotes the factorial function, which means multiplying the number by all positive integers less than itself.
Plugging in the numbers, we get:
²⁴C₁₆ = 24! / 16!(24-16)! = 735471
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Hannah put 2,364 pieces of candy into a bags with 57 pieces of candy each. How many full bags did she make?
2,364 ÷ 57 ≈ 41. Therefore, Hannah made 41 full bags of candy.
To solve this problem, we use integer division to find the number of full bags Hannah made. We divide the total number of candy pieces by the number of pieces in each bag and take the integer part of the result. This is because we are only interested in the number of full bags, not partial bags. In this case, we have 2,364 pieces of candy and each bag holds 57 pieces, so 2,364 ÷ 57 ≈ 41. This means that Hannah made 41 full bags of candy.
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DUE TOMORROW PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!!!
Here is the graph of a function describing the relationship between the height y, in feet, of the tip of a windmill blade and the angle of rotation Θ made by the blade. Describe the windmill.
However, it is important to note that without additional information about the function and the windmill itself, further conclusions about its design and performance cannot be made.
Hi! I'd be happy to help you describe the windmill based on the provided graph.The graph of the function represents the relationship between the height (y) of the tip of a windmill blade and the angle of rotation (Θ) made by the blade. This function is periodic, indicating that the windmill blade follows a repetitive motion as it rotates.
The height of the blade tip varies sinusoidally with respect to the angle of rotation, suggesting that the windmill has a circular or rotational motion. The amplitude of the function gives the length of the windmill blade, while the period of the function represents a full rotation (360 degrees) of the windmill blade.
In summary, the windmill has a rotational motion, with the height of the blade tip following a sinusoidal pattern. The length of the windmill blade and the time it takes to complete a full rotation can be determined by analyzing the amplitude and period of the function.
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alexis puts dimes and quarters aside for the parking meter. she has a total of 20 coins and they are worth $3.80. how many quarters does alexis have?
Alexis has 12 quarters and 8 dimes.
Let's use d to represent the number of dimes and q to represent the number of quarters. We know that Alexis has a total of 20 coins, so d + q = 20.
We also know that the value of these coins is $3.80. Since dimes are worth $0.10 and quarters are worth $0.25, we can write an equation for the total value in cents:
10d + 25q = 380
To make things easier, let's divide both sides of the equation by 5:
2d + 5q = 76
Now we can use the first equation to solve for d in terms of q:
d + q = 20
d = 20 - q
Substituting this into the second equation gives:
2(20 - q) + 5q = 76
Expanding the parentheses and simplifying, we get:
40 - 2q + 5q = 76
3q = 36
q = 12
Therefore, Alexis has 12 quarters. We can check this by plugging q back into the first equation to find that she has 8 dimes as well:
d + q = 20
d + 12 = 20
d = 8
The total value of 12 quarters and 8 dimes is:
12 quarters x $0.25 per quarter + 8 dimes x $0.10 per dime = $3.00 + $0.80 = $3.80
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WILL GIVE BRIANLIAT TO BEST ABWWER
The graph of an exponential of the form y = ab contains the points (2, 60) and (4, 960). What are the values of a and b
Answer:
(15/4)4^x
Step-by-step explanation:
Substituting the x and y values of the first point, we get:
y = ab
60 = ab^(2)
Substituting the x and y values of the second point, we get:
y = ab
960 = ab^(4)
Now we can solve for a and b by eliminating one of the variables. One way to do this is to divide the second equation by the first equation:
960/60 = (ab^(4))/(ab^(2))
16 = b^(2)
Taking the square root of both sides, we get:
b = ±4
Since an exponential function can only have positive values for b, we choose b = 4. Now we can solve for a by substituting b = 4 into one of the original equations:
60 = a(4^(2))
60 = 16a
a = 60/16
a = 15/4
Therefore, the values of a and b are a = 15/4 and b = 4, and the exponential function is y = (15/4)4^x.
Find the missing angle to the nearest degree.
What is the area of this figure? Do not include a label. Number only.
Therefore, the area of the polygon is 24 square units.
What is coordinate?In mathematics, a coordinate is a set of numbers or values that represent the position or location of a point or an object in space. Typically, coordinates are used to describe points in two-dimensional (2D) or three-dimensional (3D) space.
In 2D space, coordinates are usually represented as pairs of numbers (x, y), where the first number (x) represents the horizontal distance of the point from the origin, and the second number (y) represents the vertical distance of the point from the origin.
by the question.
To find the area of the polygon defined by the given coordinates, we can use the Shoelace Formula:
[tex]Area = 1/2 * |(x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1)|[/tex]
where?[tex](x_{1} ,y_1), (x_2,y_2), ..., (x_n,y_n)[/tex] are the coordinates of the vertices listed in order.
Plugging in the given coordinates in order, we get:
[tex]Area = 1/2 * |(-12 + -5(-3) + (-5)(-5) + (-2)(-2) + 22 + 4(-2)) - (4*(-5) + (-5)(-5) + (-3)(-2) + (-2)2 + 2(-1) + 2*(-5))|= 1/2 * |-2 - 125 + 25 - 4 + 8 + 8 + 20 + 10 + 2 + 10|= 1/2 * |-48|=24[/tex]
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if the cycle time is 2 minutes/customer then how many customers are served per hour? multiple choice question. 15 20 30 60
If the cycle time is 2 minutes per customer, 30 customers can be served per hour.
The given cycle time is 2 minutes per customer. To calculate how many customers can be served per hour, we need to calculate the number of minutes in an hour as follows: 60 minutes = 1 hour.
The time taken for each customer is 2 minutes. Therefore, the number of customers that can be served per hour can be calculated as follows:
Number of customers per hour = (60 minutes/hour) ÷ (2 minutes/customer)
Number of customers per hour = 30 customers.
Therefore, the number of customers that can be served per hour is 30, according to the given cycle time of 2 minutes per customer.
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I've been waiting to order your cupcakes all day!
I'll have 4 Nom-Nom-Nom cupcakes -- that's
80% of my order. The rest of the order are Wow.
Using fraction, the total number of cupcakes is obtained to be 5.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
If 4 cupcakes represent 80% of the order, then we can use proportional reasoning to find the total number of cupcakes.
Specifically, if x is the total number of cupcakes, then we can write -
4/x = 80/100
where the left-hand side represents the fraction of the order that is Nom-Nom-Nom cupcakes, and the right-hand side represents the percentage of the order that is Nom-Nom-Nom cupcakes.
Solving for x, we get -
x = 4 / (80/100) = 5
So the total number of cupcakes is 5. Since 4 of them are Nom-Nom-Nom cupcakes, the remaining 1 cupcake must be a Wow cupcake.
Therefore, in total there are 5 cupcakes.
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I've been waiting to order your cupcakes all day! I'll have 4 Nom-Nom-Nom cupcakes -- that's 80% of my order. The rest of the order are Wow.
Find the total number of cupcakes.
rotate 270 degrees…what are the coordinates of B
PLS HELP
Answer:
8;-2
Step-by-step explanation:
8 is the x axis and -2 is the y axis
Answer:
Step-by-step explanation:
What are the integer solutions to the inequality below?
−
1
≤
x
≤
3
Answer:
i don't know i haven't done integers in a long time
Step-by-step explanation:
8. A rectangular room is shown.
4x - 1
--x
2
3x + 6
A. (4x-1)-2x
B. (3x2+6) + (4x - 1) + x
C. (4-1)-(3x² + 6)
(3x2+6) + 2(4x - 1) + 2x
Door
X
4x - 1
Port A: Which of the following expressions represents the perimeter of the room without th
door?
(3x²+6)+(x-1)x2+²x = (3x²+6) + 2(9x-=
Port B: What is the perimeter of the room without the door in simplest form? Show you
work.
I only need part b
Answer: 14x + 10
Step-by-step explanation: The perimeter of the room without the door can be found by adding up the lengths of all four sides:
Perimeter = 2(4x-1) + 2(3x+6)
Simplifying and combining like terms, we get:
Perimeter = 14x + 10
Therefore, the perimeter of the room without the door in simplest form is 14x + 10.
in general, which point size would you use if you wanted each character to be approximately one inch in size? a.) 1 pt b.) 72 pts c.) 24 pts d.) 36 pts
If you want each character to be approximately one inch in size, you would use a point size of 72 pts.
Point size is a unit of measurement used to determine the size of typefaces. It represents the height of the characters in a font. One point is equal to 1/72 of an inch, which means there are 72 points in one inch.
Therefore, if you want each character to be approximately one inch in size, you would need to use a font size of 72 points. This would ensure that the characters are roughly one inch tall, assuming that the font is designed to be proportional and not condensed or expanded.
Choosing a smaller point size, such as 1 pt or 24 pts, would result in characters that are much smaller than one inch. Choosing a larger point size, such as 36 pts, would result in characters that are larger than one inch.
Therefore the correct answer is option b.) 72 pts.
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A particle of mass 1. 2 kg is moving with speed of 8 ms inn a straight line on a horizontal table. A resistance force is app. Lied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, ao that F=0,3v^2
The speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2[/tex], or 19.2 N.
A particle of mass 1.2 kg is moving with a speed of 8 m/s in a straight line on a horizontal table. A resistance force is applied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, such that [tex]F=0.3v^2[/tex]
The force of resistance is an opposing force that acts to reduce the speed of the particle. As the particle moves faster, the resistance force increases. The force is proportional to the square of the speed, meaning that if the speed doubles, the force is multiplied by four. The force is also in the same direction as the motion, meaning that it will reduce the speed of the particle.
The equation for the force of resistance is [tex]F=0.3v^2[/tex], where v is the speed of the particle. Therefore, if the speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2,[/tex] or 19.2 N. This means that the force of resistance acting on the particle is 19.2 N.
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what is the measure of x
The value of angle x in the given figure is 79°.
An angle meaning is what?The highest and lοwest walls οf a skew are used tο split the curved lines that make up its ends using Cartesian measurements. A cοllisiοn between twο pοles at an intersectiοn is a pοtential. Angle is anοther οutcοme οf twο things interacting. They resemble dihedral fοrms the mοst clοsely. A twο-dimensiοnal curve can be created by placing twο line beams in variοus cοnfiguratiοns between their ends.
In ΔBFG, ∠FBG = 46°
So according to angle sum property
46° + ∠BFG + BGF = 180°
Here ΔBFG is an isosceles triangle
46° + 2∠BFG = 180°
2∠BFG = 180° - 46°
2∠BFG = 134
∠BFG = 134/2
∠BFG = 67° = ∠BGF
Using Vertically opposite angle
∠AFJ = 67°
With that in mind ∠BFA = ∠JFG
2∠JFG + 2∠AFJ = 360°
2∠JFG = 360° - 2∠AFJ
2∠JFG = 360° - 2(67)
2∠JFG = 360° - 134
2∠JFG = 226
∠JFG = 226/2
∠JFG = 113°
In ΔFDC, ∠JFG + ∠JDI + ∠HCG = 180°
113° + 33° + ∠HCG = 180°
∠HCG = 180° - (113° + 33°)
∠HCG = 34°
Also, ∠HGC = ∠BGF = 67°
Now, In ΔCGH, ∠HGC + ∠HCG + x = 180°
67° + 34° + x = 180°
x = 180° - (67° + 34°)
x = 79°
Thus, the value of angle x in the given figure is 79°.
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Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle B?
The following statement should determine if x is not greater than 20. Explain what is wrong with it and write the correction. if (!x > 20)
The student's original statement has an issue in the way the "not" operator is used. The "not" operator (!) is negating the entire expression, including the variable 'x', rather than just the inequality. This leads to incorrect evaluation.
To correctly determine if x is not greater than 20, you should use the "less than or equal to" (<=) operator instead. Here is the corrected statement:
if (x <= 20)
This statement will be true if x is less than or equal to 20, which is the intended condition.
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In terms of the water lily population change, the value 3.915 represents: the value 1.106 represents:
The value 1.106 represents the slope of the regression line or the rate of change of y with respect to x.
In the given regression equation y = 3.915(1.106)x:
The value 3.915 represents the y-intercept or the predicted value of y when x=0. In the context of the water lily population change, this value could represent the initial population of water lilies or the minimum population that can sustain in the given environment.The value 1.106 represents the slope of the regression line or the rate of change of y with respect to x. In the context of the water lily population change, this value could represent the rate at which the water lily population increases or decreases with respect to some independent variable x, such as time or environmental factors.Learn more about slope here https://brainly.com/question/19131126
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help please image attached
The first inequality -4 ≤ x ≤ 3 represents the values of x that fall between the two vertical lines, while the second inequality 1 ≤ y ≤ 6 represents the values of y that fall between the two horizontal lines.
Describe Inequality?An inequality is a mathematical statement that compares two quantities or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).
Inequalities can involve variables or constants, and can be expressed in one variable or multiple variables. The solution to an inequality is the set of values that satisfy the inequality.
For example, the inequality 2x + 3 > 7 is true for values of x that are greater than 2, since if we substitute x = 2, we get 2(2) + 3 = 7, which is not greater than 7. On the other hand, if we substitute x = 3, we get 2(3) + 3 = 9, which is greater than 7, so the inequality is true for x > 2.
Inequalities have many applications in mathematics and other fields, such as economics, physics, and engineering. They are used to represent constraints in optimization problems, to model relationships between variables, and to describe ranges of possible values for a quantity or variable.
To determine the double inequalities that define the shaded region, we need to find the equations of the two boundary lines that form the sides of the shaded region.
The two vertical lines are x=-4 and x=3. The two horizontal lines are y=1 and y=6.
The shaded region is enclosed by these four lines, so the double inequalities that define it are:
-4 ≤ x ≤ 3 and 1 ≤ y ≤ 6
The first inequality -4 ≤ x ≤ 3 represents the values of x that fall between the two vertical lines, while the second inequality 1 ≤ y ≤ 6 represents the values of y that fall between the two horizontal lines. Together, they define the rectangular shaded region with vertices (-4,1), (-4,6), (3,6), and (3,1).
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A circle with radius of 2 cm sits inside a circle with of 4 cm
Answer:
Diameter is equal to twice the radius. Given, radius is 4 cm. Diameter = 2(4) = 8 cm. Hence, diameter of the circle with radius as 4 cm is 8 cm.
Step-by-step explanation:
please
give brianliest
Answer: Area = 0
Step-by-step explanation:
((2*2)*3.14)-(4*3.14) = 0
7(x+4)= -21 i need help pls help me its hard 8th grade btw
The given equation is 7(x+4) = -21 . Therefore, the value of x is 7
In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal. An equation is made up of two expressions joined by an equal sign ("="). Expressions for both sides of the equals sign are called the "left side" and the "right side" of the equation. Many times the right side of the equation is assumed to be zero. Assuming this does not reduce generality, this can be achieved by subtracting the right side from both sides.
According to the Question:
The given equation is:
7(x+4)= -21
⇒ 7x + 28 = -21
⇒ 7x = -49
⇒ x = 7
Complete Question:
Solve the Equation : 7(x+4)= -21
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Jaxon invested $710 in an account paying an interest rate of 8\tfrac{7}{8}8 8 7 % compounded quarterly. Jason invested $710 in an account paying an interest rate of 8\tfrac{5}{8}8 8 5 % compounded continuously. After 8 years, how much more money would Jaxon have in his account than Jason, to the nearest dollar?
Answer:
I attached your answer along with an explanation
Step-by-step explanation:
Please Like me follow me and Give me Crown for more help. :)
For the given figure, can you conclude mlln? Explain.
if a random sample of size 555 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 5% ? round your answer to four decimal places.
The probability that the proportion of persons with a retirement account in a random sample of size 555 differs from the population proportion by less than 5% is approximately 0.8327.
We need to make some assumptions about the population proportion of persons with a retirement account and the standard deviation of the sampling distribution of sample proportions. Let's assume that the population proportion is p = 0.5 (i.e., half of the population has a retirement account) and that the standard deviation of the sampling distribution is given by:
σ = sqrt((p*(1-p))/n)
where n is the sample size.
Substituting the values given in the question, we have:
σ = sqrt((0.5*(1-0.5))/555) = 0.0258
To find the probability that the sample proportion differs from the population proportion by less than 5%, we need to find the probability that the absolute difference between the sample proportion and the population proportion is less than 0.05. This can be written as:
P(|p_hat - p| < 0.05)
where p_hat is the sample proportion.
We can standardize this expression by subtracting the population proportion from both sides and dividing by the standard deviation:
P(|p_hat - p|/σ < 0.05/σ)
P(-0.97 < Z < 0.97)
where Z is a standard normal variable. We can find this probability using a standard normal table or a calculator:
P(-0.97 < Z < 0.97) = 0.8327
Rounding to four decimal places, we have:
P(|p_hat - p| < 0.05) = 0.8327
Therefore, the probability that the proportion of persons with a retirement account in a random sample of size 555 differs from the population proportion by less than 5% is approximately 0.8327.
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Sarah has 43 bananas, she gives Steve 10. How many bananas does she have left?
Answer:
33
Step-by-step explanation:
43-10=33 sarah has 33 bananas ledt
A plane ticket to Barcelona cost £175 the price decreases by 6% work out the new price of the plane ticket
Answer:
£164.50
Step-by-step explanation:
If the discount is 6%, then the discounted price is 94% of the original price.
95% of £175 = 0.94 × £175 = £164.50
If the width and length of a rectangle is 3 by 8 what is the width and length actually if the width is 10. 5
The new length of the rectangle is approximately 2.29 units. We use the formula for the area of a rectangle to solve for the new length, given the new width.
If the width and length of a rectangle are 3 and 8, respectively, and the width is increased to 10.5, we can calculate the new length of the rectangle using the formula for the area of a rectangle, which is length multiplied by width.
The original area of the rectangle is 3 x 8 = 24 square units. If we increase the width to 10.5, the new area of the rectangle becomes: 10.5 x length = 24 Solving for the length, we get: length = 24/10.5 = 2.29 (rounded to two decimal places)
It's important to note that changing one dimension of a rectangle can affect the other dimension, especially if we want to maintain the same area.
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Find the volume of a right circular cone that has a height of 20 ft and a base with a radius of 18 ft. Round your answer to the nearest tenth of a cubic foot
Answer:
The answer should be 20,365.714 but I am not sure
Step-by-step explanation:
In ΔPQR, r = 7.8 cm, q = 6 cm and ∠Q=30°. Find all possible values of ∠R, to the nearest 10th of a degree.
The twο pοssible values οf ∠R tο the nearest 10th οf a degree are 33.6° and 326.4°.
What is a triangle?A triangle is a clοsed twο-dimensiοnal geοmetric shape with three straight sides and three angles. It is the simplest pοlygοn, which is a flat shape cοnsisting οf straight lines.
We can use the Law οf Cοsines tο find the length οf side QR:
[tex]c^2 = a^2 + b^2 - 2ab[/tex] cοs(C)
where c is the length οf side QR, a is the length οf side PQ (which is unknοwn), b is the length οf side PR (which is 7.8 cm), and C is the angle οppοsite side c (which is 30°). Substituting the given values, we get:
[tex]QR^2 = PQ^2 + 7.8^2 - 2(PQ)(7.8)cos(30^\circ )[/tex]
[tex]QR^2 = PQ^2 + 60.84 - 7.8PQ[/tex]
Next, we can use the Law οf Sines tο relate the length οf side PQ tο the angle οppοsite it, ∠P:
PQ/sin(30°) = QR/sin(P)
PQ = QR(sin(30°)/sin(P))
Substituting this expressiοn fοr PQ intο the equatiοn fοr [tex]QR^2[/tex] abοve, we get:
[tex]QR^2 = [QR(sin(30^\circ)/sin(P))]^2 + 60.84 - 7.8[QR(sin(30^\circ)/sin(P))][/tex]
Simplifying and rearranging, we get a quadratic equatiοn in terms οf QR:
[tex]QR^2 - 3.9QR + 28.99 = 0[/tex]
Using the quadratic fοrmula, we find that:
QR ≈ 7.466 cm οr QR ≈ 3.866 cm
Since we knοw that QR < PQ + PR = 6 + 7.8 = 13.8, the οnly valid sοlutiοn is QR ≈ 7.466 cm. Therefοre, we have:
[tex]cos(R) = (PQ^2 + QR^2 - PR^2)/(2PQQR)[/tex]
[tex]cos(R) = (PQ^2 + 7.466^2 - 7.8^2)/(2PQ(7.466))[/tex]
[tex]cos(R) = (PQ^2 - 4.928)/[2PQ(7.466)][/tex]
Since cοs(R) ≤ 1, we have:
[tex]PQ^2 - 4.928 ≤ 2PQ(7.466)[/tex]
Sοlving fοr PQ using the quadratic fοrmula, we get:
PQ ≤ 5.474 cm οr PQ ≥ 20.032 cm
Since PQ < PR, the οnly valid sοlutiοn is:
PQ ≈ 5.474 cm
Nοw we can use the Law οf Cοsines again tο find ∠R:
[tex]cos(R) = (PQ^2 + PR^2 - QR^2)/(2PQPR)[/tex]
[tex]cos(R) = (5.474^2 + 7.8^2 - 7.466^2)/(2(5.474)(7.8))[/tex]
cοs(R) ≈ 0.828
R ≈ 33.6° οr R ≈ 326.4°
Therefοre, the twο pοssible values οf ∠R tο the nearest 10th οf a degree are 33.6° and 326.4°.
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Help Please
m-6=50
i need to find the value of m
please urgent
Answer:
m = 50 + 6
m= 56
lol easy ques
This one is easy. All you have to do is add 6 to both sides to get the value of m
m-6=50
m=50+6
m=56