Answers
The length of the X using law of cosine is 34.30yd.
What is cosine?
In a right angled triangle, the cosine of an angle is:
The length of the adjacent side divided by the length of the hypotenuse.
The abbreviation is cos
cos(θ) = adjacent / hypotenuse
Consider that;
[tex]X = \sqrt{a^2+b^2-2abcosX}[/tex] (using law of cosine)
[tex]X = \sqrt{21^2+18^2-2\times 21\times 18\times cos(123 ^\circ)}[/tex]
[tex]X = \sqrt{441+324-756\times (-0.5446)}[/tex]
X = 34.30 yd
If A, B, and C are the measures of the angles of an oblique triangle, and a, b, and c are the lengths of the sides opposite the corresponding angles, then the square of a side of the triangle is equal to the sum of the squares of the other two sides minus twice the product of the two sides and the cosine of the included angle.
[tex]c^2 = a^2+ b^2- 2abcos C[/tex]
We have to the value of X which is present on the side c,
so, from the above formula we modified for the X,
and the formula become,
[tex]X = \sqrt{a^2+b^2-2abcosX}[/tex](using law of cosine)
rest of the solutions are only calculation which is elaborated above which provide us the value of X = 34.30 yd.
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Related Questions
Can someone teach me how to do this?
Answers
sin^-1(-1/2) enter directly into a calculator and you'll find your answer
Shift+sin then Fraction
Find the length of each side of triangle XYZ, then classify the triangle by its side: X(7,6), Y(5,1), Z(9,1) show work, please!!!
Answers
Answer:
(9,1), Z(5,1)
Step-by-step explanation:
A rectangle plot of land has a width of 3x+5 feet, and a length of 2x-1 feet.
A- express the area of the plot as a function of x.
B- express the perimeter of the plot as a function of x
Answers
A- the area of the plot as a function of x. is 6 x^2 +10x-5
B- the perimeter of the plot as a function of x is 10x+8
A rectangle plot of land has a width of 3x+5 feet,
and a length of 2x-1 feet.
A) the area of the plot as a function of x is given by
A= length * width
= ( 2x-1) * ( 3x+5)
=6 x^2 +10x-5
B) the perimeter of the plot as a function of x
P = 2( l+ W)
= 2 (( 2x-1) +( 3x+5))
= 2( 5x +4)
= 10x +8
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Hey I would rlly appreciate if someone can help IVE been stuck on this and pls make sure to find measure BCD
Answers
Answer:
140
Step-by-step explanation:
2x+5x+40=180
7x+40=180
7x=140
x=20
5x+40=BCD
5(20)+40
100+40
140
Jose has $580 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax. He buys a new bicycle for $284.52. He buys 4 bicycle reflectors for $15.65 each and a pair of bike gloves for $11.31. He plans to spend some or all of the money he has left to buy new biking outfits for $31.95 each. What is the greatest number of outfits Jose can buy with the money that's left over?
Answers
The greatest number of outfits Jose can buy is 6
How to determine the greatest number of outfits he can buy?The given parameters are:
Budget = $580New bicycle = $284.524 bicycle reflectors = $15.65 eachPair of a bike gloves = $11.31New biking outfits = $31.95 each.Let the number of new biking outfits be x
So, we have
New bicycle + 4 * price of bicycle reflectors + Pair of a bike gloves + New biking outfits ≤ Budget
This gives
284.52 + 4 * 15.65 + 11.31 + 31.95x ≤ 580
This gives
358.43 + 31.95x ≤ 580
Solve the inequality
31.95x ≤ 221.57
Divide
x ≤ 6.93
This gives
x ≤ 6
Hence, the greatest number of outfits is 6
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solve this equation using the most direct method:
3x(x+6)=-10
Enter your solution in the exact, most simplified form. If there are two solutions, write the answer using (+-) symbol
Answers
The solution set for the given quadratic equation is (-0.62, -5.38).
The given equation is 3x(x+6)=-10.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, 3x(x+6)=-10
⇒ 3x²+18x=-10
⇒ 3x²+18x+10=0
By comparing 3x²+18x+10=0 with ax²+bx+c=0, we get
a=3, b=18 and c=10
Using quadratic formula x = [-b ± √(b² - 4ac)]/2a
= [-18 ± √(18² - 4×3×10)]/2×3
= [-18 ± √(324 - 120)]/6
= [-18 ± √(204)]/6
= [-18 ± √(204)]/6
= [-18 ± 14.28]/6
= [-18 + 14.28]/6 and [-18 - 14.28]/6
= -0.62 and -5.38
Hence, the solution set for the given quadratic equation is (-0.62, -5.38).
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3/8 - 5/6 Please put a step by step
Answers
Answer:
(-11/24)
Step-by-step explanation:
3 5
------- - -------
8 6
3(3) 5(4)
------- - -------
8(3) 6(4)
9 20 - 11
------- - ------- = -------
24 24 24
I hope this helps!
what is 5(-4)+(-6)+2(-2)
Answers
Answer:
-30
Step-by-step explanation:
Distribute
5 x -4= -20 2 x -2= -4
-20+(-6)+(-4)
Add together
-20 + -6= -26
-26 + (-4)
Add again
-26 + -4= -30
-30
an employee group requires 6 people be chosen for a committee from a group of 12 employees. determine the following probabilities of randomly drawn committee of 6 employees. write your answers as percents rounded to 4 decimal places. the employee group has 9 women and 3 men. what is the probability that 3 of the people chosen for the committee are women and 3 people chosen for the committee are men? % the committee requires that exactly 2 people from human resources serve on the committee. there are 4 people in human resources. what is the probability that exactly 2 of the people chosen for the committee are from human resources? %
Answers
The probability of choosing 3 men and 3 women to form the committee is 0.4329 and the probability to select exactly 2 people from the human resources is 0.4545.
It is given that there are 12 employees.
The number of male employees is 6
number of female employees is 6
A committee of 6 is to be formed. We need to find the probability that out of 6, 3 are male and 3 are female.
Let A be the event of having 3 men and 3 women on the committee
The total number of ways to choose 6 people is
¹²C₆
Probability = number of favorable outcomes / total number of outcomes
n(A) = ⁶C₃ X ⁶C₃
Therefore,
P(A) = (⁶C₃ X ⁶C₃) / ¹²C₆
= (20 X 20) / 924
= 400/924
= 0.4329
It is given that the number of employees in human resources from the group is 4
Let B be the event to choose exactly 2 employees from the human resource
n(B) = ⁴C₂ X ⁸C₄
P(B) = ⁴C₂ X ⁸C₄ / ¹²C₆
= 6 X 70 / 924
= 420 / 924
= 0.4545
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you and your friend were studying, and you left your cell phone either in the computer lab or in the cafe (these were the only two places you visited). you think that with probability 0.4 it was left in the computer lab, because you always take it out of your backpack there, otherwise, it was left in the cafe. if you left the phone in the computer lab, the probability that someone stole it is 0.3. in the cafe, the probability that someone stole it is twice that of
Answers
There is a 0.48 percent chance that your phone will not be found and will therefore be stolen.
Define the law of total probability?A fundamental statistician's rule governing conditional and marginal probabilities is known as the Total Probability Rule/Law of Total Probability. According to the rule, if the chance of an occurrence is uncertain, it can be derived using the probabilities of numerous different instances that have already transpired.Let P(S|L) represent the likelihood that your phone was stolen if you left it in the computer lab.
Let P(S|C) indicate the likelihood that your phone was stolen if you left it at the cafe.
The likelihood that your phone will be stolen can be determined using law of total probability by:
P(S) = P(S|L)P(L) + P(S|C)P(C)
= 0.3 * 0.4 + 0.6 * 0.6
= 0.12 + 0.36
P(S) = 0.48
Therefore, there is a 0.48 percent chance that you won't find your phone and that it was stolen.
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one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches. what is the area of the parallelogram? express your answer in simplest radical form.
Answers
The area of parallelogram with "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches" is 60√3 inch².
What is parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus. A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a type of polygon with four sides (also known as a quadrilateral) in which each parallel pair of sides is the same length.
Here,
A parallelogram has adjacent angles that add up to 180 degrees.
Since one angle of parallelogram is 120°.
240+2x=360
2x=120
x=60
The other will be 60°
The area of parallelogram= lh
l=15 inch
h=b(sin 60°)
=8*√3/2
h=4√3 inch
area of parallelogram= 15*4√3
= 60√3 inch²
The parallelogram's area is 60√3 inch² when "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches."
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over the past month, george the tortoise has been flipped onto his back 146 times by angie the tortoise. george has been able to get back on his feet without help 3 times. what's the empirical probability that george will be able to get back on his feet without help the next time angie flips him over?
Answers
The empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.
Describe the term empirical probability?The likelihood of an event is closely related to an empirical probability, also described as an experimental probability. Empirical probability bases its evaluation of the likelihood that a specific result will recur on the number of instances of that outcome together within sample set.For the given question.
We include George the turtle, who Angie has successfully turned over 146 times the turtle.3 times George has used the assistance to get back up on his feet. The empirical probability is really what we seek.Therefore, it follows that we are doing an experimental calculation based on the observation whether George will indeed be able to stand again the following time.
empirical probability = 3/146
Thus, the empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.
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Don't understand problem. Need help solving problem.
Answers
Answer:
x = -12
Step-by-step explanation:
x/-3 + 5 - 5 = 9 - 5
x/-3 = 4
x/-3 (-3) = 4(-3)
x = -12
PLEASE HEIP MEE
What sequence equation would represent this graph?
Answers
The equation would represents the graph is y = 20000 + 1750x and the graph has been plotted
From the table
The investment in 1 year = $20000
The investment in 2 year = $21750
The investment in 3 year = $23500
The investment in 4 year = $25250
The investment in 5 year = $27000
Then the equation will be
y = 20000 + 1750x
Where y is the investment in dollars
x is the number of years
Draw the graph as number of years in x axis and the amount of investment in y axis
Hence, the equation would represents the graph is y = 20000 + 1750x and the graph has been plotted
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Find the length of the missing segment.
Answers
In accordance to Thales's theorem, the geometric system has a missing side length of 15 units.
How to determine missing lengths in geometric systems by ratiosIn this problem we find a geometric system formed by two proportional trapezoids. This similarity and proportionality is defined by Thales's theorem, which states that a triangle segmented by several lines parallel to each other and parallel to the base of the figure creates triangles and quadrilaterals proportional to each other.
Then, two figures of the given trapezoids are represented by side proportionality ratios. Then, the proportionality ratio is described and its variable x is cleared within by algebra properties:
First, define the proportionality ratio associated to the geometric system:
4 / (10 + 4) = (21 - x) / 21
Second, simplify the equation and clear the variable x:
4 / 14 = 1 - x / 21
2 / 7 = 1 - x / 21
42 / 7 = 21 - x
6 = 21 - x
x = 21 - 6
x = 15
The missing length is equal to 15 units.
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Clay asks Donte to play the following number puzzle:
Pick a number
Add 4
Multiply by 2
Subtract 3
Add your original number
Donte’s final result is 32. Which number did he start with?
Group of answer choices below
A. 7
B. 9
C. 4
D. 23
E. 0
Answers
13 x 2 = 26.
26-3 =23
23+9= 32
How do I know where to shade on this graph?
Answers
y≤-3x+4 has lesser than or equal to symbol so we shade the below line.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Relationship between two expressions or values that are not equal to each other is called 'inequality.
y≤-3x+4 is the given inequality.
The sign of the inequality will let you know which half-plane to shade. If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.
In the inequality we have lesser than or equal to symbol so we shade the below line.
Hence, y≤-3x+4 has lesser than or equal to symbol so we shade the below line.
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what is the quotient of 84/0.729
Answers
Answer:
115.226337449
Step-by-step explanation:
84/0.729= 115.226337449
And thank you and your welcome
Answer: the quotient of 84/0.729 is 115.226337
A seasoning blend is 4% onion powder, by mass? How much pure onion powder should they include in a 72g bottle to make the final blend have 20% onion powder.
Answers
Answer: 14.4g of onion powder
Step-by-step explanation: To get 20% of a number, you need to divide the original amount by 5, so 72 ÷5 is 14.4g
They should include 14.4 grams of onion powder in a bottle.
Given that, a seasoning blend is 4% onion powder, by mass.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let x be the seasoning blend.
Now, 4% of 72=20% of x
⇒ 0.04×72=0.2×x
⇒ 0.2x=2.88
⇒ x=2.88/0.2
⇒ x=14.4 g
Hence, they should include 14.4 grams of onion powder in a bottle.
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a right cylindrical tank is full of water. the tank has a radius of 10 inches. how fast is the height of water in the tank changing if the water is being drained at 34 cubic inches per hour?
Answers
The answer is 3/25π m/h.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:
v=πr²hThere is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:V=π(5m)2hby solving the equation with the given valueshence,The answer is 3/25π m/h.
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A solon prices bottles of conditioner by the ounce. An 8-ounce bottle of Brand C cost $14. tHe cost of Brand S is represented by the equations y = 1.5x, where y is the total cost for a bottle with x ounces
Answers
Store´s B bottle cost less per ounce.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Store A
Cost of a 8-ounce bottle of water: $14
Store B
Cost of bottle: y= 1.5x
Cost per ounce (A)
=$14/ 8
= $1.75per ounce
Cost per ounce (B); $1.5 per ounce
So, $1.75 > $1.5
Hence, Store´s B bottle cost less per ounce.
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explain how to select a cluster sample of fans. what is the benefit of using a cluster sample in this context?
Answers
The cluster sample represents the the characteristic of group of same types objects.
What is the cluster sampling?
A population is divided into clusters, such as districts or schools, and some of these clusters are randomly chosen as your sample via the probability sampling technique known as cluster sampling. In a perfect world, each cluster would be a tiny reflection of the entire population.
A researcher intends to carry out a study to evaluate sophomores' abilities in business education across the United States. There is no way to carry out a research study with participants from every university. Instead, the researcher can group the universities from each city into a single cluster by utilizing cluster sampling. The sophomore student population in the United States is then comprised of these clusters. Next, select clusters at random for the research project using either simple random sampling or systematic random sampling. The sophomores from each of these determined groups can then be picked on whom to perform the research study utilizing simple or systematic sampling.
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
The vertex is (-2,2), axis of symmetry is x = -2 and the parabola is downward.
From the graph:
vertex:
The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry.
here vertex = (-2,2)
Axis of symmetry:
The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric.
x = -2.
Parabola:
It is clearly visible that the parabola is facing downward so it is a downward parabola.
Therefore the vertex is (-2,2), axis of symmetry is x = -2 and the parabola is downward.
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50 points!!! Are rational functions and hyperbolas the same? Please explain why or why not.
Answers
HELPPPP MEEEEE PLEASE!!!!
Answers
2+(2x2)
this is because GT is 1/3 of QT
What is the value sine?
5/12
5/13
12/13
13/5
Answers
Answer:
(C.) 5/13
Step-by-step explanation:
The sine proportion is opposite / hypotenuse
Given the reference angle, the side measuring 5 units is the opposite side and the side measuring 13 units (and opposite of the right angle) is the hypotenuse
Thus, sine is 5/13
4. Which theorem would explain why TU > SV?
Answers
Answer:
B. Hınge theoremStep-by-step explanation:
We can observe:
ST = UV, marked as equal;VT = TV, common side;m∠TVU = 45° > m∠STV = 44°, as marked.According to Hınge theorem if two sides of different triangles are equal and the angles between the two sides are different, then the larger angles has greater side opposite to it.
As TU is opposite to the larger angle, and SV is opposite to smaller angle, then TU > SV.
Correct angle choice is B.
Which of the following is the independent variable of F(G(x))?
O A. V
• B. x
• C. F(x)
• D. F(G(x))
Answers
Answer:
D
Step-by-step explanation:
suppose that 10 green balls and 14 purple balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a purple ball if the first ball is replaced before the second is drawn? a) 0.1224 b) 0.6250 c) 0.8333 d) 0.4167 e) 0.5833 f) none of the above.
Answers
The probability that the second ball drawn is a purple ball is (e) 0.5833
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Green balls = 10
Purple balls = 14
This means that the total number of balls is
Total = 10 + 14
Evaluate the equation
So, we have
Total = 24
From the question, we understand that the ball is replaced
So, the probability that the second ball is purple ie
P(second purple) = purple/total
This gives
P(second purple) = 14/24
Evaluate
P(second purple) = 0.5833
Hence, the probability is (e) 0.5833
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A= (a+b+c+d)/4 solve for b
Answers
Answer:
b = 4A-a-c-d
Step-by-step explanation:
A = (a+b+c+d)/4 |*4
4A = a+b+c+d |-a-c-d
4A-a-c-d = b