Question 7 of 12 View Policies Current Attempt in Progress Solve the given triangle. a = 6.b = 2.c = 5 Round your answers to the nearest integer. Enter NA in each answer area if the triangle does not
Answers
Since -1 ≤ cos A ≤ 1, this triangle does not exist, as the cosine of an angle cannot be less than -1.
In a triangle, given a = 6, b = 2 and c = 5, we need to find the angle measures.
We can use the law of cosines to find the unknown angle:
cos A = (b² + c² - a²) / 2bc
Now we can substitute the given values and simplify:
cos A = (2² + 5² - 6²) / (2×2×5)
cos A = -15/20
cos A = -0.75
Since -1 ≤ cos A ≤ 1, this triangle does not exist, as the cosine of an angle cannot be less than -1.
Thus, we would enter NA in each answer area.
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The triangle ABC is not valid since the sum of the angles of the triangle must be exactly 180°.
Given data: a = 6, b = 2, c = 5To solve the triangle, we can use the law of cosines.
The law of cosines states that for any triangle ABC with sides a, b, and c, and angle A opposite side a, the following formula holds:
c² = a² + b² - 2abcos( A) Similarly, b² = a² + c² - 2accos( B) And, a² = b² + c² - 2bccos( C)
Solving for the angle A:
cos( A) = (b² + c² - a²)/(2bc)
cos( A) = (2² + 5² - 6²)/(2×2×5)
cos( A) = (4+25-36)/20
cos( A) = -0.35A = cos⁻¹ (-0.35)A
≈ 109.47°
Solving for the angle B:
cos( B) = (a² + c² - b²)/(2ac)
cos( B) = (6² + 5² - 2²)/(2×6×5)
cos( B) = (36+25-4)/60
cos( B) = 0.85B
= cos⁻¹ (0.85)B
≈ 31.8°
Solving for the angle C:
cos( C) = (a² + b² - c²)/(2ab)
cos( C) = (6² + 2² - 5²)/(2×6×2)
cos( C) = (36+4-25)/24
cos( C) = 0.25C
= cos⁻¹ (0.25)C
≈ 75.5°
The angles of the triangle ABC are A ≈ 109.47°, B ≈ 31.8°, and C ≈ 75.5°.
The sum of the angles of the triangle is 216.77°, which is slightly more than 180°.
Therefore, the triangle ABC is not valid since the sum of the angles of the triangle must be exactly 180°.
Therefore, the triangle does not exist. Thus, the answer is NA.
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Related Questions
Triangle X Y Z is translated up 2 and right 3 units to form triangle C A B. Triangle XYZ was translated up 2 and right 3 units, creating triangle CAB. Which relationship between the parts of the two triangles must be true? ∠X ≅ ∠A ZX ≅ CA YZ ≅ AB ∠Z ≅ ∠C
Answers
Answer:
YZ ≅ AB
Step-by-step explanation:
A translation is a correspondence between two mathematical figures, for instance, the coordinates of each point in a straight line of one figure that is added to the coordinates of the corresponding point on the other figure.
But here, we are given a Δ XYZ which is translated to ΔCAB. This tells us more about how the corresponding points preserve their congruence nature.
i.e.
X corresponds to C
Y corresponds to A
Z corresponds to B
Similarly;
XY corresponds to CA
YZ corresponds to AB
XZ corresponds to CB
Since both triangles preserve their congruence nature, then all corresponding points are congruent as well.
Therefore, from the choice of options given, only YZ corresponds to AB is the right answer.
i.e.
YZ ≅ AB
Answer:
C
Step-by-step explanation:
the wall thickness of 21 randomly selected glass 2-liter bottles was measured by a quality-control engineer. the wall thickness of those glass 2-liter bottles follows a normally distribution with unknown variance. the sample mean and the sample standard deviation of those 21 selected bottales was found to 4.15 millimeters and 0.09 millimeter, respectively. which of the following is the correct 90% two-sided confidence interval for the mean wall thickness?
Answers
The 90 % Prediction interval on the wall thickness of next bottle tested is (4.41, 4.99).
What is meant by Prediction Interval?A prediction interval is a form of confidence interval (CI) used with regression analysis predictions; it is a range of values that forecasts the value of a new observation based on your existing model.
Confidence intervals and predictions are frequently used interchangeably. They are not exactly the same thing, though.
A confidence interval is a set of values connected to a population parameter. the population's mean, as an illustration.
Where you anticipate an upcoming number to fall is called a prediction interval.
The Interval Uncertainties
It doesn't imply that you can forecast with confidence where a single number will fall, just like with most things in statistics.
Confidence intervals are usually accompanied with a confidence level, which represents the amount of uncertainty.
How to solve?
X=4.7
s=0.7
n=25
The tabulated value of t at 24 degree of freedom is 2.06
t24=2.064
The 90 % Prediction interval on the wall thickness of next bottle tested is given by:
=(4.7±t24×0.7√25)
=(4.7−2.064×0.75,4.7+2.064×0.75)
=(4.7−0.28896,4.7+0.28896)
=(4.41,4.99)
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The diagram shows a sector of a circle radius 10 cm.
Find the perimeter of the sector, giving your answer correct to 1 decimal place.
Answers
Answer:
P ≈ 43.6 cm
Step-by-step explanation:
the perimeter (P) is the sum of the 2 radii and the arc
arc length = circumference of circle × fraction of circle
= 2πr × \(\frac{135}{360}\)
= 2π × 10 × 0.375
= 20π × 0.375
≈ 23.6 cm ( to 1 decimal place )
Then
P = 23.6 + 10 + 10 = 43.6 cm
In kickboxing, it is found that the force, fneeded to break a board, varies inversely with the length, of the board. If it takes 8 pounds of pressure to break a board that is 3 feet long, how long is a board that requires 5 pounds of pressure to break?
Answers
The board with a length of 4.8 feet would require 5 pounds of pressure to break.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Let p represent the pressure and l represent the length.
l ∝ 1/p
l = k/p (k is constant)
When l = 3, p = 8, hence:
3 = k/8
k = 24
For p = 5:
l = k/p = 24/5 = 4.8 feet
The board with a length of 4.8 feet would require 5 pounds of pressure to break.
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2/5 divided 1/3 give answer in simplest form as a mixed number
Answers
A computer monitor has a width of 14.60 inches and a height of 10.95 inches. What is the area of the monitor display in square meters? area How many significant figures should there be in the answer? 2 3 4 5
Answers
The area of the computer monitor display is approximately 0.103 square meters, with three significant figures.
The area of the monitor display in square meters is found by converting the measurements from inches to meters and then calculate the area.
The conversion factor from inches to meters is 0.0254 meters per inch.
Width in meters = 14.60 inches * 0.0254 meters/inch
Height in meters = 10.95 inches * 0.0254 meters/inch
Area = Width in meters * Height in meters
We calculate the area:
Width in meters = 14.60 inches * 0.0254 meters/inch = 0.37084 meters
Height in meters = 10.95 inches * 0.0254 meters/inch = 0.27813 meters
Area = 0.37084 meters * 0.27813 meters = 0.1030881672 square meters
Now, we determine the number of significant figures.
The measurements provided have four significant figures (14.60 and 10.95). However, in the final answer, we should retain the least number of significant figures from the original measurements, which is three (10.95). Therefore, the answer should have three significant figures.
Thus, the area of the monitor display in square meters is approximately 0.103 square meters, with three significant figures.
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What is the quadratic function that fits the following data: (4, 9), (6, 21), (–2, –3)
Answers
The equation that fits into the given data is
\(x^2+2x-6=0 \\\)
Quadratic EquationThis is an algebraic equation or expression that have a second degree as it highest power. An example of quadratic equation is given below
\(f(x)=ax^2+bx+c\\\)
The given data are set of points attached to a quadratic equation and we can use it to find the quadratic equation.
given that \(f(x)=ax^2+bx+c\\\)
Data;
(4,9)(6,21)(-2,-3)The point at (4)(9) will give us the equationLet's substitute the value of x and y in the equation and solve
\(f(4)=9\\a(4)^2+b(4)+c=9\\16a^2+4b+c-0...equation 1\)The point at(6)(21) will give the equationLet's substitute the value of x and y in the equation and solve
\(f(6)=21\\a(6)^2+b(6)+c=21\\36a+6b+c=21...equation 2\)
The point at (-2)(-3) gives the equationLet's substitute the value of x and y in the equation and solve
\(f(-2)=-3\\a(-2)^2+b(-2)+c=-3\\4a-2b+c=-3...equation 3\)
We have the following system of equation
\(16a+4b+c=9...equation1\\36a+6b+c=21...equation2\\4a-2b+c=-3...equation3\\\)
When we solve the above system of equation either using elimination or substitution method, we have
\(a=1/2, b=1, c= -3\)
substituting these values into f(x)
\((\frac{1}{2})x^2+(1) + (-3)=0\\\frac{1}{2}x^2+x-3=0\\\)
multiply through by 2
\((2)\frac{1}{2}x^2+(2)x-(2)3=0\\x^2+2x-6=0\)
The quadratic equation is \(x^2+2x-6=0\)
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HELP ASAP PLEASE ASAP PLEASE
Answers
Answer:
Step-by-step explanation:
x intercept the coordinate : (-4,0)
y intercept coordinate(0,3)
y=mx+b
y=b=3 when x=0
m=3-0/0+4
m=3/4
y= 3/4 x +3
-3/4 x+y=3
first choice -3/4 x second choice - 1 (y) third choice 3
-x/5-8=12
Show work
And check
Answers
Answer:
\(\huge\boxed{\sf x = -100}\)
Step-by-step explanation:
Given equation:\(\displaystyle -\frac{x}{5} -8=12\\\\Add \ 8 \ to \ both \ sides\\\\-\frac{x}{5} = 12+ 8\\\\-\frac{x}{5} = 20\\\\Multiply \ both\ sides \ by \ 5\\\\-x = 20 \times 5\\\\-x = 100\\\\Multiply\ both \ sides \ by\ -1\\\\x = -100\\\\\rule[225]{225}{2}\)
Lorinda can walk 1.8 miles in 30 minutes.
Which proportion can be used to find how many miles she can walk in 45 minutes?
Answers
Answer:
B. (1.8)/(30) = (x)/(45)
Venus and Molly are selling candies to raise money for charity. They buy 80 bags of candy for $0.50 each. They sell all of them for $1.25 each. How much profit did they make? Hint: The profit is the difference between what the candies cost them and what they sold them for.
Answers
Answer: $60
Step-by-step explanation:
From the question, we are told that Venus and Molly are selling candies to raise money for charity and that they buy 80 bags of candy for $0.50 each. This means that the total cost will be:
= 80 × $0.50
= $40
They sell all of them for $1.25 each. This means that the total selling price will be:
= 80 × $1.25
= $100
Profit = Selling price - Cost price
= $100 - $40
= $60
Which set of algebra tiles represents the sentence below? Ada drove 2 fewer miles today than she drove yesterday. 2 boxes contain negative x and 1 box contains a plus sign. 1 box contains x and 2 boxes contain a minus sign. 1 box contains negative x and 2 boxes contain plus signs. 2 boxes contain x and 1 box contains a minus sign.
Answers
Answer:
The correct option is;
1 box contains x and 2 boxes contain minus sign
Step-by-step explanation:
Algebra tiles are used in teaching students algebraic concepts. The unit (small) tile represents the number one. The rectangular tile represents the variable x and the large square tile represents x²
The parameters given are;
Ada drove 2 fewer miles today than she drove yesterday, therefore;
Let X = number of miles Ada drove yesterday
We have number of miles Ada drove today = X - 2
Therefore, the correct option is 1 box contains x and 2 boxes contain minus sign
Answer:
its b
Step-by-step
i got it right on my test
Subtract 1/8 minus 3/4
Answers
Answer: 5/8
Step-by-step explanation:
Is 4/8 equivalent to 7/8
Answers
Answer:
is 7 more than 4 or 4 more than 7?
Step-by-step explanation:
JUST USE YOUR BRAIN!
Answer:
no
Step-by-step explanation:
of course not. since the denominators are the same, the numerators have to be equal. since the numerators aren't equal, the answer is no
How many different lines can a plane contain?
Answers
Answer:
For example if the three points are A, B and C in your diagram then there are infinitely many planes that contain the points. The final point is that if the three points do not lie on a line then there is exactly one plane that contains the points.
Step-by-step explanation:
Un par de zapatos más dos pantalones valen $ 70.000 en una tienda. Se ofrece una oferta, al comprar dos o más pares de zapatos del mismo precio se descuenta un 10% en cada par y por tres o más pantalones del mismo precio un 15% en cada pantalón. Juan paga por tres pantalones $ 38.250 y luego, compra dos pares de zapatos. ¿Cuánto pagó Juan por los dos pares de zapatos?
Answers
Answer:
49.5 $
Step-by-step explanation:
Comencemos por lo siguiente:
Si llamamos x al precio del par de zapatos y "y" al precio de cada pantalón, entonces la tienda ofrece:
un par de zapatos x más dos pantalones 2*y en 70.000 $ (deben ser 70 $ pero esa cifra no importa a los fines de resolver el problema, habrá solo que hacer el ajuste correspondiente, en lo que aqui respecta hablaremos de 70 $)
Entonces de acuerdo a lo expuesto
x + 2y = 70 or y = ( 70 - x) /2 (1)
Esa es la condición inicial.
Ahora bién Juan paga por tres pantalones 38.25 $
Eso quiere decir ( como los pantalones son iguales) que pago 38.25/3 por cada pantalón
38.25/3 = 12.75 $
Ahora bién ese precio tubo una rebaja del precio original del 15 % ( quiere decir que el precio original de cada pantalón es de
12.75/0.85 = 15 $ x = 15 $
Entonces si nos vamos a la ecuación (1) (alli los precios son originales) tenemos que
y = ( 70 - x ) / 2 y = ( 70 - 15 ) / 2 y = 55/2 y = 27.5 $
Ahora Juan paga por dos pares de zapatos donde según las ofertas de la tienda el debera tener un descuento del 10 % en cada par
Por lo que si un par cuesta 27.5 $ le darán un descuento del 10% es decir pagará 27.5 *0.9 = 24.75 por cada par, como son dos pares
pagará 2 * 24.75 = 49.5 $
You tie a spherical balloon that is 2 feet in diameter to a
stake in the ground. The string is 15 feet long. The wind
blows and you observe that the top of the balloon is
8 feet over from the stake, as shown in the diagram.
What is the height, b, of the balloon?
Show your work.
15 ft
2 ft
8 ft
Answers
Answer:
Step-by-step explanation:
What is half of a 3/4 cup?
Answers
Answer:0.375
Step-by-step explanation:
3/4=0.75
0.75/2=0.375
(3/4)/2=0.375
Is is greater than less or equal to 4.09_4.90
Answers
Its less than i think yeah
PLSSS HURRY!!!
Here are the answer choices
A. counterclockwise rotation
B.Clockwise rotation
C.90 rotation
D. 45 rotation
E. 180 rotation
Answers
Answer:
B. Clockwise RotationStep-by-step explanation:
i hope it helps ;)
Find the maximum rate of change of f at the given point and the direction in which it occurs.
f(x, y) = 4y sqrt( x ) , (4, 9)
maximum rate of change =
direction vector =
Find the maximum rate of change of f at the given point and the direction in which it occurs.
f(x, y, z) = sqrt( x2 + y2 + z2) , (9, 7, -2)
maximum rate of change =
direction vector =
Answers
(a)The direction vector in which the maximum rate of change occurs is \((3/\sqrt{13})i + (2/\sqrt{13})j\), and the maximum rate of change is \(6\sqrt{13}\).
(b)The direction vector in which the maximum rate of change occurs is \((9/\sqrt{178})i + (7/\sqrt{178})j - (2/\sqrt{178})k\), and the maximum rate of change is \(\sqrt{(89/49)\)
How to find the maximum rate of change of f(x, y)?(a) To find the maximum rate of change of f(x, y) = 4y√x at the point (4, 9), we need to find the gradient vector ∇f(4, 9) and its magnitude.
Then, the maximum rate of change occurs in the direction of the gradient vector.
∂f/∂x = 2y/√x
∂f/∂y = 4√x
∇\(f(x, y) = (2y/\sqrt{x}) i + (4\sqrt{x}) j\)
∇f(4, 9) = 18i + 12j
The magnitude of the gradient vector is |∇f(4, 9)| = √(18² + 12²) = √468 = 6√13.
Therefore, the maximum rate of change of f at the point (4, 9) is \(6\sqrt{13\), and it occurs in the direction of the gradient vector, which is \((18/6\sqrt{13})i + (12/6\sqrt{13})j = (3/\sqrt{13})i + (2/\sqrt{13})j\).
Thus, the direction vector in which the maximum rate of change occurs is \((3/\sqrt{13})i + (2/\sqrt{13})j\), and the maximum rate of change is \(6\sqrt{13}\).
(b) To find the maximum rate of change of f(x, y, z) = √(x² + y² + z²) at the point (9, 7, -2), we need to find the gradient vector ∇f(9, 7, -2) and its magnitude.
Then, the maximum rate of change occurs in the direction of the gradient vector.
∂f/∂x = x/√(x² + y² + z²)
∂f/∂y = y/√(x² + y² + z²)
∂f/∂z = z/√(x² + y² + z²)
\(f(x, y, z) = (x/\sqrt{(x^2 + y^2 + z^2)}) i + (y/\sqrt{(x^2 + y^2 + z^2)}) j + (z/\sqrt{(x^2 + y^2 + z^2)}) k\)
∇\(f(9, 7, -2) = (9/\sqrt{98}) i + (7/\sqrt{98}) j - (2/\sqrt{98}) k\)
The magnitude of the gradient vector is |∇f(9, 7, -2)| = √(9² + 7² + (-2)²)/√98 = √178/√98 = √(89/49).
Therefore, the maximum rate of change of f at the point (9, 7, -2) is √(89/49), and it occurs in the direction of the gradient vector, which is (9/√178)i + (7/√178)j - (2/√178)k.
Thus, the direction vector in which the maximum rate of change occurs is \((9/\sqrt{178})i + (7/\sqrt{178})j - (2/\sqrt{178})k\), and the maximum rate of change is \(\sqrt{(89/49)\).
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Which number sentence is true?
A. –2.0 + (–0.5) = 2.5
B. –4.5 + 6.5 = –2.0
C. 3.0 + (–0.5) = –2.5
D. 5.5 + (–2.5) = 3.0
answer soon please!
Answers
Answer:
B. and D.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Here are the correct sums:
A. –2.0 + (–0.5) = -2.5
B. –4.5 + 6.5 = 2.0
C. 3.0 + (–0.5) = 2.5
D. 5.5 + (–2.5) = 3.0
Only D is correct.
Answer: D
Find the area of the triangle.
Answers
Answer:
12.86
Step-by-step explanation:
Area=ab *siny/2
a=side
b=base
y=angle
put the values and you got the answer...
hope it helps
Answer:20
Step-by-step explanation: The answer is 20 because to find the Area you use the formula of 1/2 x base x height. 8 is the height and 5 is the base.
8 x 5 =40
Then multiply by 1/2 which will equal 20
help me I need help on this
Answers
Answer:
It is 1.
Step-by-step explanation:
Hope this helped have an amazing day!
Ayo runs a fairground game.In each turn, a player rolls a fair dice numbered 1 - 6 and spins a fair spinner numbered 1 - 12.It costs a player £1.40 for a turn.A player can win £6 or £3 as in the diagrams:If 216 people are to play, how much profit can Ayo expect to make?
Answers
Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.
The expected value is given by the sum of each outcome multiplied by it's respective probability.
In this problem:
The player wins $6, that is, Ayo loses £6, if he rolls a 6 and spins a 1, hence the probability is \(\frac{1}{6} \times \frac{1}{12} = \frac{1}{72}\).The player wins $3, that is, Ayo loses £3, if he rolls a 3 on at least one of the spinner or the dice, hence, considering three cases(both and either the spinner of the dice), the probability is \(\frac{1}{6} \times \frac{1}{12} + \frac{1}{6} \times \frac{11}{12} + \frac{5}{6} \times \frac{1}{12} = \frac{1 + 11 + 5}{72} = \frac{17}{72}\)In the other cases, Ayo wins £1.40, with \(1 - \frac{18}{72} = \frac{54}{72}\) probability.Hence, his expected profit for a single game is:
\(E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583\)
For 216 games, the expected value is:
\(E = 216(0.2583) = 55.8\)
Ayo can be expected to make a profit of £55.8.
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10x - 4 + 5x + 19 = 180
What is the value of x
Answers
Answer:
x=11
Step-by-step explanation:
Answer:
x=11
Step-by-step explanation:
10x-4+5x+19=180
Combine like terms
15x+15=180
-15 -15
15x=165
divide by 15
x=11
The sum of 3 consecutive integers is less than or equal to 15 what is one possible set of three integers to satisfy this inequality hint let n represent the first number so then the next number would be n+1 and so on
Answers
Step 1
Let the first consecutive integer be n
Then the second will be n+1
The third will be n+2
Step 2
Write an inequality for the problem
\(n+n+1+n+2\leq15\)Step 3
Solve the inequality
\(\begin{gathered} 3n+3\leq15 \\ 3n\leq15-3 \\ 3n\leq12 \\ \frac{3n}{3}\leq\frac{12}{3} \\ n\leq4 \end{gathered}\)Step 4
Find the possible set of three integers to satisfy the inequality.
\(\begin{gathered} n=4---\text{ first integer} \\ n+1=4+1=5---\text{ second integer} \\ n+2=4+2=6---\text{ Third integer} \\ \text{check} \\ 4+5+6\leq15 \\ \text{Hence the set of thr}ee\text{ integers are; }\mleft\lbrace4,5,6\mright\rbrace \end{gathered}\)One possible set of three integers that satisfy the inequality is;
{4,5,6}
− 1 / 3 − 1 2 / 3
pzzzzzzzzzzzzzzz
Answers
Answer:
- 2
Step-by-step explanation:
-1/3 - 1 2/3 =
- 1/3 - 5/3 =
-6/3 = -2
A minimum element is deleted from a (min) binary heap with N elements. The running time worst case of this operation is
a. O(N)
b. O(N2)
c. O(logN)
d. O(NlogN)
Answers
The running time wοrst case οf deleting a minimum element frοm a (min) binary heap with N elements is O(lοgN). Therefοre, the cοrrect answer is c. O(lοgN).
What happens when deleting minimum element?When deleting the minimum element frοm a binary heap, the heap needs tο be restructured tο maintain its heap prοperty. This restructuring prοcess invοlves mοving elements within the heap and pοtentially swapping elements tο maintain the heap's structure and οrdering.
Since a binary heap is a cοmplete binary tree and has a height οf lοgN, the wοrst-case running time fοr deleting the minimum element is prοpοrtiοnal tο the height οf the heap, which is O(lοgN). This is because the number οf cοmparisοns and swaps required during the restructuring prοcess is dependent οn the height οf the heap.
Therefοre, the cοrrect answer is c. O(lοgN).
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if -5,3 and 5,3 are two vertices of an equilateral triangle, then find the coordinates of the third vertex, given that orgin lies inside the triangle (Take √3 = 1.7)
Answers
Therefore, The Coordinates of the THIRD VERTEX is: ( 5, -3 )
Step-by-step explanation:Calculate the midpoint of the given vertices:
MidPoint = ( -5 + 5/2, 3 + 3/2 )
MidPoint = ( 0, 3 )
Calculate the distance between the given vertices:Distance = √( -5 -5 )^2 + ( 3 - 3 )^2
Distance = √( -10 )^2 + (0)^2
Distance = √100
Distance = 10
Calculate the side length of the equilateral triangle:Side Length = 10/√3
Side Length = 10/1.7
Side Length = 5.88
Calculate the height of the Third Vertex:Height = √3/2 * Side Length
Height = 1.7/2 * 5.88
Height = 5
Calculate the Coordinates of the Third Vertex:Since the origin lies inside the triangle, The Third Vertex will have a Positive X-Coordinate and a Negative Y-Coordinate.
Now, Let the Third Vertex Be:( x, y )
Using the MidPoint Formula now we have:x = -5 + x/2
y = 3 + y/2
Solve for X and Y, we now get:x = 5
y = -3
Draw a conclusion:Hence, The Coordinate of the Third Vertex is: ( 5, -3 )
I hope this helps!