The indicated trigonometric values in the specified quadrant are sec(O) = 1/3, sin(O) = sqrt(-8), and csc(O) = 1/sqrt(-8).
To find the indicated trigonometric value in the specified quadrant using the function value, we need to use the relationships between the different trigonometric functions. The given function value is cosich (C) = 3 in quadrant 2.
First, we can use the relationship between cosine and secant to find the value of secant. The relationship is:
sec(O) = 1/cos(O)
Since cosich (C) = 3, we can substitute this value into the equation and solve for sec(O):
sec(O) = 1/3
Next, we can use the relationship between cosine and sine to find the value of sine. The relationship is:
sin^2(O) + cos^2(O) = 1
Substituting the value of cosich (C) = 3 into the equation, we get:
sin^2(O) + 3^2 = 1
Solving for sin^2(O), we get:
sin^2(O) = 1 - 9 = -8
Taking the square root of both sides, we get:
sin(O) = sqrt(-8)
Since we are in quadrant 2, the value of sine will be positive. Therefore, the value of sin(O) is sqrt(-8).
Finally, we can use the relationship between sine and cosecant to find the value of cosecant. The relationship is:
csc(O) = 1/sin(O)
Substituting the value of sin(O) = sqrt(-8) into the equation, we get:
csc(O) = 1/sqrt(-8)
Therefore, the value of csc(O) is 1/sqrt(-8).
In conclusion, the indicated trigonometric values in the specified quadrant are sec(O) = 1/3, sin(O) = sqrt(-8), and csc(O) = 1/sqrt(-8).
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△ABC is similar to both △ACD and △CBD.∙∣∣AC∣∣2+∣∣BC∣∣2=∣∣A B∣∣2
Explain why these claims are correct or incorrect. Provide valid mathematical reasoning to support your responses.
△ABC is cοngruent tο bοth △ACD and △CBD.
What is triangle?Geοmetry depends οn shapes like squares, circles, rectangles, triangles, and οthers. Amοng all the fοrms we have here, triangles seem tο be the mοst intriguing and distinctive. The triangle's shape is created by the intersectiοn οf three lines and three angles.
△ABC is a right triangle, right angled at C.
CD is altitude drawn tο hypοthesis AB.
Tο prοve, △ACD ~ △CBD
In △ACD and △CBD.
∠ACB= ∠ADC=90°
∠CAB=∠DAC (Cοmmοn angle)
By AA similarity we can say that, △ACD and △CBD.
Anοther side,
Need tο prοοf ∣AC∣²+∣BC∣²=∣A B∣²
If is a right triangle at C with a prοjectiοn tο as shοwn, then
BC²=BD*AB
AC²= AD*AB
A further beneficial cοnclusiοn can be demοnstrated by cοmbining the Pythagοrean and Euclidean theοrems. The Pythagοrean Theοrem prοvides us with
CD²= BC²-BD²
By putting the value οf BC²,
CD²= BD*AB-BD²
OR, CD²= BD*(AB-BD)
OR, CD²= BD*AD
AB²= (AD*AB)+(BD*AB)
Or, AB(AD+BD)=AB²
Or, AB²=AB²
Or, ∣AC∣²+∣BC∣²=∣A B∣² (prοved)
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A toy car is placed on the floor. What is the total distance travelled by the car in metres?
If the car moves in a straight line starting from the rest, then the total distance travelled by the toy car is 18m.
We first break the motion of the car into two parts:
So, the first part of the motion.
We know that the car accelerates from rest to a velocity of 5 m/s with a constant acceleration for 4 seconds.
We use the equation of motion : v = u + at;
where v = final velocity, u = initial velocity (which is 0 in this case), a is = acceleration, and t = time.
⇒ a = (v - u)/t
⇒ a = (5 - 0)/4,
⇒ a = 1.25 m/s²
Now, we can use another equation of motion to find the distance travelled during this time:
⇒ s = ut + (1/2)at²
where s=distance travelled, u=initial velocity (which is 0), a=acceleration, and t = time.
Substituting the values,
We get,
⇒ s = 0 + (1/2)(1.25)(4)²
⇒ s = 10 m
So, the distance travelled during the first part of the motion is 10 meters.
In the second part of the motion,
Car decelerates from 5 m/s to a complete stop with a constant deacceleration of 1 m/s² for 2 seconds.
So, we have : s = ut + (1/2)at²
where s = distance travelled, u = initial velocity (5 m/s), a = deacceleration (-1 m/s² ), and t = time.
Substituting the values,
We get,
⇒ s = 5(2) + (1/2)(-1)(2)²
⇒ s = 8m
So, the distance travelled during second part of motion is 8 meters.
The total distance travelled by the car is sum of distances travelled during the motion is :
⇒ Total distance = 10 m + 8 m = 18 m
Therefore, the total distance travelled is 18 meters.
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The given question is incomplete, the complete question is
A toy car is placed on the floor. It moves in a straight line starting from the rest, It travels with constant acceleration for 4 seconds reaching a velocity of 5 m/s, It then slows down with constant deacceleration of 1 m/s² for 2 seconds, It then hits a wall and stops.
What is the total distance travelled by the car in meters?
Setup a system of equations for the following::
Farmer Swinger started to raise chickens and cows on his farm. Someone asked how many animals he has and Farmer Swinger replies, "I have a total of 35 animals a total number of legs is 102. Can you figure out how many chickens and cows that I have?"
x + y = 35 and 2x + 4y = 102 represents the required system of equations.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the number of chickens and y be the number of cows.
Each chicken has 2 legs, so x chickens have 2x legs.
Each cow has 4 legs, so y cows have 4y legs.
The total number of animals is 35 and the total number of legs is 102, so we can set up the following system of equations:
x + y = 35 (the total number of animals)
2x + 4y = 102 (the total number of legs)
Hence, x + y = 35 and 2x + 4y = 102 represents the required system of equations.
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Find the vertices, foci, center, and asymptotes of the given hyperbola y + 1 )2 = (x, y) = ( 21,-1 X ) (smaller x-value) (x, y) = ( -5,-1 X ) (larger x-value) (x, y) = | 8 + V 185 ,-1 ) (smaller x-value) (x, y) = | 8-V 185 ,-1 ) (l ) (x, y) = (3,-1 vertices smaller X-Value foci arger X-value center 45 13 X (negative slope) asymptotes 13 19 13 X (positive slope) 13
The vertices of the given hyperbola are (-1, -1 + sqrt(21)) and (-1, -1 - sqrt(21)), the foci are (-1, -1 ± sqrt(66)), the center is (-1, -1), and the asymptotes are y = -1 ± (sqrt(21)/sqrt(45))(x + 1).
To find the vertices, foci, center, and asymptotes of the given hyperbola, we need to use the standard form of a hyperbola equation:
(y - k)^2 / a^2 - (x - h)^2 / b^2 = 1
First, we need to find the center (h, k) of the hyperbola. From the given equation, we can see that h = -1 and k = -1, so the center of the hyperbola is (-1, -1).
Next, we need to find the values of a and b. From the given equation, we can see that a^2 = 21 and b^2 = 45, so a = sqrt(21) and b = sqrt(45).
Now, we can find the vertices of the hyperbola. The vertices are located at (h, k ± a), so the vertices are (-1, -1 ± sqrt(21)). This gives us the vertices (-1, -1 + sqrt(21)) and (-1, -1 - sqrt(21)).
Next, we need to find the foci of the hyperbola. The foci are located at (h, k ± c), where c = sqrt(a^2 + b^2). So, c = sqrt(21 + 45) = sqrt(66), and the foci are (-1, -1 ± sqrt(66)).
Finally, we need to find the asymptotes of the hyperbola. The equations of the asymptotes are y = k ± (a/b)(x - h). So, the equations of the asymptotes are y = -1 ± (sqrt(21)/sqrt(45))(x + 1).
So, the vertices of the given hyperbola are (-1, -1 + sqrt(21)) and (-1, -1 - sqrt(21)), the foci are (-1, -1 ± sqrt(66)), the center is (-1, -1), and the asymptotes are y = -1 ± (sqrt(21)/sqrt(45))(x + 1).
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I need this asapppppppp
The measure of the smaller angle is 45°.
How to find the measure of the smallest angle?An heptagon is a figure with 7 sides, and the sum of the interior angles is equal to 900°.
Then here we can write a linear equation that depens on x, where we add all the given angles and we know that it must be equal to 900.
2x + 3x + 4x + 5x + 7x + 9x + 10x = 900
Solving that linaer equation for x:
(2 + 3 + 4 +5 + 7 + 9 + 10)*x = 900
40x = 900
x = 900/40 = 22.5
The measure of the smaller angle is:
(2x)°
replacing the value of x that we just got we will get:
2*22.5° = 45°
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(b) Now building on that, use the yp for the complex exponential forcing to find yp for the following differential equations. Warning: no credit if you are not showcasing this specific technique.
i. y′′−6y′−7y=5e2tsin(t). ii. y′′−6y′−7y=5e2tcos(t).
yp(t) = Aexp(2t) + Bexp(-2t) + Cexp(5t) + Dexp(-5t)
To find the solution to these two differential equations, we must use the technique of complex exponential forcing. The general solution for these types of equations is:
yp(t) = Aexp(2t) + Bexp(-2t) + Cexp(5t) + Dexp(-5t)
We can then use the given equations to substitute for y′ and y′′, and solve for the four constants A, B, C, and D. Doing so for equation (i), we get:
Aexp(2t) + Bexp(-2t) + Cexp(5t) + Dexp(-5t) = 5e2tsin(t) - 6[Aexp(2t) + Bexp(-2t)] - 7[Aexp(2t) + Bexp(-2t) + Cexp(5t) + Dexp(-5t)]
We can then solve this equation using algebraic manipulation to determine the four constants, and thus find the solution to this equation.
We can then use a similar method to solve equation (ii). The same general solution is used, and the constants can be determined using the same algebraic manipulation. The solution to this equation is then:
yp(t) = Aexp(2t) + Bexp(-2t) + Cexp(5t) + Dexp(-5t)
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Let T: VV be a linear operator and let Z: V→V be the zero linear transformation defined by Z(u) = 0 for all u EV. Prove that
Im(T) ker(T) - T.T=Z
The statement Im(T) ker(T) - T.T=Z is not necessarily true for all linear operators T.
To prove that Im(T) ker(T) - T.T=Z, we must first understand the terms "operator," "transformation," and "linear."
An "operator" is a function that maps one vector space to another. A "transformation" is a function that maps one set to another. A "linear" transformation is a transformation that satisfies the properties of linearity, meaning that it preserves addition and scalar multiplication.
Now, let's look at the equation Im(T) ker(T) - T.T=Z. The term "Im(T)" refers to the image of the linear operator T, which is the set of all vectors that can be obtained by applying T to any vector in V. The term "ker(T)" refers to the kernel of the linear operator T, which is the set of all vectors that are mapped to the zero vector by T.
To prove that Im(T) ker(T) - T.T=Z, we must show that the difference between the image of T applied to the kernel of T and the composition of T with itself is equal to the zero linear transformation.
First, let's consider the image of T applied to the kernel of T. Since the kernel of T is the set of all vectors that are mapped to the zero vector by T, applying T to any vector in the kernel of T will result in the zero vector. Therefore, Im(T) ker(T) = 0.
Next, let's consider the composition of T with itself, T.T. Since T is a linear operator, the composition of T with itself will also be a linear operator. However, there is no guarantee that T.T will equal the zero linear transformation.
Therefore, Im(T) ker(T) - T.T=Z can be simplified to 0 - T.T=Z. Since T.T is not necessarily equal to the zero linear transformation, the equation does not hold true for all linear operators T.
In conclusion, the statement Im(T) ker(T) - T.T=Z is not necessarily true for all linear operators T.
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Boris is ordering supplies for his company. He ordered 15 boxes of pencils and 24 boxes of pens. What is the ratio of boxes of pens ordered to boxes of pencils ordered?
A.
5:8
B.
1:15
C.
8:5
D.
15:1
Answer:
To find the ratio of boxes of pens ordered to boxes of pencils ordered, we need to divide the number of boxes of pens by the number of boxes of pencils:
24 boxes of pens ÷ 15 boxes of pencils = 8/5
Therefore, the ratio of boxes of pens ordered to boxes of pencils ordered is 8:5.
The correct answer is (C) 8:5.
Answer:
C. 8:5
Step-by-step explanation:
pens: 24
pencils: 15
pens : pencils
24 : 15 = 8 : 5
What are the following Sets, Factors, Real numbers for these two
rational expressions: 22x + 11 x2 – 3x – 10
1 – 2c 20c2 + 10c
Its set of factors would include all real numbers and the complex roots of the polynomial.
The first rational expression, 22x + 11 x2 – 3x – 10, is a polynomial of degree 2. Its set of factors would include all real numbers, since it has no real-number roots. The second rational expression, 1 – 2c 20c2 + 10c, is a polynomial of degree 3. Its set of factors would include all real numbers and the complex roots of the polynomial.
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Given f(x) = 6x and g(x) = 3x² + 1, find the following expressions. {a) (og)(4) (b) (gof)(2) (C) (fof)(1) (d) (gog(0)
The result would be:
a) (og)(4) = 294
b) (gof)(2) = 433
c) (fof)(1) = 36
d) (gog)(0) = 4
Given f(x) = 6x and g(x) = 3x² + 1, we can find the following expressions:
a) (og)(4)
To find (og)(4), we first need to find g(4).
g(4) = 3(4)² + 1 = 3(16) + 1 = 49
Now we can find (og)(4) by plugging in 49 for x in f(x):
(og)(4) = f(49) = 6(49) = 294
b) (gof)(2)
To find (gof)(2), we first need to find f(2).
f(2) = 6(2) = 12
Now we can find (gof)(2) by plugging in 12 for x in g(x):
(gof)(2) = g(12) = 3(12)² + 1 = 3(144) + 1 = 433
c) (fof)(1)
To find (fof)(1), we first need to find f(1).
f(1) = 6(1) = 6
Now we can find (fof)(1) by plugging in 6 for x in f(x):
(fof)(1) = f(6) = 6(6) = 36
d) (gog)(0)
To find (gog)(0), we first need to find g(0).
g(0) = 3(0)² + 1 = 1
Now we can find (gog)(0) by plugging in 1 for x in g(x):
(gog)(0) = g(1) = 3(1)² + 1 = 4
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x=y-6 pls help me quick
Answer:
Solve for x: x = x +
solve for y: y = x + 6
Coordinate: (0,6)
I didnnt know which answer you wanted cuz you didn't specify
Compute the discriminant. Then determine the number and type of solutions of the given solution.
2x2−7x+4=0
What is the discriminant?
Choose the sentence that describes the number and type of solutions of the quadratic equation.
(a) There are two unequal real solutions.
(b) There are two imaginary solutions.
(c) There is one real solution.
(d) There are infinite numbers of real solutions.
The correct option that describes the number and type of solutions of the quadratic equation is: There are two unequal real solutions. The correct answer alternative is option a.
The discriminant of a quadratic equation is the part of the equation under the square root in the quadratic formula, which is b² - 4ac. In the given equation, 2x² - 7x + 4 = 0, the values of a, b, and c are 2, -7, and 4, respectively.
To compute the discriminant, we plug in these values into the formula:
Discriminant = b² - 4ac
= (-7)² - 4(2)(4)
= 49 - 32
= 17
The discriminant is 17.
To determine the number and type of solutions of the quadratic equation, we look at the value of the discriminant. If the discriminant is greater than 0, there are two unequal real solutions. If the discriminant is equal to 0, there is one real solution. If the discriminant is less than 0, there are two imaginary solutions.
Since the discriminant in this case is 17, which is greater than 0, there are two unequal real solutions. Therefore, the correct answer is (a) There are two unequal real solutions.
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Three clocks ring once at the same time. After that, the first clock rings after every 90 minutes,
the second after every 30 minutes, and third after every 60 minutes. After how many minutes will they again ring together?
Answer:
me no habla ingles?
Step-by-step explanation:
Find the area of the shaded sector. Round your
answer to the nearest hundredth
154
7 km
65.85 km²
20.96 km
65.85 km
20.96 km²
The area of the sector is (a) 65.85 km square
How to determine the area of the sectorFrom the question, we have the following parameters that can be used in our computation:
Angle = 154 degrees
Radius = 7 km
Using the above as a guide, we have the following:
Sector area = Angle/360 * πr²
substitute the known values in the above equation, so, we have the following representation
Sector area = 154/360 * π * 7²
Evaluate
Sector area = 65.85
Hence, the area is 65.85 km square
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If the tires on a car each have a diameter of 25 inches how far will the car travel in 100 rotations of its tires?
In other words, in 100 tyre rotations, the vehicle will have travelled 7,854 inches, or roughly 196.06 feet or 59.79 metres.
what is order of rotation ?The amount of rotations around a central point or axis that a shape or object undergoes is referred to in mathematics as the order of rotation. For illustration, a shape with a 180-degree revolution about its centre has an order of rotation of 2. Similar to this, a shape rotated by 120 degrees has an order of revolution of 3. The idea of rotational symmetry, which describes a property of some shapes and objects that enables them to appear the same after a certain amount of rotation, and the order of rotation are closely related concepts.
given
The circumference of the tyre, which is determined by the following calculation, equals the distance covered by the vehicle in one rotation of its tyres.
C = πd
where the tire's width is d and its circumference is C. Using the tire's circumference of 25 inches as a plug-in, we obtain:
C is 25 times 78.54 inches.
As a result, one tyre rotation on the vehicle will cover a distance of 78.54 inches.
We can easily multiply the distance covered by one tyre rotation by 100 to determine how far the car will drive in 100 rotations:
78.54 inches per revolution times 100 rotations equals 7,854 inches of distance travelled.
In other words, in 100 tyre rotations, the vehicle will have travelled 7,854 inches, or roughly 196.06 feet or 59.79 metres.
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-3 2 Part A Enter a number in the box to create an expression equivalent to 2-5. 2+ 4 Part B Which expressions represent the distance between the two points on the number line? Select all that apply. A. 2-5 B. 2+(-5) C. 1-3-21 D. 12-(-3)| E. 1-3+(-2) F. 1-3-(-2)|
When 1 is put in the box, it generates an equation that is equal to 2 - 5. The expressions |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)|, etc., represent the distance between the two points integers on number line.
A number line is used to display integers. A number line is a graphic representation of a straight line of numbers. It consists of positive and negative integers such as 1, 2, and so forth, as well as a zero that is neither positive nor negative.
Part A:
2 - 5 = -3
2 + 1 = 3
The absolute value of a number is the distance on the number line between that number and 0.
That distance is always positive.
b. The absolute value symbol is " | | ".
Part B: |-3 -2| = 1
On the number line, this point represents the distance of one unit from -3 to -2.
|2-(-3)| = 5
On the number line, this point represents the distance of 5 units between 2 and -3.
|-3 + (-2)| = 5
The 5 units at this point on the number line reflect the distance from -3 to -2.
|-3 - (-2)| = 1
On the number line, this point represents the distance of one unit between -3 and -2.
It's a good idea to have a backup plan in place in case something goes wrong. The expressions |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)|, etc., represent the distance between the two points on the number line.
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Question 10 Determine the size (n) of the given arithmetic series. 38+48+58+68dots, S_(n)=968
The size (n) of the given arithmetic series is 4.
To determine the size (n) of the given arithmetic series, we need to use the formula for the sum of an arithmetic series, which is S_n = (n/2)(a_1 + a_n), where S_n is the sum of the series, n is the number of terms, a_1 is the first term, and a_n is the last term.
In this case, we are given that S_n = 968, a_1 = 38, and the common difference is 10 (since each term is 10 more than the previous one). We need to find the value of n.
Rearranging the formula to solve for n, we get:
n = (2S_n)/(a_1 + a_n)
Substituting in the given values, we get:
n = (2(968))/(38 + a_n)
Since we don't know the value of a_n, we can use the formula for the nth term of an arithmetic series, which is a_n = a_1 + (n-1)d, where d is the common difference. Substituting in the given values, we get:
a_n = 38 + (n-1)(10)
Simplifying, we get:
a_n = 10n + 28
Now we can substitute this value of a_n back into the equation for n:
n = (2(968))/(38 + 10n + 28)
Simplifying, we get:
n = (1936)/(66 + 10n)
Multiplying both sides by (66 + 10n), we get:
n(66 + 10n) = 1936
Expanding, we get:
10n^2 + 66n - 1936 = 0
Using the quadratic formula, we get:
n = (-66 ± √(66^2 - 4(10)(-1936)))/(2(10))
Simplifying, we get:
n = (-66 ± √(19396))/(20)
n = (-66 ± 139.27)/(20)
n = 3.66 or n = -10.26
Since n must be a positive integer, the only valid solution is n = 4.
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67 07 – 4(67) 4 a) -25.633 b) -258.429 c) -21.057 d) -20.1 Find the value of the expression. Give the result as a decimal. ()? + (5.9) (3.6) a) 21.28 b) 21.265 Oc) 21.49 d) 22.28
The expression 67 07 – 4(67) 4 + (5.9) (3.6) is equal to 21.265. Correct answer is option B.
To solve this expression, we must first understand the order of operations. The order of operations is Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. We start by solving the part of the expression in parentheses, which is 4(67) 4. We must do this first, as parentheses indicate that the expression within should be evaluated first.
This expression is equal to 268. We then proceed to solve the expression from left to right, following the order of operations. 67 07 – 268 = -258.429. We then add the part of the expression with the parentheses, which is (5.9) (3.6). -258.429 + (5.9) (3.6) = -21.265.
Therefore, the value of the expression 67 07 – 4(67) 4 + (5.9) (3.6) is equal to 21.265 as a decimal. Therefore the Correct answer is option B.
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how many integers satisfy
a) -102
b)-102≤x≤105
All the integers between -102 and 105 including the two satisfy the expression.
What are integers?
All whole numbers and negative numbers are considered integers. This indicates that if we combine negative numbers with whole numbers, a collection of integers results.
The meaning of integers: An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.
The given expression is:
-102 ≤ x ≤ 105
All the numbers between -102 and 105 including the two satisfy the expression.
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how many integers satisfy
a) -102
b)-102≤ x≤ 105
Please Help Struggling with Geometry :)
Find x. Show your work.
Answer:
36.87o
Step-by-step explanation:
Since ABC is a right triangle
cos(x) = adjacent/hypotenuse
cos(x) = 12/15
x = cos^-1 (12/15) = 36.87o
$44 is what percent of $88?
Write your answer using a percent sign (%). For example, 0.5%, 12.7%, or 56%.
Answer:
0.5
Step-by-step explanation:
0.5
Divide. If the divisor contains 2 or more terms, (6x^(2)y+18x^(2)y^(2)-xy^(2))/(6xy)
If the divisor contains 2 or more terms, (6x^(2)y+18x^(2)y^(2)-xy^(2))/(6xy) it can simplifies to x+3xy-y.
To divide the given expression, we need to factor out the common term from the numerator and then simplify by canceling out the common terms from the numerator and denominator. Here is the step-by-step explanation:
Step 1: Factor out the common term from the numerator:
(6x²y+18x²y²)-xy²)/(6xy) = 6xy(x+3xy-y)/(6xy)
Step 2: Cancel out the common terms from the numerator and denominator:
6xy(x+3xy-y)/(6xy) = (x+3xy-y)
Step 3: Simplify the expression:
(x+3xy-y) = x+3xy-y
Therefore, the final answer is x+3xy-y.
So, the given expression (6x²y+18x²y²-xy²)/(6xy) simplifies to x+3xy-y.
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100 points pls help me in my math
Answer:
1. YES
2.NO
3. NO
4. YES
Step-by-step explanation:
Answer:
yes, no,no,yes
Step-by-step explanation:
I need to find each angle measures. From 1-21!! Please help!! I will mark you brainiest!
The measure of each angle of the triangle is 30 degrees, 60 degrees, and 90 degrees.
Let's assume that the three angles of the triangle are x, 2x, and 3x, respectively. We are given that these angles are in the ratio of 1:2:3. This means that:
x : 2x : 3x = 1 : 2 : 3
To solve for x, we need to add the three angles together and equate them to 180 degrees (since the sum of the angles in a triangle is 180 degrees). Therefore:
x + 2x + 3x = 180
6x = 180
x = 30
Now that we know the value of x, we can substitute it back into our original equation to find the measure of each angle. Therefore:
First angle: x = 30 degrees
Second angle: 2x = 60 degrees
Third angle: 3x = 90 degrees
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Complete Question:
The angles of a triangle are in the ratio of 1:2:3. Find the measure of each angle of the triangle
A water valve controls the amount of water flowing through the dabney dam. The probability for the water flow is uniform between 0 and 4 b/s (barrels per second), uniform between 4 and 9 b/s, and uniform between 9 and 14 b/s. The water flow cannot be 14 b/s or greater. The probability of being in the second range is half of the first range. The probability of being in the third range is a fifth of of being in the first range. In other words, the pdf looks like this:
The value of the constant "k", which make the given pdf valid is 6/17 .
Let x be the amount of water flowing through the Dabney dam;
The Probability Density Function(pdf) of x is given as
⇒ f(x) = { k , 0≤x≤2
(1/3)k , 2<x≤4
(1/6)k , 4<x<5
We know that for a valid p.d.f. [tex]\int\limits^{\infty}_{-\infty} {f(x)} \, dx[/tex] = 1 ;
Substituting the functions for the different intervals ,
We get;
⇒ [tex]\int\limits^{0}_{-\infty} {0} \, dx[/tex] + [tex]\int\limits^{2}_{0} {k} \, dx[/tex] + [tex]\int\limits^{4}_{2} {\frac{1}{3} k} \, dx[/tex] + [tex]\int\limits^{5}_{4} {\frac{1}{6} k} \, dx[/tex] + [tex]\int\limits^{\infty}_{5} {0} \, dx[/tex] = 1 ;
⇒ 0 + [kx]²₀ + [kx/3]⁴₂ + [kx/6]⁵₄ + 0 = 1 ;
⇒ 2k + (k/3)(4-2) + (k/6)(5-4) = 1 ;
⇒ 2k + 2k/3 + k/6 = 1 ;
⇒ (12k + 4k + k)/6 = 1;
⇒ 17k/6 = 1;
⇒ k = 6/17.
Therefore, the value k=6/17 will make the pdf valid.
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The given question is incomplete, the complete question is
A water valve controls the amount of water flowing through the Dabney dam. The probability for the water flow is uniform between 0 and 4 b/s (barrels per second), uniform between 4 and 9 b/s, and uniform between 9 and 14 b/s. The water flow cannot be 14 b/s or greater. The probability of being in the second range is half of the first range. The probability of being in the third range is a fifth of of being in the first range.
In other words, the pdf looks like this:
f(x) = { k , 0≤x≤2
(1/3)k , 2<x≤4
(1/6)k , 4<x<5.
Find the value of k , that will make the pdf valid.
The table of values below represents a linear function and shows Marco’s progress as he is pumping gas into his car. What is the output for the initial value?
Gas in Marco’s Car
Seconds Spent Pumping Gas
0
12
24
36
48
Gallons of Gas in Car
3
5
7
9
11
The initial value obtained using the slope-intercept relation is 3 gallons.
We need to obtain the rate of change which gives the amount of gas entering into his car per second :
Rate of change = Rise / Run
Rate of change = - 11 - 3) / (48 - 0)
Rate of change = 8/48 = 1/6 gallons
Using the slope intercept relation :
y = bx + c
b = slope ; c = initial amount of gas
Choosing any pair of (x, y) point on the table :
(0, 3)
3 = 1/6x + c
3 = 1/6(0) + c
3 = 0 + c
c = 3
Therefore, the initial value is 3 gallons.
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Solve the equation. Check your solution.
11+ 3q = 12 + 2q
q=_
11+ 3q = 12 + 2q
subtract 11 from both sides
3q = 1 + 2q
subtract 2q from both sides
q = 1
Calculate the mean: 13, 21, 45, 62, 10
Answer:30.2
Step-by-step explanation:
Answer:
30.2Calculate the mean: 13, 21, 45, 62, 10
13 + 21 + 45 + 62 + 10
= 151151 ÷ 5
= 30.2
Step-by-step explanation:
You're welcome.
number pattern
please help!!!
Answer:
it appears to be going up by adding odd numbers
Step-by-step explanation:
2+3=5+5=10+7=17+9=26 ect....
Help me solve this homework please
Hence Proved that the sum of two consecutive exponents of the number 5 is divisible by 30. and if two consecutive exponents are 5^n and 5^n+1, then their sum can be written as 5^n-1*30.
What is exponents?Exponentiation is a mathematical operation, written as aⁿ. An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
Let suppose two consecutive exponents of 5 are :
5^n and 5^n+1,
Sum of these exponents is
5^n + 5^n+1
So we writes this expression as
5^n + 5^n*5
=5^n(1 + 5)
=5^n * 6
=5^n-1 * 30
So it will be divisible by 30 .
Hence Proved that the sum of two consecutive exponents of the number 5 is divisible by 30. and if two consecutive exponents are 5^n and 5^n+1, then their sum can be written as 5^n-1*30.
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