Using Pythagoras theorem If sin tetha = x/4, then cos tetha = √(16-x²)/4
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
The sides of this triangle have been named Perpendicular, adjascent and Hypotenuse. If sin (tetha) = x/4, this means
x = opposite and
4 = hypotenuse
From hypotenuse² = opposite² + adjacent²
4² = x²+y²
y² = 16-x²
y = √ ( 16-x²)
cos (tetha) = adjacent/ hypotenuse
cos (tetha) = √(16-x²)/4
Therefore the value of cos (tetha) = √(16-x²)/4
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Point A is at ( -3,4) and Point C is at ( 2,-6 )
Find the coordinates of point B on line AC suck as the ratio of AB to AC is 4:5
The required coordinates of point B will be (2/9, -14/9).
Point A is at ( -3,4) and Point C is at ( 2,-6 )
Given that point B on line, AC suck as the ratio of AB to AC is 4:5
The coordinates of point B will be,
{[(mx2+nx1)/(m+n)],[(my2+ny1)/(m+n)]}
Breaking it down, the x coordinate is (mx2+nx1)/(m+n) and the y coordinate is (my2+ny1)/(m+n)
As per the question, m = 4 and n = 5
The coordinates of point B :
⇒ {[(4×-3+5×2)/(4+5)],[(4×4+5×-6)/(4+5)]}
⇒ {[(-12+10)/(9)],[(16-30)/(9)]}
⇒ (2/9, -14/9)
Thus, the required coordinates of point B will be (2/9, -14/9).
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In a class of 25 students, 15 of them have a cat, 16 of them have a dog and 3 of them have neither.
Find probability that a student chosen at random has a cat or a dog.
The probability that a student chosen at random has a cat or a dog is; P(cat or dog) = 22/25.
What is probability?
Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.
Main body:
According to the question, the total number of students is; 25.
15 of them have a cat
16 of them have a dog
while, 3 of them have neither
where, x = number if students who own a cat and a dog.
Consequently, the total number of students who own a cat, a dog, both or neither is as follows;
15-x + x + 16-x + 3 = 25.
-x = 25 - 34
In essence, x = 9
the number of students who own a cat and a dog is 9.
Therefore, probability that a student chosen at random has a cat and a dog is therefore;
P(cat and dog) = 9/25.
Therefore probability that a student chosen at random has a cat or a dog is 22/25.
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A report card shows that a student earns 21 21 points on a test with a total of 25 25 points. What percentage of the total points has the student earned on the test?.
When a report card shows that a student has earned 21 points on a test with a total of 25 points, it can be concluded to state that the student has secured 84 percentage of the total points of the test.
The computation of the percentage of points secured by the student out of the total available points in a test can be done using the generalized formula and the use of provided information into the same as below,
Percentage = Scored Secured / Total Points x 100
Percentage = 21 / 25 × 100
Percentage = 0.84 × 100
Percentage = 84 percentage.
Therefore, the student has earned 84 percentage of total points on a test.
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if n is an integer for which the greatest common factor of n and 18 is 6 and the least common multiple of n and 9 is 126, what is the value of n?'
The value of n is 42.
What is greatest common factor?
Greatest Common Factor. The highest number that divides exactly into two or more numbers. It is the "greatest" thing for simplifying fractions.
The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number. 18 and 24 share one 2 and one 3 in common. We multiply them to get the GCF, so 2 * 3 = 6 is the GCF of 18 and 24.Similarily , for 42 and 18 , greatest Common Factor is 6.
What is least common multiple?
The least common multiple of two numbers is the smallest number that is a multiple of both of them.
How do you find least common multiple?
Find the LCM by listing multiples.
List the first several multiples of each number.Look for multiples common to both lists. If there are no common multiples in the lists, write out additional multiples for each number.Look for the smallest number that is common to both lists.This number is the LCM.thus , LCM of 42 and 9 is 126.
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You work at Mike's pizza shop. You have the following information about the 7 pizzas in the oven: 3 of the 7 have thick crust and 2 of the 3 thick crust pizzas have mushrooms. Of the remaining 4 pizzas, 2 have mushrooms. Choose a pizza at random from the oven. Make a two-way table to model this chance process.
make a Venn diagram to model this chance process.
4/7 is probability a two-way table to model this chance process.
What are examples and probability?
A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.
No events getting thick crust pizza and getting pizza with mushrooms are not disjoint as we can have pizza that has thick crust and mushroom both.
No events are not independent as
P(thick and having mushroom) is not equal to P(thick crust)*P(having mushroom)
P( thick and having mushroom) = 2/7
P(thick crust) = 3/7
P( having mushroom) = 4/7
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If y varies directly with x what is the equation when y=-64andx=16
Answer: when y = -64 and x = 16 is y = -4x. This equation states that for every value of x, the corresponding value of y is equal to -4 times the value of x.
i want the answer
fast
Answer:
original fraction = [tex]\frac{4}{5}[/tex]
Step-by-step explanation:
let the denominator of the fraction be x then the numerator is x - 1 , so
original fraction is
[tex]\frac{x-1}{x}[/tex]
if 1 is added to the numerator and 5 to the denominator , then fraction is
[tex]\frac{-1+1}{x+5}[/tex] = [tex]\frac{x}{x+5}[/tex]
equate this to [tex]\frac{1}{2}[/tex]
[tex]\frac{x}{x+5}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = x + 5 ( subtract x from both sides )
x = 5
then original fraction is
[tex]\frac{x-1}{x}[/tex] = [tex]\frac{5-1}{5}[/tex] = [tex]\frac{4}{5}[/tex]
Answer:
Below
Step-by-step explanation:
Original fraction (x-1) / x <====given (use in final step below)
Altered fraction (x-1 +1) / (x+5) = 1/2 <====solve this for 'x'
x / (x+5) = 1/2 cross multiply
2x = x+5
x = 5
So original fraction was 4/5
What is 15% of Jasmine's number?
I am thinking of a number.
10% of my number is 64.
Answer:
96
Step-by-step explanation:
100% of her number is 64015% of 640 is 96Please check if ur able to help with these Segments OA and OB are radii ofthe semicircle above. Arc AB has length 3n and OA = 5. What is the value of x ?'
OA=5 and the length of arc AB is 3π. The x value is [tex]108[/tex]°.
The circle's radius and arc length are both provided. Finding the angle that the arc occupies on the center O is necessary.
The correct formula is
s=rФ
Where
arc length is measured in radians,
r is the radius, and
Ф is the angle (in radians)
If Ф is in degrees, we apply the formula.
s= Ф[tex]*\frac{\pi }{180} *r[/tex]
In order to determine the value of theta, we must enter the specified values of s and r into the formula above.
[tex]3\pi =[/tex]Ф[tex]*\frac{\pi }{180} *5[/tex]
[tex]3\pi *\frac{180}{\pi } *\frac{1}{5}=[/tex]Ф
Ф=[tex]108[/tex]°
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Cual es la respuesta
The required simplified equivalent fraction of 0.32 is 8/25. Option A is correct.
What is decimal value?Decimal value is defined as showing the place value of the digits in a decimal number. If any proportion of the digit is lower than 1 it would be represented after the dot right to the absolute value,
Here,
Given the terminating decimal value,
= 0.32
= 32/100
= 8/25
Thus, the required simplified equivalent fraction of 0.32 is 8/25. Option A is correct.
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Caroline babysit for two families-Nelsons and the smiths. use the information below to compare her earnings
Answer:
6.25h
Step-by-step explanation:
suppose you have 1/6 chance of winning with a scratch-off lottery ticket. if you buy 30 ticket what is the probability of winning with all 3
Answer: 18%
Step-by-step explanation:
I gogled
a jet airliner travels 1680 miles in 3 hours with a tail wind. the return trip, into the wind, takes 3.5 hours. write a system of equations whose solution is the ground speed of the airplane and the wind speed.
A system of equation is 1680mi3hr = p−w×600×2hr -p + w for a jet airliner travels 1680 miles in 3hours with a tail wind.
Let p be the speed of the jet airliner
and w be the speed of the tail wind
It takes the plane 3 hours to go 1680 miles when a jet airliner travels with a tail wind and and 3.5 hours to go 1680 miles against the wind.. So, using system of equations we get
1680mi3hr = p−w×600×2hr = p + w
Solving for the left sides we get:
200mph = p - w
300mph = p + w
Now solve for one variable in either equation, we use
200mph = p - w
Add w to both sides:
p = 200mph + w
Using the value of x, we can found the value of w using system of equations.
300mph = (200mph + w) + w
Combine like terms:
300mph = 200mph + 2w
Subtract 200mph on both sides:
100mph = 2w
On dividing by 2:
50mph = w
So the speed of the tail wind is 50mph.
Therefore, 200mph = p - 50mph
Add 50mph on both sides:
250mph = p
Hence, speed of jet airliner is 250mph.
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find the flux of the constant vector field v→=3i→ 2j→−5k→ through a square plate of area 25 in the xz-plane oriented in the positive y-direction.
The flux across a surface is an indicator of the rate at which fluid is flowing through it when there is a fluid flowing in three dimensions and a surface positioned inside that space.
What is Electric Flux?A feature of an electric field is electric flux. One way to conceptualize it is as the quantity of forces interacting in a specific space. According to conventional wisdom, electric field lines begin with positive electric charges and conclude with negative charges. A closed surface's field lines are seen as negative when they are directed into it, and as positive when they are directed out of it.Every field line that is directed into a closed surface continues through the interior and is often directed outward somewhere else on the surface if there is no net charge present within the surface. The net, or total, electric flux is zero because the size of the negative and positive fluxes are just about equal.A closed surface that contains a net charge will have a total flux that is proportional to the enclosed charge, positive if it is positive and negative if it is negative.To Learn more About flux across refer to:
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Answer:
The flux of the field through a square of 25 area whose plane is the xz-plane oriented in the positive y-direction.is 50
What is Flux?
Any effect that seems to pass through or move through a surface or substance is referred to as a flux, whether it actually flows or not. There are numerous applications of the concept of flux in applied mathematics and vector calculus. Flux, a vector quantity that describes the size and direction of the flow of a substance or attribute for transport phenomena. Flux is a scalar number in vector calculus, defined as the surface integral of a vector field's perpendicular component over a surface.
According to question
The flux of an field is given by,
ΦE = E.A = EA cos θ
where θ is the angle formed by the field lines and the normal (perpendicular) to the surface, S, and E, the magnitude of the field
vector field is v→=3i→ 2j→−5k→
Solving for each direction separately
Clearly
For i and k then flux is Zero because the angle b/w field and normal to surface is 90° and Cos(90) = 0
Now for j
E = 2
S = 25
θ = 0° (cos0° = 1)
Φ = EScosθ
= 2*25*1
= 50
Therefore, the flux of the field through a square of 25 area whose plane is the xz-plane oriented in the positive y-direction.is 50
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Please help me, really need help
The pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.
What is vertical opposite angle ?
When 2 lines meet one another, then the other angles, shaped thanks to intersection ar known as vertical angles or vertically opposite angles. A try of vertically opposite angles ar continuously adequate to one another. Also, a angle and its adjacent angle are supplementary angles, i.e., they add up to a hundred and eighty degrees.
Main body:
1st pair of line intersect each other , so ∠1 = ∠2 by using vertical opposite angle.
2nd pair of line also intersect each other , so ∠3 ,∠4 are adjacent angles.
Hence ,pair of 1st line is vertical opposite angle and 2nd one is adjacent angles.
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Determine the measure of the indicated angle 100 80 90 or 110
Answer: The answer is 80 degrees
Step-by-step explanation:
Interior consecutive angles add up to 180 degrees
1. If the required reserve ratio is 10% and the Fed conducts an open market purchase of $100, what is the maximum possible change in the money supply?
100, 1,000, 10,000 or 10
The maximum possible change in the money supply is $1000.
In the given question, if the required reserve ratio is 10% and the Fed conducts an open market purchase of $100, we have to find the maximum possible change in the money supply.
The required reserve ratio is 10%.
The Fed conducts an open market purchase of $100.
So the maximum possible change in the money supply is
money multiplier=1/RRR
money multiplier=100/10
money multiplier=10
Open market purchase of $100
Change in money supply is 10*100=$1000
So, the maximum possible change in the money supply is $1000.
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solve (x 1)2 – 4(x 1) 2 = 0 using substitution. u = x 4(x 1) x 1 (x 1)2 select the solution(s) of the original equation. x = 1 x = 2 x = 3 x = 1 - x = 2 - x = 3 -
The necessarily simplified answer to the provided experiment is given as x = 1 ± √2.
What is simplification?A mathematical expression is simplified when it is replaced with a simpler, usually shorter, equivalent expression.
So, for the given phrase (x + 1)2 - 4(x + 1) + 2 = 0, find the simple answer as follows:
The expression is: (x + 1)² – 4(x + 1) + 2 = 0
Replace x + 1 = u in the preceding equation:
u² - 4u + 2 = 0
u² - 4u +4 - 4 + 2 = 0
(u - 2)² = 2
u - 2 = ±√2
replace with u = x + 1:
x + 1 - 2 = ±√2
x - 1 = ±√2
x = 1 ± √2
Therefore, the necessarily simplified answer to the provided experiment is given as x = 1 ± √2.
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Correct question:
Solve (x + 1)2 – 4(x + 1) + 2 = 0 using substitution. u = Select the solution(s) of the original equation.
what is half of 7 3/4 on a tape measure
So, the half of [tex]7\frac{3}{4}[/tex] is [tex]3\frac{7}{8}[/tex]. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
A fraction is a numerical value that represents a part of a whole. It is typically written as a ratio of two numbers, with a line separating the numerator and the denominator. For example, the fraction one-half can be written as 1/2. Fractions are often used to represent a part of a whole number or a part of a whole object, such as a pie that has been cut into several pieces.
To find half of 7 3/4 on a tape measure, we need to follow these steps:
Convert the mixed number 7 3/4 to an improper fraction. This can be done by multiplying the whole number, 7, by the denominator of the fraction, 4, and adding the numerator, 3, to the product. This gives us 7 x 4 + 3 = 31. So, 7 3/4 is equal to 31/4.Divide the numerator of the improper fraction by 2 to find half of the original mixed number. In this case, we divide 31 by 2 to get 31/2.Convert the resulting improper fraction, 31/2, back into a mixed number. To do this, we divide the numerator, 31, by the denominator, 2, and write the remainder, 1, as the numerator of the fraction part of the mixed number. This gives us the final answer of 3 7/8.Learn more about improper fraction, here https://brainly.com/question/21449807
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Calculator
What is the measure of angle A in this triangle?
Enter your answer as a decimal in the box. Round only your final
answer to the hundredths place (2 decimal places).
Answer: 73.74
Step-by-step explanation: I just used a calculator. I hope it's right. Check me if I'm wrong.
What is the slope of the line that passes through the points(3,−3) and(18,−3)? Write your answer in simplest form.
Answer: (3, -3) and (18, -3) is 0
Step-by-step explanation:
The slope of a line is a measure of the line's steepness, and it is calculated by taking the difference in the y-coordinates of two points on the line, divided by the difference in their x-coordinates. In this case, the line passes through the points (3, -3) and (18, -3), and the y-coordinates of both points are -3. Therefore, the difference in the y-coordinates is 0, and the slope of the line is 0.
To write this answer in simplest form, we can simply express the slope as 0/1, which can be simplified to 0. Therefore, the slope of the line that passes through the points (3, -3) and (18, -3) is 0.
Answer:
0
Step-by-step explanation:
We can find the slope of the line given two points
m= ( y2-y1)/(x2-x1)
= ( -3 - -3)/(18 -3)
= (-3+3)/(15
= 0/15
= 0
Which statement describes the graph of 4x7 40x6 100x5?O The graph crosses the x axis at x = 0 and touches the x axis at x = 5.O The graph touches the x axis at x = 0 and crosses the x axis at x = 5.O The graph crosses the x axis at x = 0 and touches the x axis at x = –5.O The graph touches the x axis at x = 0 and crosses the x axis at x = –5.
The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5.
Option (C) is correct.
What is a function in mathematics?
In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. The set of inputs is called the domain of the function, and the set of possible outputs is called the range of the function.
First, factorize the function f(x):
[tex]f(x)=4x^7+40x^6+100x^5\\\\f(x)=4x^5(x^2+10x + 25)\\\\f(x)=4x^5(x+5)^2[/tex]
When f(x)=0, you get that
[tex]4x^5(x+5)^2 = 0\\\\x=0 $ or $ x = -5[/tex]
This means that the graph intersects the x-axis at points (0,0) and (-5,0). But:
1. since the degree at term [tex]x^5[/tex] is odd, point (0,0) is x-intercept;
2. since the degree at term [tex](x+5)^2[/tex] is even, point (-5,0) is the tangent point (see the attached graph of the function).
Hence, The graph crosses the x-axis at x = 0 and touches the x-axis at x = –5.
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Which values are solutions to the inequality?
3r≤4r−6
Select each correct answer.
Responses
r = 4
r = , 4
r = 5
r, = 5
r = 6
r, = 6
r = 7
The solution of the inequality 3r ≤ 4r - 6 is r ≥ 6.
How to solve inequality?In Mathematics, the relationship between two values that are not equal is defined by inequalities.
An inequality have the symbol <, >, ≤ and ≥. Hence, the inequality can be solved as follows:
3r ≤ 4r - 6
subtract 4r from both sides of the inequality,
3r ≤ 4r - 6
3r - 4r ≤ 4r - 4r - 6
3r - 4r ≤ - 6
- r ≤ -6
divide both sides of the inequality by -1
Therefore, the solution is r ≥ 6
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Pedro takes 3.5 hours to drive 238 kilometers. What is his speed?
Group of answer choices
35 kilometers per hour
24 kilometers per hour
68 kilometers per hour
83 kilometers per hour
Answer: 68 kilometers per hour
Step-by-step explanation:
Take 238 divided by 3.5 hours = 68 km per hour
the vertices of a triangle are A(-2,1), B(2,2) and C(6,-2). find the equation of the altitude AD drawn from A to BC
Answer:
To find the equation of the altitude from point A to side BC, we can use the formula for the equation of a line in point-slope form, which is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
We can find the slope of the line by using the formula for the slope of a line between two points:
m = (y2 - y1)/(x2 - x1)
We can use this formula to find the slope of line BC, which is the line connecting points B and C. Substituting the coordinates of these points into the formula gives us:
m = (2 - (-2))/(2 - 6) = 4/-4 = -1
Next, we can use the point-slope form of the equation of a line to find the equation of the altitude from point A to line BC. Substituting the coordinates of point A and the slope of line BC into the point-slope formula gives us:
y - 1 = -1(x + 2)
This is the equation of the altitude from point A to line BC.
Step-by-step explanation:
SELF EXPLANATORY
leaning ladder a -ft ladder is leaning against a building. if the base of the ladder is ft from the base of the building, what is the angle of elevation of the ladder? how high does the ladder reach on the building?
The angle of elevation is 72.5° and the height at which the ladder will elevate on the building is 19.06 ft.
Here we have to find the angle of elevation of the ladder and the height the ladder will reach on the building if the ladder is leaned against a building.
Data given:
length of the ladder = 20 ft
the base of the ladder = 6ft
we have to find the angle of elevation.
cos Ф = base/ hypotenuse
= 6/20
Ф = [tex]cos^{-1}[/tex] ( 6/20)Ф
= 72.5°
Now we have to find how high the ladder reaches on the building when leaned against a building.
sin(72.5°) = x/ 20
x = 0.953 ×20
x = 19.06 ft
Therefore the angle of elevation is 72.5° and the ladder will elevate to 19.06.
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Angel Sum Theorem PLEASE HELP with explanation if possible
Answer:
y = 90°
Step-by-step explanation:
You want the value of y in the diagram showing y as the angle at the base where the isosceles triangle a.pex angle bisector meets the base.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°.
Consider the large outside triangle. The sum of its angles is ...
60° +2x +60° = 180°
2x = 60° . . . . . . . . . . . . subtract 120°
x = 30° . . . . . . . . . . divide by 2
Now, consider the left smaller triangle. The sum of its angles is ...
60° +x +y = 180°
60° +30° +y = 180° . . . . . . use the known value of x
y = 90° . . . . . . . . . . . . subtract 90°
__
Additional comment
The a.pex angle bisector of an isosceles triangle is always an altitude that meets the base at right angles. The meeting point is the midpoint of the base, so that segment is also a median.
The halves of the isosceles triangle are congruent right triangles, so the base angle is complementary to the angle marked x.
A resort manager is choosing a committee of four people to discuss employment issues. He'll choose from eight housekeepers, three desk clerks, and five maintenance workers. How many possible committees are there if there have to be at least two housekeepers?
Answer:
There are 1,680 possible committees if there have to be at least two housekeepers.
Step-by-step explanation:
In the figure below, m||n. Match the angle pairs with the
correct label for the pairs.
On solving the provided question, by properties of parallel lines we got to know that - 1 - A 2 - C 3 - B 4 - D
what is alternate exterior angles?When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.
Matches are -
1 - A
2 - C
3 - B
4 - D
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an 7.40-cm-diameter, 370 g solid sphere is released from rest at the top of a 2.00-m-long, 19.0 ∘ incline. it rolls, without slipping, to the bottom.
The angular velocity of the sphere at the bottom of the incline is 88.1 rad/s.
What is angular velocity?In physics, angular velocity or angular speed, also recognized as angular frequency vector, is a pseudovector portrayal of how fast the angular position or orientation of an object changes over time.
So, angular velocity will be:
mg(h sinθ) = 1/2 Iω² + 1/2mv²
I of solid sphere = 2/5 mr²
Hence,
mg(h sinθ) = 1/2 (2/5 mr²) ω² + 1/2 mv²
Now remove the mass:
g h sin θ = 1/5 r² ω² + 1/2 v²
ω = v/r, v = ωr
Now, calculate angular velocity as follows:
g h sin θ = 1/5 r² ω² + 1/2 (ωr)²
g h sin θ = (7/10) r² ω²
ω² = 10 g h sin θ/7 r²
ω = √10 g h sin θ/7 r²
= √10 (9.8) (2.1) sin 25° / 7 (0.04)²
= 88.1 rad/s
Therefore, the angular velocity of the sphere at the bottom of the incline is 88.1 rad/s.
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Complete question:
An 8.0 cm diameter, 400 g sphere is released from rest ta the tip of a 2.1 m long, 25-degree incline. It rolls, without slipping, to the bottom. What is the sphere's angular velocity at the bottom of the incline?
