An acute angle, θ, is in a right triangle such that sin of theta is equal to 3 over 8 period The value of cot θ is (√55)/3.
What is the value of cot θ?To determine the value of cot(θ), Since is an angle in a right triangle and sin() = 3/8, we obtain:
cot(θ) = (√55)/3
In light of the fact that is an acute angle in a right triangle, we may calculate:
sin(θ) = 3/8
Keep in mind:
Hypotenuse = ((opposite cathetus)2 + (adjacent cathetus)2), where sin() = (opposite cathetus)/(hypotenuse)
Next, we have:
contrary cathetus = 3
Using the formula hypotenuse = 8 = (3 + neighboring cathetus)2,
In order to solve this for the nearby cathetus, we obtain:
(82 - 32) = 55 adjacent cathetus
And we are aware of:
(Cot) = (nearby cathetus) (opposite cathetus)
Next, we have:
cot(θ) = (√55)/3
The value of cot θ is (√55)/3.
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Find the LCM of the first five primes
Answer:
The first 5 prime numbers are 2, 3, 5, 7 and 11. Their LCM is 2310
(Pythagorean Theorem and the Coordinate Plane MC)
Determine the perimeter of the right triangle shown
O 10 units
O 24 units
O 36 units
O 64 units
Answer:
A
Step-by-step explanation:
refer the sketch for step by step answer
In the algebraic expression, 6x + 10, x is the (blank), 6 is the (blank), and 10 is the (blank)?
In the algebraic expression, 6x + 10, x is the variable, 6 is the coefficient and 10 is the constant.
What are algebraic expressions?
Algebraic expressions are mathematical phrases that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. They can be used to represent mathematical operations and relationships between numbers.
Examples of algebraic expressions include:
2x + 3 (This is an expression that represents the sum of 2 times the value of x plus 3)
A letter or symbol that denotes an unknowable value is called a variable. The variable here is represented by x.
A coefficient is a number that is multiplied by a variable in an algebraic expression. In this case, 6 is the coefficient of x.
A constant is a value that does not change in an algebraic expression. In this case, 10 is the constant.
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Find the volume of the given solid. Bounded by the cylinder y^2+z^2=4 and the planes x=2y, x=0, z=0 in the first octant
The volume of the given solid. Bounded by the cylinder y^2+z^2=4 and the planes x=2y, x=0, z=0 in the first octant is 16/3 unit cute
V = ∫ dV
= ∫0→2 ∫ 0→π/2 ∫ 0→ 2·r·sin(φ) [ r ] dzdφdr
Factorize to have
= ∫0→2 ∫ 0→π/2 [ r·2·r·sin(φ) - r·0 ] dφdr
= ∫0→2 ∫ 0→π/2 [ 2·r²·sin(φ) ] dφdr
= ∫0→2 [ -2·r²·cos(π/2) + 2·r²·cos(0) ] dr
= ∫0→2 [ 2·r² ] dr
= (2/3)·2³ - (2/3)·0³
Conclusively, this implies that the volume is = 16/3
In conclusion, the volume of the given solid is 16/3. cubic units
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The temperature during the night was -4. In the morning the temperature increased by 3. What is the temperature in the morning
Answer:
-1
Step-by-step explanation:
Night: -4
Morning: -4 + 3 = -1
Find the radius of the circle, if the big square is 30 square units more than the area of the small square.
Answer:
The area of a square is equal to the side length of the square squared. If the side length of the small square is "s" and the side length of the big square is "b", then we can write the following two equations to represent the area of the two squares:
Area of small square = s^2
Area of big square = b^2
Since the area of the big square is 30 units more than the area of the small square, we can write the equation:
b^2 = s^2 + 30
To find the radius of the circle, we need to find the side length of the small square. To do this, we can rearrange the equation above to solve for s:
s^2 = b^2 - 30
s = sqrt(b^2 - 30)
Now we just need to find the value of "b", which is the side length of the big square. To do this, we can use the fact that the big square is inscribed in the circle, so the side length of the big square is equal to the diameter of the circle. Let's call the diameter of the circle "d". Then we can substitute "d" for "b" in the equation above:
s = sqrt(d^2 - 30)
To find the radius of the circle, we just need to divide the diameter of the circle by 2, so the radius is equal to "d" divided by 2. Therefore, the radius of the circle is:
r = d/2 = sqrt(d^2 - 30)/2
So to find the radius of the circle, we just need to know the diameter of the circle. Can you provide the diameter of the circle in the question?:
The radius of the circle is: r = d/2 = sqrt(d^2 - 30)/2
What is area of circle?The area of a circle is π multiplied by the square of the radius. The area of a circle, (A) when the radius 'r' is given is πr2. π is approximately 3.142
Here, we have,
The area of a square is equal to the side length of the square squared. If the side length of the small square is "s" and the side length of the big square is "b", then we can write the following two equations to represent the area of the two squares:
Area of small square = s^2
Area of big square = b^2
Since the area of the big square is 30 units more than the area of the small square, we can write the equation:
b^2 = s^2 + 30
To find the radius of the circle, we need to find the side length of the small square. To do this, we can rearrange the equation above to solve for s:
s^2 = b^2 - 30
s = sqrt(b^2 - 30)
Now we just need to find the value of "b", which is the side length of the big square. To do this, we can use the fact that the big square is inscribed in the circle, so the side length of the big square is equal to the diameter of the circle. Let's call the diameter of the circle "d". Then we can substitute "d" for "b" in the equation above:
s = sqrt(d^2 - 30)
To find the radius of the circle, we just need to divide the diameter of the circle by 2, so the radius is equal to "d" divided by 2. Therefore, the radius of the circle is:
r = d/2 = sqrt(d^2 - 30)/2
So to find the radius of the circle, we just need to know the diameter of the circle.
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Use partial quotients to solve 5,140 ÷ 9 = ___.
The correct answer is 571 quotient and 1 is remainder.We can solve easily by partial quotients.
What are partial quotients division?Partial quotients division is a deviation from the standard method. The divisor is multiplied with a number and the multiple obtained is deducted from the dividend. This multiple of the divisor is as close as possible to the dividend, that is less than or equal to the dividend.
Why do we use partial quotient division?Partial quotient division provides natural differentiation because we can have students solve at a level they are comfortable with and then we can challenge them to find a more efficient way. And this means using fewer steps and solve easily.
Now we solve
first 9 multiply with 500 so we get 4500. 5140-4500=640
then 9 multiply with 70 so we get 630. 640-630=10
then 9 multiply with 1 so we get 9. 10-9=1
Hence 500+70+1=571
And our remainder is 1.
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Which of these systems of equations has infinitely many solutions? Explain your choice(s).
a. (1/2)x - 5y = 10
(-1/2)x + 5y = -10
b. 7x + 2y = -14
-7x + 2y = -14
c. x + 6y = -18
x - 6y = 18
d. (3/4)x - 9y = 12
(-3/4)x + 9y = 12
Does the table below represent a proportional relationship?
A. Yes, because all the ratios of y to x are equal to 2.
B. Yes, because all the ratios of y to x are equal to 3.
C. No, because all the ratios of y to x are not equal.
D. No, because all the numbers are positive.
The table represents a proportional relationship because all the ratios of y to x are equal to 3. (option B)
What is a proportional relationship?Two variables exhibit a proportional relationship if the constant of proportionality remains constant for all the given values in the table.
The equation that is used to represent a proportional relationship is:
y = kx
Where:
k = constant of proportionality
Value of k when x is 1:
3 = k
Value of k when x is 2:
6 = 2k
k = 6 / 2
k = 3
Value of k when x is 3:
9 = 3k
k = 9 / 3
k = 3
Value of k when x is 4:
12 = 4k
k = 12 / 4
k = 3
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Write the following expression in expanded form:9 to power of 3× 7to the power of 4
Exponential Expressions into Expanded Form into Answer:
[tex]9^{3}[/tex] = 9⋅9⋅9 = 729
[tex]7^{4}[/tex] = 7⋅7⋅7⋅7 = 2401
I hope this helps, have a good day!
Answer:
= 9⋅9⋅9 = 729
= 7⋅7⋅7⋅7 = 2401
Step-by-step explanation:
find quotient 5/4 divided by 13/12
Answer: 1.15384615385
Step-by-step explanation:
divide
(2,1)
H
-8-6-4-2
(6,-3)
948
6+Q
4
y
·N··
2+
-2-
-6-
-8
P
2
4 6
R
8
What is the image of R for a dilation with center (0, 0) and a scale factor of
2
X
Answer: free allah long live
Step-by-step explanation:
46564
type an (x,y) ordered pair to put a point on this line.
The ordered pair (x, y) for the given line can be obtained from the graph as (-4, 1).
What is the equation for a straight line?A straight line can be written in the form of an equation as, y = mx + c.
Two straight lines intersect each other only at one point.
When two straight lines are parallel to each other the angle between them is zero.
The graph of the line is given.
In order to find the coordinate of a point do as follows,
Draw a perpendicular line from any point on the line to the x-axis.
The intersection of this line with the x-axis will give the x-coordinate.
Similarly, find the y-coordinate by drawing a perpendicular line to the y-axis.
Applying the above procedure, a point is obtained as (-4, 1).
Hence, the ordered pair for the line shown in the graph is (-4, 1).
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for a pendulum with a length of l meters, the time in seconds that it takes the pendulum to swing back and forth is 2L^1/2. how long does it take a pendulum that is 9 meters long to swing back and forth
It will take 9 seconds a pendulum that is 9 meters long to swing back and forth.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
WE are Given the expression of length L in feet of a pendulum to the time t in seconds that it takes to swing back and forth modeled as;
T = 2√L
Given
Length of the pendulum = 9 meters
Required Time (period)
Substitute the given value into the formula
T = 2√L
T = 2√9
T = 2 x 3
T = 6 seconds
Hence the period is 6 seconds
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Colton works in a department store selling clothing. He makes a guaranteed salary of $500 per week, but is paid a commision on top of his base salary equal to 10% of his total sales for the week. How much would Colton make in a week in which he made $1075 in sales? How much would Colton make in a week if he made xx dollars in sales?
Answer:
Step-by-step explanation:
If Colton makes a guaranteed salary of $500 per week, and he is paid a commission of 10% on top of that for a total of $1075 in sales, he would make an additional $107.50 in commission (1075 x .1 = 107.5). In total, Colton would make 500 + 107.5 = $607.50 in a week where he made $1075 in sales.
Solve for -10 - 9/2 x <80
Answer:
X > -20
Step-by-step explanation:
-10 - 9/2 x < 80
Move 10 to the other side
- 9/2 x < 80 + 10
Simplify
-9/2 x < 90
-9 x < 180
x > -20
(We switch the inequality sign if we are dividing with negatives)
Toni runs around her school's baseball diamond. Each side is 27 m long. Note: A baseball diamond is square. How far does Toni run? m
Answer:
If we assume she runs around it once and since they tell us its a square: 27x4=108
Step-by-step explanation:
Use the diagram to find the indicated angle measures. Please do 1, 2, and 3. Please need ASAP!!!!!!!!!!!!!!! 30 POINTS
The measures of given figures are m∠ADC is 90 degrees and m∠DAC will be 34 degrees
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given m∠B= 57 degrees
m∠c= 51 degrees
segment AD bisects m∠BAC
then m∠ADC we need to find.
As AD is perpendicular to BC, the angle of m∠ADC is 90 degrees.
Given m∠B= 66 degrees
m∠BAD=34 degrees
Now we need to find m∠DAC
m∠DAC will be 34 degrees
Hence, the measures of given figures are m∠ADC is 90 degrees and m∠DAC will be 34 degrees
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p.
Sue uses of a pitcher of sweet tea to fill
each of 6 matching glasses. What fraction of
the pitcher does Sue use to fill 1 glass?
Answer:
P. Sue uses 1/6 of the pitcher to fill 1 glass
Step-by-step explanation:
Hot dogs and corndogs were sold at last night's football game. A total of 81 were sold which allowed the concession stand to bring in $201. How many of each were sold?
The total number of corn dogs sold is 28 corn dogs and number of hotdogs is 53
What is total cost?Total cost is the overall expense incurred for a particular product, service, or project. It includes both fixed and variable costs, such as materials, labor, and overhead. It is often used in business and economic analysis as a measure of the efficiency and profitability of a particular venture. The total cost of a product or service can also be used to set prices and make pricing decisions.
According to question:-
step1
h = number of hotdogs
c = number of corndogs.
cost of hotdog = $3
corn dog = $1.50
The equation:
3h + 1.50c = 201 (1)
h = 2c - 3 (2)
step2
substitute (2) into (1)
3(2c - 3) + 1.50c = 201
6c - 9 + 1.50c = 201
7.50c - 9 = 201
7.50c = 201 + 9
7.50c = 210
c = 210/7.50
c = 28
Therefore,
h = 2c - 3
= 2(28) - 3
= 56 - 3
= 53
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5.7935 rounded to the nearest thousand
Answer:
5.794
Step-by-step explanation:
The seven after the decimal point is the tenth digit, the nine is the hundredth, and the 3 is the thousandth place. Therefore, we look at our neighbor (the number next to the thousandth place) and if its 5 or more we round up, but if its 4 or less we keep it the same.
12 divided by four
plus 2 x 6+4
Answer:
19
Step-by-step explanation:
12 divided by four plus 2 x 6+4
assuming that the question is:
12 : 4 + 2 x 6 + 4 =
3 + 12 + 4 = (remember PEMDAS)
19
What the answer to this 9 - 3y +3y =4
Answer:
its the answer
Step-by-step explanation:
the answer to the question is the answer
hehe
On Saturday, a local hamburger shop sold a combined total of 396 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Let x be the number of hamburgers sold, then the number of cheeseburgers sold can be represented as 2x. The total number of hamburgers and cheeseburgers sold is the sum of these two quantities, so we can write an equation:
x + 2x = 396
To solve for x, we can combine like terms on the left side of the equation:
3x = 396
Then we can divide both sides by 3 to get:
x = 132
So, the number of hamburgers sold on Saturday is 132.
A parade traveled 8 miles in 4 hours. How far did the parade travel per minute?
Answer:
1/30 of a mile per minute.
Step-by-step explanation:
8/4 = 2 miles per hour.
2/60 = 1/30 of a mile per minute.
2. Avea checked out 18 books
from the library. Half of them
are nonfiction. How many
nonfiction books did she check
out?
Answer: she checked out 9 nonfiction books
Step-by-step explanation:
18-9=9
List five vectors in Span (V₁ V₂). Do not make a sketch.
V₁ = (8 2 7 )
V₂ = (-6 4 0 )
List five vectors in Span (V₁ V₂).
(Use the matrix template in the math palette. Use a comma to separate vectors as needed. Type an integer or a simplified fraction for each vector element.)
Five vectors in Span (V₁ V₂) where V₁ = (8 2 7 ) and V₂ = (-6 4 0 ) is.
n(V₁ + V₂), n ∈ I, I = 1, 2, 3, 4, 5.
What is span in vector space?In mathematics, the set of all linear combinations of the vectors in S is referred to as the linear span, Denoted span(S), Either the intersection of all linear subspaces containing S, or the smallest subspace containing S, can be used to describe it. A vector space is therefore nothing more than the linear range of a set of vectors.
The vectors that are in the same span should be a multiple of the vectors
V₁ = (8 2 7 ), V₂ = (-6 4 0 )
Now, V₁ + V₂ = (2 6 7).
So, The five vectors in the span of V₁ and V₂ is,
2×(2 6 7).
= (4 12 14).
- 2×(2 6 7).
= (- 4 - 12 - 14).
3×(2 6 7).
= (6 18 21)
- 3×(2 6 7)
= (- 6 - 18 - 21).
5×(2 6 7).
= (10 30 35).
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HELPPP ASPPO!!
4x -y=6
-4x +y =8
which statement correctly describes the system of equations
The equation system is appropriately described by the formula 4x - y=6.A mathematical formula known as an equation combines two assertions .
what is equations ?A mathematical formula known as an equation combines two assertions using the equal sign (=) to denote equivalence. The terms 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14, for example. Mathematical equations are used to express the relationship between two phrases on either side of a letter. In most cases, the symbol serves as the sole variable. a good example is 2x - 4 = 2.
given
Graphing, substitution, and elimination are the three techniques used to solve systems of equations.
By graphing the given equations, you can easily solve a system by finding the point(s) where they all cross.
The values of the variables you are solving for will be provided by the coordinate of this point.
The equation system is appropriately described by the formula 4x - y=6.
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Find the distance between the points
(-5/2, 9/4) and(-1/2,-3/4)
Give the exact distance and an approximate distance rounded to at least 2 decimal places.
Make sure to fully simplify any radicals in first answer
Answer:
Step-by-step explanation:
distance = [tex]\sqrt{(-5/2+1/2)^{2} +(9/4+3/4)^{2} }=\sqrt{13}[/tex]=3.61
Help me please 35 points on the line
Answer shown in bold
401924109147The non-bolded values to the left are not to be typed in the answer box. They're present to keep track of the values. In other words, you'll type "40" without quotes into the first box, then "19" without quotes in the second box, and so on.
========================================================
Explanations:
Add up all of the values in the Venn diagram to find the total. Therefore, 9+10+14+7 = 40 students were surveyed.We add the values in the "social interaction activities" circle only. There are 9+10 = 19 students here.This time add up the values in the "technology driven activities" to get 10+14 = 24 students.The answer is 10 because this value is in the overlapped region between the two circles. The answer is 9 since this value is in the "social interaction activities" circle, but outside the other circle. The answer is 14 as this value is in the "technology driven activities" circle, but outside the other circle.The answer is 7 because this value is outside both circles.Let me know if you have any questions.