Answers
The missing side is [tex]5\sqrt{3}[/tex].
What are basic Trigonometric functions?
The angles of sine, cosine, and tangent are the primary classification of functions of trigonometry. And the three functions which are cotangent, secant, and cosecant can be derived from the primary functions. Basically, the other three functions are often used as compared to the primary trigonometric functions.
In a Right-angled triangle, the tangent of an angle is equal to the opposite side/adjacent side.
from the given figure,
tan 60° = x/5
[tex]\sqrt{3}=\frac{x}{5}\\ x=5\sqrt{3}[/tex]
Therefore, The missing side is [tex]5\sqrt{3}[/tex].
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Related Questions
Compact fluorescent light (CFL) bulbs reduce energy waste. The amount of energy
waste that is reduced each day in a certain community can be estimated by -b² + 8b
where b is the number of bulbs. Divide by b to find the average amount of energy
saved per CFL bulb.
Answers
So, the average energy saved per bulb (E) can be represented as follows:
E = (-b^2 + 8b) / b
To simplify, we can factor out the b term in the numerator:
E = (-b + 8)
So, the average energy saved per CFL bulb is equal to -b + 8.
It's important to note that this equation assumes a linear relationship between the number of bulbs and the energy saved, which may not necessarily hold true in reality. It's also important to take into account other factors that could affect the amount of energy saved, such as the usage patterns of the bulbs and the efficiency of the electrical system they are used in
80% of a number is x. What is 100% of the number? Assume x>0
Answers
100% of the number is: the number x ÷ 0.8 × 1 = the number If 80% of a number is x, then the number can be found by dividing x by the percentage as a decimal.
To convert a percentage to a decimal, divide the percentage by 100.
So, if 80% of the number is x, then:
x ÷ 0.8 = the number
In other words, to find the whole number, we need to divide the part (x) by the percentage as a decimal (0.8).
Once we have the whole number, we can find 100% of it by simply multiplying the whole number by 1.
So, 100% of the number is:
the number x ÷ 0.8 × 1 = the number
In conclusion, if 80% of a number is known, the whole number can be found by dividing the part by the percentage as a decimal, and 100% of the number can be found by simply multiplying the whole number by 1. Understanding the concept of percentage and the ability to convert between percentages, decimals, and whole numbers is an important skill in various areas of life and work.
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Linda wants new carpeting for her bedroom her bedroom is a 75m by 50m rectangle if carpeting cost AED 12 per square meters how much will it cost to lay carpet for her entire bedroom?
(please answer as soon as possible i need this answer) thank you
Answers
If carpeting cost AED 12 per square meters for the bedroom of 75m by 50m, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.
To calculate the cost of laying carpet for Linda's bedroom, we need to know the area of the bedroom and the cost per square meter of the carpeting.
Linda's bedroom is a rectangle with a length of 75 meters and a width of 50 meters. To calculate the area of the bedroom, we multiply the length by the width:
Area = length x width = 75 meters x 50 meters = 3750 square meters
Now that we know the area of the bedroom is 3750 square meters, we can find the total cost of the carpeting by multiplying the area by the cost per square meter. The cost per square meter is given as AED 12, so:
Total cost = area x cost per square meter = 3750 square meters x AED 12/square meter
Multiplying the area by the cost per square meter gives us:
Total cost = AED 45,000
Therefore, it will cost AED 45,000 to lay carpet for Linda's entire bedroom.
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Which residual plot shows that the line of best fit is a good model?
Answers
A residual plot that shows clear patterns or trends in the residuals suggests that the line of best fit is not a good model.
Here are some characteristics of a residual plot that suggest that the line of best fit is a poor model,
The residuals show a clear pattern or trend, such as a curve or a U-shape.
The residuals are not evenly distributed above and below zero.
There are one or more outliers or extreme values that stand out from the rest of the data.
The variability of the residuals changes across the range of the predictor variable.
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How does the distance change during the last section of tom’s journey? What does this mean? Explain your reasoning
Answers
The distance is decreasing with time meaning that the object is going back to the starting point.
What does it mean when distance decreases with time?When distance decreases with time, it means that the object is moving towards its starting point or moving in the opposite direction from its initial position. In other words, the object is moving backwards or reversing its direction of motion.
Distance is a measure of the total amount of ground covered by an object in motion, while time is a measure of how long it takes the object to cover that distance. If the object is moving towards its starting point, it means that it is covering less and less distance over time, or the distance it covers is decreasing.
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Write a linear equation in slope intercept form y=mx+b that passes through (-6,-1) and is parallel to y=-2/3x+1
Answers
On solving the provided question we can say that the slope intercept of line is y = (3/2)x + 8
What is slope intercept?In mathematics, the intersectiοn point is the place on the y-axis where the slοpe of the line crosses. a place where the y-axis crosses οn a line or curve. Y = mx+c, where m stands fοr the slope and c for the y-intercept, is used as the equatiοn for the straight line to shοw this. The slope (m) οf the line and its y-intercept (b) are emphasised in the equatiοn's intercept form.
When an equation has the intercept fοrm (y=mx+b), the slope is m and the y-intercept is b. Sοme equations can alsο be rewritten such that they seem to be slοpe intercepts. If y = x is rewritten as y=1x+0, for instance, the slοpe and y-intercept are bοth changed to 1.
the line is y = -2/3x+1
so the slope, m = -2/3
since it parallel , new slope = 3/2
the slope intercept of line is
y +1 = 3/2(x+6)
y + 1= (3/2)x + 9
y = (3/2)x + 9 - 1
y = (3/2)x + 8
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5. Pilihan ganda5 menit1 ptQ. An equilateral triangle has an altitude of 15 m. What is the perimeter of the triangle? Leave your answer in radical form.Pilihan jawaban30√3 m10√3 m5√3 m30 m
Answers
If an equilateral triangle has an altitude of 15 meters, then the perimeter of the equilateral triangle is 30[tex]\sqrt{3}[/tex] meters
The altitude of the equilateral triangle = 15 meters
The equilateral triangle is the triangle with equal side. The interior angle of the equilateral triangle will be 60 degrees. Number of vertices and edges will be three . The line of symmetry is 3
The altitude of of the equilateral triangle h = [tex]\sqrt{3}[/tex]a /2
Where h is the altitude of the equilateral triangle
a is the side of the equilateral triangle
Then the equation will become
15 = [tex]\sqrt{3}[/tex] a /2
[tex]\sqrt{3}[/tex]a = 15 × 2
Multiply the terms
[tex]\sqrt{3}[/tex]a = 30
Move [tex]\sqrt{3}[/tex] to the right hand side of the equation
a = 30 / [tex]\sqrt{3}[/tex]
a = 10[tex]\sqrt{3}[/tex] meters
The perimeter of the equilateral triangle = 3 × 10[tex]\sqrt{3}[/tex]
= 30[tex]\sqrt{3}[/tex] meters
Therefore, perimeter of the equilateral triangle is 30[tex]\sqrt{3}[/tex]
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Electric utility poles in the form of right cylinders are made out of wood that costs $25.81 per cubic foot. Calculate the cost of a utility pole with a radius of 0.5 ft and a height of 25 ft. Round your answer to the nearest cent.
Answers
The volume of a cylinder can be calculated as π * radius^2 * height. In this case, the radius is 0.5 ft and the height is 25 ft, so the volume is:
π * 0.5^2 * 25 = 19.63 cubic feet
So the cost of the utility pole would be 19.63 * $25.81 = $509.24
Rounding to the nearest cent, the cost of the utility pole would be $509.24, which can be rounded to $509.00.
POINTS UP FOR GRABS!!!!
Answers
The ordinary numbers for the expressions will be
a. 3.25*10⁴ = 32500
b. 6.04*10⁻³= 0.00604
c. 2400000 = 2.4*10⁶
d. 0.00147 = 1.47*10⁻³
What are expressions exactly?
In mathematics, expressions are mathematical assertions made up of at least two sentences that contain numbers, variables, or both and are linked by an operator. Mathematical operations include addition, subtraction, multiplication, and division. For example, x + y is an equation that uses an addition operator to separate the components x and y. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.
e.g. A number is six times the size of another number, x. This sentence is mathematically stated as x/2 + 6. Mathematical expressions are used to address complex problems.
Now,
Given expressions/Numbers are a. 3.25*10⁴ then ordinary form is
3.25*10000
=32500
b. 6.04*10⁻³ then ordinary numbers is
=6.04/1000
=0.00604
c. 2400000 then standard from is
=2.4*1000000
=2.4*10⁶
d. 0.00147 then standard form is
=1.47/1000
=1.47*10⁻3
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the price of gasoline is $2.27 per gallon and decreases at the rate of $0.03 every two months. oil costs $0.45 per gallon and increases at a rate of $0.05 every six months. how many years will it take for them to be equal in price?
Answers
The price of gasoline and oil will be equal in price after 4 years when the price of gasoline is $2.27 per gallon and decreases at the rate of $0.03 every two months.
To find out when the price of gasoline and oil will be equal, we have to set the two prices equal to each other and solve for time. The price of gasoline decreases at the rate of $0.03 every two months and the price of oil increases at a rate of $0.05 every six months.
We can start with the initial prices and solve for the time when they are equal:
$2.27 - 0.03t = 0.45 + 0.05t
where t represents the time in years.
Solving for t, we get:
$2.27 - 0.03t = 0.45 + 0.05t
$1.82 = 0.08t
t = 22.5
Since t is in months, we have to divide by 12 to convert it to years:
t = 22.5 / 12 = 1.875
So the price of gasoline and oil will be equal in price after approximately 4 years.
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6. A triangle has two side lengths
3 feet. Select all the measures that could be the
length of the third side.
3 ft
9.2 ft
4.6 ft
8 ft
7.4 ft
2 ft
Answers
The length of the third side of the triangle will be 2 feet. Then the correct option is F.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
Any two parts of a triangle can be added together to have a length larger than the third side.
A triangle has two side lengths of 3 feet. Let 'x' be the third side.
By the theorem, the inequality is given as,
x < 3
The length of the third side of the triangle will be 2 feet. Then the correct option is F.
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what is 13 over 16 as a decimal rounded to the nearest tenth
Answers
13/16 as a decimal rounded to the nearest tenth is 0.8.
A decimal is a way to represent the same thing but in a different form. In this case, we will convert the fraction 13/16 into a decimal and round it to the nearest tenth.
To convert a fraction to a decimal, we divide the numerator (top number) by the denominator (bottom number). In this case, 13 divided by 16 is equal to 0.8125. This means that 13/16 as a decimal is 0.8125.
To round a decimal to the nearest tenth, we look at the digit in the hundredths place (the second digit after the decimal point).
If this digit is 5 or greater, we round up the tenths place (the first digit after the decimal point). If it is less than 5, we leave the tenths place as is. In this case, the digit in the hundredths place is 2, which is less than 5.
Therefore, we leave the tenths place as is, and the final answer is 0.8.
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A fruit Juice blend is made by mixing the juice of oranges and apples in the ratio 7:5 If 168 litres of orange juice is used How much litres of Apple juice must be used ?
Answers
A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
If the ratio is 7: 5 (oranges to apples) we can use this equation to solve the problem:
168 × 0.714285714 = 120Why do we multiply by 0.714285714?We multiply by 0.714285714 because we can see that 7 is being multiplied by 0.714285714 to get 5.
Therefore, if the ratio stays proportional, you will need 120 litres of apple juice for every 168 litres of orange juice.
simplify (4x+5y)(2x-3y)+3xy
Answers
Answer: 8x^2 + xy - 15y^2
Step-by-step explanation:
first do the FOIL method than add 3xy to the equation after
Answer:
[tex]8x^2+xy-15y^2[/tex]
Step-by-step explanation:
[tex](4x+5y)(2x-3y)+3xy\\\\=(4x)(2x)+(4x)(-3y)+(5y)(2x)+(5y)(-3y)+3xy\\\\=8x^2-12xy+10xy-15y^2+3xy\\\\=8x^2+xy-15y^2[/tex]
in
2. The park charges $24 to enter and
$0.45 per ticket. Write an algebraic
expression to represent the total
amount spent by a guest.
Answers
Answer:
C = $24 + 0.45x
Step-by-step explanation:
If we let total amount spent by a guest to the park as $C and number of tickets bought is x then the algebraic expression to represent the total amount spent by a guest is
C = $24 + 0.45x
What is the perimeter of the parallelogram?
A 12
B 15
C 30
D 44
Answers
Answer:
C. P = 30
Step-by-step explanation:
Parallelogram opposite (or parallel) sides are equal,
so:
2x = x + 2
5y - 9 = 2y + 3
For x:
2x = x + 2
2x - x = 2
x = 2
For y:
5y - 9 = 2y + 3
5y - 2y = 3 + 9
3y = 12
y = 4
the smallest sides are equal 2x and x + 2 => 2 * 2 = 4
the biggest sides are equal 5y - 9 and 2y + 3 => 2 * 4 + 3 = 11
P = 2 * (a + b)
P = 2 * (4 + 11)
P = 2 * 15
P = 30
Please help, I’ll give brainliest!!!!!!!!!!!!
Answers
Answer: (2, -1)
Step-by-step explanation:
(-2,7),(2,-1)
Find the sum of each infinite geo sequence WILL MARK BRANLIEST
48, 24, 12, ...
Answers
Answer:
S∞ = 96
Step-by-step explanation:
what is the missing
equivalent ratio of 4 : 2 = 10: _
Answers
Answer:
4 : 2 = 10 : 5.
Step-by-step explanation:
Let's put this in a fraction way. 4/2 = 2, and 10/5 = 2. Likewise, we can keep going and putting things that equal to 2. (e.g. 42 : 21)
You type 170 words per minute. How many minutes does it take you to type 3400 words?
Answers
Answer:
Step-by-step explanation:
3400/170 = 20 minutes.
Answer:
20 minutes
Step-by-step explanation:
3400 words / 170 wpm
20 minutes
A, B & C form the vertices of a triangle, where ∠CAB = 90°.AB = 10.5 m and AC = 5.2 m.
Evaluate ∠CBA, giving your answer rounded to 3 SF.
Answers
Answer: In a right-angled triangle, we can use the Pythagorean Theorem to find the length of the remaining side. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length of side BC can be found using the Pythagorean Theorem:
BC^2 = AB^2 + AC^2
BC^2 = 10.5^2 + 5.2^2
BC^2 = 110.25 + 27.04
BC^2 = 137.29
BC = √137.29
BC ≈ 11.68 m
Now that we have the length of side BC, we can use the inverse cosine function (cos^-1) to find the angle ∠CBA:
∠CBA = cos^-1 (BC / AB)
∠CBA = cos^-1 (11.68 / 10.5)
∠CBA ≈ 68.194°
Rounding to 3 significant figures, the answer is ∠CBA = 68.2°.
Step-by-step explanation:
Pls answer! Lots of points! Question down below!
Answers
The dimensions of Yura's picture 10×7 square units. The length of Yura's picture 10 units and the width of 7 units.
What is a rectangle?
An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.
The number of lines along the length is 11.
The length of the frame is 10 units.
The number of lines along the width is 8.
The width of the frame is 7 units
The dimension of an object is length × width.
The dimension of the frame is 10 units × 7 units.
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Write an exponential function in the form y=ab x that goes through points ( 0 , 12 ) and ( 2 , 300 )
Answers
The exponential function that goes through points (0,12) and (2,300) is [tex]y = 12(5)^x[/tex].
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The coordinate points are (0,12) and (2,300).
The exponential function has form [tex]y=ab^x[/tex].
So, the x values are 0,2 and y values are 12,300.
Substitute the first x and y values in the equation -
[tex]12=ab^0[/tex]
a = 12 ...... equation (1)
Substitute the second x and y values in the equation -
300 = ab² ...... equation (2)
Substitute the value of equation (1) in equation (2) -
300 = (12)b²
b² = 300 / 12
b² = 25
b = √25
b = 5
Substitute the values of a and b in exponential function -
[tex]y = 12(5)^x[/tex]
Therefore, the exponential function is [tex]y = 12(5)^x[/tex].
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robin is twice as old as earl and adam is 8 years younger than earl. in 6 years robin will be three times as old as adam. find their present ages
Answers
The present age of Earl is 12 years, Robin is 24 years and Adam is 4 years old.
Let us consider the present age of Earl to be x years.
According to the given question, the present age of Robin is twice that of Earl = 2x
And since it is given that Adam is 8 years younger than Earl, then his age
= x - 8
After 6 years, the age of Earl will be x + 6
Robin's age will be = 2x + 6
Adam's age will be = x - 8 + 6 = x - 2
According to the given question, Robin's age will be thrice the age of Adam.
Hence, 2x + 6 = 3 (x - 2)
⇒ 2x + 6 = 3x - 6 ⇒ 6 + 6 = 3x - 2x ⇒ 12 = x
Thus, the present age of Earl is 12 years,
Robin's age = 2x = 2 x 12 = 24 years
Adam's age = x - 8 = 12 - 8 = 4 years
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selecting christmas presents if a person can select presents from presents under a christmas tree, how many different combinations are there?
Answers
Sselecting A, B, and C is the same as selecting B, C, and A, so = 720/(3*2*1) = 120 combinations
When the decision's order is unimportant, a combination is a choice made in mathematics from among a group of distinct elements. A pear and an orange, an apple and an orange, or a trio of fruits—an apple, an orange, and a pear—can be paired into one of three pairs. An official definition of a k-combination of a set S is a subset of S's k unique items. Consequently, two combinations are considered to be same if and only if they both contain the same elements. If a collection contains n elements, a combination is any set of n objects taken k at a time without repetition.
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if $m$ is a real number and $x^2 mx 4$ has two distinct real roots, then what are the possible values of $m$? express your answer in interval notation.
Answers
The m values that allow the quadratic equation [tex]x^2 + mx + 4[/tex] to have two independent real roots are m in the open range (-∞ , -4) (4 , ∞). This may be expressed in interval notation as:
m ∈ (-∞, -4) ∪ (4, ∞).
The quadratic formula tells us that the quadratic equation's roots
[tex]x^2 + mx + 4 = 0[/tex]
are provided by:
[tex]x = (-m[/tex] ± [tex]sqrt(m^2 - 16))/2[/tex]
The discriminant [tex](m^2- 16)[/tex]must be positive, i.e., [tex]m^2[/tex] > 16, for the quadratic to have two separate real roots. As a result, we have two instances to consider:
Case 1: m > 4. Because [tex](-m + sqrt(m^2 - 16)/2[/tex]and[tex](-m - sqrt(m^2 - 16)/2[/tex]are both real and unique in this case, the quadratic has two separate real roots.
Case 2: m < -4. In this situation, [tex](-m + sqrt(m^2 - 16)/2[/tex] is negative, whereas[tex](-m - sqrt(m^2 - 16)/2[/tex] is positive, indicating that the quadratic has two separate real roots.
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Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6} if you roll the die once, calculte the following probabilities. Write you answers in fraction form and in lowest terms (e. G. 1/4) a) the probability of getting a 6 is. B) the probability of getting an even number is. C) the probability of getting a number greater than 2 is
Answers
The probability for the sample space of a fair die rolled out {1, 2, 3, 4, 5, 6} with different conditions are :
a. Probability of getting 6 = 1/6
b. Probability of an even number on a die = 1/2
c. Probability of number more than 2 = 2/3.
Sample space is equal to {1, 2, 3, 4, 5, 6}
Number of times die rolled out = only once.
Total number of outcomes = 6
Probability = ( Number of favourable outcomes ) / ( Total outcomes )
Required probability in fraction form with lowest terms:
a. Probability of getting 6
Favourable outcomes ={ 6 }
Number of favourable outcomes = 1
Probability of getting 6 = 1 / 6
b. Probability of getting an even number
Favourable outcomes = { 2, 4, 6 }
Number of favourable outcomes = 3
Probability = 3 / 6
= 1 / 2
c. Probability of getting number greater than 2
Favourable outcomes = { 3, 4, 5, 6 }
Number of favourable outcomes = 4
Probability = 4 / 6
= 2 / 3
Therefore, the required probability as per the mentioned conditions are:
a. Probability of getting 6 = 1/6
b. Probability of even number = 1/2
c. Probability of number greater than 2 = 2/3.
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Multiply out the brackets and then simplify: 12(-10x+5y)
Answers
Answer:
-120x + 60y
In 2004, $6,000 was invested in a mutual fund that earned 9% interest per year.
a) Tell whether the model represents an exponential growth or decay and create a function that models it
b) How much was in the account in 2012?
Answers
a) The function would be A(t) = 6000(1 + 0.09)ᵗ
b) The amount in the account in 2012 was approximately $11,737.51.
What is the function model?
In mathematics, a function model is a mathematical equation or expression that represents a relationship between two or more variables. It is a way of describing the behavior or pattern of a particular phenomenon or system.
a) The model represents exponential growth since the amount in the account is increasing with time. The function that models the growth of the investment over time is given by:
A(t) = 6000(1 + 0.09)ᵗ
where A(t) is the amount in the account after t years.
b) To find the amount in the account in 2012, we need to find the value of A(2012 - 2004) = A(8). Substituting t = 8 into the function above, we get:
A(8) = 6000(1 + 0.09)⁸
= 6000(1.09)⁸
≈ $11,737.51
Therefore, the amount in the account in 2012 was approximately $11,737.51.
Hence,
a) The function would be A(t) = 6000(1 + 0.09)ᵗ
b) The amount in the account in 2012 was approximately $11,737.51.
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Eric owes his brother $17. He recently got some money for his birthday and plans to use some of it to pay his brother back. Use the variable to represent the amount of money Eric got for his birthday, and use this variable to write an expression for the amount of money Eric will have left after he pays his brother back. Choose the expression for the amount of money Eric has after he pays his brother back.
A. 17-x
B. x-17
C. 17x
D. x+17
Answers
The expression for the amount of money Eric has after he pays his brother back is x- 17.
What is Expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given:
Eric owes his brother $17.
let x be the amount of money Eric got for his birthday.
If Eric gave the money back to his brother then he left with
= x - 17
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