Answers
The value of each variable include the following:
x = 5 units.
y = 5√2 units.
How to determine the value of x?From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:
Opposite side = 5.
Adjacent side = x.
Hypotenuse = y.
Therefore, we would determine the value of x by using Tan trigonometric function:
Tanθ = Opposite side/Adjacent side
Tan45 = 5/x
x = 5Tan45
x = 5(1)
x = 5 units.
Next, we would determine the value of y by using Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:
a² + b² = c²
Where:
a, b, and c represents the side lengths of a right-angled triangle.
y² = 5² + 5²
y = √50
y = 5√2 units.
Read more on right-angled triangle here: https://brainly.com/question/2223099
#SPJ1
Related Questions
A rectangular aquarium 7 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump the top half of the water out of the aquarium by raising it over the top of the aquarium. (Use the facts that the density of water is 1000 kg/m3 and g ≈ 9.8 m/s2.)
Answers
The work needed to pump the top half of the water out of the aquarium by raising it over the top of the aquarium is 34,300 J.
How to find the work needed to pump the top half of the water out of the aquarium?First we need to calculate the total amount of water that needs to be lifted and the height it needs to be lifted to.
The volume of water in the aquarium is given by:
V = 7 m * 1 m * 1 m = 7 m^3
Since we need to pump out the top half of the water, the volume of water that needs to be lifted is:
V = (1/2) * 7 m^3 = 3.5 m^3
The mass of the water can be calculated as:
m = V * density of water = 3.5 m^3 * 1000 kg/m^3 = 3500 kg
The height that the water needs to be lifted to is equal to the height of the aquarium, which is 1 m.
The work needed to lift the water can be calculated using the formula:
W = m * g * h
where
M is the mass of the water G is the acceleration due to gravity (9.8 m/s^2) H is the height the water needs to be lifted toSo, the work needed is:
W = 3500 kg * 9.8 m/s^2 * 1 m = 34,300 J (joules)
Therefore, the work needed to pump the top half of the water out of the aquarium by raising it over the top of the aquarium is 34,300 J.
Learn more about volume here : brainly.com/question/1972490
#SPJ1
PLEZ HELP WILL MARK Brainliest WITH ALL OF THEM DUE TONIGHT!!!!
Answers
Answer:
the answer you are looking for here is 3/7
Answer:
3/7
Step-by-step explanation:
6/7 ×1/2 = 6×1 × 7×2 = 6/14 ÷ 2 = 3/7
Jonathan can jog 3 2/5 miles in 7/8 hour. find his average speed per hour
Answers
The average speed with the given distance and time is 119/40 miles per hour.
What is the average speed?Average speed is calculated by dividing a quantity by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t, where S is the average speed, d is the total distance, and t is the total time, is used to determine average speed.
Given that, number of miles jogged = [tex]3\frac{2}{5}[/tex] = 17/5 miles and the time taken = 7/8 hours
Here, average speed = 17/5 ÷ 7/8
= 119/40 miles per hour
Therefore, the average speed is 119/40 miles per hour.
Learn more about the average speed here:
brainly.com/question/9834403.
#SPJ1
The brass section of a middle school jazz band has 4 trumpets and 3 trombones. What is the ratio of trombones to all the brass section members?
7/3
, 7:3, or 7 to 3
4/7
, 4:7, or 4 to 7
4/3
, 4:3, or 4 to 3
3/7
, 3:7, or 3 to 7
Answers
The ratio of trombones to all the brass section members is 3:7.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
Number of Trumpets = 4
Number of Trombones= 3
Total = 4 + 3= 7
So, the ratio of trombones to all the brass section members
= Number of Trombones/ Total
= 3 /7
= 3:7
Learn more about Ratio here:
https://brainly.com/question/13419413
#SPJ9
how to read 2/10 net 30 ?
Answers
2/10 Net 30 represents credit given to the buyer for the sale of goods or services. 2/10 net 30 means that the customer gets a 2% discount if the outstanding balance is paid within 10 days. Otherwise, full payment is due within 30 days.
2/10 Net 30:
The terms and conditions of the transaction are set forth in the purchase order and the corresponding invoice. These terms include terms of credit between the seller (also known as the payee) and the buyer (also known as the payer). A typical net credit period of 30 means the balance must be paid within 30 days of the invoice date. 2/10 Net 30 (also known as 2 10 Net 30) means that if a buyer pays within the first 10 days, their balance will be reduced by 2%. So "2" is the discount amount (2%) and "10" is the due date (10 days).
For example, if your company purchased $500 worth of goods or services on June 1st, you have entered into a loan agreement with the seller. If your company pays the net amount between June 1st and June 10th, you get a 2% discount, bringing the total amount to $490.
This example 2/10 net 30 step by step.
Day Start counting days from the invoice date.
Quick Formula: 100% Discount % x Invoice Amount.
100% - 2% = 98% x $500 = $490.
Formula:
(immediate discount) x (invoice amount) = less payment
Learn more about Balance:
https://brainly.com/question/28699225
#SPJ4
Convert the Cartesian equation 2 xy = 1 in polar equation form.
Answers
The Cartesian equation 2xy = 1 has the following polar equation r²·sen2θ = 1.
To convert the Cartesian equation 2xy = 1 into polar equation form, we need to use the relationships between Cartesian coordinates and polar coordinates. The relationships are as follows:
x = r cos θy = r sin θSubstituting these relations in the Cartesian equation, we proceed to solve:
2 (r·cosθ)(r·sinθ) = 1
2r²·cosθ·sinθ = 1
r²·(2cosθ·sinθ) = 1
r²·sen2θ = 1
In conclusion, the polar equation has the following form: r²·sen2θ = 1.
See more about polar equation at https://brainly.com/question/10208508.
#SPJ11
5) After surveying a sample of high school teachers, Enrique concluded that
adults like to eat dinner at The Bistro more than other restaurants in town.
Terry disagreed with Enrique's conclusion, saying that Enrique's population
was too specific for such a broad question. Which question would have
been more appropriate for Enrique's survey of high school teachers?
Answers
The question that would be more appropriate for Enrique's survey of high school teachers is Among high school teachers, what is the most popular restaurant to eat dinner at in town?
The appropriate question for Enrique's survey of high school teachersEnrique's conclusion about adults liking to eat dinner at The Bistro more than other restaurants in town may not be accurate since his survey was only limited to high school teachers.
To make his conclusion more reliable, Enrique could have asked a more specific question that is relevant to high school teachers. Here are a few examples of more appropriate questions for Enrique's survey of high school teachers:
Among high school teachers, what is the most popular restaurant to eat dinner at in town?
Learn more about survey at:https://brainly.com/question/27396612
#SPJ1
Find the measure of angle B
Equation form
Answers
The measure of the angle B in the triangle is 51.34 degrees.
How to find the angle of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The triangle above is a right angle triangle. A triangle is right triangle because one of its angles is 90 degrees.
The angle of a right triangle can be found using trigonometric ratios as follows:
tan B = opposite / adjacent
tan B = 25 / 20
B = tan⁻¹ 5 / 4
B = tan⁻¹ 1.25
B = 51.3401917459
Therefore,
B = 51.34 degrees
learn more on triangle here: https://brainly.com/question/13337013
#SPJ1
Describe the type and degree of association in the scatter plot and what it means in terms of the time the player spent practicing and the number of points he scored in the game.
As the time a basketball player practices increases, the number of points scored in a game increases with a strong linear association.
As the time a basketball player practices increases, the number of points scored in a game increases with a strong nonlinear association.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak linear association.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association.
Answers
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given a scatter plot in terms of the time the player spent practicing and the number of points he scored in the game.
A scatter plot uses dots to represent values for two different numeric variables.
The position of each dot on the horizontal and vertical axis indicates values for an individual data point.
As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association.
Hence, As the time a basketball player practices increases, the number of points scored in a game decreases with a weak nonlinear association
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ1
What is interval of increase and decrease
Answers
Interval of increase and decrease refers to a period of time in which a quantity rises or falls. For example, a stock market index may have an interval of increase and decrease over a certain period, such as a month or a year.
Interval of increase and decrease is a term used to describe a period during which a certain quantity either increases or decreases. This phenomenon is commonly seen in financial markets, such as the stock market, where indices may go up and down over a certain period of time. This interval of increase and decrease can be measured using different measures such as time, percentage growth, and movement. This interval helps investors and analysts to determine how the stock market is performing and if there are any changes in the market. It also helps them to predict future trends and make better investment decisions. During this interval, it is important to monitor the stock market and any changes that may occur. This helps to ensure that investments are made with the best possible outcome.
Learn more about interval here
https://brainly.com/question/24131141
#SPJ4
Jose pays 10% of his balance each month. If Jose borrowed $5000 with no interest, how much does he still owe after 1 year?
Answers
Answer: 1,422
Step-by-step explanation:
x[tex]x^{2} =[/tex]-81
Answers
Answer:
[tex]x=\pm\,9i[/tex]
Step-by-step explanation:
[tex]x^2=-81\\x=\pm\,9i[/tex]
Which four statements that are true?
y=e" and y = ln x are inverses.
are not equivalent.
In een
In(x) = log. (x)
ln e = 1
In (x) = log10 (x)
In e = 10
In(e) and en both equal x.
Answers
The statements are:
y=e" and y = ln x are inverses.
This is false. The inverse of y = e^x is y = ln x, and the inverse of y = ln x is y = e^x. So, the two functions y = e^x and y = ln x are inverses of each other, but y = e^x and y = e^ln x are not.
In een In(x) = log. (x)
This is false. The statement should be: e^ln(x) = x, which is true by the definition of logarithms.
ln e = 1
This is true. The natural logarithm of e is 1.
In (x) = log10 (x)
This is false. The statement should be: log10(x) = log(x) / log(10).
In e = 10
This is false. The natural logarithm of e is 1.
In(e) and en both equal x.
This is false. In(e) = 1, and e^n = x does not necessarily imply that In(e) = x.
What is the antiderivative of 1x?
Answers
The antiderivative of 1x (or simply x) is (1/2)x² + C, where C is the constant of integration. In other words, the antiderivative of x is the function whose derivative is equal to x.
This is a basic result in calculus, and it is derived using the power rule of integration. The antiderivative of 1x (or simply x) is the function whose derivative is equal to x. This function is (1/2)x² + C, where C is the constant of integration. To find the antiderivative, one can use the power rule of integration, which states that the antiderivative of xⁿ is (1/(n+1))x⁽ⁿ⁺¹⁾ + C. In the case of x, n is equal to 1, so the antiderivative is (1/2)x² + C. The constant of integration represents the family of functions that have the same derivative, so it is added to the antiderivative to reflect this.
Learn more about antiderivative here: brainly.com/question/15522062
#SPJ4
The measure of angle DEF is ___ degrees.
Answers
Because of the SSS postulate for proving triangles congruent, you can say that triangles DEG and FEG are congruent. Corresponding parts of congruent triangles are congruent (CPCTC) means that angles DEG and FEG are congruent, which means their measures are equal. So 3y + 4 = 5y - 10.
4 = 2y - 10
14 = 2y
7 = y
The measure of angle DEF is 50 degrees
HELP PLEASE!!
Ramon is filling cups with juice. Each cup is shaped like a cylinder and has a diameter of 4.4 inches and a height of 7 inches. How much juice can Ramon pour into 6 cups? Round to the nearest hundredth and approximate using π = 3.14.
Answers
The total volume in the 6 cups is 638.30 in^2
How much juice can Ramon pour into 6 cups?Remember that the volume of a cylinder of height H and radius R is:
V = pi*R^2*H
Here the diameter is 4.4 inches, then the radius is half of that:
R = 4.4in/2 = 2.2in
The height is 7 inches, then the volume of each cup is:
V = 3.14*(2.2in)^2*7in = 106.38 in^2
And in 6 cups the total volume will be:
volume = 6*106.38 in^2 = 638.30 in^2
Learn more about volume at:
https://brainly.com/question/1972490
#SPJ1
Help please…………………………………..
Answers
Answer:
35
Step-by-step explanation:
DUDE JUST PLUG IN THE NUMBER.
[tex]x^4 -3x^3 + x -3\\(-2)^4 - 3(-2)^3 + (-2) -3\\16 + 24 -2 - 3\\35[/tex]
Which statements correctly describe the relationships between x and y for each table? Responses Table A represents an additive relationship because y is 2.5 more than x, and Table B represents a multiplicative relationship because y is 9.2 times x. Table A represents an additive relationship because , y, is 2.5 more than , x, , and Table B represents a multiplicative relationship because , y, is 9.2 times , x, . Both tables represent additive relationships. In Table A, y is 2.5 more than x, and in Table B, y is 8.2 more than x. Both tables represent additive relationships. In Table A, , y, is 2.5 more than , x, , and in Table B, , y, is 8.2 more than , x, . Both data sets represent multiplicative relationships. In Table A, y is 3.5 times x, and in Table B, y is 9.2 times x. Both data sets represent multiplicative relationships. In Table A, , y, is 3.5 times , x, , and in Table B, , y, is 9.2 times , x, . Table A represents a multiplicative relationship because y is 3.5 times x, and Table B represents an additive relationship because y is 8.2 more than x.
Answers
The requried statement is mentioned in C where Table A represents y = 2.5x and table B represents y = 3x describe the relationships between x and y for each table. Option C is correct.
What is proportionality?Proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
In Table A, y is 2.5 more than x, and in Table B, y is 3 more than x. Both tables represent additive relationships. the requried statement is mentioned in C where Table A represents y = 2.5x and table B represents y = 3x describing the relationships between x and y for each table. Option C is correct.
Learn more about proportionality here:
https://brainly.com/question/22620356
#SPJ9
the product of 5/8 x 6/15
Answers
Answer: 1/4
Step-by-step explanation:
To find the product of two fractions, you simply multiply the numerators together and multiply the denominators together. That is:
(5/8) x (6/15) = (5 x 6) / (8 x 15)
Simplifying the numerator and denominator by dividing both by their greatest common factor, which is 2, we get:
(5 x 6) / (8 x 15) = 30 / 120
Further simplifying the fraction by dividing both the numerator and denominator by their greatest common factor, which is 30, we get:
30 / 120 = 1 / 4
Therefore, the product of 5/8 and 6/15 is 1/4.
Answer:
To multiply two fractions, you simply multiply their numerators (top numbers) and denominators (bottom numbers), respectively.
So, 5/8 x 6/15 = (5 x 6) / (8 x 15) = 30 / 120
To reduce this fraction to its simplest form, we can divide both the numerator and denominator by their greatest common factor, which is 30.
30 / 120 = (30 ÷ 30) / (120 ÷ 30) = 1/4
Therefore, the product of 5/8 x 6/15 is 1/4
Which of the following forms are best to use if we want to identify the vertex of a
quadratic equation?
Answers
Step-by-step explanation:
[tex]y = a(x - h) {}^{2} + k[/tex]
Help please I don’t think I have any idea with what I’m doing
Answers
If the triangles are similar but no congruent, then the triangles have different size, thus the only correct option is the dilation (first option).
Which transformation is the correct one?We know that two figures are congruent if the figures have the same shape and size, while two figures are similar only if have the same shape (but the figures can have different size).
Here we know that the triangles are similar but no congruent, so the triangles must have different size. From the given transformations, the only one that changes the size is the first option, a dilation.
And for example, if we apply a dilation AND the other transformations, then we still will get a similar figure, but if we apply a reflection/rotation/translation alones, we will get a congruent triangle.
Learn more about similar figures at:
https://brainly.com/question/14285697
#SPJ1
a first time homebuyer is given the choice of two loans: loan a: 390,000, 15 year-fixed, 4 discount points, M=$3,509.71. loan b: 390,000, 15 year-fixed, 0 discount points, M=3,659.86. how much does the hole buyer save in total by choosing loan A? a) 27,027 b) 11,427 c) 26,351.02 d) 42,627.05
Answers
The amount the the home buyer saves in total by choosing Loan A is most closest to $11,427. The Option B is correct.
How much does the buyer save by choosing Loan A?In order to compare the total cost of each loan, we need to consider both the monthly payment and the discount points.
For Loan A, we have Loan amount: $390,000, Loan term: 15 years, Discount points: 4 and Monthly payment: $3,509.71. For Loan B, we have Loan amount: $390,000, Loan term: 15 years Discount points: 0 and Monthly payment: $3,659.86.
The total cost of Loan A is the sum of the discounted upfront cost (discount points) and the total of all monthly payments over the life of the loan:
= (4% of $390,000) + ($3,509.71 x 180)
= $15,600 + $631,948.80
= $647,548.80
The total cost of Loan B is the total of all monthly payments over the life of the loan:
= ($3,659.86 x 180)
= $658,574.80
Now, the amount saved by choosing Loan A over Loan B is the difference between their total costs which equals:
= Total cost of Loan B - Total cost of Loan A
= $658,574.80 - $647,548.80
= $11,026
Read more about loans
brainly.com/question/20688650
#SPJ1
What is the volume of each hemisphere in the picture below? (Use 3.14 for)
Answers
Answer:
The answer is C.
106.0 in^3
Answer:
106.0 in^3
Step-by-step explanation:
Find the value of the variable x. If your answer is not an integer, write it in simplest radical form with
the denominator rationalized
Answers
The values of the variable are:
x is 45.
y is 18.
z is 18.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
From the figure,
Sin 45 = z / (18√2)
Sin 45 = 1 /√2
So,
1/√2 =z / 18√2
z = 18
Cos 45 = y / (18√2)
1/√2 = y/18√2
y = 18
Tan x = y / z
Tan x = 18/18
Tan x = 1
x = [tex]tan^{-1}[/tex]1
x = [tex]tan^{-1}[/tex] tan 45
x = 45
Thus,
x is 45.
y is 18.
z is 18.
Learn more about trigonometric identities here:
https://brainly.com/question/14746686
#SPJ1
n the metric system, each millimeter increment is equal to _____.A. 1/1000 of a centimeterB. 1/100 of a centimeterC. 1/10 of a centimeterD. 10 centimeters
Answers
The answer is C. 1/10 of a centimeter.
Circle � ′ A ′ A, prime is the result of rotating circle � AA by 18 0 ∘ 180 ∘ 180, degrees about point � PP. A coordinate plane. The x- and y-axes both scale by one. A circle with a center at negative three, zero and a radius of two. A point P is plotted at one, negative two. A coordinate plane. The x- and y-axes both scale by one. A circle with a center at negative three, zero and a radius of two. A point P is plotted at one, negative two. Select all of the correct statements about the unchanged properties of circle � AA and circle � ′ A ′ A, prime. Choose all answers that apply: Choose all answers that apply: (Choice A) A Circle � AA and circle � ′ A ′ A, prime have the same circumference. (Choice B) B The radii of circle � AA and circle � ′ A ′ A, prime have the same lengths. (Choice C) C Points � AA and � ′ A ′ A, prime are both on the � xx-axis. (Choice D) D None of the above
Answers
Circle A and circle A' have the same circumference and the radii of circle A and circle A' have the same lengths. Therefore, options A and B are the correct answers.
What is rotation?Rotations are transformations that turn a shape around a fixed point. To rotate a shape we need: a centre of rotation. an angle of rotation (given in degrees) a direction of rotation – either clockwise or anti-clockwise.
Given that, circle A' is the result of rotating circle A by 180° about point P.
When we rotate any object its shape and size does not change, only its position changes.
Therefore, options A and B are the correct answers.
Learn more about the rotation here:
brainly.com/question/1571997.
#SPJ9
Samantha has two anthills in her yard. The first anthill has 982 ants. The second PLEASE HELP QUICKLY // anthill has one and one-third the amount of ants of the first hill. Which statement correctly compares the two anthills?
The first anthill is one and one-third times as many than the second anthill.
The first anthill is equal in size to the second anthill.
The second anthill is one and one-third times as many than the first anthill.
The second anthill is one and one-third times fewer ants than the first anthill.
Answers
The statement that correctly compares the two anthills is "the second anthill is one and one-third times as many ants as the first anthill."
Which statement correctly compares the two anthills?From the question, we have the following parameters that can be used in our computation:
The first anthill has 982 antsThe second anthill has one and one-third the amount of ants of the first hillUsing the above as a guide, we have the following:
First = 982
Second = 1 1/3 * First
This means that "the second anthill is one and one-third times as many ants as the first anthill."
Read more about expressions at
https://brainly.com/question/15775046
#SPJ1
Bisecting Bakery sells cylindrical round cakes. The most popular cake at the bakery is the red velvet cake. It has a radius of 17 centimeters and a height of 13 centimeters.
If everything but the circular bottom of the cake was iced, how many square centimeters of icing is needed for one cake? Use 3.14 for π and round to the nearest square centimeter.
3,203 cm2
2,295 cm2
1,020 cm2
731 cm2
Answers
Answer:
2,295 cm2
Step-by-step explanation:
Answer:
(b) 2295 cm²
Step-by-step explanation:
You want the area of icing on a cake 13 cm high and 17 cm in radius.
Icing areaThe area of the top is ...
A = πr²
The area of the side is ...
A = 2πrh
Then the total area of icing on the cake is ...
πr² +2πrh = πr(r +2h)
= 3.14(17 cm)(17 cm + 2·13 cm) = 2295.34 cm²
The area of icing needed for the cake is about 2295 cm².
<95141404393>
2.) Emmanuel is at a sporting goods store. The store
offers a 9% discount on all items. At checkout a 6%
sales tax is added to the discounted price. Select the
two that apply.
A. $25 pants cost $24.12 at checkout
B. $89 cleats cost $76.50 at checkout
C. A $29 basketball costs $37.97 at checkout.
D. $189 glove costs $183.33 at checkout
Answers
What is the square root rule?
Answers
The square root function involves the square root symbol √ which is mostly read as "square root of", the rule says that the square root of a number 'x' is a number 'y' such that y² = x.
We know that the square root of a number can be either positive or negative, but while defining the square root function, we restrict its range to be the set of all positive real numbers and hence making all square roots possible to be positive.
If the range for the square root of a number is set to be positive as well as negative it wont be a function that is why there is a restriction to the range of this set allowing only positive real numbers.
To learn more about square root, click here:
brainly.com/question/29286039
#SPJ4