Final answer:
In mathematics, the right triangle definition of tan theta is the ratio of the length of the side opposite to theta (y) to the length of the side adjacent to theta (x).
Explanation:
The right triangle definition of tan theta (tan θ) involves the ratio of the lengths of two specific sides of the triangle. According to SOHCAHTOA, a mnemonic used to remember the definitions of the sine, cosine, and tangent functions, tan theta is the ratio of the opposite side (y) to the adjacent side (x) of the right triangle, where theta (θ) is one of the non-right angles. This can be written as tan(θ) = y/x.
In other words, the tangent of an angle θ in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
This can be represented as:
tan(θ) = Opposite side / Adjacent side = y / x
For example, if the opposite side y is 5 units and the adjacent side x is 3 units, then tan(θ) = 5 / 3
The Pythagorean Theorem may be applied in conjunction with the definitions of trigonometric functions to solve various problems involving right triangles, but it specifically relates to the relationship between the sides of a right triangle: a² + b² = c², where 'a' and 'b' are the lengths of the legs, and 'c' is the length of the hypotenuse.
When solving problems related to right triangles, it is beneficial to remember that the sum of the angles of a triangle is always equal to two right angles (or 180 degrees).
The function h(x) is given below:
h(x) ={3,5),(5,-7)(6,-9)(10,-12)(12,16)}
which of the following gives h^-1(x) ?
Step-by-step explanation:
The domain and range of a function and its inverse are inverted i.e. The domain of the function will become range of its inverse and the range of the function will become the domain of its inverse.
When representing the function in ordered pairs, the first values in the pair represents the domain and second values represent the range of the function.
h(x) = {3,5),(5,-7)(6,-9)(10,-12)(12,16)}
Domain of h(x) is: {3, 5, 6, 10, 12}
Range of h(x) is: (5, -7, -9, -12, 16}
So,
Domain of [tex]h^{-1}(x)[/tex] = Range of h(x) = (5, -7, -9, -12, 16}
Range of [tex]h^{-1}(x)[/tex] = Domain of h(x) = {3, 5, 6, 10, 12}
Therefore, [tex]h^{-1}(x)[/tex] will be represented as:
{(5,3), (-7,5), (-9, 6), (-12, 10), (16,12)}
It seems like you have made some error while writing the original function because of which we are not getting an exact match in the answer. However by looking at the answers, option B is the nearest most and seems the correct answer.
Simplify 5-2+9-8 step by step
Answer:
I don't know if this is right but I hope it helped
Step-by-step explanation:
5-2+9-8
3+1
4
Answer:
4
Step-by-step explanation:
5-2+9-8
3+9-8
12-8
4
hope it helped :)
Find the product.
4x3y(-2x2y)
Answer:
[tex]\large\boxed{4x^2y(-2x^2y)=-8x^4y^2}[/tex]
Step-by-step explanation:
[tex](4x^2y)(-2x^2y)=(4\cdot(-2))(x^2\cdot x^2)(y\cdot y)=-8x^4y^2[/tex]
The product of 4x3y and -2x2y is -8x5y2, found by multiplying coefficients and adding exponents.
Explanation:The question is asking us to multiply two algebraic expressions together, namely 4x3y and -2x2y. When multiplying algebraic expressions, you multiply the coefficients together and add the exponents of like variables. The coefficient of the first expression is 4 and the coefficient of the second expression is -2. Multiply these two together gives -8. The first expression has x raised to the power of 3 and the second has x raised to the power of 2. Add these exponents together gives x raised to the power of 5. Similarly, both expressions have y with exponent 1, two of them give y squared. Hence, the product of 4x3y and -2x2y is -8x5y2.
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A group of friends are playing a game of lawn darts. Each player has thrown six lawn darts so far in the game. The results of their throws are shown in the dot plot below.
The number that best summarizes the data is __ hits.
The best measure of center is the __.
Answer:
The number that best summarizes the data is 2 hits.
The best measure of center is the median.
Step-by-step explanation:
Since there are 25 players represented in the data, the median would be the 13th, or middle, number when the data is ordered from least to greatest.
0,0,0,0,0,1,1,1,1,1,1,2,2,2,2,2,3,3,3,4,4,5,5,6,6
best summaries the data is 2 hits
center is the median
Answer:
"Number of", Mean
What would the area of each triangle be if the base is 10 and the height is 3/5?
Answer:
3 square units
Step-by-step explanation:
The formula is 1/2*b*h. You plug in and solve 1/2*10*3/5.
Which of the following offer is better value of money?
200ml of toothpaste for 50p or 400ml for 90p
Answer:
200ml of toothpaste for 50p
Step-by-step explanation:
200/50=4
and
400/90=4.4444444444444444 (4.45 rounded up)
So, you would be getting more bang for your buck with 200ml for 50p
Hope this helps!
which polygon will tessellate a plane?
Answer:
797
Step-by-step explanation:
Answer:
C) Regular Octagon.
Step-by-step explanation:
First let's see what a tessellation is.
Tessellation is a floor made by regular types of tiles without overlapping and gap.
We cannot use all shape of tiles to tessellate a plane.
We are given Regular pentagon, irregular triangle and regular octagon.
The pentagon has 5 sides, all sides are in the same length. We cannot tessellate a plane using pentagon.
The second figure is a irregular triangle, we cannot make tessellate a plane using irregular shapes.
The third figure is a regular octagon. We can tessellate a plane using a regular octagon.
Therefore, answer is C) Regular Octagon.
Consider the following line plot.
Will give brainlest!!!!!!!!!!!
What is the mean of the data? Explain. Round to the Nearest tenth.
Answer: 4.7
Step-by-step explanation:
Joe paid $12.53 for a 7.03-kg bag of dog food. A few weeks later, he paid $14.64 for a 7.98-kg at a different store. Find the unit price for each bag. Then state which bag is the better buy based on the unit price. Round your answers to the nearest cent
Answer:
The unit price for the 7.03 kg bag is about $1.78 per kg. The unit price for the 7.98 kg bag is about $1.83 per kg. The 7.03 kg is a better deal because you pay less per kg.
Step-by-step explanation:
1) To find the unit price, you need to find the price per unit. The unit here being kg. So, you need to divide the price by the number of units.
2) Here is this written out...
7.03 kg bag:
$12.53 / 7.03 kg = 1.78236130868 dollars per kg, or about $1.78 per kg
7.98 kg bag:
$14.64 / 7.98 kg = 1.83458646617 dollars per kg, or about $1.83 per kg
3) As you can see, if Joe purchases the 7.98 kg bag of dog food, he is paying more for every kg of dog food than if he were to purchase the 7.03 kg bag of dog food. This makes the 7.03 bag of dog food a better deal.
Hopefully this helps.
The unit price for the first bag of dog food is $1.78/kg, and the unit price for the second bag is $1.83/kg. Therefore, the first bag is cheaper and thus the better buy based on unit price.
Explanation:To find the unit price of the dog food, we need to divide the total cost of the bag by its weight. For the first bag, we take the total cost of $12.53 divided by its weight of 7.03 kg. For the second bag, we take the total cost of $14.64 divided by its weight of 7.98 kg.
For example, using these calculations, the unit price for the first bag is $1.78/kg and the unit price for the second bag is $1.83/kg .
Therefore based on unit price, the first bag of dog food is the better buy as it is cheaper per kilogram.
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Factorising and making m the subject of...
Answer:
a)
[tex]4x {}^{2} - 9 = (2x + 3)(2x - 3)[/tex]
b) g - 3m = am + 5
am + 3m = 5 - g
m (a + 3) = 5 - g
m =
[tex] \frac{5 - g}{a + 3} [/tex]
Step-by-step explanation:
[tex]a {}^{2} - b {}^{2} = (a + b)(a - b)[/tex]
Answer:
see explanation
Step-by-step explanation:
(a)
4x² - 9 ← is a difference of squares which factors in general as
a² - b² = (a + b)(a - b)
4x² = (2x)² ⇒ a = 2x and 9 = 3² ⇒ b = 3, thus
4x² - 9 = (2x + 3)(2x - 3)
----------------------------------------------
(b)
g - 3m = am + 5 ( collect the terms in m together )
Add 3m to both sides
g = am + 3m + 5 ( subtract 5 from both sides )
g - 5 = am + 3m ← factor out m from each term
g - 5 = m(a + 3) ← divide both sides by (a + 3)
m = [tex]\frac{g-5}{a+3}[/tex]
Which process helps regulate Earth's climate by transporting warm seawater to colder regions of seawater?
A. The tides
B. Thermohaline circulation
C. Surface tension
D. Centrifugal force
Answer:
B. Thermohaline circulation
Step-by-step explanation:
Thermohaline circulation is driven by global density gradients which are created by the surface heat and fluxes of fresh water, as a part of the large scale ocean circulation.
Answer:
B. Thermohaline circulation
Step-by-step explanation:
Due to temporary tax cuts in 2010, a person with typical deductions earning $50,000 per year would have saved 2% of their income plus $850 in federal taxes.
How much money would this person save?
$
What percent did this person save on her income? Round to the nearest tenth of a percent.
%
Answer:
a) $1850
b) 3.7%
Step-by-step explanation:
a) This is a straight calculation based on the description in the problem statement.
2%×$50,000 +850 = $1000 +850 = $1850
__
b) To find the percentage of income saved, find the ratio of savings to income and multiply that by 100%.
$1850/$50,000×100% = 3.7%
Answer:
Part A: $1850
Part B : 3.7%
Step-by-step explanation:
Due to temporary tax cuts in 2010, a person with typical deductions earning $50,000 per year would have saved 2% of their income plus $850 in federal taxes.
Part A:
Total savings will be = [tex](0.02\times50000)+850[/tex]
= [tex]1000+850=1850[/tex] dollars
Part B:
The percent did this person save on her income will be = [tex]\frac{1850}{50000}\times100= 3.7[/tex]%
Find the area of the trapezoid by decomposing it into other shapes.
A) 33 cm2
B) 36 cm2
C) 38 cm2
D) 42 cm2
Answer:
(C) 38 cm²
Step-by-step explanation:
Top length = 6 cm
Bottom length = 5 + 8 = 13 cm
Area
= 1/2 ( 6 + 13) (4)
= 1/2(19)(4)
= 38 cm²
The area of the trapezoid is 38 cm2.
what is the lcm of 12 18 and 21
Answer:
The largest Common Factor of 12,18 and, 21 is 3
Practice Test.
Don't think I am stupid for asking this question. I will give brainliest to the first person who answers these question.
1. 1 + 1
2. 5 + 5
3. 12 x 12
Answer:
1. 2
2. 10
3. 144
Find a number so 56 divide n is greater than 1. But less than 7
Answer:
6 < n < 56
Step-by-step explanation:
Let's translate that into a symbolic relationship:
1 < (56/n) < 7
This produces two inequalities to be solved: 1 < (56/n) and (56/n) < 7.
Dividing both sides of (56/n) < 7 by 7 results in (6/n) < 1
which can be rewritten as 6 < n or n > 6.
Multiplying both sides of 1 < (56/n) by n results in n < 56.
There's no one solution. Rather, the solution set is 6 < n < 56.
The solution set is 8 < n < 56 for number so 56 divide n is greater than 1 but less than 7
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
Given,
a number so 56 divide n is greater than 1. But less than 7
56/n>1
56/n < 7
This sentence can be written as
1 < (56/n) < 7
Two inequalities to be solved:
1 < (56/n) and (56/n) < 7.
n<56 and 56/7<n
n<56 and 8<n
Dividing both sides of (56/n) < 7 by 7 results in (8/n) < 1
which can be rewritten as 8 < n or n > 8.
Multiplying both sides of 1 < (56/n) by n results in n < 56.
There's no one solution.
Hence, the solution set is 8 < n < 56.
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What is the line of best fit for this data? (1,5)(2,8)(3,11)(4,14)(5,17)(6,20)(7,23)
y = 3x + 2
When you graph this line, it goes across every single point, so it is the line of best fit. See the attached graph.
Given: △ABC with side lengths a, b, and c, and height h
Prove: Area=1/2 ab sin C
Triangle A B C has sides a b c. A vertical dashed line extends from angle B perpendicular to side b.
Drag and drop the statements into the boxes to correctly complete the proof.
Statement: Reason
△ABC with side lengths a, b, and c, and height h: Given
: Triangle area formula
: Definition of sine
asinC=h: Multiplication Property of Equality
Area=1/2 ba sin C: Substitution Property
: Commutative Property of Multiplication
Options
Area = 1/2 ab sin C
Area = 1/2 bh
Area = 1/2 ah
sin C = h/a
sin C = h/b
The area of a triangle △ABC with side lengths a, b, c and height h is shown to be equal to 1/2 ab sin C using the triangle area formula, definition of sine in right triangles, multiplication property of equality and commutative property of multiplication.
Explanation:In the triangle △ABC with side lengths a, b, and c, and height h, we can start with the triangle area formula, which is Area = 1/2 bh. Here, h denotes the height of the triangle, which when drawn from the angle C would be adjacent to the angle while b represents the side that is opposite to the angle C. By the definition of sine in right-angled triangles, sin C = h/a. Now, we can use the Multiplication Property of Equality to write asinC=h. Mixing the given formula of the area with this equality, we get Area=1/2 ba sin C. As the multiplication is commutative, we can re-write this as Area = 1/2 ab sin C.
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To prove the area of a triangle, use the formula 1/2 base × height and substitute sin C with h/a.
Explanation:To prove that the area of △ABC is equal to 1/2 ab sin C, we can use the formula for the area of a triangle: Area = 1/2 base × height. In this case, the base is b and the height is h, so the area is 1/2 bh. We also know that sin C = h/a, so we can substitute h/a for sin C in the area formula to get Area = 1/2 ab sin C.
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Four sizes of scaled text are shown.
Four rows of text and numbers. The first row contains the number one point nine five four followed by the phrase Website text size. The next row contains the number one point five six three followed by the phrase Website text size, but smaller than the previous row. The third row contains a question mark followed by the phrase Website text size, but smaller than the previous row. The fourth row contains the number one followed by the phrase Website text size, but smaller than the previous row.
What is the unknown scale size?
Enter your answer as a decimal in the box. Round only your final answer to the nearest thousandth.
Answer:
I just took my math test and used the answer already provided which came up as wrong, the correct answer is 1.250. Sorry I don't know how to get to the answer.
A ratio shows us the number of times a number contains another number. The size of unknown scale size will be 1.25.
What is a Ratio?A ratio shows us the number of times a number contains another number.
As it is given the size of the first row is 1.954, while the size of the second row is 1.563. therefore, the ratio of the first row to the second row will be,
[tex]\rm \dfrac{First\ row}{Second\ row} = \dfrac{1.954}{1.563}\\\\\\\rm \dfrac{First\ row}{Second\ row} =1.25[/tex]
Similarly, if the ratio of the second row and the third row is taken then the size of the third row can be written as,
[tex]\rm \dfrac{Second\ row}{Third\ row} =1.25\\\\\\\rm \dfrac{1.563}{Third\ row} =1.25\\\\\\Third\ row=1.2504 \approx 1.25[/tex]
Similarly, if the ratio of the third row and the fourth row is taken to verify the ratio, we will get,
[tex]\rm \dfrac{Third\ row}{Fourth\ row} = \dfrac{1.25}{1}\\\\\\\rm \dfrac{Third\ row}{Fourth\ row} = 1.25[/tex]
Thus, the size of unknown scale size will be 1.25.
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A fair six-sided die is tossed. After it lands, the bottom face cannot be seen. What is the probability that the product of the visible numbers on the five faces is divisible by 12?
Answer:
5/6
Step-by-step explanation:
Only 5 is not divisible by 12
Suppose you invest $2,400 into a regular savings account with 3.95% annual interest rate that compounds quarterly. What would your investment be worth in 10 years? a. $2,400 b. $2,647.80 c. $3,555.63 d. $11,303
Answer:
C, $3,555.63
Step-by-step explanation:
to answer this, we have to use the compound interest formula which is:
A = P(1 + r/n)^nt
the meanings of each variable are:
A = result
P = principal amount
r = rate (in decimal form)
n = the number of compound periods (eg: annually, quarterly, etc)
t = time
in the word problem, we need to solve for A. we are given P, r, n, and t.
P = 2,400
r = 0.0395 also known as 3.95%
n = 4 keyword being quarterly which is equal to the value of 4
t = 10
we can plug these values into the formula:
A = 2400(1 + 0.0395/4)^(4)(10)
we can use a calculator to calculate this easier but ill break it down:
A = 2400(1 + 0.0395/4)^(4)(10)
A = 2400(1 + 0.0395/4)^40
A = 800(1.009875)^40
A = 2400(1.48151088)
A ≈ 3555.626
we can round 3555.626 to the nearest hundredth which is $3555.63
you would have earned $3555.63 in 10 years
our answer would be C
a cannonball was launched with an initial upward velocity of 55 feet per second from a tower 28 feet off the ground. The height of the ball above the ground, in feet, can be modeled by an expression having the form -16t^2 + bt + c, where t is the number of seconds since the cannonball was launched.
What is the value of b, the coefficient of t? ___
What is the value of c, the constant term? ___
Therefore, the expression for the height of the ball at time t is ___
Answer:
The value of b is 55
The value of c is 28
The expression for the height of the ball at time t is h(t) = -16t² + 55t + 28
Step-by-step explanation:
* Lets discus the situations in the problem
- The ball was lunched up from a tower of height 28 feet above
the ground
∴ The initial height = 28 feet ⇒ (initial means time is zero)
- The ball launched with an initial velocity 55 feet/second
∴ The initial velocity = 55 feet/second ⇒ (at t = 0)
- The equation of the height of the ball after t second is:
h = ut + 1/2 at² + hi, where u is the initial velocity, a is the acceleration of
gravity, t is the number of seconds since the ball was lunched
hi is the initial height which the ball was lunched from it and h is the
height above the ground
∵ The ball was lunched up
∴ The gravity acceleration is -16 feet/second²
∵ The initial velocity is upward
∴ u = 55 feet/second
∵ The tower is 28 feet above the ground
∴ hi = 28 feet
- Substitute these values in the equation
∴ h = 55t + 1/2(-32)t² + 28 ⇒ simplify
∴ h = 55t - 16t² + 28 ⇒ start with t²
∴ h = -16t² + 55t + 28
* Now compare between the two equation
∵ h = -16t² + bt + c
∵ h = -16t² + 55t + 28
∴ b = 55 ⇒ coefficient of t
∴ c = 28
∴ h(t) = -16t² + 55t + 28
(1,-7) with a slope of -5 as an equation
Answer:
y=-5x-2
Step-by-step explanation:
y=mx+b
where m is the slope
y=-5x+b
to solve for b, which is the y intercept, plug in (1,-7)
-7=-5(1)+b
-7=-5+b
-2=b
y=-5x-2
Plz help asap... Explain as much as possible to me plz
Answer:
see explanation
Step-by-step explanation:
Since the 2 figures are similar then the ratios of corresponding sides are equal, that is
[tex]\frac{8}{x}[/tex] = [tex]\frac{18}{6}[/tex] ( cross- multiply )
18x = 48 ( divide both sides by 18 )
x = [tex]\frac{48}{18}[/tex] = [tex]\frac{8}{3}[/tex] = 2 [tex]\frac{2}{3}[/tex]
Similarly
[tex]\frac{5}{y}[/tex] = [tex]\frac{18}{6}[/tex] ( cross- multiply )
18y = 30 ( divide both sides by 18 )
y = [tex]\frac{30}{18}[/tex] = [tex]\frac{5}{3}[/tex] = 1 [tex]\frac{2}{3}[/tex]
What would the answer be if a cylinder was 6 and 8 inches?
which is the radius and which one is the hieght??
Substitution -just 4.g)
r=-3.2p+q^2
Answer is 25.6 you just put the numbers and multiply them and then add them
HIJK is a trapezoid with H(5, 4), I(10, -2), J(-8, -2), and K(-3, 4). Find the coordinates of the image of H under the translation vector 〈10, -11〉.
H'(20,-13)
H'(15,-7)
H'(-5,15)
H'(7,-7)
Answer:
H'(15, - 7)
Step-by-step explanation:
Given the translation < 10, - 11 >
Add 10 units to the x- coordinate of H and subtract 11 units from the y- coordinate of H, that is
H(5, 4) → H'(5 + 10, 4 - 11) → H'(15, - 7)
H’(15;-7) is my answer for your question
PLEASE HELP I AM BEING TIMED!! A company gives each new salesperson a commission of $300 for the sale of a new car. The salesperson will receive a $100 increase for each additional car the person sells that week, so the person gets $400 for the next sale that week. which equation can find the number of car as a salesperson must sell to earn $4200 in a week? Recall that a1+d(n-1) is equivalent to an.
Answer:
I would say B
Hope This Helps! Have A Nice Day!!
Answer: IT Is Not B !
Step-by-step explanation:
Please answer ASAP!
80 points because there are 5 questions.
Pictures provided.
D, C, 432, 3112, and C :)
eEvaluate please question in pic
Answer:
Option D is correct.
Step-by-step explanation:
[tex]\frac{\sqrt[3]{5}\sqrt{5}}{\sqrt[3]{5^5} }[/tex]
We need to solve this equation.
We know that √ is equal to 1/2 and ∛ is equal to 1/3 so solving the question:
[tex]=\frac{5^{1/3}X5^{1/2}}{5^{5/3}}[/tex]
We can add powers if the bases are same and numbers are multiplied.
[tex]=\frac{5^{1/3 +1/2}}{5^{5/3}}\\=\frac{5^{5/6}}{5^{5/3}}\\[/tex]
We can subtract powers if the bases are same and numbers are divided.
[tex]=5^{5/6-5/3}\\=5^{-5/6}[/tex]
So, Option D is correct.