Remembering the ratio of 1: 3: 2 and understanding that the smallest side length is always opposite the shortest angle (30°) and the longest side length is always opposing the greatest angle (90°) can help you recall the 30-60-90 triangle principles.
A 30-60-90 triangle can have three sides, and if you only know one, you can use shortcuts to discover the other two. The three scenarios you encounter when performing these computations are as follows:
You are aware of the short leg (the side across from the 30-degree angle). To determine the hypotenuse, multiply the length by two. The long leg may be calculated by multiplying the short side by the square root of 3.You are aware of the hypotenuse. To get the short side, divide the hypotenuse by two. To determine the long leg, multiply this response by the square root of 3.You are aware of the long leg (the side across from the 60-degree angle). To determine the short side, divide this side by the square root of 3. To determine the hypotenuse, multiply that amount by two.To know more about the 30-60-90 triangle on brainly : brainly.com/question/11751274
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What are the factors of x^3 Y^3?
The factors of (x^3 + y^3) are ( x + y )(x^2 - x . y + y^2).
In order to find the factors of (x^3 + y^3), you need to apply the sum of cubes formula:
(x^3 + y^3) = ( x + y )(x^2 - x . y + y^2)
(x^3 + y^3) = ( x + y )(x^2 - x y + y^2)
Therefore, in order to find the factor of the given expression, you just simply need to learn the sum of cubes formula.
Similarly, the difference of cubes formula is as follows:
(x^3 - y^3) = ( x - y )(x^2 + x y + y^2)
Which gives factors of (x^3 - y^3).
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HELPPPPPP PLEASEeeeeeeeeeeeeee
Answer:
x > 3
Step-by-step explanation:
6x - 2 - 3x + 9 > 16
3x + 7 > 16
3x > 9
x > 3
geometry stuff pls help
Answer:
Step-by-step explanation:
SQR-PRQ-SRP
SP/RP=RP/PQ
QP/QR=RQ/SQ
can someone please help me ( check the link for the question
The equation of the line that passes through the point (3, 2) and is perpendicular to 3x + 5y = 15 is y = (5/3)x - 3
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of the line is y = m(1)x + c
The line passes through (3, 2) and is perpendicular to 3x + 5y = 15.
This means,
3x + 5y = 15
5y = -3x + 15
y = (-3/5)x + 3
m(2) = (-3/5)
Now,
m(1) x m(2) = -1
m(1) = -1 / ((-3/5)
m(1) = 5/3
Now,
(3, 2) = (x, y)
y = m(1)x + c
2 = (5/3) x 3 + c
2 = 5 + c
c = 2 - 5
c = -3
Thus,
The equation of the line is y = (5/3)x - 3.
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a paint roller has a width of 12 inches and a radius of 3 inches, what is the surface area that can be painted with one complete rotation of the roller
The surface area that can be painted with one complete rotation of the roller is 226.19 inches².
Surface area is defined as the total amount of area that covers the surface or outside of a three-dimensional figure.
A paint roller is in the shape of a cylinder. To determine the surface area that can be painted with one complete rotation of the roller, solve for the surface area of a cylinder without the circular bases.
SA = 2πrh
where SA = surface area
r = radius of the base = 3 inches
h = height of the cylinder = width = 12 inches
Plug in the values and solve for the surface area.
SA = 2πrh
SA = 2π(3 inches)(12 inches)
SA = 226.19 inches²
Hence, the surface area that can be painted with one complete rotation of the roller is 226.19 inches².
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Can someone please help me? :(
Kelly started running around a track two laps before Anne. They are running at the same speed. Write an equation to find the number of laps, y Kelly
has run given the number of laps, X Anne has run.
1. X= 2y
2. Y= 2x
3. X= y+2
4. Y= x+2
Answer:
Step-by-step explanation:
I am stuck on this question and i honestly am stuck and do not know what to do.
The basic parts of a circle include its diameter, circumference, radius, arc, chord, tangent, tangent, section, and segment.
What is Circle radius?the surface or circumference of a circle, ball, and other object measured in a straight line The radius and diameter of a circle are equal. The length of such a line. whatever radiating or radial component. A circle's chord is the line segment that connects any two locations on the circle's circumference. It should be remembered that a circle's diameter is defined as the lengthiest chord that runs across the center of the circle.
Here,
given
The letter "C" should be in the center.
radius=r=AC=CB
Diameter=d=2r=AB.
Therefore , the solution to the given problem of circle comes out to be ,the basic parts of a circle include its diameter, circumference, radius, arc, chord, tangent, tangent, sector, and segment.
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A whale is swimming due north at a speed of 40 kilometers per hour. Just 6 kilometers away,
a whale-watching tour boat is traveling south, directly toward the whale, at a speed of 83
kilometers per hour. How long will it be before they meet?
Answer:
O hrs and 30 minutes is the answer
Step-by-step explanation:
want proof?
Answer:
about 0.04878 hours ≈ 2 minutes 56 seconds
Step-by-step explanation:
You want the time until a whale-watching boat and a whale meet if the boat is traveling south at 83 km/h and the whale is traveling north at 40 km/h when they start 6 km apart.
Closing speedThe speed at which the gap between the boat and the whale is closed is the sum of their respective speeds:
closing speed = 83 km/h + 40 km/h = 123 km/h
TimeThe time it takes to close the 6 km gap is ...
time = distance/speed
time = (6 km)/(123 km/h) ≈ 0.04878 h
Converted to minutes and seconds, that is about ...
0.04878 h ≈ 2 minutes 55.6 seconds
It will be about 2 minutes 56 seconds before the boat and whale meet.
__
Additional comment
NOAA recommends a distance of at least 100 yards be maintained between a boat and a whale. In some areas, the recommended distance is 400 yards when approaching head-on. The recommended boat speed is 15 knots or less, about 28 km/h.
Find an equation for the line that passes through the points (-5, 2) and (3, 4)
Vanessa will sell yogurt for $2.50 a cup. Fill in the table to show how much money Vanessa will make if she sells 19 cups of vanilla yogurt.
Answer:
2.50 × 19 = 47.5
Therefore, she would get $47.5 if she sold 19 cups.
help me i been stuck for like a good 20 min
[tex]4(x+7) \leqslant 4(2x+8)\implies 4x+28\leqslant 8x+32\implies 28\leqslant 4x+32 \\\\\\ -4\leqslant 4x\implies \cfrac{-4}{4}\leqslant x\implies \boxed{-1\leqslant x}[/tex]
notice, in the division by "4" we didn't flip the inequality sign, because the division was by a positive value, we only flip it when the division involves a negative value.
Question 12(Multiple Choice Worth 4 points) (02.01 LC) Which sampling method is the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country? Simple random sampling, because the people in the sample are accessible and available Stratified sampling, because there are specific subgroups to investigate Systematic sampling, because of the ease in selecting every nth person Cluster sampling, because the studied population is spread across a wide area such that simple random sampling would be difficult to implement All the above sampling methods
The option 1 "Simple random sampling, because the people in the sample are accessible and available" is correct for the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country.
In the given question, we have to find which sampling method is the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country.
As we know that, you must carefully consider how you will choose a sample that is representative of the group as a whole if you want to make accurate conclusions from your data. It is known as a sampling method.
Every individual in the population has an equal chance of being chosen in a simple random sample. The entire population should be included in your sampling frame.
You might utilize instruments like random number generators or other methods that just rely on chance to carry out this kind of sampling.
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The complete question is:
Which sampling method is the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country?
(1) Simple random sampling, because the people in the sample are accessible and available
(2) Stratified sampling, because there are specific subgroups to investigate
(3) Systematic sampling, because of the ease in selecting every nth person
(4) Cluster sampling, because the studied population is spread across a wide area such that simple random sampling would be difficult to implement
(5) All the above sampling methods
What is the center of a circle (x y) with the equation (x + 3)^2 + (y − 5)^2 = 16
Step-by-step explanation:
the center of the circle is (−3,5) and radius is 16 =
: Find the pherical coordinate of the point whoe rectangular coordinate are
(-2, 2√3,4)
The spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).
What is a peripheral coordinate?
A peripheral coordinate is a set of three coordinates (r, θ, φ) that describes the position of a point in space in relation to a fixed origin. r is the distance from the origin to the point, θ is the angle between the positive x-axis and the projection of the point onto the xy-plane, and φ is the angle between the positive z-axis and the line connecting the point to the origin.
To find the spherical coordinates of a point whose rectangular coordinates are (-2, 2√3,4), we can use the following formulas:
[tex]r=\sqrt{(x^2 + y^2 + z^2)} = \sqrt{((-2)^2 + (2\sqrt3)^2 + 4^2)} = \sqrt{(4 + 12 + 16)} = \sqrt32 = 4\sqrt2[/tex]
θ = [tex]tan^{-1}(y/x) = tan^{-1}(2\sqrt3/(-2)) = tan^{-1}((-\sqrt3)/1) = -60^o[/tex]
φ = [tex]cos^{-1}(z/r) = cos^{-1}(4/4\sqrt2) = cos^{-1}(1/\sqrt2) = \degree 45 ^o[/tex]
So, the spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).
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The spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).
What is a peripheral coordinate?
A peripheral coordinate is a set of three coordinates (r, θ, φ) that describes the position of a point in space in relation to a fixed origin. r is the distance from the origin to the point, θ is the angle between the positive x-axis and the projection of the point onto the xy-plane, and φ is the angle between the positive z-axis and the line connecting the point to the origin.
To find the spherical coordinates of a point whose rectangular coordinates are (-2, 2√3,4), we can use the following formulas:
[tex]r=\sqrt{x^2+y^2+z^2} = \sqrt{(-2)^2+(2\sqrt{3})^2+4^2}=4\sqrt{2}[/tex]
θ = [tex]tan^{-1}(y/x)=tan^{-1}(2\sqrt{3}/(-2))=60^o[/tex]
φ = [tex]cos^{-1}(z/r)=tan^{-1}(4/4\sqrt{4})=45^o[/tex]
So, the spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).
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Sabreena is playing a card game, and the odds of her winning after drawing the next card are 5:7. What is the probability of her not winning? Enter your answer as a decimal rounded to the nearest thousandth, like this: 0.423
The probability that Sabreena is going to lose is given as 0.5833
How to solve for the probabilityProbability is a measure of the likelihood of a specific event or outcome occurring. It is typically expressed as a decimal number between 0 and 1, or as a percentage between 0% and 100%.
A probability of 0 indicates that an event is impossible and will never occur, while a probability of 1 indicates that an event is certain and will always occur.
If the odds that Sabreena has of winning in this game is 5: 7, this is written as 5 / 7
In this case, the odds of Sabreena winning are 5:7,
so the probability of winning is 5/(5+7)
the probability of not winning is 1 - 5/12
The probability of not winning is approximately 0.5833
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pls solve me this functions question
On solving the provided question, we can say that - the value of the function is f(x) = [tex]x^2 + 9 + 3x -5[/tex] = [tex]x^2 +3x +4[/tex]; f(x) = x= it doesn't factor
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
f(x) = [tex](x+3)^2 - 5[/tex]
f(x) = [tex]x^2 + 9 + 3x -5[/tex] = [tex]x^2 +3x +4[/tex]
f(x) = x= it doesn't factor
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Alexis sells stuffed animals. she sells a stuffed elephant for $14.95, and the sales tax is 5% of the sale price. about how much is the sales tax on the elephant?
The price of the sales tax on the elephant could be 0.75$
What is percentage ?
percentage can be defined as the product of ratio of given value and total value and hundred.
Given
he sells a stuffed elephant for $14.95,
the sales tax is 5% of the sale price .
So,
as the tax is 5% of the given value.
so we are here multiplying the given value to the 5/100
we get,
The amount of the tax could be
= 14.95*5/100
= 0.7475
≈ 0.75 (rounded)
Hence the price of the sales tax on the elephant could be 0.75$
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pls help with this its due today
Using PEMDAS to solve the algebraic expression, the value is 2
What is Mathematical OperationMathematical operations are operations that involve the manipulation of numbers, variables, and/or equations. Examples of mathematical operations include addition, subtraction, multiplication, division, exponentiation, and root extraction.
In this problem, we can use PEMDAS to solve this algebraic expression.
[(3/5 + 0.425 - 0.005) ÷ 0.1] / [30.5 + 1/6 + 3 (1/3)] + [6(3/4) + 5(1/2)] / 26 ÷ 3(5/7)] - 0.05
This will become;
[10.2 / 34] + [12.25 / 7] - 0.05
Dividing and adding the numbers will give us;
(0.3 + 1.75) - 0.05 = 2
The value is 2
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What is the equation of the straight line shown below? Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms. Y 14- 13- 12- 11- 10- 9 8- 97654 MNE 7- 6- 5- 4- 3- 2- 1- -10-9-8-7-6-5-4-3-2 0 1 2 3 4 5 6 7 8 9 10 x -1 -2- -3- بنا -4- 56 -5- -6+
Answer:
y = 2x + 10
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, 10) ← 2 points on the line
m = [tex]\frac{10-0}{0-(-5)}[/tex] = [tex]\frac{10}{0+5}[/tex] = [tex]\frac{10}{5}[/tex] = 2
the line crosses the y- axis at (0, 10 ) ⇒ c = 10
y = 2x + 10 ← equation of line
Robert is building a deck in his backyard. Each piece of wood measures 42.5 inches. If he has 8 boards, how long are they altogether?
The length of the wood altogether is 340 inches
How to calculate the length of the wood?Robert is building a deck
Each piece of the wood measures 42.5 inches
Robert has 8 boards
The length of the wood altogether is
= 42.5 × 8
= 340
Hence the length of the wood is 340 inches
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please i really need help! anything will help at the moment
Answer:
-2 i think hope this helps
Step-by-step explanation:
At Central Middle School the 108 students who take the AMC 8 meet in theevening to talk about problems and eat an average of two cookies apiece.Walter and Gretel are baking Bonnie's Best Bar Cookies this year. Their recipe,1 which makes a pan of 15 cookies, lists this items: 1- cups of flour, 2 eggs, 323 tablespoons butter, cups sugar, and 1 package of chocolate drops. They will 4 make only full recipes, not partial recipes.Walter can buy eggs by the half-dozen. How many half-dozens should he buy to make enough cookies? (Some eggs and some cookies may be left over.)(A) 1(B) 2(C) 5(D) 7 (E) 15
5 half-dozens he should buy to make enough cookies.
What is an average?
Average, mean, median, and norm all refer to something that sits in the middle. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. scored 85 on tests on average. The term "mean" can refer to the simple average or a figure that lies halfway between two extremes.
Here, we have
If 108 students eat 2 cookies on average, there will need to be 108× 2 = 216 cookies.
There are 15 cookies per pan, meaning there need to be {216}/{15} = 14.4 pans.
However, since half-recipes are forbidden, we need to round up and make{216}/{15} = 15 pans.
1 pan requires 2 eggs, so 15 pans require 2×15 = 30 eggs.
Since there are 6 eggs in a half dozen,
we need 30/6 = 5 half-dozens of eggs.
Hence, 5 half-dozens he should buy to make enough cookies.
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What is the smallest positive multiple of $13$ that is greater than $500?$
Answer:
Step-by-step explanation:
The smallest possible multiple of 13 dollars greater than 500 dollars would be 507 which is 13*39 (i assume you mean whole numbers when you say positive numbers, if not the other answer would be 13*38.461)
need this rn
solving system of linear equation in two variables. Show your COMPLETE SOLUTION
1) 4x + 8y = 24 2) 2x + y = 19 3) 3x + y = 15
4x + 2y = 12 x + y = 11 x + 2y = 10
The solution to the system of equations is x = 4 and y = 2.
CalculationsWe would use the elimination method to solve the system of equations:
4x + 8y = 242x + y = 193x + y = 154x + 2y = 12x + y = 11x + 2y = 10Let's eliminate the variable y by adding equations 1 and 2:
4x + 8y = 24
2x + y = 19
.
.
.,
6x + 9y = 43
Now we can eliminate the variable x by subtracting equation 3 from the above equation:
6x + 9y = 43
3x + y = 15
.
.
.
3x + 8y = 28
We now have an equation with one variable: 3x + 8y = 28. We can solve for x by dividing both sides by 3:
x = (28 - 8y) / 3
Now we can substitute this expression for x into one of the original equations and solve for y. Let's use equation 4:
4x + 2y = 12
Substituting x = (28 - 8y) / 3:
4((28 - 8y) / 3) + 2y = 12
If we simplify:
28 - 8y + 2y = 128y = 16y = 2Finally, we can use this value of y to find x by plugging it into the expression we found earlier:
x = (28 - 8(2)) / 3
x = (28 - 16) / 3
x = 12 / 3
x = 4.
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The the mesure of……..
The measure of angle B is 82°
What is angle ?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
∠A = 180° - 143°
= 37°
∠A + ∠B + ∠C = 180°
37° + ∠B + 61° = 180
∠B = 180 - 61 - 37
= 82°
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please help me
please help me
Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of % in hr
The expression when Buffalo New York had 2ft of snow on the ground before a snowstorm is 2 - 0.25h.
How to illustrate the expression?From the information, Buffalo New York had 2ft of snow and we want to find the. expression based on the information given.
An expression have at least two terms which have to be related by through an operator.
Since Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of 25% in every hr. The expression will be:
2 - (25% × h)
= 2 - 0.25h
h = number of hours.
The expression is 2 - 0.25h.
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Complete question
Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of 25% in every hr. Illustrate the expression
The top-notch middle school had athletes from all the grades playing on a sports team. 6th grade 7th grade 8th grade basketball 2 4 7 baseball 1 6 5 soccer 7 4 4 football 8 15 10 explain what the ratio 5:73 represents. the ratio 5:73 represents the ratio of 8th grade baseball players to total athletes. the ratio 5:73 represents the ratio of 7th grade football players to total athletes. the ratio 5:73 represents the ratio of total athletes to 7th grade football players. the ratio 5:73 represents the ratio of 6th grade athletes to total athletes.
The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
What is ratio?In mathematics, a ratio is a comparison of two or more numbers that demonstrates how large one number is relative to the other. The divisor or number that is dividing is known as the consequent, while the dividend or number being divided is known as the antecedent. A ratio divides two numbers to compare them.
Given that the Total number of athletes are 2+4+7+1+6+5+7+4+4+8+15+10
= 73
Ratio of 5:73 represent the athletes in a particular grade with specific games to total number of athletes in the school.
There are on one event is where 5 athletes are, that is 8th grade baseball players.
So the correct answer is The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
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pls answer all questions
Spiders are arachnids with eight legs, as do all arachnids. Spiders differ from insects in that they have only six legs.
Do spiders have 6 or 8 legs?Crabs and prawns are also members of the phylum Arthropoda, which includes spiders. Spiders walk on eight legs, but they also have two additional legs that they utilise as hands. The front legs are called pedipalps, or palps for short.
Proteins are secreted by glands on spiders, which aid in the formation of the web. For a number of objectives, including prey capture, prey detection, tunnel lining, egg sacs, and prey wrapping, spiders can create a variety of webs or silks.
Spiders are venomous carnivores who hunt their prey with poison.In Everglades National Park, arachnids such as spiders, scorpions, mites, ticks, whip scorpions, and pseudoscorpions are all common.
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