Trig ratios can only be used on right triangles with acute measures.
If given an angle and there are adjacent and opposite sides, then use tan(opposite/adjacent)
If given an angle and there is an adjacent side and a hypotenuse, then use cosine(adjacent/hypotenuse)
If given an angle and there is an opposite and adjacent side, then use sin(opposite/hypotenuse)
A common mnemonic device used to memorize the trig rules is SOH-CAH-TOA
Trig ratios refer to the ratios of sides of a right triangle expressed about an angle. These include sine (sin), cosine (cos), and tangent (tan), as well as their reciprocals cosecant (csc), secant (sec), and cotangent (cot). They are fundamental in many real-world applications, including engineering, navigation, and physics.
Explanation:The trigonometric ratios are ratios of sides of a right triangle. Specifically, we have the following respected relations between angles and sides: Sine (sin) is the ratio of the length of the side opposite the angle to the length of the hypotenuse. Cosine (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse. Tangent (tan) is the ratio of the opposite side's length to the adjacent side's length. This is also equivalent to sin/cos. Respective reciprocal ratios are: cosecant (csc), secant (sec), and cotangent (cot).
These trig ratios allow us to determine distances, angles, and other aspects within a right triangle or representation of a circle.
For example, suppose we have a right triangle where the angle A is 30°, and the hypotenuse (the side opposite the right angle) is 10. In that case, we can determine the length of the opposite side by using the sin ratio, which is sin(30°) = Opposite/Hypotenuse. Solving, we get Opposite = sin(30°) * 10.
How do these trig ratios apply to real-world examples? Consider a ladder leaning against a wall, creating a right triangle with the ground. With the angle made at the ground and the length of the ladder, we can figure out how high up the ladder reaches on the wall using sin or how far from the base of the ladder's base should be placed using cos.
In conclusion, understanding trig ratios is an essential part of trigonometry and has numerous practical applications in real life, from construction and engineering to navigation and physics.
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Jessica bought 10 pieces of candy at the store. She spent $8.60. How much did each piece of candy cost?
Answer:
Each piece of candy cost
$0.86
Step-by-step explanation:
Step one This problem bothers on well we can do and understand our division of numbers
Step two
Given that Jessica spent $8.60
To buy 10 pieces of candy
Step three
We can get the unit cost of each candy by simply divide the total amount spent by the total Candy purchased
Hence
A candy cost = 8.60/10
= $0.86
A child’s pool is in the shape of a rectangular prism with a height of 2 ft and a base that is 4 ft wide by 5 ft long. During the course of the summer, the child’s pool needed to be filled 3 times.
How many cubic feet of water were needed to fill the pool during the summer?
A. 40 ft³
B. 80 ft³
C. 120 ft³
D. 160 ft³
Answer:
C. 120 ft^3
Step-by-step explanation:
Area of rectangular prism is Length * Width * Height.
4 * 5 * 2 = 40
It was filled 3 times so multiply 40 by 30
40 * 30 = 120 ft^3
please help me find the surface area of the triangular prism ( number 3)
Check the picture below.
so the triangular prism is really 3 rectangles and two triangles stacked up to each other at the edges, so if we simply get the area of each figure individually and sum them up, that's the area of the prism.
let's notice, the triangles have a base of 2.4 and a height/altitude of 1.
[tex]\bf \stackrel{\textit{2 triangles's area}}{2\left[ \cfrac{1}{2}(2.4)(1) \right]}~~+~~\stackrel{\textit{right rectangle}}{(2\cdot 1.5)}~~+~~\stackrel{\textit{left rectangle}}{(2\cdot 1.7)}~~+~~\stackrel{\textit{bottom rectangle}}{(2\cdot 2.4)} \\\\\\ 2.4+3+3.4+4.8\implies 5.4+8.2\implies 13.6[/tex]
The diagram shows the net of a juice box. The box is a reactangular prism
I don’t not know the answer for this question sorry
Answer:
its is B.
Step-by-step explanation:
each separate net has a twin so you find out the area of each net and multiply each one by two
If the radius of this cylinder is doubled, its volume will be
twice as much
four times as much
eight times as much
Answer:
V = \pi r^2h
When the radius is doubled, then
V=\pi (2r)^2h=4\pi r^2h
Therefore, when the radius is doubled, it volume will be four times as much.
Step-by-step explanation:
Answer: four times as much
Step-by-step explanation:
The volume of a cylinder is given by :-
[tex]V=\pi r^2h[/tex], where r is the radius and h is the height of the cylinder.
If the radius of this cylinder is doubled, then the radius of the new cylinedr will be:
R=2r
Now, the volume of the new cylinder is given by :-
[tex]V_1=\pi (2r)^2h\\\\\Rightarrow\ V_1=\pi(4r^2)h\\\\\Rightarrow\ V_1=4\pi r^2h\\\\\Rightarrow\ V_1=4(\pi r^h)\\\\\Rightarrow\ V_1=4(V)[/tex]
Hence, If the radius of cylinder is doubled, its volume will be four times as much.
PLEASE HELP!!!
1. A bag contains 10 identical balls numbered from 1 to 10. What is the probability that a person reaches into the bag and randomly selects a ball with a number that is a multiple of 3?
2. A bag contains 10 identical balls numbered from 1 to 10. What is the probability that a person reaches into the bag and randomly selects a ball with a number that is EVEN?
Enter your answer as a fraction in simplest form
Hello there (:
1)) Is 3/10
2)) Is 1/2
I hope this helps ya ;)
What is two thousand, six hundred nine dollars and seventy five cents written in expanded notation
Answer:
2000+600+9+.75 maybe?
Step-by-step explanation:
Omar knows the numbers to his locker combination are 24,38, and 6
Answer:
There are 6 possible combinations
Step-by-step explanation:
the number of numbers (3) times the other numbers (2)
Mary is going for a walk. She walks 12.5 miles in 5 hours. What is her speed
To find her speed, divide the total distance by the total time:
12.5 miles / 5 hours = 2.5 miles per hour.
What is the area of the trapezoid?
Answer:
Hi there!
I got the answer: 88 units^2
Step-by-step explanation:
to find the area you the formula: A=(a+b)/2 times height
"a" in this case is 17 and "b" is 27 because 5+5+17 is 27
height is 4
then you plug what you know into the equation
(17+27)/2 times 4 to get 88
Please Answer This Idk It 15 Points
Answer: The answer is D
Step-by-step explanation:
Each point on the house was divided by 2.
Answer:
D: (x,y) -> (2x, 2y)
Step-by-step explanation:
Take a look at the top of the roof, in the small house it is at (6,4) and in the big house it is at (12, 8).
To get from (6,4) to (12,8) you have to multiply x and y by 2.
You can test this with multiple points. Only the (x,y) -> (2x, 2y) mapping works for all of them.
what is the input value for an output value of -4 for the function g(x)=28/x-7
Final answer:
The input value for an output of -4 for the function g(x) = 28/x - 7 is x = 28/3.
Explanation:
To find the input value for a given output value of a function, we need to set the function equal to the output value and solve for the variable. The student is asking for the input value that results in an output of -4 for the function g(x) = 28/x - 7. To solve for x, we follow these steps:
Set the function g(x) equal to -4: g(x) = -4.
Substitute g(x) with the function definition: -4 = 28/x - 7.
Isolate the term with x by adding 7 to both sides: -4 + 7 = 28/x.
Simplify the left side of the equation: 3 = 28/x.
To find x, multiply both sides by x and then divide by 3: x = 28/3.
Therefore, the input value for an output value of -4 for the function g(x) = 28/x - 7 is x = 28/3.
Find the solution of this system of equations -x-4y=-37 -2x-5y=-53
Answer:
The solution in point form is (9,7) and the equation would be x+9, y=7
Step-by-step explanation:
By using moving the -4y to the right side and by flipping the signs you can turn the equation -x-4y=-37 into x=37-4y.
With this new equation you can use the substitution method and replace the x in -2x-5y=-53 with 37-4y, making it look like this: -2(37-4y)-5y=-53.
Then you solve for y getting y=7.
With the value of y, you can plug that into the equation x=37-4y so it will look like x=37-4(7)
Then you solve for x getting x=9
And with that you get the point (9,7)
the length of AB_ is 9 cm a dilation with a scale factor of 2 is applied to AB_ what is the length of the image of AB after the dilation is applied
The scale factor of two means you need to multiply the original length by 2:
9 x 2 = 18
The new length would be 18 cm.
What is the area of the trapezoid?
168 square inches
192 square inches
44 square inches
64 square inches
The answer is 192 square inches.
Answer:
192 square inches.
Step-by-step explanation:
Can y’all please help me
Answer:
Step-by-step explanation:
1. 6(7) +5
= 6x7 + 5
= 47
2. A =1/2 bh
= 1/2 x 18 x 6
= 54 squared inches
3. V = l x w x h
= 6 x 3 x 4
72 cubic inches
4. C
The solution is done on your page
You want to buy a new cell phone. The sale price is
$149
$149
. The sign says that this is
$35
$35
less than the original cost. What is the original cost of the phone?
Step-by-step explanation:
if you put in the numbers twice ill just ignore that.
If 149 is 35less than the original cost, add 35 for the original cost
The original cost was 184 dollars
Answer:
184
Step-by-step explanation:
Select all of the terms that apply to the shape. pentagon hexagon heptagon octagon nonagon decagon regular polygon irregular polygon concave convex
Answer: Convex, heptagon, regular polygon
Answer:
Heptagon, Irregular Polygon, and Concave
Step-by-step explanation:
From The figure shown in the picture we can see that it has the following characteristics. These characteristics are the following
7 straight sides2- 90° angles2 angles less than 90°2 angles greater than 180°1 angles greater than 90° but less than 180°Based on these characteristics we can say that the figure meets all the requirements to be classified as Heptagon, Irregular Polygon, and Concave
Heptagon: are figures with 7 straight sides and 7 angles
Irregular Polygons: are polygons that can have sides of any length and each interior angle can be of different angles
Concave: are polygons that have one or more interior angles bigger than 180°
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Prove: If a chord of a circle makes an angle of 30° with a diameter, prove that the distance from the center to the chord is one-fourth the length of the diameter.
Answer:
See explanation.
Step-by-step explanation:
Let BC be the diameter of the circle with center at point O, AB be the chord and ∠ABC=30°. OD is the distance from the center to the chord.
Consider triangle BDO. This triangle is special 30°-60°-90° right triangle. The leg OD is opposite to the angle of 30° and is half of the hypotenuse. The hypotenuse of the triangle BDO is BO. BO is the radius of the circle and is equal to half of the diameter AB. Thus,
[tex]OD=\dfrac{1}{2}BO=\dfrac{1}{2}\cdot \dfrac{1}{2}AB=\dfrac{1}{4}AB.[/tex]
Can someone help me with these problems? Please!
Step-by-step explanation:
2) Slope can be written as rise over run:
rise: add to the y-valuerun: add to the x-value[tex]a) Slope=-1\ over\ 1\quad \rightarrow \quad (11 + 1, -8 - 1)\implies (12, -9)\\b) Slope=7\ over\ 2\quad \rightarrow \quad (2+2,2+7)\implies (4, 9)\\c) Slope=9\ over\ 4\quad \rightarrow \quad (-5+4,-2+9)\implies (-1, 7)[/tex]
3) Slope formula is: [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]slope=\dfrac{15-3}{5-1}=\dfrac{12}{4}=\boxed{3}[/tex]
4) Average rate of change is the slope of the given interval:
a) when x = 0, y = 0 and when x = 1, y = -3
[tex]Slope=\dfrac{-3-0}{1-0}=\dfrac{-3}{1}=-3[/tex]
b) when x = -2, y = 0 and when x = -1, y = 3
[tex]Slope=\dfrac{3-0}{-1+2}=\dfrac{3}{1}=3[/tex]
c) when x = 0, y = 0 and when x = 2, y = 0
[tex]Slope=\dfrac{0-0}{2-0}=\dfrac{0}{2}=0[/tex]
what is 7.5÷46.55 please help
Answer:
0.16111707
Step-by-step explanation:
solve by completing y^2+7y+12=0
Answer:
y = -3,-4
Step-by-step explanation:
Factor the equation, which gives you (y+3)(y+4)=0
Then, all you do is find the values that give the equation an answer of 0.
Since anything times 0 is 0, all you have to do is make one of the (y+x) values equal 0.
Since -3 and -4 added to 3 and 4 make 0 the answers are -3 and -4.
You can check by plugging it back into the equation or graphing it.
Help me please because I’m trying to make it up
Answer:
7/8 or 0.875 units^3
Step-by-step explanation:
The volume for a rectangular prism is l*w*h. What you must remember is that l*w can be rewritten as the base of the prism. Thusly, the volume formula can be reduced to B*h, where B is the area of the base. You are given the area of the base as 1/2, so just multiply 1/2 by 1&3/4 (I rewrote it as 7/4) to get 7/8.
The perimeter of a square is 76.4m calculate the length of its diagonal
Answer:
The length of its diagonal is [tex]27.01\ m[/tex]
Step-by-step explanation:
Let
b------> the length side of the square
d-----> the diagonal of the square
we know that
The perimeter of the square is
[tex]P=4b[/tex]
[tex]P=76.4\ m[/tex]
Find the value of b
[tex]4b=76.4[/tex]
[tex]b=76.4/4=19.1\ m[/tex]
Applying the Pythagoras theorem find the length of the diagonal
[tex]d^{2}=19.1^{2}+19.1^{2}\\ \\d^{2}=729.62\\ \\ d=27.01\ m[/tex]
The length of the diagonal of a square is approximately 27.02m.
The perimeter of a square is the total length of all four sides of the square. Since we know that the perimeter is 76.4 meters, we can calculate the length of one side by dividing the perimeter by 4.
Length of one side = Perimeter ÷ 4 = 76.4m ÷ 4 = 19.1m.
To find the length of the diagonal, we can use the Pythagorean theorem for a square, which is a² + a² = diagonal². Here, a is the length of one side of the square. Thus, diagonal² = 2 × (19.1m)².
Diagonal = √(2 × (19.1m)²) = √(2 × 364.81m²) = √729.62m² = 27.02m (rounded to two decimal places).
Therefore, the length of the diagonal of the square is approximately 27.02 meters.
How many solutions exist for the system of equations graphed below?
None
One
Two
Infinite
Answer:
One
Step-by-step explanation:
The graphs of these two equations intersect at one point. This means there will only be one solution to the system.
The count of point of intersection of a graphed system of equation is the number of its solution.
The number of solution is (b) one
From the attached graph, we observe that:
The system equations on the graph have just one point of intersection.
This means that the number of solution of the system of equations is one.
Hence, the correct option is (b) one.
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4(x + 5) > 10(x - 1)
Answer:
x < 5
Step-by-step explanation:
Solve the inequality by using the distributive property and inverse operations.
4(x + 5) > 10(x - 1)
4x + 20 > 10x - 10
20 > 10x - 4x - 10
20 > 6x - 10
20 + 10 > 6x
30 > 6x
5 > x
School A and B are competing in an academic contest. at the beginning of the final round, school A has 174 points and school B has 102 points, in the final round, correct answers earn 10 points and incorrect answers loose 6 points. school A hives the same number of correct and incorrect answers during the final round. school B gives no incorrect answers and the same number of correct answers as school A. the contest ends with te two schools tied. which equation models the scoring in the final round and outcome of the contest?
Answer:
School A gave 12 correct and 12 incorrect answers. School B gave 12 correct answers and the competition was tied.
Step-by-step explanation:
We are given the following information:
School A points = 174
School B points = 102
Every correct answer is awarded 10 points and every incorrect answer reduces 6 points.
Let x be the number of correct answer given by school A and thus x is the number of incorrect answer given by school A. The, school B also gives x number of correct answer.
Thus, the scored can be modeled with the following equations:
School A: [tex]174 + 10x - 6x = 174 + 4x[/tex]
School B: [tex]102 + 10x[/tex]
Since, both the schools tied, equating both the equations:
[tex]174 + 4x = 102 + 10x\\\Rightarrow 10x - 4x = 174 -102\\\Rightarrow 6x = 72\\\Rightarrow x= 12[/tex]
Thus, school A gave 12 correct and 12 incorrect answers. School B gave 12 correct answers and the competition was tied.
Can I get help on this please someone
Answer:
C
Step-by-step explanation:
Let's break down the definitions.
Supplementary = degrees add up to 180
Vertical = share a common vertex
Complementary = degrees add up to 90
Adjacent = share a common side and vertex
Since the degrees add up to 90 and don't share a common side/vertex, the angles are complementary.
You work for a video streaming company that has two monthly plans to choose from plan1:A flat rate of 7$ per month
Answer:
Step-by-step explanation:
The cost will be 7$ per month
Best regards
NEED HELP ASAP 20POINTS The energy (and cost) needed to operate an air conditioner is proportional to the volume of a space that is being cooled it cost ZAP electronics about $125.00 per day to run an air conditioner in its small rectangular warehouse the company’s large warehouse a few blocks away is 2.5 times as long,wide,and high as the small warehouse estimate the daily cost of cooling the large warehouse with the same model of air conditioner round answer to the nearest dollar? show work to solve
Answer:
$1,953
Step-by-step explanation:
So, we need to figure out how many times the big warehouse is actually bigger than the small one, in order to calculate the air conditioner cost for the large warehouse.
Let's say x represents the dimensions of the small warehouse, and y represents the dimensions of the large warehouse.
We have y = 2.5x, for every dimension (length, width, height)
The formula to calculate the volume of a cubic space is the following:
volume = length * width * height
Now, we don't know the exact measurements involved, but we know the large warehouse is 2.5 times bigger in every dimension, so...
volume = 2.5x * 2.5x * 2.5x = 2.5³x³ = 15.625 x³
So, the larger warehouse is 15.625 times larger than the small one. We then multiply that by the cost of cooling down the small warehouse:
cost for large warehouse = 15.625 * $125/month = $1,953.25
Rounded to the nearest dollar: $1,953