Answer:
The Pythagorean identity [tex]\sin^2\theta+\cos^2\theta=1[/tex] comes from Pythagorean theorem and the unit circle. In the unit circle, for any point on the circle, there y-coordinate represents the sine of the angle and the x-coordinate represents the cosine of the angle. For any angle [tex]\theta[/tex], we can create a right triangle using the x-coordinate and y-coordinate as legs of the triangle. The hypotenuse of this triangle would be the radius of the unit circle, which is given as 1.
The Pythagorean theorem states that in all right triangles, the following must be true:
[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are two legs of the triangle.
Therefore, we have the following equation:
[tex](\sin\theta)^2+(\cos\theta)^2=1^2,\\\boxed{\sin^2\theta+\cos^2\theta=1}[/tex]
The Pythagorean identity comes from Pythagorean theorem and the unit circle. In the unit circle, for any point on the circle, there y-coordinate represents the sine of the angle and the x-coordinate represents the cosine of the angle. For any angle , we can create a right triangle using the x-coordinate and y-coordinate as legs of the triangle. The hypotenuse of this triangle would be the radius of the unit circle, which is given as 1.
The Pythagorean theorem states that in all right triangles, the following must be true:
, where is the hypotenuse of the triangle and and are two legs of the triangle.
Therefore, we have the following equation:
Can someone please tell me if this angle is supplementary or complementary
Answer:
Step-by-step explanation:
Since the angles both come off of the straight line, they are supplementary, and they add up to equal 180 degrees.
2x + 4x + 24 = 180 and
6x + 24 = 180 and
6x = 156 so
x = 26
Find the volume of the pyramid
volume
18 cm
10 cm
10 cm
options
1,800 cm
900 cm
600 cm
750 cm
[tex]_____________________________________[/tex]
ANSWER:V = 1,800 cmSOLUTION:V = l × w × hV = 18 × 10 × 10[tex]\large\boxed{\tt{\green{V = 1,800}}}[/tex][tex]_____________________________________[/tex]
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Answer:
<FGH and <JKL are supplementary
<AED and <BEC are complementary
Step-by-step explanation:
For supplementary angles, the sum of the pair of angles must be 180degrees
Given;
<FGH = 109degrees
<JKL = 71degrees
Taking the sum
<FGH + <JKL
= 109 + 71
= 180
Since the sum of the angles is 180, hence <FGH and <JKL are supplementary
Similarly;
Given
<AED = 45degrees
<BEC = 45degrees
Taking the sum
<AED + <BEC
= 45 + 45
=90degrees
Since the sum of complementary angles is 90degrees, hence <AED and <BEC are complementary
-2x + 4 = 3
how would you solve this problem?
A hiker leaves her camp in the morning. She walks 9 miles west then 10 miles north. Explain how you would find how far she has traveled from her camp.
Answer:
About 13.45 miles ( rounded )
Step-by-step explanation:
You would use the pythagorean theorem to solve this. ([tex]a^{2}[/tex]+ [tex]b^{2}[/tex] = [tex]c^{2}[/tex])
[tex]a^{2}[/tex] would be one length of that triangle, we'll use 9.
[tex]b^{2}[/tex] would be the other length of that triangle, we'll use 10.
So, now you have to square both of them.
[tex]9^{2}[/tex] = 81 ( 9 x 9 ) [tex]10^{2}[/tex] = 100 ( 10 x 10 )
Which you will get 81 and 100. Then you add those two numbers together.
100 + 81 = 181
Now that you have 181, you have to square root 181.
[tex]\sqrt{181}[/tex]
With that you should get 13.45 miles. (rounded)
PLEASE HELP I HAVE A C ALREADY I NEED TO GET THIS RIGHT PLEASE
You want to estimate the number of students in your school who support extra funding for the science club. You survey the first 13 students who arrive at a science class.
Determine whether the sample is biased or unbiased.
Answer:
BRO I HAVE THE SAME QUESTION FOR MY TEST....
ITS BIASED IM REALLLLY SURE
Step-by-step explanation:
A sports team is building a new stadium on a rectangular lot of land. If the lot measures 7x by 7x and the sports field will be 5y by 5y, how much of the lot will be left over to build bleachers on?
Answer:
Area of rectangular lot= l * f
Step-by-step explanation:
Area of rectangular lot= l * f=7x*7x = 49x^2
Area of stadium= 5y*5y = 25y^2
Area left of build bleachers = 49x^2 - 25y^2
For which function does f decrease by 15% every time x increase by 1? A: f(x)= 0.15^x B: f(x)=8.5^x C: f(x)=15^x. D: f(x)=85^x
Answer:
[tex]f(x) = (0.85)^x[/tex]
Step-by-step explanation:
Exponential amount of decay:
The equation for an amount that decays exponentially has the following format:
[tex]A(x) = A(0)(1 - r)^x[/tex]
In which r is the decay rate, as a decimal.
Decrease by 15%
This means that [tex]r = 0.15[/tex]. So
[tex]f(x) = (1 - r)^x = (1 - 0.15)^x = (0.85)^x[/tex]
So
[tex]f(x) = (0.85)^x[/tex]
which expression is equivalent to 6x*3 + 3y*2 - 5x*3 + 2y*2
Answer:
3x + 10y
Step-by-step explanation:
Calculate: (6x*3)+(3y*2)-(5x*3)+(2y*2) = 18x + 6y - 15x + 4y
Collect Like Terms: 18x + 6y - 15x + 4y = 3x +10y
Solution: 3x + 10y
T: 76x + 3) = 7(x + 5) Part B: Luisa knows only one number was torn off, and she knows that the equation has an infinite number of solutions. What must be the missing number? Show and explain your work?
Answer:
yea same
Step-by-step explanation:
The largest jaw breaker in a store is spherical with a radius of 2 in, and sells for $4.00. A
store wants to make a 6 in. radius jaw breaker. How much should they charge for this
foot long jaw breaker?
Answer:
$36
Step-by-step explanation:
1. Determine the surface area of the largest jaw breaker
Surface area of a sphere = 4πr²
4 x 3.14 x 2² = 50.24in²
2. Determine the surface area of the new jaw breaker
4 x 3.14 x 6² = 452.16 in²
3. Determine the cost per area
4/ 50.24
4. Determine the price for the new jaw breaker
4/ 50.24 x 452.16 = $36
PLEASE HELPPPP I NEED THIS FASTTTTT
Answer:
[tex]there \: are \: 8 \: values \\ = \frac{8}{17} \times 100\% \\ = 47\%[/tex]
Solve for x.
0.5x+78.2=287
Answer:
x =417.6
Step-by-step explanation:
0.5x+78.2=287
Subtract 78.2 from each side
0.5x+78.2-78.2=287-78.2
.5x =208.8
Divide each side by .5
.5x/.5 = 280.8/.5
x =417.6
In the diagram below of triangle UVW, X is a midpoint of UV and Y is a
midpoint of VW. If mZXYV = 7x + 21, and mZUWY = 91 – 7x,
what is the measure of ZXY?
V
X
Y
U
W
Given:
In triangle UVW, X is the midpoint of UV and Y is the midpoint of VW.
[tex]m\angle XYV=7x+21[/tex]
[tex]m\angle UWY=91-7x[/tex]
To find:
The measure of angle XYV.
Solution:
Since X is the midpoint of UV and Y is the midpoint of VW, therefore XY is the mid-segment of the triangle UVW and parallel to the base of the triangle, i.e., UW.
If a transversal line intersect two parallel lines, then the corresponding angles are congruent and their measures are equal.
[tex]\angle XYV \cong \angle UWY[/tex] [Corresponding angle]
[tex]m\angle XYV=m\angle UWY[/tex]
[tex]7x+21=91-7x[/tex]
We need to solve this equation for x.
[tex]7x+7x=91-21[/tex]
[tex]14x=70[/tex]
[tex]x=\dfrac{70}{14}[/tex]
[tex]x=5[/tex]
Now,
[tex]m\angle XYV=7x+21[/tex]
[tex]m\angle XYV=7(5)+21[/tex]
[tex]m\angle XYV=35+21[/tex]
[tex]m\angle XYV=56[/tex]
Therefore, the measure of angle XYV is 56 degrees.
hey! please help i’ll give brainliest
Answer:
C
Step-by-step explanation:
"grow or develop in a healthy or vigorous way, especially as the result of a particularly favorable environment."
Answer:
C.
hope this helps
have a good day :)
Step-by-step explanation:
Mark packed 1-inch cubes into a box with a volume of 96 cubic inches. How many layers of 1-inch cubes would it take to fill the box?
Answer:
4 approx.
Step-by-step explanation:
The number of layers of 1-inch cubes that Mark packed is determined by assuming that the larger box is also a cube.
let the N be the number of layers of 1-inch cubes that would it take to fill the box.
Since the larger box is also a cube
Therefore, 96 = N^3
N = (96)^(1/3)
N = 4√6
Therefore, there would be 4 layers of the 1-inch cube and some extra incomplete layer
Which of the following choices is NOT one of the six tenses of verbs?
past participle
future perfect
future
present perfect
Answer:
past participle
Step-by-step explanation:
all of the other ones are correct
What is the answer to this question
Answer:
∠ A = 70°
Step-by-step explanation:
The opposite angles in a cyclic quadrilateral are supplementary, then
∠ A + ∠ Q = 180°
∠ A + 110° = 180° ( subtract 110° from both sides )
∠ A = 70°
Find the value of x please I need help
Answer:
Step-by-step explanation:
113+90+90+12x+7=360(sum of four angles is always 360 degree)
300+12x=360
12x=360-300
x=60/12
x=5
Answer:
X = 5
Step-by-step explanation:
Shapes with 4 sides have angles that add to 360 degrees
So you have two right angles and 113 degrees.
This is
90+90+113=293
360-293=67
12x5=60
60+7=67
This means that x=5
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Answer:
[tex]speed = \frac{Distance}{time}[/tex]
York Canal
Distance = 5miles
Time = 15 minutes
[tex]speed = \frac{5}{15} = \frac{1}{3} miles\ per \ minute[/tex]
Stover Lake
Same speed , S = 1/3 miles per minute
Time = 30minute
[tex]Distance = speed \times time = \frac{1}{3}\times 30 = 10 miles[/tex]
[tex]Distance_{York} = 5 miles\\\\Distance_{Stover} = 10 miles\\\\[/tex]
Clearly, Distance travelled in York in half the distance travelled in Stover
option. 3
Thirty students were asked what their favorite number from 1 through 9 was. The results were 8 students said 3. 6 students said 4, 9 students said 7, and 2 students said 9. What is the experimental probability that the number 7 was picked as the favorite number?
Answer:
3/10
Step-by-step explanation:
From the question, we have the total number of sampled students as 30
9 students said 7 was their favorite
So the experimental probability that we have 7 picked as the favorite number will be the number of respondents who chose 7 as their favorite divided by the total number of respondents
We have this as;
9/30 = 3/10
y = x2 – 14x + 23
y = - 3x + 5
Answer:
let first equation be y=x^2-14x+23
second equation be y=-3x+5
now substitute the vale of y in equation second
y=-3x+5
x^2-14x+23=-3x+5
x^2-14x+3x=5-23
x^2-11x=-18
x^2-11x+18=0
x^2-(9+2)x+18=0
x^2-9x-2x+18=0
x(x-9)-2(x-9)=0
(x-2)(x-9)=0
either x-2=0 Or, x-9=0
x-2=0
x=0+2
x=2
x-9=0
x=0+9
x=9
therefore x=2,9
Step-by-step explanation:
-
Answer:
(2, - 1 ) and (9, - 22 )
Step-by-step explanation:
Given the 2 equations
y = x² - 14x + 23 → (1)
y = - 3x + 5 → (2)
Substitute y = x² - 14x + 23 into (2)
x² - 14x + 23 = - 3x + 5 ( subtract - 3x + 5 from both sides )
x² - 11x + 18 = 0 ← in standard form
(x - 2)(x - 9) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 9 = 0 ⇒ x = 9
Substitute these values into (2) for corresponding values of y
x = 2 : y = - 3(2) + 5 = - 6 + 5 = - 1 ⇒ (2, - 1 )
x = 9 : y = - 3(9) + 5 = - 27 + 5 = - 22 ⇒ (9, - 22 )
The softball in the mitt is 4.9 inches in diameter. What is its volume? (Use 3.14 for )
Volume is a three-dimensional scalar quantity. The volume of the softball is 61.6 cubic inches.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Given that the diameter of the softball is 4.9 inches. Since the radius is half the diameter, therefore, the radius of the softball can be written as,
Radius = Diameter
= 4.9 inches / 2
= 2.45 inches
Now, the volume of the softball can be written as,
Volume of the softball = (4/3) × π × r³
= (4/3) × π × (2.45 inches)³
= 61.6 inches³
Hence, the volume of the softball is 61.6 cubic inches.
Learn more about Volume:
https://brainly.com/question/13338592
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write a liner equation that passes through the point (2, -9) and has a slope of -5
Answer:
y=-5x-9
Step-by-step explanation:
If −2x + 3 = 13, then 2x =____?
helppppp meeeee plz i'll give brainliest!!!
Answer:
1
Step-by-step explanation:
2m + 4 = 6
2m = 6 - 4
2m = 2
m = 1
the answer is one.. ....
please help i have an exam next week and im really stuck on this
Answer:
Area = 96 square cm
Step-by-step explanation:
Area of the figure = (2 x Area of triangles) + Area of square
[tex]Area \ of \ triangle = \frac{1}{2} \times base \ height = \frac{1}{2} \times 8\times 4 = 16cm^2\\\\Area \ of \ square = side \times side = 8 \times 8 = 64cm^2[/tex]
Therefore, [tex]Area \ of \ the\ figure = (2 \times 16) + 64 = 32 + 64 = 96cm^2[/tex]
The student enrollment of South High School was 1,350 students in 1995 and increased by 15% per year until 2010. Approximately how many students were enrolled at South High School in 2010?
Answer: 10,985 students
Step-by-step explanation:
You are given the original number of students, the rate of growth and the number of years. The Future value formula can therefore be used:
Number of students in 2010 = Number of students in 1995 * ( 1 + growth rate) ^ number of years
Number of years = 2010 - 1995 = 15 years
Number of students in 2010 = 1,350 * ( 1 + 15%)¹⁵
= 10,985 students
Can someone help?
Solve each triangle. Round to the nearest tenth.
Answer:
17 no for side c
take 37 degree as reference angle
using sine rule
sin 37 =p/h
0.60=6/c
0.60c=6
c=6/0.c0
c=10
for side d
using pythagors theorem
H^2=P^2+B^2
(10)^2=(6)^2+B^2
100=36+B^2
100-36=B^2
64=B^2
[tex]\sqrt{64}[/tex]=B
8=B
Step-by-step explanation:
Find the range of the relation {(-8,1),(-3,-6),(-7,-5),(9,5),(-2,9)}