Some help? Like bro literally how?!
Answers:
[tex]\text{OA} = \cos(\alpha)\\\\\text{AB} = \sin(\alpha)\\\\\text{DC} = \tan(\alpha)\\\\[/tex]
You can use the word "alpha" without quotes in place of the symbol [tex]\alpha[/tex] if you want (though it will depend if your teacher allows it of course).
======================================================
Explanation:
Focus entirely on triangle AOB.
With respect to reference angle alpha (symbol [tex]\alpha[/tex]), the side OA is the adjacent side since it's the leg closest to or touching the reference angle.
In this same triangle, side OB is the hypotenuse. Because its the radius of the unit circle, we know that OB = 1.
We'll use the cosine rule to connect the adjacent over hypotenuse like so
[tex]\cos(\text{angle}) = \frac{\text{adjacent}}{\text{hypotenuse}}\\\\\cos(\alpha) = \frac{\text{OA}}{\text{OB}}\\\\\cos(\alpha) = \frac{\text{OA}}{1}\\\\\text{OA} = \cos(\alpha)\\\\[/tex]
So you'll type either [tex]\cos(\alpha)[/tex] or cos(alpha) into the box for OA.
----------------------------------------
We're still working with triangle AOB only.
Side AB is the opposite side with respect to reference angle alpha.
We can say
sin(angle) = opposite/hypotenuse
sin(alpha) = AB/OB
sin(alpha) = AB/1
AB = sin(alpha)
Basically it's almost identical to the previous section's steps, but we're using sine instead of cosine this time. Like before, you can type in either [tex]\sin(\alpha)[/tex] or sin(alpha) depending on your teacher's preferences.
----------------------------------------
This next section can be a bit tricky.
Sides AB and DC are parallel due to them being both vertical. We can use the AA (angle angle) similarity theorem to prove triangle BOA is similar to triangle DOC. The order of the letters is important. The order helps us see how the sides pair up, or how they correspond, so we can form the correct proportion.
The vertical sides of the triangles are AB and DC as mentioned earlier, so they form one fraction AB/DC. I'm dividing small over big.
Another fraction we can form is OA/OC which is dividing the horizontal legs (again small/big).
Overall, due to the similar triangles, we can set up this equation
AB/DC = OA/OC
We'll plug in what we found earlier. Also, OC = 1 because it's another radius of the same unit circle.
Lets solve for side DC.
AB/DC = OA/OC
sin(alpha)/DC= cos(alpha)/1
sin(alpha)*1 = DC*cos(alpha)
DC = sin(alpha)/cos(alpha)
DC = tan(alpha)
--------------------------------------
In summary, segments OA, AB and OC represent the cosine, sine and tangent of the reference angle alpha. These are visual ways to see how the trig ratios correspond to lengths of triangles when connecting them to the unit circle like this.
Side notes:
Point B is at the location (cos(alpha), sin(alpha)). Point D is at (1, tan(alpha)).If f and g are positive, (f+g)^2=54 and 2fg = 24, what is f^2+g^2?
Answer:
D. 30
Step-by-step explanation:
f²+g² = (f+g)²-2fg
= 54-24 = 30
Rhode Island Red chicks cost $3.20 each and Buckeye chicks cost $3.44 each.
A farmer buys 4 Rhode Island Red chicks for every 3 Buckeye chicks.
He buys 70 chicks in all. What is the total cost of the farmer's chicks?
Show your work
Answer:
Step-by-step explanation:
Rhode Island Red chicks = 3.20 Dollars
Buckeye chicks = 3.44 Dollars
For every3 times as 3.44 Dollars, The farmer buys 4 times as 3.20 Dollars so simply Multiply until you reach 70 S0..
3.44 x 3
= 10.32
3.20 x 4
= 12.8
With 7 chicks, combine the prices of the chicks and multiply it by 10.
= 12.8 + 10.32
= 23.12
= 23.12 x 10
= 231.2
So 231.2 Dollars were spent for 70 chicks`in total.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The total cost of farmers' chicks is $231.2
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 5 is an equation.
We have,
Total chicks = 70
4 Rhode Island Red chicks = 3 Buckeye chicks.
Multiply 10 on both sides.
40 Rhode Island Red chicks = 30 Buckeye chicks.
We see that,
40 + 30 = 70
Now,
Rhode Island Red chicks cost = $3.20
Buckeye chicks cost = $3.44
Now,
= 40 x 3.20 + 30 x 3.44
= 128 + 103.2
= $231.2
Thus,
The total cost of farmers' chicks is $231.2
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ2
Write the word sentence as an inequality.
3.2 less than a number t is at most 7.5
Answer:
[tex]t - 3.2 \le 7.5\\[/tex]
Step-by-step explanation:
Given
Represent as inequality
Taking the statement one at a time
3.2 less than t means: t - 3.2at most, 7.5 means less than or equal to 7.5So, the inequality is:
[tex]t - 3.2 \le 7.5\\[/tex]
Determine the standard form of the equation of the line that passes through (6, -9) and (-8, 6)
A. 15x+14y=-36
B. 14x+15y=-36
C. 15x+14y=36
D. 15x-14y=-36
Please select the best answer from the choices provided
9514 1404 393
Answer:
A. 15x +14y = -36
Step-by-step explanation:
Since we are given two points, we can start with the 2-point form of the equation for a line.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (6 -(-9))/(-8 -6)(x -6) +(-9)
y = 15/-14(x -6) -9
Multiplying by -14, we have ...
-14y = 15x -90 +126
Adding 14y-36 to both sides gives ...
-36 = 15x +14y . . . . matches choice A
The standard-form equation is ...
15x +14y = -36
_____
Additional comments
It can be easier to start with the form ...
(Δy)x -(Δx)y = (Δy)x1 -(Δx)y1 . . . . . where Δx = x2-x1 and Δy = y2-y1
This gives ...
(6+9)x -(-8-6)y = 15(6) +14(-9)
15x +14y = -36 . . . simplified
__
You can also start with the slope-intercept form or the point-slope form, if you're more familiar with those. The result will be the same. I find it handy to be familiar with a number of different forms of the equation for a line.
2) There are 12 sweets in a bag.
4 are lemon flavour.
4 are caramel flavour.
4 are orange flavour.
Jude takes at random 3 sweets at the same time.
Work out the probability that exactly 2 of the sweets are the same flavour.
Answer:
0.654
Step-by-step explanation:
There are 12 sweets in a bag.
4 are lemon flavour.
4 are caramel flavour.
4 are orange flavour.
Jude takes at random 3 sweets at the same time.
Work out the probability that exactly 2 of the sweets are the same flavour.
Probability = Required outcome / Total possible outcomes
Required outcome = either exactly 2 of lemon or 2 of caramel or 2 of Orange
Required outcome = 3[4C2 * 8C1) = 3(6*8) = 144
Total possible outcomes = 12C3 = 220
P(exactly 2 are same flavor) = 144 / 220 = 0.654
Jenn determined that the graph of the quadratic funtion f(x) =x^2 -9 has two x-intercepts. do you agree with her? why or why not?
Answer:
Jenn is correct, as the function has two x-intercepts, at x = -3 and x = 3.
Step-by-step explanation:
x-intercepts of a function:
The x-intercepts of a function are the values of x for which f(x) = 0.
In this question:
[tex]f(x) = x^2 - 9[/tex]
x-intercepts:
[tex]x^2 - 9 = 0[/tex]
[tex]x^2 = 9[/tex]
[tex]x = \pm \sqrt{9}[/tex]
[tex]x = \pm 3[/tex]
Jenn:
Jenn is correct, as the function has two x-intercepts, at x = -3 and x = 3.
Sketch the plane representing -2x²=-8
I found this answer from Brainly.
Somebody else did this question.
**But it's not my answer**
I hope it's helpful and correct!!
x2 + 5x + 9.
Find the equation of the axis of symmetry for the parabola y =
Answer:
x = -5/2
Step-by-step explanation:
From the quadratic equation
the axis of symmetry for quadratics of the form
y = ax² + bx + c is
x = -b/2a
x² + 5x + 9
x = -5/2
If f(x) = 2x+1, what would the function look like once you substitute in a 1 to find f(1)?
Answer:
It would result in a constant line of [tex]y=3[/tex].
Step-by-step explanation:
[tex]f(x)=2x+1[/tex]
[tex]f(1)=2(1)+1[/tex]
[tex]f(1)=2+1[/tex]
[tex]f(1)=3[/tex]
[tex]y=3[/tex]
See the graph for a visual.
Drag each tile to the correct box.
Arrange the numbers as they appear from left to right on a horizontal number line.
-2.5
-2.57
-1.85
2.5
-2.76
-1.58
2.85
I
Answer:
-2.76
-2.57
-2.5
-1.85
-1.58
2.5
2.85
Hopefully this is what you mean. Have a nice day!
Step-by-step explanation:
Using the equation for the line of best fit what is a good approximation for x when f(x) =30?
Answer:
48.6
Step-by-step explanation:
Given the equation for the line of best fit ; f(x) ≈ 1.8x − 5.4 ;
This equation is used to make prediction for any given value of x ; Here, we are to make prediction for when x = 30
f(x) ≈ 1.8x − 5.4 ; we substitute into the equation, x = 30
f(30) = 1.8(30) - 5.4
f(30) = 54 - 5.4 = 48.6
Prediction at x = 30 is 48.6
Help me out please???
9514 1404 393
Answer:
x = 5
Step-by-step explanation:
DE being a midsegment means that D is a midpoint. Then BD = DA, or x = 5.
Help pls I need help
Answer:
From the origin , move 3 units to the right and 2 units up. B
Please help i need it
Write 4/5 with denominator 15
Answer:
12 / 15
Step-by-step explanation:
4/5 = x /15
15 / 5 = 3
So multiply both numerator and denominator by 3
4/5 * 3/3 = 12 / 15
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
To get this fraction, we multiply top and bottom by 3
4*3 = 12
5*3 = 15
We get the value 3 through trial and error, or you can note how 15/5 = 3.
The side view is a bookend is shown. The perimeter of the bookend is 58 centimeters
Answer:
Step-by-step explanation:
The equation to represent the perimeter of given figure is 5m-14+2m-7+3/2 m+2+3m+8=58 and value of m is 6.
Given that, the perimeter of the bookend is 58 centimeters.
What is the perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.
Now, the perimeter is
5m-14+2m-7+3/2 m+2+3m+8=58
⇒ 10m+3/2 m-11=58
⇒ (20m+3m)/2=69
⇒ 23m=138
⇒ m=138/23
⇒ m=6
Therefore, the equation to represent the perimeter of given figure is 5m-14+2m-7+3/2 m+2+3m+8=58 and value of m is 6.
To learn more about the perimeter visit:
https://brainly.com/question/6465134.
#SPJ2
The demand function of a product is q = 7,000 - 50p, where p is the price.
The cost function is given by C = 2,000 + 259. At what price is the break-even
Production attend?
Answer: 139.65 or 25.34.
Step-by-step explanation:
The revenue function will be:
= Price × Quantity
= P × (7,000 - 50p)
= 7000p - 50p²
The coat function is given as:
C = 2,000 + 25q
C = 2000 + 25(7000 - 50p)
C = 2000 + 175000 - 1250p
C = 177000 - 1250p
Then, we'll equate the revenue function to the cost function. This will be:
7000p - 50p² = 177000 - 1250p
-50p² + 7000p + 1250p - 177000 = 0
-50p² + 8250p - 177000 = 0
Divide through by -50
p² - 165 + 3540 = 0
Solving to get the value of P will then give us 139.65 or 25.34.
Find the area
10
7
12
4
5
5
Answer:
[tex]{ \tt{area = (7 \times 10) + (12 \times 4) + (5 \times 5)}} \\ { \tt{ = 70 + 48 + 25}} \\ { \tt{ = 143 \: {in}^{2} }}[/tex]
Answer: break into 2 rect and 1 sqr the sum areas of each
Step-by-step explanation: square = 5x5
Rectangle 1 = 10x7
Rectangle 2 = 12x4
Sum each shape area = total area
A number is multiplied by 8, and that product is added to 4. The sum is equal to the the product of 4 and 13. Find that number
Answer:
n = 6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify + set up
8n + 4 = 4 · 13
Step 2: Solve for x
Multiply: 8n + 4 = 52[Subtraction Property of Equality] Subtract 4 on both sides: 8n = 48[Division Property of Equality] Divide 8 on both sides: n = 6can someone help me please?! I'll give brainlest for correct answer
1.)
A) BME
B) MER
C) Mm
D) xBy
E) Straight
F) REB
G) MEB and BER
H) xBy
Triangle F E D is cut by line segment H G. Line segment H G goes from side F D to side E D. The length of E G is 6 and the length of F H is 8. Lines E F and G H are parallel.
What is the length of Line segment G D?
GD =
Answer:
10.5
Step-by-step explanation:
built different
Triangle F E D is cut by line segment H G. Line segment H G goes from side F D to side E D. The length of E G is 6 and the length of F H is 8. Lines E F and G H are parallel. 5.5 is the the length of Line segment G D.
What is triangle?A triangle is a polygon that has three vertices on each of its three sides. The point shaped inside the triangle is equivalent to 180 degrees. It implies that the amount of the inside points of a triangle is equivalent to 180°. This is a polygon with the fewest sides.
To put it another way, a triangle is a two-dimensional figure with three sides and interior angles of 180 degrees. Six main types of triangles are distinguished by their angles and side lengths. Allow us to examine exhaustively about the six kinds of triangles. In light of the length of the sides, the triangle is arranged
EG / GD = FH / HD
6 / GD = 8 / 2
GD = 22 / 4
GD = 5.5
Therefore, 5.5 is the the length of Line segment G D.
To know more about triangle, here:
https://brainly.com/question/2773823
#SPJ7
pls plz anyone i’ll pass the class
Answer:
what's the question???
Answer:
x = 3.721
Step-by-step explanation:
Since, the triangle is right triangle, we can use trignometery equations ;
In this case, we need to use tangent equation in perpendicular :
tan θ = opposite side / adjacent side
Where , we've
opposite side = xθ , angle = 28 °Adjacent side = 7tan 28 ° = x / 7
7 × tan 28 ° = 7 × x / 7 ..( Multiply each side by 7 )
7 × tan28° = x
Rewrite
x = 7 tan ×28°
multiply to get
x = 7 × 0.531709432
x = 3.72196602
This is the graph of y= x2 + 4x + 7 what is the range of this function?
Answer:
C
Step-by-step explanation:
Answer:c
Step-by-step explanation:the answers we’ll change we careful
the figure has angle mediates as shown
what is the measure of
Answer:
of what............? you did not finish the question ⁉️
critical observations thinking is the best deomstrated by which of the following action
Answer: spotting trends in data
Step-by-step explanation:
Write the expression as a square of a binomial if possible
(1/2x +3)²
Refer to the above picture for complete calculation...
Answer:
Step-by-step explanation:
1/4 x^2 + 3x + 9
Answer: (1/2x + 3)^2
Now we have to explain it.
If it is going to be a binomial squared then it will be the square root of the first term and the square root of the third term.
[tex](\frac{\sqrt{1} }{\sqrt{4} } + \sqrt{9})^2[/tex]
[tex](\frac{1}{2}+3)^2[/tex]
Suppose that it is reported in the news that 12% of the people living and working in Kokomo feel that their commute is too long. What is the travel time to work that separates the top 12% of people with the longest travel times and the lower 88%
Answer:
22.3 minutes
Step-by-step explanation:
The computation of the travel time is as follows:
Given that
[tex]\mu[/tex] = 17
And, the standard deviation is 4.5
P(X≤C) = 0.88
P( x - [tex]\mu[/tex]) ÷ [tex]\sigma[/tex] ≤ (C - [tex]\mu[/tex]) ÷ [tex]\sigma[/tex] = 0.88
(C - [tex]\mu[/tex]) ÷ [tex]\sigma[/tex] = 1.175
c = [tex]\mu[/tex] + 1.175 × [tex]\sigma[/tex]
= 17 + 1.175 × 4.5
= 22.3 minutes
Hence, the travel time is 22.3 minutes
For "downhill" lines, if the rise is negative, the run must be
?
9514 1404 393
Answer:
positive
Step-by-step explanation:
When considering the slope of a line, we usually choose "rise" and "run" so that "run" is positive, and "rise" measures the vertical change as one moves from left to right.
If we assume that "downhill" lines refers to lines that go from upper left to lower right (downhill to the right), then the rise is negative while the run is positive.
__
Additional comment
Here, we assume a line is considered to be "downhill" if it has negative slope. In the real world, "downhill" is the direction the ball rolls under the influence of gravity. That direction might be behind you, or to your left, instead of in front of you or to the right.
Definitions are important in math. "Downhill" is not a term that is widely used to describe lines, so we have to guess the intended meaning here.
15
2 pts
Find the area of the given shape,
a) 18
b) 15
c) 24
d) 21
9514 1404 393
Answer:
A. 18
Step-by-step explanation:
The area of a trapezoid is given by the formula ...
A = 1/2(b1 +b2)h
Here, the parallel bases have lengths 3 and 9. The height is 3, so the area is ...
A = 1/2(3 +9)(3) = 18
The area of the trapezoid is 18 square units.