Step-by-step explanation:
just think back to the standard circle of radius = 1.
there the trigonometric functions are all represented as sides of right-angled triangles, where the radius is the baseline.
just like the triangle we are seeing here.
the only difference : the baseline (radius) is 17 and not 1.
and that is fine. everything is as in the standard circle, but multiplied by the radius (which is also true for the standard circle, but multiplying by 1 does not change anything, right ?).
a)
angle A is or focus. so, just imagine the triangle turned counterclockwise by 90° (so that AC is horizontal and CB is vertical).
do you see it now ?
sin is the vertical leg, cos the horizontal leg. and the leg lengths here are the standard functions multiplied by the radius.
so,
17 × sin A = 8
sin A = 8/17 = 0.470588235... ≈ 0.47
b)
17 × cos A = 15
cos A = 15/17 = 0.882352941... ≈ 0.88
c)
now B is our focus. imagine the triangle being mirrored at point B, so that B is left, and AC is right. your see it now ?
tan B = sin B / cos B
sin B = 15/17 = 0.882352941... ≈ 0.88
cos B = 8/17 = 0.470588235... ≈ 0.47
tan B = 15/17 / 8/17 = 15/8 = 1.875 ≈ 1.88
d)
cos B = 8/17 = 0.470588235... ≈ 0.47
Please help ASAP
Find all the values of k so that the quadratic expression factors into two binomials. Explain the process used to find the values.
3x^2 + kx - 8
Answer:
Any value of kStep-by-step explanation:
The quadratic expression can be factored into two binomials if it has two real roots.
Two real roots possible with non-negative discriminant:
D ≥ 0As D = b² - 4ac, we get the following inequality
k² - 4(3)(-8) ≥ 0k² + 96 ≥ 0k² ≥ - 96This is true for any value of k
k ∈ (- ∞, + ∞)Answer:
(-∞, ∞) or [tex]k \in \mathbb{R}[/tex]
Step-by-step explanation:
Binomial: two terms connected by a plus or minus sign.
Discriminant
[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]
[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]
[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]
[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]
If a quadratic expression factors into two binomials, it will have two real roots. Therefore, the discriminant will be greater than zero.
Given quadratic expression:
[tex]3x^2+kx-8[/tex]
[tex]\implies a=3, \quad b=k, \quad c=-8[/tex]
Substitute the values of a, b and c into the discriminant, set it to > 0:
[tex]\implies k^2-4(3)(-8) > 0[/tex]
[tex]\implies k^2+96 > 0[/tex]
As k² ≥ 0 for all real numbers,
[tex]\implies k^2+96 \geq 96[/tex]
Therefore, the values of k are (-∞, ∞) or [tex]k \in \mathbb{R}[/tex]
All digits in a dropdown number are different and one of its digits is the average of all its digits. It has at least two digits. For example, 5021 is a dropdown number, but neither 4389 nor 6033 is a dropdown number. a Find the smallest dropdown number.
The dropdown numbers is an illustration of combination
The smallest dropdown number is 1025
How to determine the smallest dropdown number?From the question, we have the following parameters:
The dropdown number is 4-digitThe digits are different.We start counting from 1023, 1024, 1025, 1026...........
The sum of digits in 1023 is 6, and the average is 1.5The sum of digits in 1024 is 7, and the average is 1.75The sum of digits in 1025 is 8, and the average is 2The number 1025 satisfies the given conditions
Hence, the smallest dropdown number is 1025
Read more about combination at:
https://brainly.com/question/11732255
Can the following set be the domain of an odd function?
(-3,-2)U(2,3)
Yes, the given set can be the domain of an odd function if:
f(-3) = -f(3)
f(-2) = -f(2).
What is the domain of a function?For a function y = f(x), we define the domain of the function as the set of possible values of x that we can input into the function.
And an odd function is a function such that:
f(-x) = -f(x).
In this case, we want to see if the set:
(-3,-2)U(2,3) = (-3, -2, 2, 3)
can be the domain.
It would only be the domain of an odd function if:
f(-3) = -f(3)
f(-2) = -f(2).
If you want to learn more about odd functions, you can read:
https://brainly.com/question/1561362
You roll a number cube ten times and it lands on a 5 two times. What is the theoretical probability that it lands on a 5 on your next roll?
Answer:
2/10 = 1/5
Step-by-step explanation:
It landed five 2 times and you rolled it 10 times
I’m confused I need this answered please
Answer:
30°
Step-by-step explanation:
145-115=30°
it is the answer
Answer:
30
Step-by-step explanation:
Since Angle FGH=FGJ+JGH, we can set the equation 145=115+x
[tex]145=115+x\\145-115=x\\30=x[/tex]
what is 8(4 - x) = 7x + 2
Answer: x = 2
Step-by-step explanation:
8(4 - x) = 7x + 2= 8(-x + 4) = 7x + 2= -8x + 32 = 7x + 2= -8x + 32 - 32 = 7x + 2 - 32= -8x = 7x + 2 - 32 = -8x = 7x = 30= -8x - 7x = 7x + 30 - 7x= -15x = 7x - 30 - 7x= -15x = 30 -15x/-15 = -30/-15 = x = -30/-15= x = 2And thats how you get the answer!
PLEASE HELP (questions in photo) I’ll mark brainliest
Answer:
a) 405, -315 b) 540, -180 c)195, -525
Step-by-step explanation:
a) 45+360= 405, 45-360=-315
b) 180+360=540, 180-360=-180
c) -165+360=195, -165-360=-525
hope this helped
1) Advertisement XYZ Company charges $35 for the first four lines and $5.25 per extra
line to run the ad for one week. Jacqueline plans to sell her house and places a 15-line
ad.
a. What will Jacqueline's ad cost to run for one week?
b. What will Jacqueline's ad cost to run for four weeks?
Answer:
a) $92.75
b) $371
Step-by-step explanation:
Let x = number of lines in the ad
Let x = total charge per week to run the ad
Given:
Charge per week for first 4 lines = $35Charge per week for each additional line = $5.25Create equations based on the given information:
y = 35 for x < 4
y = 35 + 5.25(x - 4) for x ≥ 4
Part (a)
Given:
Jacqueline's ad = 15 lines⇒ y = 35 + 5.25(15 - 4)
= 35 + 5.25(11)
= 35 + 57.75
= 92.75
So the ad will cost $92.75 to run for 1 week.
Part (b)
Cost to run the ad for 4 weeks = 4 × cost of 1 week
= 4 × 92.75
= $371
If f(x) = x-3/x and g(x) = 5x-4, what is the domain of (f•g)(x)?
Answer: x cannot equal 4/5 (3rd choice)
Step-by-step explanation:
f(g(x)) = f(5x-4)
plug 5x-4 into all values of x in the f(x) equation
f(5x-4)= ((5x-4) - 3))/ (5x-4)
f(5x-4) = (5x-7)/(5x-4)
set denom = 0 and solve for x to find domain
5x-4 = 0
5x = 4
x = (4/5)
x cannot equal (4/5)
15. What effect does reducing sample size have on s?
standard deviation and margin of error?
Step-by-step explanation:
I don't know I don't know this answer really I don't know this and so sorry sorry sorry sorry
what is the area,in the square units,of the rectangle?
Step-by-step explanation:
[tex]area = l \times b[/tex]
[tex]area = \frac{3}{7} \times \frac{2}{9} [/tex]
[tex]area = \frac{6}{64} [/tex]
[tex]area = 0.09375units ^{2} [/tex]
What does s equal? (Write your answer like this: s = __)
Answer:
S= -15/5
the slashes are supposed to be fractions.
Step-by-step explanation:
a sector has radius 14 in central angle 120 find the area of the sector
Answer:
205.25072
Step-by-step explanation:
1. A(sector)=x/360πr^2
2. A(sector)=120/360π(14^2)
3. A(sector)=1/3π(196)
4. A(sector)=205.25072
5. Round as necessary
I NEED THIS IN 10 MINUTES
Answer:
I believe the answer is C, the area of a circle, because pi is irrational, and anything multiplied by it will always result in an irrational number.
Step-by-step explanation:
I hope this helps and please mark me as brainliest!
Use the calculator to find the product of 4.17 and 2.3 × 106. Which statements are true about finding the product? Check all that apply.
4.17 is equivalent to 4.17 × 100.
4.17 is equivalent to 4.17 × 101.
The product has a positive exponent.
The coefficient is 6.
The E in the product is the indicator that the solution is in scientific notation.
The exponent of the product is the product of the original exponents.
PLSSS HELP
Answer:
I'm assuming that "106" is really 10^6Step-by-step explanation:
4.17 is equivalent to 4.17 × 100. NO 4.17 x 100 = 417
[If this is really 4.17 is equivalent to 4.17 × 10^0. Then YES. 10^0 = 1]
4.17 is equivalent to 4.17 × 101. NO 4.17 x 101 = 421.17
Again, if this is 10^1, then no. 10^1 = 10
The product has a positive exponent. YES
The coefficient is 6.
Coefficient? NO. Exponent? Then YES
The E in the product is the indicator that the solution is in scientific notation. YES 4.17E6 is 4.17 x 10^6
The exponent of the product is the product of the original exponents.
NO. In multiplication, the exponents are added (as long as they have the same base)
EDGE 2022
1. What is the center of dilation used to dilate quadrilateral WXYZ to quadrilateral W'X'Y'Z'?
A. (-1,3)
B. (0,0)
C. (-3,4)
D. (-1,0)
Answer: I believe the answer is C. (-3,4)
Step-by-step explanation:
Tony cut a piece of string 90 cm long into three in the ratio of 2:5:3.What is the length of the medium piece?
a. 18cm b. 24cm c. 27cm d. 45cm
Answer:
D
Step-by-step explanation:
We know the ratio of the cut string is 2 : 5 : 3. If we add 2, 5, and 3 together, we get 10. We can do 90 ÷ 10 = 9. Each number in the ratio should be multiplied by 9 to find the actual length after it is cut.
Left piece : 2 x 9 = 18 cm
Middle piece : 5 x 9 = 45 cm
Right piece : 3 x 9 = 27 cm
D is the correct answer.
I hope this helps and please mark me as brainliest!
Fatima will go to the swimming pool 15 days this month. A one day pass is $2.25. A monthly pass is $25. How much money will Fatima save by buying a monthly pass?
A. $33.75
B. $8.75
C. $7.75
D. $6.00
Answer:
B. 8.75
Step-by-step explanation:
b) x2 - 2x - 3
I need help with factorising :/
I know that answer
..............please mark as brainliest
PLS HELP
Ignore everything above and below the simplify question
Nevaeh spots an airplane on radar that is currently approaching in a straight line, and
that will fly directly overhead. The plane maintains a constant altitude of 7475 feet.
Nevaeh initially measures an angle of elevation of 16° to the plane at point A. At
some later time, she measures an angle of elevation of 43° to the plane at point B.
Find the distance the plane traveled from point A to point B. Round your answer to
the nearest tenth of a foot if necessary.
INTL
0
Using the slope concept, it is found that the distance the plane traveled from point A to point B was of 18052.4 ft.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
At point A, the vertical change is of 7475 ft, with an angle of 16º, hence the equation below can be solved to find the position:
[tex]\tan{16^\circ} = \frac{7475}{x_A}[/tex]
[tex]x_A = \frac{7475}{\tan{16^\circ}}[/tex]
[tex]x_A = 26068.4[/tex]
At point B, the angle is of 43º, hence:
[tex]\tan{43^\circ} = \frac{7475}{x_B}[/tex]
[tex]x_B = \frac{7475}{\tan{43^\circ}}[/tex]
[tex]x_B = 8016[/tex]
Hence, the distance in feet is given by:
[tex]d = x_A - x_B = 26068.4 - 8016 = 18052.4[/tex]
More can be learned about the slope concept at https://brainly.com/question/18090623
(1+i)^2(x+yi)=4+5i
Solve for x and y
Answer:
x = 5/2
y = -2
Step-by-step explanation:
(1+i)² (x+yi) = 4+5i
(1+2i+i²)(x+yi) = 4+5i
(1+2i-1)(x+yi) = 4+5i
2i(x+yi) = 4+5i
2i²y + 2xi = 4+5i
-2y + 2xi = 4 + 5i
By comparing both sides,
-2y = 4
y = -2,
2x = 5
x = 5/2
If ABCDE is translated 7 units to the right and 2 units up, what will happen to the polygon?
Answer:
D.
Step-by-step explanation:
It will move but stay the same size. You are translating the shape to a different spot, not adding onto its size.
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I hope this helps!
-No one
What is the sum of 2/5 and 1/8
Which of the x values are solutions to both of the following inequalities
100< X and x<150
From both equations
100<x<150Hence the solution set in interval notation
x[tex]\in[/tex](100,150)pls help
x values: -7, -2, 3, 8,
y values: 1, 2, 6, 12,
Is the relationship linear, exponential, or neither?
Determine the value of the angle.
Angle BDC=
90°-53°=37°
The whole angle is right angled
What is the sun of this question somebody tell me
Answer:
2/10 +28/10020+28/10048/10012/25Answer:
first of all you have to take the L.C.M of both which will be 100
Step-by-step explanation:
[tex]2 \div 10 + 28 \div 100 \\ = \frac{20 + 28 }{100} \\ = \ \frac{12}{25} [/tex]
will someone please help me?
Answer:
x=-1
Step-by-step explanation:
1.(-9-11)(-4)/-7^2+(11*2^2)
2. =-20/-4/-7^2+11(2^2)
3. =5/7^2+11(2^2)
4. =5/-49+11(2^2)
5. =5/-49+(11)(4)
6. = 5/-49+44
7.=5/-5
8. x=-1
pls answer (10 points given)
Answer:
C
Step-by-step explanation:
Its not greater than or equal to and its less than 6.
Answer:
A. x < 3
Step-by-step explanation:
2x < 6
Simplify:
2x < 6 <== divide both sides by 2
/2 /2
x < 3
Rules:
Open circle: < (going left) or > (going right)
Closed circle: ≤ (going left) or ≥ (going right)
For our answer: x < 3
It would be an open circle going left. The only number line that illustrates this is line A.
Hope this helps!