Answer:
a. The required proof is obtained from triangles OAB and ABC formed by joining AB and that we have;
A[tex]\hat O[/tex]B + 2∠C = 180°, 2·A[tex]\hat P[/tex]B + 2∠C = 180°
∴ A[tex]\hat O[/tex]B = 2·A[tex]\hat P[/tex]B
b. i) P[tex]\hat S[/tex]S = P[tex]\hat R[/tex]Q, given that angles subtended by the same arc or chord are equal, therefore, in ΔPQS, we have;
[tex]\left | PS \right |[/tex] = [tex]\left |PQ \right |[/tex]
ii) S[tex]\hat Q[/tex]P = 45°, [tex]S\hat R Z[/tex] =90°
Step-by-step explanation:
a. The given parameters are;
The center of the circle is point O
Points on the circumference of the circle = A, B, and P
Required to be proved, A[tex]\hat O[/tex]B = 2·A[tex]\hat P[/tex]B
Let ∠O represent A[tex]\hat O[/tex]B and let ∠P' represent A[tex]\hat P[/tex]B
We draw a line from the center O to the point P, and a line joining points A and B on the circumference of the circle
In ΔOAB, we have;
∠O + 2∠C = 180° (The sum of the interior angles of a triangle)
In ΔAPB, we have;
∠P' + ∠(C - a) + ∠(P' + C + a) = 180°
∴ 2·∠P' + 2·∠C = 180°
Therefore, by addition property of equality, we get;
∠O = 2·∠P'
Therefore;
A[tex]\hat O[/tex]B = 2·A[tex]\hat P[/tex]B
b. i) The given parameters are;
Points on the circle = P, Q, R, and S
P[tex]\hat Q[/tex]S = P[tex]\hat R[/tex]Q
According to circle theory, the angles which an arc or chord subtends in a given segment are equal, therefore;
P[tex]\hat S[/tex]S = P[tex]\hat R[/tex]Q
Therefore, P[tex]\hat S[/tex]S = P[tex]\hat Q[/tex]S by transitive property of equality
P[tex]\hat S[/tex]S and P[tex]\hat Q[/tex]S are base angles of ΔPQS, given that P[tex]\hat S[/tex]S = P[tex]\hat Q[/tex]S, we have;
ΔPQS is an isosceles triangle with base QS and therefore, the sides PS and PQ are the equal sides
Therefore, we have;
[tex]\left | PS \right |[/tex] = [tex]\left |PQ \right |[/tex]
ii) Given that SQ is the diameter of the circle, we have by circle theorem, the angle subtended on the circumference by the diameter = 90°
∴ [tex]S\hat PQ[/tex] = 90°
From (i), we have that P[tex]\hat S[/tex]S = P[tex]\hat Q[/tex]S, therefore, in triangle ΔPQS, we have;
[tex]S\hat PQ[/tex] + P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 180°
Therefore;
90° + P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 180°
P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 180° - 90° = 90°
P[tex]\hat S[/tex]S = P[tex]\hat Q[/tex]S, therefore, P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 2·S[tex]\hat Q[/tex]P
P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 2·S[tex]\hat Q[/tex]P = 90°
S[tex]\hat Q[/tex]P = 90°/2 = 45°
S[tex]\hat Q[/tex]P = 45°
Similarly, given that SQ is the diameter, of the circle the angle [tex]S\hat R Q[/tex] formed by jointing S to Q is 90°
[tex]S\hat R Q[/tex] = 90°
[tex]S\hat R Q \ and \ S\hat R Z[/tex] are angles on a straight line and are therefore, supplementary, therefore;
[tex]S\hat R Z[/tex] = 180° - [tex]S\hat R Q[/tex]
[tex]S\hat R Z[/tex] = 180° - 90° = 90°
[tex]S\hat R Z[/tex] =90°.
Which of the following equations would not have a solution that is the same as the solution to the system. shown below?
4x+y=7
-2x+5y=1
———————————————
1) 11y = 9
2) 2x + 6y = 8
3) -4x + 10y = 1
4) 12x + 3y = 21
please help asap and thank you in advance to anyone who answers this for me ! :)
Answer:
Step-by-step explanation:
Given the function F (x) 2/3 x -5 , evaluate f(9)
what’s the answer to this ?
Answer:
|||
Step-by-step explanation:
the answer is c (|||)
Answer:
the answer is c
Step-by-step explanation:
the answer is C(111)
I’m stuck on this one help anyone?
Answer:
just add a small amount to the 2.8 and square the result
Step-by-step explanation:
x x^2
2.8 7.84
2.81 7.8961
2.82 7.9524
2.83 8.0089
2.84 8.0656
2.85 8.1225
2.86 8.1796
2.87 8.2369
Find the measure of each angle indicated.
890
50°
A) 44°
C) 47°
B) 51°
D) 71°
Answer:
51
Step-by-step explanation:
See the other answer
Answer:
(B). 51°
Step-by-step explanation:
SOMEONEEEE HELPPP MEEEEE PLEASEEEE!!!!
Answer:
[tex]{ \tt{ \tan(x) = \frac{opposite}{adjacent} }} \\ \\ { \tt{ \tan( \theta) = \frac{30}{16} }}[/tex]
Help and please explain I don't get khan academy
Answer:
same y intercept
Step-by-step explanation:
The y intercept is when r = 0
Function 1
p = -3/2 r - 5
Let r = 0
p = 0-5
p = -5
Function 2
When r = 0 p = -5
They both equal -5, so they both have the same y intercept
4(7x 3)-2(3 -5x) -5 [2x+1)
n(a)=60% n(o)=70% N(ano)=400 n(auo)complenment=10 find U and a only
n(A∪B)=n(A)+n(B)−n(A∪B)=50+60−40=70
n(AΔB)=n(A∪B)−n(A∩B)
⇒70−40=30.
Which graph shows the solution set of
Below, the two-way table is given for a
class of students.
Please HELP ME!!!!!!!!
i think 51 is answer......
Two walls of a canyon form the walls of a steady flowing river. From a point on the shorter wall, the angle of elevation to the top of the opposing wall is 20° and the angle of depression to the bottom of the opposing wall is 230 feet. Using the appropriate right triangle solving strategies, solve for the following: (Do not round intermediate calculated values. Only the final answer should be rounded to one decimal place.)
the height of the short wall (x)
the height of the tall wall (y)
the distance between the canyon walls (z)
How do I solve this and get to the answer.
We found that the height of the short wall "x" is 162.6 ft, the height of the tall wall "y" is 221.8 ft, and the distance between the canyon walls "z" is 162.6 ft.
To find the x, y, and z values we need to denote the right triangles from top to bottom as triangles 1, 2, and 3.
1. Finding the height of the short wall "x"
We can find the height of the short wall "x" (in triangle 3) with the following trigonometric function:
[tex] cos(\theta) = \frac{x}{H} [/tex]
Where:
H: is the hypotenuse = 230 ft
θ: is the angle between x and H.
Knowing that the sum of θ and the angle 45° must be equal to 90°, θ is:
[tex] \theta = 90 - 45 = 45 [/tex]
Hence, the height of the short wall "x" is:
[tex]x = cos(\theta)*H = 230cos(45) = 162.6 ft[/tex]
2. Finding the height of the tall wall "y"
The height of the tall wall "y" is given by the sum of the bases of the two first right triangles (the right triangles 1 and 2):
[tex] y = y_{1} + y_{2} [/tex]
Where y₁ and y₂ can be calculated with the tangent and sine trigonometric functions.
[tex]y_{1} = A*tan(20)[/tex]
[tex] y_{2} = 230sin(45) [/tex]
Where A is the adjacent side to the angle 20°.
[tex] y = A*tan(20) + 230sin(45) [/tex]
Since the right triangles 2 and 3 form a square, with all the sides equals to x, we have:
[tex] A = z = y_{2} = x = 230cos(45) [/tex]
We can use 230cos(45) or 230sin(45) to calculate y₂, so the height of the tall wall "y" is:
[tex] y = y_{1} + y_{2} = A*tan(20) + 230cos(45) = 230cos(45)tan(20) + 230cos(45) = 221.8 ft [/tex]
3. Finding the distance between the canyon walls "z"
As we said above, the "z" value is the same as "x", then:
[tex]z = x = 230cos(45) = 162.6 ft[/tex]
Learn more about trigonometric functions here: https://brainly.com/question/14272510?referrer=searchResults
I hope it helps you!
Solve the equation 15x + 22 = 7x +62
Answer:
hope it helps you........
Answer:
x = 5
Step-by-step explanation:
1. Subtract 22 from both sides.
15x = 7x + 62 - 22
2. Simplify 7x + 62 - 22 to 7x + 40.
15x = 7x + 40
3. Subtract 7x from both sides.
15x - 7x = 40
4. Simplify 15x - 7x to 8x.
8x = 40
5. Divide both sides by 8.
x = [tex]\frac{40}{8}[/tex]
6. Simplify [tex]\frac{40}{8}[/tex] to 5.
x = 5
[tex]y = \frac{qx}{p} [/tex]
Write x in terms of p,q and y
[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]
[tex]y=\dfrac{qx}{p}\\\\qx=py\\\\x=\dfrac{py}{q}[/tex]
Answer:
[tex]x = \frac{yp}{q}[/tex]
Step-by-step explanation:
[tex]y = \frac{qx}{p}[/tex][tex]yp = qx[/tex][tex]x = \frac{yp}{q}[/tex]What is the solution to the system of equations represented by these two lines?
(3, 1)
(3, 0)
(1, 3)
(0, 6)
Answer:
Step-by-step explanation:
it is a function because if you look on the x side 3 is repeating
George earned e extra credit points. Kate earned 35 fewer extra credit points than George. Choose the expression that shows how many extra credit points Kate earned.
Answer:
D. e - 35
Step-by-step explanation:
We have that:
George earned e extra points.
Kate earned k extra points.
Kate earned 35 fewer extra credit points than George.
This means that k is e subtracted by 35, that is:
k = e - 35
So the correct answer is:
D. e - 35
Step-by-step explanation:
Someone help me please
===============================================
Explanation:
The table says that
5 students got an A10 students got a B15 students got a CThat's 5+10+15 = 30 students out of 35 total.
The probability is therefore 30/35 = 0.8571 approximately which rounds to 0.86
There's roughly an 86% chance of picking someone who got an A, B or C.
5x2 + 6x – 8= –7 to the nearest tenth
The slope of line segment AB is -3. What is the slope of a line segment parallel
to AB?
Answer:
-3
Step-by-step explanation:
We know that parallel lines have the same slope so if AB has a slope of -3 then all lines that are parallel have a slope of -3
Mr. Bartolome's salary is Php 18 500 per month. If 40% of his salary was spent for food., how much was spent for food?
Answer:
Amount of his salary spent on food = Php 7400
Step-by-step explanation:
Mr. Bartolome's salary = Php 18500
Percentage of salary spent on food = 40%
Amount of his salary spent on food = 40% of Php 18,500
= 40/100 × Php 18,500
= 0.4 × Php 18,500
= Php 7400
Amount of his salary spent on food = Php 7400
The difference between 1/2 of a number and 1/6 of a number is equal to 10 more than 1/8 of that number which equation could be used to find the number?
Step-by-step explanation:
let the number be x
1/2(x) - 1/6(x) =10 -1/8(x)................this is the equation
1/12(x) + 1/8(x)=10
5/24(x)=10
cross multiply
5x= 240
x=240/5
x=48
In a company of 35 employees, four-sevenths work in sales. How many of the employees work in sales ?
Answer:
20
Step-by-step explanation:
Multiply 4/7 with 35, this will get you 140/7, which simplifies to 20 employees
Let j=+5 - 5+ |-5 x 1/5
What is the value of+J?
Answer:
j=|x|
Step-by-step explanation:
help me in this plz....
Answer:
70. 8x⁴
71. 3n - 10
72. a/5 + 12
Step-by-step explanation:
70. a number "x" raised to the fourth = x⁴
Product of 8 and x⁴ = 8 × x⁴
= 8x⁴
71. 3 times a number "n" = 3 × n = 3n
3n decreased by 10 = 3n - 10
72. Quotient of a number "a" and 5 = a/5
12 more than a/5 = a/5 + 12
plz help me it is very imp for me plz I beg you..
Answer:
Answer is derived according to the procedure of calculating LCM of any two numbers
Step-by-step explanation:
If you have any other questions
ask in comments
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
[tex]x^2-y^2-1-2y \\\\x^2-(y^2+2y+1)\\\\x^2-(y+1)^2\\\\(x)^2-(y+1)^2\\\\(x+y+1)(x-y-1)[/tex]
[tex]\\\\[/tex]
[tex] y^2-1-x^2-2x\\\\y^2-(x^2+2x+1)\\\\y^2-(x+1)^2\\\\(y)^2-(x+1)^2\\\\(y+x+1)(y-x-1) [/tex]
According to the question,
we have to find the LCM
LCM=[tex]\sf{(x+y+1)(x-y-1)(y-x-1) }[/tex]Solve EFD. Round the answers to the nearest hundredth.
A. m F ≈ 26, m D ≈ 64.01, FD = 7,921
B. m F ≈ 26, m D ≈ 64.01, FD = 89
C. m F ≈ 64.01, m D ≈ 26, FD = 89
D. m F ≈ 64.01, m D ≈ 26, FD = 7,921
Answer:
Option B
<F = 26°
<D = 64.01°
FD = 89
Answered by GAUTHMATH
For right triangle EFD, m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89
The correct answer is an option (B)
What is hypotenuse?It is the longest side of the right triangle.
What is Pythagoras theorem?For a right triangle,
[tex]a^{2}+ b^{2} = c^{2}[/tex], where c is hypotenuse and a, b area other two sides of the right triangle
For given example,
We have been given a right triangle EFD with hypotenuse FD.
Also, EF = 80, ED = 39
Using the Pythagoras theorem,
[tex]\Rightarrow FD^{2}= EF^{2} + ED^{2}\\\\ \Rightarrow FD^{2}= 80^{2} + 39^{2}\\\\ \Rightarrow FD^2 = 6400 + 1521\\\\ \Rightarrow FD^2 = 7921\\\\\Rightarrow FD = 89[/tex]
Consider, sin(F)
[tex]\Rightarrow sin(F)=\frac{ED}{FD} \\\\\Rightarrow sin(F)=\frac{39}{89}\\\\ \Rightarrow sin(F)=0.4382\\\\\Rightarrow \angle F=sin^{-1}(0.4382)\\\\\Rightarrow \angle F=25.98^{\circ}\\\\\Rightarrow \angle F\approx 26^{\circ}[/tex]
Now, consider sin(D)
[tex]\Rightarrow sin(D)=\frac{FE}{FD}\\\\ \Rightarrow sin(D)=\frac{80}{89}\\\\ \Rightarrow \angle D = sin^{-1}(0.8988)\\\\\Rightarrow \angle D = 64.009^{\circ}\\\\\Rightarrow \angle D \approx 64.01^{\circ}[/tex]
Therefore, for right triangle EFD, m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89
The correct answer is an option (B)
Learn more about Pythagoras theorem here:
https://brainly.com/question/343682
#SPJ2
Si un proyectil asciende verticalmente, y después de 3 segundos alcanza su altura máxima, calcule la velocidad que lleva a la mitad de su trayectoria descendente
Answer:
The speed is 20.8 m/s
Step-by-step explanation:
If a projectile ascends vertically, and after 3 seconds it reaches its maximum height, calculate the velocity that it carries to the middle of its downward trajectory
Let the maximum height is h and initial velocity is u.
From first equation of motion
v = u + at
0 = u - g x 3
u = 3 g.....(1)
Use third equation of motion
[tex]v^2 = u^2 - 2 gh \\\\0 = 9 g^2 - 2 gh \\\\h = 4.5 g[/tex]
Let the speed at half the height is v'.
[tex]v^2 = u^2 + 2 gh \\\\v'^2 = 0 + 2 g\times 2.25 g\\\\v'^2 = 4.5\times 9.8\times9.8\\\\v' = 20.8 m/s[/tex]
A photo printer is on sale for $195.50. The regular price is $230. What is the percent of the discount on the photo
printer?
Choose the correct description of the graph of the inequality X - 3 greater than or equal to 25
A. Open circle on 8, shading to the left
B. Closed circle on 8, shading to the left.
C. Open circle on 8, shading to the right.
D. Closed circle on 8, shading to the right.
I’m pretty sure it’s D
Answer:
D. Closed circle on 8, shading to the right.
Now use GeoGebra to measure the length of each side of quadrilateral ABCD, and use those lengths to calculate the perimeter of the quadrilateral. Do you get the same result that you obtained in part E? Take a screenshot of your work, and paste it below.
Answer:
Step-by-step explanation:
