Responder:
2
Explicación paso a paso:
El valor absoluto de una expresión es el también conocido como valor positivo devuelto por la expresión. Una expresión en un signo de módulo se conoce como valor absoluto de la expresión y dicha expresión siempre toma dos valores (tanto el valor positivo como el negativo).
Por ejemplo, el valor absoluto de x se escribe como | x | y esto puede devolver tanto + x como -x debido al signo del módulo.
Pasando a la pregunta, debemos determinar el valor absoluto de | 13-11 |. Esto significa que debemos determinar el valor positivo de la expresión como se muestra;
= | 13-11 |
= | 2 |
Este módulo de 2 puede devolver tanto +2 como -2, pero el valor absoluto solo devolverá el valor positivo, es decir, 2.
Por tanto, el valor absoluto de la expresión es 2
13.
а/8 = $1.25
Can someone help explain
Answer:
a= $10.00
Step-by-step explanation:
It's very simple. Move /8 to the other side of the equation. It should give you $1.25 x 8. Solve the multiplication and you should get $10.00.
If I didn't make my explanation clear enough, please comment. I sometimes don't even explain myself very well.
Answer:
a = 10
Step-by-step explanation:
a/8 = 1.25
multiply both sides by 8 to isolate a.
(8)(a/8) = 1.25(8)
which gives you
a = 1.25(8)
which simplifies to
a = 10
Please help me understand this question!
Answer:
C
Step-by-step explanation:
The first sentence basically sets up the equation which is given, so we can read it for knowledge but it is not crucial to solve the problem.
We start here:
we are given: $120 - 0.2($120)
= 120 - (0.2)(120) (factoring out 120)
= 120 (1 - 0.2)
= 120 (0.8)
= 0.8 (120) (answer c)
Graph the function f(x)=x^2+2x-8
what are x intercepts
what are y intercepts
what is maximum or minimum value
Answer:
The x intercepts are 2, -4
The y intercept is -8
The minimum is -9
Step-by-step explanation:
f(x)=x^2+2x-8
To find the x intercepts, set equal to zero and factor
0 =x^2+2x-8
0 = (x+4)(x-2)
Using the zero product property
0 = x+4 0 = x-2
x = -4 x = 2
The x intercepts are 2, -4
To find the y intercepts, set x =0 and solve for y
y = 0^2 +2(0) -8
y = -8
The y intercept is -8
Since the coefficient of the x^2 is positive, the parabola opens up so we have a minimum.
The vertex is halfway between the x intercepts
(-4+2)/2 = -2/2 = -1
To find the minimum substitute x= -1 into the equation
f(x)=x^2+2x-8
f(-1) = (-1)^2 +2(-1)-8 = 1-2-8 = -9
The minimum is -9
Graph attached
y=x²+2x-8y=x²+4x-2x-8y=x(x+4)-2(x+4)y=(x+4)(x-2)x intercepts (-4,0) and (2,0)
Y intercept :-
Put x=0
y=-8(0,-8)
Vertex is the minimum
(-1,-9)An observer standing on a cliff 320 feet above the ocean measured angles of depression of the near and far sides of an island to be 16.5 and 10.5 respectively. How long is the island ?
Answer:
154.10 Feets
Step-by-step explanation:
Given the following :
Height (h) of cliff = 320 feet
Angle of depression of near side = 16.5°
Angle of depression of far side = 10.5°
Using trigonometry :
We can obtain x and y as shown in the attached picture :
Tanθ = opposite / Adjacent
Adjacent = height of cliff = 320 Feets
For the near side :
Tanθ = opposite / Adjacent
Tan (16.5°) = x / 320
0.2962134 = x / 320
x = 0.2962134 * 320
x = 94.788318 Feets
For the far side :
Tanθ = opposite / Adjacent
Tan (10.5°) = x / 320
0.1853390 = x / 320
x = 0.1853390 * 320
x = 59.308494 Feets
Length of island = (59.308494 + 94.788318) feet
= 154.10 Feets
Three ducks and two ducklings weigh 32 kg. Four ducks and three ducklings weigh 44kg. All ducks weigh the same and all ducklings weigh the same. What is the weight of two ducks and one duckling?
Answer:
20kg
Step-by-step explanation:
Let the weight of one duck be x and the weight of one duckling be y
ATQ, 3x+2y=32 and 4x+3y=44, solving for x and y we get, weight of one duck is 8kg and one duckling is 4kg. The weight of two ducks and one duckling is 20kg
which of the following equations is a linear equation in one variable?
A. 5x-3=4(x+y)
B. 2a+5b-c=2
C. 3m=8
D. x=2/y+5
Answer:
Option C, 3m=8
Step-by-step explanation:
In the equation,
3m=8
or, 3m-8=0
there is only one variable which is m and it's in the form of ax+b=0
so it's an one variable linear equation
Which of the following relations is a function? A. (1, 4), (-4, 2), (8, 1), (-8, 2) B. (1, 4), (-4, 6), (1, 3), (-8, 2) C. (1, 0), (-4, 3), (8, 1), (-4, 5) D. (8, 1), (-4, 4), (1, 1), (8, 2)
Answer:
A. (1, 4), (-4, 2), (8, 1), (-8, 2)
Step-by-step explanation:
Each x goes to only 1 y to be a function
A. (1, 4), (-4, 2), (8, 1), (-8, 2)
function
B. (1, 4), (-4, 6), (1, 3), (-8, 2)
1 goes to 4 and 3 so not a function
C. (1, 0), (-4, 3), (8, 1), (-4, 5)
-4 goes to 3 and 5 so not a function
D. (8, 1), (-4, 4), (1, 1), (8, 2)
8 goes to 1 and 2 so not a function
Answer:
[tex]\Large \boxed{\mathrm{A. \ (1, 4), (-4, 2), (8, 1), (-8, 2)}}[/tex]
Step-by-step explanation:
[tex]\sf A \ function \ is \ a \ relation \ if \ each \ x \ value \ is \ for \ each \ y \ value.[/tex]
[tex](1, 4), (-4, 2), (8, 1), (-8, 2) \ \sf represents \ a \ function.[/tex]
[tex](1, 4), (-4, 6), (1, 3), (-8, 2) \ \sf does \ not \ represent \ a \ function.[/tex]
[tex](1, 0), (-4, 3), (8, 1), (-4, 5) \ \sf does \ not \ represent \ a \ function.[/tex]
[tex](8, 1), (-4, 4), (1, 1), (8, 2) \ \sf does \ not \ represent \ a \ function.[/tex]
Mr Osei has a rectangular field measured 85m long and 25m wide. How long is the distance around the field?
Answer:
220m
Step-by-step explanation:
l=85m
b=25m
perimeter=2(l+b)
2(85+25)
2(110)
=220m
perimeter is 220m
Answer:
Distance around the field is 220mStep-by-step explanation:
The distance around the field means the perimeter of the field
Since the field is rectangular
Perimeter of a rectangle = 2l + 2w
where l is the length
w is the width
From the question
l = 85m
w = 25m
Perimeter = 2(85) + 2(25)
Perimeter = 170 + 50
The final answer is
Perimeter = 220m
Hope this helps you
3. CD is the diameter of a circle. The coordinates are C(-2, -3) and D(-12,-5). At what coordinate
is the center of the circle located?
A. (5,1)
B. (-5,-1)
C (-4,-7)
D. (-7,-4)
Answer:
D) (-7,-4)
Step-by-step explanation:
Halfway from -2 to -12 is -7
Halfway from -3 to -5 is -4
Snoopy has a spoon that measures out 2(3)/(4) cups of sugar with every scoop. Snoopy takes 5(1)/(3) scoops with this spoon. How many cups of sugar does Snoopy scoop out?
33/64 cups of sugar does snoopy scoop out.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
The amount of sugar needed = 2 3/4 cups
Amount of sugar per scoop = 5 1/3 cups/scoop
So, number of cups of sugar scoops
= cups of sugar needed/ cups of sugar per scoop
=11/4 /16/3
=11/4 *3/16
=33/64
Hence, 33/64 cups of sugar does snoopy scoop out.
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The circumference of the circle shown below is 75 inches. Which expression
gives the length in inches of DE?
D
A.
. 75
72
O B.
360
75
O C.
361
. 75
O D.
360
75%
Answer:
B. 360 .75
Step-by-step explanation:
The circumference of the circle is represented by π * diameter of the circle. The circumference of the circle is its perimeter. The circumference is arc length of the circle. The perimeter is curve length around the figure of the circle. The circumference of the circle of 75 inches is represented by 75/360.
Answer: 72/360 multiply by 75
Step-by-step explanation:
i just did this question
When determining the sample size necessary for estimating the true population mean, which factor is NOT considered when sampling with replacement
Answer:
Population Size
Step-by-step explanation:
When sampling with replacement, we can expect that the population size will remain the same. Sampling with replacement occurs when a unit or subject for research is chosen from a population at random. This chosen unit can be returned to the population and another random selection done with the possibility that a unit that was chosen before could be chosen again. So in applying this system of selection, the population size is not taken into consideration. When samples are chosen in this form, it can be referred to as a simple random sample.
So, when determining the sample size necessary for estimating the true population mean, using the sampling with replacement method, the population size is not considered.
On an exam, the average score is 76 with a standard deviation of 6 points What is the probability that an individual chosen at random will have a score below 67 on this exam
Answer:
P [ X < 67 ] = 0,66,81 or 66,81 %
Step-by-step explanation:
We assume Normal Distribution N ( μ ; σ ) N ( 76 ; 6 )
z score for 67 is :
z(s) = ( X - μ ) /σ
z(s) = ( 67 - 76 ) / 6
z(s) = - 9 / 6
z(s) = - 1,5
with 1,5 we fnd n z-table area undr the curve α = 0,6681
Then P [ X < 67 ] = 0,66,81 or 66,81 %
23. f(x) is vertically shrank by a factor of 1/3. How will you represent f(x) after transformation?
A. f(3x)
B. 3f(x)
C. 13f(x)
D. f(13x)
Answer:
Step-by-step explanation:
vertical stretching / shrinking has the following transformation.
f(x) -> a * f(x)
when a > 1, it is stretching
when 0< a < 1, it is shrinking.
when -1 < a < 0, it is shringking + reflection about the x-axis
when a < -1, it is stretching + reflection about the x axis.
Here it is simple shrinking, so 0 < a < 1.
I expect the answer choice to show (1/3) f(x).
However, if the question plays with the words
"shrink by a factor of 1/3" to actually mean a "stretching by a factor of three", then B is the answer (stretch by a factor of three).
If m(x) =x+5/x-1 and n(x) = x - 3, which function has the same domain as (mºn)(x)?
We have
M(X) = (X + 5)/(X - 1)
N(X) = X - 3
So,
M(N(X)) = [(X - 3) + 5]/[(X - 3) - 1]
M(N(X)) = [X + 2]/[X - 4]The M(N(X)) domain will be:
D = {X / X ≠ 4}
4 ∉ to the M(N(X)) domain, otherwise we would have a/0, which is not possible (a denominator with zero). An equivalent function would be
H(X) = 1/(X - 4)
There are two pitchers of lemonade in the fridge there are 1.5 gallons of lemonade in 1 pitcher and 9 quarts of lemonade in the other pitcher how many cups of lemonade are there in the fridge
Answer:
52 cups
Step-by-step explanation:
1 gallon = 4 quarts
1.5 gallons = 6 quarts
6 + 9 = 13 quarts of lemonade in the fridge.
1 quart = 4 cups
13 quarts = 4 × 13 = 52 cups
52 cups of lemonade are in the fridge.
I would really appreciate it if you would mark me brainliest!
Have a blessed day!
Answer:
60 cups
Step-by-step explanation:
1 gal = 16 cups
1 quart = 4 cups
16 cups
1.5 gal x ------------- = 24 cups
1 gal.
4 cups
9 quarts x ----------- = 36 cups
1 quart
number of cups of lemonade in the fridge = 24 cups + 36 cups = 60 cups
What is the scale factor of this dilation?
Answer:
5/3
Step-by-step explanation:
on both sides we can see that the orginal length of 3 increased to five
therfore if we multiply 3 by 3/5 we get five which means the scale factor is 5/3
what is (2y + 5)(y - 3) in simplified form using the distributive property
Answer:
[tex]\boxed{2y^{2} - y - 15}[/tex]
Step-by-step explanation:
Use the FOIL technique in order to distribute the terms properly. FOIL stands for First Terms, Outside Terms, Inside Terms, and Last Terms. In order to properly distribute, multiply the common terms based on the steps in the FOIL technique. So, in this case:
The first terms are 2y and y. The outside terms are 2y and -3. The inside terms are 5 and y.The last terms are 5 and -3.Therefore, multiply the terms:
2y and y to get 2y²2y and -3 to get -6y5 and y to get 5y5 and -3 to get -15Then, add or subtract based on the signs:
2y² - 6y + 5y - 15
Then, add like terms to finish simplifying the expression. This leaves you with 2y² - y - 15.
Answer:
2y2 – y – 15
Step-by-step explanation:
(2y + 5)(y – 3)
= 2y(y – 3) + 5(y – 3)
= 2y2 – 6y + 5y – 15
= 2y2 – y –15
savanah solved the equation 3+4 multiplied by the absolute value of x/2+3=11 for one solution. her work is shown below. what is the other solution to the given absolute value equation: savanah's solution was x= -2
Answer:
-10Step-by-step explanation:
Given the equation solved by savanah expressed as [tex]3+4|\frac{x}{2} + 3| = 11[/tex], IF she solved for one of the solution and got x = -2, we are to solve for the other value of x.
Note that the expression in modulus can be expressed as a positive expression and negative expression.
For the positive value of the expression [tex]|\frac{x}{2} + 3|[/tex] i.e [tex]\frac{x}{2} + 3[/tex], the expression becomes;
[tex]3+4(\frac{x}{2} + 3) = 11[/tex]
On simplification;
[tex]3+4(\frac{x}{2} + 3) = 11\\\\3 + 4(\frac{x}{2} )+4(3) = 11\\\\3 + \frac{4x}{2}+ 12 = 11\\\\3 + 2x+12 = 11\\\\2x+15 = 11\\\\Subtract \ 15 \ from \ both \ sides\\\\2x+15-15 = 11-15\\\\2x = -4\\\\x = -2[/tex]
For the negative value of the expression [tex]|\frac{x}{2} + 3|[/tex] i.e [tex]-(\frac{x}{2} + 3)[/tex], the expression becomes;
[tex]3+4[-(\frac{x}{2} + 3)] = 11[/tex]
On simplifying;
[tex]3+4[-(\frac{x}{2} + 3)] = 11\\\\3+4(-\frac{x}{2} - 3)= 11\\\\3-4(\frac{x}{2}) -12 = 11\\\\3 - \frac{4x}{2} - 12 = 11\\\\3 - 2x-12 = 11\\\\-2x-9 = 11\\\\add \ 9 \ to \ both \ sides\\\\-2x-9+9 = 11+9\\-2x = 20\\\\x = -20/2\\\\x = -10[/tex]
Hence her other solution of x is -10
The sum of two positive number is 6 times their difference. what is the reciprocal of the ratio of the larger number to the smaller?
let the numbers be a and b, a>b
a+b=6(a-b)
we need to find reciprocal of ratio of larger to smaller , which will be same as ratio of smaller to larger or b/a, let's call it x
divide the equation by a.
1+x=6(1-x)
on solving, x=5/7
generate a continuous and differentiable function f(x) with the following properties: f(x) is decreasing at x=−5 f(x) has a local minimum at x=−3 f(x) has a local maximum at x=3
Answer:
see details in graph and below
Step-by-step explanation:
There are many ways to generate the function.
We'll generate a function whose first derivative f'(x) satisfies the required conditions, say, a quadratic.
1. f(x) has a local minimum at x = -3, and
2. a local maximum at x = 3
Therefore f'(x) has to cross the x-axis at x = -3 and x=+3.
Furthermore, f'(x) must be increasing at x=-3 and decreasing at x=+3.
f'(x) = -x^2+9
will satisfy the above conditions.
Finally f(x) must be decreasing at x= -5, which implies that f'(-5) must be negative.
Check: f'(-5) = -(-5)^2+9 = -25+9 = -16 < 0 so ok.
f(x) can then be obtained by integrating f'(x) :
f(x) = integral of -x^2+9 = -x^3/3 + 9x = 9x - x^3/3
A graph of f(x) is attached, and is found to satisfy all three conditions.
A function is differentiable at [tex]x = a[/tex], if the function is continuous at [tex]x = a[/tex]. The function that satisfy the given properties is [tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]
Given that:
The function decreases at [tex]x = -5[/tex] means that: [tex]f(-5) < 0[/tex]
The local minimum at [tex]x = -3[/tex] and local maximum at [tex]x = 3[/tex] means that:
[tex]x = -3[/tex] or [tex]x = 3[/tex]
Equate both equations to 0
[tex]x + 3 = 0[/tex] or [tex]3 - x = 0[/tex]
Multiply both equations to give y'
[tex]y' = (3 - x) \times (x + 3)[/tex]
Open bracket
[tex]y' = 3x + 9 - x^2 - 3x[/tex]
Collect like terms
[tex]y' = 3x - 3x+ 9 - x^2[/tex]
[tex]y' = 9 - x^2[/tex]
Integrate y'
[tex]y = \frac{9x^{0+1}}{0+1} - \frac{x^{2+1}}{2+1} + c[/tex]
[tex]y = \frac{9x^1}{1} - \frac{x^3}{3} + c[/tex]
[tex]y = 9x - \frac{x^3}{3} + c[/tex]
Express as a function
[tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]
[tex]f(-5) < 0[/tex] implies that:
[tex]9\times -5 - \frac{(-5)^3}{3} + c < 0[/tex]
[tex]-45 - \frac{-125}{3} + c < 0[/tex]
[tex]-45 + \frac{125}{3} + c < 0[/tex]
Take LCM
[tex]\frac{-135 + 125}{3} + c < 0[/tex]
[tex]-\frac{10}{3} + c < 0[/tex]
Collect like terms
[tex]c < \frac{10}{3}[/tex]
[tex]c <3.33[/tex]
We can then assume the value of c to be
[tex]c=3[/tex] or any other value less than 3.33
Substitute [tex]c=3[/tex] in [tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]
[tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]
See attachment for the function of f(x)
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What is the value of the logarithm below? (Round your answer to two decimal
places.)
log4 12
Answer:
1.68
Step-by-step explanation:
log(4)12=log(48)
log(48)=1.6812... or rounded, 1.68
10 orange sodas, 15 cream sodas and 7 cherry sodas are in an ice chest. How many sodas must be removed from the chest to guarantee that on type of soda has been chosen?
PLEASE, GIVE A STEP BY STEP EXPLANATION
Answer:
25 sodas if the type of soda chosen is cherry sodas
HELP NEED PRECALC HELP WILL GIVE BRAINLIEST PLEASE HELP
From your earlier questions, we found
[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]
so the wave has amplitude √29. The weight's maximum negative position from equilibrium is then -√29, so you are solving for t in the given interval for which
[tex]\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)=-\dfrac{\sqrt{29}}2[/tex]
Divide both sides by √29:
[tex]\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)=-\dfrac12[/tex]
Take the inverse sine of both sides, noting that we get two possible solution sets because we have
[tex]\sin\left(\dfrac{7\pi}6\right)=\sin\left(\dfrac{11\pi}6\right)=-\dfrac12[/tex]
and the sine wave has period 2π, so [tex]\sin x=\sin(x+2\pi)=\sin(x+4\pi)=\cdots[/tex].
[tex]\implies 4\pi t+\tan^{-1}\left(\dfrac52\right)=\dfrac{7\pi}6+2n\pi[/tex]
OR
[tex]\implies 4\pi t+\tan^{-1}\left(\dfrac52\right)=\dfrac{11\pi}6+2n\pi[/tex]
where n is any integer.
Now solve for t :
[tex]t=\dfrac{\frac{7\pi}6+2n\pi-\tan^{-1}\left(\frac52\right)}{4\pi}[/tex]
OR
[tex]t=\dfrac{\frac{11\pi}6+2n\pi-\tan^{-1}\left(\frac52\right)}{4\pi}[/tex]
We get solutions between 0 and 0.5 when n = 0 of t ≈ 0.196946 and t ≈ 0.363613.
I will name you Brainly hurryyyy What two integers are in between 0.7142
Answer:
0.71419 &0.71421 are the correct.
U = { z | z is an integer and − 1 ≤ z < 2 }
Answer:
(-1,0,1,2)
Step-by-step explanation:
in listing the values of z it will now be (z:z= -1,0,1,2)
The regular hexagon ABCDEF rotates 240º counterclockwise about its center to form hexagon A′B′C′D′E′F′. Point C′ of the image coincides with point
of the preimage. Point D′ of the image coincides with point
of the preimage.
Answer:
Point C: G
Point D: F
Step-by-step explanation:
A hexagon has 6 sides.
360/6=60
Every 60°, it moves one section.
240/60=4.
So it moves 4 sections.
C would move 4 sections BACK (B, A, F, G)
D would also move 4 sections back (C, B, A, F)
Answer:
Point C is: E
point D is : F
Step-by-step explanation:
State the correct polar coordinate for the graph shown:
clearly, r=3 units
and 8 segments (sectors actually) in anti-clockwise direction , with each sector having 30° angle so angle is 240°
so option C
Answer:
Solution : ( 3, 240° )
Step-by-step explanation:
In polar coordinates the point is expression as the ordered pair ( r, θ ) where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis. When r > 0, we can tell it = 3 as the point lies on the third circle starting from the center. Now let's start listing coordinates for when r is positive ( r > 0 ). There are two cases to consider here.
( 3, θ ) here theta is 60 degrees more than 180, or 180 + 60 = 240 degrees. Right away you can tell that your solution is ( 3, 240° ), you don't have to consider the second case.
Let the sample size of leg strengths to be 7 and the sample mean and sample standard deviation be 630 watts and 32 watts, respectively.
(a) Is there evidence that leg strength exceeds 600 watts at significance level 0.05? Find the P-value. There is_________ evidence that the leg strength exceeds 600 watts at ? = 0.05.
A. 0.001 < P-value < 0.005
B. 0.10 < P-value < 0.25
C. 0.010 < P-value < 0.025
D. 0.05 < P-value < 0.10
(b) Compute the power of the test if the true strength is 610 watts.
(c) What sample size would be required to detect a true mean of 610 watts if the power of the test should be at least 0.9? n=
Answer:
a. There is_sufficient evidence that the leg
C. 0.010 < P-value < 0.025
b. Power of test = 1- β=0.2066
c. So the sample size is 88
Step-by-step explanation:
We formulate the null and alternative hypotheses as
H0 : u1= u2 against Ha : u1 > u2 This is a right tailed test
Here n= 7 and significance level ∝= 0.005
Critical value for a right tailed test with 6 df is 1.9432
Sample Standard deviation = s= 32
Sample size= n= 7
Sample Mean =x`= 630
Degrees of freedom = df = n-1= 7-1= 6
The test statistic used here is
Z = x- x`/ s/√n
Z= 630-600 / 32 / √7
Z= 2.4797= 2.48
P- value = 0.0023890 > ∝ reject the null hypothesis.
so it lies between 0.010 < P-value < 0.025
b) Power of test if true strength is 610 watts.
For a right tailed test value of z is = ± 1.645
P (type II error) β= P (Z< Z∝-x- x`/ s/√n)
Z = x- x`/ s/√n
Z= 610-630 / 32 / √7
Z=0.826
P (type II error) β= P (Z< 1.645-0.826)
= P (Z> 0.818)
= 0.7933
Power of test = 1- β=0.2066
(c)
true mean = 610
hypothesis mean = 600
standard deviation= 32
power = β=0.9
Z∝= 1.645
Zβ= 1.282
Sample size needed
n=( (Z∝ +Zβ )*s/ SE)²
n= ((1.645+1.282) 32/ 10)²
Putting the values and solving we get 87.69
So the sample size is 88
Find the value of z.
A. 25.25
B. 76.25
C. 51
D. 129
Answer:
25.25
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)
The angle formed by the two chords is (180 -x)
We need to find x first
x = 1/2 (54+204)
x = 129
The angle formed by the two chords is (180 -129) = 51
51 = 1/2 ( z+3z+1)
Multiply by 2
102 = 4z+1
101 = 4x
Divide by 4
101/4 = z
25.25 =z