Answer:
The cost of an adult ticket is $12.50
Step-by-step explanation:
The given information are;
The cost of two adult tickets and three children tickets = $43.00
The cost of one adult ticket and one child ticket = $18.50
Whereby the cost of an adult ticket is represented by x and the cost of a child's ticket is represented by y, we get the following two simultaneous equations;
2·x + 3·y = 43.00...(1)
x + y = 18.5...(2)
(ii) Multiplying equation (2) by 2 and subtracting the result from equation (1) gives;
2·x + 3·y - 2×(x + y) = 43 - 2×18.5 = 6
2·x - 2·x + 3·y - 2·y = 0 + y = 6
∴ y = 6
The cost of each the children ticket = $6.00
From equation (2), where y = 6, we get;
x + y = 18.5
∴ x + 6 = 18.5
x = 18.5 - 6 = 12.5
The cost of an adult ticket, x = $12.50.
which of the following are identities? check all that apply.
A. (sinx + cosx)^2= 1+sin2x
B. sin6x=2 sin3x cos3x
C. sin3x/sinxcosx = 4cosx - secx
D. sin3x-sinx/cos3x+cosx = tanx
Answer: (a), (b), (c), and (d)
Step-by-step explanation:
Check the options
[tex](a)\\\Rightarrow [\sin x+\cos x]^2=\sin ^2x+\cos ^2x+2\sin x\cos x\\\Rightarrow [\sin x+\cos x]^2=1+2\sin x\cos x\\\Rightarrow \Rightarrow [\sin x+\cos x]^2=1+\sin 2x[/tex]
[tex](b)\\\Rightarrow \sin (6x)=\sin 2(3x)\\\Rightarrow \sin 2(3x)=2\sin (3x)\cos (3x)[/tex]
[tex](c)\\\Rightarrow \dfrac{\sin 3x}{\sin x\cos x}=\dfrac{3\sin x-4\sin ^3x}{\sin x\cos x}\\\\\Rightarrow 3\sec x-4\sin ^2x\sec x\\\Rightarrow 3\sec x-4[1-\cos ^2x]\sec x\\\Rightarrow 3\sec x-4\sec x+4\cos x\\\Rightarrow 4\cos x-\sec x[/tex]
[tex](d)\\\Rightarrow \dfrac{\sin 3x-\sin x}{\cos 3x+\cos x}=\dfrac{2\cos [\frac{3x+x}{2}] \sin [\frac{3x-x}{2}]}{2\cos [\frac{3x+x}{2}]\cos [\frac{3x-x}{2}]}\\\\\Rightarrow \dfrac{2\cos 2x\sin x}{2\cos 2x\cos x}=\dfrac{\sin x}{\cos x}\\\\\Rightarrow \tan x[/tex]
Thus, all the identities are correct.
A. Not an identity
B. An identity
C. Not an identity
D. An identity
To check whether each expression is an identity, we need to verify if the equation holds true for all values of the variable x. If it is true for all values of x, then it is an identity. Let's check each option:
A. [tex]\((\sin x + \cos x)^2 = 1 + \sin 2x\)[/tex]
To check if this is an identity, let's expand the left-hand side (LHS):
[tex]\((\sin x + \cos x)^2 = \sin^2 x + 2\sin x \cos x + \cos^2 x\)[/tex]
Now, we can use the trigonometric identity [tex]\(\sin^2 x + \cos^2 x = 1\)[/tex] to simplify the LHS:
[tex]\(\sin^2 x + 2\sin x \cos x + \cos^2 x = 1 + 2\sin x \cos x\)[/tex]
The simplified LHS is not equal to the right-hand side (RHS) 1 + sin 2x since it is missing the sin 2x term. Therefore, option A is not an identity.
B. [tex]\(\sin 6x = 2 \sin 3x \cos 3x\)[/tex]
To check if this is an identity, we can use the double-angle identity for sine:[tex]\(\sin 2\theta = 2\sin \theta \cos \theta\)[/tex]
Let [tex]\(2\theta = 6x\)[/tex], which means [tex]\(\theta = 3x\):[/tex]
[tex]\(\sin 6x = 2 \sin 3x \cos 3x\)[/tex]
The equation holds true with the double-angle identity, so option B is an identity.
C. [tex]\(\frac{\sin 3x}{\sin x \cos x} = 4\cos x - \sec x\)[/tex]
To check if this is an identity, we can simplify the right-hand side (RHS) using trigonometric identities.
Recall that [tex]\(\sec x = \frac{1}{\cos x}\):[/tex]
[tex]\(4\cos x - \sec x = 4\cos x - \frac{1}{\cos x} = \frac{4\cos^2 x - 1}{\cos x}\)[/tex]
Now, using the double-angle identity for sine, [tex]\(\sin 2\theta = 2\sin \theta \cos \theta\),[/tex] let [tex]\(\theta = x\):[/tex]
[tex]\(\sin 2x = 2\sin x \cos x\)[/tex]
Multiply both sides by 2: [tex]\(2\sin x \cos x = \sin 2x\)[/tex]
Now, the left-hand side (LHS) becomes:
[tex]\(\frac{\sin 3x}{\sin x \cos x} = \frac{\sin 2x}{\sin x \cos x}\)[/tex]
Using the double-angle identity for sine again, let [tex]\(2\theta = 2x\):[/tex]
[tex]\(\frac{\sin 2x}{\sin x \cos x} = \frac{2\sin x \cos x}{\sin x \cos x} = 2\)[/tex]
So, the LHS is 2, which is not equal to the RHS [tex]\(\frac{4\cos^2 x - 1}{\cos x}\)[/tex]. Therefore, option C is not an identity.
D. [tex]\(\frac{\sin 3x - \sin x}{\cos 3x + \cos x} = \tan x\)[/tex]
To check if this is an identity, we can use the sum-to-product trigonometric identities:
[tex]\(\sin A - \sin B = 2\sin \frac{A-B}{2} \cos \frac{A+B}{2}\)\(\cos A + \cos B = 2\cos \frac{A+B}{2} \cos \frac{A-B}{2}\)[/tex]
Let A = 3x and B = x:
[tex]\(\sin 3x - \sin x = 2\sin x \cos 2x\)\(\cos 3x + \cos x = 2\cos 2x \cos x\)[/tex]
Now, we can rewrite the expression:
[tex]\(\frac{\sin 3x - \sin x}{\cos 3x + \cos x} = \frac{2\sin x \cos 2x}{2\cos 2x \cos x} = \frac{\sin x}{\cos x} = \tan x\)[/tex]
The equation holds true, so option D is an identity.
To know more about identity:
https://brainly.com/question/28974915
#SPJ3
(cos2a *cos 4a+ sin 2a*sin 4a)/sin4a
Answer:
Step-by-step explanation:
(cos 4a*cos 2a+sin 4a*sin 2a)/sin 4a
=[cos (4a-2a)]/sin 4a
=(cos 2a)/sin 4a
=(cos 2a) /(2 sin 2a cos 2a)
=1/(2 sin 2a)
=1/2 csc 2a
You deposit $100 into a savings account that gives you 5.5% annual interest rate, compounded quarterly. What will be your balance after 4 years?
Answer:
$124.42.
Step-by-step explanation:
Given data
Principqp= $100
Rate= 5.5%
time=4 years
First, convert R as a percent to r as a decimal
r = R/100
r = 5.5/100
r = 0.055 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt // Since we are compounding quarterly
A = 100.00(1 + 0.055/4)(^4)(4)
A = 100.00(1 + 0.01375)^(16)
A = $124.42
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $100.00 at a rate of 5.5% per year compounded 4 times per year over 4 years is $124.42.
You go out to lunch with some friends. Your lunch came to $9.76. If you want to leave a 15% tip, how much will you pay in total?
Answer:
1.47
Step-by-step explanation:
9.76/10=10% = 0.976 round to 0.98
5%=0.97/2 = 0.49
add them = 1.47 tip
Find the measures of the angles formed by two intersecting lines if the
sum of the measures of three of the four angles is 270°
50 points! Please help quick!
Answer:
every single angle is 90°
Step-by-step explanation:
remember that,
4 angles will form if two lines intersect and the sum of those 4 angles is 360°
we are given the sum of 3 angles i.e 270
so one of the angles should be
[tex] \displaystyle {360}^{\circ} - {270}^{\circ}[/tex]
simplify substraction:
[tex] \displaystyle {90}^{\circ}[/tex]
therefore since one of the angles is 90° the intercepting lines are Perpendicular as a result every single angle formed by the two intercepting lines is 90°
Answer:
90°
Step-by-step explanation:
We know that sum of angle around a point is 360° . Here its already given that sum of three Angles out of 4 is 270°
Therefore :-
Measure of remaining one angle ,
360 - 270 90 °Therefore the measure of the fourth angle is 90°
Sam rolls a fair dice and flips a fair coin.
What is the probability of obtaining an odd number and a head?
Answer:
The probability that this occurs is 25%, as 3/6 (chance to roll an odd number) multiplied by 1/2 (chance to flip a head) is .25.
Step-by-step explanation:
Which represents f(x)=g
HURRRRRRY ITS A TIME TESSS
Answer:
B
Step-by-step explanation:
f(x) = g(x) at the intersection points of the two graphs.
The graphs intersect at x = -4 and x = 0.
At x = -4, f(-4) = g(-4).
At x = 0, f(0) = g(0)
Answer: B
PLISSSSSS HELPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1.3
Step-by-step explanation:
The Rest Of Them Are Writen As Fractions
Answer:
[tex]\sqrt{10}[/tex]
NOTE: the other answer is WRONG...
irrational means can not be written as a fraction (with whole numbers)
4/3 = 1.33333333333
Step-by-step explanation:
Write an equation that represents the line.
Answer:
y = 7/5x + 7
Step-by-step explanation:
I have like no clue what this means, please help! :)
Answer:
1/9
You are being asked to "complete the square"
you need to find a value to make the quadratic a "perfect square:
the focus is -2/3 you need to "add" one half of -2/3 squared to the
equation (1/2 * -2/3)^2 .... (-2/6)^2 .... 4/36 .... 1/9
Step-by-step explanation:
A biased 3-coloured spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times.
If you spin this spinner 1000 times, how many times do you expect it to land on Red?
(Hint: Find n first)
Given:
A biased 3-colored spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times.
To find:
The expected number of times it land on Red if you spin this spinner 1000 times.
Solution:
A biased 3-colored spinner was spun 240 times. It landed on Red n times, on Orange 3n times and on Yellow 8n times. So,
[tex]n+3n+8n=240[/tex]
[tex]12n=240[/tex]
[tex]n=\dfrac{240}{12}[/tex]
[tex]n=20[/tex]
The value of n is 20. It means the spinner land on red 20 times if the spinner was spun 240 times. So, the probability of getting red is:
[tex]P(Red)=\dfrac{20}{240}[/tex]
[tex]P(Red)=\dfrac{1}{12}[/tex]
If you spin this spinner 1000 times, then the expected number of times to getting red is:
[tex]E(Red)=1000\times P(Red)[/tex]
[tex]E(Red)=1000\times \dfrac{1}{12}[/tex]
[tex]E(Red)=83.333...[/tex]
[tex]E(Red)\approx 83[/tex]
Therefore, the expected number of times to land on red is 83.
Which is the equation of a line parallel to the line with the equation: y = 14x + 2
y = -4x - 7
y = 4x + 2
y = 14x − 12
y = −14x + 3
Hi!
y = ax + b
y = 14x + 2 → a = 14 ∧ b = 2
Parallel lines have the same slope factor (a) so line parallel to the line with the equation y = 14x + 2 will be y = 14x - 12
HELP WILL GIVE BRAINLIEST
Answer:
6
Step-by-step explanation:
Follow 1 hour on the y axis to where it meets the line of best fit. In this case it is about 6 puzzles.
The rocket that carried the Curiosity Rover to Mars traveled at a speed of 21,000 miles per hour. What is this speed to the nearest mile per second?
6 miles per second
350 miles per second
1,260,000 miles per second
75,600,000 miles per second
Answer:
6 mps to the nearest mps.
Step-by-step explanation
The rocket that carried the Curiosity Rover to Mars traveled at a speed of 21,000 miles per hour. What is this speed to the nearest mile per second?
1 hr = 3600 sec
Since an hour is 3600 seconds (i.e., 60 x 60), you simply need to divide that number by 3600
→ 21000 mph = 21000 ÷ 3600 mps = 5 5/6 mps →
ANSWER : 6 mps to the nearest mps.
Answer:
Believe the other person
Step-by-step explanation:
I got a 100%, and also got this question.
The following table shows a direct variation.
3 y
15 5
18 6
27 9
Answer:
Yes, it shows direct variation
Step-by-step explanation:
Given
The above table
Required
Is it a direct variation?
The constant of variation (k) is:
[tex]k = y/x[/tex]
For each pair x and y, we have:
[tex]k = 5/15 = 1/3[/tex]
[tex]k = 6/18 = 1/3[/tex]
[tex]k =9/27 = 1/3[/tex]
Since the calculate constant have the same value for all pair or x and y, then the table shows direct variation
Answer:1
Step-by-step explanation:3/3=1
Solve the following equa
8 (2v + 8) = 96
оа
v = 2
ii need help
Answer:
1
Step-by-step explanation:
64+32 =96 that'd how I got the answer
Answer:
[tex]{ \tt{8(2v + 8) = 96}} \\ { \tt{2v + 8 = 12}} \\ { \tt{2v = 4}} \\ { \bf{v = 2}}[/tex]
HELP ME ASAP I need help with this problem
B.
the solution is in the picture
Write each as a percent. Use proportions.
7/25, 2/3, 3/8
Answer:
Step-by-step explanation:
[tex]\dfrac{7}{25} =0.28=28\%\\\\\dfrac{2}{3} \approx 0.67=67\%\\\\\dfrac{3}{8} =0.375=37.5%[/tex]
PLEASE HELP ASAP!
Cynthia bought a bag of wafers weighing 543 grams. There are about 0.035 ounces in 1 gram. About how many ounces does the
bag of wafers weigh?
OA.
15.51
B. 0.035
C. 0.64
OD
19.01
Answer:
19.005 ounces
Step-by-step explanation:
I believe that all you have to do is mutilply the 2 numbers which is 543 and 0.035 to find the amount of ounces it weighs. So 543 × 0.035 = 19.005. The answer is 19.005 ounces. (i hope)
help asap please ------------------
Answer:
Correct answer 1
Step-by-step explanation:
Graph each equation by using the y-intercept and slope
y=-x-4
Y-int=______
Slope=_____
whats the y-intercept and slope for this equation?
Answers:
y intercept = -4
slope = -1
==========================================
Explanation:
The given equation is the same as y = -1x + (-4)
Compare this to y = mx+b form, and we see that
m = -1 is the slope
b = -4 is the y intercept
To graph y = -x-4, you could plot the two points (0,-4) and (1,-5) and draw a straight line through them. Extend the line as far as you can in either direction.
Notice how going from (0,-4) to (1,-5) follows the process "down 1, right 1" which is directly pulled from the slope = -1 = -1/1.
What is the center of the circle:What is the center of the circle: (x+1)^2+(y-12)^2=25
1. 25
2. (1, -12)
3. 5
4. (-1, 12)
Answer:
option 4
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x + 1)² + (y - 12)² = 25 ← is in standard form
with centre = (- 1, 12 ) and radius = [tex]\sqrt{25}[/tex] = 5
Every 24 hours, Earth makes a full rotation around its axis. Earth's speed of rotation at the equator is 1.670 km per hour. What is the
circumference of Earth's equator?
(Hint. Earth's circumference at the equator is equal to the distance that Earth rotates around the equator).
Answer:
The circumference of Earth's equator is 40,080 km.
Step-by-step explanation:
Given that every 24 hours, Earth makes a full rotation around its axis, and Earth's speed of rotation at the equator is 1,670 km per hour, to determine what is the circumference of Earth's equator the following calculation must be performed:
24 x 1,670 = X
40,080 = X
Therefore, the circumference of Earth's equator is 40,080 km.
(a) Determine a cubic polynomial with integer coefficients which has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.
(b) Prove that $\sqrt[3]{2} + \sqrt[3]{4}$ is irrational.
Answer:
(a) [tex]x\³ - 6x - 6[/tex]
(b) Proved
Step-by-step explanation:
Given
[tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex] --- the root
Solving (a): The polynomial
A cubic function is represented as:
[tex]f = (a + b)^3[/tex]
Expand
[tex]f = a^3 + 3a^2b + 3ab^2 + b^3[/tex]
Rewrite as:
[tex]f = a^3 + 3ab(a + b) + b^3[/tex]
The root is represented as:
[tex]r=a+b[/tex]
By comparison:
[tex]a = $\sqrt[3]{2}[/tex]
[tex]b = \sqrt[3]{4}$[/tex]
So, we have:
[tex]f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3[/tex]
Expand
[tex]f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
Evaluate like terms
[tex]f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)[/tex]
Recall that: [tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex]
So, we have:
[tex]f = 6 + 6r[/tex]
Equate to 0
[tex]f - 6 - 6r = 0[/tex]
Rewrite as:
[tex]f - 6r - 6 = 0[/tex]
Express as a cubic function
[tex]x^3 - 6x - 6 = 0[/tex]
Hence, the cubic polynomial is:
[tex]f(x) = x^3 - 6x - 6[/tex]
Solving (b): Prove that r is irrational
The constant term of [tex]x^3 - 6x - 6 = 0[/tex] is -6
The divisors of -6 are: -6,-3,-2,-1,1,2,3,6
Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values
[tex]f(-6) = (-6)^3 - 6*-6 - 6 = -186[/tex]
[tex]f(-3) = (-3)^3 - 6*-3 - 6 = -15[/tex]
[tex]f(-2) = (-2)^3 - 6*-2 - 6 = -2[/tex]
[tex]f(-1) = (-1)^3 - 6*-1 - 6 = -1[/tex]
[tex]f(1) = (1)^3 - 6*1 - 6 = -11[/tex]
[tex]f(2) = (2)^3 - 6*2 - 6 = -10[/tex]
[tex]f(3) = (3)^3 - 6*3 - 6 = 3[/tex]
[tex]f(6) = (6)^3 - 6*6 - 6 = 174[/tex]
For r to be rational;
The divisors of -6 must divide f(x) without remainder
i.e. Any of the above values must equal 0
Since none equals 0, then r is irrational
I need help with 7 and 8 please
Answer:
Can't See 7 clearly
8) (9,9)
Step-by-step explanation:
[tex]\frac{10+8}{2}[/tex] , [tex]\frac{10+8}{2}[/tex]
Add x's and divide by 2
Add y's and divide by 2
Like taking the average of the coordinates.
help me with this please
Get three real world examples of a rectangle prism
Answer:
a shipping container ,the ones they use in large cargo ships
find the percent of soccer and cross country kids in the fall
This afternoon Zoe left school, rode the bus 11/12 of a mile, and then walked 1/12 of a mile to get home. How much farther did Zoe ride than walk?
Write your answer as a fraction or as a whole or mixed number.
Answer:
Zoe rode [tex]\frac{5}{6}[/tex] of a mile more than she walked.
Step-by-step explanation:
[tex]\frac{11}{12}-\frac{1}{12} =\frac{5}{6}[/tex]
If the measure of angle 5 is (3x + 50) degrees and the measure of angle 6 is (5x + 16) degrees, what value of x will guarantee equation AB \\ DE
Answer:
x = 17
Step-by-step explanation:
If AB // DE, then angle 5 and angle 6 are alternate interior angle and they should be congruent.
5x + 16 = 3x + 50
Subtract 16 from both sides
5x = 3x + 50 - 16
5x = 3x + 34
Subtract 3x from both sides
5x - 3x = 34
2x = 34
Divide both sides by 2
x = 34/2
x = 17
Answer:
To AB \\ DEangle 5 should be equal to angle 63x + 50 = 5x + 16
5x - 3x = 50-16
2x = 34
x = 17