solve by substitution method 2x+y=-2 5x-2y=-23
Answers
Step-by-step explanation:
SOLVED BY SUBSTITUTION !
Answer:
x= -3
Step-by-step explanation:
2x + y = -2 ---> y = -2 - 2x
instead: 5x-2y = -23 ---> 5x - 2(-2 -2x) = -23 ----> 5x+4+4x= -23 ---> 9x= -27
---> x = -3
Related Questions
What is the equation of the graph that represents the parent function f(x)= x^4 stretched vertically by a factor of 2, then shifted down 3 spaces
Answers
The equation of the function is f"(x) = 2x^2 - 3
How to determine the equation?The parent function is given as:
f(x) = x^4
When it is stretched vertically by a factor of 2, the rule is
f'(x) = 2f(x)
So, we have
f'(x) = 2x^2
When shifted down 3 spaces, the rule is
f"(x) = f'(x) - 3
So, we have:
f"(x) = 2x^2 - 3
Hence, the equation of the function is f"(x) = 2x^2 - 3
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The area of the top of a square table
is 269 in2. What are the dimensions
of the top?
Answers
Answer:
[tex]\sqrt{269}[/tex] is ≈ 14.01
Step-by-step explanation:
If the table top is a square, to find the area, you would multiply one side times itself.
If you are given the area, and need to find the sides, you will take the square root of the area to find the side length.
Your question doesn't say to round, but 269 is not a perfect square.
[tex]\sqrt{269}[/tex] is ≈ 14.01
If the area of the base was 169, that is a perfect square. [tex]\sqrt{169}[/tex] = 13
Help!!! cant find answers
Answers
As the intervals moves from left to right on the graph, the average rate of change increases
How to determine the change in the rate of change?The function is an exponential growth function.
This is known because it has an initial value at (0, 2), and the value increases to the right
The average rate of change of exponential growth functions increases towards the right.
This means that:
The initial statement is "as the intervals moves from left to right on the graph, the average rate of change increases
Because the average rate of change keeps changing, the final statement is:
Since the average rate of change is also changing, the function is changing and approaches infinity
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Which ordered pair is the best estimate for the solution of the system of equations?
{y=4x−19.4
{y=0.2x−4.2
(−3.5, 4)
(4.9, −3.5)
(4, −3.4)
(4.9, 0)
Answers
The ordered pair which is a solution of the system of equations is; (4.9, 0).
Which solution pair is the best estimate of the system solution?The equations given in the task content can be solved as a system as follows, since y = y;
4x -19.4 = 0.2x -4.2
4x -0.2x = 19.4 -4.2
3.8x = 15.2
x = 15.2/3.8
x = 4.9
y = 4(4.9) -19.4
y = 0.2
Hence, the best ordered pair solution is; (4.9, 0).
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I need help with question 30 please! :)
Answers
Answer:
B ∩ (¬A ∩ ¬C)
Step-by-step explanation:
You want to exclude the section C shares with A, the one C shares with B and the one it shares with both. Intersecting ¬A (not A) with ¬C (not C) you obtain the entire area except A and C, which then can be intersected with B to obtain the highlighted area.
The circle below is centered at the point (-3, 4) and has a radius of length 3.
What is its equation?
A. (x- 4)2 + (y + 3)2 =
32
0
B. (x + 4)2 + (y- 3)2 =
32
T c. (x- 3)2 + (y + 4)2 = 9
O D. (x+ 3)2 + (y- 4)2 = 9
Answers
Answer: [tex](x+3)^2 + (y-4)^2 = 9[/tex]
Step-by-step explanation:
See attached image, this is straight formula substitution.
The average early morning temperature in Churchill, Manitoba is "-4°C" in October. In January, it is 27°C colder. What is the average early morning temperature in January?
Answers
Answer:
-31 degrees
Step-by-step explanation:
-4-27=-31
Consider the graph of the function f(x) = 10^x
Which statement describes a key feature of function g if g(x) = f(x + 4)
Answers
The statement that describes a key feature of g if g(x) = f(x + 4) and f(x) = 10ˣ is "horizontal asymptote of y = 0". (Correct choice: B)
How to analyze a function resulting from a transformation rule
According to the statement, we have an original function f(x) = 10ˣ and a transformation rule for horizontal translation g(x) = f(x + 4). By applying this rule, we have that g(x) = 10ˣ ⁺ ⁴, which have these features:
The y-intercept of g(x) is located at (0, 10000).Horizontal asymptote of g(x) is y = 0.There are no x-intercepts.Therefore, the statement that describes a key feature of g if g(x) = f(x + 4) and f(x) = 10ˣ is "horizontal asymptote of y = 0". (Correct choice: B)
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The arithmetic-geometric mean (AM-GM) inequality: if a,b ≥ 0, then [tex]\frac{a+b}{2} \geq \sqrt{ab}[/tex]. (1)
(a) Let a, b, c, d ≥ 0 and consider the positive real numbers [tex]\sqrt{ab} [/tex] and [tex]\sqrt{cd} [/tex]. Use (1) to prove the four-variable AM-GM inequality:
[tex]\frac{a+b+c+d}{4} \geq \sqrt[4]{abcd}[/tex]. (2)
(b) Let a, b, c ≥ 0 and define [tex]m= \frac{a+b+c}{3}[/tex].
(i) Show that [tex]m=\frac{a+b+c+m}{4}[/tex].
(ii) Hence use (2) to prove the three-variable AM-GM inequality:
[tex]\frac{a+b+c}{3} \geq \sqrt[3]{abc}[/tex].
Answers
(a) The inequality follows from the binomial theorem.
[tex](a - b)^2 = a^2 - 2ab + b^2 \ge 0 \implies a^2 + 2ab + b^2 = (a+b)^2 \ge 4ab \\\\ \implies \dfrac{(a+b)^2}4 \ge ab \\\\ \implies \dfrac{a+b}2 \ge \sqrt{ab} ~~~~~~~~ (1)[/tex]
By the same reasoning,
[tex]\dfrac{c+d}2 \ge \sqrt{cd}[/tex]
Adding these results together, we have
[tex]\dfrac{a+b}2 + \dfrac{c+d}2 = \dfrac{a+b+c+d}2 \ge \sqrt{ab} + \sqrt{cd}[/tex]
and since [tex]\sqrt{ab}[/tex] and [tex]\sqrt{cd}[/tex] are both positive, they also satisfy the AM-GM inequality,
[tex]\dfrac{\sqrt{ab} + \sqrt{cd}}2 \ge \sqrt{\sqrt{ab}\times\sqrt{cd}} = \sqrt[4]{abcd}[/tex]
and the 4-variable result follows,
[tex]\dfrac{a+b+c+d}2 \ge 2\times\dfrac{\sqrt{ab}+\sqrt{cd}}2 \ge 2 \sqrt[4]{abcd} \\\\ \implies \dfrac{a+b+c+d}4 \ge \sqrt[4]{abcd} ~~~~~~~~ (2)[/tex]
(b.i) With [tex]m=\frac{a+b+c}3[/tex], we have
[tex]\dfrac{3m}4 = \dfrac{a+b+c}4 \implies m - \dfrac m4 = \dfrac{a+b+c}4 \\\\ \implies m = \dfrac{a+b+c+m}4[/tex]
(b.ii) From (2) it follows that
[tex]\dfrac{a+b+c+m}4 \ge \sqrt[4]{abcm} = \sqrt[4]{abc\times\dfrac{a+b+c+m}4}[/tex]
Using the result from (b.i), this is equivalent to
[tex]\dfrac{a+b+c}3 \ge \sqrt[4]{abc\times\dfrac{a+b+c}3}[/tex]
Take 4th powers on both sides.
[tex]\left(\dfrac{a+b+c}3\right)^4 \ge abc \times \dfrac{a+b+c}3[/tex]
Divide both sides by [tex]\frac{a+b+c}3[/tex].
[tex]\left(\dfrac{a+b+c}3\right)^3 \ge abc[/tex]
Finally, take the cube root of both sides.
[tex]\dfrac{a+b+c}3 \ge \sqrt[3]{abc}[/tex]
as required.
9. If f(x)=x². g(x)=2x-1. and h(x) =find the following.
Answers
Answer:
Please see the attached picture ! :D
-------- HappY LearninG <3 ----------
Leigh earned the following score from the judges for her balance bean routine. 9.20 9.30 9.20 9.30 9.20 9.00. Q2 cross off the lower score and the highest score
Answers
Answer: I am not so sure but I think it’s asking for the median so that would be ANSWER 9.2
Step-by-step explanation:
f= 2/T + 5 solve for t
Answers
Answer: [tex]T=\frac{2}{F-5}[/tex]
Step-by-step explanation:
[tex]F=\frac{2}{T}+5\\\\F-5=\frac{2}{T}\\\\\frac{1}{F-5}=\frac{T}{2}\\\\T=\frac{2}{F-5}[/tex]
find x and y !!!!!!! pls help 50 points !!
Answers
Answer:
x = 15
y = 60
Step-by-step explanation:
Angles (x + 50) and (3x + 20) follows corresponding angle theorem.
corresponding angles are equal to each other.-----
⇒ x + 50 = 3x + 20
⇒ x - 3x = 20 - 50
⇒ -2x = -30
⇒ x = 15
The angles (x + 50) and (2y - 5) lies on a straight line which sum ups to 180°
⇒ (x + 50) + (2y - 5) = 180
⇒ 2y + x + 45 = 180
⇒ 2y + 15 + 45 = 180
⇒ 2y + 60 = 180
⇒ 2y = 120
⇒ y = 60
Which numbers should replace the question marks?
Answers
The first missing number in the sequence is 35, and the last missing number is 77.
Next number of the given sequenceThe two missing numbers in the given sequence is calculated as follows;
= ? 49 63 ?
The given sequence is factor 7 which increases by 2
= 7 x 5 7 x 7 7 x 9 7 x 11
= 35 49 63 77
Thus, the first missing number in the sequence is 35, and the last missing number is 77.
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The sequence's initial missing number is 35, and its last missing number is 77.
The following number in the list is
The two missing numbers are determined as follows for the given sequence:
= ? 49 63 ?
The sequence is factor 7, which rises by 2 in the specified order.
= 7 x 5 7 x 7 7 x 9 7 x 11
= 35 49 63 77
Thus, the first missing number in the sequence is 35, and the last missing number is 77.
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How many Squares are there ?
Answers
Answer:
6
Step-by-step explanation:
most of them are rectangles
Explain how to solve a system of equations using the addition method. Use 3x - 4y=12 and 2x+y=8 to illustrate.
Answers
The solution to the equations 3x - 4y=12 and 2x+y=8 are x = 4 and y = 0
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have two equations:
3x - 4y=12 and
2x+y=8
Multiplu by 4 on both side in equation 2x+y=8
8x + 4y = 32
Add the equaton 8x + 4y = 32 and 3x - 4y=12
3x - 4y=12
8x + 4y = 32
11x = 44
x = 4
Similarly, we can find the value of y:
y = 0
Thus, the solution to the equations 3x - 4y=12 and 2x+y=8 are x = 4 and y = 0
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According to the food and nutrition service of the u.s. department of agriculture, in one school year, the national school lunch program (NLP) served 31.2 million school lunches. of these, 16.1 million were free lunches, 3.2 million were reduced-price lunches, and 11.9 million were full-price lunches. the federal government reimburses school districts $2.68 for each free lunch, $2.28 for each reduced-price lunch, and $0.25 for each paid lunch. in addition to cash reimbursements, schools are entitled to receive USDA foods called "entitlement" foods at a value of 19.50 cents for each lunch served. you are the administrator in charge of the school lunch program for your school district. last month, the schools in your district served 27,000 free lunches, 18,000 "reduced-price" lunches, and 54,000 regular-priced lunches. (a) calculate the amount of reimbursement (in $) you expect to receive from the nslp for last month. $____. (b) in addition to the lunch reimbursement, the nslp program pays your district $.035 per one-half pint of milk served with each meal. if each student averaged 1 one-half pint of milk per meal, calculate the total amount of milk reimbursement (in $) you expect for last month. $_____ . (c) the bottom line—what is the total amount of reimbursement (in $) your district will receive for last month? $_______. (d) red tape—the government paperwork you must submit requires that you report the average reimbursement (in $) per meal for both lunch and milk combined last month. calculate this amount. (round your answer to the nearest cent.) $________.
Answers
a) The amount of meal reimbursement (in $) you expect to receive from the NSLP for last month is $146,205.
b) The total amount of milk reimbursement (in $) you expect for last month is $103,950.
c) The total amount of reimbursement (in $) your district will receive for last month is $250,155 ($146,205 + $103,950).
d) The average reimbursement (in $) per meal for both lunch and milk combined last month is $2.53 ($250,155/99,000).
What is reimbursement?Reimbursement is a process by which an entity is compensated for the expenses it incurs under a stated program.
Examples of expenses under the reimbursement policy include business expenses, insurance costs, and overpaid taxes.
Data and Calculations:Annual NSLP lunches = 31.2 million
Lunches Free Reduced Price Full-Price Total
National Quantity 16.1 million 3.2 million 11.9 million 31.2 million
District Lunches 27,000 18,000 54,000 99,000
Reimbursement rate $2.68 $2.28 $0.25 $0.195
Reimbursement $72,360 $41,040 $13,500 $19,305
Total reimbursement = $146,205 ($72,360 + $41,040 + $13,500 + $19,305)
Amount for milk reimbursement = $103,950 ($0.35 x 1.5 x 2 x 99,000)
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What linear function represents the sequence 8,3,-2,-7
Answers
X=-5
Explanation:
In simplicity, the numbers go down by 5, and therefore you subtract 5 each time.
Algebraically, adding negative 5 to each number lowers it by five.
Hope that helps.
Linear model function
Answers
Using equations of linear model function, the number of hours Jeremy wants to skate is calculated as 3.
How to Write the Equation of a Linear Model Function?The equation that can represent a linear model function is, y = mx + b, where m is the unit rate and b is the initial value.
Equation for Rink A:
Unit rate (m) = (35 - 19)/(5 - 1) = 16/4 = 4
Substitute (x, y) = (1, 19) and m = 4 into y = mx + b to find b:
19 = 4(1) + b
19 - 4 = b
b = 15
Substitute m = 4 and b = 15 into y = mx + b:
y = 4x + 15 [equation for Rink A]
Equation for Rink B:
Unit rate (m) = (39 - 15)/(5 - 1) = 24/4 = 6
Substitute (x, y) = (1, 15) and m = 6 into y = mx + b to find b:
15 = 6(1) + b
15 - 6 = b
b = 9
Substitute m = 6 and b = 9 into y = mx + b:
y = 6x + 9 [equation for Rink B]
To find how many hours (x) both would cost the same (y), make both equation equal to each other
4x + 15 = 6x + 9
4x - 6x = -15 + 9
-2x = -6
x = 3
The hours Jeremy wants to skate is 3.
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What is the product of the polynomials below?
(5x²-x-3)(2x+6)
OA. 10x² +28x² +12x+3
OB. 10x³ +28x2² -12x-18
OC. 10x²+28x²-12x-3
OD. 10x² +28x² + 12x+18
Answers
Answer: B
Step-by-step explanation:
[tex](5x^2 -x-3)(2x+6)\\\\=2x(5x^2 - x-3)+6(5x^2 - x-3)\\\\=10x^3 - 2x^2 - 6x+30x^2 - 6x-18\\\\=\boxed{10x^3 +28x^2 - 12x-18}[/tex]
find 2^-6 as a fraction
Answers
Answer:
1/64Step-by-step explanation:
find 2^-6 as a fraction
2^-6 = 0.015625
0.015625 as a fraction
(0.015625/1) × (1000000/1000000) =
15625/1000000
simplified = 1/64.
[tex]\frak{Hi!}[/tex]
[tex]\orange\hspace{300pt}\above2[/tex]
Let's find [tex]\boldsymbol{\sf{2^{-6}}}[/tex] as a fraction
Did you know that if we have a number with negative
exponents, we flop it over? This is how it's done-:
[tex]\boldsymbol{\sf{2^{-6}=\displaystyle\frac{1}{2^6}}}[/tex]. And Now we need to evaluate
[tex]\boldsymbol{\sf{\displaystyle\frac{1}{64}}}[/tex].
done!!
[tex]\orange\hspace{300pt}\above3[/tex]
The speed of light is approximately 299,000,000 meters per second.
What is the speed of the light, in meters per second, using scientific notation?
Answers
Answer:
2.99 x 10⁸ meters per second
Step-by-step explanation:
Scientific notation (also called "Standard form") is written in the form of [tex]a \times 10^n[/tex], where [tex]1\leq a < 10[/tex] and [tex]n[/tex] is any positive or negative whole number.
To convert a number into scientific notation, move the decimal point to the left or right until there is one digit before the decimal point.
The number of times you have moved the decimal point is the power of 10 ([tex]n[/tex]).
If the decimal point has moved to the left, the power is positive.
If the decimal point has moved to the right, the power is negative.
To convert the given number to scientific notation
The decimal point for the given number 299000000 is after the last zero:
⇒ 299000000.
Move the decimal point 8 places to the left:
⇒ 2.99000000
Get rid of the redundant zeros:
⇒ 2.99
Multiply by 10 to the power of the number of decimal places moved:
⇒ 2.99 x 10⁸
Therefore, the speed of light using scientific notation is:
2.99 x 10⁸ meters per second
• What sorts of follow up questions about the statistics might you ask that person in order to obtain the
data needed to make a decision about the validity of that statement? Be sure to use concepts and
vocabulary from this week to guide your response.
Answers
The type of follow-up questions that can be asked to obtain the data needed to make a decision about the validity of that statement are:
How was the data obtained?Was the experiment controlled?How large were the control group and the placebo group?Was it a blind/double-blind test?Were extreme outliers removed from the data before running the experiment?What are Follow-Up Questions?This refers to the type of questions that are asked to a person in order to get extra information about a topic.
Hence, we can see that from the complete question, there is the need to perform tests to get results which would involve the procurement of data, controlled experiments, etc, and the follow-up questions that can be used are given above.
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the entire school went 250 students went to the soap box derby the math club went in 2 busses each holding 6 students
Answers
The number of students from the math club that went to the soap box derby.
How to solve algebra word problems?From the question, we see that there are two vans and 6 students in each van.
Thus, to get the number of students from the math club that went to the soap box derby, we will solve as follows;
Number of students that went to derby = 2 × 6 = 12
Complete question is;
The entire school 250 students went to the soap box derby. The math club went in 2 vans and each van held 6 students how many students from the math club went to the soap box derby
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Jesse wants to gift wrap a cylindrical pencil case that has a radius of 1.5 inches and a height of 8 inches. What is the area of the paper she will need to cover the entire surface?
Answers
Answer:
Jesse will need about 89.5 square inches of gift wrap.
Step-by-step explanation:
We need to find the amount of wrapping paper that will cover the entire outside surface of the cylindrical gift. This means that we need to find its surface area, which is the total area an object's surface occupies.
The formula for cylinder surface area is as follows:
[tex]A=2\pi rh+2\pi r^{2}[/tex] (where r = radius and h = height)
In this case, the radius, or r, is 1.5 in, and the height, or h, is 8 in. Plugging these values into our formula, we get a total surface area of:
[tex]A=2\pi rh+2\pi r^{2}\\= 2\pi *1.5*8+2\pi * 1.5^{2} \\= 24\pi +4.5\pi \\=28.5\pi \\ \approx \text{\bf 89.5 \bf $in^{2}$ }[/tex]
Hope this helps!
Answer:
28.5 pi square inches
Step-by-step explanation:
The surface area of a cylinder is the lateral area plus two times the area of the base circle. The lateral area is the perimeter of the base circle times the height, and the perimeter of a circle is 2*pi*r.
Therefore the lateral area is:
LA = Perimeter*Height
= 2*pi*r*h
= 2*pi*1.5*8
= 24pi
The base area would be A = pi*r*r since the bases of cylinders are circles.
BA = pi*r*r
= pi*1.5*1.5
= 2.25 pi
Since there are two circles (top AND bottom) in a cylinder, the final surface area of the cylinder would be:
SA = LA + 2BA
= 24pi + 2*2.25pi
= 24pi + 4.5pi
= 28.5 pi
solve (x - 3)^2 = 5 p
please help
Answers
Hello!
Let's solve !
⇒ (x - 3)² = 5
⇒ x² - 6x + 9 = 5
⇒ x² - 6x + 4 = 0
⇒ x = -(-6) ± √36 - 4(1)(4) / 2
⇒ x = 6 ± √20 / 2 = 6 ± 2√5 / 2
⇒ x = 3 ± √5
∴ The solutions are x = 3 + √5 and x = 3 - √5.
Answer:
p=(x−3)25
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(x-3)^2-(5*p)=0
STEP1:
1.1 Evaluate : (x-3)2 = x2-6x+9
Equation at the end of step1:
x2 - 6x - 5p + 9 = 0
STEP2:
Solving a Single Variable Equation:
2.1 Solve x2-6x-5p+9 = 0
Find the amount of simple interest earned for depositing the given principle in an account.
P
=
P
=
$7600
r
=
r
=
8.5%
t
=
t
=
4 months
Answers
Answer:
kkrg=u/d
-678/09
=12 ans
If cos(x)=-4/5 in quadrant II then determine the following sin(x/2),cos(x/2),tan(x/2)
Answers
Answer:
[tex]sin(\frac{143.13}{2} )=0.9487\\\\cos(\frac{143.13}{2} )=0.3162\\\\tan(\frac{143.13}{2} )=2.9999=3\\[/tex]
Step-by-step explanation:
angles in II quadrant are found by solvig 180- ∅ where ∅ is the acute angle
Let us then find the acute angle: in[tex]cos^{-} (\frac{4}{5}) = 36.86^{0} \\\\so \ x \ the \ angle \ in \ the \ second \ quadrant \ is \ 180-36.86=143.13^{0} \\\\sin(\frac{143.13}{2} )=0.9487\\\\cos(\frac{143.13}{2} )=0.3162\\\\tan(\frac{143.13}{2} )=2.9999=3\\[/tex]
expressions is equivalent
to a(b-c)-b(a+c)-c(a-b)?
Answers
After solving the algebraic expression a(b-c)-b(a+c)-c(a-b) we get the equivalent answer as ₋2(ab ₊ ac).
What is equivalent of algebraic expression?
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Given the expression is a(b₋c)₋b(a₊c)₋c(a₋b)
The first step is to multiply the terms.
⇒(a×b ₋ a×c) ₋ (b×a ₊ b×c) ₋ (c×a - c×b)
= (ab ₋ ac) ₋ (ba ₊ bc) ₋ (ca ₋ cb)
Now open the brackets.
= ab ₋ ac ₋ ba ₋ bc ₋ ca ₊ cb
Now comes main step of combining the like terms.
Put similar terms together on both sides of the equation.The two phrases are equal if each of the terms in both of them is the equivalent.
= ab ₋ ba ₋ ac ₋ ca ₋ bc ₊bc
Since, bc is a like term with opposite sign, therefore bc gets cancelled.
= ab ₋ ba ₋ ac ₋ ca
= ₋2ab ₋ 2ac
Take 2 as a common term from both the terms.
= ₋2(ab ₊ ac)
Hence we get the required equivalent of a(b-c)-b(a+c)-c(a-b) as
₋2(ab ₊ ac)
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2. The graph shows the vertical displacement y, in centimeters, that a weight bouncing from a spring would achieve if there were no friction, for a given number of seconds, x
(a) What is the weight’s maximum displacement?
(b) From its resting position, how long does it take the weight to bounce one direction, then the other, and then return to its resting position?
(c) What is the graph’s frequency and what does it indicate in this situation?
(d) How is the weight moving during the time period x = 6 to x = 7.5?
Answers
(a) The maximum displacement of the wave is 14 cm.
(b) The time for the wave to bounce opposite directions before coming to rest is 3.0 s.
(c) The period of the wave is 3.0 s and the amplitude is 14 cm.
(d) The graph’s frequency is 0.33 Hz
(e) The wave attained maximum displacement at time 6 s and 7.5 s.
How to Interpret period of a wave?A) The maximum displacement of the wave is the point of maximum rise of the curve = 14 cm
B) Time of motion of the wave; This is the time for the wave to bounce opposite directions before coming to rest makes a complete cycle
It takes the wave 0.75s to bounce up and the 2.25 s to bounce down, and finally it came to rest at 3.0 s.
C) The period of the wave is the time taken for the wave to make a complete cycle = 3 s
Frequency of the wave
f = 1/T
f = 1/3 = 0.33 Hz
The frequency indicates the number of cycles in a second.
D) Position of the wave at time 6 s and 7.5 s
The wave attained maximum displacement at time 6 s and 7.5 s.
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