The solution to the given second-order linear homogeneous differential equation is y(t) = e^(-t) * [A * cos(sqrt(9)t) + B * sin(sqrt(9)t)], where A and B are constants determined by the initial conditions.
The given differential equation is a second-order linear homogeneous equation with constant coefficients. To solve it, we assume a solution of the form y(t) = e^(rt), where r is a constant to be determined. Plugging this into the differential equation, we get the characteristic equation r^2 + 2r + 10 = 0.
Solving the characteristic equation, we find two complex conjugate roots: r = -1 ± sqrt(9)i. These roots give rise to a general solution of the form y(t) = e^(-t) * [A * cos(sqrt(9)t) + B * sin(sqrt(9)t)], where A and B are arbitrary constants.
To determine the specific values of A and B, we use the initial conditions. Given y(0) = 7, we substitute t = 0 into the general solution and obtain 7 = A.
Differentiating y(t) with respect to t, we find y'(t) = -e^(-t) * [A * cos(sqrt(9)t) + B * sin(sqrt(9)t)] + e^(-t) * [-A * sqrt(9) * sin(sqrt(9)t) + B * sqrt(9) * cos(sqrt(9)t)].
Plugging t = 0 and y'(0) = 2 into the derived expression, we get 2 = -A + B * sqrt(9). Substituting A = 7 from the previous equation, we find B = 2 + sqrt(9).
Therefore, the solution to the given differential equation with the initial conditions y(0) = 7 and y'(0) = 2 is y(t) = e^(-t) * [7 * cos(sqrt(9)t) + (2 + sqrt(9)) * sin(sqrt(9)t)].
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Solve the inequality. Express the solution both on the number line and in interval notation. Use exact forms (such as fractions) instead of decimal approximations. 3x-4 a) x²-2x-3≥0 b) 6x-2x² > 0 c); ≤0 9x+17
a) The solution to x²-2x-3≥0 is x ≤ -1 or x ≥ 3, expressed in interval notation as (-∞, -1] ∪ [3, ∞).
b) The solution to 6x-2x² > 0 is x < 0 or x > 3, expressed in interval notation as (-∞, 0) ∪ (3, ∞).
c) The solution to 9x+17 ≤ 0 is x ≤ -17/9, expressed in interval notation as (-∞, -17/9].
a) To solve the inequality x²-2x-3≥0, we can factor the quadratic expression as (x-3)(x+1) ≥ 0. We find that the inequality is satisfied when x ≤ -1 or x ≥ 3. The solution is expressed in interval notation as (-∞, -1] ∪ [3, ∞).
b) To solve the inequality 6x-2x² > 0, we can factor out 2x from the expression to get 2x(3-x) > 0. We find that the inequality is satisfied when x < 0 or x > 3. The solution is expressed in interval notation as (-∞, 0) ∪ (3, ∞).
c) To solve the inequality 9x+17 ≤ 0, we isolate x by subtracting 17 from both sides to get 9x ≤ -17. Dividing both sides by 9, we find x ≤ -17/9. The solution is expressed in interval notation as (-∞, -17/9].
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Find the charge on the capacitor in an LRC-series circuit at t = 0.03 s when L = 0.05 h, R = 3.12, C = 0.008 f, E(t) = 0 V, 9(0) = 4 C, and i(0) = 0 A. (Round your answer to four decimal places.) 0.8630 хс Determine the first time at which the charge on the capacitor is equal to zero. (Round your answer to four decimal places).
At t = 0.03 s, the charge on the capacitor in the LRC-series circuit is 0.8630 C.
In an LRC-series circuit, the charge on the capacitor can be calculated using the formula Q(t) = Q(0) * e^(-t/(RC)), where Q(t) is the charge at time t, Q(0) is the initial charge on the capacitor, R is the resistance, C is the capacitance, and e is the base of the natural logarithm.
Given the values L = 0.05 H, R = 3.12 Ω, C = 0.008 F, E(t) = 0 V, Q(0) = 4 C, and i(0) = 0 A, we can substitute these values into the formula. Using the given time t = 0.03 s, we can calculate the charge on the capacitor.
Plugging in the values, we have Q(0.03) = 4 * e^(-0.03/(3.12*0.008)). Evaluating this expression gives us Q(0.03) ≈ 0.8630 C, rounded to four decimal places.
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The integral ſ sin(x - 2) dx is transformed into ', g(t)dt by applying an appropriate change of variable, then g(t) is: g(t) = cos (33) g(t) = sin (5) This option This option g(t) = cos (3 g(t) = sin This option
The integral oſ sin(x - 2) dx is transformed into g(t)dt by applying an appropriate change of variable is g(t) = sin(t).
To transform the integral ∫sin(x - 2) dx into the form ∫g(t) dt using a change of variable, we can let u = x - 2.
Then, differentiating both sides with respect to x gives du = dx.
Substituting these values in the integral, we have:
∫sin(x - 2) dx = ∫sin(u) du
The integral has now been transformed into the integral of sin(u) with respect to u, denoted as g(t) dt.
Therefore, g(t) = sin(t).
So, the correct option is g(t) = sin(t).
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Help me please with this problem!!
Answer:
139°
Step-by-step explanation:
Corresponding angles theorem:
When a transversal line intersects two parallel lines, the angles formed from the intersection are congruent in pairs. For example with your problem, using the Corresponding Angles Theorem (one of the few theorems/postulates used to find angles on transversals), the angles are paired on the same place on the first parallel line as they are on the second. Since the corresponding pair of (x)° is given, the angle of x is given. (x)° = 139°
I've provided an image courtesy of tutors.com that will help remember corresponding angles for you.
Help on here too plz there’s more in my acc I need help on all
task 1
Find the surface area of the Trumpet.
The surface area of the trumpet is [tex]\( 1256.64 \pi \)[/tex] square feet.
To find the surface area of the trumpet, we need to calculate the areas of the curved surface and the base separately, and then sum them.
The curved surface area of a truncated cone can be calculated using the formula:
[tex]\[ CSA = \pi \times (r_1 + r_2) \times l \][/tex]
Where [tex]\( r_1 \) and \( r_2 \)[/tex] are the radii of the two bases, and [tex]\( l \)[/tex] is the slant height of the truncated cone.
Given that the base diameter is [tex]40[/tex] feet, the radius of the larger base [tex](\( r_1 \))[/tex] is half of that, which is [tex]20[/tex] feet. The slant height [tex](\( l \))[/tex] can be calculated using the Pythagorean theorem:
[tex]\[ l = \sqrt{(h^2 + (r_1 - r_2)^2)} \][/tex]
The height [tex]h[/tex] of the truncated cone is [tex]30[/tex] feet, and the radius of the smaller base [tex](\( r_2 \))[/tex] can be calculated as half the diameter, which is [tex]10[/tex] feet.
Substituting the values into the equations:
[tex]\[ l = \sqrt{(30^2 + (20 - 10)^2)} = \sqrt{(900 + 100)} = \sqrt{1000} = 10\sqrt{10} \]\[ CSA = \pi \times (20 + 10) \times (10\sqrt{10}) = 30\pi\sqrt{10} \][/tex]
The base area of the truncated cone is the area of a circle with radius [tex]\( r_1 \):\[ BA = \pi \times r_1^2 = \pi \times 20^2 = 400\pi \][/tex]
Finally, we can find the total surface area by adding the curved surface area and the base area:
[tex]\[ Surface \, Area = CSA + BA = 30\pi\sqrt{10} + 400\pi \][/tex]
[tex]\[ Surface \, Area = 30\pi\sqrt{10} + 400\pi \]\[ Surface \, Area = \pi(30\sqrt{10} + 400) \]\[ Surface \, Area \approx 1256.637 \pi \]\[ Surface \, Area \approx 1256.64 \pi \][/tex]
Therefore, the simplified surface area of the trumpet is approximately [tex]\( 1256.64 \pi \)[/tex] square feet.
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cars that are ready for shipping weigh 2 tons. a car being built weighs 1,135 pounds. how much more weight, in pounds, will be added to the car so it will be ready for shipping!?!
Let D be the region bounded by the two paraboloids z = 2x2 + 2y2 – 4 and z=5 - x2 - y2 where x > 0 and y > 0. Which of the following triple integral in cylindrical coordinates allows us to evaluate the volume of D? - √3 5-2 Salon dzdrde None of thes
Option D is the correct choice.
To evaluate the volume of D, the triple integral in cylindrical coordinates is required. So, let's derive the required triple integral.
Region D is bounded by two paraboloids z = 2x2 + 2y2 - 4 and z = 5 - x2 - y2 where x > 0 and y > 0.
In cylindrical coordinates,r = √(x^2 + y^2)z = zθ = tan-1(y/x)For the first paraboloid, the cylindrical equation of the paraboloid is: z = 2x2 + 2y2 - 4
By substituting the cylindrical coordinates values in this equation we get z = 2r2 sin2θ + 2r2 cos2θ - 4z = 2r2 (sin2θ + cos2θ) - 4z = 2r2 - 4 Now for the second paraboloid, the cylindrical equation of the paraboloid is: z = 5 - x2 - y2By substituting the cylindrical coordinates values in this equation we get:z = 5 - r2 The limits of r are 0 and √5; and the limits of θ are 0 and π/2.
Finally, the limits of z are obtained by equating the above two paraboloids.2r2 - 4 = 5 - r22r2 + r2 = 9r2 = 3z = 3We have got all the limits of cylindrical coordinates, we can now write the triple integral in cylindrical coordinates which evaluates the volume of D.
The triple integral is:∫(0 to π/2)∫(0 to √5)∫(2r2 - 4 to 3) r dz dr dθ
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Write your answer in simplest form 11/12- 3/4
Answer: 1/6 is its simplest form :)
Using the rate of Rs 105 per US Dollar, calculate
the US Dollars for Rs 21000.
Answer:
Hey Aryabd interested to talk with me. Come in comments.
The US Dollars for Rs 21000 would be 200 USD
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that the rate of Rs 105 per US Dollar,
We have to calculate the US Dollars for Rs 21000.
105 Rs = 1 USD
21000 Rs = x USD
Now the proportion can be;
105x =21000
x =21000 /105
x= 200 USD
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A 20-inch television screen has a width of 12 inches. What is the length of the television screen?
helppppppppppp meeeeeeeeeee
Answer:
It's 11.72
Step-by-step explanation:
Area=)1/2×15/4×25/4
Answer》11.72
Hope it helps...
Have a great day
Answer:
i have made it in above picture
Cindy lost 28 pounds while on a diet. She now weighs 157 pounds. Write and solve an equation to find her initial weight
Answer:
The equation is 157+28=185.
157+ 28= 185
I think that’s right
A small internet trading company estimates that each network blackout results in a $500 loss. Compute expectation and variance of this company’s daily loss due to blackouts.
x = 0, 1, 2
Px = 0.7, 0.2, 0.1
The expectation (mean) of the company's daily loss due to blackouts is $200, and the variance is $350.
To compute the expectation of the company's daily loss, we multiply each possible loss value by its corresponding probability and sum them up. In this case, we have three possible loss values (0, 1, and 2) with their respective probabilities (0.7, 0.2, and 0.1). Multiplying each loss value by its probability and summing them gives us the expected value of $200.
To calculate the variance, we need to find the squared differences between each possible loss value and the expected value, multiply them by their respective probabilities, and sum them up. Squaring the differences ensures that negative differences do not cancel out positive differences. In this case, the variance is calculated as (0 - 200)^2 * 0.7 + (1 - 200)^2 * 0.2 + (2 - 200)^2 * 0.1, resulting in a variance of $350.
The expectation and variance provide useful measures of the central tendency and variability, respectively, of the company's daily loss due to blackouts.
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For matrices: A = -1-41] 0 2 2 2 30] B = 33 -1 2 A. What is the dimension of A and B? B. What is the dimension of A B? C. What is A'B?
A. the dimension of A is 3x3. the dimension of B is 3x2.
B. the dimension of AB will be 3x2.
C. The value of AB = [[ -15 14] [ 4 -2] [ 13 -9]]
A. The dimension of a matrix is given by the number of rows and columns it has.
For matrix A, we have:
A = [[-1 -4 1], [0 2 2], [2 3 0]]
The matrix A has 3 rows and 3 columns, so the dimension of A is 3x3.
For matrix B, we have:
B = [[2 0], [3 -3], [-1 2]]
The matrix B has 3 rows and 2 columns, so the dimension of B is 3x2.
B. To multiply two matrices, the number of columns in the first matrix must be equal to the number of rows in the second matrix. In this case, A has 3 columns and B has 3 rows, so we can multiply them.
The dimension of AB will be the number of rows of A and the number of columns of B. Therefore, the dimension of AB will be 3x2.
C. [-1 -4 1] * [2 0]
[0 2 2] [3 -3]
[2 3 0] [-1 2]
[-2-12-1 0+12+2]
= [0+6-2 0-6+4]
[4+9+0 0-9+0]
[ -15 14]
= [ 4 -2]
[ 13 -9]
The value of AB = [[ -15 14] [ 4 -2] [ 13 -9]]
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Given question is incomplete, the complete question is below
For matrices: A =[[ -1 -4 1] [0 2 2][ 2 3 0]] B =[[2 0] [3 -3 ][-1 2] ]
A. What is the dimension of A and B?
B. What is the dimension of A*B?
C. What is A*B?
Triangle CDE, with vertices C(-8,-7), D(-2,-8) and E(-5,-2), is drawn on the coordinate grid below.
What is the area, in square units, of triangle CDE?
Answer:
Area = 24.75 sqr units
Step-by-step explanation:
You will need these formulas:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
Midpoint = [tex](\frac{x_{1} + y_{1} }{2} , \frac{x_{2} + y_{2} }{2})[/tex]
Area = b x h
Let us treat CD as the base. Find the length of the base with the distance formula. Use the coordinates for points C & D.
[tex]d = \sqrt{(-2 - (-8))^2 + (-8-(-7))^2}[/tex]
[tex]d = \sqrt{37}[/tex]
The base is [tex]\sqrt{37}[/tex].
The height is the distance between point E and the midpoint of line CD.
Midpoint of CD = [tex](\frac{-8 + (-7) }{2} , \frac{-2 + (-8) }{2})[/tex] = ([tex]-\frac{15}{2}[/tex], [tex]-5[/tex])
Use the distance formula to find the height.
[tex]d = \sqrt{(-5 - (-\frac{15}{2} ))^2 + (-2-(-5))^2}[/tex]
[tex]d = \frac{\sqrt{61} }{2}[/tex]
Find the area with the two distances that were found.
Area = [tex](\sqrt{37}) (\frac{\sqrt{61} }{2})[/tex]
Area = [tex]\frac{\sqrt{2257} }{2}[/tex]
Area = 24.75 sqr units
You must estimate the mean temperature (in degrees Fahrenheit)
with the following sample temperatures:
79.5
102.8
80.8
76.8
80.4
79.2
86
67.7
Find the 98% confidence interval. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place). * Answer should be obtained without any preliminary rounding.
98% C.I. =
The interval value at 98% confidence level for the given scenario is (73.51 ; 89.79)
From the data :
Mean(x) = (79.5+102.8+80.8+76.8+80.4+79.2+86+67.7)/8
Mean = 81.65
Sample standard deviation :
s = √[(x1 - mean)² + (x2 - mean)² + ... + (x(n) - mean)²] / n
Using a statistical calculator :
s = 9.98
The confidence interval is defined thus :
Mean ± Tcritical × s/√n
Tcritical at 98% = 2.306
Substituting values into the formula :
81.65 ± (2.306 × 9.98/√8)
81.65 ± 8.137
(73.51, 89.79)
Therefore, the confidence interval for the given scenario is (73.51 ; 89.79)
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PLEASE HELP!!
In a right triangle, the length of one of the sides is 13.7, while one of the other sides measures 14.3. Find the length of the hypotenuse.
The length of the hypotenuse is approximately 19.8 units.
In a right-angled triangle, the hypotenuse is the longest side, and it is opposite to the right angle. To find its length, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Therefore, we have:
h^2 = 14.3^2 + 13.7^2
h^2 = 204.49 + 187.69
h^2 = 392.18
h = sqrt(392.18)
h ≈ 19.8
We can round the answer to one decimal place, as this is the nearest level of precision to the data provided. Note that for a right-angled triangle, the hypotenuse is always the longest side, so it makes sense that the hypotenuse is longer than both of the other sides in this case.
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please help please it would me me sm <3
Answer:
25
Step-by-step explanation:
4x25=100
100-25=75 degrees
Answer:
25°
Step-by-step explanation:
(4x-25)=75
4x=100
x=25
HELPPP PLSSSS ASAPP What is the slope of the line below? If necessary, enter your answer as a
fraction in lowest terms, using the slash (/) as the fraction bar. Do not enter
your answer as a decimal number or an equation.
(2,2) (-1,-4)
Answer:
2
Step-by-step explanation:
The formula to find the slope given 2 points is y2-y1/x2-x1. Now lets plug in the numbers. (2,2) is the first set of points and (-1,-4) is the second set of points. So we have -4-2/-1-2. We have -6/-3. Now we must simplify, giving us 2.
Please someone help with this
I’v been stuck on it all day
By the way I have already been sent that link that hacks you
Just show the work
ok, i will help you.
For the first equation, we have points
(-1, -4)
and
(1, -1)
we also know the y-intercept is
(0, -2)
we can make systems of equations to solve for the equation of this exponiental function
y=ab^x
-1=ab
-2=a*1
a=-2
-1=-2(b)
b=1/2
The exponiental fufnction here is y=(-2)(1/2)^x
2nd equation
(0, 6)
(1, 12)
12=ab
6=a*b^0=6
a=6
12=6(b)
b=2
2nd equation is
y=6(2)^x
what is the equation of the line that passes through the point (-6,-6) and has a slope of 2/3?
Answer:
-6=2/3*-6
Step-by-step explanation:
y=mx+b
slope = m b=y intercept
What is (-49(49 x 5982+3)^2
Answer:
[tex] - 49 \times (49 \times 5982 + 3) {}^{2} \\ = - 49 \times 85919920641 \\ = - 4,210,076,111,409[/tex]
What do you know about a triangle with an adjacent leg to hypotenuse ratio value of 0.839?
Step-by-step explanation:
Use soh cah toa to solve
it is cos(α)=.839
so the angle of α is 32.9653
Hope that helps :)
Trigonometric identity is cosine. And a is 32.965327740597°.
What are the trigonometric identities?
Equations using trigonometric functions that hold true for all possible values of the variables are known as trigonometric identities.
Given:
A triangle with an adjacent leg to hypotenuse ratio value of 0.839.
Assume the triangle is a right-angled triangle.
In the right-angled triangle,
the ratio of adjacent leg to hypotenuse is cosine.
So,
Cos(a) = Adjacent leg/Hypotenuse
Cos(a) = 0.839
a = Cos⁻¹(0.839)
a = 32.965327740597°
Therefore, angle measure of a is 32.965327740597°.
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The science and technology class is studying robotics. One group builds a robot that can be controlled by entering positive and negative numbers into a control unit. Negative numbers make the robot roll backwards a specific number of inches. Positive numbers make it move forward a certain number of inches. For example, if −5 is entered, then the robot moves backwards 5 inches. The students enter the numbers −37, +22, and −16. What number do they need to enter to make the robot return to its original position of 0?
To achieve this, the students must enter +31 (forward) to bring the robot back to its starting position of 0.
The robot can move forward or backward depending on the type of number entered into the control unit. For example, entering a negative number causes the robot to roll backward a specific number of inches,
while entering a positive number makes it move forward a certain number of inches. If −5 is entered, the robot moves backwards by 5 inches. As a result, the students entered the numbers −37, +22, and −16 to move the robot.
The question asks what number needs to be entered to bring the robot back to its starting position of zero. To do so, we must first calculate how far the robot has traveled in total.
When a negative number is entered into the control unit, the robot rolls backward.
As a result, when we add the negative numbers and subtract them from the positive number,
we can determine the total distance traveled by the robot.-37 (back) + 22 (forward) - 16 (back) = -31 (inches traveled)Since the robot moved a total of 31 inches,
the students must enter the opposite number to bring the robot back to its starting position of 0.
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Help Please! Find The Area Of A Circle With D=8.2
Answer:
52.81
Step-by-step explanat
1. What is the domain of
f (x)= 9 - x?
Answer:
theres no answer
Step-by-step explanation:
1. The values, x in a sample of 15 are summarized as follows
Σ(x-c) = 72,Σ(x-c)2 = 499.6
where c is a constant. Given that the sample mean is 104.8.
(a) Find the value of constant c.
(b) Find the variance of x.
Answer:
(a) 100
(b) 10.27
Step-by-step explanation:
We are given
No of elements = 15
Σ(x-c) = 72,Σ(x-c)^2 = 499.6
,where c is a constant
and the sample mean is 104.8.
(a) lets take into account Σ(x-c) = 72
this means that we have the sum of the 15 elements of x and each element of x is subtracted by the constant c
so the equation becomes Σxi -15c = 72, ............(1)
where xi means the sum of the elements of x from 1 to 15.
we are given the mean as 104.8
this means that Σxi/15 = 104.8
Σxi = 15*104.8 = 1572 .............(2)
substituting (2) in (1)
we get
1572 - 15c = 72
15c = 1500
c = 100
(b) We will use the property that variance does not change when a constant value is added or subtracted to the elements. This we can observe in the given equation that c is a constant that has the value of 100.
so the variance is
σ^2 = Σ(x-c)^2/15 - (Σ(x-c)/15 )^2
= 499.6/15 - (72/15)^2
= 33.31 - 23.04
σ^2 = 10.27
Therefore the variance of the given problem is 10.27.
I NEED HELP
Please write the right answer
Your portfolio must include a minimum of the following five types of equations and solutions:
Two one-step equations
Two equations that contains fractions
One equation with distributive property
One equation with decimals
One real-world problem that is solved by an equation
Remember that each equation must include at least one variable. Once you have created each equation, you will solve it and show your work. Pretend that you are teaching the equations to a new pre-algebra student. Or you can actually teach them to a sibling or friend!
This is a total of 7 equations and solutions.
Answer:
1). (x - 4 = 13)
2). (r + 17 = 51)
3). (7/9x =28)
4). (2/3x = 2)
5). { 3(x-2) = -9 }
6). (x -1.75 = 8.85)
7). Natalie buys organic almonds priced at $77 from the grocery store. How much did
she pay the cashier, if she received $23 in change?
Step-by-step explanation:
1. add 4 on both sides and it will be x=17
2. subtract 17 on both sides and it will be x= 34
3. multiply 9/7 on both sides and it will be x= 257/7 then you divide 257 by 7 then the final answer will be x= 36
4. multiply 3/2 on both sides and it will be x=6/2 then you divide 6 from 2 and the finial answer will be x= 3
5. you will distribute 3 into x and 2 and you will be 3x-6=-9 then you will add 6 on both sides so you will get 3x=3 and then divide 3 on both side so you will get x=1
6. add 1.75 on both sides so x= 10.6
7. the equation will be 23 +x = 77 so first you will subtract 23 on both sides and x will equal 54 so Natalie paid $54
Answer:
i'm taking that test rn
Step-by-step explanation:
BRAINLY TO WHOEVER HELPS AND GETS IT RIGHT
~no links pls~
Answer:
the answer is C
Step-by-step explanation:
BABYSHARK
Answer:
I think its c?
Step-by-step explanation:
Hope this helps and have a wonderful day!!!