What is the value of x in the equation 8x - 2y = 48, when y = 4?
O 6
07
O 14
O 48

Hooke’s law states that the amount of deformation produced in an object is proportional to the force applied to it. Hooke’s law formula is

F=kx, where F is the force applied, x is the displacement produced, and k is the force constant.

a) Knowing F and x, solve for the force constant k:

F=kxF=800 N, x=−0.0120 mk=800 N/-0.0120 m=-66667 N/m.

The force constant k is -66667 N/m.b).

The maximum velocity (v) of the car can be calculated using the formula:

v=√(k/m) × A

where k is the force constant,

m is the mass of the car, and

A is the amplitude of the motion.

Amplitude, A=0.100 m

Mass of car, m=800 kg

Force constant, k=66667 N/mv=√(66667 N/m ÷ 800 kg) × 0.100 m = 2.31 m/s.

Therefore, the maximum vertical velocity of the car when it hits the bump and bounces with an amplitude of 0.100 m is 2.31 m/s if we assume no damping occurs.

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Answer:

Your answer is 180

Step-by-step explanation:

180 x 5 = 900

There are a total of 12870 paths that stay outside or on the boundary of the square.

To go from (-4, -4) to (4, 4) with each step increasing either the x-coordinate or the y-coordinate by 1, you can only move diagonally upwards or diagonally to the right. This means that you can only move in one of two directions at each step.

In order to stay outside or on the boundary of the square -2 < x < 2, -2 < y < 2 at each step, you need to make sure that you don't move too far in either direction. Since there are 16 steps in total, you need to choose 8 steps to move in the x-direction and the remaining 8 steps to move in the y-direction.

The number of ways to choose 8 steps out of 16 to move in the x-direction is given by the binomial coefficient "16 choose 8" which can be calculated as C(16, 8) = 12870. Similarly, the number of ways to choose 8 steps out of 16 to move in the y-direction is also 12870.

Therefore, there are a total of 12870 paths that stay outside or on the boundary of the square -2 < x < 2, -2 < y < 2 at each step.

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Answer:

15.64

Step-by-step explanation:

92% of 17 we can write it like this!

\(\frac{part}{whole} = \frac{part}{whole}\)

92% goes in part, 17 goes in whole then 100% below 92!

\(\frac{92}{100} =\frac{x}{17}\)

Then, 17 × 92 = 1,564 ÷ 100 = 15.64

The type of sampling used by the BLS (Bureau of Labor Statistics) for its National Compensation Survey, where employers are divided by size in the second stage of sampling, is known as stratified sampling.

Stratified sampling involves dividing the population into subgroups or strata based on certain characteristics or criteria. In this case, the BLS divides the employers into different size categories. Within each stratum, a sample is then randomly selected to represent that specific subgroup. This approach allows for a more precise estimation of employment costs within each size category. By using stratified sampling, the BLS ensures that the sample is representative of the different employer sizes and allows for more accurate and reliable estimates of employment costs at a national level.

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Answer:

The correct answer is C

Step-by-step explanation:

Tbh I just guessed but I got a 100% on the test, so I hoped that helped

Answer:

yeah its c

Step-by-step explanation:

The value of x from the given figure is 12 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

Consider ΔADC and ΔABC,

∠C=∠C (Reflex property)

AC=AC (Reflex property)

∠BAC=∠CDA=90°

By AA similarity, ΔADC ~ ΔABC

So, AC/BC = DC/AC

x/36 = 4/x

x²=36×4

x²=144

x=12 units

Therefore, the value of x from the given figure is 12 units.

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Answer:

14. :D

Step-by-step explanation:

Answer:

(5,4)

Step-by-step explanation:

To solve a system of equations by substitution, you need to solve one of the equations for one variable (either x or y). In this case, we can solve the second equation for x: x=2y-3. Then substitute this expression into the first equation and solve for y: 5(2y-3)-y=21. Solving for y gives us y=4. Substitute this value back into the second equation and solve for x: x=2(4)-3=5. Therefore, the solution is (5,4).

yw;)

The two vectors [2x + 4y; 6x + 8y] and [2x; 2y], we can see that they are not equal. Therefore, lambda = 2 is not an eigenvalue of matrix A. To determine if lambda is an eigenvalue of the matrix A, we need to find if there exists a non-zero vector v such that Av = lambda * v.

1. Let's start by computing the matrix-vector product Av.
2. Multiply each element of the first row of matrix A by the corresponding element of vector v, then sum the results. Repeat this for the other rows of A.
3. Next, multiply each element of the resulting vector by lambda.
4. If the resulting vector is equal to lambda times the original vector v, then lambda is an eigenvalue of matrix A. Otherwise, it is not.

For example, consider the matrix A = [1 2; 3 4] and lambda = 2.
Let's find if lambda is an eigenvalue of A by solving the equation Av = lambda * v.

1. Assume v = [x; y] is a non-zero vector.
2. Compute Av: [1 2; 3 4] * [x; y] = [x + 2y; 3x + 4y].
3. Multiply the resulting vector by lambda: 2 * [x + 2y; 3x + 4y] = [2x + 4y; 6x + 8y].
4. We need to check if this result is equal to lambda times the original vector v = 2 * [x; y] = [2x; 2y].

Comparing the two vectors [2x + 4y; 6x + 8y] and [2x; 2y], we can see that they are not equal. Therefore, lambda = 2 is not an eigenvalue of matrix A.

In summary, to determine if lambda is an eigenvalue of matrix A, we need to find if Av = lambda * v, where v is a non-zero vector. If the equation holds true, then lambda is an eigenvalue; otherwise, it is not.

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If the parent function \(\sf y=(1.6)^x\) is translated 5 units up and 9 units to the right, then you should subtract 9 from x and add 5 to the whole function. Thus,

1) translation the parent function \(\sf y=(1.6)^x\) 9 units to the right gives you the function \(\sf y=(1.6)^{x-9}\).

2) translation the function \(\sf y=(1.6)^{x-9}\) 5 units up gives you the function \(\sf y=(1.6)^{x-9}+5\)

Therefore, the correct choice is C

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Answer:

I got 15.6

Step-by-step explanation:

I subtracted 28.8 percent from 68.4 then subtracted that number from 68.4

The answer is option B) 09. To find the mean (average) of the yards gained by Roger during his seven carries, we need to add up all the yards gained and divide the sum by the number of carries.

So, for the given data set {2, 6, 20, 11, 8, 12, 4}, the total yards gained is:

2 + 6 + 20 + 11 + 8 + 12 + 4 = 63

The number of carries is 7.

Therefore, the mean yards gained per carry is:

Mean = Total yards gained / Number of carries

= 63 / 7

= 9

Hence, the answer is option B) 09.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$740\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &8 \end{cases} \\\\\\ A=740\left(1+\frac{0.12}{12}\right)^{12\cdot 8}\implies A=740(1.01)^{96}\implies A\approx 1923.46\)

To compute the given derivative, we will use the product rule and the properties of the dot product.

d/dt [t²(i+2j-2tk) •\((e^{t i}+2e^t{ j}-6e^-{t k})] = (16ti + 32tj - 32tk)e^t - 7t^{2}(i + 2j - 2tk)e^-t}\)

Let's start by expanding the expression inside the derivative:

[t²(i+2j-2tk) • (\(e^{t} i+2e^{t j}-6e^{-t k}\))]

= t²(i+2j-2tk) • (\(e^t\) i) + t²(i+2j-2tk) • (2\(e^{t}\)j) - t²(i+2j-2tk) • (6\(e^{-t}\)k)

Next, let's calculate the derivatives of each term:

d/dt [t²(i+2j-2tk) • (\(e^t\) i)] = (2ti+4tj-4tk) • (\(e^t\) i) + t²(i+2j-2tk) • (\(e^t\) i)

d/dt [t²(i+2j-2tk) • (2\(e^t\) j)] = (2ti+4tj-4tk) • (2\(e^t\) j) + t²(i+2j-2tk) • (2\(e^t\) j)

d/dt [t²(i+2j-2tk) • (6\(e^-t\) k)] = (2ti+4tj-4tk) • (6\(e^-t\) k) + t²(i+2j-2tk) • (-6\(e^-t\)k)

Now, let's combine the derivatives and simplify:

d/dt [t²(i+2j-2tk) • (\(e^t\)i+2\(e^t\) j-6\(e^{-t}\) k)]

= [(2ti+4tj-4tk) • (\(e^t\) i) + t²(i+2j-2tk) • (\(e^t\) i)]

+ [(2ti+4tj-4tk) • (2\(e^t\) j) + t²(i+2j-2tk) • (2\(e^t\) j)]

+ [(2ti+4tj-4tk) • (6\(e^{-t}\) k) + t²(i+2j-2tk) • (-6\(e^{-t}\) k)]

Simplifying further:

= (2ti+4tj-4tk)\(e^t\) + t²(i+2j-2tk)\(e^t\)

+ 2(2ti+4tj-4tk)\(e^t\) + 2t²(i+2j-2tk)\(e^t\)

+ 6(2ti+4tj-4tk)\(e^{-t}\) - 6t²(i+2j-2tk)\(e^{-t}\)

Now, let's group like terms:

= (2ti + 4tj - 4tk + 2ti + 4tj - 4tk + 12ti + 24tj - 24tk)\(e^-t\)

+ (t²(i + 2j - 2tk) - 2t²(i + 2j - 2tk) - 6t²(i + 2j - 2tk))\(e^-t\)

= (16ti + 32tj - 32tk)\(e^t\) - 7t²(i + 2j - 2tk)\(e^{-t}\)

Therefore, the derivative of [t²(i+2j-2tk) • (\(e^t\) i+2\(e^t j-6e^{-t }\)k)] with respect to t is:

d/dt [t²(i+2j-2tk) • (\(e^t i+2e^t j-6e^{-t }\)k)] = (16ti + 32tj - 32tk)\(e^t\) - 7t²(i + 2j - 2tk)\(e^{-t}\)

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Step-by-step explanation:

1=2 and 2=4 being vertically opposite angle

The mean is 20.7

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Class     Frequency{f}      Midpoint of frequency{x}                fx    

1-7                    13                              4                                             72

8-10                  14                             9                                              126

11-15                  18                            13                                            234

16-20                6                           18                                              108

21-35                 13                           28                                           364

36-50                19                            43                                          817

Sum                   83                                                                          1721

So,

Mean = 1721/83 = 20.7

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Answer:

  none of the above

Step-by-step explanation:

All of these abbreviations represent postulates that can be used to prove congruence. The HL postulate only applies to right triangles, but all of the others apply to any shape triangle.

All can be used to show congruence.

Answer:

√121 - rational

√2 - irrational

π - irrational

√50 - rational

1.3 - rational

3/7 - rational

0.27 - rational

Step-by-step explanation:

A number is considered rational if it can be written as the ratio of two integers (i.e., a fraction), and it is considered irrational if it cannot be written as a ratio of two integers. In the given list, √121, √50, and 1.3 are all rational numbers because they can be written as fractions (√121 = 11/3, √50 = 5/2, and 1.3 = 13/10), while √2, π, and 0.27 are irrational numbers because they cannot be written as fractions. Note that 3/7 is also a rational number because it is a fraction with an integer numerator and an integer denominator.

Answer:

x1:0 , x2 : 1

Step-by-step explanation:

Answer:

A c is 1 and equation B d is  1

There is a 50% chance that both students are upperclassmen.

Given: Two students meet at a library, where at least one of them is an upperclassman who is currently taking EECS 126, assume each student is an upperclassman and underclassmen with equal probability and each student takes 126 with probability 1/10, independent of each other and independent of their class standing. To find: Probability that both students are upperclassmen.

Solution: Let P(A) be the probability that a student is an upperclassman, and P(B) be the probability that a student is taking EECS 126.P(A) = 1/2 (Given, Assume each student is an upperclassman and underclassmen with equal probability) P(B) = 1/10 (Given, each student takes 126 with probability 1/10, independent of each other and independent of their class standing) Let C be the event that both students are upperclassmen. Then, P(C) = Probability that both students are upperclassmen P(C') = Probability that one student is an underclassman or both are underclassmen P(C') = P(Ac) ...(i) P(C') = 1 - P(C) ...(ii) P(Ac) = P(underclassman) = 1/2 (Given, Assume each student is an upperclassman and underclassmen with equal probability)

Now, P(C') = P(Ac) = 1/2 ...from (i) P(C) = 1 - P(C') = 1 - 1/2 = 1/2 Also, P(B) and P(A) are independent events as given in the question, So, P(AB) = P(A)P(B) = (1/2) x (1/10) = 1/20 Hence, the probability that both students are upperclassmen is P(AB) = 1/20.In other words, there is a 50% chance that both students are upperclassmen.

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To find the magnitude and direction of a vector using trigonometry, you can follow these steps:

1. Identify the components of the vector: A vector can be represented by its horizontal (x) and vertical (y) components. For example, if we have a vector A with components Ax and Ay, we can express it as A = (Ax, Ay).

2. Calculate the magnitude of the vector: The magnitude of a vector is the length of the vector. To find the magnitude of a vector A, you can use the Pythagorean theorem. The formula is:
  magnitude(A) = √(Ax^2 + Ay^2)

3. Find the direction of the vector: The direction of a vector can be given in different forms, such as angles or degrees. Two common ways to express the direction of a vector are:
  a. Angle with the positive x-axis: This angle is measured counterclockwise from the positive x-axis to the vector. You can use trigonometric functions to find this angle. The formula is:
     angle = arctan(Ay / Ax)
  b. Angle with the positive y-axis: This angle is measured counterclockwise from the positive y-axis to the vector. To find this angle, you can subtract the angle obtained in step 3a from 90 degrees (or π/2 radians).

4. Convert the direction to degrees or radians, depending on the required format.

Let's consider an example to illustrate these steps:

Suppose we have a vector A with components Ax = 3 and Ay = 4.

1. Identify the components: A = (3, 4).

2. Calculate the magnitude:
  magnitude(A) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

3. Find the direction:
  angle = arctan(4 / 3) ≈ 53.13 degrees.

4. Convert the direction:
  angle with positive y-axis = 90 degrees - 53.13 degrees ≈ 36.87 degrees.

So, the magnitude of vector A is 5, and its direction is approximately 36.87 degrees with a positive y-axis.

Remember, trigonometry can be used to find the magnitude and direction of a vector when you have its components.

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Answer:

5 feet

Step-by-step explanation:

By triangle inequality, the sum of lengths of any two sides has to be strictly greater than the length of the third side.

Let x feet be the length of the third side.

We have 3+x>7, x+7>3 and 3+7>x.

Solving these, we get x > 4, x > -4 and x < 10.

The solution is therefore 4 < x < 10 and the smallest whole number which satisfies the inequality is 5.

Therefore the answer is 5 feet.

Answer:

Yes what is the question I would surely love to help u

Step-by-step explanation:

Answer:

5.04 seconds

Step-by-step explanation:

According to the graph :

Observe the end points on x axis of the parabola

They are

Time is x axis

So total time

Answer:

D. The distance traveled during the time interval from one minute to 2 minutes is between 8 m and 10 m

Answer:

Step-by-step explanation:

Given :

x = -6

-7x + 6y = -18 ... i)

Putting the value of x in equation ...i)

=> -7 (-6) + 6y = -18

=> 42 + 6y = -18

=> 6y = -18 -42

=> 6y = - 60

=> y = -60/6

=> y = -10

The value of y = -10 and x = -6

Answer:

x= 4, y=6

Step-by-step explanation:

9x-9y = -18

9x=-18+9y

x=-2+y

-6(-2+y) + 9y = 6

-12-6y+9y=6

3y=18

y=6

9x -9(6)=-18

9x-54=-16

9x=36

x=4

The two numbers are 7 and 10 whose sum is 17 and whose difference is 3.

Two or more expressions with an Equal sign is called as Equation.

Given that the sum of two numbers is 17 and the difference of those same two numbers is 3.

We need to find those two numbers.

Let x and y are the two numbers.

Sum of two numbers is 17

x+y=17..(1)

Difference of two numbers is 3

x-y=3..(2)

From equation 1,

x=17-y

Now substitute this in equation 2.

17-y-y=3

17-2y=3

17-3=2y

14=2y

Divide both sides by 2

y=7

Now add y value in equation 1

x+7=17

Subtract 7 from both sides

x=10

Hence, the two numbers are 7 and 10.

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