Find the values of x and y.
Write answers in simplest radical form.
x=______ y=_____

The direction of the electric field can be determined by taking the negative gradient of the electric potential function. At the point (3.0 m, 2.0 m), the electric field is directed in the positive x-direction.

To find the electric field at a given point, we can take the negative gradient of the electric potential function. The electric potential function V(x, y) is given as V = 2.0x^2 - 3.0y^2 + 5xy.

Taking the partial derivatives with respect to x and y, we obtain:

dV/dx = 4.0x + 5y

dV/dy = -6.0y + 5x

At the point (3.0 m, 2.0 m), we substitute x = 3.0 and y = 2.0 into the partial derivatives:

dV/dx = 4.0(3.0) + 5(2.0) = 22.0

dV/dy = -6.0(2.0) + 5(3.0) = 1.0

The electric field E is given by E = -∇V, where ∇ is the gradient operator. Therefore, the electric field at (3.0 m, 2.0 m) is E = (-22.0 i + 1.0 j) N/C.

To find the magnitude of the electric field, we calculate:

|E| = sqrt((-22.0)^2 + (1.0)^2) ≈ 60.1 N/C.

The magnitude of the electric field is approximately 60.1 N/C, and its direction is in the positive x-direction.

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Answer:

c, 14

Step-by-step explanation:

Answer:

the ansewr is b

Step-by-step explanation:

Answer:

The tree is about 27.77 meters tall

Step-by-step explanation:

I attached a helpful sheet that explains all my work visually.

Answer:

x=50

Step-by-step explanation:

The equation of the line for the given graph is y = - 4x + 110.

1)We can calculate the slope of the given line by,

m = (y2 - y1)/(x2 - x1)

where, (x1, y1) are the initial points and (x2,y2) are the final points of the line.

here, (x1, y1) = (5,90)

and, (x2,y2) = (0,110)

so,

m = (110 - 90)/(0 - 5) = -4

therefore, the equation of the line will be,

y = - 4x + 110

where 110 is the y-intercept of the line

2) Slope is the rate of change of the dependent variable with respect to the independent variable.

Here we can say that the slope shows the decrease in the balance of the savings accounts with respect to the weeks.

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Answer:

\(\dfrac{1}{2}\)

Step-by-step explanation:

It is given that triangle ACB is the preimage and triangle DFE is the image.

We need to find the scale factor of the dilation.

\(\text{Scale factor}=\dfrac{\text{Side of image}}{\text{Corresponding side of preimage}}\)

In the given triangles, side AC and DF are corresponding sides.

\(\text{Scale factor}=\dfrac{DF}{AC}\)

\(\text{Scale factor}=\dfrac{6}{12}\)

\(\text{Scale factor}=\dfrac{1}{2}\)

Therefore, the scale factor of the dilation is \(\dfrac{1}{2}\).

Answer:

2nd leg^2 = 17^2 + 15^2

2nd leg^2 = 64

2nd leg = 8

a = 17  b = 15  c = 8

We use heron's formula to find area when we know 3 sides.

We first must calculate the semi-perimeter:

semi-perimeter = 17 + 15 + 8 / 2  = 20

area = square root  [s * (s -a) * ( s-b) * (s-c)]

area = sq root [20 * 3 * 5 * 12]

area = sq root [3,600]

area = 60 square meters

Step-by-step explanation:

Answer:

73.1

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = mx +b

m- Slope ; b - y-intercept

1) y = 2x + 5

Slope = 2

y-intercept = 5

2) 2y = 4x - 5

 Divide the equation by 2

\(\frac{2y}{2}=\frac{4x}{2}-\frac{5}{2}\\\\y = 2x - \frac{5}{2}\)

Slope = 2

y-intercept = \(\frac{-5}{2}\)

3) 3x + 6y = 8

           6y = -3x + 8

            \(\frac{6y}{6}=\frac{-3x}{6}+\frac{8}{6}\\\\ y = \frac{-1}{2}x+\frac{4}{3}\\\\)

Slope = -1/2

y-intercept = 4/3

Answer:

1 \(\frac{1}{3}\) miles.

Step-by-step explanation:

2/4 + 5/6 = ?

We must convert these fractions to the same denominator so we can add fractions. Least common multiple of 4 and 6 is 12.

2/4 = 6/12

5/6 = 10/12

6/12 + 10/12 = 16/12

16/12 = 4/3

4/3 = 1 \(\frac{1}{3}\)

O Zeema gets paid £1870 per month in equal monthly payments.

The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original amount borrowed, but also the interest that accrues, must be repaid.

Now when the total amount earned in a month is given then the monthly payment is calculated by dividing the total amount by 12 as there are 12 months in a year.

Annual amount earned by O Zeema=£22,440

Therefore monthly amount earned=£22,440 ÷12=£1870

Hence O Zeema earns £1870 per month

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Answer:

∠1 = 82°

Step-by-step explanation:

Sum of angles in a triangle = 180°

Now,we have two sides as 49° and 49°.

The third angle is denoted as ∠1.

Thus;

∠1 + 49 + 49 = 180

∠1 = 180 - (49 + 49)

∠1 = 180 - 98

∠1 = 82°

The Deposit Fees 15% VAT amount on goods sold at a VAT-inclusive price of R1,500 would be approximately R195.65.

To answer the questions using the provided information, we'll refer to TABLE 2 for the deposit fees.1.2.1 The minimum amount one will pay when making a deposit of notes and coins:

Notes: R2.25 per R100 or part thereof

Coins: R5 per R100 or part thereof

Therefore, the minimum amount one will pay depends on the value of the deposit. For notes, it will be R2.25 per R100 or part thereof, and for coins, it will be R5 per R100 or part thereof.

1.2.2 To determine if Mr Mbhalati's statement is valid, let's calculate the deposit fees for his deposit of notes and coins.

Deposit of notes:

Deposit amount: R1,500

Deposit fee for notes: R2.25 per R100 or part thereof

Calculation:

Deposit fee = (Deposit amount / 100) * Deposit fee per R100

= (1500 / 100) * 2.25

= 33.75

Deposit of coins:

Deposit amount: R500

Deposit fee for coins: R5 per R100 or part thereof

Calculation:

Deposit fee = (Deposit amount / 100) * Deposit fee per R100

= (500 / 100) * 5

= 25

Total deposit fee = Deposit fee for notes + Deposit fee for coins

= 33.75 + 25

= 58.75

Therefore, Mr Mbhalati's statement is not valid. The total deposit fee for his deposit of notes to the value of R1,500 and R500 in coins would be R58.75, not R180.

1.2.3 To calculate the 15% VAT on the amount of goods sold at a VAT-inclusive price:

Amount from the sale of goods: R1,500

Calculation:

VAT amount = (Amount from the sale of goods / (100 + VAT rate)) * VAT rate

= (1500 / (100 + 15)) * 15

= (1500 / 115) * 15

≈ 195.65

Therefore, the Deposit Fees 15% VAT amount on goods sold at a VAT-inclusive price of R1,500 would be approximately R195.65.

1.2.4 One method Mr Mbhalati can use to send money to a person who does not have a bank account is by using a money transfer service like Western Union or MoneyGram. These services allow individuals to send money to recipients who can collect it in cash from designated locations, even if they don't have a bank account.

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Answer: About 91.54 times.

Step-by-step explanation:

The sequence −33,−26,−19,−12,...,86 is an arithmetic sequence with a common difference of 7. There are 20 terms in the sequence.

In an arithmetic sequence, each term is obtained by adding a constant value, called the common difference, to the previous term. In this case, the common difference is 7 because each term is 7 more than the previous one.

To determine the number of terms in the sequence, we can find the difference between the first and last term and divide it by the common difference. The first term is −33 and the last term is 86, so the difference between them is 86 − (−33) = 119. Dividing 119 by 7 (the common difference) gives us 17.

However, this calculation only gives us the number of intervals between the terms. To obtain the total number of terms, we need to add 1 to the result because the first term is not counted in the intervals. Therefore, there are 17 + 1 = 18 terms in the sequence.

Hence, the sequence −33,−26,−19,−12,...,86 contains 18 terms.

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Answer:

\(\bold{f(x)=-\frac{1}{2}}\)

Step-by-step explanation:

\(f(x)= x^2-\frac{3}{2}\)              replace x with -1

\(f(x)= -1^2-\frac{3}{2}\)           solve exponents

-1² = -1 × -1 = 1

\(f(x)= 1-\frac{3}{2}\)                subtract

\(\bold{f(x)=-\frac{1}{2}}\)

Based on the survey results, a typical parent would spend around $44 on their child's birthday gift, with a margin of error of approximately $2.9 at a 99% confidence level.

To estimate how much a typical parent would spend on their child's birthday gift, we use the sample mean and standard deviation as estimates of the population parameters. The sample mean of $44 serves as the point estimate for the population mean.

To determine the margin of error, we use the standard error, which is the standard deviation divided by the square root of the sample size. In this case, the standard error is approximately $2.5 (standard deviation of $10 divided by the square root of 20). Multiplying the standard error by the critical value corresponding to a 99% confidence level (z-value of 2.58 for a large sample size) gives us the margin of error.

Therefore, the typical amount spent on a child's birthday gift is estimated to be $44, with a margin of error of approximately $2.9. This means that we can be 99% confident that the true mean amount spent by parents falls within the range of $41.1 to $46.9.

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Answer:

all positive real numbers and 0

Step-by-step explanation:

The function has a square root in the x value, so this function can't have negative values, because a negative value of x would give a complex number for f(x), and positive values of x gives positive values of f(x).

The function f(x) can be zero, if the value of x is zero:

\(f(0) = \sqrt{0} /2 = 0/2 = 0\)

So the function f(x) can only have positive values and the value 0.

Correct option: "all positive real numbers and 0"

The line that passes through the given point and is parallel to the graph

y = -4x - 23.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Equation: y=-4x+3

As, we know that the slope of parallel line are same.

Now, using slope- intercept form

y = mx+ b

y = -4x+ b

Now, the line passes through (-4, -7).

So, y= -4x + b

-7 = -4(-4) + b

-7 = 16 + b

b = -23

So, the equation of parallel line is

y = -4x - 23

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The side x of the right angle triangle is 6√3 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sides of a right triangle is named according to the position of the angle. The side of a right triangle are as follows:

The hypotenuse side is the longest side of a right triangle.

Therefore, let's find the x side of the right triangle using trigonometric ratios.

tan 60 = opposite / adjacent

opposite side = x

adjacent side = 6

tan 60 = x / 6

cross multiply

x = 6 tan 60

x = 6 × √3

x = 6√3

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Answer:

25.8

258.

2580.

Step-by-step explanation:

just move the decimal that many times

Answer:

25.8

258

2580

Step-by-step explanation:

10 to the power of 2 is 100

10 to the power of 2 is 1000

10 to the power of 4 is 10000

100 * 0.258

1000 * 0.258

10000 * 0.258

Answer:

The angles of both triangles are the same

The two triangles are both acute because they all have acute angles

Answer:

-107

Step-by-step explanation:

180 (sum of all angles in a triangle)

180-79-x+48+x+65 (collect like terms

2x+214=0 (evaluate

2x=-214 (evaluate

X= -107

Answer: It equals 12 Just kidding it equals 3

We can use the exponential growth model to represent the situation and there will be 73,628,928 bacteria in the petri dish after 2 days.

To determine the number of bacteria in a petri dish after 2 days, when there are 2214 bacteria at the beginning of an experiment, where the number of bacteria doubles every 3 hours, the following approach may be applied.

Every 3 hours, the number of bacteria doubles.

Then, we can say that the bacteria grow exponentially.

Therefore, we can use the exponential growth model to represent the situation. That is:

B(t) = B0 * 2^(t/k),

where:

B(t) is the number of bacteria at time t (measured in hours),

B0 is the initial number of bacteria,

t is the elapsed time since the beginning of the experiment (measured in hours), and

k is the doubling time (measured in hours).

The doubling time k is 3 hours since the number of bacteria doubles every 3 hours.

Thus, the exponential growth model for the bacteria in the petri dish is:

B(t) = 2214 * 2^(t/3)

We want to find the number of bacteria after 2 days.

Since 1 day = 24 hours, then 2 days = 48 hours.

So, t = 48 in the formula above, which gives:

B(48) = 2214 * 2^(48/3) = 2214 * 2^16 = 73,628,928

Therefore, there will be 73,628,928 bacteria in the petri dish after 2 days.

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Answer:

Step-by-step explanation:

In the experiment, the experimenter is studying the effects of temperature, pressure, and type of catalyst on the yield of a chemical reaction. There are three different temperatures, five different pressures, and six different catalysts being considered.

The purpose of this study is to investigate how changes in temperature, pressure, and catalyst type affect the yield of the chemical reaction. By varying these factors, the experimenter can observe and analyze their individual and combined effects on the outcome.

Through the experimental design, the experimenter will be able to gather data on the yield at different temperature, pressure, and catalyst conditions. This will allow them to identify any patterns or trends and draw conclusions about the optimal combination of these variables for maximizing the yield of the chemical reaction.

The study aims to provide valuable insights into the factors that influence the yield of the reaction, enabling scientists and engineers to optimize the process and potentially improve production efficiency.

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D) A^2 = A + 1 this equation represents diagonal matrices with the same eigenvalues on the diagonal.

Let λ be an eigenvalue of the matrix A, and let v be the corresponding eigenvector. Since A is diagonalizable, we can write A = PDP^(-1), where D is the diagonal matrix containing the eigenvalues on the diagonal, and P is the matrix whose columns are the eigenvectors.

We know that A^2 = A + 1, so we can substitute A with its diagonalizable form:

(PDP^(-1))^2 = PDP^(-1) + 1.

Expanding the square and applying the matrix multiplication rules, we get:

PD^2P^(-1) = PDP^(-1) + 1.

Since D is a diagonal matrix, D^2 will have the eigenvalues squared on the diagonal. Therefore, we have:

P(D^2)P^(-1) = PDP^(-1) + 1.

Multiplying both sides by P^(-1) on the right, and by P on the left, we obtain:

D^2 = D + 1.

This equation holds because P^(-1)P = I (the identity matrix), and D and D^2 are diagonal matrices with the same eigenvalues on the diagonal.

Therefore, the correct answer is D) A^2 = A + 1.

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The diagonal of Larry's television is less than 46.9 inches, we can conclude that his television will fit in the space. Specifically, the television's diagonal is 42 inches, which is less than the diagonal of the space. Therefore, Larry's television will fit in the space provided for it.

Larry's television has a diagonal of 42 inches, which means that the screen measures 42 inches from one corner to the opposite corner. The space for the television measures 30 inches by 36 inches. To determine if the television will fit, we need to make sure that the diagonal of the television is less than or equal to the diagonal of the space.
To find the diagonal of the space, we can use the Pythagorean theorem, which states that the square of the diagonal of a rectangle is equal to the sum of the squares of its sides. So, the square of the diagonal of the space is equal to 30^2 + 36^2 = 900 + 1296 = 2196. Taking the square root of 2196, we get the diagonal of the space, which is approximately 46.9 inches.
Since the diagonal of Larry's television is less than 46.9 inches, we can conclude that his television will fit in the space. Specifically, the television's diagonal is 42 inches, which is less than the diagonal of the space. Therefore, Larry's television will fit in the space provided for it.

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Answer:

10

Step-by-step explanation:

divide 20 by 2. so the answer is 10.

Answer:

x<25

Step-by-step explanation:

Let's solve your inequality step-by-step.

2.4x−9<1.8x+6

Step 1: Subtract 1.8x from both sides.

2.4x−9−1.8x<1.8x+6−1.8x

0.6x−9<6

Step 2: Add 9 to both sides.

0.6x−9+9<6+9

0.6x<15

Step 3: Divide both sides by 0.6

0.6x/0.6 < 15/0.6

x<25

Answer:

Side-Side-Side (SSS)

Step-by-step explanation:

I believe these triangles are congruent by the postulate SSS because both triangles have all three sides equal.