calculate the formula by using simultaneous equation

1: 2x+3y = -1
x+y = -1 ​

Answer:

true

Step-by-step explanation:

Answer:

A =13.5 yd^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh where b is the base and h is the height

A = 1/2 (4.5) ( 6)

A =13.5 yd^2

Answer:

22.5

Step-by-step explanation:

7.5ydx6yd

=45yd

45yd/2

=22.5yd^2

Hello !

Answer:

\(\boxed{\sf V{cone} \approx 2408.55 m^3}\)

Step-by-step explanation:

To find the volume of a cone with the radius of its base and its height, we will apply the following formula:

\( \sf V{cone} = \dfrac{\pi \times r^2 \times h}{3} \)

Where r is the radius of its base and h is its height.

Given:

Let's substitute our values into the formula:

\(\sf V{cone} = \dfrac{\pi (10)^2(23)}{3} = \dfrac{2300\pi}{3} \ \ \\\boxed{\sf V{cone} \approx 2408.55 m^3}\)

Have a nice day ;)

Answer:

$22,880.04 Without paying off the debt

$18,880.04 After paying off the debt

Step-by-step explanation:

Answer:

12:7

Step-by-step explanation:

Answer:

1/9 and 7/11

Step-by-step explanation:

hope this is helpful :)

Answer:

1.square root of 10, pie, 3.5

2. 2 square root of 7, square root of 24, 2pie

3.square root 12/3, square root 3, 1.5

4.square root 8/2, 2, square root of 7

Step-by-step explanation:

The value of x from the trigonometric equation sin2x = 1/2 is

x = 15° + 180°n

x = 75° + 180°n

The value of x in radians is

x = π/12 + πn

x = 5π/12 + πn

where n is an integer

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the equation be represented as A

Now , the value of A is

sin ( 2x ) = 1/2

Taking inverse on both sides of the equation , we get

2x = arcsin ( 1/2 )

2x = π/6

Divide by 2 on both sides of the equation , we get

x = π/12

Now , In the first quadrant, sin, cos and tan are all positive.

In the second quadrant going anti-clockwise, only sin is positive.

So , the second solution will be

2x = π - π/6

2x = 5π/6

Divide by 2 on both sides of the equation , we get

x = 5π/12

So , the values of x in radians is

x = π/12 + πn

x = 5π/12 + πn

where n is an integer

Hence , the value of the trigonometric relation is x = π/12 + πn and

x = 5π/12 + πn

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Answer:

x=40

Step-by-step explanation:

4x-20+x=180

5x-20=180

5x=200

x=200/5

x=40

Answer:

40

Step-by-step explanation:

Step 1:

4x - 20 + x = 180

Step 2:

5x - 20 = 180

Step 3:

5x = 180 + 20

Step 4:

5x = 200

Answer:

x = 40

Hope This Helps :)

Answer:

The answer is 4.6.

Step-by-step explanation:

If you look at the graph closely, you would see that the intersection is very close to 4, so the answer is 4.6.

The row vectors of the matrix are [-2 -3 1 0], and the column vectors are:

In a matrix, row vectors are the elements listed horizontally in a single row, while column vectors are the elements listed vertically in a single column. In this case, the given matrix is a 1x4 matrix, meaning it has 1 row and 4 columns. The row vector is [-2 -3 1 0], which represents the elements in the single row of the matrix. The column vectors, on the other hand, can be obtained by listing the elements vertically. Therefore, the column vectors for this matrix are -2, -3, 1, and 0, each listed in a separate column.

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Answer:

Rate of change would be 1/4

Hope this helps!

Answer:

Ok, the speed is 18 mph.

The angle is 293°, and we usually measure the angles from the x-axis, so we can write our coordinates of velocity as:

Vx = 18mph*cos(293°) = 7mph.

Vy = 18mph*sin(293°) = -16.6mph.

Then we can write this as a vector (Vx, Vy)

Velocity = (7mph, -16.6mph)

Now, for the position, we can integrate over time, and using that the position (0,  0) is the starting point of the ship, we have that the position vector is:

P(t) = (7mph*t, -16,6mph*t)

Where t is the number of hours after the ship leaved the port.

If t = 0 is 0:00pm, then at 3:30pm we have t = 3 hours and 30 minutes

one hour has 60 minutes, then 30 minutes is equivalent to 0.5 hours.

Then 3:30pm we have t = 3.5 houes.

Now we replace this in the position vector and the location of the ship at 3:30pm is:

P(3.5h) = (7mph*3.5h, -16.6mph*3.5h) = (24.5 mi, -58.1 mi)

Where the first component describes the displacement in the x-axis, and the second component describes the displacement in the y-axis.

Answer: 1) -58  2) 24.6  3) 24.6  4) north  5) 58  6) west

Step-by-step explanation: I took the test.

From the information in the word problem we are able to set up the following inequality:  

3y + 2 - y = 12   |   where x is the larger number of two numbers in a set (x, y)  

We know this because the problem states that [x = 3y + 2] or 3 times the smaller number plus two.  

We also know that x - y = 12.

So, we substitute x in [x - y = 12] with 3y + 2 that we found out above, and we get the following:

3y + 2 - y = 12

Now, we solve the inequality

3y + 2 - y = 12

-> subtract 2 from both sides :: 3y - y = 10

-> subtract y from 3y              :: 2y = 10

-> divide both sides by 2        :: y = 5

So now we have y, the smaller number, which is equal to 5. Next, to find x we simply plug y=5 back in to either the value of x, [3y + 2], or the inequality of x - y = 12. I will show both:  

x - y = 12

-> substitute y for 5     :: x - 5 = 12

-> add 5 to both sides :: x = 17

OR

3y + 2 = x

-> substitute y with 5 :: 3(5) + 2 = x

-> multiply 3, 5          :: 15 + 2 = x

-> add 15, 2              :: 17 = x

So there you have it:  

x = 17 , y = 5

You can go back and use these values to check your answer and make sure they work with the word problem.  

Remember to look for the setup to an inequality in the word problem. Anything that says BLANK times this number, or 4 less than that number, is trying to set you up with an inequality problem.  

(just another form of the equation)

brainliest will be appreciated as well

In this case, the equation is in vertex form. To graph the parabola, we need to determine the y-intercept, x-intercept(s), and the vertex.

Vertex form: y = a(x + h)² - k

Assume "y" as 0.

\(\implies 0 = 3(x + 2)^{2} - 1\)

\(\implies 1 = 3(x + 2)^{2}\)

Take square root both sides and simplify:

\(\implies\sqrt{1} = \sqrt{3(x + 2)^{2}}\)

\(\implies1 = \sqrt{3 \times (x + 2) \times (x + 2)}\)

\(\implies1 = (x + 2) \times \sqrt{3\)

Divide √3 both sides:

\(\implies \±\huge\text{(}\dfrac{1 }{\sqrt{3}} \huge\text{)} = (x + 2)\)    

\(\implies \±\huge\text{(}\dfrac{\sqrt{1} }{\sqrt{3}} \huge\text{)} = (x + 2)\)    

Multiply √3 to the numerator and the denominator:

\(\implies \±\huge\text{(}\dfrac{\sqrt{1} \times \sqrt{3} }{\sqrt{3\times \sqrt{3}}} \huge\text{)} = (x + 2)\)

\(\implies \±\huge\text{(}\dfrac{\sqrt{3} }{3}} \huge\text{)} = (x + 2)\)

\(\implies \±\huge\text{(}\dfrac{\sqrt{3} }{3}} \huge\text{)} - 2 =x\)

\(\implies x = \underline{-2.6...} \ \text{and} \ \underline{-1.4...} \ \ \ \ (\text{Nearest tenth})\)

Assume "x" as 0.

y-intercept = 11 ⇒ (0, 11)

Since the first cooeficient is positive (+3), the direction of the parabola will be upwards.

Axis of symmetry line: x-coordinate of vertex

Axis of symmetry line: x = -2

Plot the following on the graph:

Refer to graph attached.

Answer:

Vertex form of a quadratic equation:

\(y=a(x-h)^2+k\quad \textsf{where }(h,k)\:\textsf{is the vertex}\)

Given equation:  \(y=3(x+2)^2-1\)

Therefore, the vertex is (-2, -1)

The x-intercepts are when \(y=0\):

\(\implies 3(x+2)^2-1=0\)

\(\implies 3(x+2)^2=1\)

\(\implies (x+2)^2=\dfrac13\)

\(\implies x+2=\pm\sqrt{\dfrac13}\)

\(\implies x+2=\pm\dfrac{\sqrt{3}}{3}\)

\(\implies x=-2\pm\dfrac{\sqrt{3}}{3}\)

\(\implies x=\dfrac{-6\pm\sqrt{3}}{3}\)

Therefore, the x-intercepts are at -2.6 and -1.4 (nearest tenth)

The y-intercept is when \(x=0\):

\(\implies 3(0+2)^2-1=11\)

So the y-intercept is at (0, 11)

The axis of symmetry is the x-value of the vertex.  Therefore, the parabola is symmetrical about x = -2

**You don't need to plot the axis of symmetry - I have added it so that it is easier to draw the curve**

the greatest possible product of a four-digit number and a three-digit number obtained from seven distinct digits is 2,463,534.

To find the greatest possible product of a four-digit number and a three-digit number obtained from seven distinct digits, we can start by considering the largest possible values for each digit.

Since we need to use seven distinct digits, let's assume we have the digits 1, 2, 3, 4, 5, 6, and 7 available.

To maximize the product, we want to use the largest digits in the higher place values and the smallest digits in the lower place values.

For the four-digit number, we can arrange the digits in descending order: 7, 6, 5, 4.

For the three-digit number, we can arrange the digits in descending order: 3, 2, 1.

Now, we multiply these two numbers to find the greatest possible product:

7,654 * 321 = 2,463,534

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Answer:

You can . , ... : ' , .

Answer:

What subject is this? Is this Geometry?

Step-by-step explanation:

If an F statistic is negative, the true statement would be option C, there has been a calculation error. Since both the numerator and denominator are positive, the F statistic will always be positive.

The F statistic is used to compare the variance between groups with the variance within groups. It is always positive, as both the between-groups and within-groups variances are positive. Therefore, if an F statistic is negative, it indicates that there has been a calculation error.

The correct formula for the F statistic is:

F = (between-groups variance) / (within-groups variance)

A negative F statistic is not possible and indicates that there has been a mistake in the calculation.

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Step-by-step explanation:

We have the points (0, 0) and (8, 14).

Rise between the points = 14 - 0 = 14.

Run between the points = 8 - 0 = 8.

Slope of Line

= Rise/Run = 14/8 = 1.75.

1. The cheese production for 2006 is 7.76 billion.

2. The cheese produced in 2014 is 9.84 billion.

It should be noted that a function is simply used to show the relationship between the variables that are given.

In this situation, there's a 3% growth per year and the function for the cheese production is modelled as:

y = 7.1(1.03)^x

y = cheese production

x = number of years after 2003.

1. Therefore, since 2006 is 3 years after 2003, this will be

y = 7.1(1.03)^x

y = 7.1(1.03)³

y = 7.1 × 1.093

y = 7.76 billion

The production is 7.76 billion.

2. The production in 2014 will be;

y = 7.1(1.03)^x

y = 7.1(1.03)^11

y = 7.1 × 1.385

y = 9.84 billion

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In 10,000 independent tosses of a coin and the coin landed on heads 5800 times, is it reasonable to assume that the coin is not fair and may be biased towards heads.

In order to determine if the coin is fair or not, we need to calculate the probability of getting 5800 or more heads in 10,000 tosses assuming the coin is fair.

The probability of getting a head on any one toss of a fair coin is 0.5. The number of heads in 10,000 tosses is a binomial random variable with parameters n=10,000 and p=0.5. We can use the normal approximation to the binomial distribution to calculate the probability of getting 5800 or more heads.

The mean of the binomial distribution is np = 5000 and the standard deviation is sqrt(np(1-p)) = 50.

We can standardize the variable X = number of heads in 10,000 tosses by subtracting the mean and dividing by the standard deviation:

Z = (X - 5000) / 50

The probability of getting 5800 or more heads can be calculated as:

P(X >= 5800) = P(Z >= (5800-5000)/50)

Using a standard normal table or calculator, we find that P(Z >= 1.6) = 0.0548.

This means that the probability of getting 5800 or more heads in 10,000 tosses assuming the coin is fair is only 0.0548, which is quite low.

Therefore, it is reasonable to conclude that the coin is not fair and may be biased towards heads.

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Answer:

---------------------------

Midpoint divides the segment in half, therefore:

Answer:

3.8 units

Step-by-step explanation:

Given that AB = 7.6, we can find AP by dividing AB by 2:

AP = AB/2

AP = 7.6/2

AP = 3.8

Therefore, the length of AP is 3.8.

Identifying Eigenvalues and Eigenvectors, A should be a n x n matrix. By resolving the det(λI−A)=0 problem, first determine the eigenvalues of A. Find the fundamental solutions to (λI−A)X=0 to determine the fundamental eigenvectors X≠0 for each.

In linear algebra, a nonzero vector is said to have an eigenvector, or characteristic vector, when a linear transformation is applied to it; this characteristic vector only changes by a scalar amount. The scaling factor for the eigenvector is known as the associated eigenvalue, frequently represented by the symbol. Linear transformations are made intelligible by the usage of eigenvectors. Eigenvectors can be thought of as a non-directional stretching or compressing of an X-Y line chart. In mathematics, eigenvalues are regarded as the factor by which a transformation is stretched, whereas eigenvectors are the real non-zero eigenvalues that point in the direction stretched by the transformation. The direction of the transformation is negative if the eigenvalue is negative.

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Step-by-step explanation:

obviously you can find the triangle area using this formula a*b/2

so A= 2*11/2 =11

and also for triangle a*b

so B= 7*11 =77

the whole area would be =88

Step-by-step explanation:

you can just put in some values to check.

I actually used p =2 and q=3

the It will be

2^3-1 + 3^2-1 = 1 (mod 2×3)

2^2 +3^1 = 1 (mod 6)

4+3= 1 (mod6)

7= 1 (mod6)

which is true.

therefore p^(q-1) + q^( p-1) = 1 ( mod pq) is true

To show that p^(q-1) + q^(p-1) = 1 (mod pq), we can use Fermat's Little Theorem, which states that if p is a prime number and a is an integer not divisible by p, then a^(p-1) = 1 (mod p). Using this theorem, we can first show that p^(q-1) = 1 (mod q), since q is a prime number and p is not divisible by q. Similarly, we can show that q^(p-1) = 1 (mod p), since p is a prime number and q is not divisible by p.

Therefore, we can write:

p^(q-1) + q^(p-1) = 1 (mod q)
p^(q-1) + q^(p-1) = 1 (mod p)

By the Chinese Remainder Theorem, we can combine these two equations to obtain:

p^(q-1) + q^(p-1) = 1 (mod pq)

Thus, we have shown that p^(q-1) + q^(p-1) = 1 (mod pq).
We'll use Fermat's Little Theorem to show that p^(q-1) + q^(p-1) = 1 (mod pq).

Fermat's Little Theorem states that if p is a prime number and a is an integer not divisible by p, then:
a^(p-1) ≡ 1 (mod p)

Step 1: Apply Fermat's Little Theorem for p and q:
Since p and q are prime numbers, we have:
p^(q-1) ≡ 1 (mod q) and q^(p-1) ≡ 1 (mod p)

Step 2: Add the two congruences:
p^(q-1) + q^(p-1) ≡ 1 + 1 (mod lcm(p, q))

Step 3: Simplify the congruence:
Since p and q are prime, lcm(p, q) = pq, so we get:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

In your question, you've mentioned that the result should be 1 (mod pq), but based on Fermat's Little Theorem, the correct result is actually:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

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Answer:

my answer would be 2500

Step-by-step explanation:

just a guess

To find the critical points at which profit is maximized given the total revenue TR = 4700 - 302 and total cost TC = 320/10,500, we need to compute the marginal revenue and marginal cost, equate MR = MC to find the optimal quantity Q∗, verify if Q∗ is a relative maximum point, and compute the maximum profit level (π) by evaluating π∗ = 9(π(Q∗)).

Marginal Revenue (MR) is the derivative of the total revenue function with respect to quantity (Q). In this case, MR = dTR/dQ. By taking the derivative of TR = 4700 - 302 with respect to Q, we can find the expression for MR.

Marginal Cost (MC) is the derivative of the total cost function with respect to quantity (Q). In this case, MC = dTC/dQ. By taking the derivative of TC = 320/10,500 with respect to Q, we can find the expression for MC.

To find the optimal quantity Q∗, we equate MR and MC by setting MR = MC and solve for Q. This is because profit is maximized when MR equals MC.

Once we have found Q∗, we need to verify if it is a relative maximum point. This can be done by checking the second derivative of the profit function and determining if it is negative at Q∗. If the second derivative is negative, it confirms that Q∗ is a relative maximum point.

Finally, to compute the maximum profit level (π∗), we evaluate π(Q∗) by substituting Q∗ into the profit function. In this case, we can multiply the value of π(Q∗) by 9 to obtain the maximum profit level (π∗).

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Answer:

sim tem final sim amigo se eu erra mi disputa por favor