please help me with this ​

Answer:

Step-by-step explanation:

plug in 3 for x then simplify

-3(3) - 2

= -9 - 2

= -11

hope this helps <3

Answer:

5

Step-by-step explanation:

58+78=131

180-131=49

10(5)-1

=5

Answer:

x=5

Step-by-step explanation:

A triangle= 180

53+78+10x-1=180

Combine like terms

130+10x=180

Subtract by 130 on both sides

10x=50

Divide by 10 on both sides

x=5

Answer:

D) is the correct answer

Step-by-step explanation:

To define a function, so one x can only corresponding to one y.

Then for A) we have x = -5, but y can be 1 and 4, so it is to a function,

for B) x =1, y = -1 or -4, so not. For C) x =0, y = -3 or 0, so wrong. Then left with D) which each x only corresponding to one y, so D) is correct.

If it is helpful, plz give me Brainliest.

Answer:

-205/69

Step-by-step explanation:

-41/3÷23/5

reciprocate, then the sign changes

-41/3×5/23

=-205/69

The equation of the plane passing through the point (2, 8, -5) and containing the line x = 2 - 4t, y = 1 + 2t, z = 3 + 4t is given by 2x - 4y + 8z = -23. To derive this equation, we need to first find a vector parallel to the given line. To do this, we can take the difference of two points that lie on the line. Let us take the points P(2, 1, 3) and Q(2 - 4t, 1 + 2t, 3 + 4t) as our two points. The vector PQ is then given by: PQ = (2 - 4t - 2, 1 + 2t - 1, 3 + 4t - 3) = (-4t, 2t, 4t).

Since the given plane passes through the point (2, 8, -5), we can take the vector from this point to any point on the line, say the point Q, as our normal vector for the plane. This vector is then given by: n = (2 - 4t - 2, 8 - 1, -5 - 3) = (-4t, 7, -8).

Now, using the formula Ax + By + Cz = D for a plane passing through the origin and with a normal vector n = (A, B, C), the equation of the plane is given by A(x - x0) + B(y - y0) + C(z - z0) = 0, where (x0, y0, z0) is any point that lies on the plane.

Substituting A = -4t, B = 7, C = -8, x0 = 2, y0 = 8, z0 = -5 into the above equation, we get: -4t(x - 2) + 7(y - 8) - 8(z + 5) = 0. Simplifying this equation, we get 2x - 4y + 8z = -23, which is the equation of the plane that passes through the point (2, 8, -5) and contains the line x = 2 - 4t, y = 1 + 2t, z = 3 + 4t.

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what is the probability that a random sample of n=30 healthy koalas has a mean body temperature of more than 36.2°c?

The probability that a random sample of n = 30 healthy koalas has a mean body temperature of more than 36.2°C is 0.023.

In order to solve the given problem, we will use the central limit theorem. The formula for finding the standard error of the mean is as follows: Standard error of the mean = σ / √n, where σ is the standard deviation and n is the sample size. For the given problem, we have not been given the value of σ. So, we will assume that the population standard deviation is equal to the sample standard deviation. The formula for finding the sample standard deviation is given below: Sample standard deviation = s / √n, where s is the sample standard deviation, which can be found by calculating the standard deviation of the sample. For finding the probability that a random sample of n = 30 healthy koalas has a mean body temperature of more than 36.2°C, we need to calculate the z-score first. The formula for finding the z-score is as follows:z = (x - μ) / (σ / √n)where x is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size. Since we do not know the population mean or the standard deviation, we will use the sample mean and standard deviation for finding the z-score.μ = 36.2

x= ?s = 0.5 (given)n = 30 (given)Using the above values in the formula, we get z = (x - μ) / (s / √n)z = (x - 36.2) / (0.5 / √30)We need to find the value of x for which the z-score is greater than 0. Thus, we have z > 0, so (x - 36.2) / (0.5 / √30) > 0, x - 36.2 > 0.5 / √30, x > 36.2 + 0.5 / √30, x > 36.304, Now, we will find the probability that a random sample of n = 30 healthy koalas has a mean body temperature of more than 36.2°C by using the z-table. The area to the right of the z-score is the probability that we are looking for.z = (x - μ) / (s / √n)z = (36.304 - 36.2) / (0.5 / √30), z = 0.644. Using the z-table, we find that the probability of getting a z-score greater than 0.644 is 0.2611.

However, we need the probability of getting a z-score less than 0.644. This is because we need to find the probability of getting a mean body temperature of more than 36.2°C, which is to the right of the mean. So, we subtract 0.2611 from 0.5 (which is the probability of getting a z-score less than 0) to get the probability of getting a z-score less than -0.644.0.5 - 0.2611 = 0.2389

Therefore, the probability that a random sample of n = 30 healthy koalas has a mean body temperature of more than 36.2°C is 0.2389. Rounding this to three decimal places, we get 0.023.

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Catelyn will have approximately $1,647.62 in her account after 3 years of making deposits every 6 months.

To calculate how much Catelyn will have after 3 years, we need to determine the total number of compounding periods and then apply the compound interest formula.

Given:
Principal deposit (P) = $1537
Interest rate (r) = 2.07% per year (expressed as a decimal, r = 0.0207)
Compounding period (n) = 4 times per year (quarterly)
Time (t) = 3 years

First, we calculate the total number of compounding periods:
Number of compounding periods (N) = n * t = 4 * 3 = 12

Next, we can use the compound interest formula to calculate the future value (A):
A = P * (1 + r/n)^(n*t)

Plugging in the values:
A = $1537 * (1 + 0.0207/4)^(4*3)
A = $1537 * (1 + 0.005175)^12
A = $1537 * (1.005175)^12
A ≈ $1,647.62

Therefore, Catelyn will have approximately $1,647.62 in her account after 3 years of making deposits every 6 months.

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Answer:

c

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

T = temperature

-52 < T < 108

Temperatures fall between the values of -52 and 108.  D is the number line that shows this.

The standard form of the equation of the parabola is  y = -1/4(x + 3)² + 3.

A plane curve produced by a moving point such that its separation from a fixed point equals that of a fixed line is a parabola.

The function form of a parabola:

y = ±a (x - h)² + k,

where,

(h, k) is the vertex, ±a is the upward and downward direction of the parabola.

Here, the vertex is (-3, 3).

So, y = a (x + 3)² + 3.

When x = -1, then y = 2,

2 = a (-1 + 3)² + 3.

a = -1/4

Therefore, the equation is y = -1/4(x + 3)² + 3.

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The components of the support reaction at the fixed support A of the beam are as follows:

1. Vertical component (Ay): 8.5 kN upward

2. Horizontal component (Ax): 3 kN rightward

3. Moment (MA): 51 kN·m counterclockwise

To determine the components of the support reaction, we need to analyze the forces acting on the beam and create a Free Body Diagram (FBD) of the beam.

Given:

- A vertical load of 3 kN at a distance of 6 m from the support.

- A distributed load of 0.5 kN/m along the beam.

- A clockwise moment of 5 kN·m applied at the support.

Step 1: Draw the FBD of the beam.

```

     3 kN          0.5 kN/m        5 kN·m

      |_____________|_______________|

A      |             |               |

      |             |               |

```

Step 2: Calculate the vertical component (Ay) of the support reaction.

Since there is a vertical load of 3 kN and a distributed load of 0.5 kN/m acting upward, the total vertical force is:

Vertical force = 3 kN + (0.5 kN/m) * 6 m = 6 kN

Therefore, the vertical component of the support reaction at A is 6 kN acting upward.

Step 3: Calculate the horizontal component (Ax) of the support reaction.

There are no horizontal forces acting on the beam, except for the support reaction at A. Hence, the horizontal component of the support reaction is 3 kN acting rightward.

Step 4: Calculate the moment (MA) at the support.

The clockwise moment of 5 kN·m applied at the support needs to be balanced by the counterclockwise moment caused by the support reaction. Let's assume the counterclockwise moment as MA.

To balance the moments:

Clockwise moment = Counterclockwise moment

5 kN·m = MA

Therefore, the moment at the support is 51 kN·m counterclockwise.

Hence, the components of the support reaction at the fixed support A are Ay = 8.5 kN upward, Ax = 3 kN rightward, and MA = 51 kN·m counterclockwise.

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(i × j) × k = 0, is the vector, not with determinants, but by using properties of cross products.

The procedure for multiplying two vectors is called the cross product of the two vectors. The sign(×) of multiplication between two vectors indicates a cross product. It is a three-dimensional system-defined binary vector operation.

A cross product in three dimensions is a binary operation on two vectors. It generates a vector that is parallel to both vectors. A and B together form a vector product, which is represented by the symbol a b. The vector that results from it is parallel to both a and b. Cross products and vector products are similar terms.

As we know,

i × j = | i | × | j | × sin 90° × k

or, i × j = 1 × 1 × 1 × k

or, i × j = k

thus,  (i × j) × k = k × k

or,  (i × j) × k = 0

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Perimeter of a triangle = Sum of all sides of triangle

The unit of perimeter of a triangle is same as length of its sides

The partial derivatives of A with respect to h, r, and t are dh/dA = 2πr, dr/dA = 4πr, and dt/dA = 0, if h is constant.

The area A is given by the following equation:

A = 2πr^2 + 2πrh

We can take the partial derivative of A with respect to h to get the following equation: dh/dA = 2πr

This equation says that the change in A with respect to h is proportional to the radius r. The constant of proportionality is 2π.

We can take the partial derivative of A with respect to r to get the following equation: dr/dA = 4πr

This equation says that the change in A with respect to r is proportional to the square of the radius r. The constant of proportionality is 4π.

If h is constant, then the partial derivative of A with respect to t is 0. This is because the area A does not depend on t.

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Answer:

7.48 X 10^4

Step-by-step explanation:

Hope it helps!!

Given the word problem, we can deduce the following information:

1. A recipe for cookies includes 1/4 cup of brown sugar for 12 cookies.

To determine the

When the angle of depression is 40° then the distance of the car from the foot of the building is 20.9775 m.

Here given that,

Height of the building =  150 m

Angle of depression = 40°

We have to find distance of car from the foot of the building.

x m be the distance between the car and the building.

So here let imagine it as ΔABC,

Tan 40° = AC/AB

Tan 40° = 0.8391

Therefore the distance,

x = 25 x 0.8391

x = 20.9775 m

Therefore the distance of car from the foot of the building is 20.9775m

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Answer

1

The congruent side must be between the congruent angles to be ASA

"1" has a congruent angle and a congruent side, but there are vertical angles, and these angles are congruent, so it is ASA

Answer:

r=-10

Step-by-step explanation:

Plug in the value of t into the equation.

r=3t-1; t = -3

r=3(-3)-1

r= -10

Answer:

the answer of the t=-3 is r=-10

Answer:

2/12

Step-by-step explanation:

Answer:

C) 2/12

Step-by-step explanation:

You need to convert the fractions to decimals (by dividing the top number by the bottom number).

5/12 = 0.416...

8/12 = 0.666...

2/12 = 0.166...

4/6 = 0.666...

As you can see, 2/12 in decimal form is closer to 0 than the other fractions.

The required change in the price of the share of stock is $4.4.

Given that,
On September 1, you own 12.5 shares of stock that are worth $149.87. On December 1, the shares are worth $94.87, and the change in the price per share of stock is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Initial total cost shares of stock = $149.87
A total number of shares = 12.5
The initial cost of single share = 149.87/ 12.5 = $11.98
Now final cost of the total share = $94.87
The final cost of the single share is = 94.87 / 12.5 = $7.58
Change in price of shares of stock = 11.98 - 7.58 = $4.4

Thus, the required change in the price of the share of stock is $4.4.

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answer:

$0.75

Step-by-step explanation:

the function can be represented as:

f(x)=0.25x+3.5

the function produces the following values for years 1, 2, and 3 respectively:

f(1)=0.25(1)+3.5=3.75

f(2)=0.25(2)+3.5=4.00

f(3)=0.25(3)+3.5=4.25

therefore, 

there is a $0.75 increase per year

Answer:

It is still 549.5

Step-by-step explanation:

Rounding to 1 decimal place is just rounding by the tenth place

So it is still 549.5

Hope this helps!

Answer:

(-4,-52)

(1/12,-3)

(1/3,0)

(0,-4)

(3,32)

Step-by-step explanation

i think thats right

Best Fit Line

Given a series of points that represent some measures in the real world, for example, the heights vs the age of a group of children, when we plot it on a rectangular grid, we get a scatter plot, not necessarily aligned as to form a specific graph.

Sometimes is vital to have a known function that best represents the whole dataset, so we can make predictions.

The best fit line is widely used to do that. We can recognize the best fit line because it usually goes through the maximum number of points and the sum of the distances to each one of them is minimum.

From the three graphs given in the question, it's evident the first line is totally outside the set of points, so it does not do a good job representing the dataset.

The second graph approximates much better to a best-fit line but we can still see the trend of the line does not follow the trend of the dotted path.

Finally, the third graph looks very adequate to represent the scattered points because it keeps always close to them and follows their trend.

dy/dx = (1/(e^(x^2)+1)) * (e^(x^2) * 2x) + e*cos(x)

This is the derivative of the given function y with respect to x.

We want to find the derivative dy/dx of the function y = ln(e^(x^2)+1) + e*sin(x). To do this, we will apply the rules of differentiation.

First, we'll differentiate the function term-by-term. For the natural logarithm function, the derivative is (1/u) * du/dx, where u is the function inside the natural logarithm. In our case, u = e^(x^2) + 1.

The derivative of e^(x^2) is found by applying the chain rule, which gives us (e^(x^2) * 2x). The derivative of 1 is 0. Therefore, the derivative of u is (e^(x^2) * 2x). Now we can find the derivative of ln(u):

d[ln(u)]/dx = (1/(e^(x^2)+1)) * (e^(x^2) * 2x)

Next, we will differentiate e*sin(x). The derivative of e*sin(x) is found by applying the product rule. The derivative of e is e, and the derivative of sin(x) is cos(x). Applying the product rule, we have:

d[e*sin(x)]/dx = e*cos(x) + e*sin(x) * 0 = e*cos(x)

Now, adding the derivatives of both terms, we get:

dy/dx = (1/(e^(x^2)+1)) * (e^(x^2) * 2x) + e*cos(x)

This is the derivative of the given function y with respect to x.

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The tables that represent a proportional relationship are :

x 1 2 3 4 5

y 4 5 6 7 8

b 2 3 8 9 14

c 4 6 16 18 28

Two variables have a proportional relationship when the ratios of the rate of change of the variables are constant.

Ratio = change in the value of y / change in the value of x

First table:

(5 - 4) / (2 - 1) = 1

(6 - 5) / (3 - 2) = 1

(7 - 6) / (4 - 3) = 1

(8 - 7) / (5 - 4) - 1

Second table:

(5 - 3) / (3 - 2) = 2

(6 - 5) / (4 - 3) = 1

(8 - 6) / (5 - 4) = 2

(9 - 8) / (6 - 5) = 1

Third table:

(6 - 4) / (3 - 2) = 2

(16 - 6) / (8 - 3) = 2

(18 - 16) / (9 - 8) = 2

(28 - 18) / (14 - 9) = 2.

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