Which statements are correct steps in finding the linear equation of a line that passes through the points (−1, 7) and (2, 4) using the point-slope form method? Select all that apply.
y = x + 6
7 = –1(–1) + b
y – 4 = –1 (x – 2)
y – 7 = –1 (x – (–1))
y – 2 = x – 4
y = –x + 6

Given:

\(f(x)=2x\)

\(g(x)=f(x)+4\)

To find:

The y-intercept of g(x).

Solution:

We have,

\(g(x)=f(x)+4\)

Putting \(f(x)=2x\), we get

\(g(x)=2x+4\)

Substitute x=0 to find the y-intercept of g(x).

\(g(0)=2(0)+4\)

\(g(0)=0+4\)

\(g(0)=4\)

Therefore, the y-intercept of g(x) is at point (0,4). So, the y-intercept of g(x) is 4.

Answer:

sin(0)=15/17

Step-by-step explanation:

17 is the hypotnuse and when working with sin,you need the opppsite and the hypotnuse. Meaning 17 would be the denominator because it is the hypotnuse and then 15 would be opposite i believe.hope this helps!

Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

Answer:

Step-by-step explanation:

that a huge prob but yah

Answer:

The answer is 80%

Step-by-step explanation:

BRAINLIEST PLEASEEEE

Answer:

-223/35

Step-by-step explanation:

thats the answer idk how to describe it coz im slow

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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The area enclosed by the curve r=2sin(θ) 3sin(9θ) over the interval [0,2π/9] is (243π/64) - (3√3/16).

To find the area enclosed by the curve r=2sin(θ) 3sin(9θ), we first need to determine the limits of integration for θ.

Since the curve is periodic with period 2π/9 (due to the 9 in the second term), we only need to consider the portion of the curve in the interval [0, 2π/9].

Next, we need to convert the polar equation to rectangular coordinates, which can be done using the formulas x = r cos(θ) and y = r sin(θ).

Plugging in the given equation, we get:

x = 2sin(θ) cos(θ) + 3sin(9θ) cos(θ)
y = 2sin(θ) sin(θ) + 3sin(9θ) sin(θ)

Now we can find the area enclosed by the curve by integrating over the given interval:

A = ∫[0,2π/9] (1/2) [x(θ) y'(θ) - y(θ) x'(θ)] dθ

Using the formulas for x and y, we can find the derivatives x'(θ) and y'(θ):

x'(θ) = 2cos(θ) cos(θ) - 2sin(θ) sin(θ) + 27cos(9θ) cos(θ) - 27sin(9θ) sin(θ)
y'(θ) = 2cos(θ) sin(θ) + 2sin(θ) cos(θ) + 27cos(9θ) sin(θ) + 27sin(9θ) cos(θ)

Substituting these expressions into the formula for A and evaluating the integral, we get:

A = (243π/64) - (3√3/16)

Therefore, the area enclosed by the curve r=2sin(θ) 3sin(9θ) over the interval [0,2π/9] is (243π/64) - (3√3/16).

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The derivative \(\( y' \)\) of the implicit function \(\( y^2 - xy = -2 \)\) is 0, indicating a constant slope with no change in relation to \(\( x \)\).

To find \(\( y' \)\)for the implicit function \(\( y^2 - xy = -2 \)\), we can differentiate both sides of the equation with respect to \(\( x \)\) using the chain rule. Let's go step by step:

Differentiating \(\( y^2 \)\) with respect to \(\( x \)\) using the chain rule:

\(\[\frac{d}{dx}(y^2) = 2y \cdot \frac{dy}{dx}\]\)

Differentiating \(\( xy \)\) with respect to \(\( x \)\) using the product rule:

\(\[\frac{d}{dx}(xy) = x \cdot \frac{dy}{dx} + y \cdot \frac{dx}{dx} = x \cdot \frac{dy}{dx} + y\]\)

Differentiating the constant term (-2) with respect to \(\( x \)\) gives us zero since it's a constant.

So, the differentiation of the entire equation is:

\(\[2y \cdot \frac{dy}{dx} - (x \cdot \frac{dy}{dx} + y) = 0\]\)

Now, let's rearrange the terms:

\(\[(2y - y) \cdot \frac{dy}{dx} - x \cdot \frac{dy}{dx} = 0\]\)

Simplifying further:

\(\[y \cdot \frac{dy}{dx}\) \(- x \cdot \frac{dy}{dx} = 0\]\)

Factoring out:

\(\[(\frac{dy}{dx})(y - x) = 0 \]\)

Finally, solving:

\(\[\frac{dy}{dx} = \frac{0}{y - x} = 0\]\)

Therefore, the derivative \(\( y' \)\) of the given implicit function is 0.

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Answer:

Sorry This Is Late

The Answer Is "g(x)= 3^(x+1)-2"

Step-by-step explanation:

I Just Took The Test :)

The required value of b (width of the beam) is approximately 192 mm.

What is  Plastic centroid and Mp for general cross-section?

For a cross-section with at least one axis of symmetry, the neutral axis corresponds to the centroidal axis in the elastic region. However, at Mp the neutral axis will correspond to the plastic gravity axis. For a doubly symmetric cross-section, the elastic and plastic centers lie at the same point. Mp = y x A/2 x (y1+y2)

To design the cross-section of the beam, we need to determine the required value of the width (b) of the timber beam.

Given:

Load: 3 kN/m

Span: 2.4 m

Allowable normal stress of timber: 13.5 MPa

To calculate the required value of b, we'll start by finding the maximum bending moment (M) in the beam.

The maximum bending moment can be determined using the formula:

M = (w * L^2) / 8

Where:

w = load per unit length (3 kN/m)

L = span (2.4 m)

Plugging in the values:

M = (3 * 2.4^2) / 8

M = 2.16 kNm

Next, we can calculate the section modulus (S) required for the beam using the formula:

S = (M * 10^6) / σ

Where:

M = maximum bending moment (2.16 kNm)

σ = allowable normal stress of timber (13.5 MPa)

Converting the stress to N/mm^2:

σ = 13.5 MPa = 13.5 N/mm^2

Plugging in the values:

S = (2.16 * 10^6) / 13.5

S ≈ 160,000 mm^3

The section modulus (S) of a rectangular beam can be calculated using the formula:

S = (b * h^2) / 6

Where:

b = width of the beam

h = height of the beam

Substituting the known value for S and rearranging the formula, we get:

b = (6 * S) / h^2

We can rearrange this formula to solve for b:

b = (6 * S) / h^2

To proceed, we need to assume a height (h) for the beam. Let's assume a reasonable value of h = 200 mm.

Plugging in the values:

b = (6 * 160,000) / 200^2

b ≈ 192 mm

Therefore, the required value of b (width of the beam) is approximately 192 mm.

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Answer:

a

Step-by-step explanation:

To calculate the probability that a randomly chosen applicant will score between 500 and 600 on the test, we need to use the standard normal distribution.

We'll convert the given scores into z-scores and then find the corresponding probabilities using a standard normal distribution table or a statistical calculator. First, let's calculate the z-score for the lower boundary of 500: z1 = (500 - 560) / 90 = -0.667

Next, let's calculate the z-score for the upper boundary of 600:
z2 = (600 - 560) / 90 = 0.444. Now, we can find the probability associated with each z-score. Using a standard normal distribution table or a calculator, we find that the probability corresponding to z1 is approximately 0.2525, and the probability corresponding to z2 is approximately 0.6700.

To find the probability between these two boundaries, we subtract the lower probability from the upper probability:
P(500 < X < 600) = P(z1 < Z < z2) = P(Z < z2) - P(Z < z1) = 0.6700 - 0.2525 = 0.4175 Therefore, the probability that a randomly chosen applicant will score between 500 and 600 on the test is approximately 0.4175, or 41.75%.

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Answer:

3 km/m

Step-by-step explanation:

since speed is distance over time; you devide 503km over 180 minutes and get 2.79km/m and round 2.79 to nearest km and get 3km/m

Answer:

Step-by-step explanation:

The y-intercept is (0,1).

The explicit formula for f^-1 is (x-3)^(1/4) and this is obtained by switching the roles of x and y and solving for y in terms of x.

To find the inverse function of f(x)=x^4+3, we need to switch the roles of x and y, and solve for y.
Let y = x^4+3
Subtract 3 from both sides to get:
y - 3 = x^4
Take the fourth root of both sides to isolate x:
(x^4)^(1/4) = (y-3)^(1/4)
Simplify:
x = (y-3)^(1/4)
So the inverse function of f(x) is:
f^-1 (x) = (x-3)^(1/4)
This is the explicit formula for the inverse function of f(x).
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Answer:

no photooooooooooooooooooooooooooooo

Answer:

no photttttoooooooo

Step-by-step explanation:

Using a regression equation, the predicted carbon dioxide emission amount can be determined for various values of GDP. The predictions will be provided in their original units without rounding.

Regression analysis allows us to establish a mathematical relationship between two or more variables. In this case, we have a regression equation that can be used to predict the carbon dioxide emission amount based on GDP. However, it's important to note that the specific regression equation is not provided, so we'll assume it is a valid equation for this analysis.

To make predictions, we substitute different values of GDP into the regression equation and calculate the corresponding predicted carbon dioxide emission amount. The predictions will be presented without any rounding, maintaining the precision of the calculation.

Please provide the specific values of GDP for which you would like the carbon dioxide emission predictions, and the corresponding regression equation. With that information, I will be able to generate the predictions accurately.

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(a) Example question: "How often do you look at social media while doing schoolwork?

(b) Sofie can select a simple random sample of students by using a random number generator to assign a unique identification number to each student in the online high school.

(c) The sample for Sofie's research is the 32 completed surveys she received. These surveys represent the responses of a subset of the population. The population, in this case, refers to all the students at the online high school.

(d) If Sofie uses only the completed surveys, she can conclude that approximately 50% (16 out of 32) of the students who completed the survey reported using social media while doing schoolwork.

(a) Please select one of the following options: never, rarely, occasionally, frequently, or always."

(b) She can then use the random number generator again to select a specific number of students from the entire population of students, ensuring that each student has an equal chance of being selected. For example, if there are 500 students in total and Sofie wants a sample size of 50, she can generate 50 random numbers and select the corresponding students based on their identification numbers.

(d) However, it is important to note that this conclusion is specific to the sample of completed surveys and cannot be generalized to the entire population of high school students.

To make an inference about the percent of all high school students who use social media while doing schoolwork, Sofie would need a larger and more representative sample that covers a wider range of students in the online high school.

Additionally, she should consider potential biases in the sample, such as non-response bias if the students who chose not to complete the survey have different social media usage patterns compared to those who did respond.

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Given data:

The given expression is -4/9 x=3/8

The given expression can be written as,

The product is less than both the factors.

Thus, option C) is correct.

The limit of f(x) as x goes to 2 is given by:

C. 0.

A limit is given by the value of function f(x) as x tends to a value a, that is, we have to look to the left of x = a and to the right of x = a, and if these values are equal, this is the limit of the function.

In this problem, we have that:

Since the lateral limits are equal, the limit of the function as x approaches 2 is of 0 and option C is correct.

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Answer:

  1/6^3

Step-by-step explanation:

The applicable rules of exponents are ...

  a^-b = 1/a^b

  (a^b)(a^c) = a^(b+c)

__

Your expression can be simplified as follows:

  \(\dfrac{6^{-5}}{6^{-2}}=\dfrac{1}{(6^{-2})(6^5)}=\dfrac{1}{6^{-2+5}}=\boxed{\dfrac{1}{6^3}}\)

_____

Additional comment

If you think of an exponent as signifying repeated multiplication, the rules of exponents may be easier to remember. The exponent tells you how many times the base is a factor in the product.

Consider multiplication:

  \((x\cdot x\cdot x)\cdot(x\cdot x)=x^3\cdot x^2=x^{3+2}=x^5\\\\(x\cdot x\cdot x)\cdot(x\cdot x\cdot x)=(x^3)^2=x^{3\cdot2}=x^6\)

Consider division:

  \(\dfrac{x\cdot x\cdot x}{x\cdot x}=x\quad\Longleftrightarrow\quad\dfrac{x^3}{x^2}=x^{3-2}=x^1\\\\\dfrac{x\cdot x}{x\cdot x\cdot x}=\dfrac{1}{x}\quad\Longleftrightarrow\quad\dfrac{x^2}{x^3}=x^{2-3}=x^{-1}\)

This may help you see that a positive exponent in the denominator is equivalent to a negative exponent in the numerator (and vice versa).

(a) The expected number of board-feet of timber next year is 102.9. (b) The interest rate at the bank matters in deciding to cut the trees down now or in the future due to the opportunity cost of waiting and potential earnings from investing the proceeds. (c) In order for cutting the trees down next year to be a better choice than cutting them down now, the interest rate at the bank has to be lower.

(a) To calculate the expected number of board-feet of timber next year, we multiply the probabilities of each outcome by the corresponding timber quantity and sum them. With a 98% probability of growth and a 5% increase in timber, and a 2% probability of fire and no timber, the expected number of board-feet of timber next year would be: (0.98 * 100 * 1.05) + (0.02 * 0) = 102.9 board-feet.

(b) The interest rate at the bank matters in deciding to cut the trees down now or in the future because it represents the opportunity cost of waiting. By cutting the trees down now and selling the timber, you can invest the proceeds in the bank and earn interest over time. If the interest rate is high, the present value of the future timber may be lower compared to the immediate cash flow from selling the timber now, making it more favorable to cut the trees down earlier.

(c) In order for cutting the trees down next year to be a better choice than cutting them down now, the interest rate at the bank has to be lower. A lower interest rate implies that the present value of future cash flows (from selling the timber next year) is higher relative to the immediate cash flow (from selling the timber now). Therefore, a lower interest rate makes it more advantageous to delay cutting the trees and wait for them to grow, maximizing the forester's profit.

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The solution to the problem ut - kuxx + tu = 0 with u(x,0) = e^-x and ux(0,t) = 0 is given by u(x,t) = e^(-x+t^2/2k).

To solve the problem ut - kuxx + tu = 0, with initial condition u(x,0) = e^-x and boundary condition ux(0,t) = 0 using the Fourier cosine transform, we can follow these steps:

Step 1: Apply the Fourier Cosine Transform

Apply the Fourier cosine transform to both sides of the partial differential equation with respect to the spatial variable x. The Fourier cosine transform pair for the derivative is given by:

C{uxx} = -ω^2C{u}

Using the properties of the Fourier cosine transform, we obtain:

∂(C{u})/∂t + kω^2C{u} + tC{u} = 0

Step 2: Solve the Transformed Equation

The transformed equation is now an ordinary differential equation in terms of the transform variable ω. Solve this equation using standard techniques for ordinary differential equations. The solution will involve an arbitrary function C{u}(ω) and the initial condition C{u}(ω, 0) = C{e^-x}(ω).

Step 3: Apply the Inverse Fourier Cosine Transform

Apply the inverse Fourier cosine transform to the solution obtained in step 2 to obtain the solution u(x, t) in the original variables:

u(x, t) = C^(-1){C{u}(ω)}

Step 4: Apply the Initial and Boundary Conditions

Use the given initial condition u(x, 0) = e^-x and boundary condition ux(0, t) = 0 to determine the specific form of the arbitrary function C{u}(ω) and obtain the final solution u(x, t).

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The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

125

Step-by-step explanation:

There are four right angles in a triangle so i divided 500 by 4