If a line crosses the y-axis at (0,1) and has a slope of 4/5 what is the equation of the line

Step-by-step explanation:

y = 4/5x + 1

Step-by-step explanation:

y = mx + b

m = slope

b = y-intercept

y = 4/5x + 1

Related Questions

Find the value of X.

2+3x=62

3x=60

x=20

Hope this helps! Brainliest? :D

Can someone help me and can y’all show me how you got the answer

x = -8

Step-by-step explanation:

Step 1: Write equation

1/2x + 13 = 9

Step 2: Solve for x

1. Subtract 13 on both sides: 1/2x = -4
2. Multiply both sides by 2: x = -8

Step 3: Check

Plug in x to verify it's a solution.

1/2(-8) + 13 = 9

-4 + 13 = 9

9 = 9

-8

Step-by-step explanation:

you use inverse operation

meaning opposite signs

subtract -13 from 13 cross it out

subtract 13 from 9

you get 1/2x=-4

divide 1/2 on both sides

-4 divided by 1/2 =-8

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) π/2 0 3 1 + cos(x) dx, n = 4

Split up the integration interval into 4 subintervals:

The left and right endpoints of the -th subinterval, respectively, are

for , and the respective midpoints are

• Trapezoidal rule

We approximate the (signed) area under the curve over each subinterval by

so that

• Midpoint rule

We approximate the area for each subinterval by

so that

• Simpson's rule

We first interpolate the integrand over each subinterval by a quadratic polynomial , where

so that

It so happens that the integral of reduces nicely to the form you're probably more familiar with,

Then the integral is approximately

Compare these to the actual value of the integral, 3. I've included plots of the approximations below.

The question is asking to approximate the definite integral of 1 + cos(x) from 0 to π/2 using the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule for n=4. These are numerical methods used for approximating integrals by estimating the area under the curve as simpler shapes.

Explanation:

This question asks to use several mathematical rules, specifically the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule, to approximate the given integral with a specified value of n which is 4. The integral given is the function 1 + cos(x) dx from 0 to π/2. Each of these rules are techniques for approximating the definite integral of a function. They work by estimating the region under the graph of the function and above the x-axis as a series of simpler shapes, such as trapezoids or parabolas, and then calculating the area of these shapes. The 'dx' component represents a small change in x, the variable of integration. The cosine function in this integral is a trigonometric function that oscillates between -1 and 1, mapping the unit circle to the x-axis. The exact solution would require calculus, but these numerical methods provide a close approximation.

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True or false: The number 0 (zero) IS an integer

true. zero is an integer number

Step-by-step explanation:

True,  it is Known as a neutral integer Because it is neither negative or positive whole number

Step-by-step explanation:

An elementary school is offering 3 language classes: one in Spanish, one inFrench, and one in German. The classes are open to any of the 100 students inthe school. There are 28 students in the Spanish class, 26 in the French class,and 16 in the German class. There are 12 students that are in both Spanish andFrench, 4 that are in both Spanish and German, and 6 that are in both Frenchand German. In addition, there are 2 students taking all 3 classes.(a) If a student is chosen randomly, what is the probability that he or she isnot in any of the language classes

0.5 = 50% probability that he or she is not in any of the language classes.

Step-by-step explanation:

We treat the number of students in each class as Venn sets.

I am going to say that:

Set A: Spanish class

Set B: French class

Set C: German class

We start building these sets from the intersection of the three.

In addition, there are 2 students taking all 3 classes.

This means that:

6 that are in both French and German

This means that:

So

4 French and German, but not Spanish.

4 that are in both Spanish and German

This means that:

So

2 Spanish and German, but not French

12 students that are in both Spanish and French

This means that:

So

10 Spanish and French, but not German

16 in the German class.

This means that:

8 in only German.

26 in the French class

10 only French

28 students in the Spanish class

14 only Spanish

At least one of them:

The sum of all the above values. So

None of them:

100 total students, so:

(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?

50 out of 100. So

50/100 = 0.5 = 50% probability that he or she is not in any of the language classes.

Calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess. (Round your answers to three decimal places.) f(x) = x9 − 9, x1 = 1.6

Iteration 1:

Iteration 2:

Step-by-step explanation:

Formula for Newton's method is,

Given the initial guess as , therefore value of n = 1.

Also, .

Differentiating with respect to x,

Applying difference rule of derivative,

Applying power rule and constant rule of derivative,

Substituting the value,

Calculating the value of and

Calculating

Calculating ,

Substituting the value,

Therefore value after second iteration is

Now use as the next value to calculate second iteration. Here n = 2

Therefore,

Calculating the value of and

Calculating

Calculating ,

Substituting the value,

Therefore value after second iteration is

To calculate two iterations of Newton's Method, use the formula xn+1 = xn - f(xn)/f'(xn). Given an initial guess of x1 = 1.6 and the function f(x) = x9 - 9, calculate f(xn) and f'(xn) at x1 and then use the formula to find x2 and x3.

Explanation:

To calculate two iterations of Newton's Method, we need to use the formula:

xn+1 = xn - f(xn)/f'(xn)

Given an initial guess of x1 = 1.6 and the function f(x) = x9 - 9, we can proceed as follows:

1. Calculate f(xn) at x1: f(1.6) = (1.6)9 - 9 = 38.5432
2. Calculate f'(xn) at x1: f'(1.6) = 9(1.6)8 = 368.64
3. Calculate x2: x2 = 1.6 - f(1.6)/f'(1.6) = 1.6 - 38.5432/368.64 = 1.494
4. Repeat the process to find x3 using the updated x2 as the initial guess.