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

Answers

Answer 1
Answer:

Answer:4y-5x=5

Step-by-step explanation:

Answer 2
Answer:

Answer:

y = 4/5x + 1

Step-by-step explanation:

y = mx + b

m = slope

b = y-intercept

y = 4/5x + 1


Related Questions

Mr. Ruiz drove 205 miles in 5 hours on Saturday and 180 miles in 4 hours on Sunday. What was his average speed, in miles per hour, for the two days
Can someone help me with this please?
Хf(x)What is the initial value of the exponential functionrepresented by the table?-218e8-114012111222
In the game of tic-tac-toe, if all moves are performed randomly the probability that the game will end in a draw is . Suppose six random games of tic-tac-toe are played. What is the probability that at least one of them will end in a draw?
A square is a figure with four sides of equal length and four right anglesa)conditional statementb)postulatec)definitiond)conjecture

Find the value of X.

Answers

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

Answers

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

Answer:

-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

Answers

Split up the integration interval into 4 subintervals:

\left[0,\frac\pi8\right],\left[\frac\pi8,\frac\pi4\right],\left[\frac\pi4,\frac{3\pi}8\right],\left[\frac{3\pi}8,\frac\pi2\right]

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

\ell_i=\frac{i-1}4\left(\frac\pi2-0\right)=\frac{(i-1)\pi}8

r_i=\frac i4\left(\frac\pi2-0\right)=\frac{i\pi}8

for 1\le i\le4, and the respective midpoints are

m_i=\frac{\ell_i+r_i}2=\frac{(2i-1)\pi}8

  • Trapezoidal rule

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

T_i=\frac{f(\ell_i)+f(r_i)}2(\ell_i-r_i)

so that

\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4T_i\approx\boxed{3.038078}

  • Midpoint rule

We approximate the area for each subinterval by

M_i=f(m_i)(\ell_i-r_i)

so that

\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4M_i\approx\boxed{2.981137}

  • Simpson's rule

We first interpolate the integrand over each subinterval by a quadratic polynomial p_i(x), where

p_i(x)=f(\ell_i)((x-m_i)(x-r_i))/((\ell_i-m_i)(\ell_i-r_i))+f(m)((x-\ell_i)(x-r_i))/((m_i-\ell_i)(m_i-r_i))+f(r_i)((x-\ell_i)(x-m_i))/((r_i-\ell_i)(r_i-m_i))

so that

\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4\int_(\ell_i)^(r_i)p_i(x)\,\mathrm dx

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

S_i=\displaystyle\int_(\ell_i)^(r_i)p_i(x)\,\mathrm dx=\frac{r_i-\ell_i}6(f(\ell_i)+4f(m_i)+f(r_i))

Then the integral is approximately

\displaystyle\int_0^(\pi/2)\frac3{1+\cos x}\,\mathrm dx\approx\sum_(i=1)^4S_i\approx\boxed{3.000117}

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

Final answer:

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.

Learn more about Numerical Integration Rules here:

brainly.com/question/36635050

#SPJ11

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

Answers

Answer:

true. zero is an integer number

Step-by-step explanation:

Answer:

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

Answers

Answer:

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:

(A \cap B \cap C) = 2

6 that are in both French and German

This means that:

(B \cap C) + (A \cap B \cap C) = 6

So

(B \cap C) = 4

4 French and German, but not Spanish.

4 that are in both Spanish and German

This means that:

(A \cap C) + (A \cap B \cap C) = 4

So

(A \cap C) = 2

2 Spanish and German, but not French

12 students that are in both Spanish and French

This means that:

(A \cap B) + (A \cap B \cap C) = 12

So

(A \cap B) = 10

10 Spanish and French, but not German

16 in the German class.

This means that:

(C - B - A) + (A \cap C) + (B \cap C) + (A \cap B \cap C) = 16

(C - B - A) + 2 + 4 + 2 = 16

(C - B - A) = 8

8 in only German.

26 in the French class

(B - C - A) + (A \cap B) + (B \cap C) + (A \cap B \cap C) = 26

(B - C - A) + 10 + 4 + 2 = 26

(B - C - A) = 10

10 only French

28 students in the Spanish class

(A - B - C) + (A \cap B) + (A \cap C) + (A \cap B \cap C) = 16

(A - B - C) + 10 + 2 + 2 = 28

(A - B - C) = 14

14 only Spanish

At least one of them:

The sum of all the above values. So

(A \cup B \cup B) = 14 + 10 + 8 + 10 + 2 + 4 + 2 = 50

None of them:

100 total students, so:

100 - (A \cup B \cup B) = 100 - 50 = 50

(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

Answers

Answer:

Iteration 1: x_(2)=1.446

Iteration 2: x_(3)=1.337

Step-by-step explanation:

Formula for Newton's method is,

x_(n+1)=x_n-(f\left(x_n\right))/(f'\left(x_n\right))

Given the initial guess as x_(1)=1.6, therefore value of n = 1.

Also, f\left(x\right)=x^(9)-9.

Differentiating with respect to x,

(d)/(dx)\left(f\left(x\right)\right)=(d)/(dx)\left(x^9-9\right)

Applying difference rule of derivative,

(d)/(dx)\left(f\left(x\right)\right)=(d)/(dx)\left(x^9\right)-(d)/(dx)\left(9\right)

Applying power rule and constant rule of derivative,

(d)/(dx)\left(f\left(x\right)\right)=\left(9x^(9-1)\right)-0

(d)/(dx)\left(f\left(x\right)\right)=9x^(8)

Substituting the value,

x_(1+1)=x_1-(f\left(x_1\right))/(f'\left(x_1\right))

x_(2)=1.6-(f\left(1.6\right))/(f'\left(1.6\right))

Calculating the value of f\left(1.6\right) and f'\left(1.6\right)

Calculating f\left(1.6\right)

f\left(1.6\right)=\left(1.6\right)^(9)-9

f\left(1.6\right)=59.71947674

Calculating f'\left(1.6\right),

f'\left(1.6\right)=9\left(1.6\right)^(8)

f'\left(1.6\right)=386.5470566

Substituting the value,

x_(2)=1.6-(59.71947674)/(386.5470566)

x_(2)=1.446

Therefore value after second iteration is x_(2)=1.446

Now use x_(2)=1.446 as the next value to calculate second iteration. Here n = 2

Therefore,

x_(2+1)=x_2-(f\left(x_2\right))/(f'\left(x_2\right))

x_(3)=1.446-(f\left(1.446\right))/(f'\left(1.446\right))

Calculating the value of f\left(1.446\right) and f'\left(1.446\right)

Calculating f\left(1.446\right)

f\left(1.446\right)=\left(1.446\right)^(9)-9

f\left(1.446\right)=18.63851065

Calculating f'\left(1.446\right),

f\left(1.446\right)=9\left(1.446\right)^(8)

f\left(1.446\right)=172.0239252

Substituting the value,

x_(3)=1.446-(18.63851065)/(172.0239252)

x_(3)=1.337

Therefore value after second iteration is x_(3)=1.337

Final answer:

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.

Learn more about Newton's Method here:

brainly.com/question/31910767

#SPJ3