All categories

3 years ago

How do I Find the slope and Y intercept of each equation:

1 answer:

6 0

$1.\\ \\ the \ slope \ intercept \ form \ is : \\ \\ y= mx +b \\ \\y=2x+1 \\ \\ the \ slope \ (the multiplier \ of \ x \ represented \ by \ m ) \ is \ 2 \\ \\ and \ the \ y-intercept \ (the constantrepresented \ by \ b \ ) \ is \ 1$

$2.\\ \\ y= \frac{1}{3}x-3 \\ \\ the \ slope \ m = \frac{1}{3} \ \ and \ y = -3$

$3.\\ \\ y= -2x + 1\\ \\ the \ slope \ m = -2 \ \ and \ y = 1$

$4.\\ \\-2x +5y=10\\ \\5y=2x +10 \ \ /:5\\ \\y = \frac{2}{5}x +2\\ \\ the \ slope \ m =\frac{ 2}{5} \ \ and \ y = 2$

$5.\\ \\ 4x-2y-5=0\\ \\-2y =-4x +5 \ \ /:(-2)\\ \\y=2x-\frac{5}{2} \\ \\ the \ slope \ m = 2 \ \ and \ y = -\frac{5}{ 2}$

$6.\\ \\ y=-4x-3 \\ \\ the \ slope \ m =-4 \ \ and \ y = -3$

$7.\\ \\3x-5y=20\\ \\-5y=-3x +20 \ \ / :(-5) \\ \\ y= \frac{3}{5}x - 4\\ \\ the \ slope \ m = \frac{3}{5} \ \ and \ y = -4$

You might be interested in

Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y2

exis [7]

The Jacobian for this transformation is

$J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}$

with determinant $|J| = 12$ , hence the area element becomes

$dA = dx\,dy = 12 \, du\,dv$

Then the integral becomes

$\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv$

where $R'$ is the unit circle,

$\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1$

so that

$\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv$

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

$\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}$

Then

$\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}$

3 0

2 years ago

Evaluate the expression –0.4(3x – 2) + 2x+4/3 for x=4

fomenos

Answer:

-1.07

Step-by-step explanation:

–0.4(3x – 2) + 2x+4/3

–0.4(24 – 2) + 8+4/3

-9.6-0.8+8+1.33

-2.4+1.33

-1.07

8 0

3 years ago

Find the measures of the angles of the triangle whose vertices are A = (-3,0) , B = (1,3) , and C = (1,-3).A.) The measure of ∠A

alekssr [168]

Answer:

$\theta_{CAB}=128.316$

$\theta_{ABC}=25.842$

$\theta_{BCA}=25.842$

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

$r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

$AB= \sqrt{(-3-1)^2+(0-3)^2}=5$

$BC= \sqrt{(1-1)^2+(3-(-3))^2}=9$

$CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5$

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

$BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}$

$\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}$

$\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}$

$\theta_{CAB}=\arccos{-\dfrac{0.62}}$

$\theta_{CAB}=128.316$

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

$\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}$

$\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)$

$\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)$

$\theta_{ABC}=\arcsin{0.4359}\right)$

$\theta_{ABC}=25.842$

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

$\theta_{BCA}=25.842$

this can also be checked using the fact the sum of all angles inside a triangle is 180

$\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180$

$25.842+128.316+25.842$

$180$

6 0

3 years ago

Read 2 more answers

Select the best method of finding an accurate solution to a system of linear equations

Flura [38]

The best method for solving the system of linear equation is by the use of algebraic methods.

The system of linear equations can be solved by using the method of simultaneous equations. Here we are given two equations and two unknown variables. We can solve the same by eliminating one of the variables and then either adding or subtracting, find the value of the other variable. Once we know the value of one variable, then we can substitute its value in any one given equation and find the second variable. This method is said to be accurate and does not involve any error.

Hence answer is : USE ALGEBRAIC METHODS

4 0

3 years ago

Read 2 more answers

It’s a new semester! Students are grouped into three clubs, which each has 10, 4 and 5 students. In how many ways can teacher se

ozzi

Here we must see in how many different ways we can select 2 students from the 3 clubs, such that the students <em>do not belong to the same club. </em>We will see that there are 110 different ways in which 2 students from different clubs can be selected.

So there are 3 clubs:

Club A, with 10 students.
Club B, with 4 students.
Club C, with 5 students.

The possible combinations of 2 students from different clubs are

Club A with club B
Club A with club C
Club B with club C.

The number of combinations for each of these is given by the product between the number of students in the club, so we get:

Club A with club B: 10*4 = 40
Club A with club C: 10*5 = 50
Club B with club C. 4*5 = 20

For a total of 40 + 50 + 20 = 110 different combinations.

This means that there are 110 different ways in which 2 students from different clubs can be selected.

If you want to learn more about combination and selections, you can read:

brainly.com/question/251701

6 0

2 years ago