(Please Help Asap) Evaluate 1/6 + 2/3 A. 1/5 B. 3/18 C. 5/6 D. 1 1/6

Write the equation of the line with x-intercept -2 and y-intercept -1 in slope-intercept form

eduard

The x-intercept of -2 gives us an idea that point (-2,0) if found along the line. The y-intercept of -1, tells us that point (0,-1), this also tells us that b = -1.

Now that we have two points, we can solve for slope m

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Given two points} \\ (-2,0)\rightarrow(x_1,y_1) \\ (0,-1)\rightarrow(x_2,y_2) \\ \\ \text{Substitute} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-0}{0-(-2)} \\ m=-\frac{1}{2} \end{gathered}$

Now that we have both m and b. Substitute these values to the slope intercept form

$\begin{gathered} \text{Slope intercept form is} \\ y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \\ \\ \text{Substitute the values from before and we get} \\ y=-\frac{1}{2}x-1 \end{gathered}$

5 0

1 year ago

4. What is the system of equations that describes the following graph?

GarryVolchara [31]

Answer:

The system of inequalities is

$y$

$y>0.25x$

Step-by-step explanation:

step 1

Find the equation of the dashed line with negative slope

The line passes through the points

(0,-2) and (-2,0)

Find the slope

$m=(0+2)/(-2-0)=-1$

Find the equation of the line in slope intercept form

$y=mx+b$

we have

$m=-1\\b=-2$

substitute

$y=-x-2$

The solution of the inequality is the shaded area below the dashed line

therefore

The equation of the inequality A is

$y$

step 2

Find the equation of the dashed line with positive slope

The line passes through the points

(0,0) and (4,1)

Find the slope

$m=(1-0)/(4-0)=0.25$

Find the equation of the line (direct variation)

$y=kx$

we have

$k=0.25$

substitute

$y=0.25x$

The solution of the inequality is the shaded area above the dashed line

therefore

The equation of the inequality B is

$y>0.25x$

therefore

The system of inequalities is

$y$

$y>0.25x$

4 0

3 years ago

Alonso leans a 28-foot ladder against a wall so that it forms an angle of 65° with the

lorasvet [3.4K]

The horizontal distance between the base of the ladder and the wall is: 11.8 foot

7 0

2 years ago

Richard is planning a banquet for the wrestling

Dvinal [7]

Y= total price
x= amount of people
b= one time fee

answer is y = 22x + 405

4 0

3 years ago

Use the quadratic formula to solve the equation. -2x^2-x+7=0.

Furkat [3]

-2x^2-x+7=0
Variable with the highest degree's (exponent) constant, -2 is a, next variable's constant, -1 is b, the constant or number without a variable, 7 is c

using substitution put the numbers into the formula
(-b±√(b^(2)-4ac))/(a^(2))

(-(-1)±√((-1)^(2)-4(-2)(7))/((-2)^(2)) simplify

(1±√(1+56))/4

1±√(57)/4 is your answer

8 0

3 years ago