the sum of three consecutive even integers is 30. what are the integers? 2, 3, 5 9, 10, 11 –8, –10,

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) an

ExtremeBDS [4]

Answer:

$y\geq x-2$

$x+2y$

Step-by-step explanation:

step 1

Find the equation of the first inequality

Find the equation of the first solid line

we have the ordered pairs

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

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{0+2}{2-0}$

$m=\frac{2}{2}$

$m=1$

The equation in slope intercept form is equal to

$y=mx+b$

we have

$m=1$

$b=-2$ ---> the y-intercept is given

substitute

$y=x-2$

Remember that

Everything to the left of the solid line is shaded

so

The inequality is

$y\geq x-2$

step 2

Find the equation of the second inequality

Find the equation of the second dashed line

we have the ordered pairs

(0,2) and (4,0)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the values

$m=\frac{0-2}{4-0}$

$m=\frac{-2}{4}$

$m=-\frac{1}{2}$

The equation in slope intercept form is equal to

$y=mx+b$

we have

$m=-\frac{1}{2}$

$b=2$ ---> the y-intercept is given

substitute

$y=-\frac{1}{2}x+2$

Remember that

Everything below and to the left of the line is shaded

so

The inequality is

$y$

Rewrite

Multiply by 2 both sides

$2y$

$x+2y$

therefore

The system of inequalities is

$y\geq x-2$

$x+2y$

see the attached figure to better understand the problem

5 0

3 years ago

Read 2 more answers

Will mark brainliest, pls help it's urgent due in 1 hour

dem82 [27]

Answer:

she shouldn't adjust the compass width.

3 0

2 years ago

What is the equivalent expression of 8x+7y+5x+4y+2y

Natalija [7]

Answer:

13x+13y

Step-by-step explanation:

(combine like terms)

8x+5x=13x

7y+4y+2y=13y

hope this helped you!

4 0

3 years ago

find the equations of the tangents to the curve y= x(x-1)(x+2) at the points where the curve cuts the x axis

antoniya [11.8K]

First of all, we compute the points of interest, i.e. the points where the curve cuts the x axis: since the expression is already factored, we have

$x(x-1)(x+2) = 0 \iff x=0\ \lor\ x-1=0\ \lor\ x+2=0$

Which means that the roots are

$x=0\ \lor\ x=1\ \lor\ x=-2$

Next, we can expand the function definition:

$y = x(x-1)(x+2) = x^3 + x^2 - 2x$

In this form, it is much easier to compute the derivative:

$y' = 3x^2+2x-2$

If we evaluate the derivative in the points of interest, we have

$y'(-2) = 6,\quad y'(0)=-2,\quad y'(1)=3$

This means that we are looking for the equations of three lines, of which we know a point and the slope. The equation

$y-y_0=m(x-x_0)$

is what we need. The three lines are:

$y-0=6(x+2) \iff y = 6x+12$ This is the tangent at x = -2

$y-0=-2(x-0) \iff y = -2x$ This is the tangent at x = 0

$y-0=3(x-1) \iff y = 3x-3$ This is the tangent at x = 1

7 0

3 years ago

The following data represent the number of grams of fat in breakfast meals offered at a local fast food restaurant. (a) Constru

rewona [7]

Answer:

The following are the answer to this question:

Step-by-step explanation:

In the question some data is missing, which is defined in the attached file please find it.

The table for point a:

plot for the Stem-and-leaf:

0 3 4 5 7 4

1 2 2 4 4 5 7 7 7

2 0 3 4 4 5 8 6

3 3 4 7 9 4

4 1

In point b:

Its distributed skewed is correct because in its points 1 is a tail on its right side.

please find the attached file.

8 0

3 years ago

the sum of three consecutive even integers is 30. what are the integers? 2, 3, 5 9, 10, 11 –8, –10, –12 8, 10, 12