What is the unit (1 pound) price (rounded to the nearest penny) for a piece of cheese if 1.24 pounds costs $11.25?

A line passes through (10,2) and (14,-22). Write the equation of the line in standard form.

jarptica [38.1K]

Answer:

The equation of the line in standard form is:

$6x + y = 62$

Step-by-step explanation:

Given the points

(10,2)

(14,-22)

Determining the slope between (10, 2) and (14, -22)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(10,\:2\right),\:\left(x_2,\:y_2\right)=\left(14,\:-22\right)$

$m=\frac{-22-2}{14-10}$

$m=-6$

The point-slope form of the line equation is

$y-y_1=m\left(x-x_1\right)$

where

m is the slope of the line

(x₁, y₁) is the point

substituting the values m = -6 and the point (10, 2) in the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

$y - 2 = -6(x - 10)$

$y - 2 = -6x +60$

adding 2 to both sides

$y-2+2 = -6x + 60 + 2$

$y = -6x + 62$

We can write the equation in the standard form such as

Ax + By = C

Thus,

$y = -6x + 62$

adding -6x to both sides

$6x + y = -6x + 62 + -6x$

$6x + y = 62$

Therefore, the equation of the line in standard form is:

$6x + y = 62$

4 0

3 years ago

Fins the zeros, multiplicity, and effect on the graph of the function in

tekilochka [14]

Answer:

See explanation

Step-by-step explanation:

Zeroe of the function is such velue of x at which f(x)=0.

1. Consider the function $f(x)=-x(3x-2)^2 (x+9)^5.$

Zeros are:

$-x(3x-2)^2(x+9)^5=0\\ \\x=0\text{ or }x=\dfrac{2}{3}\text{ or }x=-9.$

Zero $x=0$ has multiplicity of 1, zero $x=\dfrac{2}{3}$ has multiplicity of 2, zero $x=-9$ has multiplicity of 5.

At $x=0$ or $x=-9$ the graph of the function crosses the x-axis, at $x=\dfrac{2}{3}$ the graph of the function touches the x-axis.

2. Consider the function $f(x)=x^3+10x^2+25x=x(x^2+10x+25)=x(x+5)^2.$

Zeros are:

$x(x+5)^2=0\\ \\x=0\text{ or }x=-5.$

Zero $x=0$ has multiplicity of 1, zero $x=-5$ has multiplicity of 2.

At $x=0$ the graph of the function crosses the x-axis, at $x=-5$ the graph of the function touches the x-axis.

8 0

4 years ago

How many sides does a regular polygon have if the measure of each interior angle is 1600?

Art [367]

Answer:

18 sides

Step-by-step explanation:

with regular polygons it is best to remember that:

(1) all the EXTERIOR angles add up to 3600

(2) 1 exterior angle+1 interior angle =1800

Work with the exterior angles. In this case:

1 int. <=180−160=200

No. of sides =36020=18

7 0

3 years ago

Which of the following points would be a solution to this system of linear inequalities?

pychu [463]

Let's plug in both x and y values in the equation and check if the inequality is true...

$\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}$

$(4,1) \\ y \leqslant x + 1 \\ y < - \frac{x}{2} - 1$

Substitute x as 4 and y as 1

$1 \leqslant 4 + 1 \\ 1 < - \frac{4}{2} - 1$

$0 \leqslant 4 + 1 \\ 1 < - 2 - 1$

$0 \leqslant 5 \\ 1 < - 3$

This is not a solution because both are not true, Only one equation is giving true as answer which is not correct!~

$\purple{ \rule{300pt}{3pt}}$

$(0, - 3) \\ y \leqslant x + 1 \\ y < - \frac{x}{2} - 1$

Substitute x as 0 and y as -3

$- 3 \leqslant 0 + 1 \\ - 3 < - \frac{0}{2} - 1$

$- 3 \leqslant 1 \\ - 3 < - 0 - 1$

$- 3 \leqslant 1 \\ - 3 < - 1$

This is a solution because both are true, Both the equations are true which means the ordered pair is a solution!~

Thus, Option B (0,-3) is the correct choice....

6 0

3 years ago

Simplify the expression by combining like terms. 16+8−3+6−9

lyudmila [28]

Answer=18
First step combine the positive like terms
16+8+6
|
|
\/
30
Second step is to combine negative like terms with 30
30-3-9

When you do this you add 9 and 3 together since they are similar to each other so it equals 12 there for the equation becomes.....
30-12

Final answer 18

4 0

3 years ago