(y +12) (y - 18) (x) (z) x= y = Z =

Find and simplify an expression for the area of three rows of m squares with side lengths of m centimeters. Please help

Anna [14]

Answer:

3m²

Step-by-step explanation:

A square is quadrilateral (four sides) in which all sides are equal. Also, opposite sides are parallel to one another and all the four angles in a square are 90 degrees each.

The area of a square is given as:

Area = length * length

Given that the square has side lengths of m centimeters, therefore:

The area of each square = m cm × m cm = m² cm²

There are three rows of m squares, hence the total number of square is:

Total square = 3 rows * m squares per row = 3m squares

The total area of the square = area of each square * total number of square = m² * 3m = 3m² cm²

3 0

3 years ago

Show that the following argument with hypotheses on lines 1–2 and conclusion on line c is

Sonja [21]

Answer:

Step-by-step explanation:

$p \Rightarrow q \equiv (\neg p \vee q)$ [logical equivalence]

$\neg (q \vee r) \equiv (\neg q \wedge \neg r)$ [morgan laws]

if $(\neg q \wedge \neg r)$ is true, then $\neg q$ is true and $\neg r$ is too.

with $\neg q$ true, then $q$ is false [double denial]

In the first equivalence it follows that $\neg p$ is true [identity law]

Then it can be concluded that $\neg p$

7 0

3 years ago

Which of the following expressions represents a function? (5 points) a {(1, 2), (4, −2), (8, 3), (9, −3)} b y2 = 16 − x2 c 2x2 +

34kurt

Answer: Option "a" is the only expression that represents a function.

Step-by-step explanation:

A function f(x) = y is a "operator" that takes an input element, x, and assigns it to only one output element, y.

So, if we have that for a given value of x.

f(x) = y and f(x) = h

where y and h are different values, then this is not a function, because is assigning the input value x to two different output values.

Let's see the different options:

a) {(1, 2), (4, −2), (8, 3), (9, −3)}

This points are of the form (x, y)

We can see that each value of x is assigned to only one value of y, so this can represent a function.

b) y^2 = 16 − x^2

Ok, suppose that x = 0, then:

y^2 = 16 - 0 = 16

then we have that y*y = 16.

So y can take two different values:

y = 4 ---> 4*4 = 16

y = -4 ---> -4*-4 = 16.

So this is not a function.

c) 2x^2 + y^2 = 5

First, we want to isolate y in one side:

y^2 = 5 - 2*x^2

Here we have a similar case to the option b, and we can use a similar argument to prove that this is not a function, so we can discard this.

d) x = 7.

Ok, this is not a relation between two variables, so this is not a function, as if x is the input value, we have only one value of x that solves the equation.

7 0

4 years ago

Isaac wants to buy tomatoes and a loaf of bread. Tomatoes are $1.20 a pound, and a loaf of bread is $2.00. He has $8.00 to spend

Anestetic [448]

Answer:

Isaac has $4.80 left

Step-by-step explanation:

$1.20 + 2.00 = 3.20

$8.00 - 3.20 = 4.80

4 0

4 years ago

Find the coordinates of the centroid of the triangle formed by the x-axis, the y-axis, and the line 12x + 9y = 36, show work ple

emmainna [20.7K]

Given the line 12x + 9y = 36

the line intersects the x-axis when y = 0,

i.e. 12x = 36 ⇒ x = 3

Thus the x-intecept is (3, 0)

the line intersects the y-axis when x = 0,

i.e. 9y = 36 ⇒ y = 4

Thus, the y-intercept is (0, 4)

Thus, the coordinates of the vertices of the triangle are (0, 0), (0, 4) and (3, 0)

The midpoint of the side of the rectangle joining points (0, 0) and (0, 4) is (0, 2) and the equation of the median joining points (0, 2) and (3, 0) is given by

$\frac{y-2}{x} = \frac{-2}{3} \\ \\ \Rightarrow3(y-2)=-2x \\ \\ \Rightarrow y=- \frac{2}{3} x+2$

The midpoint of the side of the rectangle joining points (0, 0) and (3, 0) is (1.5, 0) and the equation of the median joining points (1.5, 0) and (0, 4) is given by

$\frac{y}{x-1.5} = \frac{4}{-1.5} \\ \\ \Rightarrow1.5y=-4(x-1.5)=-4x+6 \\ \\ \Rightarrow y=- \frac{8}{3} x+4$

The point of intersetion of the two medians is given by

$- \frac{2}{3} x+2=- \frac{8}{3} x+4 \\ \\ \Rightarrow2x=2 \\ \\ \Rightarrow x=1 \\ \\ \Rightarrow y=-\frac{2}{3}+2=\frac{4}{3}$

Therefore, the centroid of the given triangle is located at point $\left(1, \frac{4}{3} \right)$

4 0

3 years ago