Because I see a graph in the picture, I am assuming you need to graph the equations. The two equations are in slope-intercept form. They are in the form
y = mx + b
Where m is the slope and b is the y-intercept. That is why it is called the slope-intercept form.
If you want to graph a slope-intercept form equation, first plug in a value for x then compute it to get the y-coordinate.
First, let's get some points with the equation y = 4x + 3
We will plug in three values for x. 0, 1, and 2.
When x = 0
y = 4(0) + 3
y = 3
When x = 1
y = 4(1) + 3
y = 7
When x = 2
y = 4(2) + 3
y = 11
Now we have the points (0, 3), (1, 7), and (2, 11)
These points are called ordered pairs. Where the first number is the x-coordinate and the second number is the y-coordinate.
The ordered pairs tell you how many times you move your point away from the origin. The origin is (0, 0).
The first number of an ordered pair tells you how many times to move in the x direction and the second number how many times in the y direction.
Now graph the second equation. y = -x - 2
Just plug in some values for x.
I picked 0, 1, and 2.
When x = 0
y = 0 - 2
y = -2
When x = 1
y = -1 - 2
y = -3
When x = 2
y = -2 - 2
y = -4
Now we have the points (0, -2), (1, -3), and (2, -4)
Now plot those points and draw a line through them.
If you need to find the intersection of the equations y = 4x + 3 and y = -x - 2 you need to find where they intersect. Or in other words, share a common point.
After playing around with the numbers, I got the intersection point for the both of the equations.
It is the ordered pair (-1, -1). This the solution to both of the equations. If you plug in the ordered pairs into both of the equations, they will show it belongs to their graphs.
Plug in the values for y = 4x + 3
-1 = 4(-1) + 3
-1 = -4 + 3
-1 = -1
Plug in the values for y = -x - 2
-1 = -(-1) - 2
-1 = 1 - 2
-1 = -1
So, this ordered pair is on both equations!
The question in English
<span>1 Determine the length and area of a circle whose measures are:
a) radius 11cm b) radius 4.2 cm c) diameter 42.3 cm
2 considering that a large traditional pizza is 36 cm in radius and a small traditional pizza has 26 cm.Determine the difference between the area of the two pizzas
3.a worker spends 3 hours to clear a circular terrain of 6 meters radius. If the terrain was 12 meters radius, how much time would the worker spend to clean such terrain ???
4, transform the following arcs into radians
a) 27 ° b) 81 ° c) 144 ° d) 225 ° d) 315 °
Part 1)
we know that
length of a circle is equal to the circumference
circumference=2*pi*r
area of the circle=pi*r²
part a ) radius 11 cm
</span><span>circumference=2*pi*11-----> 69.08 cm
area of the circle=pi*11²----> 379.94 cm²
</span>
<span><span>part b) radius 4.2 cm
</span><span>circumference=2*pi*4.2-----> 26.38 cm
area of the circle=pi*4.2²----> 55.39 cm²
</span></span>
<span><span>part c ) diameter 42.3 cm
radius r=42.3/2=21.15 cm
</span><span>circumference=2*pi*21.15-----> 132.82 cm
area of the circle=pi*21.15²----> 1404.59 cm²
Part 2)
</span></span>
<span>area large traditional pizza
r=36 cm
area=pi*36²----> 4069.44 cm²
area </span><span>small traditional pizza
r=26 cm
area=pi*26²-----> 2122.64 cm²
</span><span>difference between the area of the two pizzas
=4069.44-2122.64
difference </span><span>between the area of the two pizzas=1946.80 cm²
Part 3)
Area of the </span><span>circular terrain of 6 meters radius
area=pi*6²-----> 113.04 m²
</span><span>Area of the <span>circular terrain of 12 meters radius
area=pi*12²-----> 452.16 m²
</span></span>
if a <span>worker spends 3 hours to clear a circular terrain of--------> 113.04 m²
x hours---------------------------> 452.16 m²
x=452.16*3/113.04-----> x=12 hours
Part 4) </span><span>transform the following arcs into radians
a) 27°
pi radians------> 180°
x radians-----> 27°
x=27*pi/180-----> x=0.15*pi radians------> 0.47 radians
</span><span>b) 81°
pi radians------> 180°
x radians-----> 81°
x=81*pi/180-----> x=0.45*pi radians------> 1.41 radians
</span>
<span>c) 144°
pi radians------> 180°
x radians-----> 144°
x=144*pi/180-----> x=0.80*pi radians------> 2.51 radians
</span>
<span>d) 225°
pi radians------> 180°
x radians-----> 225°
x=225*pi/180-----> x=1.25*pi radians------> 3.93 radians
</span>
<span>e) 315°
pi radians------> 180°
x radians-----> 315°
x=315*pi/180-----> x=1.75*pi radians------> 5.50 radians
</span><span>
the answer in Portuguese
</span>
<span>Parte 1)
</span>
<span>nós sabemos isso
</span><span>comprimento de um círculo é igual à circunferência
</span><span>circunferência=2*pi*r
</span>área do círculo<span>=pi*r²
parte a )
</span>raio<span> 11 cm
</span><span>circunferência=2*pi*11-----> 69.08 cm
</span><span><span>área do círculo=pi*11²----> 379.94 cm²
</span>
<span>parte b) raio 4.2 cm
</span></span><span>circunferência=2*pi*4.2-----> 26.38 cm
</span><span><span>área do círculo=pi*4.2²----> 55.39 cm²
</span>
<span>parte c )
</span></span>diâmetro<span> 42.3 cm
</span><span>raio r=42.3/2=21.15 cm
</span><span>circunferência=2*pi*21.15-----> 132.82 cm
</span><span><span>área do círculo=pi*21.15²----> 1404.59 cm²
Parte 2)
</span>
</span>
área grande pizza tradicional<span>r=36 cm
</span><span>área=pi*36²----> 4069.44 cm²
</span>
<span>área pequena pizza tradicional<span>
r=26 cm
</span></span><span>área=pi*26²-----> 2122.64 cm²
</span>diferença entre a área das duas pizzas<span> =4069.44-2122.64
</span>diferença entre a área das duas pizzas<span>=1946.80 cm²
Parte 3)
</span><span><span>
Área do terreno circular de 6 metros de raio</span>
</span><span>área=pi*6²-----> 113.04 m²
</span>
<span>Área do terreno circular de 12 metros de raio
</span><span><span>área=pi*12²-----> 452.16 m²
</span>
</span>se um trabalhador gastar 3 horas para limpar um terreno <span>-----> 113.04 m²
x hours---------------------------> 452.16 m²
x=452.16*3/113.04-----> x=12 horas
Parte 4) </span><span><span>transformar os seguintes arcos em radianos
a) 27°
pi radianos------> 180°
x radianos-----> 27°
x=27*pi/180-----> x=0.15*pi radianos------> 0.47 radianos
</span><span>b) 81°
pi radianos------> 180°
x radianos-----> 81°
x=81*pi/180-----> x=0.45*pi radianos------> 1.41 radianos
</span>
<span>c) 144°
pi radianos------> 180°
x radianos-----> 144°
x=144*pi/180-----> x=0.80*pi radianos------> 2.51 radianos
</span>
<span>d) 225°
pi radianos------> 180°
x radianos-----> 225°
x=225*pi/180-----> x=1.25*pi radianos------> 3.93 radianos
</span>
<span>e) 315°
pi radianos------> 180°
x radianos-----> 315°
x=315*pi/180-----> x=1.75*pi radianos------> 5.50 radianos</span></span>
Answer:
Step-by-step explanation:
13
