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posledela
3 years ago
5

An equilateral triangle has a perimeter of 18 feet. If a square whose sides have the same length as one side of the triangle is

built, what will be the area of the square?
Mathematics
1 answer:
Komok [63]3 years ago
6 0

Answer:

36 ft²

Step-by-step explanation:

equilateral means all sides are equally long.

a triangle has 3 sides.

in our case they are all equally long.

and their sum (all 3 sides together) is the perimeter

P = 18 = 3 × side length

side length = 18/3 = 6 ft

a square with the same side length (6) had then an area of

side length × side length = 6×6 = 6² = 36 ft²

it is important to remember : a length is measured e.g. in feet (ft). an area is then meshed in square-feet (ft²). it is important to add this to the calculated numbers to express the right dimension of these numbers.

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Four Questions, 60 points & Brainliest! (Please show all steps)
pogonyaev

Answer:

a) -2, 1 and 2

b) 4

Step-by-step explanation:

The given equation is:

g(x) = (x + 2)(x - 1)(x - 2)

Part a1 and a2) Finding zeros of the function

By zeroes of the function we mean the points the graph where the value of the function is zero. In order to find the zeroes of the function we equate the  function equation to zero and find the corresponding values of x. This is shown below:

0 = (x + 2)(x - 1)(x - 2)

According to the zero product property, we can write:

x + 2 = 0     ⇒     x = -2

x - 1 = 0      ⇒     x = 1

x - 2 = 0     ⇒     x = 2

Therefore, the zeroes of the given function are -2, 1 and 2. In ordered pairs we can write these as (-2, 0), (1, 0) and (2, 0)

Part b1 and b2) y-intercept of the function

y-intercept is the point on the graph where the function crosses the y-axis. Since on y-axis, the value of x coordinate is zero, in order to find the y-intercept we simply substitute zero for all occurrences of x. This is shown below:

g(0) = (0 + 2)(0 - 1)(0 - 2)

g(0) = 2(-1)(-2)

g(0) = 4

Thus, the y-intercept of the function is 4, which in ordered pair can be written as (0, 4)

Part c) End behavior of the graph

End behavior of the graph depends on:

  • Sign of the leading coefficient
  • Degree of the function

Degree of the function is 3 i.e. odd and sign of leading coefficient is positive. This means the end behavior of the graph will be:

  • Rising towards Right end
  • Falling towards Left end

Part d) Graph of polynomial

Based on all the above discussion, a graph of the function can be plotted. The graph is attached below.

4 0
3 years ago
NEED HELP WITH ALGEBRA PLEASE!!!!!!Arrange these functions from the greatest to the least value based on the average rate of cha
slamgirl [31]
F(x)=x²+3x ; [-2;3]⇒Δf/Δx=(f(3)-f(-2))/(3-(-2))=4   (A)
f(x)=3x-8 ; [4;5]⇒Δf/Δx=<span>(f(5)-f(4))/(5-4)=3           (B)
f(x)=x</span>²-2x ;[-3; 4]⇒<span>Δf/Δx=(f(4)-f(-3))/(4-(-3))= -1  (C)
f(x)=x</span>²-5 ;[-1; 1]⇒<span>Δf/Δx=(f(1)-f(-1))/(1-(-1))= 0     (D)

answer: A, B, D, C

</span><span>
</span>
8 0
3 years ago
Read 2 more answers
Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = –5x2 + 100x – 450? Select three
RSB [31]

Answer:

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

Step-by-step explanation:

we have

f(x)=x^{2}

This is a vertical parabola open upward

The vertex is a minimum

The vertex is the origin (0,0)

g(x)=-5x^{2}+100x-450

This is a vertical parabola open downward

The vertex is a maximum

The first thing to note is that fx) is a parabola that opens up and g(x) opens down, so a reflection across the x-axis must have been applied.

Find the vertex of g(x)

Convert to vertex form

g(x)=-5x^{2}+100x-450

Complete the square

g(x)=-5(x^{2}-20x)-450

g(x)=-5(x^{2}-20x+100)-450+500

g(x)=-5(x^{2}-20x+100)+50

g(x)=-5(x-10)^{2}+50

The vertex is the point (10,50)

so

To translate the vertex of (0,0) to (10,50)

The rule of the translation is

(x,y) ------> (x+10,y+50)

That means ----> The translation is 10 units at right and 50 units up

therefore

The transformations are

The graph of f(x) is shifted up 50 units

The graph of f(x) is shifted right 10 units

The graph of f(x) is reflected over the x-axis

5 0
3 years ago
Read 2 more answers
The combined perimeter of the rectangle and triangle is 63 inches. The model shows the dimensions of the rectangle. What is the
katrin2010 [14]

*See diagram in the attachment

Answer:

27 inches

Step-by-step explanation:

Combined perimeter = perimeter of rectangle + perimeter of triangle = 63 inches

Perimeter of rectangle = 2(L + W)

L = 11 in.

W = 7 in.

Perimeter of rectangle = 2(11 + 7) = 36 in.

Let perimeter of the triangle be represented by x

Therefore:

36 + x = 63

Subtract 36 from each side

x = 63 - 36

x = 27

Perimeter of triangle = 27 inches

7 0
2 years ago
Determine the measure of ABC<br> 125<br> 50°<br> The measure of ABC is<br> degrees
MAVERICK [17]

Answer:

90 degrees

Step-by-step explanation:

angle ABC is a right angle

5 0
3 years ago
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