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Alja [10]
2 years ago
7

Dacey wants to find out if the quadrlateral shown is a rectangle

Mathematics
1 answer:
Gekata [30.6K]2 years ago
5 0

Answer:

Yes, because all rectangles have perpendicular and parallel sides.

Step-by-step explanation:

You might be interested in
State whether each sequence is arithmetic and justify your answer. If the sequence is arithmetic, write a recursive and an expli
nasty-shy [4]

Answer:

Part A

f(n)=52-12(n-1)

f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.

Part B

(2,4,8,16,32)\: \: Geometric Sequence

Part C

1/4,3/4,5/4,7/4,9/4

g(n)=\frac{1}{4}+\frac{2}{4}(n-1)\\f(n)=\left\{\begin{matrix}1/4if \: \:n=1 & \\ f(n+1)+2/4& if\: n\geq 2 \end{matrix}\right

Part D:

h(n)=1.1+0.4(n-1)\\h(n)=\left\{\begin{matrix}1.1 & if\:n=1 \\ h(n+1)+0.4 & if\:n\geq 2\end{matrix}\right

Step-by-step explanation:

By definition, an Arithmetic Sequence holds the same difference between each following number.

Part A

(52,40, 28, 16)\\52-40=12\\40-28=12\\28-16=12\\d=12

<u>Explicit Formula</u>

To write an explicit formula is to write it as function.

f(n)=52-12(n-1)

<u>Recursive Formula</u>

To write it as recursive formula, is to write it as recurrence given to some restrictions:

f(n)=\left\{\begin{matrix}52\: \:if \: \:n=1 & \\f(n+1)+12& if\: n\geq 2 \end{matrix}\right.

Part B

(2,4,8,16,32)\: \:

Geometric Sequence, since 2*2=4 8*2=16 and 16*2=32 and 8+2=10 8+16=24

Part C

(\frac{1}{4},\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4})\\\

Arithmetic Sequence, difference

d=\frac{2}{4}

<u>Explicit Formula:</u>

g(n)=\frac{1}{4}+\frac{2}{4}(n-1)

<u>Recursive Formula</u>

g(n)=\left\{\begin{matrix}\frac{1}{4} &if\:n=1 \\ g(n+1)+\frac{2}{4} &if\: n\geq 2\end{matrix}\right.

Part D

(1.1,1.5,1.9,2.3,2.7) Arithmetic Sequence, difference d=0.4

<u>Explicit formula</u>

h(n)=1.1+0.4(n-1)\\

<u>Recursive Formula</u>

h(n)=\left\{\begin{matrix}1.1 &if\:n=1 \\ h(n+1)+0.4 &if\: n\geq 2\end{matrix}\right.

6 0
3 years ago
The area of a room is 600 square feet. The length is (x + 5) feet and the width is (x + 4) feet. Find the dimensions of the room
tangare [24]
I'm going to assume that the room is a rectangle.

The area of a rectangle is A = lw, where l=length of the rectangle and w=width of the rectangle. 

You're given that the length, l = (x+5)ft and the width, w = (x+4)ft. You're also told that the area, A = 600 sq. ft. Plug these values into the equation for the area of a rectangle and FOIL to multiply the two factors:
A = lw\\&#10;600 = (x+5)(x+4)\\&#10;600 =  x^{2} + 9x + 20&#10;

Now subtract 600 from both sides to get a quadratic equation that's equal to zero. That way you can factor the quadratic to find the roots/solutions of your equation. One of the solutions is the value of x that you would use to find the dimensions of the room:
600 = x^{2} + 9x + 20\\&#10;x^{2} + 9x - 580 = 0\\&#10;(x + 29)(x - 20) = 0\\&#10;x + 29 = 0, \:\: x - 20 = 0\\&#10;x = -29, x = 20

Now you know that x could be -29 or 20. For dimensions, the value of x must give you a positive value for length and width. That means x can only be 20. Plugging x=20 into your equations for the length and width, you get:
Length = x + 5 = 20 + 5 = 25 ft.
Width = x + 4 = 20 + 4 = 24 ft.

The dimensions of your room are 25ft (length) by 24ft (width).
8 0
3 years ago
Read 2 more answers
Complete the square to transform the quadratic equation into the form (x – p)2 = q.
yulyashka [42]
If this problem is expecting you to show a graph photo, then a dependable website for a problem like this would be www.desmos.com. message me if you're not sure how to use it.
3 0
3 years ago
The quotient of 365.085 and 79.8
Paul [167]

Answer:

4.575

Step-by-step explanation:

365.085/79.8=4.575

5 0
3 years ago
Add (-x + 4) + (3x + 2).
VashaNatasha [74]

Answer:

2x+6

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
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