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3 years ago

It takes 36 minutes for 7 people to paint 4 walls. How many minutes dose it take for 9 people to paint 7 walls?

1 answer:

4 0

4 walls need 262 people/minutes (7)(36)
1 wall takes 63 people/minutes (262/4)
7 walls need 441 people/minutes (63)(7)
9 people could do that in 49 minutes (441/9)

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A qué se le llama factor comun

Archy [21]

Answer: spanish no

Step-by-step explanation:

7 0

2 years ago

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

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

Explicit Formula

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

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

Recursive Formula

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

$d=\frac{2}{4}$

Explicit Formula:

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

Recursive Formula

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

Part D

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

Explicit formula

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

Recursive Formula

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

6 0

3 years ago

Find the sum

lakkis [162]

Answer:

Numerator = 2(b^2+a^2) or equivalently 2b^2+2a^2

Denominator = (b+a)^2*(b-a), or equivalently b^3+ab^2-a^2b0-a^3

Step-by-step explanation:

Let

S = 2b/(b+a)^2 + 2a/(b^2-a^2) factor denominator

= 2b/(b+a)^2 + 2a/((b+a)(b-a)) factor denominators

= 1/(b+a) ( 2b/(b+a) + 2a/(b-a)) find common denominator

= 1/(b+a) ((2b*(b-a) + 2a*(b+a))/((b+a)(b-a)) expand

= 1/(b+a)(2b^2-2ab+2ab+2a^2)/((b+a)(b-a)) simplify & factor

= 2/(b+a)(b^2+a^2)/((b+a)(b-a)) simplify & rearrange

= 2(b^2+a^2)/((b+a)^2(b-a))

Numerator = 2(b^2+a^2) or equivalently 2b^2+2a^2

Denominator = (b+a)^2*(b-a), or equivalently b^3+ab^2-a^2b0-a^3

4 0

2 years ago

Simplify. [72/(-9)]/(-1/3)

Nutka1998 [239]

Answer:

Step-by-step explanation:

(72/-9) / (-1/3)

72/-9) x (-3/1)

(72)*(-3) = - 216/ -9

= 24

4 0

2 years ago

Polygon CCC has an area of 404040 square units. K 2ennan drew a scaled version of Polygon CCC using a scale factor of \dfrac12 1

nikdorinn [45]

Answer:

Area of polygon D = 10 square units

Step-by-step explanation:

Given:

Polygon C has an area of 40 square units.

It is scaled with a scale factor of $\frac{1}2$ to form a new polygon D.

To find:

The area of polygon D = ?

Solution:

When any polygon is scaled to half, then all the sides of new polygon are half of the original polygon.

And the area becomes one-fourth of the original polygon.

Let us consider this by taking examples:

First of all, let us consider a right angled triangle with sides 6, 8 and 10 units.

Area of a right angled triangle is given by:

$A = \dfrac{1}{2} \times Base \times Height\\\Rightarrow A = \dfrac{1}{2} \times 6 \times 8 = 24\ sq\ units$

If scaled with a factor $\frac{1}{2}$ , the sides will be 3, 4 and 5.

New area, A':

$A' =\dfrac{1}{2} \times 3 \times 4 = 6\ sq\ units = \dfrac{1}4\times A$

i.e. Area becomes one fourth.

Let us consider a rectangle now.

Sides be 8 and 10 units.

Area of a rectangle, A = $Length \times Width$ = 8 $\times$ 10 = 80 sq units.

Now after scaling, the sides will be 4 and 5 units.

New Area, A' = 4 $\times$ 5 =20 sq units

So, $\bold{A' = \frac{1}4 \times A}$

Now, we can apply the same in the given question.

$\therefore$ Area of polygon D = $\bold{\frac{1}{4}}$ $\times$ Area of polygon C

Area of polygon D = $\bold{\frac{1}{4}}$ $\times$ 40 = 10 sq units

4 0

2 years ago