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2 years ago

Write an eplicit ewuation for the nth term of the following sequence: 4,12,36,108

Mathematics

1 answer:

kkurt [141]2 years ago

5 0

324, 972, 2,916, 8,746, 26,244 hope this helped. you multiply each number by 3 to get the next number

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The area of a triangular garden can be no more than 120 square feet. The base of the triangle is 16 feet. What is the height of

Alinara [238K]

The height is 15 feet.

0.5xbxh<_120 (equate formula for area of triangle to 120)

0.5x16xh<_120

16xh<_240 (120 divided by 0.5)

h<_15 (240 divided by 16)

5 0

2 years ago

Read 2 more answers

Determine which, if any, of the three statements are equivalent.

patriot [66]

Answer:

Statement (b) is equivalent to statement (c), but neither is equivalent to statement (a).

Step-by-step explanation:

Let $F$ denote that "Fido is our fish's name" and let $R$ denote that "Rex is our dog's name". The statements listed in this question would then become:

(a) $F \implies R$ ;
$F$ implies $R$ .
(b) $\lnot ((\lnot F) \land (\lnot R))$ ;
not ((not $F$ ) or (not $R$ )).
(c) $F \lor R$ ;
$F$ or $R$ .

Apply de Morgan's Law $\lnot (P \land Q) \iff (\lnot P) \lor (\lnot Q)$ to rewrite statement (b). Let $P = (\lnot F)$ and $Q = (\lnot R)$ . By de Morgan's Law:

$\begin{aligned} & \lnot ((\lnot F) \land (\lnot R)) \\ \iff \; & \lnot (P \land Q)\\ \iff \; & (\lnot P) \lor (\lnot Q) && (\text{by de Morgan's Law}) \\ \iff \; & (\lnot (\lnot F)) \lor (\lnot (\lnot R)) \\ \iff \; & F \lor R\end{aligned}$ .

In other words, statement (b) $\lnot ((\lnot F) \land (\lnot R))$ is equivalent to statement (c) $F \lor R$ .

Statement (a) $F \implies R$ isn't equivalent to $F \lor R$ .

For example, when $F = \texttt{True}$ and $R = \texttt{False}$ , $F \implies R$ would be false since $\texttt{True}$ does not imply $\texttt{False}$ . However, for the same $F$ and $R$ , $F \lor R$ would be true since $F = \texttt{True}\!$ .

5 0

2 years ago

The two triangles are similar. What is the value of x? Enter your answer in the box. x = Two right triangles, one smaller than t

inysia [295]

<span>x = 4
Given the description of the triangles, you have 2 similar right triangles. The smaller triangle has a height of 20 and a base of 3x, while the larger has a height of (20+8) = 28 and a base of 4x + 2. We wish to determine the value of x. Since the triangles are similar, the ratio of corresponding sides will be a constant. So:
20/28 = (3x)/(4x+2)
(4x+2)20/28 = (3x)
(20/28)*4x+(20/28)*2 = (3x)
(80/28)*x+(40/28) = (3x)
(20/7)*x + 4/7 = 3x
4/7 = 3x - (20/7)*x
4/7 = (21/7)x - (20/7)*x
4/7 = x/7
4 = x
So the value of x is 4.</span>

4 0

3 years ago

Read 2 more answers

HELP!!!!!!!!! ILL GIVE YOU BRAINLIEst!!!

Lena [83]

Answer:

it is true.

Step-by-step explanation:

the proportions 4:6 and 10:15 can both be simplified into 2/3.

hope this helped! :)

8 0

2 years ago