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3 years ago

A rectangular lawn is twice as long as its breadth and its perimeter is 90 m.

1 answer:

7 0

Answer: length = 30, breadth = 15

length = l
breadth = b

l = 2b

2b + b + 2b + b = 90
6b = 90
b = 15

l = 2b
l = 2(15)
length = 30

b = 15
breadth = 15

You might be interested in

You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? Yes No (b) Find P(1 on green die an

ASHA 777 [7]

Answer:

Yes

$P(1 \& 5) = \frac{1}{36}$

$P(5 \& 1) = \frac{1}{36}$

$P(5 \& 1 | 1\& 5 ) = \frac{1}{18}$

Step-by-step explanation:

From the question we are told that

Two fair dice, one green and one red were rolled

Generally the outcomes on the dice independent because the outcome on the first dice is not affected by the second die

Generally the probability of getting a 1 on a dice rolled is $P(1) = \frac{1}{6}$

the probability of getting a 5 on a dice rolled is $P(5) = \frac{1}{6}$

Generally the probability of P(1 on green die and 5 on red die) is mathematically represented as

$P(1 \& 5) = \frac{1}{6} *\frac{1}{6}$

$P(1 \& 5) = \frac{1}{36}$

Generally the probability of P(5 on green die and 1 on red die) is mathematically represented as

$P(5 \& 1) = \frac{1}{6} *\frac{1}{6}$

$P(5 \& 1) = \frac{1}{36}$

Generally the probability of P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)) is mathematically represented as

$P(5 \& 1 | 1\& 5 ) = \frac{1}{36} + \frac{1}{36}$

$P(5 \& 1 | 1\& 5 ) = \frac{1}{18}$

8 0

3 years ago

Choose the correct simplification of the expression (2x - 6)(3x2 - 3x - 6). (4 points) Select one: a. 6x3 - 24x2 + 6x + 36 b. 6x

attashe74 [19]

Answer:

a. 6x^3 - 24x^2 + 6x + 36

Step-by-step explanation:

These are expanded using the distributive property, which is also used for collecting terms.

(2x - 6)(3x2 - 3x - 6) = 2x(3x^2 - 3x - 6) - 6(3x^2 - 3x - 6)

= 6x^3 -6x^2 -12x -18x^2 +18x +36

= 6x^3 +(-6-18)x^2 +(-12 +18)x +36

= 6x^3 -24x^2 +6x +36 . . . . . . matches selection A

_____

<em>Comment on strategy</em>

For multiple-choice questions, it often works well to find a way to identify a viable answer with the minimum amount of work. Comparing these answer choices, you can see that determining the correct values of the x-term and the constant term will let you pick the right choice.

The constant term is easy, because it is simply the product of the constants (-6)(-6) = 36. This narrows the choices to A and C.

The x-term will be the sum of products of x-terms and constants:

2x(-6) +(-6)(-3x) = -6(2x-3x) = -6(-x) = 6x

This narrows the choices to A alone.

5 0

4 years ago

An = an-1 + <br><br>What number belongs in the blank space in the recursive formula?

-Dominant- [34]

Answer: D) 8

-------------------------

The number outside the (n-1) term, which is 8, is the common difference. It tells us how much to increment by each time. In this case, the next term is found by adding 8 onto the previous term. That's exactly what $a_n = (a_{n-1}) + 8$ is saying.

3 0

4 years ago

Find the sum. 1-2+3-4+5-6+7-8...99-100

zysi [14]

Answer:

-50

Step-by-step explanation:

1 - 2 + 3 - 4 + 5 - 6 + 7 - 8...99 - 100

just means,

1 - 2 = -1

3 - 4 = -1

5 - 6 = - 1

7 - 8 = - 1

99 - 100 = -1

basically, -1 + -1 + -1 + -1 + ....+ -1 or -1 - 1 - 1 - 1 - ... - 1

$(-1)^{n}$

Treating Grandi's series as a divergent geometric series we may use the same algebraic methods that evaluate convergent geometric series to obtain a third value:

S = 1 − 1 − 1 + ..., so

1 − S = 1 − (1 − 1 − 1 ...) = 1 − 1 − 1 ... = S

1 - S = S

1 = 2*S

resulting in S = 1/2. The same conclusion results from calculating −S, subtracting the result from S, and solving 2S = 1

1/2 of the last term is 100 x 1/2 = 50

This because you are using 2 numbers per -1

example: 1 - 2 = -1 or 3 - 4 = -1 resulting in 50 of the -1 being subtracted

8 0

2 years ago

Three-fifths of the students in a room are girls. One-third of the girls have blond hair. One-half of the boys have brown hair.

yan [13]

Answer:

a. Of all the students, $\frac{1}{5}$ are girls with blond hair.

b. Of all the students, $\frac{1}{5}$ are boys without brown hair.

Step-by-step explanation:

a. You know that $\frac{3}{5}$ of the students are girls (This means that $\frac{2}{5}$ of the studes are boys) and $\frac{1}{3}$ of these girls have blond hair.