MATHEMATICS HIGH SCHOOL

The perimeter of a rectangle is 360m. If its length is decresed by 20 % and its breadth is increased by 25% we get the same perimeter . Find the dimention of the rectangel

Answers

Answer 1

Answer:

Answer: the length of the rectangle is 100m and the breadth is 80m

Step-by-step explanation:

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(length + breadth)

Let the length of the initial rectangle be and the breadth of the initial rectangle be b

The perimeter of a rectangle is 360m. Therefore,

2(l + b) = 360

l + b = 180

If its length is decreased by 20 %, the new length would be l - 0.2l = 0.8l

its breadth is increased by 25%, the new breadth would be b + 0.25b = 1.25b

we get the same perimeter. Therefore

2(0.8l + 1.25b) = 360

0.8l + 1.25b = 180 - - - - - - - 1

Substituting l = 180 - b into equation 1,it becomes

0.8(180 - b) + 1.25b = 180

144 - 0.8b + 1.25b = 180

- 0.8b + 1.25b = 180 - 144

0.45b = 36

b = 36/0.45 = 80

Substituting b = 80 into l = 180 - b, it becomes

l = 180 - 80 = 100

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Lim
θ→0 (cos 9θ − 1)/(sin 8θ)

Answers

lim as θ → 0 of (cos 9θ - 1)/sin 8θ = lim as θ → 0 of (-9sin 9θ) / 8cos 8θ = 0/8 = 0

$\lim_(t \to 0) (cos 9 t - 1)/(sin 8 t) = (1-1)/(0)= (0)/(0)$
We can use the L`Hospitals rule:
$\lim_(t \to 0) (cos 9 t - 1)/(sin 8 t)= \n =\lim_(t \to 0) (-9 * sin 9 t)/(8 * cos 8 t)= (0)/(8)= 0$

What is 81 to the power of -1/4?

Answers

81^(-1/4) is the same as the fourth root of (1/81). Which can be written as 4th root of 1 divided by the 4th root of 81.
The 4th root of 1 is 1 (because 1x1x1x1x1=1).
The 4th root of 81 is 3 (because 3x3x3x3=81).
So 81^(-1/4) = 1/3

How do i solve this problem 4s -12 = -5s + 51

Answers

$4s-12=-5s+51\ \ \ \ /+12\n\n4s-12+12=-5s+51+12\n\n4s=-5s+63\ \ \ /+5s\n\n4s+5s=-5s+5s+63\n\n9s=63\ \ \ /:9\n\n9s:9=63:9\n\ns=7$

4s-12=-5s+51
+12= +12
4s=-5s+63
+5s =+5s
9s=63
9/9=63/9
s=7

The perimeter of a rectangular garden is 338 m.If the width of the garden is 74 m, what is its length?

Answers

Answer:

l=95

Step-by-step explanation:

Perimeter is all the sides add up. So the equation if you know two of the sides, it should be: 338=(2*74)+(2*l)

Answer:

Step-by-step explanation:

the perimeter is 2w plus 2l

so 338 = 74(2)+2l

338 = 148+2l

190=2l

l=95

your length would be 95 m

Which long division problem can be used to prove the formula for factoring the difference of two perfect cubes?

Answers

Some of the possible options of the questions are;

A) $(a - b) | \overline {a^2 + a \cdot b + b^2}$

B) $(a + b) | \overline {a^2 - a \cdot b + b^2}$

C) $(a + b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3}$

D) $(a - b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3}$

The difference of two perfect cubes has a binomial factor and a trinomial factor

The option that gives the long division problem that can be used to prove the difference of two perfect cubes is option D

D) $\underline {(a - b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3}}$

Reason:

The formula for factoring the difference of twoperfect cubes is presented as follows;

a³ - b³ = (a - b)·(a² + a·b + b²)

Given that a factor of the difference of two cubes is (a - b), and that we

have; (a³ + 0·a·b² + 0·a²·b - b³) = (a³ - b³), both of which are present in

option D, by long division of option D, we have;

${} \hspace {33} a^2 + a \cdot b + b^2\n(a - b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a^2 \cdot b - b^3}\n{} \hspace {33} \underline{a^3 - a^2 \cdot b }\n{} \hspace {55} a^2 \cdot b + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3\n {} \hspace {55} \underline{a^2 \cdot b - a \cdot b^2}\n{} \hspace {89} a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3\n{} \hspace {89} \underline{a \cdot b^2 - b^3}\n{}\hspace {89} 0$

By the above long division, we have;

$(a - b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3}$ = a² + a·b + b²

Which gives;

$(a - b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3}$ = (a³ + 0·a·b² + 0·a·b² - b³)/(a - b)

We get;

(a³ + 0·a·b² + 0·a·b² - b³)/(a - b) = a² + a·b + b²

(a - b)·(a² + a·b + b²) = (a³ + 0·a·b² + 0·a·b² - b³) = (a³ - b³)

(a - b)·(a² + a·b + b²) = (a³ - b³)

(a³ - b³) = (a - b)·(a² + a·b + b²)

Therefore;

The long division problem that can be used to prove the formula for

factoring the difference of two perfect cubes is

$(a - b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3}$ , which is option D

D) $(a - b) | \overline {a^3 + 0 \cdot a \cdot b^2 + 0 \cdot a \cdot b^2 - b^3}$

Learn more here:

brainly.com/question/17022755

Answer:

The correct options, rearranged, are:

Options:

$A)(a^2+ab+b^2)/(a-b)\n\nB)(a^2-ab+b^2)/(a+b)\n\nC)(a^3+0a^2+0ab^2-b^3)/(a+b))\n\n D)(a^3+0a^2+0ab^2-b^3)/(a-b)$

And the asnwer is the last option (D).

Explanation:

You need to find which long division can be used to prove the formula for factoring the difference of two perfect cubes.

The difference of two perfect cubes may be represented by:

$a^3-b^3$

And it is, as a very well known special case:

$a^3-b^3=(a-b)(a^2+ab+b^2)$

Then, to prove, it you must divide the left side, $a^3-b^3$ , by the first factor of the right side, $a-b$

Note that, to preserve the places of each term, you can write:

$(a^3-b^3)=(a^3+0a^2+0ab^2-b^3)$

Then, you have:

$(a^3+0a^2+0ab^2-b^3)=(a-b)(a^2+ab+b^2)$

By the division property of equality, you can divide both sides by the same factor, which in this case will be the binomial, and you get:

$(a^3+0a^2+0ab^2-b^3)/(a-b)=(a^2+ab+b^2)$

That is the last option (D).

Q6: Women's heights have a mean of 63.6 inches and a standard deviationof 2.5 inches. What is the z-score corresponding to a woman with a height
of 70 inches? Is this usual or unusual?
A. Z-score is 2.56 and is usual. B. Z-score is 2.56 and is unusual
C. Z-score is -2.56 and is usual D. Z-score is -2.56 and is unusual

Answers

The corresponding z-score for a height of 70 inches is 2.56, which is considered unusual based on the standard threshold.

Use the concept of statistics defined as:

Statistics is a discipline of mathematics that deals with all aspects of data. Statistical knowledge aids in the selection of the appropriate technique of data collection and the use of those samples in the appropriate analysis process in order to effectively create the results. In short, statistics is an important procedure that assists in making data-driven decisions.

Given that,

The mean height of women: 63.6 inches

The standard deviation of women's heights: 2.5 inches

Height in question: 70 inches

Z-score formula: Z = (X - μ) / σ

The Z-score calculation for a height of 70 inches: Z = 2.56

Z-score interpretation: Unusual (greater than 2)

To find the z-score,

Use the formula:

Z = (X - μ) / σ

Where,

X is the value (in this case, 70 inches),

μ is the mean (63.6 inches),

σ is the standarddeviation (2.5 inches).

Calculating the z-score for a height of 70 inches:

Z = (70 - 63.6) / 2.5

Z = 6.4 / 2.5

Z = 2.56

So, the z-score corresponding to a woman with a height of 70 inches is 2.56.

Now, to determine if this z-score is usual or unusual,

Use the standard z-score table.

Usually, z-scores greater than 2 or less than -2 are considered unusual.

In this case,

The z-score is 2.56, which is greater than 2.

Hence,

The correct answer is B. The z-score is 2.56 which is unusual.

To learn more about statistics visit:

brainly.com/question/30765535

#SPJ3

Answer:

Step-by-step explanation:

Hopefully this helps

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