MATHEMATICS HIGH SCHOOL

The length and a quarter of the width of a rectangle add up to 7 in, while the length and the width add up to 10 in. What are the rectangle's length and width?

Answers

Answer 1

Answer:

The length of rectangle is 6 inches and width is 4 inches.

Step-by-step explanation:

Let,

l be the length of rectangle

w be the width of rectangle.

Quarter means $(1)/(4)$ .

According to given statement;

$l+(1)/(4)w=7\nl+0.25w=7\ \ \ Eqn\ 1$

l+w = 10 Eqn 2

Subtracting Eqn 1 from Eqn 2

$(l+w)-(l+0.25w)=10-7\nl+w-l-0.25w=3\n0.75w=3$

Dividing both sides by 0.75

$(0.75w)/(0.075)=(3)/(0.75)\nw=4$

Putting w=4 in Eqn 2

$l+4=10\nl=10-4\nl=6$

The length of rectangle is 6 inches and width is 4 inches.

Keywords: rectangle, linear equation

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Y=5cos(20x) find amplitude, period & graph

Answers

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period is 360/20 = 18 degree
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Use the slider to change the scale factor. The rectangle is 20 by 16 and the scale factor is 0.25. What are the dimensions of the reduced rectangle?

Answers

Answer:

5 by 4

Step-by-step explanation:

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Answer:

THe answer 5 by 4

Step-by-step explanation:

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Answers

Answer: X(to the power of 0) over 3(to the power of 2)

Explanation: It is equal to 1/9

Fiona has proved that a function, f(x), is an arithmetic sequence. How did she prove that? A. She showed that an explicit formula could be created. B. She showed that a recursive formula could be created. C. She showed that f(n) ÷ f(n - 1) was a constant ratio. D. She showed that f(n) - f(n - 1) was a constant difference.

Answers

Answer:

Option D is correct

Step-by-step explanation:

Option D is correct

Being an arithmetic sequence there will be common difference between the consecutive terms

Option A is incorrect because it is not necessary that explicit formula is an arithmetic sequence we can create explicit formula for any sequence

Option B is incorrect because recursive formula can be created for any sequence for geometric series also.

Option C is incorrect because the sequence that has constant ratio is the geometric sequence not an arithmetic sequence.

Answer:

D. She showed that f(n) - f(n - 1) was a constant difference.

Step-by-step explanation:

∵ A sequence is called arithmetic if there is constant difference between consecutive numbers,

Thus, option D is correct.

In Explicit formulas, we define each term in a sequence directly,

Thus, there are many sequences other than arithmetic that have explicit formula,

i.e. Option A can not be true.

Now, recursive formula defines the relation between successive terms,

Thus, there are many sequences other than arithmetic that have recursive formula,

i.e. Option B can not be true.

Also, if the ratio between successive terms is constant then the sequence is a Geometric sequence,

A GP can not be an AP,

i.e. Option D can not be true.

The area of a rectangle is 507 centimeters squared. The length is 3 times the width. What is the length of the rectangle? 1) 3 cm 2) 13 cm 3) 26 cm 4) 39 cm

Answers

Answer:

option 4

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

let width be w then length = 3w ( 3 times the width )

given A = 507

substitute these values into the formula for A

507 = 3w × w , that is

507 = 3w² ( divide both sides by 3 )

169 = w² ( take square root of both sides )

$√(169)$ = $√(w^2)$ , that is

13 = w

Then

length = 3w = 3 × 13 = 39 cm

Which sentence correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14?68% of the data points lie between 10 and 14.

68% of the data points lie between 8 and 12.

68% of the data points lie between 10 and 18.

68% of the data points lie between 10 and 16.

Answers

Answer:

Option (c) is correct.

68% of the data points lie between 10 and 18.

Step-by-step explanation:

Given : a normal distribution with a standard deviation of 4 and a mean of 14

We have to choose the sentence that correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14.

Since, given 68% data.

We know mean of data lies in middle.

And standard deviation is distribute equally about the mean that is 50% of values less than the mean and 50% greater than the mean.

So, 68% of data lies

mean - standard deviation = 14 - 4 = 10

mean + standard deviation = 14 + 4 = 18

So, 68% of the data points lie between 10 and 18.

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That means that, for this distribution, 68% of it will lie between 14-4=10 and 14+4=18."

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