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3 years ago

The product of two consecutive positive integers is 18 more than eight times the smaller number. Find the two numbers.

Mathematics

1 answer:

olga2289 [7]3 years ago

6 0

Let , smallest integer is x.

So , other one is x + 1.

By , given conditions :

$x( x + 1 ) = 8x + 18\\\\x^2+x=8x+18\\\\x^2-7x-18=0\\\\x^2-9x+2x-18=0\\\\x(x-9)+2(x-9)=0\\\\x=-2 \ ,\ x = 9$

Since, the numbers are positive so, x = -2 is ignored.

Therefore, the numbers are 9 and 10.

Hence, this is the required solution.

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A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year:

Kaylis [27]

Answer:

mean = 724.2

Median = 715

Mode = 768

Range = 85

Standard deviation = 29.30

Interval = [665.6, 782.8]

Step-by-step explanation:

Number of samples n = 25

Summation X= 769 + 691 + 699 +730+711+ 765+ 702 718 +719 +712+ 768 +688 +757+695 768 +735 +709 +758 +708+ 693 +736 700+ 687 +772 +715 = 18105

1. Mean = 18105/25

= 724.2

2. Median is the middle value when arranged from the least value to the highest = 715

3. Mode is the number with the highest frequency = 768 (occured two times)

1. Range = highest value - lowest value

Highest value = 772

Lowest value = 687

772-687 = 85

2. Standard deviation = √(X-barX)²/n-1

= √20604/25-1

=√858.5

= 29.30

Please check attachment for the full calculation of the standard deviation

Interval

[Mean - 2(sd), mean + 2(sd)]

= [724.2-2x29.3, 724.2+2x29.3]

=[665.6, 782.8]

4 0

2 years ago

Triangle X Y Z is shown. Angle Y X Z is a right angle. The length of Y X is 12 inches and the length of X Z is 10 inches. Angle

mario62 [17]

The best approximation for the measure of angle XYZ is 39.8° ⇒ 2nd answer

Step-by-step explanation:

Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle

The trigonometry ratios of the angle BAC, the opposite side to this angle is BC and the adjacent side to it is AB are

$sin(BAC)=\frac{opposite}{hypotenuse}=\frac{BC}{AC}$
$cos(BAC)=\frac{adjacent}{hypotenuse}=\frac{AB}{AC}$
$tan(BAC)=\frac{opposite}{adjacent}=\frac{BC}{AB}$

In Δ XYZ

∵ ∠ YXZ is a right angle

∴ The hypotenuse is YZ

∵ The adjacent side to ∠XYZ is XY

∵ The opposite side to ∠XYZ is XZ

∵ YX = 12 units

∵ XZ = 10 units

- Use tan ratio to find the measure of the angle because you

have the adjacent and opposite sides of the angle XYZ

∵ m∠XYZ is x

∵ $tan(x)=\frac{XZ}{XY}$

∴ $tan(x)=\frac{10}{12}$

- To find x use the inverse of tan(x)

∵ $x=tan^{-1}(\frac{10}{12})$

∴ x = 39.8°

∴ m∠XYZ = 39.81°

The best approximation for the measure of angle XYZ is 39.8°

Learn more:

You can learn more about the trigonometry ratios in brainly.com/question/4924817

#LearnwithBrainly

4 0

3 years ago

Read 2 more answers

What is the next term in the number pattern? 21, 31, 36, 46, 51, … Enter your answer in the box.

Leni [432]

Answer:

Step-by-step explanation:

first it goes up by 10 then 5 now 10

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3 years ago

Read 2 more answers

(ASAP FOR 24P)Noah started to solve the equation –4.6p – 6.3p + 3.9 = –9.18 below. Combine like terms: –10.9p + 3.9 = –9.18 Appl

viva [34]

Answer:1.2

Step-by-step explanation:

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3 years ago

Solve the following system of equations by the substitution method.

Dahasolnce [82]

Answer:

Step-by-step explanation:

5x=y+6 --------- equ 1

2x-3y=4 -------- equ 2

5x - 6 = y

y = 5x - 6

substitute in equ 2

2x-3(5x - 6) =4

2x - 3*5x + 3*6 = 4

2x - 15x + 18 = 4

- 13x = 4 - 18

-13x = -14

x = -14/-13

x = 14/13

substitute in equ 1

5*14/13 = y+6

70/13 - 6 = y

y = ( 70 - 78)/13

y = -8/13

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3 years ago