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2 years ago

18. Express the following as the sum of two consecutive integers. (i) 152 (ii) 192

Mathematics

1 answer:

zhenek [66]2 years ago

3 0

Explanation:

Let the two consecutive numbers be x and (x +1)

⇒ x + (x + 1) = 152

⇒ 2x + 1 = 152

⇒ 2x = 152 - 1

⇒ 2x = 151

⇒ x = 151/2

⇒ x = 75.5

So, the integers are: 75.5, 76.5

⇒ x + (x + 1) = 192

⇒ 2x + 1 = 192

⇒ 2x = 192 - 1

⇒ 2x = 191

⇒ x = 191/2

⇒ x = 95.5

So, the integers are 95.5, 96.5

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Li wants to add these items to her suitcase: a hairdryer (1.25 lb), a hand-held video game (0.6 lb), an extra video game (0.25 l

slamgirl [31]

Answer:

She will leave an extra video game which weighs 0.25lb

Step-by-step explanation:

Li wants to add these items to her suitcase: a hairdryer (1.25 lb), a hand-held video game (0.6 lb), an extra video game (0.25 lb), and a music player (0.4 lb). Using the inequality x ≤ 2.25, can she add all these items to the suitcase? If not, what could be left out to be closest to the maximum weight allowed?

Solution:

Weight of the items

hairdryer = 1.25 lb

hand-held video game = 0.6 lb

an extra video game = 0.25 lb music player = 0.4 lb

The total weight of the items

= 1.25lb + 0.25lb + 0.6lb + 0.4lb

= 2.5 lb.

Total weight - required weight

= 2.5lb - 2.25lb

= 0.25lb

2.5lb is 0.25lb greater than 2.25lb

Therefore, not all items can be added.

She has to leave out an item equivalent to 0.25lb

Item equivalent to 0.25lb is the extra video game

If Li leaves out the extra game, which weighs 0.25 lb, she’d have the maximum weight allowed.

5 0

3 years ago

A movie theater has been charging $10.00 per person and selling about 500 tickets on a typical weeknight. After surveying their

kifflom [539]

Answer:

$p(x) = -0.01x + 15$

Step-by-step explanation:

Given

Let x represent the number of tickets, and p the charges

$(x_1,p_1) = (500,10)$

A reduction of 50c gives an increment of 50 tickets.

This gives:

$(x_2,p_2) = (500+50,10-0,5)$ ---- $50c = \$0.5$

$(x_2,p_2) = (550,9.5)$

Required

Determine the demand function

First, calculate the slope:

$m = \frac{p_2 - p_1}{x_2 - x_1}$

$m = \frac{9.5 - 10}{550-500}$

$m = \frac{-0.5}{50}$

$m = -0.01$

So, the equation is:

$p = m(x - x_1) + y_1$

$p = -0.01(x - 500) +10$

$p = -0.01x + 5 +10$

$p = -0.01x + 15$

Hence, the function is:

$p(x) = -0.01x + 15$

4 0

3 years ago

The deck off the back of the house creates a right triangle. The side of the deck resting against the house is the hypotenuse of

goblinko [34]

Approximately 2 gallons will be needed if each gallon of stain and the project will cost be $73.96 if each gallon costs $36.98

<h3>How to find the area of a triangle</h3>

The formula for calculating the area of a triangle is expressed as:

A = 0.5bh

where

base = 15feet

height = 20feet

Area of the deck = 20 * 15 * 0.5

Area of the deck is 150 square feet

Number of gallons needed = 350/150 = 2.3

Hence approximately 2 gallons will be needed if each gallon of stain covers a maximum of 350 square feet.

Cost of the two gallons = 36.98 * 2

Cost of the two gallons = $73.96

Hence the project will cost be $73.96 if each gallon costs $36.98

Learn more on area of a triangle here: brainly.com/question/23945265

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2 years ago

Suppose the population of a certain city is 5289 thousand. It is expected to decrease to 4530 thousand in 50 years. Find the per

Tcecarenko [31]

Answer:

14.4% decrease

Step-by-step explanation:

Here is the formula for finding the percentage of decrease:

(starting value - final value) / starting value * 100.

So for your question,

$\frac{5289-4530}{5289} =.0144\\.0144 * 100 = 14.4\\$ /

There was a 14.4% decrease within 50 years.

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3 years ago

Lydia's teacher wants her class to take note of the gas prices around town and round them all to the nearest whole number. Lydia

Dima020 [189]

3.41, due to it being below .50

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3 years ago