MATHEMATICS HIGH SCHOOL

In ΔOPQ, p = 180 inches, q = 120 inches and ∠O=171°. Find the length of o, to the nearest inch.

Answers

Answer 1

Answer:

Given:

In ΔOPQ, p = 180 inches, q = 120 inches and ∠O=171°.

To find:

The length of o, to the nearest inch.

Solution:

According to cosine formula,

$a^2=b^2+c^2-2bc\cos A$

Using cosine formula in ΔOPQ, we get

$o^2=p^2+q^2-2pq\cos O$

On substituting the values, we get

$o^2=(180)^2+(120)^2-2(180)(120)\cos (171^\circ)$

$o^2=32400+14400-43200(-0.9877)$

$o^2=46800+42668.64$

$o^2=89468.64$

Taking square root on both sides.

$o=√(89468.64)$

$o=299.113$

$o\approx 299$

Therefore, the length of o is about 299 inches.

Answer 2

Answer:

Answer:299

Step-by-step explanation:

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when a measurement in inches is converted to centimeters, will the number of centimeters be greater or less than the number of inches? Explain

Answers

greater because a centimeter is smaller than an inch.

Liquid A has a density of 0.7g/cm^3liquid B has a density of 1.6g/cm^3

140g of liquid A is and 128g of liquid B are mixed to make liquid C

work out the density of liquid C

Answers

density is defined as mass per unit volume

in this case liquids A and B with 2 different densities are mixed and we are asked to find the density of the liquid C

liquid A has a density of 0.7 g/cm³

mass of liquid A added is 140 g

therefore volume of liquid A added is - 140 g / 0.7 g/cm³ = 200 cm³

liquid B has a density of 1.6 g/cm³

mass of liquid B added is 128 g

volume of liquid B added is - 128 g / 1.6 g/cm³ = 80 cm³

the total mass of liquid C after adding liquid A and B = 140 g + 128 g = 268 g

total volume in liquid C - 200 cm³ + 80 cm³ = 280 cm³

density of liquid C = mass / volume

= 268 g / 280 cm³ = 0.957 g/cm³

density of liquid C - 0.957 g/cm³

$\rho = (m)/(V) \Rightarrow V=(m)/(\rho)$
ρ - density, m - mass, V - volume

Liquid A:
$\rho=0.7 \ (g)/(cm^3) \nm=140 \ g \n\n V=(140 \ g)/(0.7 \ (g)/(cm^3))=200 \ cm^3$

Liquid B:
$\rho=1.6 \ (g)/(cm^3) \nm=128 \ g \n\n V=(128 \ g)/(1.6 \ (g)/(cm^3))=80 \ cm^3$

Liquid C:
$m=140 \ g + 128 \ g=268 \ g \nV=200 \ cm^3 + 80 \ cm^3=280 \ cm^3 \n \n\rho=(268 \ g)/(280 \ cm^3) \approx 0.96 \ (g)/(cm^3)$

The density of liquid C is approximately 0.96 g/cm³.

What is factors of 14

Answers

Answer: 1, 2, 7, and 14

Step-by-step explanation: The factors of 14 are natural numbers that divide 14 without leaving any remainder. In other words, the factors of 14 divide 14 evenly.

Example: 7 is a factor of 14 because when we divide 14 by 7, it gives us 2 as the quotient and 0 as the remainder. Here, the quotient 2 is also a factor of 14.

So, to check if any number is a factor of 14 or not, divide 14 by that number and verify whether the remainder is zero or not. If the remainder is zero, the number is a factor of 14, otherwise not.

The sum of three fourths of a number and 1 is -5

Answers

We need to give the mystery number an easy name so that
we can work with it. Let's call it it ' M ' , for 'mystery number'.

The number . . . . . . . . . . . . . M
3/4 of it . . . . . . . . . . . . . . . . . 3/4 M
the sum of 3/4 of it and 1 . . . (3/4 M + 1)

You said that sum is equal to -5 .
OK. The equation we need to solve is

   3/4 M + 1 = - 5

Subtract 1 from each side: 3/4 M      = - 6

Multiply each side by 4 : 3 M      = -24

Divide each side by 3 :     M      = - 8

Does it work ?

Check it :

-- Assume the mystery number is . . . -8 .
-- 3/4 of the number . . . . . . . . . . . . . - 6 .
-- sum of 3/4 of the number and 1 . . . -5 <== yay !

Answer:

We need to give the mystery number an easy name so that we can work with it. Let's call it it ' M ' , for 'mystery number'.The number . . . . . . . . . . . . . M3/4 of it . . . . . . . . . . . . . . . . . 3/4 Mthe sum of 3/4 of it and 1 . . . (3/4 M + 1)You said that sum is equal to -5 .OK. The equation we need to solve is 3/4 M + 1 = - 5Subtract 1 from each side: 3/4 M = - 6Multiply each side by 4 : 3 M = -24Divide each side by 3 : M = - 8Does it work ?Check it :-- Assume the mystery number is . . . -8 .-- 3/4 of the number . . . . . . . . . . . . . - 6 .-- sum of 3/4 of the number and 1 . . . -5 <== yay !

Step-by-step explanation:

Simplify.5y(4x - 3z)

20xy - 3z
4x - 15yz
20xy - 15yz
54xy - 53yz

Answers

Answer:

20xy-15yz

Step-by-step explanation:

Given the following information, choose the brand that is the better buy.Brand A: $1.25 for 10 ounces
Brand B: $1.47 for 12 ounces
Brand C: $1.68 for 14 ounces
Brand D: $1.84 for 16 ounces

Answers

By using proportions, it is found that the better buy would be d. Brand D: $1.84 for 16 ounces.

What is a proportion?

A proportion is defined as the fraction of a total amount.

In the given problem, the better buy will be given by the lowest ratio of price to ounces.

Hence:

1.25/10 = 0.125

1.47/12 = 0.1225

1.68/14 = 0.12

1.84/16 = 0.115

Hence brand D is the better buy.

More can be learned about proportions;

brainly.com/question/24372153

#SPJ2

The best buy would be Brand D, because you get more for the money you spend. $1.84 for 16 oz of product comes to .115 cents per ounce which is the cheapers per ounce price of the 4 brands.

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