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4 years ago

Match the inequality with its symbolic form.

Mathematics

1 answer:

jek_recluse [69]4 years ago

3 0

Answer/Step-by-step explanation:

The following inequalities can be translated and matched as follows:

1. A number is larger than 5:

Let that number be x. Numbers that are larger than 5 are 6, 7, 8 and so on. Therefore, the number that is larger is greater than 5. This can be represented in the symbolic form as:

x > 5

2. A number is below 5:

Numbers that are below 5 are 4, 3, 2 and so on. Therefore, we can say the number, x, is less than 5. This can be written in symbolic form as:

x < 5

3. A number is not less than 5:

A number that is not less than 5 could equal 5 or any other number that is larger than 5. Therefore, we can say the number, x, equals 5 or greater than 5. This can be written as:

x ≥ 5

4. A number is at most 5:

At most 5, means the number, x, is either 5 or less than 5. This can be written as:

x ≤ 5

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Two gears are adjusted so that the smaller gear drives the larger one. if the smaller gear of 3.7cm rotates through an angle of

zepelin [54]

Answer:

<em>The larger gear will rotate through 156°</em>

Step-by-step explanation:

<u>Arc Length</u>

The arc length S of an angle θ on a circle of radius r is:

$S = \theta r$

Where θ is expressed in radians.

The smaller gear of r1=3.7 cm drives a larger gear of r2=7.1 cm. The smaller gear rotates through an angle of θ1=300°.

Convert the angle to radians:

$\displaystyle \theta_1=300*\frac{\pi}{180}=\frac{5\pi}{3}$

The arc length of the smaller gear is:

$\displaystyle S_1=\frac{5\pi}{3}\cdot 3.7$

$\displaystyle S_1=\frac{18.5\pi}{3}$

The larger gear rotates the same arc length, so:

$\displaystyle S_2=\frac{18.5\pi}{3}$

$\displaystyle \theta_2\cdot r_2=\frac{18.5\pi}{3}$

Solving for θ2:

$\displaystyle \theta_2=\frac{18.5\pi}{3r_2}$

$\displaystyle \theta_2=\frac{18.5\pi}{3*7.1}$

$\theta_2=2.73\ radians$

$\displaystyle \theta_2=2.73*\frac{180}{\pi}=156$

The larger gear will rotate through 156°

7 0

3 years ago

How do you turn two six's into ten?

solmaris [256]

This type of problem is made to test to see if you can break apart addition problems to make it easier to add. In this one, we will break apart one of the 6's into 4 and 2. This gives us 6+4+2. Now 6+4= 10, so we made two 6's into 10+2.

4 0

3 years ago

Kayson is looking at two buildings, building A and building B, at an angle of elevation of 40°. Building A is 120 feet away, and

Sav [38]

Answer: Choice B

Building A; it is around 50.34 feet taller than building B

======================================================

Explanation:

Draw two right triangles such that they both have a reference angle of 40 degrees. Since it's an angle of elevation, place the angle near the horizontal side.

Opposite each reference angle is the height of the building, which we'll call h.

The adjacent side is the horizontal distance from the person to the building.

Building A is 120 ft away so it's height is...

tan(angle) = opposite/adjacent

tan(40) = h/120

h = 120*tan(40)

h = 100.69

This value is approximate. Make sure your calculator is in degree mode.

-----------------

Repeat the same idea for building B, except the adjacent side is smaller this time.

tan(angle) = opposite/adjacent

tan(40) = h/60

h = 60*tan(40)

h = 50.35

This value is approximate.

-----------------

Now subtract the heights

100.69 - 50.35 = 50.34

This shows that building A is roughly 50.34 taller than building B.

7 0

3 years ago

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There are 2 mL of fragrance oil in a bottle of perfume. What’s the total volume of perfume in that bottle?

Anastaziya [24]

Answer:

hol up

Step-by-step explanation:

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4 years ago

Simplify (-3k + p – 1) – (2k – 6p – 2)

Rom4ik [11]

Answer:

-5k+7p+1 I THINK

Step-by-step explanation

destribute the negative

(-3k + p – 1) – (2k – 6p – 2)

-2k+6p+2

add to the (-3k + p – 1) to simplify

-5k+7p+1

3 0

3 years ago