Write the word sentence as an inequality. A number is less than or equal to 5.

Two numbers are said to be 'relatively prime' if their greatest common factor is 1. How many integers greater than 10 and less t

mars1129 [50]

Answer:

d. 9 integers

Step-by-step explanation:

Given that two numbers are said to be 'relatively prime' if their greatest common factor is 1.

We are to find relatively prime with 28 which are greater than 10 and less than 30

We have 11,12,13...29 satisfying the criteria greater than 10 and less than 30

To be relatively prime with 28, common factors should be only 1.

28 = 2x2x 7. Hence the numbers which do not have factors as 2 or 7 will be relatively prime. Remove all the even numbers from the list.

We have 11,13,15....29.

Of these 21 is the multiple of 7 so remove that.

Thus we have now 11,13,15,17,19,23,25,27,29

9 integers

d. 9 integers

3 0

3 years ago

if the product of 4 and a number is decreased by 12, the result is twice the opposite of the number. Find the number. EXPLAIN PL

ELEN [110]

Answer: The number is: "2 " .
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Explanation:
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Write the expression; which is an equation, as follows:
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" 4x − 12 = 2(-x) " ; in which "x" represents "the number for which we shall solve" .
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Note:

If the "number" = "x" ; the "opposite of the number" = " -x " ;
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Rewrite as: " 4x − 12 = -2x " ;
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→ Add "12" ; & add "2x" ; to EACH SIDE of the equation:

4x − 12 + 12 + 2x = -2x + 12 + 2x ;

to get: 6x = 12 ;
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Now, divide each side of the equation by "6" ;
to isolate "x" on one side of the equation; & to solve for "x" ;
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6x / 6 = 12 / 6 ;

to get: x = 2 .
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Answer: The number is: "2 " .
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Let us check our answer, by plugging in "2" for "x" in our original equation:
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→ " 4x − 12 = 2(-x) " ;

Let us plug in "2" for "x" ; to see if the equation holds true; that is; if both side of the equation are equal; when "x = 2" ;

→ " 4(2) − 12 = ? 2(-2) ??

→ 8 − 12 = ? -4 ? ;

→ -4 = ? -4 ?? Yes!
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6 0

3 years ago

GEOMETRY-TRIG

Andrej [43]

Answer:

6. The distance Rampy Ronald would have travelled horizontally is approximately 48.428 feet for an actual maximum height of 21.486 feet

7. Rampy Ronald is going to make the jump

Please find attached the graph of the motion of Rampy Ronald, created with Microsoft Excel

Step-by-step explanation:

6. The given parameters are;

The width of the ravine = 80 ft

The inclination of the ramp with which Rampy Ronald will jump = 30°

The distance from the edge of the ravine the ramp ends = 5 feet

The speed with which Rampy Ronald will make the jump = 60 mph

The maximum height he will reach = 30 feet

Therefore, we have;

The height of the end of the ramp = 15 × sin(30°) = 7.5

The height of the end of the ramp = 7.5 feet

The height of the jump = 30 - 7.5 = 22.5

The vertical velocity = 60 × sin(30°) = 30

The vertical velocity = 30 mph

The horizontal velocity = 60 × cos(30°) = 30·√3

The horizontal velocity = 30·√3 mph

From the kinematic equation, v² = u² - 2gh, we have;

u² = 2gh

h = u²/2g = 900/(2 × 32.17405) ≈ 13.986

The maximum height reached 13.986 + 7.5 = 21.486

From v = u - gt

t = u/g = 30/32.17405 ≈ 0.932

t ≈ 0.932 s

The distance Rampy Ronald would have travelled horizontally = 30·√3 × 0.932 ≈ 48.428

The distance Rampy Ronald would have travelled horizontally ≈ 48.428 feet

7. The time before Rampy Ronald reaches ground level again, is given by the following relation;

h = 1/2·g·t²

21.846 = 1/2 × 32.17405 × t²

t = √(21.846/16.087025) ≈ 1.165

t ≈ 1.366 s

The horizontal distance traveled is therefore;

The horizontal distance traveled from maximum height is 30·√3 × 1.165 ≈ 60.535

The horizontal distance traveled from maximum height is ≈ 70.979 feet

The total horizontal distance traveled ≈ 48.428 + 60.535 = 108.963

The total horizontal distance traveled ≈ 108.963 feet

The total horizontal distance required to make it across the ravine = 5 feet + 80 feet = 85 feet

Therefore, Rampy Ronald is going to make the jump

8 0

3 years ago

Kenzie finds purple, blue, and silver space rocks while exploring, 2/3 of the rocks are purple and 3/4 of the remainder are blue

Nadya [2.5K]

Answer:

There were 36 space rocks in total.

Step-by-step explanation:

First, you need to find what fraction of the original rocks are silver.

If 2/3 are purple, then 1/3 of them are not.

If 3/4 of the remaining 1/3 are blue, then 3/4 x 1/3 = 3/12 rocks are blue.

2/3 of the rock are purple, 3/12 of them are blue, and the remaining is silver.

So, you need to do 2/3 - 3/12, then find common denominators so, 8/12 - 3/12 which = 1/12.

This means 1/12 of the rocks are silver. If there are silver rocks, you need to find a suitable equation that needs to be solved.

So:

1/12r = 3

r = 36 silver rocks

There were 36 space rocks in total.

hope this helps :)

3 0

3 years ago

Read 2 more answers

The Correct Answer Is?

Alekssandra [29.7K]

Hello!

n≤-1/2 means that n is less than the open circle, because an open circle means the variable can not be equal to that point. so your answer is: D

I hope this helps, and have a nice day.

8 0

4 years ago