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3 years ago

Write the expression as an inequality.

Mathematics

1 answer:

g100num [7]3 years ago

6 0

For the park's ride sign, there are two pieces we need to look at.

1) "At least 44"

2) "No more than 74"

The first piece tells us anyone more than 44 inches can ride. 45 inches is okay, since 45 is more than 44 (45 > 44 is true). 44 works too since 44 ≥ 44 is true. So you can say a person's height - h that is more than 44 makes it true, h ≥ 44. We reverse its orientation and say that 44 ≤ h.

The second piece says if you are under 74 inches you can ride. "No more than" means we don't include 74 inches but 73 inches would be fine. With symbols, 74 < 74 would be false, and 73 < 74 would be true. Using anyone's height - h - that means h < 74 is true.

Put the pieces together, and we have 44 ≤ h < 74 (choice B).

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W3* 5 = 15. then 15 + 5 equals what number? 3 05 08 15

Anastaziya [24]

Answer:

Hello

ur answer is

15+5= 20

Step-by-step explanation:

thanks hope it helps

6 0

3 years ago

Which function is the same as y = 3 cosine (2 (x startfraction pi over 2 endfraction)) minus 2? y = 3 sine (2 (x startfraction p

kirza4 [7]

The function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

<h3>How to convert sine of an angle to some angle of cosine?</h3>

We can use the fact that:

$\sin(\theta) = \cos(\pi/2 - \theta)\\\sin(\theta + \pi/2) = -\cos(\theta)\\\cos(\theta + \pi/2) = \sin(\theta)$

to convert the sine to cosine.

<h3>Which trigonometric functions are positive in which quadrant?</h3>

In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.
In second quadrant(π/2 < θ < π), only sin and cosec are positive.
In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.
In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.

(this all positive negative refers to the fact that if you use given angle as input to these functions, then what sign will these functions will evaluate based on in which quadrant does the given angle lies.)

Here, the given function is:

$y= 3\cos(2(x + \pi/2)) - 2$

The options are:

$y= 3\sin(2(x + \pi/4)) - 2$
$y= -3\sin(2(x + \pi/4)) - 2$
$y= 3\cos(2(x + \pi/4)) - 2$
$y= -3\cos(2(x + \pi/2)) - 2$

Checking all the options one by one:

Option 1: $y= 3\sin(2(x + \pi/4)) - 2$

$y= 3\sin(2(x + \pi/4)) - 2\\y= 3\sin (2x + \pi/2) -2\\y = -3\cos(2x) -2\\y = 3\cos(2x + \pi) -2\\y = 3\cos(2(x+ \pi/2)) -2$

(the last second step was the use of the fact that cos flips its sign after pi radian increment in its input)
Thus, this option is same as the given function.

Option 2: $y= -3\sin(2(x + \pi/4)) - 2$

This option if would be true, then from option 1 and this option, we'd get:
$-3\sin(2(x + \pi/4)) - 2= -3\sin(2(x + \pi/4)) - 2\\2(3\sin(2(x + \pi/4))) = 0\\\sin(2(x + \pi/4) = 0$

which isn't true for all values of x.

Thus, this option is not same as the given function.

Option 3: $y= 3\cos(2(x + \pi/4)) - 2$

The given function is $y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2$

This option's function simplifies as:

$y= 3\cos(2(x + \pi/4)) - 2 = 3\cos(2x + \pi/2) -2 = -3\sin(2x) - 2$

Thus, this option isn't true since $\sin(2x) \neq \cos(2x)$ always (they are equal for some values of x but not for all).

Option 4: $y= -3\cos(2(x + \pi/2)) - 2$

The given function simplifies to: $y= 3\cos(2(x + \pi/2)) - 2 = 3\cos(2x + \pi) -2 = -3\cos(2x) -2$

The given option simplifies to:

$y= -3\cos(2(x + \pi/2)) - 2 = -3\cos(2x + \pi ) -2\\y = 3\cos(2x) -2$

Thus, this function is not same as the given function.

Thus, the function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

Learn more about sine to cosine conversion here:

brainly.com/question/1421592

4 0

2 years ago

Read 2 more answers

six girls and four boys have entered the science fair. first, second, and third place awards are to be given out. what is the pr

Dafna1 [17]

Given:
6 girls
4 boys

Probability of 1 girl being chosen: 1/6
Probability of 1 boy being chosen: 1/4
Probability of another boy being chosen: 1/3

1/6 = 0.17 x 100% = 17%
1/4 = 0.25 x 100% = 25%
1/3 = 0.33 x 100% = 33%

17% + 25% + 33% = 75%

The probability that exactly one girl and two boys will receive awards is 75%.

7 0

3 years ago

Read 2 more answers

How do you decompose 7 x 7

Elis [28]

I think u multiply and then divide by one of its multiples

8 0

4 years ago

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The diagram shows a sketch of John's yard. He wants to plant grass, so he must calculate the area of the yard. The distance from

Arturiano [62]

The area of the yard is 50,600 square feet.