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3 years ago

What is the solution to the inequality? 17 < 9 + x

Mathematics

1 answer:

dezoksy [38]3 years ago

7 0

Answer:

x > 8

Step-by-step explanation:

Given

17 < 9 + x ( subtract 9 from both sides )

8 < x , hence

x > 8

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keira has 83 spelling words to study in 8 weeks. she already knows 3 words. she will study the same number of words each week. h

Lemur [1.5K]

10 because she already knows 3 so then you divide 80 (number of words she hasn’t learned) by 8 (the number of weeks) and you get 10.

5 0

3 years ago

Read 2 more answers

If sinx = p and cosx = 4, work out the following forms :<br><br><br>

Kay [80]

Answer:

$\frac{p^2 - 16} {4p^2 + 16}$

Step-by-step explanation:

I will work with radians.

$\frac {\cos^2 \left(\frac{\pi}{2}-x \right)+\sin(-x)-\sin^2 \left(\frac{\pi}{2}-x \right)+\cos \left(\frac{\pi}{2}-x \right)} {[\sin(\pi -x)+\cos(-x)] \cdot [\sin(2\pi +x)\cos(2\pi-x)]}$

First, I will deal with the numerator

$\cos^2 \left(\frac{\pi}{2}-x \right)+\sin(-x)-\sin^2 \left(\frac{\pi}{2}-x \right)+\cos \left(\frac{\pi}{2}-x \right)$

Consider the following trigonometric identities:

$\boxed{\cos\left(\frac{\pi}{2}-x \right)=\sin(x)}$

$\boxed{\sin\left(\frac{\pi}{2}-x \right)=\cos(x)}$

$\boxed{\sin(-x)=-\sin(x)}$

$\boxed{\cos(-x)=\cos(x)}$

Therefore, the numerator will be

$\sin^2(x)-\sin(x)-\cos^2(x)+\sin(x) \implies \sin^2(x)- \cos^2(x)$

Once

$\sin(x)=p$

$\cos(x)=4$

$\sin^2(x)-\cos^2(x) \implies p^2-4^2 \implies \boxed{p^2-16}$

Now let's deal with the numerator

$[\sin(\pi -x)+\cos(-x)] \cdot [\sin(2\pi +x)\cos(2\pi-x)]$

Using the sum and difference identities:

$\boxed{\sin(a \pm b)=\sin(a) \cos(b) \pm \cos(a)\sin(b)}$

$\boxed{\cos(a \pm b)=\cos(a) \cos(b) \mp \sin(a)\sin(b)}$

$\sin(\pi -x) = \sin(x)$

$\sin(2\pi +x)=\sin(x)$

$\cos(2\pi-x)=\cos(x)$

Therefore,

$[\sin(\pi -x)+\cos(-x)] \cdot [\sin(2\pi +x)\cos(2\pi-x)] \implies [\sin(x)+\cos(x)] \cdot [\sin(x)\cos(x)]$

$\implies [p+4] \cdot [p \cdot 4]=4p^2+16p$

The final expression will be

$\frac{p^2 - 16} {4p^2 + 16}$

8 0

3 years ago

Anyone know the answer?

Cloud [144]

Answer:

y=-4x so slope is -4

Step-by-step explanation:

8 0

3 years ago

The submarine is at an elevation of -3552/7 feet

snow_tiger [21]

The answer to your problem is just through simple calculation.

Answer: -507.428571

4 0

3 years ago

function travelSpeed = CalculateTravelSpeed(startX, startY, endX, endY, travelTime) % startX, startY: Starting coordinates % end

Ilia_Sergeevich [38]

Answer:

The functions in Python is as follows:

from math import *

def CalculateTravelSpeed(startX,startY,endX,endY,travelTime):

travelSpeed = EuclideanDist(startX, startY, endX, endY) / travelTime

return travelSpeed

def EuclideanDist(startX, startY, endX, endY):

dist = sqrt((startX - endX)**2 + (startY - endY)**2)

return dist

Step-by-step explanation:

from math import *

This defines the CalculateTravelSpeed function

def CalculateTravelSpeed(startX,startY,endX,endY,travelTime):

This calls the EuclideanDist function to calculate the distance; Next, the speed is calculated

travelSpeed = EuclideanDist(startX, startY, endX, endY) / travelTime

This returns the calculated speed

return travelSpeed

This defines the EuclideanDist function

def EuclideanDist(startX, startY, endX, endY):

This calculates the distance from the given coordinates

dist = sqrt((startX - endX)**2 + (startY - endY)**2)

This returns the calculated distance

return dist

5 0

3 years ago