Ask question

Ask question

All categories

oksano4ka [1.4K]

3 years ago

12

Find the distance between each pair points (-5,3) , (-4,-5)?

1 answer:

MrRa [10]3 years ago

4 0

Answer:

$\sqrt{65}$

Step-by-step explanation:

distance between two points:

$d=\sqrt{(x_{2}-x_{1})^{2}+( y_{2}-y_{1})^{2}}$

we have:

$d=\sqrt{(-4-(-5))^{2}+(-5-3)^{2}} \\\\d=\sqrt{1^{2}+(-8)^{2}} \\\\d=\sqrt{65}$

You might be interested in

How would i draw the line y= -x

kykrilka [37]

Answer:

Hope this helps :)

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

What is the constant of proportionality as a decimal? *

irakobra [83]

Answer:

qhttps://goo.gl/search/what+is+the+constant+of+proportionality

Identifying the Constant of Proportionality - Video & Lesson ... The constant of proportionality is the ratio between two directly proportional quantities. In our tomato example, that ratio is $3.00/2, which equals $1.50. Two quantities are directly proportional when they increase and decrease at the same rate.

7 0

3 years ago

Day middle school has 24 students from the 8th grade that are in band. This is 25% of all the students in 8th grade. How many st

Volgvan

Answer:

96 in 8th grade

Step-by-step explanation:

You times 24 by four to get 96. Then to check your answer you need to do 25%96 and you will get 24 to show that you are right.

6 0

3 years ago

Given tan theta =9, use trigonometric identities to find the exact value of each of the following:_______

Ludmilka [50]

Answer:

$(a)\ \sec^2(\theta) = 82$

$(b)\ \cot(\theta) = \frac{1}{9}$

$(c)\ \cot(\frac{\pi}{2} - \theta) = 9$

$(d)\ \csc^2(\theta) = \frac{82}{81}$

Step-by-step explanation:

Given

$\tan(\theta) = 9$

Required

Solve (a) to (d)

Using tan formula, we have:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

This gives:

$\frac{Opposite}{Adjacent} = 9$

Rewrite as:

$\frac{Opposite}{Adjacent} = \frac{9}{1}$

Using a unit ratio;

$Opposite = 9; Adjacent = 1$

Using Pythagoras theorem, we have:

$Hypotenuse^2 = Opposite^2 + Adjacent^2$

$Hypotenuse^2 = 9^2 + 1^2$

$Hypotenuse^2 = 81 + 1$

$Hypotenuse^2 = 82$

Take square roots of both sides

$Hypotenuse =\sqrt{82}$

So, we have:

$Opposite = 9; Adjacent = 1$

$Hypotenuse =\sqrt{82}$

Solving (a):

$\sec^2(\theta)$

This is calculated as:

$\sec^2(\theta) = (\sec(\theta))^2$

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

Where:

$\cos(\theta) = \frac{Adjacent}{Hypotenuse}$

$\cos(\theta) = \frac{1}{\sqrt{82}}$

So:

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

$\sec^2(\theta) = (\frac{1}{\frac{1}{\sqrt{82}}})^2$

$\sec^2(\theta) = (\sqrt{82})^2$

$\sec^2(\theta) = 82$

Solving (b):

$\cot(\theta)$

This is calculated as:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

Where:

$\tan(\theta) = 9$ ---- given

So:

$\cot(\theta) = \frac{1}{\tan(\theta)}$

$\cot(\theta) = \frac{1}{9}$

Solving (c):

$\cot(\frac{\pi}{2} - \theta)$

In trigonometry:

$\cot(\frac{\pi}{2} - \theta) = \tan(\theta)$

Hence:

$\cot(\frac{\pi}{2} - \theta) = 9$

Solving (d):

$\csc^2(\theta)$

This is calculated as:

$\csc^2(\theta) = (\csc(\theta))^2$

$\csc^2(\theta) = (\frac{1}{\sin(\theta)})^2$

Where:

$\sin(\theta) = \frac{Opposite}{Hypotenuse}$

$\sin(\theta) = \frac{9}{\sqrt{82}}$

So:

$\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2$

$\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2$

$\csc^2(\theta) = \frac{82}{81}$

4 0

3 years ago

What is the value of z

vampirchik [111]

Answer:61

Step-by-step explanation:

Z+Z-11=Z+50

2Z-11=Z+50

Collect like terms

2Z-Z=11+50

Z=61

4 0

4 years ago