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bogdanovich [222]

3 years ago

13

David and Peter had $90 and $200 respectively. They were each given an equal amount of money. Then Peter had twice as much money

as David. How much money did each boy receive?

1 answer:

Aleksandr [31]3 years ago

4 0

20 dollars each! hope it helps.

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Find the inverse of the matrix <img src="https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D9%26-2%5C%5C-10%269%5C%5C

valentinak56 [21]

Answer:

The answer is (b)

Step-by-step explanation:

* Lets check how to find the inverse of the matrix,

its dimensions is 2 × 2

* To know if the inverse of the matrix exist find the determinant

- If its not equal 0, then it exist

* How to find the determinant

- It is the difference between the multiplication of

the diagonals of the matrix

Ex: If the matrix is $\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]$

its determinant = ad - bc

- After that lets swap the positions of a and d, put negatives

in front of b and c, and divide everything by the determinant

- The inverse will be $\left[\begin{array}{ccc}\frac{d}{ad-bc} &\frac{-b}{ad-bc}\\\frac{-c}{ad-bc} &\frac{a}{ad-bc}\end{array}\right]$

* Lets do that with our problem

∵ The determinant = (9 × 9) - (-2 × -10) = 81 - 20 = 61

- The determinant ≠ 0, then the inverse is exist

∴ The inverse is $\frac{1}{61}\left[\begin{array}{ccc}9&2\\10&9\end{array}\right]$ =

$\left[\begin{array}{ccc}\frac{9}{61}&\frac{2}{61}\\\frac{10}{61} &\frac{9}{61}\end{array}\right]$

* The answer is (b)

7 0

3 years ago

What is 1735/1000 written as a decimal?

Marat540 [252]

Answer:

$\frac{1735}{1000}$ as a decimal is 1.735.

Step-by-step explanation:

To convert a fraction into a decimal, you first have to put the fraction into simplest form.

1. Simplest form

$\frac{1735}{1000} = \frac{347}{200}\\\$

To do this you must find a number you can equally divide both numbers by.

That number in this situation, 5.

$1000/5= 200\\1735/5= 347\\1735:1000 = 347:200\\\frac{1735}{1000} =\frac{347}{200}$

Now you must make this simplest formed fraction into a mixed number.

2. Simplest form into Mixed number

$\frac{347}{200}= 1\frac{147}{200}$

To do this you see how many times the denominator, the bottom number of the fraction, goes into the numerator, the upper part of the fraction.

Since 200 x 2 = 400 and since 400 > 347 this means...

200 goes into 347, once.

Finally, subtract and divide.

Remember put the whole number in front of the mixed number, before the decimal

3. Subtract, divide, decimalize

$147/200= 0.735\\\\1\frac{147}{200}= 1.735$

Hopes this helps you!

Have a good afternoon!

5 0

3 years ago

Determine the measures of the unknown labeled angles in the diagrams below:

Elan Coil [88]

180 - 34 - (180 - 115). 180°, and the sum of all interior angles in a triangle is 180°.

3 0

3 years ago

If you multiply the slopes of two perpendicular lines, what is the result?

rodikova [14]

Find the gradient/slope of Line A:

(3-2)÷(-1-4)

=-0.2

Therefore, the gradient/slope of line B is 5

Using the equation y-y1=m(x-x1) we can find the equation of line B

y-7=5(x-3)

y= 5x-8

Sub in a random value for y (eg. y=2)

2=5x-8

5x=10

X=2

so (2,2)

6 0

3 years ago

In order to evaluate 7 sec(θ) dθ, multiply the integrand by sec(θ) + tan(θ) sec(θ) + tan(θ) . 7 sec(θ) dθ = 7 sec(θ) sec(θ) + ta

Maurinko [17]

Answer:

$\int {7 \sec(\theta) } \, d\theta = 7\ln(\sec(\theta) + \tan(\theta)) + c$

Step-by-step explanation:

The question is not properly formatted. However, the integral of $\int {7 \sec(\theta) } \, d\theta$ is as follows:

<h3></h3>

$\int {7 \sec(\theta) } \, d\theta$

Remove constant 7 out of the integrand

$\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) } \, d\theta$

Multiply by 1

$\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) * 1} \, d\theta$

Express 1 as: $\frac{\sec(\theta) + \tan(\theta) }{\sec(\theta) + \tan(\theta)}$

$\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) * \frac{\sec(\theta) + \tan(\theta) }{\sec(\theta) + \tan(\theta)}} \, d\theta$

Expand

$\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{\sec^2(\theta) + \sec(\theta)\tan(\theta) }{\sec(\theta) + \tan(\theta)}} \, d\theta$

Let

$u = \sec(\theta) + \tan(\theta)$

Differentiate

$\frac{du}{d\theta} = \sec(\theta)\tan(\theta) + sec^2(\theta)$

Make $d\theta$ the subject

$d\theta = \frac{du}{\sec(\theta)\tan(\theta) + sec^2(\theta)}$

So, we have:

$\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{\sec^2(\theta) + \sec(\theta)\tan(\theta) }{u}} \,* \frac{du}{\sec(\theta)\tan(\theta) + sec^2(\theta)}$

Cancel out $\sec(\theta)\tan(\theta) + sec^2(\theta)$

$\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{1}{u}} \,du}}$

Integrate

$\int {7 \sec(\theta) } \, d\theta = 7\ln(u) + c$

Recall that: $u = \sec(\theta) + \tan(\theta)$

$\int {7 \sec(\theta) } \, d\theta = 7\ln(\sec(\theta) + \tan(\theta)) + c$

8 0

3 years ago