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2 years ago

You borrowed $59,000 for 2 years at 11% which was compounded annually. What

Mathematics

1 answer:

gayaneshka [121]2 years ago

6 0

Answer:

$72693.9

Step-by-step explanation:

To get this answer you need to use the compound interest formula, which will be A=P(1+r/n)^n(t). P=59,000 r=11%=0.11 n=1 (annually) t=2 years. From there you should be able to figure the rest out and get the answer. Hope this helps!

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How do you solve this?

puteri [66]

Answer:

Width: 7

Length: 14

Step-by-step explanation:

The area of a rectangle can be found my multiplying the length by the width. We do not know neither the length nor the width. However, we do know that the length is 7 feet longer than the width. Because we do not know the value of either side, let's let $x$ represent the width.

Since the length is 7 feet longer, we can represent the length by $x+7$ .

Now that we have our values for the length and the width we can multiply them together to find our area.

$(x)(x+7)=x^{2} +7x$

Now we have our equation, so we can address the changes made by the original question. The original question states that when 7 is added to both the length and width the area becomes 3 times larger. To do so simply increase each side by 7 by adding 7 to the original values.

$(x+7)(x+14)$

And multiply our area by 3.

$3(x^{2} +7x)$

set these equal to each other to find your new equation.

$(x+7)(x+14)=3(x^{2} +7x)$

Now you need to solve for $x$ . To do this first muliply $(x+7)$ and $(x+14)$ .

$(x+7)(x+14)=\\x^{2} +14x+7x+98=\\x^{2} +21x+98$

Then multiply $3(x^{2} +7x)$

$3(x^{2} +7x)=\\3x^{2} +21x$

Now you can begin solving for $x$ .

$x^{2} +21x+98=3x^{2} +21x$

Subtract $x^{2}$ from both sides.

$21x+98=2x^{2} +21x$

Subtract $21x$ from both sides.

$98=2x^{2}$

Divide by 2.

$49=x^{2}$

And finally take the sqaure root of both sides.

$\sqrt{x^{2} }=\sqrt{49}\\x=7$

Remember, because we are dealing with length, there cannot be negative. So while normally we would get both +7 <em>and</em> -7, in this case we <em>only </em>get +7.

Now that we have the value of $x$ , we can plug it into our original values.

For width we simply get 7.

For length we get 7+7=14

To check our answer we cna multiply 7 by 14 to get 98. Then we can add 7 to our length and width to get 14 and 21. Multiply these together and we get 294. 294 divided by 3 is 98, proving our answer correct.

7 0

3 years ago

What is the angle of B?

amid [387]

Answer:

Step-by-step explanation:

4 0

3 years ago

Rewrite the system of linear equations as a matrix equation AX = B.

iren2701 [21]

Answer:

$\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]*\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]=\left[\begin{array}{ccc}5\\6\\7\end{array}\right]$

Step-by-step explanation:

Let's find the answer.

Because we have 3 equations and 3 variables (x1, x2, x3) a 3x3 matrix (A) can be constructed by using their respectively coefficients.

Equations:

Eq. 1 : x1 + 2x2 + 5x3 = 5

Eq. 2 : x1 + x2 + x3 = 6

E1. 3 : 4x1 + 6x2 + 5x3 = 7

Coefficients for x1 ; x2 ; x3

From eq. 1 : 1 ; 2 ; 5

From eq. 2 : 1 ; 1 ; 1

From eq. 3 : 4 ; 6 ; 5

So matrix A is:

$\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]$

And the vector of vriables (X) is:

$\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]$

Now we can find the resulting vector (B) using the 'resulting values' from each equation:

$\left[\begin{array}{ccc}5\\6\\7\end{array}\right]$

In conclusion, AX=B is:

$\left[\begin{array}{ccc}1&2&5\\1&1&1\\4&6&5\end{array}\right]*\left[\begin{array}{ccc}x1\\x2\\x3\end{array}\right]=\left[\begin{array}{ccc}5\\6\\7\end{array}\right]$

7 0

3 years ago

What is not a problem modular division is used for?

Oksana_A [137]

Answer:

First let's define what modular arithmetic is, what would come is an arithmetic system for equivalence classes of whole numbers called congruence classes.

Now, the modular division is the division in modular arithmetic.

Answering the question, a modular division problem like ordinary arithmetic is not used, division by 0 is undefined. For example, 6/0 is not allowed. In modular arithmetic, not only 6/0 is not allowed, but 6/12 under module 6 is also not allowed. The reason is that 12 is congruent with 0 when the module is 6.

4 0

3 years ago

Can you please explain this?

Leni [432]

Answer:

The question is giving you pairs of points in space which can be used to define lines. It is then asking you to determine if the lines defined by those points are parallel, perpendicular, or neither.

Step-by-step explanation:

Two key things you need to know to solve this is that the lines will be parallel if their slopes are the same, and perpendicular if one slope is the negative reciprocal of the other (i.e. $s_{1} = -s_{2}^{-1}$ )

Let's start with question 11. You are given two pairs of points, each of which describes a distinct line:

(3,5)-(1,1) and (0, 2)-(5, 12)

To find the slope of each pair, take the vertex with the lesser x co-ordinate, and subtract it from the vertex with the greater x co-ordinate. That will give us a valid Δx and Δy to get the slope.

In the first pair, 3 > 1, so we'll subtract the second point from the first:

$s = \Delta y / \Delta x\\s = \frac{5 - 1}{3 - 1}\\s = 4/2\\s = 2$

So the first pair of vectors describe a line with a slope of 2. Let's look at the other pair:

$s = \Delta y / \Delta x\\s = (12 - 2) / (5 - 0)\\s = 10 / 5\\s = 2$

That also gives us a slope of 2, meaning that the two lines are parallel.

This same process will need to be done for the other three questions. We can't answer questions 12 or 14 here, as the last point is cut off on the edge of the image. For question 3 though, one line has a slope of 7/3, and the other 3/7. That puts them in the "neither" category, as one is not the negative reciprocal of the other, but instead the positive reciprocal.

6 0

3 years ago