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2 years ago

The owners were happy that the house had appreciated in value at a rate of 5% each year

Mathematics

1 answer:

slava [35]2 years ago

8 0

Answer:

Exponential Growth

Step-by-step explanation:

The growth value is a positive number. So that mean's it's growing by 5%.

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If a = √3-√11 and b = 1 /a, then find a² - b²

Serga [27]

If $b=\frac1a$ , then by rationalizing the denominator we can rewrite

$b = \dfrac1{\sqrt3-\sqrt{11}} \times \dfrac{\sqrt3+\sqrt{11}}{\sqrt3+\sqrt{11}} = \dfrac{\sqrt3+\sqrt{11}}{\left(\sqrt3\right)^2-\left(\sqrt{11}\right)^2} = -\dfrac{\sqrt3+\sqrt{11}}8$

Now,

$a^2 - b^2 = (a-b) (a+b)$

and

$a - b = \sqrt3 - \sqrt{11} + \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{9\sqrt3 - 7\sqrt{11}}8$

$a + b = \sqrt3 - \sqrt{11} - \dfrac{\sqrt3 + \sqrt{11}}8 = \dfrac{7\sqrt3 - 9\sqrt{11}}8$

$\implies a^2 - b^2 = \dfrac{\left(9\sqrt3 - 7\sqrt{11}\right) \left(7\sqrt3 - 9\sqrt{11}\right)}{64} = \boxed{\dfrac{441 - 65\sqrt{33}}{32}}$

5 0

2 years ago

Joel earns $1,500 per month. If he spends $375 on rent each month, what percent of his income does he spend on rent?

cricket20 [7]

First, we must express the ratio of rent to Joel's total earning. 375 out of 1500 in its simplest form is 1/4. To express a value in percentage, we must multiply it to 100. Thus, for this case, we have 1/4 x 100 = 25% That means, out of a total of 100%, Joel spends 25%<span>of his income on rent.</span>

5 0

3 years ago

Here's a graph of a linear function. Write the

Softa [21]

Answer:

y = 3/2x - 3

Step-by-step explanation:

Slope = 3/2

y-intercept = -3

y = mx + b

y = 3/2x - 3

6 0

2 years ago

What’s the product for 27x89.5 multiply using expanded form

LUCKY_DIMON [66]

The answer is 2416.5 and i did it on paper

6 0

3 years ago

Find the equation for the plane through the points Po(3,-2,5), Qo(-3,-1,-5) and Ro(0,-4,4). The equation of the plane is:_______

ratelena [41]

Answer:

21x-24y-15z=36

Step-by-step explanation:

The equation of a plane is given a s

ax+by+cz=d

where a,b,c and d are gotten from the vector product of the vector define by subtracting one of the given points from the other two

Hence we define the vectors as follow

<3,-2,5> - <-3,-1,-5> = <6,-1,10>

also <0,-4,4> - <-3,-1,-5>=<3,-3,9>

Next we need to carry out the cross product of the newly formed vector

<6,-1,10> X <3,-3,9> =<21,-24,-15>

The newly formed vector is in orthogonal to both vector and in direction to the normal vector to the plane.

Since ax+by+cz=d is the normal vector, we can conclude that

a=21, b=-24 c=-15

Hence we have

21x-24y-15z=d

if we plug in the point <-3,-1,-5> to solve for "d" we arrive at

21(-3)-24(-1)-15(-5)=36

Hence the final equation is

21x-24y-15z=36

3 0

3 years ago