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3 years ago

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The house was bought for $125,000 in 1990, the overage rate is 7.85%, what year will the purchase of the house be worth 3 times

the purchase price?

1 answer:

olga55 [171]3 years ago

8 0

Answer: 2005

Step-by-step explanation:

Exponential function to determine the value of item after t years,

$f(x)=A(1+r)^t$ , where r= rate of growth, A=Initial value.

As per given , A = 7.85% = 0.0785

A = $125,000

Substitute all values in function, we get

$f(x)=125000(1+0.785)^t$

When f(x)= 3A , then

$3A=A(1.0785)^t\\\\\Rightarrow\ 3=(1.0785)^t$

Taking tog on both sides , we get

$\ln 3=t\ln 1.0785\\\\\Rightarrow\ t=\dfrac{\ln 3}{\ln 1.0785}\\\\\Rightarrow t=\dfrac{1.09861228867}{0.0755711868471}\approx15$

The year will be 1990+15= 2005

Hence, the required year = 2005

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The length of a rectangle is 59 inches greater than twice the width. If the diagonal is 2 inches more than the length, find the

melamori03 [73]

The question is asking us to find the dimensions of the rectangle, which would be the length and width. So, to find this, we must first state our givens, as it is Geometry.
Given: Length of rectangle = 59 + twice the width, diagonal = 2 inches longer than the width

Let's first translate all our givens to numbers. We'll start off by assigning variables that are easy to work with (x, y and z).
x = width
y = length
z = diagonal
Now that we have done that, we need to translate all our givens into numbers. Here is how that would look like:
y = 2x + 59 ←59 plus twice the width (x)
z = y + 2 ←Diagonal = 2 inches more than width
If we draw a diagram, we can see that the diagonal, length, and width all create a right triangle, which means that we can use the Pythagorean Theorem. By using right triangle postulates and theorems, we can deduce that the diagonal is the hypotenuse. Here is what our setup looks like:
x² + y² = z²
<em />Now, all we need to do is plug in the expressions we created for y and z:
x² + (2x + 59)² = [2 + (2x + 59)²]
When we solve for x, we get x = 20. Now, we just plug the x value back into the y equation to get 99. Therefore, the length equals 99 inches and the width equals 20 inches. Hope this helps and have a great day!

5 0

3 years ago

PLEASE HELP ME! I NEED THIS BY TODAY

mrs_skeptik [129]

Answer: this is a INVERSE choice C

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2 years ago

Read 2 more answers

What is the answer for this question 7(x+4)-7=48-2x

Alex777 [14]

Answer:

x = 3

Step-by-step explanation:

7(x + 4) - 7 = 48 - 2x ← distribute parenthesis and simplify left side

7x + 28 - 7 = 48 - 2x

7x + 21 = 48 - 2x ( add 2x to both sides )

9x + 21 = 48 ( subtract 21 from both sides )

9x = 27 ( divide both sides by 9 )

x = 3

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2 years ago

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I need help on these question ASAP!!!! This is Urgent

GarryVolchara [31]

Part 1: The equation of the line is $y=2x+1$

Part 2: The equation of the line in slope intercept form is $y=-3x-1$

Explanation:

Part 1: It is given that the point A is $(1,3)$ and the line B is $y=2 x-2$

To determine the line passing through the point A and parallel to line B, let us first determine the slope and y-intercept.

From the equation of line B, the slope is $m=2$

Substituting the point $(1,3)$ and $m=2$ in slope intercept form $y=mx+b$ , we have,

$3=2(1)+b$

$3=2+b$

$1=b$

Thus, the y-intercept is $b=1$

Let us substitute the values $m=2$ and $b=1$ in the slope intercept form $y=mx+b$ , we get,

$y=2x+1$

Thus, the equation of the line passing though point A and parallel to line B is $y=2x+1$

Part 2: The given two coordinates are $(-1,2)$ and $(1,-4)$

To determine the equation of line in slope intercept form, first we shall find the slope and y-intercept.

From the graph, we can see that the line touches the y-axis at -1.

Hence, the y-intercept is $b=-1$

The formula for slope is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting the coordinates $(-1,2)$ and $(1,-4)$ , we have,

$m=\frac{-4-2}{1+1} =\frac{-6}{2} =-3$

Thus, the slope is $m=-3$

Substituting the values $b=-1$ and $m=-3$ in the slope intercept formula $y=mx+b$ , we get,

$y=-3x-1$

Thus, the equation of the line in slope intercept form is $y=-3x-1$

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3 years ago

Laura is 12 years old witch 6/7 of her brothers age how old is her brother

sweet [91]

Answer:

14

Step-by-step explanation:

12:6=2

12+2=14

so her brother it's 14 years old

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3 years ago