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3 years ago

Please help! 20 Points!

2 answers:

8 0

Marcy
The school and Marcy are on the same x axis on the grid at -3 whilst Henry is the opposite end of the axis. Thus on the x axis Marcy is closer
On the y axis Henry is closer as they are both on 8 and Marcy is on 2
However overall Marcy is closer as the difference between -3 and 4 is 7 and the difference between 2 and 8 is 6

Hope this is right And hope it helps!

Alex73 [517]3 years ago

5 0

The point of Henry's house is closer to the point of the middle school than Marcy's house. One way to justify is through the distance formula.

The distance between the middle school and Marcy's house is 10, while the distance between the middle school and Henry's house is 5.

Henry's house is exactly 1/2 the distance from Marcy's house to the middle school.

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<img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7Bx%5E%7B2%7D%20%2B4x-4%7D%7Bx%5E%7B2%7D%20-2x-8%7D" id="TexFormula1"

givi [52]

i) The given function is

$f(x)=\frac{x^2+4x-4}{x^2-2x-8}$

We can rewrite in factored form to obtain;

$f(x)=\frac{x^2+4x-4}{x^2-2x-8}$

$f(x)=\frac{(x+2\sqrt{2}+2)(x-2\sqrt{2}+2)}{(x-4)(x+2)}$

The domain is

$(x-4)(x+2)\ne0$

$(x-4)\ne0,(x+2)\ne0$

$x\ne4,x\ne-2$

ii) To find the vertical asymptotes equate the denominator to zero.

$(x-4)(x+2)=0$

$(x-4)=0,(x+2)=0$

$x=4,x=-2$

iii) To find the roots, equate the numerator to zero.

$(x+2\sqrt{2}+2)(x-2\sqrt{2}+2)=0}$

$(x+2\sqrt{2}+2)=0,(x-2\sqrt{2}+2)=0}$

$(x=-2\sqrt{2}-2,x=2\sqrt{2}-2)}$

iv) To find the y-intercept, substitute $x=0$ into the equation.

$f(0)=\frac{0^2+4(0)-4}{0^2-2(0)-8}$

We simplify to obtain;

$f(0)=\frac{-4}{-8}$

$f(0)=\frac{1}{2}$

v) The horizontal asymptote is

$lim_{\to \infty}\frac{x^2+4x-4}{x^2-2x-8}=1$

The equation of the horizontal asymptote is y=1

vi) The function does not have a variable factor that is common to both the numerator and the denominator.

The function has no holes in it.

vii) The given function is a proper rational function.

Proper rational functions do not have oblique asymptotes.

7 0

3 years ago

What is the value of the expression (2 1/4 - 7 1/2) - (-1 1/4)

JulsSmile [24]

Answer:

-4

Step-by-step explanation:

2 1/4 - 7 1/2 = -5.25

-5.25 - (-1 1/4) = -4

5 0

3 years ago

Read 2 more answers

Please help me with this!!

Aleonysh [2.5K]

The perimeter is 1/2 the perimeter of ABCD because the scale factor is 1/2. It would be 10 units.

7 0

3 years ago

The Happy-Go-Lucky Beach was 163 feet long from parking lot to high tide. After last year's hurricane came ashore, the beach onl

ANTONII [103]

Answer:

About 5.5% decrease

Step-by-step explanation:

Here, we want to calculate the percentage increase or decrease and its value.

The first thing to do here is to check if we are going to have a decrease or an increase.

since the value before the change is higher than the value after the change, then what we have is a decrease.

Mathematically, the percentage decrease is calculated as follows;

% decrease = (old value - new value)/old value * 100%

old value = 163 feet

new value = 154 feet

% decrease = (154-163)/163 * 100%

% decrease = -9/163 * 100%

% decrease = -5.52%

Thus the best answer is about 5.5% decrease

4 0

3 years ago

Lisa's store collects 5% sales tax on every item sold. If she collected $22.00 in sales tax, what was the cost of the items her

Ede4ka [16]

Since we are looking for the principal amount, then all we have to do is reverse the process of getting the amount of tax. In order to get the principal, you just have to divide 22 with 0.05. The answer is 440 so that is the principal amount you are looking for.

5 0

3 years ago