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SpyIntel [72]
3 years ago
11

Katenka cross country skied a trail that was 3/4 mile each way. after skiing 2/3 of the trail she turned around. What fraction o

f a mile did katenka ski before she turned around.
Mathematics
1 answer:
allsm [11]3 years ago
3 0
We know that

[total trail]=(3/4)*2------> 6/4---------> (3/2) miles

<span>[fraction of a mile that katenka did]=(2/3)*(3/2)------> 1 mile

the answer is 1 mile</span>
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Consider the following equation: f(x)=x^2+4\4x^2-4x-8 name the vertical asymptote(s)
zhenek [66]

ANSWER

The vertical asymptotes are


\Rightarrow x=2\:or\:x=-1

<u>EXPLANATION</u>

We have

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


For vertical asymptotes we set the denominator to zero and solve the quadratic equation;

4x^2-4x-8=0


\Rightarrow x^2-x-2=0

We split the middle term to obtain,

x^2+x-2x-2=0

\Rightarrow x(x+1)-2(x+1)=0


\Rightarrow (x-2)(x+1)=0


\Rightarrow x=2\:or\:x=-1


Therefore the vertical asymptotes are


x=2\:or\:x=-1





3 0
3 years ago
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Emily draws figures P, Q, R, and S. The center of dilation is point Z. Which figures are similar to figure Q? Explain your reaso
Ainat [17]

Answer:

Two figures that have the same shape are said to be similar. When two figures are similar, the ratios of the lengths of their corresponding sides are equal. To determine if the triangles below are similar, compare their corresponding sides.

8 0
3 years ago
Factor the expression completely by first taking out a common factor<br> 3x^2 + 27x +24
Mrac [35]
The answer to this is
3(x+1)(x+8)

4 0
3 years ago
Find all critical points of the given plane autonomous system. (Enter your answers as a comma-separated list.) x′ = x 12 − x − 1
Andru [333]

Answer:

the critical points are (0,0) , (0, 20), (12, 0) , (4,16)

Step-by-step explanation:

To consider the autonomous system

x' =x (12 -x - \dfrac{1}{2})

y' = y( 20 -y - x)

The critical points of the above system can be derived by replacing x' = o and y' = 0.

i.e.

x' =x (12 -x - \dfrac{y}{2}) = 0

\dfrac{x}{2} (24 -2x - y) = 0

x = 0 or 24 - 2x - y = 0     ----- (1)

Also

y' = y( 20-y-x) = 0

y( 20 -y - x) = 0

y = 0 or 20 - y - x = 0  -----   (2)

By solving (1) and (2);

we get x = 4 and y = 16

Suppose x = 0 from (2)

y = 20

Also;

if y = 0 from (1)

x = 12

Thus, the critical points are (0,0) , (0, 20), (12, 0) , (4,16)

6 0
3 years ago
What is the x-coordinate of the solution of the following system of equations?
Varvara68 [4.7K]

The easiest way to solve this is by elimination. 

3x - y = 6 

6x + y = 21

Since you have a negative and positive y with the same coefficients (1), they cancel, and you add the other terms so it would look like:

9x = 27 

Then solving for x leaves you with x = 3 

Then you take the x value of three and plug it into to either of the equations, so 

3(3) - y = 6

9 - y = 6 

subtracting 9 

-y = -3 

then dividing by -1 

y = 3 

so the solution is x = 3 y = 3 or (3,3)

8 0
3 years ago
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