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Anna11 [10]
3 years ago
11

Runners in a long distance race start out going 8 kilometers east and then head north for the remainder of the race. The finish

line is 10 kilometers from the starting line. How far did the runners travel north?
A. 2 km
B. 6 km
C. 10 km
Mathematics
1 answer:
Ilya [14]3 years ago
5 0
B. 6 km

You have to draw it so you can better process it. From there it's just the Pythagorean theorum.
a²+b²=c²
6²+b²=10²
(10 is c because it's the hypotenuse)
64+b²=100
100-64=36
√36 = 6
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D(x)=(x^2-12x+20)/(3x)
krok68 [10]

Answers:

Vertical asymptote: x = 0

Horizontal asymptote: None

Slant asymptote: (1/3)x - 4

<u>Explanation:</u>

d(x) = \frac{x^{2}-12x+20}{3x}

      = \frac{(x-2)(x - 10)}{3x}

Discontinuities: (terms that cancel out from numerator and denominator):

Nothing cancels so there are NO discontinuities.

Vertical asymptote (denominator cannot equal zero):

3x ≠ 0  

<u>÷3</u>   <u>÷3 </u>

x ≠ 0

So asymptote is to be drawn at x = 0

Horizontal asymptote (evaluate degree of numerator and denominator):

degree of numerator (2) > degree of denominator (1)

so there is NO horizontal asymptote but slant (oblique) must be calculated.

Slant (Oblique) Asymptote (divide numerator by denominator):

  •        <u>(1/3)x - 4    </u>
  •    3x)    x² - 12x + 20
  •             <u>x²        </u>
  •                  -12x
  •                  <u>-12x         </u>
  •                             20 (stop! because there is no "x")

So, slant asymptote is to be drawn at (1/3)x - 4



6 0
3 years ago
What is the answer to:<br> 18 - 5z + 6z &gt; 3 + 6
miv72 [106K]
18 - 5z + 6z > 3 + 6
18 + z > 9
-18        -18
z > -9
3 0
3 years ago
1. In which quadrant or on which axis do each of the points (-2,4) , (3,-1) ,(-1,0), (1,2) and (-3,-5) lie? Verify your answer b
pashok25 [27]

Point (-2 , 4) lies in the 2nd quadrant

Point (3 , -1) lies in the 4th quadrant

Point (-1 , 0) lies on the negative part of the x-axis

Point (1 , 2) lies in the 1st quadrant

Point (-3 , -5) lies in the 3rd quadrant

Step-by-step explanation:

Let us revise the signs of the coordinates in each quadrant

  • x and y coordinates are positive in the 1st quadrant
  • x-coordinate is negative and y-coordinate is positive in the 2nd quadrant
  • x and y coordinates are negative in the 3rd quadrant
  • x-coordinate is positive and y-coordinate is negative in the 4th quadrant
  • The general point on the positive part of x-axis is (x , 0), and on the negative part of x-axis is (-x , 0)
  • The general point on the positive part of y-axis is (0 , y), and on the negative part of y-axis is (0 , -y)

Now let us check the points

Point (-2 , 4) ⇒ red point

∵ x = -2 and y = 4

∵ x-coordinate is negative and y-coordinate is positive

∴ Point (-2 , 4) lies in the 2nd quadrant

Point (3 , -1) ⇒ blue point

∵ x = 3 and y = -1

∵ x-coordinate is positive and y-coordinate is negative

∴ Point (3 , -1) lies in the 4th quadrant

Point (-1 , 0) ⇒ green point

∵ x = -1 and y = 0

∵ x-coordinate is negative and y-coordinate is zero

∴ Point (-1 , 0) lies on the negative part of the x-axis

Point (1 , 2) ⇒ purple point

∵ x = 1 and y =2

∵ x and y coordinates are positive

∴ Point (1 , 2) lies in the 1st quadrant

Point (-3 , -5) ⇒ black point

∵ x = -3 and y = -5

∵ x and y coordinates are negative

∴ Point (-3 , -5) lies in the 3rd quadrant

<em>Look to the attached graph for more understand</em>

Learn more:

You can learn more about the four quadrant in brainly.com/question/9381523

#LearnwithBrainly

5 0
3 years ago
3x + 2 = 14 what number makes this true?<br> A. 1<br> B. 2<br> C. 4<br> D. 6
Ksenya-84 [330]

Answer:

4

Step-by-step explanation:

3*4+2=14

12+2=14

14=14

5 0
3 years ago
Read 2 more answers
What is the axis of symmetry for f(x) = 2x2 − 8x 8? x = −2 x = −3 x = 3 x = 2
Tatiana [17]

<span>The first part of the quadratic formula, x = - b/2a, is the equation of the axis of symmetry, and the x-coordinate of the vertex. </span>

<span>In standard form: - 2x² + 8x - 5 = 0, a = - 2, b = 8, c = - 5 </span>

<span>The axis of symmetry: x = - 8/2(- 2) = - 8/- 4 = 2 </span>

<span>Go back and solve for y to find the y-coordinate of the vertex. </span>

<span>y = - 2(2)² + 8(2) - 5 </span>

<span>y = - 2(4) + 16 - 5 </span>

<span>y = - 8 + 16 - 5 </span>

<span>y = 3 </span>

<span>Vertex is (2, 3)</span>
7 0
3 years ago
Read 2 more answers
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