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bekas [8.4K]
2 years ago
7

If two lines are perpendicular, which statement must be true? A) The product of their slopes is 1. B) Their slopes are opposites

. C) Their slopes are equal. D) The product of their slopes is -1.
Mathematics
1 answer:
castortr0y [4]2 years ago
4 0
If two lines are perpendicular, the statement that must be true is : D. The product of their slopes is -1

Lets say that a line has a slope of 2, the line which perpendicular to that line would have a slope of -1/2

Which means, the product would be 2(-1/2) = -1

hope this helps
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Ana drew a map of the Panama Canal. In the scale Ana used for the map, 4 centimeters represents 20 kilometers. The actual length
yawa3891 [41]

Answer:

Length of the canal on the map is 16.4 centimeters.

Step-by-step explanation:

If actual length of Panama Canal = 20 kilometers

and length of the canal on map = 4 centimeters

Then scale factor = \frac{\text{Length of canal on map}}{\text{Actual length of canal}}

= \frac{4}{20}

= \frac{1}{5}

If the actual length of Panama Canal = 82 kilometers

Then the length of canal on the map = Actual length × Scale factor

= 82\times \frac{1}{5}

= 16.4 centimeters

Therefore, length of the canal on the map is 16.4 centimeters.

4 0
3 years ago
before tomorrow can I have a quick answer and maybe an explanation on how to answer these kinds of questions overall? need some
MA_775_DIABLO [31]

Answer:

  a) maximum; the parabola opens downward

  b) positive; it must lie above the x-axis

  c) x = 1.5

Step-by-step explanation:

The x-intercepts of a function are the points where the graph of the function crosses the x-axis. The y-values there are zero.

The "differences" of a function are related to the average slope between adjacent points. Second differences are related to the rate of change of the slope of the function. When <em>second differences are negative</em>, as here, the slope of the quadratic function is decreasing, becoming more negative. We say the <em>curvature</em> of the function is <em>negatve</em>, and that it <em>opens downward</em>.

__

<h3>a, b.</h3>

If the graph of the parabola opens downward, and it crosses the x-axis, it must have a <em>maximum</em> that is a <em>positive value of y</em>.

__

<h3>c.</h3>

The graph of a parabola is symmetrical about its vertex. That means points on the same horizontal line are the same distance from the line of symmetry, which must go through the vertex. The x-coordinate of the vertex will be the x-coordinate of the midpoint between the two x-intercepts:

  x = (-2 +5)/2 = 3/2

The x-coordinate of the vertex is x = 1.5.

______

<em>Additional comment</em>

The attachment shows a table with three evenly-spaced points on the curve. The calculations show first differences (d1) and second differences (d2). You can see that the sign of the second diffference is negative, in agreement with the given conditions.

3 0
2 years ago
Rachel had a popcorn machine at her party. Determine whether the relationship between time and the amount of popcorn popped is d
daser333 [38]
The relationship between time and amount of popcorn popped is proportional.
5 0
2 years ago
Read 2 more answers
Cuanto ganaran si compran el numero del premio mayor
elixir [45]

Answer:

is this spanish? or the real question

Step-by-step explanation:

7 0
2 years ago
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In a MBS first year class, there are three sections each including 20 students. In the first section, there are 10 boys and 10 g
KIM [24]

Answer:

3.52 \times 10^{-9} = 3.52 \times 10^{-7}\% probability that all the 15 students selected are girls

Step-by-step explanation:

The selection is from a sample without replacement, so we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

All girls from the first group:

20 students, so N = 20

10 girls, so k = 10

5 students will be selected, so n = 5

We want all of them to be girls, so we find P(X = 5).

P_1 = P(X = 5) = h(5,20,5,10) = \frac{C_{10,5}*C_{10,5}}{C_{20,5}} = 0.0163

All girls from the second group:

20 students, so N = 20

5 girls, so k = 5

5 students will be selected, so n = 5

We want all of them to be girls, so we find P(X = 5).

P_2 = P(X = 5) = h(5,20,5,5) = \frac{C_{5,5}*C_{15,5}}{C_{20,5}} = 0.00006

All girls from the third group:

20 students, so N = 20

8 girls, so k = 8

5 students will be selected, so n = 5

We want all of them to be girls, so we find P(X = 5).

P_3 = P(X = 5) = h(5,20,5,8) = \frac{C_{8,5}*C_{12,5}}{C_{20,5}} = 0.0036

All 15 students are girls:

Groups are independent, so we multiply the probabilities:

P = P_1*P_2*P_3 = 0.0163*0.00006*0.0036 = 3.52 \times 10^{-9}

3.52 \times 10^{-9} = 3.52 \times 10^{-7}\% probability that all the 15 students selected are girls

7 0
3 years ago
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