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emmasim [6.3K]
3 years ago
13

Line CD passes through points C(3, –5) and D(6, 0). What is the equation of line CD in standard form?

Mathematics
2 answers:
neonofarm [45]3 years ago
3 0
\text{The formula of a slope:}\ m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{We have:}\\C(3;\ -5)\to x_1=3;\ y_1=-5\\D(6;\ 0)\to x_2=6;\ y_2=0\\\\\text{substitute}\\\\m=\dfrac{0-(-5)}{6-3}=\dfrac{5}{3}\\\\\text{The point-slope formula:}\ y-y_1=m(x-x_1)\\\\\text{substitute}\\\\y-(-5)=\dfrac{5}{3}(x-3)\\\\y+5=\dfrac{5}{3}x-5\ \ \ |-5\\\\\boxed{y=\dfrac{5}{3}x-10}
NISA [10]3 years ago
3 0
= 5/2 x- 10.....................
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The coordinates of point A are (p, q) and coordinates of point B are (p+2q, q+2p). Provide your complete solutions and proofs in
Dafna1 [17]

Answer:

The mid-point (p + q , q + p) of AB is the same distance from the x-axis and the y-axis

Step-by-step explanation:

*<em> Lets explain how to solve the problem</em>

- Any point will be equidistant from the x-axis and the y-axis must have

 equal coordinates

- Ex: point (4 , 4) is the same distance from the x-axis and the y-axis

 because the distance from the x-axis to the point is 4 (y-coordinate)

 and the distance from the y-axis and the point is 4 (x-coordinate)

- If (x , y) is the mid-point of a segment its endpoints are

 (x_{1},y_{1})  and (x_{2},y_{2}), then

 x=\frac{x_{1}+x_{2}}{2} and y=\frac{y_{1}+y_{2}}{2}

* <em>Lets solve the problem</em>

∵ Point A has coordinates (p , q)

∵ Point B has coordinates (p + 2q , q + 2p)

- The mid-point of AB is (x , y)

∵ x=\frac{p+p+2q}{2}

∴ x=\frac{2p+2q}{2}

- Take 2 as a common factor from the terms of the numerator

∴ x=\frac{2(p+q)}{2}

- Divide up and down by 2

∴ x = p + q

∵ y=\frac{q+q+2p}{2}

∴ y=\frac{2q+2p}{2}

- Take 2 as a common factor from the terms of the numerator

∴ y=\frac{2(q+p)}{2}

- Divide up and down by 2

∴ y = q + p

∴ <em>The mid point of AB is (p + q , q + p)</em>

- p + q is the same with q + p

∵ The x-coordinate of the mid point of AB is p + q

∵ The y-coordinate of the mid point of AB is q + p

∵ p + q = q + p

∴ The coordinates of the mid-point of AB are equal

- According the explanation above

∴ The mid-point (p + q , q + p) of AB is the same distance from the

   x-axis and the y-axis

8 0
3 years ago
Prove that if a is a natural number, then there exist two unequal natural numbers k and l for which ak−al is divisible by 10.
EastWind [94]
Assume a is not divisible by 10. (otherwise the problem is trivial). 
<span>Define R(m) to be the remainder of a^m when divided by 10. </span>
<span>R can take on one of 9 possible values, namely, 1,2,...,9. </span>
<span>Now, consider R(1),R(2),......R(10). At least 2 of them must have the sames value (by the Pigeonhole Principle), say R(i) = R(j) ( j>i ) </span>
<span>Then, a^j - a^i is divisible by 10.</span>
8 0
3 years ago
Read 2 more answers
How would i plot this on a graph??
professor190 [17]

Step-by-step explanation:

This is in the form of

h(x) = y

in this case, x is 1 and y is 7. So ourbpoint would be (1,7.)

5 0
3 years ago
2.The number of tickets sold to a play for each showing is 78, 84, 87, 80, 91, 95, and 80.
Luden [163]

Answer:

Min =78

The maximum is :

Max = 95

Now we can calculate the median since the sample size os n =7 the median would be the middle value at the position 4 from the dataset ordered and we got:

Median =84

Now we can find the quartile 1 we analyze the first 4 values  78, 80,80, 84 and the first quartile would be:

Q_1= \frac{80+80}{2}= 80

Now we can find the quartile 3 we analyze the last 4 values  84,87, 91, 95 and the third quartile would be:

Q_3= \frac{87+91}{2}=89

And finally the 5 number summary would be:

Min = 78, Q_1 = 80, Median=84, Q_3 = 89, Max=96

Step-by-step explanation:

We have the following data given:

78, 84, 87, 80, 91, 95, and 80.

The first step is order the dataset on increasing way and we got:

78, 80,80, 84,87, 91, 95

We can begin finding the minimum value and for this case is:

Min =78

The maximum is :

Max = 95

Now we can calculate the median since the sample size os n =7 the median would be the middle value at the position 4 from the dataset ordered and we got:

Median =84

Now we can find the quartile 1 we analyze the first 4 values  78, 80,80, 84 and the first quartile would be:

Q_1= \frac{80+80}{2}= 80

Now we can find the quartile 3 we analyze the last 4 values  84,87, 91, 95 and the third quartile would be:

Q_3= \frac{87+91}{2}=89

And finally the 5 number summary would be:

Min = 78, Q_1 = 80, Median=84, Q_3 = 89, Max=96

5 0
3 years ago
an electronics company is designing a watch with a face that is in the shape of a hexagon and two congruent trapezoids attached.
nalin [4]

The total area of the face of the watch to the nearest tenth of a square centimemter is 9.0 cm²

Since an electronics company is designing a watch with a face that is in the shape of a hexagon and two congruent trapezoids attached. The heights of the trapezoids and the apothem of the hexagon measure 2 centimeters each, and the length of the shorter base of each trapezoid is 1.5 centimeters, the radii of the hexagon, and the base of the trapezoid form a triangle of

  • height, h = apothem of the hexagon = 2 cm and
  • base, b = length of shorter base of trapezoid.
<h3>Area of the triangle</h3>

So, the area of this triangle is A = 1/2bh

= 1/2 × 1. 5 cm × 2 cm

= 1.5 cm × 1 cm

= 1.5 cm²

<h3>Area of the hexagon</h3>

Since there are 6 of such triangles in the hexagon, the area of the hexagon, A' = 6A

= 6 × 1.5 cm²

= 9.0 cm²

So, the total area of the face of the watch to the nearest tenth of a square centimemter is 9.0 cm²

Learn more about area of a hexagon here:

brainly.com/question/369332

5 0
2 years ago
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