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gizmo_the_mogwai [7]
3 years ago
9

Given D(5, 7) and E(3, -3), find the midpoint of DE.​

Mathematics
1 answer:
just olya [345]3 years ago
4 0

Answer:

(4,2  )

Step-by-step explanation:

Midpoint Formula: (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}  )

Simply plug in your 2 coordinates into the midpoint formula to find midpoint:

(\frac{5+3}{2},\frac{7-3}{2}  )

(\frac{8}{2},\frac{4}{2}  )

(4,2  )

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Goshia [24]
Let's find the rates at which Melinda and Marcus are saving money and compare them. 
Based on the table, we can see that Melinda originally had $75. Then she got $135 in 5 weeks.  So the rate of saving money is (135–75)/5 = $12 per week.
This rate is unchanged for the next weeks. As we can see, she got $195 in the next 5 weeks. So she saved $60 more those 5 weeks, or the rate is $60/5 = $12 per week again. 

So Melinda saved $12 per week.
As for Marcus, the equation tells us that the rate of saving money is $14 which is the coefficient in front of x.

Hence, t<span>he rate at which Melinda is adding to her savings each week is 2$
less than the rate at which Marcus is adding to his savings each week.</span>
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4 years ago
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Savatey [412]

Answer: b

Step-by-step explanation:

6 0
3 years ago
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The center of a circle lies on the line y = 4x + 1 and is tangent to the x-axis at (−3,0) . What is the equation of the circle i
Hunter-Best [27]

Answer:

(x+3)^2+(y+11)^2=121

Step-by-step explanation:

Consider a sketch of the problem as shown in the picture, where:

  • Blue line is given by y = 4x + 1.
  • Point B is the center of the circle.
  • Point A is (-3, 0).

Since the center of the circle lies on the line y = 4x +1 and is tangent to the x-axis at point A, then its radius BA is perpendicular to the x-axis. To find the coordinates of point B, we must replace x = -3 into the blue line equation: y = 4x(-3) + 1 = -11.

So, we know that the center of the circle is at B=(-3, -11). And furthermore, the radius BA is of length r=11.

Since the <em>general equation of the circle</em> of radius lenght r centered at (h, k) is given by

(x-h)^2+(y-k)^2=r^2

then with h = -3, k = -11 and r= 11, the equation of our circle is

(x+3)^2+(y+11)^2=121

5 0
3 years ago
Algebraic expression for “six more than the quantity d times two.”
marusya05 [52]

Answer:

6 + (d * 2)

Step-by-step explanation:

You are adding 6 to the equation after the amount d times 2. In that case, a parentheses is required to round up d * 2.

6 0
2 years ago
"Trigonometric Models" (50 POINTS)<br> Is my graph right?
ch4aika [34]

Answer:

Yes, this graph is absolutely right for the function y = 2\sin(2x)-3.

Step-by-step explanation:

firstly we will calculate amplitude, period, phase shift, and vertical shift.

Use the standard form a\sin(bx-c)+d to calculate the values of amplitude, period, phase shift, vertical shift.

here a = 2

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Amplitude = |a|  = 2

period = \frac{2\pi}{|b|}

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phase shift = \frac{c}{b} = 0

and vertical shift = d = -3

so, by using this information, if we plot the graph then the graph obtained will be same as the given graph.

6 0
3 years ago
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