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motikmotik
3 years ago
7

Rectangle???ABCD has vertices A(8, 5) , B(8, 10) , C(14, 10) , and D(14, 5) . A dilation with a scale factor of 1.2 and centered

at the origin is applied to the rectangle. Which vertex in the dilated image has coordinates of (9.6, 6) ?
A???

B???

C???

D???
Mathematics
1 answer:
VLD [36.1K]3 years ago
4 0
I just took the test and its A :)
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A train leaves at 1314 and arrives at 1508. It travelled at an average speed of 105 km/h.
Paraphin [41]

Answer: The train traveled 199.5 km

Step-by-step explanation:

We know the relationship:

Distance = Time*Speed

We know that the speed of the train was 105km/h

And we know that it leaves at 13:14, and arrives at 15:08.

Then the total amount of time that the train was traveling is:

T = (15 hours and 8 mins) - (13 hours and 14 mins)

= (15 - 13) hours and (8 - 14) mins

=  2 hours and (-6) mins.

We know that one hour has 60 minutes, then this is equal to:

T = 1 hour and 54 minutes.

But because the speed is kilometers per hour, we need to rewrite the 54 minutes in hours.

This can be done as follows:

1 hour = 60 minutes.

Then: 54 minutes = (54/60) hours = 0.9 hours.

Then:

1 hour and 54 minutes = 1.9 hours.

Now we know the speed and the time, then the distance can be calculated as:

Distance = speed*time = 105km/h*(1.9 h) = 199.5 km

The train traveled 199.5 km

3 0
3 years ago
Read 2 more answers
The volume of a soap bubble is 555.4 mm^2 Find the radius and diameter of the soap bubble. Use 3.14 for pi
SashulF [63]

Answer:

radius=11.5

diameter=23

Step-by-step explanation:

The volume of a sphere is V=4/3 Pi r^3

We can use this to solve for the radius.

555.4= 4/3 (3.14)r^3

Solve for r how you would any other equation. Multiply 4/3 and 3.14.

555.4=4.187 r^3

Divide both sides by 4.187

132.65=r^3

To get rid of the ^3, find the cube root of both sides on a calcualtor.

r= 11.5

The diameter is the radius time two.

11.5 (2)=23.

Hope this helps!

Note: When I say both sides, I mean both sides of the = sign.

4 0
2 years ago
A man travels 20 km by car from Town P to Town Q at an average speed of x km/h. He finds that the time of the journey would be s
yuradex [85]

Answer:

x = 20.

Step-by-step explanation:

First, you should remember the relation:

Distance = Speed*Time.

First, we know that a man travels a distance of 20km at a speed of x km/h, in a time T.

We can write this as:

20km = (x km/h)*T

We know that the time is shortened by 12 minutes if the speed is increased by 5km/h

Rewriting these 12 minutes in hours (remember that 60min = 1 hour)

12 min = (12/60) hours = 0.2 hours

Then from this, he can travel the same distance of 20km in a time T minus 0.2 hours if the speed is increased by 5 km/h

We can write this as:

20km = (x + 5 km/h)*(T - 0.2 h)

Then we have a system of two equations, and we want to find the value of x:

20km = (x km/h)*T

20km = (x + 5 km/h)*(T - 0.2 h)

First, we should isolate the variable T in one of the equations, if we isolate it in the first one, we will get:

20km/(x km/h) = T

Replacing that in the other equation we get:

20km = (x + 5 km/h)*(T - 0.2 h)

20km = (x + 5 km/h)*( 20km/(x km/h) - 0.2 h)

Now we can solve this for x.

Removing the units (that we know that are correct) so the math is easier to read, we get:

20 = (x + 5)*(20/x - 0.2)

We only want to solve this for x.

20 = x*20/x - x*0.2 + 5*20/x - 5*0.2

20 = 20 - 0.2*x + 100/x - 1

subtracting 20 in both sides we get:

20 - 20 = 20 - 0.2*x + 100/x - 1 - 20

0 = -0.2*x + 100/x - 1

If we multiply both sides by x we get:

0 = -0.2*x^2 + 100 - x

-0.2*x^2 - x + 100 = 0

This is just a quadratic equation, we can solve it using the Bhaskara's equation, the solutions are:

x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4*(-0.2)*100} }{2*-0.2}  = \frac{1 \pm 9 }{-0.4}

Then the two solutions are:

x = (1 + 9)/-0.4 = -25

x = (1 - 9)/-0.4 = 20

As x is used to represent a speed, the negative solution does not make sense, so we should use the positive one.

x = 20

then the average speed initially is 20 km/h

3 0
2 years ago
Can someone answer this please?
trapecia [35]
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4 0
3 years ago
jada is using a computer’s random number generator to produce 6 random whole numbers between 1 and 100 so she can use a random s
nikdorinn [45]

Step-by-step explanation:

The random numbers are selected randomly. Just because they happen to be 6 numbers in a row does not mean that they were not. If she is confident in the random number generator, which can be assumed, then the random numbers were still randomly selected and can be used. To regenerate would be a mistake because Jada is then picking and choosing which random numbers are chosen, defeating the purpose of a random number generator

7 0
3 years ago
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