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kozerog [31]
3 years ago
12

E is the midpoint of Df, DE=2x+4, and EF=3x-1. Find all segment lengths

Mathematics
1 answer:
sertanlavr [38]3 years ago
6 0
If E is the midpoint, DE and EF are equivalent.
2x+4=3x-1
4=x-1
5=x

Plug the value of x in
2(5)+4
14

3(5)-1
14

14+14=28

Final answer: DE=14, EF=14, DF= 28
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Find the real or imaginary solutions of each equation by factoring
anyanavicka [17]
Sum of  2 perfect cubes
a³+b³=(a+b)(x²-xy+y²)
so

x³+4³=(x+4)(x²-4x+16)
set each to zero
x+4=0
x=-4

the other one can't be solveed using conventional means
use quadratic formula
for
ax^2+bx+c=0
x=\frac{-b+/- \sqrt{b^2-4ac} }{2a}
for x²-4x+16=0
x=\frac{-(-4)+/- \sqrt{(-4)^2-4(1)(16)} }{2(1)}
x=\frac{4+/- \sqrt{16-64} }{2}
x=\frac{4+/- \sqrt{-48} }{2}
x=\frac{4+/- (\sqrt{-1})(\sqrt{48}) }{2}
x=\frac{4+/- (i)(4\sqrt{3}) }{2}
x=2+/- 2i\sqrt{3}


the roots are
x=-4 and 2+2i√3 and 2-2i√3
8 0
3 years ago
Suppose the parent population has an exponential distribution with a mean of 15 and standard deviation of 12. Use the Central Li
bazaltina [42]

Answer:

The sampling distribution of the sample mean of size 30 will be approximately normal with mean 15 and standard deviation 2.19.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the population, we have that:

Mean = 15

Standard deviaiton = 12

Sample of 30

By the Central Limit Theorem

Mean 15

Standard deviation s = \frac{12}{\sqrt{30}} = 2.19

Approximately normal

The sampling distribution of the sample mean of size 30 will be approximately normal with mean 15 and standard deviation 2.19.

4 0
3 years ago
In a kitchen there are three containers that can hold different quantities of water, as shown in the figure below:
ch4aika [34]

Answer:

A) 3x

Step-by-step explanation:

The total of all the volumes is ...

(x -1) + (x) + (x +1) = (1+1+1)x +(-1+1) = 3x+0 = 3x . . . . . matches choice A

6 0
3 years ago
Is there a relationship between the area and the perimeter of a rectangle
maksim [4K]
Well, an area and perimeter have formula's. The formula of area is length times width. The formula of perimeter is to basically length plus length plus width plus width. For instance, let's say the rectangles width is 5 and length is 6. So you do 5 plus 5 which is 10 and then 6 plus 6 which is 12. And then, 12 plus 10 equals 22. So the perimeter would be 22. If you were to find the area, you would do 6 times 5 and the area would be 30.
I hope this helps :)
3 0
3 years ago
Help someoneee!!!! <br> ill give a brainliest
Serjik [45]

Answer:

-13.5

Step-by-step explanation:

-4/3w=18

You would need to get the w by itself on one side so the easiest way to do so would be to divide both sides my -4/3.

This would give you an answer of w= -27/2 or w= -13.5

8 0
3 years ago
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