1. Which congruence statement is true? I'm not sure if I'm right.

J is the midpoint of HK¯¯¯¯¯¯¯ . What are HJ, JK, and HK?

lana [24]

Since J is the midpoint of HK, that means HK is split into two sections HJ and JK that are the same length.

1) You are told that the measure of segment HJ = 9x-2 and that of segment JK = 4x+13. Since you also know they are equal lengths, you can set these equations equal to each other to find the value of x!
HJ = JK
9x-2 = 4x+13
5x = 15
x = 3

2) Now you know x = 3. Plug that into your given equations for HJ and JK to find the length of each segment (or a shortcut would be to find one of them, and then you also know the other is the same length. I'm doing both, just to make sure I don't make a silly mistake!):
HJ = 9x-2
HJ = 9(3) - 2
HJ = 27 - 2
HJ = 25

JK = 4x + 13
JK = 4(3) + 13
JK = 12 + 13
JK = 25

3) Finally, the length of HK is just the length of HJ + JK, or HK = 25 + 25 = 50.

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Answer: HJ = 25, JK = 25, HK = 50

4 0

3 years ago

Please help:) See pic attached

Lostsunrise [7]

Answer:

Adults: 75, girls: 100, Boys: 75

Step-by-step explanation:

2/5 x 250 = 100( girls)

3/10 x 250 = 75 (boys)

250 - (100 + 75) = 250 - 175 = 75 (Adults)

5 0

3 years ago

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Does there exist a di↵erentiable function g : [0, 1] R such that g'(x) = f(x) for all x 2 [0, 1]? Justify your answer

agasfer [191]

Answer:

No; Because g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Step-by-step explanation:

Assuming: the function is $f(x)=x^{2}$ in [0,1]

And rewriting it for the sake of clarity:

Does there exist a differentiable function g : [0, 1] →R such that g'(x) = f(x) for all g(x)=x² ∈ [0, 1]? Justify your answer

1) A function is considered to be differentiable if, and only if both derivatives (right and left ones) do exist and have the same value. In this case, for the Domain [0,1]:

$g'(0)=g'(1)$

2) Examining it, the Domain for this set is smaller than the Real Set, since it is [0,1]

The limit to the left

$g(x)=x^{2}\\g'(x)=2x\\ g'(0)=2(0) \Rightarrow g'(0)=0$

$g(x)=x^{2}\\g'(x)=2x\\ g'(1)=2(1) \Rightarrow g'(1)=2$

g'(x)=f(x) then g'(0)=f(0) and g'(1)=f(1)

3) Since g'(0) ≠ g'(1), i.e. 0≠2, then this function is not differentiable for g:[0,1]→R

Because this is the same as to calculate the limit from the left and right side, of g(x).

$f'(c)=\lim_{x\rightarrow c}\left [\frac{f(b)-f(a)}{b-a} \right ]\\\\g'(0)=\lim_{x\rightarrow 0}\left [\frac{g(b)-g(a)}{b-a} \right ]\\\\g'(1)=\lim_{x\rightarrow 1}\left [\frac{g(b)-g(a)}{b-a} \right ]$

This is what the Bilateral Theorem says:

$\lim_{x\rightarrow c^{-}}f(x)=L\Leftrightarrow \lim_{x\rightarrow c^{+}}f(x)=L\:and\:\lim_{x\rightarrow c^{-}}f(x)=L$

4 0

4 years ago

The eggs of birds and other animals come in many different shapes and sizes. Eggs often have a shape that is nearly spherical. W

vekshin1

Answer:

696.9 cm^3 to the nearest tenth.

Step-by-step explanation:

Radius of the egg = 1/2 * 11 = 5.5 cm.

Volume = 4/3 * pi * 5.5^3

= 696.9099703

6 0

3 years ago

Which segments are parallel?

a_sh-v [17]

Answer:

The answer is actually CD, GH, and AB. I got it incorrect from the answer above. This is for people in the future who are looking for answers and don't get messed up over that guy.

Step-by-step explanation:

I just took the test and got the answer wrong. Correct answer above. (Checkmarks next to answer means its correct)

3 0

3 years ago

Read 2 more answers