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neonofarm [45]
3 years ago
9

Find an exact solution for √5-1/x = √5/2 Then find the approximate solution to the nearest tenth.

Mathematics
1 answer:
viktelen [127]3 years ago
3 0

Step-by-step explanation:

\frac{ \sqrt{5 - 1 } }{x}  =  \frac{ \sqrt{5} }{2}  \\  \\ x \sqrt{5 }  = 2 \sqrt{5}  - 2 \\ x = 2 -  \frac{2 \sqrt{5} }{5}

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Complete the arithmetic sequence and then find the nth term.<br>__,__,6,__,15,__, 24, ...​
Rudik [331]

Given:

The arithmetic sequence is

__, __, 6, __, 15, __, 24, ...​

To find:

The missing values and the nth term of the sequence.

Solution:

The nth term of an arithmetic sequence is

a_n=a+(n-1)d         ...(1)

Where, a is the first term and d is the common difference.

3rd term of the sequence is 6.

a_3=a+(3-1)d

6=a+2d            ...(i)

5th term of the sequence is 15

a_5=a+(5-1)d

15=a+4d            ...(ii)

Subtracting (i) from (ii), we get

15-6=a+4d-a-2d

9=2d

\dfrac{9}{2}=d

4.5=d

Putting d=4.5 in (i), we get

6=a+2(4.5)

6=a+9

6-9=a

-3=a

Putting a=-3 and d=4.5 in equation (1).

a_n=-3+(n-1)4.5

a_n=-3+4.5n-4.5

a_n=4.5n-7.5

The nth term of the given arithmetic sequence is a_n=4.5n-7.5.

For n=1,

a_1=4.5(1)-7.5

a_1=4.5-7.5

a_1=-3

For n=2,

a_2=4.5(2)-7.5

a_2=9-7.5

a_2=1.5

For n=4,

a_4=4.5(4)-7.5

a_4=18-7.5

a_4=10.5

For n=6,

a_6=4.5(6)-7.5

a_6=27-7.5

a_6=19.5

The missing values are -3, 1.5, 10.5, 19.5 respectively. So, the complete arithmetic sequence is -3, 1.5, 6, 10.5, 15, 19.5, 24, ... .

5 0
3 years ago
Use the given conditions to write an equation for the line in​ point-slope form and general form. Passing through (−8,3) and par
Olenka [21]
PSF: y - y₁ = m(x - x₁)
Standard Form: ax + by = c

            Point Slope Form                                Standard Form 

1).        y - 3 = -4(x + 8)                                  2).       y = -4x - 29 
            y - 3 = -4x - 32                                          + 4x  + 4x
              + 3          +   3                                 ---------------------------------
       -----------------------------                                 4x + y = -29 
            y = =4x - 29



5 0
4 years ago
What is 2(n+5)=-2 showing work
BabaBlast [244]
2(n + 5) = -2

First, our goal to this problem is to get the variable (n) and an unknown number on each side. To start off, we can divide both sides by 2.
n + 5 =  -\frac{2}{2}

Second, we can go ahead and cancel 2 out, which will replace it with a -1.
n + 1 = -1

Third, our next step will to be to subtract 5 from each side.
n = -1 - 5

Fourth, our last step is to simplify -1 - 5. This is quite simple. -1 - 5 = -6, so -6 is what the variable (n) equals. 
n = -6

Answer: \fbox {n = -6}
4 0
3 years ago
Read 2 more answers
I need help i will mark brainliest
Kipish [7]

Answer:

Both triangles are scalene & Both triangles have an obtuse angle.

Step-by-step explanation:

<u>Key skills needed: Triangle recognition, Comparing Triangles</u>

1) We are given those 2 triangles, and we need to see if they are isosceles, scalene, obtuse, and acute.

2) To get this, let's define each thing:

Acute triangle - Means that all the angles in triangle are acute, which means they are less than 90 degrees in measure.

Obtuse triangle - Means that one angle in the triangle is obtuse, which means it is greater than 90 degrees in measure.

Scalene triangle - All the sides of the triangle are different in size/length

Isosceles triangle - 2 sides of the triangle are the same length

3) Now, we can use this to see what both triangles are:

--> Both triangles are not isosceles, they are both scalene. This is because all the sides of each triangle are different in size/length. This makes it scalene.

--> Both triangles are not acute triangles, they are both obtuse triangles. This is since the largest angle in each triangle is clear an obtuse angle (it looks like it is more than 90 degrees). Refer to the image I post as help.

With the observations above: We can say that both triangles are scalene, and both triangles are obtuse triangles.

<em>Hope you understood and have a nice day!! :D</em>

7 0
4 years ago
Lucy was trying to decide between three food choices: pizza, a salad, or a hamburger. She chose the salad. In this case, the sal
Wittaler [7]

Answer: preference

Step-by-step explanation: because she said she wanted to choose between pizza a salad and a hamburger and because she had 3 choices she picked the salad

3 0
3 years ago
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