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3 years ago

How do I rewrite this expression?

Mathematics

1 answer:

natka813 [3]3 years ago

5 0

Answer:

2 + i

Step-by-step explanation:

Given

$\frac{4+\sqrt{16-(4)(5)} }{2}$

= $\frac{4+\sqrt{16-20} }{2}$

= $\frac{4+\sqrt{-4} }{2}$

= $\frac{4+2i}{2}$

= 2 + i

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Joshua uses a rule to write the following sequence of numbers 1/6,1/2,5/6,----------,11/2 What rule did Joshua use? What is the

Pani-rosa [81]

Answer: The missing number in the sequence is $\frac{7}{6}$

Step-by-step explanation:

Since we have given that

$\frac{1}{6},\frac{1}{2},\frac{5}{6},----------,\frac{11}{2}$

First term = a= $\frac{1}{6}$

Common difference = d is given by

$d=a_2-a_1\\\\\frac{1}{2}-\frac{1}{6}\\\\=\frac{6-2}{12}\\\\=\frac{4}{12}=\frac{1}{3}\\\\Similarly,\\d=a_3-a_2\\\\=\frac{5}{6}-\frac{1}{2}\\\\=\frac{10-6}{12}\\\\=\frac{4}{12}\\\\=\frac{1}{3}$

Therefore, it forms an arithmetic sequence.

Since, $a_4$ is missing,

So,

$a_4=a+3d\\\\a_4=\frac{1}{6}+3\times \frac{1}{3}\\\\a_4=\frac{1}{6}+1\\\\a_4=\frac{1+6}{6}\\\\a_4=\frac{7}{6}$

Hence, the missing number in the sequence is $\frac{7}{6}$

4 0

3 years ago

Read 2 more answers

Solve the system of equations using substitution.

faltersainse [42]

Answer:

( $\frac{1}{3}$ , 3 )

Step-by-step explanation:

Given the 2 equations

y = 9x → (1)

6x - y = - 1 → (2)

Substitute y = 9x into (2)

6x - 9x = - 1, that is

- 3x = - 1 ( divide both sides by - 3 )

x = $\frac{1}{3}$

Substitute x = $\frac{1}{3}$ into (1) for corresponding value of y

y = 9 × $\frac{1}{3}$ = 3

Solution is ( $\frac{1}{3}$ , 3 )

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3 years ago

Oliga [24]

The bus driver arrives in Oban at 11:20

5 0

3 years ago

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Find the equation of the linear function represented by the table below in slope-intercept form.

Degger [83]

Answer:

$y=10x-6$

Step-by-step explanation:

step 1

Find the slope

we have

(0,-6) and (1,4)

The slope is equal to

$m=(4+6)/(1-0)=10$

step 2

Find the equation of the line in slope intercept form

The equation of the line in slope intercept form is

$y=mx+b$

we have

$m=10$

$b=-6$ -----> y-intercept (given value in the table)

substitute

$y=10x-6$

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3 years ago

Christiana and Marlena opened their first savings accounts on the same day. Christiana opened her account with $55 and plans to

PolarNik [594]

Answer: it will take 4 months for the amount to be the same and the amount would be $95

Step-by-step explanation:

Let x represent the number if months it will take for the two accounts have the same amount of money.

Christiana opened her account with $55 and plans to deposit $10 every month. This means that the amount that in the account after x months would be

10x + 55

Marlena opened her account with $35 and plans to deposit $15 every month. This means that the amount that in the account after x months would be

15x + 35

For the amount in the accounts to be the same, the number of months would be

15x + 35 = 10x + 55

15x - 10x = 55 - 35

5x = 20

x = 20/5

x = 4

The amount would be

15 × 4 + 35

= 60 + 35

= $95

8 0

3 years ago

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