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3 years ago

Solve the equation. Type the number for your answer. -44=w+16

Mathematics

1 answer:

WINSTONCH [101]3 years ago

8 0

Answer:

w = -60

1. w + 16 = -44

2. w + 16 - 16 = -44 - 16

Solution is -60.

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If 6:2=8:x, then 6x = 16 6x = 10 2x = 48 2x = 14

Talja [164]

The answer is 6x = 16

3 0

2 years ago

Write an expression for the 12th partial sum of the series 3/2+7/3+19/6+... using summation notation

lapo4ka [179]

Answer:

$S_{12}=\sum_{i=1}^{12} [\frac{3}{2}+(i-1)\times \frac{5}{6}]$

$S_{12}=73$

Step-by-step explanation:

$First\ term\ of\ the\ series(a_1)=\frac{3}{2}\\\\Second\ term\ of\ the\ series(a_2)=\frac{7}{3}\\\\Third\ term\ of\ the\ series(a_3)=\frac{19}{6}\\\\a_2-a_1=\frac{7}{3}-\frac{3}{2}=\frac{5}{6}\\\\a_3-a_2=\frac{19}{6}-\frac{7}{3}=\frac{5}{6}\\\\Hence\ it\ is\ an\ Arithmetic\ Series\ with\ first\ term=\frac{3}{2}\ and\ constant\ difference=\frac{5}{6}$

$a_1=\frac{3}{2}+0\times \frac{5}{6}\\\\a_2=\frac{3}{2}+1\times \frac{5}{6}\\\\a_3=\frac{3}{2}+2\times \frac{5}{6}\\\\.\\.\\.\\a_n=\frac{3}{2}+(n-1)\times \frac{5}{6}\\\\S_n=a_1+a_2+a_3+......+a_n\\\\S_n=(\frac{3}{2}+0\times \frac{5}{6})+(\frac{3}{2}+1\times \frac{5}{6})+(\frac{3}{2}+2\times \frac{5}{6})+....+(\frac{3}{2}+[n-1]\times \frac{5}{6})\\\\S_n=\sum_{i=1}^n [\frac{3}{2}+(i-1)\times \frac{5}{6}]\\\\S_n=(\frac{3}{2}+\frac{3}{2}+\frac{3}{2}+...n\ times)+\frac{5}{6}(1+2+3+4+...+(n-1))\\\\$

$S_n=\frac{3}{2}\times n+\frac{5}{6}\times \frac{n(n-1)}{2}\\\\$

$S_{12}=\sum_{i=1}^{12} [\frac{3}{2}+(i-1)\times \frac{5}{6}]$

$S_{12}=\frac{3}{2}\times 12+\frac{5}{6}\times \frac{(12)(12-1)}{2}\\\\S_{12}=18+55\\\\S_{12}=73$

5 0

3 years ago

Find the equation of the line through the points (−2,5) and (4,9).

3241004551 [841]

9514 1404 393

Answer:

2x -3y = -19

Step-by-step explanation:

Taking the differences between the given points, we have ...

(Δx, Δy) = (4, 9) -(-2, 5) = (6, 4)

The equation of the line can be written ...

Δy·x -Δx·y = Δy·(x1) -Δx·(y1) . . . . . for point (x1, y1) on the line

4x -6y = 4(-2) -6(5) = -38

Dividing by 2 gives the standard form equation ...

2x -3y = -19

_____

Additional comment

The original equation 4x-6y=-38 satisfies the requirements of this problem. However, "standard form" requires the numbers in the equation be mutually prime (in addition to the problem requirements). That is, they must have no common factors. Hence, we must remove the common factor of 2 in order to have true "standard form."

8 0

2 years ago

Production line produces 50 mouse traps every 30 minutes for the course of a 10 hour day with a half hour break for lunch how ma

Artist 52 [7]

Answer:

950 mouse traps are made in a day.

Step-by-step explanation:

Given:

Mouse traps produced in 30 minutes = 50

Total working hour in one day = 10 hours

Lunch break time = 30 minutes

To find:

Number of mouse traps are made in a day = ?

Solution:

Total number of working hours =10 hours

We know that 1 hours = 60 minutes

so 10 hours = 60 x 10 = 600 minutes

It is said that there is 30 minutes break

So total working hour is 600-30 = 570

In 570 minutes we have = $\frac{570}{30}$ =19 half hours

Now the total mouse traps produced is 19 half hours is

19 x 50 = 950

6 0

2 years ago

Find domain of g g(x)=x+5/2x^2-x-3

Katena32 [7]

$g(x)=\frac{x+5}{2x^2-x-3}\\\\D_g:\\2x^2-x-3\neq0\\\\2x^2+2x-3x-3\neq0\\\\2x(x+1)-3(x+1)\neq0\\\\(x+1)(2x-3)\neq0\iff x+1\neq0\ \wedge\ 2x-3\neq0\\\\x\neq-1\ \wedge\ x\neq1.5\\\\D_g:x\in\mathbb{R}\ \backslash\ \{-1;\ 1.5\}$

3 0

2 years ago