A door lock of the type illustrated below has a keypad with 5 buttons, numbered 1 through 5. All 5 buttons must be pressed in the correct sequence before turning the handle -- otherwise, the door remains locked. There is only one correct sequence.

9514 1404 393

Answer:

  (a, b) = (4, 8)

Step-by-step explanation:

Writing both equations in general form, we have ...

  6a -5b +16 = 0

  9a -7b +20 = 0

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We can make a little array of the numbers in the equations:

  [tex]\left[\begin{array}{cccc}6&-5&16&6\\9&-7&20&9\end{array}\right][/tex]

Note that the first column is repeated at the end.

Now, we can "cross multiply" and form the differences of products in adjacent columns:

  d1 = (6)(-7) -(9)(-5) = 3 . . . . . . left 2 columns

  d2 = (-5)(20) -(-7)(16) = 12 . . . . . middle 2 columns

  d3 = (16)(9) -(20)(6) = 24 . . . . . right 2 columns

Then the solutions to these equations are the solutions to ...

  1/d1 = a/d2 = b/d3

  a = d2/d1 = 12/3 = 4

  b = d3/d1 = 24/3 = 8

The values of a and b are 4 and 8, respectively.

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Additional Comment

There are a number of ways to solve linear equations. This is similar to what you would get by doing "elimination". It is also similar to Cramer's Rule and Vedic math techniques. The number of math operations is about the same*. Once you learn the technique, it is fairly fast and requires no decision-making. My other favorite method is using a graphing calculator.

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* This method uses 6 multiplications, 3 subtractions, 2 divisions. In the general case of "elimination", where the coefficients are not "nice" (as here), you would perform 7 multiplications, 4 subtractions and 2 divisions. This method is less work when the coefficients don't cancel easily.

Answer:

I think it might be 23. sorry if it is wrong :(

23 cubes

My answer is assuming the question uses the squares as units.

There are 20 whole squares

Two half squares= 1 square

There are 2 sets of 2 square spaces split from one corner to the opposite. They look to be split the same way, and to also be opposite halves of each other, like the two half squares mentioned before. However, this equals two squares, because 4 in total are split equally.

Answer:

distance from the Water Slide to Roller Coaster 2

Step-by-step explanation:

✔️Distance from Roller Coaster 1 (-6, 7) to Roller Coaster 3 (-6, -3):

Distance = |7 - (-3)| = |7 + 3| = 10 units

✔️Distance from the Water slide (8, -8) to Roller Coaster 2 (-6, -8):

Distance = |8 - (-6)| = |8 + 6| = 14 units

✔️The distance from the Water Slide to Roller Coaster 2 (14 units) is greater than the distance from Roller Coaster 1 to Roller Coaster 3 (10 units)

Answer:

DAM BGJF

Step-by-step explanation:

Answer:

A) 4.77%.

B) 5%.

Step-by-step explanation:

Given that Adam borrows $ 6,000 from his parents today for university fees and he promises to pay a lump sum of $ 6,900 in 3 years' time, to calculate the effective annual interest rate and the equivalent simple annual interest rate the following calculations must be performed:

A)

6,900 = 6,000 x (1 + X / 1) ^ 3x1

6,900 = 6,000 x 1X ^ 3

6,900 = 6,000 x 1 x 4.77 ^ 3

Thus, the interest rate of said investment is 4.77% per year.

B)

(6,900 - 6,000) / 3 = 300

6,000 = 100

300 = X

300 x 100 / 6,000 = X

30000 / 6,000 = X

5 = X

Thus, the simple interest rate would be 5% per year.

Answer:

2,5 and 2,7 I believe

Step-by-step explanation:

It should be 2,5 and 2,7

Answer:

your answer will be 9 cm

Step-by-step explanation:

I hope this helps u, have a great day !!!

Answer:

20m-8n

Step-by-step explanation:

0.4*50m=20m

20+_

0.4*-20n=-8n

20m+-8n

20m-8n

Answer:

yes

Step-by-step explanation:

yes but not a postitive one

Answer:

i think so yeah

Step-by-step explanation:

Answer:

N = 6

Step-by-step explanation:

1:Since the answer is 9,you can do it like this:Take away the 5 from the 15,which equals 10. Then,subtract 1 so you can get 9. Therefore,the answer is 6.

2:To check your answer,do 15 minus 9.

Answer:

your answer will be [tex]\frac{1}{36}[/tex]

Step-by-step explanation:

I hope this helps u have a nice day ^_^

Answer:

[tex]q(x)= \frac{1}{3} x -\frac{13}{3}[/tex]

Step-by-step explanation:

So you have (16, 1)

When two linear functions are parallel, they have the same slope.

So function q also has a slope of 1/3x. You have a set of points so you can plug them in a slope intercept equation to find b.

y= mx+b

m= slope

y= y-intercept

1= 1/3(16) +b

1 - (16/3) = b

b= -13/3

so then, [tex]y= \frac{1}{3} x -\frac{13}{3}[/tex]

Answer:

28

Step-by-step explanation:

Arranged it in order and got 28 :)

Answer:

The two are NOT THE SAME function.

Step-by-step explanation:

The linear function that is expressed as the equation y = -x + 3, is given in the slope-intercept form, y = mx + b, where

m = slope = -1

b = y-intercept = 3

To know if this function is the same with function expressed in the table of values, let's find the slope (m) and y-intercept (b) of the function represented as a table.

✔️Slope = change in y / change in x = ∆y/∆x

Using two pairs of values form the table, say, (-4, 1) and (-2, -1):

Slope (m) = (-1 - 1) / (-2 - (-4)) = -2/2 = -1

slope (m) = -1

To find b, substitute (x, y) = (-4, 1) and m = -1 into y = mx + b,

Thus:

1 = (-1)(-4) + b

1 = 4 + b

1 - 4 = b

-3 = b

b = -3

Write the equation for the table of values by substituting b = -3 and m = -1 into y = mx + b

Thus:

y = (-1)x + (-3)

y = -x - 3

As you can see, the equation of the function of the table of values is different from the equation of the function that was stated earlier.

Therefore, we can conclude that the two functions are not the same function expressed in different ways.

Answer:

2562.50

Step-by-step explanation:

2.5=0.025

0.025*2500=62.50

2500+62.50=2562.50

The other side would be 15 meters.

Answer:

b = 13.27

Step-by-step explanation:

b^2 + 7^2 = 15^2

b^2 + 49 = 225

b^2 = 176

b = sqrt(176)

b = sqrt(16 * 11)

b = 4sqrt(11)

b = 13.27

Answer:

400

Step-by-step explanation:

12 / 0.03

Divide 12 by 3 = 4.

Move the decimal place over 2 to the right.

400.

Answer:

3 red and 1 green , 0 blue, 0 yellow, 0 purple

2 x 2 x 2 x 3

Answer:

The answer is D. (3+22)÷5

Answer:

D. (3 + 22) / 5.

Step-by-step explanation:

Answer:

53,320 gross income

50,120 adjusted gross income

39,370 taxable income

Step-by-step explanation:

Answer:

29π/12.

Step-by-step explanation:

Multiply by π/180

= 435π/180

= 29π/12 radians.