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2 years ago

How many 4-digit odd numbers can you make using the digits 1 to 7 if the numbers must be less than 6000? No digits are repeated.

Mathematics

1 answer:

bixtya [17]2 years ago

6 0

Answer:

Step-by-step explanation:he first digit must be a 6, 7, or 8, because the number has to be bigger than 6,000.

The last digit must be a 1, 3, 5, or 7, because the number has to be odd.

So if the first digit is 6 or 8, there are 4 odd-number options for the last digit. If the first digit is a 7, then there are only 3 options for the last digit, as 7 can’t be used twice.

The other two digits can be anything that’s not already used. So for each first-and-last combination of digits mentioned above, there will be six options available for one of the middle digits, and then for each of those 3-digit combinations, five options will be available for the final remaining digit.

At this point, we have everything we need to express this as an equation:

x = (2 x 4 + 1 x 3) x 6 x 5

And then we can simplify and solve:

x = (8 + 3) x 30

x = 11 x 30

x = 330

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So someone help me explain how they found the solution to this Example 2?

Katena32 [7]

Answer:

$XY=52\\\\YZ=79\\\\XY=131$

Step-by-step explanation:

The line segment would like something like so:

X--------------------------Y---------------------------Z

The segment addition postulate says that x------y + y-------z = x-------y--------z

You are given the following measures for each:

5x-3 8x-9

X--------------------------Y---------------------------Z

|______________131______________|

You now need to substitute this in for the postulate:

$XY=5x-3\\\\YZ=8x-9\\\\XZ=131\\\\XY+YZ=XZ\\\\(5x-3)+(8x-9)=131$

Simplify the equation to solve for the value of x. Remove the parentheses:

$5x-3+8x-9=131$

Combine like terms to simplify the equation (make sure to keep the symbol of a term the same when combining. For example, since the negative symbol is in front of the three, it will be -3):

$5x+8x-3-9=131\\\\13x-12=131$

Use inverse operations. Add 12 to both sides:

$13x-12+12=131+12\\\\13x=143$

Use inverse operations to isolate the variable. Divide both sides by 13:

$\frac{13x}{13} =\frac{143}{13} \\\\x=11$

Now that we know the value of x, we can insert its value into each given length to simplify:

$XY=5x-3\\\\XY=5(11)-3\\\\XY=55-3\\\\XY=52$

--------------------

$YZ=8x-9\\\\YZ=8(11)-9\\\\YZ=88-9\\\\YZ=79$

------------------

To make sure the values are true, insert them into the postulate:

$52+79=131\\\\131=131$

Since the equation is true:

52 79

X--------------------------Y---------------------------Z

|______________131______________|

:Done

7 0

2 years ago

Point giveaway. Answer something random and you will get 17 points.

dlinn [17]

Answer:

sorry i was confused lol

5 0

2 years ago

Read 2 more answers

Find the equation of the line that is perpendicular to the given line and passes through the given point. Enter your answer in s

brilliants [131]

Step-by-step explanation:

so this is the answer for the problem for you

7 0

3 years ago

The perimeter of a rectangle is 99 inches. It’s width is 11 inches. What is the length of the rectangle? Solve algebraically and

Crank

2 (11)+2x=99
22+2x=99
2x=77
X=77/2
Width=77/2

3 0

3 years ago

Why do we use a coeficient to remove the propotionality

Salsk061 [2.6K]

Constant is the scale term in proportionality. Suppose one variable is dependent on the other and one variable become twice, other becomes also twice and if one becomes half, other too becomes half., but they are two different variables which are no-where linked (like cost(money) vs quantity). Quantity and cost are two different things but they abridge a mathematical relation of proportionality. So in the mathematics to abridge these two different variables, we need something. Constant serves that purpose.

5 0

2 years ago