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Dovator [93]
3 years ago
15

Five and nine tenths in expanded form and standard

Mathematics
1 answer:
nika2105 [10]3 years ago
3 0

Answer:

  • 5×1 +9×0.1
  • 5.9

Step-by-step explanation:

The verbiage "five and nine tenths" can refer to the mixed number 5 9/10, or to the decimal in standard form, 5.9. Simply converting the phrase to a decimal gets you the standard form.

The expanded form can be written a number of ways, depending on how you like to show the place value multipliers. The simplest expanded form is simply the sum of the digits:

  5 + 0.9

You can show the multipliers in standard form:

  5×1 + 9×0.1

Or, you can show the multipliers in exponential form:

  5×10⁰ +9×10⁻¹

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A collection of dimes and nickels is worth $5.60. The ratio of dimes to nickels is 3:2. How many dimes and how many nickels are
PolarNik [594]
Now, the nickels and dimes are at ratio of 3:2.  However, the total amount is in dollars.  So let's convert all amounts to pennies then.

$5.60 is just 560 pennies

3 dimes is just 30 pennies

2 nickels is just 10 pennies

so, the ratio from dimes to nickels is a ratio of 30:10 pennies, or 3:1 then, for a total amount of 560 pennies.

\bf \cfrac{dimes}{nickels}\qquad 3:2\qquad\cfrac{\stackrel{pennies}{30}}{\stackrel{pennies}{10}}\implies \cfrac{30}{10}\implies \cfrac{3}{1}\implies 3:1~ratio
\\\\\\
\cfrac{\stackrel{dimes}{pennies}}{\stackrel{nickels}{pennies}}\qquad 3:1\qquad \cfrac{3}{1}\implies \cfrac{3\cdot \frac{560}{3+1}}{1\cdot \frac{560}{3+1}}\implies \cfrac{3\cdot 140}{1\cdot 140}\implies \cfrac{420}{140}\\\\
-------------------------------

\bf \textit{now, how many dimes in 420 pennies?}\quad \cfrac{420}{10}\implies 42~dimes
\\\\\\
\textit{and how many nickels in 140 pennies?}\quad \cfrac{140}{5}\implies 28~nickels\\\\
-------------------------------\\\\
42~dimes + 28~nickels\implies \$5.60
3 0
3 years ago
Read 2 more answers
Define a variable and write an inequality to model each situation. A light bulb can be no more than 75 watts to be safely used i
DaniilM [7]
Let the number of watts =w ‘no more than’ means less than or equal to, thus we will use that sign. The inequality can be written as: w<75
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2 years ago
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liberstina [14]
The answer would be D
7 0
3 years ago
Which simplified fraction is equal to 0.53 repeating?
GalinKa [24]

Answer: I believe its 5/9

Step-by-step explanation:  

As you can see, the only fraction that doesn't equal 0.53, or the outlier, is 5/9 or 0.5556

5 0
3 years ago
If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of AB is ___
JulsSmile [24]

Answer:

a) y-intercept of AB is 56/5

b) equation of line CD is:

y = -7/5x + 12

Step-by-step explanation:

a) If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of AB is ___

We are given the points A(8,0) and point B (3,7)

We need to find y-intercept i.e b

Finding slope of points A and B = y₂ - y₁/x₂ - x₁

=7-0/3-8

=7/-5

= - 7/5

So, finding y intercept b by using equation

y = mx+b

And considering point A (8,0) x = 8 and y = 0 and m = -7/5

0 = 8(-7/5) + b

0 = -56/5 + b

=> b = 56/5

So, y-intercept of AB is 56/5

b) If the coordinates of point D are (5 , 5), the equation of line CD is y = __

Since AB || CD

both will have same slope

i.e m = -7/5

we need to find y-intercept given point D (5,5)

y = mx+b

5 = -7/5(5)+b

5 = -7 + b

=> b = 5+7

=> b = 12

So, equation of line CD is:

y = -7/5x + 12

9 0
2 years ago
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