21 feet to 8 yards write a ratio as a fraction in simplest form without any units

Mathematics

1 answer:

Dmitriy789 [7]3 years ago

3 0

We know, 3 feet = 1 yard.

We have to convert feet to yards to calculate the ratio so that the final answer doesn't have any unit.

Therefore, 21 feet = $\frac{21 feet}{3 feet}yards$ = 7 yards

Thus, the ratio

$\frac{21feet}{8yards} =\frac{7yards}{8yards} =\frac{7}{8}$

The fraction $\frac{7}{8}$ is already in its simplest form.

Therefore, the given ratio as a fraction in the simplest form without any units is $\frac{7}{8}$

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The sum of 2 consecutive numbers is 37. Find the numbers. If x represents the smaller integer, then the larger integer is

NARA [144]

Answer:

x + 1

Step-by-step explanation:

There are a few ways this problem could be solved. The easiest route is to note that the first part of the question says "2 consecutive numbers". If the numbers are next to each other on a number line (consecutive) and x is the smaller number, the larger number is x + 1.

To check, let's find the two numbers. We know the numbers are next to each other on a number line and that together, they equal 37. Let's begin with 15 and 16.

15 + 16 = 31

These numbers are too low, as they should add to 37. Let's try 18 and 19.

18 + 19 = 37

There are the two correct numbers. If x = the smaller number, x = 18.

18 + 1 = 19

Since this is correct, we know for sure that the answer is x + 1.

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3 years ago

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mamaluj [8]

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3 years ago

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The slope-intercept form of the equation of a line that passes through point (-3, 8) is y = -2/3x + 6. What is the point-

Elena-2011 [213]

$y = \stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{3}}x+6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

so hmmm then we know the slope of that line is -2/3, so we're really looking for the point-slope form of a line with a slope of -2/3 and that passes through (-3 , 8)

$(\stackrel{x_1}{-3}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ -\cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{(-3)})\implies y-8=-\cfrac{2}{3}(x+3)$