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1 year ago

If the quotient of a number and 6 is added to 1/3, the result is 7/6. Find the number.

Mathematics

1 answer:

lisabon 2012 [21]1 year ago

3 0

The number is 4.

<h3>What is the Quotient?</h3>

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

Let n be the number in question; then, we can write the word problem as an equation like this:

⇒ (n/6) + 1/3 = 7/6

Multiply everything by the least common multiple of all the denominators (6, 3, 6), which is 6.

⇒ 6(n/6) + 9(1/3) = 6(7/6)

⇒ n + 3 = 7

Subtract 3 from both sides,

⇒ n = 4

Hence, the number is 4.

Learn more about the quotient here:

brainly.com/question/27796160

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3 years ago

Solve the system of equations by substitution. 3/8 x + 1/3 y =17/24 and <br> x + 7y = 8

goblinko [34]

$\left \{ {{ \frac{3}{8}x+ \frac{1}{3}y = \frac{17}{14} } \atop {x+7y=8}} \right.$

To solve this system by substitution, first isolate x in the second equation.

$x+7y=8$
$x+7y-7y=8-7y$
$x=8-7y$

Now, plug this expression ( $8-7y$ ) for x in the top equation to solve for y.

$\frac{3}{8} (8-7y)+ \frac{1}{3} y= \frac{17}{14}$
$3- \frac{21}{8} y+ \frac{1}{3} y= \frac{17}{24}$
$72-63y+8y=17$
$72-55y=17$
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$-55y=-55$
$y=1$

Now that you have y, plug it into the second equation and solve for x.

$x+7y=8$
$x+7(1)=8$
$x+7=8$
$x=1$

Last step is to plug your x- and y-values in to both equations to check your work.

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$\frac{3}{8} * \frac{3}{3} = \frac{9}{24} ; \frac{1}{3} * \frac{8}{8} = \frac{8}{24}$

$\frac{9}{24} + \frac{8}{24} = \frac{17}{24}$ <--True

$1+7(1)=8$
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Answer:
$x=1 \\ y=1$

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3 years ago

A, b and c are the sides of a right triangle, where side a is across from angle a, side b is across from angle b, and side c is

Vera_Pavlovna [14]

<span>Find missing length :
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a² + b² = c²
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c² = 1517
c = √1517
c = 38.95 units.

Find missing angle A:

$\dfrac{a}{\sin(a)} = \dfrac{c}{\sin(c)}$

$\dfrac{19}{\sin(a)} = \dfrac{38.95}{\sin(90)}$

$\sin(a) = 0.488$

$a = sin^{-1} (0.488)$

$a = 29.2 \textdegree$

Find Missing B:

$\dfrac{b}{\sin(b)} = \dfrac{c}{\sin(c)}$

$\dfrac{34}{\sin(b)} = \dfrac{38.95}{\sin(90)}$

$\sin(b) = 0.873$

$b = sin^{-1}(0.873)$

$b = 60.8 \textdegree$

Answer: Missing length = 38.95 units ; Missing angles = 29.2° and 60.8°

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