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shtirl [24]
3 years ago
15

7 times as much as the sum of 1/3 and 4/5

Mathematics
2 answers:
Vlada [557]3 years ago
4 0
7( \frac{1}{3} +  \frac{4}{5} )

=7( \frac{1(5)}{3(5)} +  \frac{4(3)}{5(3)} )

=7( \frac{5}{15} +  \frac{12}{15} )

=7( \frac{17}{15})

=\frac{7}{1} ( \frac{17}{15})

=\frac{119}{15}

= 7\frac{14}{15} ≈ 7.93
algol133 years ago
4 0

¹¹⁹/₁₅ or 7¹⁴/₁₅ or 7.93

<h3>Further explanation</h3>

<u>The Problem:</u>

  • 7 times as much as the sum of \frac{1}{3} and \frac{4}{5}
  • Write an expression to match, and then solve it.

<u>The Process:</u>

Here are some early expressions that need attention.

  • one-third is \boxed{\frac{1}{3}}
  • four-fifth is \boxed{\frac{4}{5}}
  • the sum of \frac{1}{3} \ and \ \frac{4}{5} is \boxed{\frac{1}{3} + \frac{4}{5}}

Let us write an expression to match for 7 times as much as the sum of \frac{1}{3} and \frac{4}{5}

\boxed{\boxed{ \ 7 \times \bigg(\frac{1}{3} + \frac{4}{5} \bigg) \ }}

Let us calculate the operation in parentheses at first.

\boxed{\frac{1}{3} + \frac{4}{5}}

A least common multiple of 3 and 5 is 15. We use to equate the denominator.

\boxed{\frac{1 \times 5}{3 \times 5} + \frac{4 \times 3}{5 \times 3}}

\boxed{\frac{5}{15} + \frac{12}{15}}

\boxed{\frac{17}{15}}

And now we solve the full expression.

\boxed{ \ = 7 \times \bigg(\frac{1}{3} + \frac{4}{5} \bigg) \ }

\boxed{ \ = 7 \times \frac{17}{15} \ }

We do not cross out 7 and 15 because they both cannot be divided.

\boxed{ \ = \frac{119}{15} \ }

\boxed{\boxed{ \ = \frac{119}{15} \ }}

In mixed fraction:

\boxed{ \ \frac{119}{15} = \ ? \ }

\boxed{ \ = \frac{105}{15} + \frac{14}{15} \ }

\boxed{ \ = 7 + \frac{14}{15} \ }

\boxed{\boxed{ \ = 7\frac{14}{15} \ }}

In decimal:

\boxed{ \ 7\frac{14}{15} = \ ? \ }

\boxed{ \ \frac{14}{15} = 0.93 \ }

\boxed{ \ = 7 + \frac{14}{15} \ }

\boxed{ \ = 7 + 0.93 \ }

\boxed{\boxed{ \ = 7.93 \ }}

\boxed{\boxed{ \ Thus, \ the \ result \ is \ \frac{119}{15} \ or \ 7\frac{14}{15} \ or \ 7.93 \ }}

- - - - - - - - - -

<u>Quick Steps:</u>

\boxed{ \ = 3 \times \bigg(\frac{1}{3} + \frac{4}{5} \bigg) \ }

\boxed{ \ = 3 \times \bigg(\frac{5 + 12}{15} \bigg) \ }

\boxed{ \ = 3 \times \bigg(\frac{17}{15} \bigg) \ }

\boxed{\boxed{ \ = \frac{119}{15} \ }}

\boxed{\boxed{ \ = 7\frac{14}{15} \ }}

\boxed{\boxed{ \ = 7.93 \ }}

<h3>Learn more  </h3>
  1. 7 copies of the sum of 8 fifths and 4 brainly.com/question/961462
  2. \frac{2}{3} of the product of \frac{3}{8} and 16 brainly.com/question/961462
  3. 15 times as much as 1 fifth of 12 is brainly.com/question/348151

Keywords: 7 times, as much as, the sum of 1/3 and 4/5, write an expression to match, and then solve, the result, in mixed fraction, decimal, ¹³/₄ or 3¹/₄ or 3.25

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The perimeter of a triangle is 32 feet. One side of the triangle is 3 times the second side. The third side is 12 feet longer
Ivenika [448]

We have a triangle whose perimeter is 32 feet. Some information regarding the sides of the triangle is given:

GiveN:

  • One side is 3 times the second side.
  • Third side is 12 feet longer than the second side.

As we can see that, two sides of the triangle are defined the second sides. It means First and third side can be expressed in the form of second side.

  • So let the second side be x

Then,

  • First side = 3x
  • And, third side = x + 12

We know that, perimeters is the sum of the lengths of all sides of the triangle, So it can be written as:

3x + x + x + 12 = 32

Solving it further,

5x + 12 = 32

Subtracting 12 from both sides,

5x + 12 - 12 = 32 - 12

5x = 20

Dividing 5 from both sides,

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x = 4

Then,

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A rope of length 18 feet is arranged in the shape of a sector of a circle with central angle O radians, as shown in the
creativ13 [48]

Answer:

A(\theta)=\frac{162 \theta}{(\theta+2)^2}

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Let

r ---> the radius of the sector

s ---> the arc length of sector

Find the radius r

we know that

2r+s=18

s=r \theta

2r+r \theta=18

solve for r

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step 2

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s=r \theta

substitute the value of r

s=\frac{18}{2+\theta}\theta

step 3

we know that

The area of complete circle is equal to

A=\pi r^{2}

The complete circle subtends a central angle of 2π radians

so

using proportion find the area of the sector by a central angle of angle theta

Let

A ---> the area of sector with central angle theta

\frac{\pi r^{2} }{2\pi}=\frac{A}{\theta} \\\\A=\frac{r^2\theta}{2}

substitute the value of r

A=\frac{(\frac{18}{2+\theta})^2\theta}{2}

A=\frac{162 \theta}{(\theta+2)^2}

Convert to function notation

A(\theta)=\frac{162 \theta}{(\theta+2)^2}

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