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ICE Princess25 [194]

3 years ago

11

A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 13 feet mo

re than the length of the shortest side. Find the dimensions if the perimeter is 125 feet

1 answer:

allochka39001 [22]3 years ago

4 0

Parameter is sum of all sides therefore

<span>2x + x + x + 13 = 125
4x = 125-13
4x = 112
x = 28</span>

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Eight less than the quotient of a number and 3 is 18. Which equation models this sentence?

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B- n/ 3 - 8 = 18....................

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How would you write the following expression as a single term? 3[2 ln(x-1) - lnx] + ln (x+1)

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Apply the rule: $n ln x = ln x^{n}$

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You are making 5 Autumn Classic bouquets for your friends. You have $610 to spend and want 24 flowers for each bouquet. Roses co

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There are 16 Roses , 2 Tulips , 6 Lilies in each Autumn Classic Bouquet.

<h3>Further explanation</h3>

Simultaneous Linear Equations could be solved by using several methods such as :

<em>Elimination Method</em>
<em>Substitution Method</em>
<em>Graph Method</em>

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

$\texttt{ }$

<em>Let For Each Bouguet:</em>

<em>Number of Roses = R</em>

<em>Number of Tulips = T</em>

<em>Number of Lilies = L</em>

$\texttt{ }$

<em>There are 24 flowers for each bouquet.</em>

$R + T + L = 24$ → <em>Equation 1</em>

$\texttt{ }$

<em>You have $610 to spend for 5 bouguets.</em>

<em>Roses cost $6 each, tulips cost $4 each, and lilies cost $3 each.</em>

$6R + 4T + 3L = 610 \div 5$

$6R + 4T + 3L = 122$ → <em>Equation 2</em>

$\texttt{ }$

<em>You want to have twice as many roses as the other 2 flowers combined in each bouquet.</em>

$R = 2 ( T + L )$ → <em>Equation 3</em>

$\texttt{ }$

<em>Equation 1 ↔ Equation 3:</em>

$R + T + L = 24$

$2 ( T + L ) + T + L = 24$

$3T + 3L = 24$

$T + L = 8$

$T = 8 - L$ → <em>Equation 4</em>

$\texttt{ }$

<em>Equation 4 ↔ Equation 3:</em>

$R = 2 ( T + L )$

$R = 2 ( 8 - L + L )$

$R = 2 ( 8 )$

$\boxed{R = 16}$

$\texttt{ }$

<em>Equation 2 ↔ Equation 4:</em>

$6R + 4T + 3L = 122$

$6(16) + 4(8 - L) + 3L = 122$

$96 + 32 - 4L + 3L = 122$

$L = 96 + 32 - 122$

$\boxed{L = 6}$

$\texttt{ }$

<em>Equation 4:</em>

$T = 8 - L$

$T = 8 - 6$

$\boxed{T = 2}$

$\texttt{ }$

<h2>Conclusion:</h2>

There are 16 Roses , 2 Tulips , 6 Lilies in each Autumn Classic Bouquet.

$\texttt{ }$

<h3>Learn more</h3>

Perimeter of Rectangle : brainly.com/question/12826246
Elimination Method : brainly.com/question/11233927
Sum of The Ages : brainly.com/question/11240586

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations

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3 years ago

A: 2, 3, 10, and 12<br>y: 2/3, 1, 10/3, and 4<br>Constant of proportionality: <br>Equation: y =

stepladder [879]

Constant of proportionality : $\frac{1}{3}$

Equation: y = ka

How are the values calculated?

a: 2, 3, 10, and 12

y: 2/3, 1, 10/3, and 4

Let the constant of proportionality = k

If x and y are directly proportional ,

We know , k = $\frac{y}{x}$

Here, k = $\frac{y}{a}$

Considering y = 2/3 and a =2

k = $\frac{2}{3*2}$ = $\frac{2}{6}$ = $\frac{1}{3}$

Thus, the constant of proportionality ( k) = $\frac{1}{3}$

The equation y is given by ,

y = ka

Let us verify,

For k = 1/3 and a = 12

$y=\frac{1}{3} *12\\\\y=4$

Thus the equation is y = ka

What is constant of proportionality?

The constant value of the ratio between two proportional values is known as the constant of proportionality.

When the ratio or product of two changing quantities gives a constant, the two are said to be in a relation of proportionality.

The type of proportion between the two specified variables affects the constant of proportionality's value.

The formula y = kx can be used to determine the value of "k" in a direct proportionality.

Direct proportionality follows that k = y/x.

To learn more about constant of proportionality, refer:

brainly.com/question/28413384

#SPJ9

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1 year ago