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3 years ago

The sides of a triangle are in the ratio 2:3:5. The perimeter of the triangle is 55

Mathematics

1 answer:

Lynna [10]3 years ago

7 0

Answer:

The length of each sides are 11 feet, 16.5 feet, 27.5 feet.

Step-by-step explanation:

The ratio of the sides of a triangle are 2:3:5.

The sides of the triangle = 2x, 3x, 5x

The perimeter of the triangle = 55 feet.

2x + 3x + 5x = 55

10x = 55

x = 55/10 = 5.5

Length of each side : 2x = 2*5.5 = 11 feet

3x = 3*5.5 = 16.5 feet

5x = 5 * 5.5 = 27.5 feet

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A garden is shaped in the form of a regular heptagon (seven-sided), MNSRQPO. A circle with center T and radius 25m circumscribes

Alenkinab [10]

The relationship between the sides MN, MS, and MQ in the given regular heptagon is $\dfrac{1}{MN} = \dfrac{1}{MS} + \dfrac{1}{MQ}$

The area to be planted with flowers is approximately 923.558 m²

The reason the above value is correct is as follows;

The known parameters of the garden are;

The radius of the circle that circumscribes the heptagon, r = 25 m

The area left for the children playground = ΔMSQ

Required;

The area of the garden planted with flowers

Solution:

The area of an heptagon, is;

$A = \dfrac{7}{4} \cdot a^2 \cdot cot \left (\dfrac{180 ^{\circ}}{7} \right )$

The interior angle of an heptagon = 128.571°

The length of a side, S, is given as follows;

$\dfrac{s}{sin(180 - 128.571)} = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)}$

$s = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)} \times sin(180 - 128.571) \approx 21.69$

$The \ apothem \ a = 25 \times sin \left ( \dfrac{128.571}{2} \right) \approx 22.52$

The area of the heptagon MNSRQPO is therefore;

$A = \dfrac{7}{4} \times 22.52^2 \times cot \left (\dfrac{180 ^{\circ}}{7} \right ) \approx 1,842.94$

$MS = \sqrt{(21.69^2 + 21.69^2 - 2 \times 21.69 \times21.69\times cos(128.571^{\circ})) \approx 43.08$

By sine rule, we have

$\dfrac{21.69}{sin(\angle NSM)} = \dfrac{43.08}{sin(128.571 ^{\circ})}$

$sin(\angle NSM) =\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ})$

$\angle NSM = arcsin \left(\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ}) \right) \approx 23.18^{\circ}$

∠MSQ = 128.571 - 2*23.18 = 82.211

The area of triangle, MSQ, is given as follows;

$Area \ of \Delta MSQ = \dfrac{1}{2} \times 43.08^2 \times sin(82.211^{\circ}) \approx 919.382^{\circ}$

The area of the of the garden plated with flowers, $A_{req}$ , is given as follows;

$A_{req}$ = Area of heptagon MNSRQPO - Area of triangle ΔMSQ

Therefore;

$A_{req}$ = 1,842.94 - 919.382 ≈ 923.558

The area of the of the garden plated with flowers, $A_{req}$ ≈ 923.558 m²

Learn more about figures circumscribed by a circle here:

brainly.com/question/16478185

6 0

3 years ago

How many times does X squared minus 4X -12 cross the X axis

kolbaska11 [484]

We can solve this problem using discriminant.

x^2-4x-12's discriminant is

(-4)^2-4*-12=16+48 which is clearly larger than 0

This means that it crosses over the axes 2 times.

In case you don't know what discriminant is, its in equation ax^2+bx+c

the discriminant is b^2-4ac.

If its positive it has 2 crosses with x axis, if negative then 0 crosses, if 0 then 1 cross.

Hope this helped at least a little bit :D

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3 years ago

What is the measure of the missing angle?

goblinko [34]

Answer:

The missing angle measures also 110°

Step-by-step explanation:

Let's recall that If the transversal cuts across parallel lines (apparently, this particular case) then those alternate exterior angles have the same measure (.∠ 110° and ∠?) So in the figure given, the two alternate exterior angles measure the same.

The missing angle measures also 110°

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3 years ago

HELP ASAP WHAT IS THIS ANSWER

postnew [5]

Answer:

Step-by-step explanation:

x = 1/2 ( a + b)

x = 1/2 (129 + 71)

x = 1/2 (200)

x = 100 °

you just have to remember that formula

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3 years ago

Which is a quadratic function

vfiekz [6]

According to Google:

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function in one or more variables in which the highest-degree term is of the second degree.

If this is a homework question, just paraphrase!

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3 years ago