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4 years ago

Mr.Frederick bought five ceiling fans to install in his home what is the coast for each fan if the total was $608.55

Mathematics

1 answer:

lubasha [3.4K]4 years ago

3 0

Answer:

$121.71

Step-by-step explanation:

Divide $608.55 by 5 to find the cost for each fan. The quotient is $121.71.

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In equilateral ∆ABC with side a, the perpendicular to side AB at point B intersects extension of median AM in point P. What is t

Sergeeva-Olga [200]

Answer:

Perimeter = (2 + √3)·a

Step-by-step explanation:

Given: ΔABC is equilateral and AB = a

The diagram is given below :

AM is a median , PB ⊥ AB , PM = b

Now, by using properties of equilateral triangle, median is perpendicular bisector and each angle is of 60°.

We get, ∠AMB = 90°. So, by linear pair ∠AMB + ∠PMB = 180° ⇒ ∠PMB = 90°. Also, ∠ABC = 60° and ∠ABP = 90° (given) So, ∠PBM = 30°

Since, AM is perpendicular bisector of BC. So,

$MB = \frac{a}{2}$

Now in ΔAMB , By using Pythagoras theorem

$AB^{2}=AM^{2}+MB^{2}\\AM^{2}=AB^{2}-MB^{2}\\AM^{2}=a^{2}-(\frac{a}{2})^{2}\\AM=\frac{\sqrt{3}\cdot a}{2}$

Now, in ΔBMP :

$sin\thinspace 30^{o}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\sin\thinspace 30^{o}=\frac{\text{MB}}{\text{PB}}\\\\PB=\frac{\text{MB}}{\text{sin 30}}\\\\PB=\frac{\frac{a}{2}}{\frac{1}{2}}\implies PB = a\\\\tan\thinspace 30^{o}=\frac{\text{Perpendicular}}{\text{Base}}\\\\tan\thinspace 30^{o}=\frac{\text{MB}}{\text{PM}}\\\\PM=\frac{\text{MB}}{\text{tan 30}}\\\\PM=\frac{\frac{a}{2}}{\frac{1}{\sqrt3}}\implies PM=b= \frac{\sqrt{3}\cdot a}{2}$

Perimeter of ABM = AB + PB + PM + AM

$\text{Perimeter = }a+a+b+ \frac{\sqrt{3}\cdot a}{2}\\\\=2\cdot a + \frac{\sqrt{3}\cdot a}{2} +\frac{\sqrt{3}\cdot a}{2}\\\\=2\cdot a +\sqrt{3}\cdot a\\\\=(2+\sqrt3})\cdot a$

Hence, Perimeter of ΔABP = (2 + √3)·a units

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3 years ago

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3 years ago

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Step-by-step explanation:

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3 years ago

The owner of a small store buys coats for $55.00 each. Answer parts a and b. a. She sells the coats for $99.00 each. What perc

scoundrel [369]

Answer:

180% ; 5

Step-by-step explanation:

Purchase price per coat = 55

Sales price per coat = 99

% of purchase price is sales price :

X% * 55 = 99

(x / 100) * 55 = 99

0.01x * 55 = 99

0.55x = 99

x = 99 / 0.55

x = 180

180% of purchase price

B.)

180% * 45 = 81 per jacket

Number of jackets to sell to make atleast $390 in sales

$390 / $81 = 4.8

Hence, 5 jackets

3 0

3 years ago