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2 years ago

$72.75 with a 6% sales tax

Mathematics

1 answer:

lina2011 [118]2 years ago

4 0

Answer:

$77.12

Step-by-step explanation:

72.75*0.06 which is 77.12.

Hope this helps plz mark brainliest :D

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

konstantin123 [22]

Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

According to this theorem,

$BC^2=BD\cdot AB.$

Let BC=x cm, then AD=BC=x cm and BD=AB-AD=3-x cm. Then

$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

Take positive value x. You get

$AD=BC=\dfrac{-3+3\sqrt{5} }{2}\ cm.$

2. According to the previous theorem,

$AC^2=AD\cdot AB.$

Then

$AC^2=\dfrac{-3+3\sqrt{5} }{2}\cdot 3=\dfrac{-9+9\sqrt{5} }{2},\\ \\AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

Answer: $AC=\sqrt{\dfrac{-9+9\sqrt{5} }{2}}\ cm.$

This solution doesn't need CD=2 cm. Note that if AB=3cm and CD=2cm, then

$CD^2=AD\cdot DB,\\ \\2^2=AD\cdot (3-AD),\\ \\AD^2-3AD+4=0,\\ \\D$

This means that you cannot find solutions of this equation. Then CD≠2 cm.

8 0

3 years ago

Read 2 more answers

Find slope and y-intercept formed the graph if the linear equation <br>y=1/4x-8

RSB [31]

Answer:

not sure exactly what its asking but if its asking the slope and y-intercept of this equation is here.

Step-by-step explanation:

the slope is 1/4 while the y-intercept is -8 or (0,-8)

3 0

2 years ago

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4^{5} times 4^{3} WHAT'S THE ANSWER

Alchen [17]

4^8 is the answer according to the law of indices

7 0

2 years ago

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I need Smart people:)

Blababa [14]

Answer:

What? I do not even see what you are trying to get at. I have a masters in math so I could help. Whats the question you are having an issue with ?

Step-by-step explanation:

7 0

3 years ago

A boat travels 12 km upstream and back in 1 hour 45 minutes. If the speed of the current is 3 km/h throughout, find the speed of

Elza [17]

Answer:

14.3 km/h to 3 significant figures

Step-by-step explanation:

Let time travelling upstream be t1 hours and downstream = t2 hours.

t1 + t2 = 1.75..........................(1)

Let v be the speed of the boat in still water.

12 / t1 = v - 3.........................(2)

12 / t2 = v + 3........................(3)

From (1) and (3) , substituting for t2:-

12 / (1.75 - t1) = v + 3 ..................(4)

Subtract:- (2) - (4):-

12 / t1 - 12 / (1.75 - t1) = -6

12(1 .75 - t1) - 12t1 = -6t1(1.75 - t1)

21 - 12t1 - 12t1 = -10.5t1 + 6t^2

6t1^2 + 13.5t1 - 21 = 0

Solving this gives t1 = 1.058 hours

Therefore the speed in still water (v) = 12/1.058 + 3 = 14.3 to 3 sig figs

3 0

3 years ago