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3 years ago

Round 1.0649 to the nearest thousandth.

Mathematics

2 answers:

DaniilM [7]3 years ago

6 0

It will be 1.065 because 4 is in the thousandth place, and because 9 is larger than five, four rounds to five

yuradex [85]3 years ago

5 0

1.065. The 5 is the nearest thousandth

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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

Solve the equation. Check your solutions. |4b+4|=|2b+8|

anzhelika [568]

Answer:

Explanation:

|4b + 4| = |2b + 8|

Solve absolute value

|4b + 4| = |2b + 8|

Either 4b + 4 = 2b + 8 or 4b + 4 = −(2b + 8)

4b + 4 = 2b + 8 (Possibility 1)

4b + 4 − 2b = 2b + 8 − 2b (Subtract 2b from both sides)

2b + 4 = 8

2b + 4 − 4 = 8 − 4 (Subtract 4 from both sides)

2b = 4

2b / 2 = 4 / 2 (Divide both sides by 2)

b = 2

4b + 4 = −(2b + 8) (Possibility 2)

4b + 4 = −2b − 8 (Simplify both sides of the equation)

4b + 4 + 2b = −2b − 8 + 2b (Add 2b to both sides)

6b + 4 = −8

6b + 4 − 4 = −8 − 4 (Subtract 4 from both sides)

6b = −12

6b / 6 = -12 / 6 (Divide both sides by 6)

b = -2

6 0

2 years ago

How do you solve: secx=-5/2, tanx<0 Find all six trig functions

Brut [27]

Answer:

sec theta = (sqrt24/5) cos theta = -2/5 tan theta = (-[sqrt 21]/2) sec theta = 5/2 csc theta = (5sqrt21)/21 cot theta = (-2sqrt21)/21

Step-by-step explanation:

During the problem, secx = -5/2, we can assume that as cos = -2/5. -2 = x. 5 = r. find for Y with: x^2+y^2=r^2. After that, plug in for the variables and you get all the answers. Rationalize the square roots, don't forget.

5 0

2 years ago

Michelle Smith bought 30 shares of James Company stock at $34 per share. The company paid annual dividends of $0.42 per share. W

grandymaker [24]

Answer:

The right option is B) 12.60

Step-by-step explanation:

We have given,

Number of shares = 30

Cost of each share = $34

Total cost of shares = 30 × 34 = $1020

Since the company paid annual dividends of $0.42 per share.

i.e Total annual dividend company paid = 0.42 × 30

Total annual dividend company paid = $ 12.60

Hence the right option is B) 12.60

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2 years ago

Donna guessed there were 400 jellybeans in a jar. There were really 480 jellybeans. What was her percent of error?

dimulka [17.4K]

Answer:

400 +480 =880

Step-by-step explanation:

0+0=0

8+0=8

4+4=8

880

6 0

2 years ago