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Free_Kalibri [48]
3 years ago
10

Hw 43 special right triangles

Mathematics
1 answer:
Nutka1998 [239]3 years ago
4 0

Answer:


Step-by-step explanation:

Use the fact that sin 30 =0.5 and cos 30 = sqrt 3/2

we have answers as

8. u=16 and v = 8\sqrt{3}

9) y=5 and x=5\sqrt{3}

10) tan 30 =\frac{1}{\sqrt{3} }

So y=4\sqrt{3}

x=8\sqrt{3}


11) a=22 and b=11

12) b=1.5 and a=1.5\sqrt{3}

13) y=20\sqrt{3}

and x=10



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Question in attachment
ELEN [110]

Answer:

  • $20,000 at 8.5%
  • $10,000 at 10%

Step-by-step explanation:

There are a number of ways to solve mixture problems like this. Some are simple enough you can almost write down the answer. One I like uses a diagram to help you find the ratios of the components of the mix. You can do the same thing with a formula (without the diagram).

The basic idea is that you compute a ratio between two differences. The numerator is the difference between the average interest rate and the lower interest rate. Here, the average interest rate is 2700/30,000 = 0.09 = 9%. Then the numerator is 9% -8.5% = 0.5%

The denominator is the difference between the two interest rates of the investments: 10% -8.5% = 1.5%. And the ratio of these two values is ...

  0.5%/1.5% = 1/3

This is the fraction of the total investment that was invested at the higher interest rate:

  (1/3)×$30,000 = $10,000 . . . . was invested at 10%

Then the remaining amount, $20,000, was invested at 8.5%.

___

If you would prefer an equation, you can let x represent the amount invested at the higher rate. (That is the most convenient assignment of variables, as it keeps all of the numbers positive.) Then (30,000 -x) is the amount invested at the lower rate. The total amount of interest is ...

  10%(x) +8.5%(30,000 -x) = 2700

  x(10% -8.5%) = 2700 -8.5%(30000) . . . . . subtract 8.5%(30,000)

  x = (2700 -8.5%(30,000))/(10% -8.5%) . . . . divide by the coefficient of x

We have purposely left the expression unevaluated so that you can compare it to the math we described above. If you factor out 30,000 from the numerator of this fraction, you see the ratio that we described in words:

  x=30000\left(\dfrac{\dfrac{2700}{30000}-8.5\%}{10\%-8.5\%}\right)\\\\x=10,000

This tells us $10,000 was invested at 10%, and $20,000 was invested at 8.5%.

8 0
3 years ago
Standard deduction on federal income tax return for head of the household is $8350. hilda, a single mom of two, paid $6780 in st
andre [41]

The answer is Claiming standard deduction

4 0
3 years ago
Read 2 more answers
HELP ON THIS PROBLEM!!<br><br> Solve the following 0deg&lt; x&lt; 360deg: cos x= cos 2x
blsea [12.9K]

Answer:

x=0^\circ,120^\circ,240^\circ,360^\circ

Step-by-step explanation:

<u>Use identities to set the equation up as a quadratic</u>

\cos x=\cos 2x;\:0^\circ \leq x \leq 360^\circ\\\\\cos x=2\cos^2 x-1\\\\0=2\cos^2 x-\cos x-1

<u>Make the substitution u=cos(x) and solve the quadratic</u>

<u />0=2u^2-u-1\\\\0=(2u+1)(u-1)

\displaystyle 0=2u+1\\\\0=2\cos x+1\\\\-1=2\cos x\\\\-\frac{1}{2}=\cos x\\\\120^\circ,240^\circ=x

0=u-1\\\\0=\cos x-1\\\\1=\cos x\\\\0^\circ,360^\circ=x

Hence, x=0^\circ,120^\circ,240^\circ,360^\circ

7 0
1 year ago
Consider the triangles shown.
Sergeu [11.5K]
D because it’s congruent
7 0
2 years ago
Which of the following is a secant on the circle below?
boyakko [2]

A. \vec{KI} is the secant line on the below circle.

<u>Step-by-step explanation:</u>

The intersection of the circle will result in either Tangent or Secant. Secant is a line intersecting a circle at two different point. This concept explains the relation between the circle and line intersecting it.

From the given diagram,

The \vec{GJ} and \vec{GK} intersects the circle at the point H and I.

∴ It can also represented that the \vec{JH} and \vec{KI} intersects at a point G.

From the given options \vec{KI} is the secant line that intersects the circle twice.

7 0
3 years ago
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