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Lostsunrise [7]
3 years ago
5

Using the geometric mean and Pythagorean theorem, calculate the values of the missing sides. Round your answers to the thousandt

hs place (3 decimal places).

Mathematics
1 answer:
Pachacha [2.7K]3 years ago
6 0

Answer:

a = 9.849

b = 20.25

c = 491.03

Step-by-step explanation:

By using Pythagoras theorem in the right triangle BDC,

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

BC² = BD² + DC²

a² = 9² + 4²

a = \sqrt{(81+16)}

a = \sqrt{97}

a = 9.8489

a ≈ 9.849 units

By mean proportional theorem,

\frac{\text{DC}}{\text{BD}}=\frac{\text{BD}}{\text{AD}}

AD × DC = BD²

b × 4 = 9²

b = \frac{81}{4}

b = 20.25 units

BY Pythagoras theorem in ΔADB,

AB² = AD² + BD²

c² = b² + 9²

c² = (20.25)² + 9²

c² = 410.0625 + 81

c = 491.0625

c = 491. 063 units

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Kelly bought a book of 20 stamps. She has used 80% of them. A. How many stamps has Kelly used? B. How many stamps does she have
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Shannon went to an auto repair shop and paid $339.50, which included parts that cost $112 and 3.5 hours of labor. Joni went to a
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Option A, Shannon paid $ 7 per hour to labor than Joni

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Total amount paid by Shannon = $339.50

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Total cost of 3.5 hours of labor paid by Shannon = $227.5/3.5

Total cost of 1 hours of labor paid by Shannon  $65 per hour

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3 years ago
Graph the linear equation x-3y=-6
TEA [102]

Answer:

Step-by-step explanation:

One of the easier approaches to graphing a linear equation such as this one is to solve it for y, which gives us both the slope of the line and the y-intercept.

x-3y=-6 → -3y = -x - 6,  or 3y = x + 6.

Dividing both sides by 3, we get   y = (1/3)x + 2.

So the slope of this line is 1/3 and the y-intercept is 2.

Plot a dot at (0, 2).  This is the y-intercept.  Now move your pencil point from that dot 3 spaces to the right and then 1 space up.  Draw a line thru these two dots.  End.

Alternatively, you could use the intercept method.  We have already found that the y-intercept is (0, 2).  To find the x-intercept, let y = 0.  Then x = -6, and the x-intercept is (-6, 0).

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Expand the given power by using Pascal’s triangle. (9a - 10b)^6
xxMikexx [17]

Answer:

531441a^6-3542940a^5b+9841500a^4b^2-14580000a^3b^3+12150000a^2b^4-5400000ab^5+1000000b^6

Step-by-step explanation:

                     1                                n=0

                  1      1                            n=1

                 1   2   1                           n=2

                1  3  3  1                          n=3

              1  4  6  4   1                      n=4

             1  5 10 10 5  1                    n=5

           1 6 15 20 15 6 1                   n=6

This is where n is the exponent in

(x+y)^n.

(x+y)^6=1x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+1y^6

Now we want to expand:

(9a-10b)^6 or we we can rewrite as (9a+(-10b))^6.

Let's replace x with (9a) and y with (-10b) in the expansion:

(x+y)^6=1x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+1y^6

((9a)+(-10b))^6

=1(9a)^6+6(9a)^5(-10b)+15(9a)^4(-10b)^2+20(9a)^3(-10b)^3+15(9a)^2(-10b)^4+6(9a)(-10b)^5+1(-10b)^6

Let's simplify a bit:

=9^6a^6-60(9)^5a^5b+15(-10)^2(9)^4a^4b^2+20(9)^3(-10)^3a^3b^3+15(9)^2(-10)^4a^2b^4+6(9)(-10)^5ab^5+(-10)^6b^6

=531441a^6-3542940a^5b+9841500a^4b^2-14580000a^3b^3+12150000a^2b^4-5400000ab^5+1000000b^6

8 0
3 years ago
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