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Studentka2010 [4]
3 years ago
13

Solve this for me (geometry)

Mathematics
1 answer:
VashaNatasha [74]3 years ago
7 0

Given:

A figure of a circle. KJ=6,KL=x-2,ML=4.

To find:

The length of KJ.

Solution:

From the given figure it is clear that the number 6 is marked between K and J it means the number 6 represents the distance between the points K and j.

Therefore, the length of KJ is 6 units.

Note: In the given question we need to find KL instead of KJ because KJ is already given.

According to the tangent secant theorem:

a^2=bc

Where,

  • a is the length of the tangent.
  • b is the length of the external segment of the secant.
  • c is the measure of the secant.

Using the tangent secant theorem, we get

ML^2=KL\times JL

(4)^2=(x-2)\times (6+x-2)

16=(x-2)\times (4+x)

16=4x+x^2-8-2x

On further simplification, we get

16=x^2+2x-8

0=x^2+2x-8-16

0=x^2+2x-24

Splitting the middle term, we get

x^2+6x-4x-24=0

x(x+6)-4(x+6)=0

(x+6)(x-4)=0

x=-6,4

For x=-6,

KJ=-6-2

KJ=-8, which is not possible because side cannot be negative.

For x=4,

KJ=4-2

KJ=2

Therefore, the measure of KL is 2 units.

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Calvin works at a facility which processes apples. It costs the facility $0. 68 to make either a jar of applesauce or a bottle o
NNADVOKAT [17]

The number of bottles the facility requires to sell when it breaks is given by

a system of two simultaneous equations.

  • When the facility breaks even, it would have sold 7<u>7,579 bottles of apples juice</u>.

Reasons:

The cost to make a jar of applesauce or a bottle of apple juice = $0.68

Number of jars of applesauce to be sold foe every 2 bottles of apple juice = 3 jars

The selling price for a jar of applesauce = $2.20

Selling price for a bottle of apple juice = $3.15

Annual overhead cost excluding production cost = $368,500

Required: Number of bottles of apple juice sold by the facility when it breaks even annually.

Solution:

Let <em>J</em> represent the number of bottles of apple juice sold, and let <em>S</em> represent the number of jars of apple sauce, by excluding the production cost, we have;

(3.15 - 0.68)·J + (2.2 - 0.68)·S = 368,500

S : J = 3 : 2

Which gives;

\displaystyle \frac{S}{J} = \mathbf{ \frac{3}{2}}

\displaystyle S= \frac{3}{2} \cdot J

Therefore;

\displaystyle (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot S = (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot  \frac{3}{2} \cdot J = \mathbf{368,500}

Which gives;

\displaystyle  (3.15 - 0.68) \cdot J + (2.2 - 0.68) \cdot  \frac{3}{2} \cdot J = \mathbf{ \frac{19 \cdot J }{4} } =  368,500

\displaystyle  J  =   \frac{368,500 \times 4}{19}  = \frac{1474000}{19}=77578\frac{18}{19}  \approx 77,579

The number of bottles of apple juice sold, J ≈ <u>77,579 bottles</u>

Learn more about simultaneous equations here:

brainly.com/question/10724274

7 0
2 years ago
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