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vfiekz [6]
3 years ago
13

In Exercises 10 and 11, points B and D are points of tangency. Find the value(s) of x.​

Mathematics
1 answer:
Lemur [1.5K]3 years ago
7 0

In both cases,

AB^2=AD^2

(as a consequence of the interesecting secant-tangent theorem)

So we have

10.

(4x+7)^2=(6x-3)^2

16x^2+56x+49=36x^2-36x+9

20x^2-92x-40=0

5x^2-23x-10=0

(5x+2)(x-5)=0\implies\boxed{x=5}

(omit the negative solution because that would make at least one of AB or AD have negative length)

11.

(4x^2-18x-10)^2=(x^2+x+4)^2

16x^4-144x^3+244x^2+360x+100=x^4+2x^3+9x^2+8x+16

15x^4-146x^3+235x^2+352x+84=0

(x-7)(3x+2)(5x^2-17x-6)=0\implies\boxed{x=-\dfrac23\text{ or }x=7}

(again, omit the solutions that would give a negative length for either AB or AD)

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I NEED HELP PLEASEEE
Gwar [14]

Answer:

b = \sqrt{333}

Step-by-step explanation:

1. We can use the Pythagorean Theorem to find the missing side, b.

  • 14^2 + b^2 = 23^2

2. (Solving)

Step 1: Simplify both sides of the equation.

  • (14*14)+b^2 =(23*23)
  • 196 + b^2 = 529

Step 2: Subtract 196 from both sides.

  • 196 + b^2 - 196 = 529 - 196
  • b^2 = 333

Step 3: Take square root of both sides.

  • \sqrt{b^2} = \sqrt{333}
  • b = \sqrt{333}

Step 4: Check if solution is correct.

  • 14^2 + \sqrt{333^2} = 23^2
  • (14*14)+(\sqrt{333} *\sqrt{333})=23*23
  • 196 + 333 = 529
  • 529 = 529

Therefore, b = \sqrt{333}.

6 0
2 years ago
Read 2 more answers
The length of a rectangle is 3 yd longer than its width. if the perimeter of the rectangle is 50 yd , find its length and width.
leva [86]
Length = w+3
P = 2L +2W
50 = 2(w+3) + 2w
50 = 2w +6 +2w
50 = 4w +6
50-6 =4w-6
44 = 4w
44/4 = 4w/4
w = 11
l = 11+3
l = 14

50 = 2L+2W
50 = 2(14) + 2(11)
50 = 28 +22
50=50

7 0
2 years ago
V=M/D
grigory [225]
D=M/V. You just multiply both sides by D to get DV=M, then divide V by both sides.
8 0
3 years ago
If you answer this I will give you brainiest!
Helga [31]

Answer:

1 54 2 132 3 334.58 4 103.18

Step-by-step explanation:

6 0
2 years ago
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If m<1 = 7x-19 and m<2 = x+5 find m<2
lbvjy [14]

Answer:55

Step-by-step explanation:

55

7 0
2 years ago
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