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agasfer [191]
3 years ago
15

The vertex angle of an isosceles triangle measures ( 6x -9)° and one of the base angles measures (4x)°. What is the value of x?

Mathematics
1 answer:
Gnom [1K]3 years ago
5 0

Answer:

x = 13.5

Step-by-step explanation:

We know that base angles of an isosceles triangle are equal. The base angles of the triangle are (4x)° each. The vertex angle of the traingle is (6x-9)°. So according to angle sum property of triangle,

6x - 9 + 4x + 4x = 180

=  > 6x - 9 + 8x = 180

=  > 14x - 9 = 180

=  > 14x = 180  + 9 = 189

=  > x =  \frac{189}{14}  = 13.5

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33 other coins were collected
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2 years ago
Type the correct answer in each box. Use numerals instead of words.
lubasha [3.4K]

Answer:

System A has 4 real solutions.

System B has 0 real solutions.

System C has 2 real solutions

Step-by-step explanation:

System A:

x^2 + y^2 = 17   eq(1)

y = -1/2x            eq(2)

Putting value of y in eq(1)

x^2 +(-1/2x)^2 = 17

x^2 + 1/4x^2 = 17

5x^2/4 -17 =0

Using quadratic formula:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

a = 5/4, b =0 and c = -17

x=\frac{-(0)\pm\sqrt{(0)^2-4(5/4)(-17)}}{2(5/4)}\\x=\frac{0\pm\sqrt{85}}{5/2}\\x=\frac{\pm\sqrt{85}}{5/2}\\x=\frac{\pm2\sqrt{85}}{5}

Finding value of y:

y = -1/2x

y=-1/2(\frac{\pm2\sqrt{85}}{5})

y=\frac{\pm\sqrt{85}}{5}

System A has 4 real solutions.

System B

y = x^2 -7x + 10    eq(1)

y = -6x + 5            eq(2)

Putting value of y of eq(2) in eq(1)

-6x + 5 = x^2 -7x + 10

=> x^2 -7x +6x +10 -5 = 0

x^2 -x +5 = 0

Using quadratic formula:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

a= 1, b =-1 and c =5

x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(5)}}{2(1)}\\x=\frac{1\pm\sqrt{1-20}}{2}\\x=\frac{1\pm\sqrt{-19}}{2}\\x=\frac{1\pm\sqrt{19}i}{2}

Finding value of y:

y = -6x + 5

y = -6(\frac{1\pm\sqrt{19}i}{2})+5

Since terms containing i are complex numbers, so System B has no real solutions.

System B has 0 real solutions.

System C

y = -2x^2 + 9    eq(1)

8x - y = -17        eq(2)

Putting value of y in eq(2)

8x - (-2x^2+9) = -17

8x +2x^2-9 +17 = 0

2x^2 + 8x + 8 = 0

2x^2 +4x + 4x + 8 = 0

2x (x+2) +4 (x+2) = 0

(x+2)(2x+4) =0

x+2 = 0 and 2x + 4 =0

x = -2 and 2x = -4

x =-2 and x = -2

So, x = -2

Now, finding value of y:

8x - y = -17    

8(-2) - y = -17    

-16 -y = -17

-y = -17 + 16

-y = -1

y = 1

So, x= -2 and y = 1

System C has 2 real solutions

4 0
3 years ago
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Simplify the expression.
Anna35 [415]
6,372 I used a calculator, I hope this helps
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3 years ago
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Help me math is not my thing and plz tell me how you did it
mafiozo [28]
We need to get m by itself. to do that, we divide each side of the equation by -3.3. so, m = 0.333 (repeating decimal).
8 0
2 years ago
Read 2 more answers
Brandon is making a ramp . The ramp stands 3 feet tall and is 9 feet long . How long is the base of the ramp
tresset_1 [31]

Answer: 8.48 Feet

Step-by-step explanation:

We can use the Pythagorean Theorem, A^2 + B^2 = C^2

A^2 + B^2 = C^2

A^2 + 3^2 = 9^2

A^2 + 9 = 81

81 - 9 = A^2

72 = A^2

√72 = A

8.48 = A

Hope this helps!

8 0
2 years ago
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