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Paraphin [41]
3 years ago
7

(e) the equations of the asymptotes (enter your answers as a comma-separated list of equations.)

Mathematics
1 answer:
nexus9112 [7]3 years ago
4 0

Answer:

x=3,x=1

y=2,y=-2

Step-by-step explanation:

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In simplest radical form, what are the solutions to the quadratic equation 6 = x2 – 10x?
vichka [17]

Answer:

x = 5+\sqrt{31}\,\, and\,\, x=5-\sqrt{31}

Step-by-step explanation:

We need to solve the quadratic equation

6 = x^2 -10x

Rearranging we get,

x^2-10x-6=0

Using quadratic formula to solve the quadratic equation

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

a= 1, b =-10 and c=6

Putting values in the quadratic formula

x=\frac{-(-10)\pm\sqrt{(-10)^2-4(1)(-6)}}{2(1)}\\x=\frac{10\pm\sqrt{100+24}}{2}\\x=\frac{10\pm\sqrt{124}}{2}\\x=\frac{10\pm\sqrt{2*2*31}}{2}\\x=\frac{10\pm\sqrt{2^2*31}}{2}\\x=\frac{10\pm2\sqrt{31}}{2}\\x = 5\pm\sqrt{31}

So, x=5+\sqrt{31}\,\, and\,\, x=5-\sqrt{31}

3 0
3 years ago
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What property is used to show that 6(x + 7) = 6x + 42?
Ymorist [56]

Answer: Distributive because 6 has to be multiplied by x and 7

6 0
3 years ago
Let A = { x ∈ R : x 2 − 5 x + 4 ≤ 0 } , B = (3 , 5), and C = (3 , 4]. Show that A ∩ B = C . (Recall, you must show two separate
kolbaska11 [484]

Answer:

You can proceed as follows:

Step-by-step explanation:

First solve the quadratic inequality x^{2}-5x+4\leq 0. To do that, factorize, then we have that (x-4)(x-1)\leq 0. This implies that

x-1\leq 0\, \text{and}\, x-4\geq 0

or

x-1 \geq 0\, \text{and}\, x-4\leq 0

In the first case the solution is the empty set \emptyset. In the second case the solution is the interval 1\leq x \leq 4. Now we have that

A=[1,4]

B=(3,5)

C=(3,4].

To show that A\cap B\subseteq C consider x\in A\cap B. Then 1\leq x \leq 4\, \text{and}\, 1, this implies that 3, then x\in C. Now, to show that C\subseteq A\cap B consider x\in C, then 3, then 1\leq x \leq 4\, \text{and}\, 3, then x\in [1,4] \, \text{and}\, x\in (3,5), this implies that x\in A\cap B.

Observe the image below.

7 0
3 years ago
Help please my teacher isn't the greatest.
Schach [20]

Answer:

x = 9.5

Step-by-step explanation:

We see that the entire length of DF is equal to 34. That means segment DE and segment EF must combine to equal 34:

3x - 6 + x + 2 = 34

4x - 6 + 2 = 34

4x - 4 = 34

4x = 38

x = 9.5

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3 years ago
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