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Feliz [49]
1 year ago
6

MATH HELP!!! 100PTS!!!

Mathematics
1 answer:
Lostsunrise [7]1 year ago
6 0

Answer:

x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}

Step-by-step explanation:

<u>Given functions</u>:

  p(x)=2x-4

  r(x)=\dfrac{6x-1}{9x+1}

Solve for p(x) = r(x):

\begin{aligned}p(x) & = r(x)\\\implies 2x-4 & = \dfrac{6x-1}{9x+1}\\(2x-4)(9x+1)&=6x-1\\18x^2+2x-36x-4&=6x-1\\18x^2-40x-3&=0\end{aligned}

As the found quadratic equation cannot be factored, use the Quadratic Formula to solve for x:

<u>Quadratic Formula</u>

x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0

Therefore:

a=18, \quad b=-40, \quad c=-3

Substitute the values of a, b and c into the <u>quadratic formula</u> and solve for x:

\begin{aligned}\implies x & =\dfrac{-(-40) \pm \sqrt{(-40)^2-4(18)(-3)} }{2(18)}\\\\& =\dfrac{40 \pm \sqrt{1816}}{36}\\\\& =\dfrac{40 \pm \sqrt{4 \cdot 454}}{36}\\\\& =\dfrac{40 \pm \sqrt{4}\sqrt{454}}{36}\\\\& =\dfrac{40 \pm2\sqrt{454}}{36}\\\\& =\dfrac{20 \pm\sqrt{454}}{18}\end{aligned}

Therefore, the solutions are:

x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}

Learn more about quadratic equations here:

brainly.com/question/27750885

brainly.com/question/27739892

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kari74 [83]

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Step-by-step explanation:

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5 0
3 years ago
If p and q are both true, then which of the following statements has the same truth-value as ~p → q?
olganol [36]

If p and q are both true, then

\neg p \implies q

is an implication of the form

F \implies T

which is true, because every implication starting with false is true, i.e.

F \implies T = T,\quad F \implies F = T

So, we're looking for an expression evaluating to true. Let's see what we have:

A) is an AND proposition. Logical AND is true only if both parts are true. So, you have

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So it's not the right option.

B) is an OR proposition. Logical OR is true whenever one of the two parts is true. So, you have

\neg P \lor\neg Q = F \lor F = F

So it's not the right option.

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P \land \neg Q = T \land F = F

So this is not the right option.

D) Finally, the last one is again an implication, and again it starts with false:

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8 0
3 years ago
X^2-6=2-18x solve by completing the square
AnnyKZ [126]
X^1=-9[89],x^2=-9+[89]
6 0
3 years ago
Khan Acad
alexandr402 [8]

Answer:

7.222 (repeating)

Step-by-step explanation:

8 + 10 + 8 + 5 + 4 + 7 + 5 + 10 + 8 = 65

1      2    3    4    5    6    7    8     9

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6 0
2 years ago
Idk the answer can u help me
valentinak56 [21]

The answer is C) 67

Angle FGE is a right angle so it is 90 degrees and angle AGF is the same as CGD so it is 23 degrees.

Add angle FGE and angle AGF together (90 + 23 = 113) and subtract that by 180 (180 - 113 = 67)

3 0
3 years ago
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