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3 years ago

How can I do substitution method in Algebra 2? The equations are y= x^2-2x-3 and y=x^2+5x+11

1 answer:

7 0

$\bf \begin{cases} \boxed{y} = x^2-2x-3\\ y = x^2+5x+11 \end{cases}\qquad\qquad \stackrel{\textit{substituting on the 2nd equation}}{\boxed{x^2-2x-3} = x^2+5x+11} \\\\\\ ~~\begin{matrix} x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ -2x-3= ~~\begin{matrix} x^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ +5x+11\implies -2x-3=5x+11\implies -3=7x+11 \\\\\\ -14=7x\implies \cfrac{-14}{7}=x\implies \blacktriangleright -2=x \blacktriangleleft$

$\bf \stackrel{\textit{since we know that }y = x^2-2x-3}{y=(-2)^2-2(-2)-3} \implies y = 4+4-3\implies \blacktriangleright y = 5 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (-2,5)~\hfill$

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Find the values of x and y.

Nesterboy [21]

X=100°

y=180°-100°-50°
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4 years ago

Read 2 more answers

How do you factor 16-2m^2?

Free_Kalibri [48]

$-(2m^{2} - 16)$
$-2(m^{2} - 8)$
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Hope this helps!

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3 years ago

While traveling to and from a certain destination, you realized increasing your speed by 40 mph saved 4 hours on your return. If

Luden [163]

Answer:

The speed driven while returning is 88 mph.

Step-by-step explanation:

We are given that while traveling to and from a certain destination, you realized increasing your speed by 40 mph saved 4 hours on your return.

Also, the total distance of the roundtrip was 420 miles.

Let the speed driven while returning be 'x mph' which means that the speed driven while going was '(x - 40) mph' because it has been given that while returning we have increased the speed by 40 mph.

As we know that the Speed-Distance-Time formula is given by;

$\text {Speed} = \frac{\text{Distance}}{\text{Time}}$ or $\text {Time} = \frac{\text{Distance}}{\text{Speed}}$

So, according to the question;

$\frac{420}{x-40} -\frac{420}{x} = 4 \text{ hours}$ where Distance = 420 miles

$\frac{420x-420(x-40)}{x(x-40)} = 4$

$\frac{420x-420x+16800}{x^{2} -40x} = 4$

$\frac{16800}{x^{2} -40x} = 4$

$4x^{2} -160x= 16800$

$4x^{2} -160x- 16800=0$

$x^{2} -40x- 4200=0$

Now finding the roots of the above equation;

Here a = 1, b = -40 and c = -4200

$D = b^{2} -4ac$

= $(-40)^{2} -4(1)(-4200)$ = 18400

Now, the roots of a quadratic equation is given by;

$x = \frac{-b\pm \sqrt{D} }{2a}$

$x = \frac{-(-40)\pm \sqrt{18400} }{2\times 1}$

So, the two roots of x are : $x = \frac{40-\sqrt{18400} }{2}$ and $x = \frac{40+\sqrt{18400} }{2}$

Solving these two we get; $x = -47.8$ and $x = 87.8$

Here we ignore the negative value of x, so the speed driven while returning is 87.8 ≈ 88 mph.

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3 years ago

Katia has 7 chairs she wants to paint. If it takes 2/3 can of spray

zaharov [31]

Answer:

4 2/3

<h3>Step-by-step explanation: You would do 7 × 2/3, but you cannot do that so you have to make the 7, 7/1 and than it is 7/1 × 2/3</h3><h3 /><h3>7/1 × 2/3 =</h3><h3>First step: Multiply the top: 7 × 2 = 14</h3><h3>Second step: Multiply bottom: 1 × 3 = 3</h3><h3 /><h3>Answer: 14/3 and than you simplify to 4 2/3 </h3>

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3 years ago

Your teacher give you a True or false quiz with 10 questions if you randomly answer each question how many possible outcomes of

yulyashka [42]

Answer:

1024 outcomes

Step-by-step explanation:

Within a particular single question, we can select only 1 correct answer from 2 options. The number of ways of doing this is 2C1 and this is 2

This means for each question, there are only 2 possible outcomes. Now for 10 questions, the total number of possible outcomes would be the outcome of each of the questions multiplied by one another.

That would be (2)^10 which is 1024 outcomes

8 0

4 years ago