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2 years ago

Determine the solution to the system of equations graphed below and explain

Mathematics

1 answer:

lawyer [7]2 years ago

7 0

If x - 4 ≥ 0, then |x - 4| = x - 4, so

G(x) = F(x) ⇒ 3x + 2 = (x - 4) + 2

⇒ 3x + 2 = x - 2

⇒ 2x = -4

⇒ x = -2

Otherwise, if x - 4 < 0, then |x - 4| = -(x - 4), so

G(x) = F(x) ⇒ 3x + 2 = -(x - 4) + 2

⇒ 3x + 2 = -x + 6

⇒ 4x = 4

⇒ x = 1

However,

• when x = -2, we have

G(-2) = 3(-2) + 2 = -4

F(-2) = |-2 - 4| + 2 = 8

• when x = 1, we have

G(1) = 3(1) + 2 = 5

F(1) = |1 - 4| + 2 = 5

so only x = 1 is a solution to G(x) = F(x).

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ziro4ka [17]

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3 years ago

Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1

Lera25 [3.4K]

Assuming the function is

$f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}$

For $f(x)$ to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)$
$\iff\displaystyle\lim_{x\to1}2x=\lim_{x\to1}(bx^2+cx)$
$\iff2=b+c$

For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

$f'(x)=\begin{cases}2&\text{for }x1\end{cases}$

$\displaystyle\lim_{x\to1^-}2=\lim_{x\to1^+}(2bx+c)$
$\iff2=2b+c$

Now we solve for $b$ and $c$ :

$\begin{cases}b+c=2\\2b+c=2\end{cases}\implies b=0,c=2$

5 0

3 years ago

Factorise the following 27 x minus 9 y

dangina [55]

Answer:

27x-9y

3(9x-3y)

Step-by-step explanation:

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2 years ago

Write a quadratic equation for a parabola with roots at (-2, 0) & (4,0) and a y-intercept at ( 0, -16) Write your answer in

meriva

9514 1404 393

Answer:

y = 2(x +2)(x -4)

Step-by-step explanation:

The y-intercept will be a constant times the product of the roots. Here, the product of the roots is (-2)(4) = -8, so the constant of interest is -16/-8 = 2. That constant is the coefficient of the leading term of the quadratic, so is a multiplier of the factored form.

y = 2(x +2)(x -4)

For root p, (x-p) is a factor in the factored form.

8 0

3 years ago

How do you determine if polygons are similar?

Vikentia [17]

Answer:

a) corresponding angles of similar polygons are congruent

b) corresponding sides of similar polygons are proportional

c) a triangle is a polygon

Step-by-step explanation:

By <em>definition</em>, similar polygons have congruent corresponding angles and proportional corresponding sides.

A triangle is a polygon, so two triangles will be similar if they have congruent corresponding angles and proportional corresponding sides.

___

For an n-sided polygon, one only needs to show the conditions are met for n-1 angles and sides. Those will determine the measures of the final angle/side.

8 0

3 years ago