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dsp73
2 years ago
5

Use substitution to write an equivalent quadratic equation. (3x + 2)2 + 7(3x + 2) – 8 = 0

Mathematics
2 answers:
ANEK [815]2 years ago
6 0
Let z = 3x+2. Then, by substitution, your equation is
.. z^2 +7z -8 = 0

_____
This equation can be factored as
.. (z +8)(z -1) = 0
.. x = -8 or +1
Then
.. 3x +2 = -8 or +1
.. 3x = -10 or -1
.. x = -10/3 or -1/3

nirvana33 [79]2 years ago
3 0
CORRECT ANSWER : u^2+7u-8=0, where u=3x+2
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faltersainse [42]

Answer:

The angle that the ramp makes with the ground is 11.54°

Step-by-step explanation:

From the image attached, we can see that the length of 17 1/2 ft corresponds to the hypotenuse in a right triangle, the length of 3 1/2 ft corresponds to the opposite side.

We can use the fact that the sin(θ) = \frac{Opposite}{Hypotenuse} to find the angle that the ramp makes with the ground.

sin(\theta)=\frac{3.5}{17.5}

The angle is equal to

\theta = sin^{-1}(\frac{3.5}{17.5} )\\\theta = 11.54\°

3 0
3 years ago
determine whether the lines intersect and if so find the point of intersection and the cosine of the angle of intersection x=4t+
Fittoniya [83]

Answer:

As the lines are not intersecting nor parallel, they must be skew.

Step-by-step explanation:

Question is incomplete, we consider the nearest match available online.

Parametric equations of two lines are:

L₁ : x=4t+2 , y = 3 , z =-t+1

L₂: x=2s+2 , y= 2s+5 , z = s+1

If lines are parallel then parametric coordinates must be equal scalar multiple of each other which s not true here.

4t+2=2s+2 ---(1)\\ \\3=2s+5---(2) \\\\-t+1=s+1---(3)

If lines are intersecting then parametric coordinates must be equal for some value of t and s.

From (3)\\-t=s\\From (2)\\\\s=\frac{3-5}{2}\\\\s=-1\\\implies t=1\\\\To\,\,check\,\, the \,\,values \,\,of \,\,s\,\, and \,\,t \,\,for\,\,intersection\,\,put \,\,them\,\, in\,\, (1)\\\\4(1)+2= 2(-1)+2\\ 6\ne0

Hence the lines are not intersecting nor parallel, they must be skew.

6 0
3 years ago
How can you restrict the domain of the function f(x)=|x+4|-2 so the range of the inverse function f^-1(x),is [-4, )
wariber [46]

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5 0
2 years ago
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antoniya [11.8K]
I'm pretty sure its B. (9x2+2x-7)(x)+(9x2+2x-7)(-4)
Because its just splitting up the (x-4) and if you add the answers together then you get the same answer as the original<span />
3 0
3 years ago
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Which concept is used to prove that the opposite sides of a parallelogram are congruent?
Neko [114]

Answer:

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Step-by-step explanation:

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Typically, a diagonal is drawn through the figure, and the two triangles created are shown to be congruent, often by ASA. Then, by CPCTC, sides of the parallelogram are shown to be congruent.

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3 years ago
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