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scoray [572]
3 years ago
10

Use the Distributive Property to write an equivalent 2(9 + 5k)

Mathematics
1 answer:
Svet_ta [14]3 years ago
6 0

Answer:

18+10k

Step-by-step explanation:

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Could someone help me rnnn?
GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola:  y=3x^2-4

Step-by-step explanation:

Given:

  • y-intercept of parabola: -4
  • parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola:  y=a(x-h)^2+k

(where (h, k) is the vertex and a is some constant)

Substitute point (0, -4) into the equation:

\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}

Substitute point (-2, 8) and ah^2+k=-4 into the equation:

\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}

Substitute point (1, -1) and ah^2+k=-4 into the equation:

\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}

Equate to find h:

\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}

Substitute found value of h into one of the equations to find a:

\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}

Substitute found values of h and a to find k:

\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}

Therefore, the equation of the parabola in vertex form is:

\implies y=3(x-0)^2-4=3x^2-4

So the vertex of the parabola is (0, -4)

5 0
2 years ago
Read 2 more answers
The length of a triangel is three times its with.if the perimiter is at its most 112 centemeters,witch is the greates possible v
iris [78.8K]
I am assuming you do not mean The length of a triangle and you mean The length of a rectangle because the answer you given are the formula for the perimeter of a rectangle. With that said, the answer is D<span>.2w+2*(3w)112

The perimeter of a rectangle can be found by the following equation:

2L + 2W = P
OR 
P = 2L + 2W
The equation </span>P = 2L + 2W is read perimeter = 2 times Length + 2 times width

The Question:
<span>The length of a rectangle is three times its width.if the perimeter is at its most 112 centimeters ,which is the greatest possible value of the the width.
</span>
The length of a rectangle
This means the perimeter 

is
The word is means to use an equal sign

three times its width
This means 3 times w or 3w 
The w = width

perimeter is at its most 112
This means <=
<= means less than or equal to

Ok so lets look at our equation 

2L + 2W = P
2w + 2(3w) <= 112

5 0
3 years ago
Which equation has a solution of x = -5?
lyudmila [28]
The first equation has a solution of X=-5
3 0
3 years ago
Read 2 more answers
(1,3),(2,6),(3,9),(4,12)
IgorC [24]

Answer:

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
A triangle has height 15in. and area 120in squared. what is the length of its base?
Brums [2.3K]
The formula for the area of a triangle is Area=.5(b)(h)

So fill in what you know:

120=.5b*15

Then solve for b.

120=7.5b
b=16
3 0
3 years ago
Read 2 more answers
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