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3 years ago

The number 2838 is divisible by which two numbers

Mathematics

1 answer:

nadya68 [22]3 years ago

4 0

Answer:

1419 and 2

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

3 years ago

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Given f(x) = 5x + 2 and g(x) = 5x - x5x. What is the value of (f g)(1)?

AlladinOne [14]

Answer:A

Step-by-step explanation:

8 0

2 years ago

Determine the slope and point on the line for each equation<br> C. y+ 4 = %(% - 3)

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3 years ago

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In this question it is given that

Carla earns $8.43 per hour. It means that her hourly rate is $8.43 .

And we have to find her overtime pay at time-and-a-half.

First we have to understand what time and a half means .

Time and a half means 1.5 times of the normal rate. And to find the overtime pay, we have to multiply 1.5 and normal hourly rate. That is

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Step-by-step explanation:

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3 years ago

The number 2838 is divisible by which two numbers ​

The number 2838 is divisible by which two numbers