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Natasha2012 [34]
2 years ago
13

What polynomial has a graph that passes through the given points?

Mathematics
1 answer:
Evgen [1.6K]2 years ago
3 0
The answer is <span>B. y = x^3 + 4x^2 + 2x - 2 

A line that passes through all given point is the correct choice. Now, substitute x and y in all of the choices:

</span>B. y = x³ + 4x²<span> + 2x - 2 
Point 1: </span><span>(-2, 2) 
x = -2
y = 2
____
2 = (-2)</span>³ + 4 *(-2)² + 2 * (-2) - 2
2 = -8 + 4 * 4 + (-4) - 2
2 = -8 + 16 - 4 - 2
2 = 2
_____

Point 2: (-1, -1) 
x = -1
y = -1
____
-1 = (-1)³ + 4 *(-1)² + 2 * (-1) - 2
-1 = -1 + 4 * 1 + (-2) - 2
-1 = -1 + 4 - 2 - 2 
-1 = -1
____

Point 3: (1, 5) 
x = 1
y = 5
____
5 = (1)³ + 4 *(1)² + 2 * 1 - 2
5 = 1 + 4 * 1 + 2 - 2
5 = 1 + 4 + 2 - 2
5 = 5
____

Point 4: (3, 67) 
x = 3
y = 67
____
67 = (3)³ + 4 *(3)² + 2 * (3) - 2
67 = 27 + 4 * 9 + 6 - 2
67 = 27 + 36 + 6 - 2
67 = 67

So, line B passes through all choices.
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Solve:<br> 3(x - 2) = 12
Alecsey [184]

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x=6

Step-by-step explanation:

3(x-2)=12

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How do i solve for x by using natural log (in)?
Helga [31]

Unfortunately you cannot use logs to solve this.

However, it shouldn't take too long to use guess-and-check to see that

2^x+3^x = 2^2+3^2 = 4+9 = 13

Showing that x = 2 is the solution to the equation.

You can use a graphing calculator to graph out y = 2^x+3^x  and  y = 13. The two curves cross at (2,13). The x coordinate of that intersection is what we're after. GeoGebra and Desmos are two free options you can pick from in terms of a graphing calculator.

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2 years ago
Circle J is inscribed in isosceles trapezoid ABCD, as shown. Points E, F, G, and H are points of tangency. The length of AB is 1
zhuklara [117]

Answer:

15cm

Step-by-step explanation:

Theorem: All tangents to a circle from the same point are equal.

Sine E, F, G and H are points of Tangency, by the theorem above:

  • EB=BF
  • FC=GC

The diameter line EC divides the Isosceles Trapezoid into two equal parts.

Therefore:

  • EB=10/2=5cm
  • GC=20/2=10cm

We then have by the equality above that:

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BC=BF+FC

=5+10

=15cm

8 0
3 years ago
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