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Sidana [21]
3 years ago
8

Graph the line and the parabola and find the points of intersection: y= 3-x ; y=x(squared)+x-12

Mathematics
1 answer:
melomori [17]3 years ago
4 0

Answer:

Step-by-step explanation:

We have to graph a line y = 3 - x which has the slope = -1 and y intercept 3.

We will select two points where line intersects at x = 0 and y = 0

The given line will intersect x-axis at (3, 0) and at y- axis (0, 3).

Joining these two points we can draw a straight line showing y = -x + 3

Now we will draw the parabola given by equation y = x² + x - 12

We will convert this equation in vertex form first to get the vertex and line of symmetry.

Standard equation of a parabola in vertex form is

y = (x - h)² + k

Where (h, k) is the vertex and x = h is the line of symmetry.

y = x² + x - 12

y = x² + 2(0.5)x + (0.5)²- (0.5)²-12

y = (x + 0.5)² - 12.25

Therefore, vertex will be (-0.5, -12.25) and line of symmetry will be x = 0.5

For x intercept,

0 = (x + 0.5)² - 12.25

x + 0.5 = ±√12.25

x = -0.5 ± 3.5

x = -4, 3

For y- intercept,

y = (0+0.5)² - 12.25

 = 0.25 - 12.25

y = -12

So the parabola has vertex (-0.5, - 12.25), line of symmetry x = 0.5, x intercept (4, 0), (and y-intercept (0, -12).

Now we have to find the points of intersection of the given line and parabola.

For this we will replace the values of y

3 - x = x² + x - 12

x² + 2x - 15 = 0

x² + 5x - 3x - 15 = 0

x(x + 5) - 3(x + 5) = 0

(x - 3)(x + 5) = 0

x = 3, -5

For x = 3

y = 3- 3 = 0

For x = -5

y = 3 + 5 = 8

Therefore, points of intersection will be (3, 0) and (-5, 8)

 

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Find the limit if it exists lim x→0 sqrtx+7-sqrt7 over x
Triss [41]

Answer:

\frac{1}{ 2\sqrt{7} }

Step-by-step explanation:

\lim_{x\to 0}  \frac{ \sqrt{x + 7}  -  \sqrt{7} }{x}  \\  \\  = \lim_{x\to 0}  \frac{( \sqrt{x + 7}  -  \sqrt{7}) }{x}  \times  \frac{( \sqrt{x + 7}   +   \sqrt{7}) }{( \sqrt{x + 7}   +  \sqrt{7}) }  \\  \\   = \lim_{x\to 0}  \frac{( \sqrt{x + 7} )^{2}  -  (\sqrt{7})^{2}  }{x( \sqrt{x + 7}   +  \sqrt{7})}  \\  \\   = \lim_{x\to 0}  \frac{( {x + 7}  -  {7}) }{x( \sqrt{x + 7}   +  \sqrt{7})}   \\  \\ = \lim_{x\to 0}  \frac{ {\cancel x}}{\cancel x( \sqrt{x + 7}   +  \sqrt{7})} \\  \\ = \lim_{x\to 0}  \frac{ {1}}{\sqrt{x + 7}   +  \sqrt{7}}  \\  \\  =  \frac{1}{ \sqrt{0 + 7} +  \sqrt{7}  } \\  \\  =  \frac{1}{ \sqrt{7} +  \sqrt{7}  }  \\  \\  =  \frac{1}{ 2\sqrt{7} }

6 0
3 years ago
In 195019501950, the per capita gross domestic product (GDP) of Australia was approximately \$1800$1800dollar sign, 1800. Each y
mezya [45]

Answer:

The function of capita GDP is given by

G(t)= 1800(1+0.067)^t

where G(t) is in dollar and t is years after 1950.

Step-by-step explanation:

Given that,

in 1950, the per capita GDP of Australia was $1800.

The capita GDP is increased by 6.7 % per year.

In 1951, the capita GDP was increased =6.7% of $1800

The capita GDP was= $1800+ 6.7% of $1800

                                 =$1800(1+6.7%)

In 1952, the capita GDP was increased =$1800(1+6.7%)

The capita GDP was=$1800(1+6.7%)+ 6.7% of$1800(1+6.7%)

                                 =$1800(1+6.7%)(1+6.7)

                                 = $1800(1+6.7%)²

                                 =$1800(1+0.067)²

In 1952, the capita GDP was increased =$1800(1+6.7%)²

The capita GDP was=$1800(1+6.7%)²+ 6.7% of$1800(1+6.7%)²

                                 =$1800(1+6.7%)²(1+6.7)

                                 = $1800(1+6.7%)³

                                  =$1800(1+0.067)³

and so on.

The function of capita GDP is given by

G(t)= 1800(1+0.067)^t

where G(t) is in dollar and t is years after 1950.

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Fill in the blank. ___ x 9 = 45? Please
tia_tia [17]

Answer:

The correct answer is "5"

5 times 9 equals 45.

5 x 9 = 45

6 0
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