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3 years ago

This table represents a function plot the points to represent the function as a graph

Mathematics

1 answer:

yKpoI14uk [10]3 years ago

6 0

Answer:

The graph in the attached figure N 2

Step-by-step explanation:

The complete question in the attached figure N 1

we have the ordered pairs

(-4,9),(-1,3),(0,1),(2,-3)

Using a graphing tool

Plot the given ordered pairs in the coordinate plane

Remember that

In a ordered pair (x,y), the first coordinate is the location of the point in the x-axis and the second coordinate is the location of the point in the y-axis

see the attached figure

The graph represent a line

Find the equation of the line

Find the slope

take two points

$(0,1),(2,-3)\\m=(-3-1)/(2-0)=-2$

The equation of the line in slope intercept form is equal to

$y=mx+b$

we have

$m=-2\\b=1$

substitute

$y=-2x+1$

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Is this equation an identity? (2x+1)^2-(x+1)^2=3(x+1)^2-1

sergey [27]

Answer:

See below, please

Step-by-step explanation:

Left side

${(2x + 1)}^{2} - {(x + 1)}^{2}$

$= (4 {x}^{2} + 4x + 1) - ( {x}^{2} + 2x + 1)$

$= (4 {x}^{2} - {x}^{2} ) + (4x - 2x) + (1 -1 )$

$= 3 {x}^{2} + 2x$

Right side

$3 \times {(x + 1)}^{2} - 1$

$= 3 \times ( {x}^{2} + 2x + 1) - 1$

$= 3 {x}^{2} + 6x + 3 - 1$

$= 3 {x}^{2} + 6x + 2$

After compared with both sides, we can make a conclusion that

This equation isn't an identity.

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2 years ago

You and three friends are making a gift basket. You want to keep the cost below $12 per person. Write and solve an inequality th

riadik2000 [5.3K]

Someone would end up having to pay more.

5 0

3 years ago

Match the parabolas represented by the equations with their foci.

Elenna [48]

Function 1 $f(x)=- x^{2} +4x+8$

First step: Finding when $f(x)$ is minimum/maximum
The function has a negative value $x^{2}$ hence the $f(x)$ has a maximum value which happens when $x=- \frac{b}{2a}=- \frac{4}{(2)(1)}=2$ . The foci of this parabola lies on $x=2$ .

Second step: Find the value of y-coordinate by substituting $x=2$ into $f(x)$ which give $y=- (2)^{2} +4(2)+8=12$

Third step: Find the distance of the foci from the y-coordinate
$y=- x^{2} +4x+8$ - Multiply all term by -1 to get a positive $x^{2}$
$-y= x^{2} -4x-8$ - then manipulate the constant of y to get a multiply of 4
$4(- \frac{1}{4})y= x^{2} -4x-8$
So the distance of focus is 0.25 to the south of y-coordinates of the maximum, which is $12- \frac{1}{4}=11.75$

Hence the coordinate of the foci is (2, 11.75)

Function 2: $f(x)= 2x^{2}+16x+18$

The function has a positive $x^{2}$ so it has a minimum

First step - $x=- \frac{b}{2a}=- \frac{16}{(2)(2)}=-4$
Second step - $y=2(-4)^{2}+16(-4)+18=-14$
Third step - Manipulating $f(x)$ to leave $x^{2}$ with constant of 1
$y=2 x^{2} +16x+18$ - Divide all terms by 2
$\frac{1}{2}y= x^{2} +8x+9$ - Manipulate the constant of y to get a multiply of 4
$4( \frac{1}{8}y= x^{2} +8x+9$

So the distance of focus from y-coordinate is $\frac{1}{8}$ to the north of $y=-14$
Hence the coordinate of foci is (-4, -14+0.125) = (-4, -13.875)

Function 3: $f(x)=-2 x^{2} +5x+14$

First step: the function's maximum value happens when $x=- \frac{b}{2a}=- \frac{5}{(-2)(2)}= \frac{5}{4}=1.25$
Second step: $y=-2(1.25)^{2}+5(1.25)+14=17.125$
Third step: Manipulating $f(x)$
$y=-2 x^{2} +5x+14$ - Divide all terms by -2
$-2y= x^{2} -2.5x-7$ - Manipulate coefficient of y to get a multiply of 4
$4(- \frac{1}{8})y= x^{2} -2.5x-7$
So the distance of the foci from the y-coordinate is - $\frac{1}{8}$ south to y-coordinate

Hence the coordinate of foci is (1.25, 17)

Function 4: following the steps above, the maximum value is when $x=8.5$ and $y=79.25$ . The distance from y-coordinate is 0.25 to the south of y-coordinate, hence the coordinate of foci is (8.5, 79.25-0.25)=(8.5,79)

Function 5: the minimum value of the function is when $x=-2.75$ and $y=-10.125$ . Manipulating coefficient of y, the distance of foci from y-coordinate is $\frac{1}{8}$ to the north. Hence the coordinate of the foci is (-2.75, -10.125+0.125)=(-2.75, -10)

Function 6: The maximum value happens when $x=1.5$ and $y=9.5$ . The distance of the foci from the y-coordinate is $\frac{1}{8}$ to the south. Hence the coordinate of foci is (1.5, 9.5-0.125)=(1.5, 9.375)

8 0

3 years ago

Find f(-3). f(x) = 4(2)^x

Ray Of Light [21]

Answer:

D - 1/2

Explanation:

f(-3) = 4(2)^-3

f(-3) = 4 • 1/8

f(-3) = 1/2

4 0

3 years ago

12 divided by x = 50

olga2289 [7]

the answer to 12 divided by 50 calculated using Long Division is:

12 Remainder

7 0

3 years ago

Read 2 more answers