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4 years ago

99 POINTS AND IF CORRECT, WILL GIVE BRAINLYIST

Mathematics

2 answers:

Arisa [49]4 years ago

8 0

The functions are both increasing

the function for plan II has a greater unit rate

The function for plan I has a greater y intercept

Vlada [557]4 years ago

8 0

Answer: The functions are both increasing.

The function for plan II has a greater unit rate.

The function for plan I has a greater y-intercept.

Step-by-step explanation:

According to the given question we have two functions.

Function 1. $y=12,000+400x$

Function 2. $y=11,000+420x$

Both are written in intercept form of linear equation $y=mx+c$ , where m is the slope of line or rate of change of y w.r.t. x.

Slope of function 1. = 400

i.e. Unit rate = $400 per month

Slope of function 2. = 420

i.e. Unit rate = $420 per month

⇒The function for plan II has a greater unit rate.

As both has positive slopes.

∴ Both functions are increasing functions.

For y intercept , put x=0 in the functions.

The y-intercept of function 1 = $12000

The y-intercept of function 2= $11000

⇒The function for plan I has a greater y-intercept.

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RideAnS [48]

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Step-by-step explanation:

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3 years ago

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Ira Lisetskai [31]

Answer:

5 2/3

Step-by-step explanation:

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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)

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3 years ago

What is x in rx+h=sx-k

julia-pushkina [17]

Answer:

-k-h/r-s

When solving the goal is to get x on one side and not x on the other.

rx + h = sx - k

rx - sx + h = -k <------- subtract sx from both sides

rx - sx = -k - h <-------subtract h from both sides

x (r - s) = -k -h <------factor out x which is in both rx and sx

x = - k - h / r - s <-------divide by r-s on both sides

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3 years ago

There are 8 students in a group. There is 3/4 of a cake. How much of the cake will each student get if it is split evenly betwee

andre [41]

You need to split something 8 ways, you need to divide it by 8, or multiply it by 1/8.

If you need to split 3/4 of a cake 8 ways, you can multiply it by 1/8

(3/4)(1/8)
=(3x1)/(4x8)
=3/32

Therefore, every one will get 3/32 of the cake

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4 years ago