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3 years ago

5

Based on the residuals, which data set is best fit by the regression line?

1 answer:

Levart [38]3 years ago

7 0

What are the options?

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A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

sdas [7]

Answer:

$y=-\dfrac{13}{49}x^2$

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

$y=ax^2+bx+c$

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

$-13=a(-7)^2+b(-7)+c$

$49a-7b+c=-13$

(x,y) = (7,-13)

$-13=a(7)^2+b(7)+c$

$49a+7b+c=-13$

(x,y) = (0,0)

$0=a(0)^2+b(7)+c$

$c=0$

so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

$49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13$

$49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13$

we can solve these two equation using the elimination method, by simply adding the two equations

$\quad\quad49a-7b=-13\\+\quad49a+7b=-13$

------------------------------

$\quad\quad 98a=-26$

$\quad\quad a=-\dfrac{13}{49}$

Now we can plug this value of a in any of the two equations.

$49a-7b=-13$

$49\left(-\dfrac{13}{49}\right)-7b=-13$

$-13-7b=-13$

$-7b=0$

$b=0$

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

$y=\left(-\dfrac{13}{49}\right)x^2+0x+0$

$y=-\dfrac{13}{49}x^2$

$49y=-13x^2$

This our equation of the arch!

5 0

3 years ago

In 1990, a glacier was 400 meters away from a road. Every year since then, it has moved 7 meters closer to the road. At this rat

kupik [55]

Answer:

57 years

Step-by-step explanation:

Divide 400 by 7.

3 0

3 years ago

the volume of hemisphere is 1527.4cm^3.find the radius of the hemisphere to the nearest whole whole number.(take π to be 22/7)

skelet666 [1.2K]

Answer:

radius of the hemisphere = 9 cm approx

Step-by-step explanation:

Volume of hemisphere = $\frac{2}{3} \pi r^{3}$

1527.4 = $\frac{2}{3} * \frac{22}{7} * r^{3}$

$\frac{7*15274*3}{2*22*10}$ = $r^{3}$

$\frac{320754}{440}$ = $r^{3}$

$r^{3}$ = 729

r = $\sqrt[3]{729}$

r = 9 cm approx.

6 0

3 years ago

OMG HELP ME PLSSSSSS!!!

miv72 [106K]

8*2*5= 80 because volume= length*width*height

8 0

3 years ago

What can be concluded about the sphere? Check all that apply. The sphere has a radius of 10 cm. The diameter measure is substitu

MA_775_DIABLO [31]

Answer: Its C and E on engenuity

Step-by-step explanation:

The radius is half the diameter.

The volume of the sphere is two-thirds the volume of a cylinder with the same radius and height.

4 0

3 years ago

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