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2 years ago

By which rule are these triangles congruent?

Mathematics

1 answer:

GrogVix [38]2 years ago

3 0

Answer:

sss

Step-by-step explanation:

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A circle has a diameter with endpoints at (6, 5) and (8, 5). Write the equation for the circle.

mario62 [17]

Answer:

$(x-7)^2+(y-5)^2=1$

Step-by-step explanation:

The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!

Center of the circle:

The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).

Using the midpoint formula we'll get:

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)$

$(x_m, y_m) = (7,5)$

This is the center coordinate of our circle.

Radius:

The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)

We can use the distance formula:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}$

$r = \sqrt{(6-7)^2+(5-5)^2}$

$r = \sqrt{1^2}$

$r = 1$

Equation of the circle:

The equation is written as:

$(x-a)^2+(y-b)^2=r^2$

here, (a,b) are the center points of the circle

in our case this is $(a,b)=(x_m,y_m)=(7,5)$

and r = 1

$(x-7)^2+(y-5)^2=1^2$

$(x-7)^2+(y-5)^2=1$

This is the equation of the circle!

3 0

2 years ago

A family has two cars. the first car has a fuel efficiency of 30 miles per gallon of gas and the second has a fuel efficiency of

jeka57 [31]

X : the gas used by first car in 1 particular week
y : the gas used by second car in 1 particular week
$x + y = 60 \\ x = 60 - y$
$30x + 35y = 1975 \\ 30 \times (60 - y) + 35y = 1975 \\ ... \\ y = 35 \\ x = 60 - y = 60 - 35 = 25$

5 0

2 years ago

Why does it work to break apart a number by place values to multiply

densk [106]

Because you are still multiplying the same values of the number you are multiplying and it's standard form

5 0

2 years ago

In 3-4 sentences, describe how you would find a line parallel to the line 2x + 5y = 15 that goes through the point (-10, 1). Be

larisa86 [58]

the parallel line is 2x+5y+15=0.

Step-by-step explanation:

ok I hope it will work

soo,

Solution

given,

given parallel line 2x+5y=15

which goes through the point (-10,1)

now,

let 2x+5y=15 be equation no.1

then the line which is parallel to the equation 1st

2 x+5y+k = 0 let it be equation no.2

now the equation no.2 passes through the point (-10,1)

or, 2x+5y+k =0

or, 2*-10+5*1+k= 0

or, -20+5+k= 0

or, -15+k= 0

or, k= 15

putting the value of k in equation no.2 we get,

or, 2x+5y+k=0

or, 2x+5y+15=0

which is a required line.

6 0

5 months ago

Find the volume of a right circular cone that has a height of 17.6 cm and a base with a

Morgarella [4.7K]

Answer:

1239.3 cm^3

Step-by-step explanation:

8 0

2 years ago