Draw to show regrouping. Write how many tens and ones in the sum. Write the sum. This has me so confused.

raph the equation with a diameter that has endpoints at (-3, 4) and (5, -2). Label the center and at least four points on the ci

andreyandreev [35.5K]

Answer:

Equation:

${x}^{2} + {y}^{2} + 2x - 2y - 35= 0$

The point (0,-5), (0,7), (5,0) and (-7,0)also lie on this circle.

Step-by-step explanation:

We want to find the equation of a circle with a diamterhat hs endpoints at (-3, 4) and (5, -2).

The center of this circle is the midpoint of (-3, 4) and (5, -2).

We use the midpoint formula:

$( \frac{x_1+x_2}{2}, \frac{y_1+y_2,}{2} )$

Plug in the points to get:

$( \frac{ - 3+5}{2}, \frac{ - 2+4}{2} )$

$( \frac{ -2}{2}, \frac{ 2}{2} )$

$( - 1, 1)$

We find the radius of the circle using the center (-1,1) and the point (5,-2) on the circle using the distance formula:

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

$r = \sqrt{ {(5 - - 1)}^{2} + {( - 2- - 1)}^{2} }$

$r = \sqrt{ {(6)}^{2} + {( - 1)}^{2} }$

$r = \sqrt{ 36+ 1 } = \sqrt{37}$

The equation of the circle is given by:

$(x-h)^2 + (y-k)^2 = {r}^{2}$

Where (h,k)=(-1,1) and r=√37 is the radius

We plug in the values to get:

$(x- - 1)^2 + (y-1)^2 = {( \sqrt{37}) }^{2}$

$(x + 1)^2 + (y - 1)^2 = 37$

We expand to get:

${x}^{2} + 2x + 1 + {y}^{2} - 2y + 1 = 37$

${x}^{2} + {y}^{2} + 2x - 2y +2 - 37= 0$

${x}^{2} + {y}^{2} + 2x - 2y - 35= 0$

We want to find at least four points on this circle.

We can choose any point for x and solve for y or vice-versa

When y=0,

${x}^{2} + {0}^{2} + 2x - 2(0) - 35= 0$

${x}^{2} +2x - 35= 0$

$(x - 5)(x + 7) = 0$

$x = 5 \: or \: x = - 7$

The point (5,0) and (-7,0) lies on the circle.

When x=0

${0}^{2} + {y}^{2} + 2(0) - 2y - 35= 0$

${y}^{2} - 2y - 35= 0$

$(y - 7)(y + 5) = 0$

$y = 7 \: or \: y = - 5$

The point (0,-5) and (0,7) lie on this circle.

3 0

2 years ago

Vugar has a maximum of 30 batteries for toys. Each toy helicopter uses the same number of batteries, and each toy car uses the s

Leno4ka [110]

Answer: 3H+4C<_ 30

The coefficients of the variables H and C represent the number of batteries each toy helicopter and each toy car uses.

Step-by-step explanation:

Each toy helicopter uses 3 batteries, and each toy car uses 4 batteries.

Now let's check whether Vugar has enough batteries for 5 toy helicopters and 4 toy cars. To do this, we substitute H=5 and C= 4 in the given inequality:

Does Vugar have enough batteries to play with 5 toy helicopters and 4 toy cars?

No, because if you plug in the value for H and C:

3H + 4C<_ 30

3(5) + 4(4) <_30

15 + 16 <_ 30

31 <_ 30; false

Since the inequality is false, Vugar does not have enough batteries to play with 555 toy helicopters and 444 toy cars.

Each toy helicopter uses 333 batteries, and each toy car uses 444 batteries.

No, Vugar does not have enough batteries to play with 555 toy helicopters and 444 toy cars.

6 0

3 years ago

Read 2 more answers

Are these 2 triangles congruent? 0 If no, type "not congruent" If yes, state what postulate or theorem proves it.

Novosadov [1.4K]

Answer:

the triangles are congruent

6 0

1 year ago

What is the answer to (8+5) to the 2nd power +(15 Divided by 5) =

gavmur [86]

(8+5)^2 + (15/5)

8 + 5 = 13

13 * 13 = 169

169 + (15/5)

15/5 = 3

169 + 3

172

4 0

3 years ago

Read 2 more answers

Vocabulary Choose the example of an inverse relationship.

natulia [17]

Answer:

which statement is equivalent to the inequality 14x-14>-7x+7

x>21

x>1

x<