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3 years ago

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I want to take a trip to California. I need to choose if I want to fly, drive, or take a train. Once I am there, I can stay at a

hotel or rent a house. I need to choose if I want to go to DisneyLand, the Zoo,
SeaWorld, or the beach.
How many different ways can I plan my vacation?

1 answer:

vfiekz [6]3 years ago

5 0

20 is the answered this

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A computer repairman makes $25 per hour. Which equation models the situation?

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3 years ago

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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.

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3 years ago

Solve, be sure to show each step under the original problem for any credit.<br> 1 =k/12 +5

Naya [18.7K]

K = -48

1. subtract 5 from both sides
-4 = k/12

2. multiply 12 from both sides to get k alone
-48 = k

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3 years ago

Hi could someone just help me with this I'm not sure if i'm doing it correctly.

salantis [7]

Two angles are supplementary when they <span>add up to 180 degrees </span>⇒
m∠1 + m∠2 = 180°
4y + 7 + 9y + 4 = 180
13y + 11 = 180
13y = 180 - 11
13y = 169
y = 169/13
y = 13

m∠2 = 9y + 4 = 9 * 13 + 4 = 121°

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3 years ago

En mi clase hay 30 alumnos. Hoy es el cumpleaños de Marta y regala 2 piruletas de fresa a cada chica y 1 de limón a cada chico.

Alenkasestr [34]

Answer:

La respuesta es solo dividir

Step-by-step explanation:

ara que sepas que hay 30 estudiantes y que se les dieron 49 lolipops a los estudiantes y 2 se los dieron a las niñas y 1 a los niños, todo lo que tienes que hacer es dividir

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