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3 years ago

15

Two angles are supplementary. One angle has a measure that is five less than four times the other. What is the measure of the la

rger angle?

1 answer:

sattari [20]3 years ago

4 0

Answer:

C

Step-by-step explanation:

4x-5+x=180. Add 5 to both sides

5x=185. Divide by 6

X=37

180-37=143

143

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Solve the system of equations. 2 x − 6 y = 5 x + y = 2 no solution ( 17 8 , − 1 8 )

s2008m [1.1K]

Answer:

it seems you have made a typo

Step-by-step explanation:

5 0

3 years ago

Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

DiKsa [7]

Answer:

The standard equation of the sphere is $(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Let the first endpoint be represented as $(x_{1}, y_{1}, z_{1})$ and the second endpoint be $(x_{2}, y_{2}, z_{2})$ .

Hence,

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Midpoint = $(\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})$

Midpoint = $(\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\$

Midpoint = $(5, 5, 4)$

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

$d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }$

$d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}$

$d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}$

$d = \sqrt{16 +196 + 0$

$d =\sqrt{212}$

$d = 2\sqrt{53}$

This is the diameter

To find the radius, r

From $Radius = \frac{Diameter}{2}$

$Radius = \frac{2\sqrt{53} }{2}$

∴ $Radius = \sqrt{53}$

r = $\sqrt{53}$

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is $(5, 5, 4)$

Radius of the sphere is $\sqrt{53}$

The equation of a sphere of radius r and center $(h,k,l)$ is given by

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

Hence, the equation of the sphere of radius $\sqrt{53}$ and center $(5, 5, 4)$ is

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}$

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

This is the standard equation of the sphere

6 0

3 years ago

Please answer I really need help with these just answer at least one.

aleksandrvk [35]

.50(150)+30=$105
8(32)+12 = $268

7 0

3 years ago

Please Help!!! NOW!!! Need answer, and quick.

cluponka [151]

40 or 45 degrees I say dis cuz if u find da overall area then u can find the degrees

5 0

3 years ago

Read 2 more answers

Solve the system of equations using the substitution method. y=2+1/4x,

skelet666 [1.2K]

Answer: (4,3)

Step-by-step explanation:

1. In this method you must solve one of the equation for one of the variables and substitute it into the other equation to find the other variable. Then, substitute the value of that variable into one of the original equation to obtain the value of the other one.

2 You have that:

$y=2+1/4x$

3. Then, you can substitute it into the other equation and solve for x:

$3x-5(2+1/4x)=-3\\3x-10-5/4x=-3\\7/4x=7\\x=4$

4. Now you can obtain y:

$y=2+1/4x$

$y=2+1/4(4)\\y=3$

5. The answer is:

(4,3)

6 0

3 years ago