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3 years ago

Select two ratios that are equivalent to 27:927:927, colon, 9.

Mathematics

2 answers:

kherson [118]3 years ago

8 0

Answer:

9:3 and 3:1

Step-by-step explanation:

Marysya12 [62]3 years ago

7 0

Answer:

9 : 3, 12 : 4, 54 : 18, 18 : 6 and so on

Step-by-step explanation:

Ratios equivalent to 27 : 9

Although, choices are not available to pick from, however, we can still find equivalent ratio to 27 : 9

27 : 9

= 27 / 9

= 3 / 1

= 3 : 1

Equivalent ratio

9 : 3

= 9 / 3

= 3 / 1

= 3 : 1

Another equivalent ratio is

12 : 4

= 12 / 4

= 3 / 1

= 3 : 1

Another equivalent ratio

54 : 18

= 54 / 18

= 3 / 1

= 3 : 1

Another equivalent ratio is

18 : 6

= 18 / 6

= 3 / 1

= 3 : 1

Therefore, equivalent ratio to 27 : 9 includes 9 : 3, 12 : 4, 54 : 18, 18 : 6 and so on

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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

Which is the equation of the given line in slope-intercept form? (-1, 2) and (1, -4)

Natalka [10]

1. Find the slope using the slope formula.
$\frac{2 - ( - 4)}{ - 1 - 1} = \frac{2 + 4}{ - 2} = - \frac{6}{2} = - \frac{3}{1} = - 3$
2. Plug that slope and either point into an equation in slope-intercept form and solve for b.
$2 = - 3( - 1) + b \\ 2 = 3 + b \\ - 1 = b$
3. Now write your answer as a slope-intercept form equation
$y = - 3x - 1$

6 0

4 years ago

Read 2 more answers

What is the factored form of 4(3x + 12) + 4?

Elanso [62]

Answer:

12x + 52

Step-by-step explanation:

Distribute.

(4 • 3x + 4 • 12) + 4

12x + 48 + 4

12x + 52

8 0

3 years ago

Factor the linear expression 24y - 40 using the greatest common factor of the terms

ANEK [815]

Factor: 24y-40
Answer: 8(3y-5)

Simplifying: 24y-40
Answer: There are no like terms.

7 0

3 years ago

In 2015 Organization raised $543. The following year they raised $89. How many money did they raised over the two period? Show h

galina1969 [7]

Answer:

632

Step-by-step explanation:

So you take one from the 3 to make it 2 and add it on to 89 to make 90. next take 10 from 542 and add it to the 90, you get 100. Then 532 + 100 = 632

Hope this helps

8 0

3 years ago

Read 2 more answers