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3 years ago

6. To check whether the rose bush lies on the circle, see if its coordinates make the

Mathematics

1 answer:

Alexxandr [17]3 years ago

3 0

Part of question :

(x-10)^2+(y-10)^2=100

(16-10)^2+(18-10)^2=100

Answer:

Yes, equation of circle is true

Step-by-step explanation:

(x-10)^2+(y-10)^2=100

(16-10)^2+(18-10)^2=100

100=100

plugging the coordinates into the equation of the circle, we observe that the equation is true since both sides of the equation are equal(value on both sides of the equal sign are same). This wouldn't be true if for instance the left side of the equation evaluated to ≠100. Therefore we can conclude that the rose bush lies on circle since the equation is true

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Translate each equation into slope-intercept form. Then, state the slope and y-intercept . 4y=2x+20

likoan [24]

Answer:

The slope-intercept form of the equation: y = 0.5x + 5

The slope: m = 0.5

The y-intercept: b = 5

Step-by-step explanation:

Slope-intercept form is y = mx + b, where m is the slope and b is y-intecept

4y = 2x + 20 {divide both sides by 4}

y = 0.5x + 5 ⇒ m = 0.5 and b = 5

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3 years ago

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Flauer [41]

Answer:

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Step-by-step explanation:

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3 years ago

PLEASE HELP!

3241004551 [841]

The question is incomplete. Here is the complete question.

The salary of members of two governing bodies in 2008 was $167.2 thousand, and has increased by approximately $2 thousand per year since then. Complete parts (a) and (b).

(a) Complete the following table to help find an expression that stands for the the salary (in thousands of dollars) of members of the two governing bodies t years since 2008.

Number of years and salaries of members of the two governing bodies

------------------------------------------------------------------------------------------------

Years since 2008 Salary (thousands of dollars)

------------------------------------------------------------------------------------------------

0 (2._) + ___

1 (2._) + ___

2 (2._) + ___

3 (2._) + ___

4 (2._) + ___

t ________

----------------------------------------------------------------------------------------------------

(b) Evaluate the expression that is found in part (a) for t = 5. What does the result means in this situation?

Answer: (a) The blank space inside the parenthesis is the number of years and the 2nd blank space is the salary: $167.2 thousand.

The last blank space is 2.t + 167.2.

(b) The value for t = 5 is 177.2 thousand.

Step-by-step explanation: The table in (a) is the description of the salaries per year. After 2008, there is an increase of 2000 per year.

Assuming t is in years, the expression for the salaries per year will be:

s = 2.t + 167.2

For part (b), t = 5. Substitute it into the equation, it is:

s = 2.t + 167.2

s = 2.5 + 167.2

s = 177.2

This means that in <u>year</u> <u>5</u>, the salary will be $ 177.2 thousand.

4 0

3 years ago

A triangle has side lengths of 7 in., 9 in., and 11 in. Determine whether this is a right triangle and why.

Harlamova29_29 [7]

Answer:

Not a right triangle. See below for my reasoning.

Step-by-step explanation:

If this is a right triangle, then the sum of the squares of the two shorter sides will equal the square of the longest side: 7^2 + 9^2 = 11^2 => 49 + 81 = 121 But this is false.

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3 years ago

Whats the radius for the circle? x^2+2x+y^2+4y-6=0

MAXImum [283]

Answer:

r = $\sqrt{11}$

Step-by-step explanation:

So we need to complete the square for both parts of the equation

First though we can add the 6 to the other side so we have x² + 2x + y² + 4y = 6

So first we can complete the square for x² + 2x

To do so we need to use $(\frac{b}{2} )^{2}$ to figure out the number we need to add to both sides

In this case our b is 2, so substituting this in we get $(\frac{2}{2} )^{2} =(1)^{2} =1$

Here we add 1 to both sides and now we have x² + 2x + 1 + y² + 4y = 6 + 1

Now we can follow the same steps to complete the square for y² + 4y

Here our b is 4, so substituting this in we get $(\frac{4}{2} )^{2}=(2)^{2} =4$

Now we add 4 to both sides and now we have x² + 2x + 1 + y² + 4y + 4 = 6 + 1 + 4

Now condensing everything we have (x + 1)² + (y + 2)² = 11

The formula for a circle is (x - h)² + (y - k)² = r²

In our equation we have r² = 11

To find the radius we need to take the square root of both sides $\sqrt{r^{2}} =\sqrt{11}$ to get r = $\sqrt{11}$

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3 years ago