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3 years ago

Hey I really need help on this question please

Mathematics

1 answer:

Dmitry_Shevchenko [17]3 years ago

5 0

A circle’s standard form of an equation is:
(x-h)^2 + (y-k)^2 = radius^2

Plug in h and k immediately because that is something you automatically know. H and k are derived from the center of the circle. The center of the circle is (h,k). Don’t get tripped up though, your center of a circle has negative coordinates. When you have two negatives, they become positive.

So now you have:
(x+4)^2 + (y-2)^2 = radius^2

So figure out what the radius is. Use the distance formula to find out. You have a change of 5 from -4 to 1 in x. You have a change of 2 from 2 to 4 in y. Distance formula has the distance as the square root of x distance squared and y distance squared. That would mean that the distance/radius is equal to the square root of (25 + 4). 5 squared is 25 while 2 squared is 4.

The radius of the circle is equal to the square root of (29). However, looking back at the circle equation the radius should be squared for the equation. Square root of 29 squared gets you 29.

Plug that in and you get:
(x+4)^2 + (y-2)^2 = 29

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2 years ago

Case exploration method and ex.

Kay [80]

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4 years ago

Cell phone plan A costs 79 per month and comes with a free 500 phone. Cell phone plan B costs 50 per month but does not come wit

meriva

Answer: it will take 25 months

Step-by-step explanation:

Let x represent the number of months that it will take for the cost of both plans to be the same.

Cell phone Plan A costs $70 per month and comes with a free $500 phone. This means that the total cost of x months with plan A would be

70 × x = $70x

Cell phone plan B costs 50 per month but does not come with a phone. If you buy the 500 phone and choose plan B, then the total cost of x months with plan B would be

500 + 50 × x = 500 + 50x

To determine the number of months until your cost is the same as Plan A's, we would equate both costs. It becomes

70x = 500 + 50x

70x - 50x = 500

20x = 500

x = 500/20 =25

8 0

3 years ago

05.06A)The figure below shows triangle XYZ and some of its transformed images on a coordinate grid: A coordinate plane is shown

Luba_88 [7]

A translation of triangle XYZ is triangle B shifted by 7 units to left.

Given that, triangle XYZ (2, 4), (5, 5) and (3, 0).

<h3>What is translation?</h3>

A translation moves a shape up, down or from side to side but it does not change its appearance in any other way. Translation is an example of a transformation. A transformation is a way of changing the size or position of a shape. Every point in the shape is translated the same distance in the same direction.

We can see from given figure ΔXYZ and the triangle B are alike.

From ΔXYZ translated to triangle B by 7 units left.

Therefore, a translation of triangle XYZ is triangle B shifted by 7 units to left.

To learn more about the translation visit:

brainly.com/question/8797028.

#SPJ1

7 0

1 year ago

Please need help on these two cause I’m very lost on them

vesna_86 [32]

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = (x - 4)(2x - 1)²(x - 2)²

To find the roots equate f(x) to zero, that is

(x - 4)(2x- 1)²(x - 2)² = 0

Equate each of the factors to zero and solve for x

x - 4 = 0 ⇒ x = 4

2x - 1 = 0 ⇒ x = $\frac{1}{2}$ ← with multiplicity 2

x - 2 = 0 ⇒ x = 2 ← with multiplicity 2

Hence the roots are

{ 4, $\frac{1}{2}$ , 2 }

Given

f(x) = x³ + 4x² + 7x + 6

Note that

f(- 2) = (- 2)³ + 4(- 2)² + 7(- 2) + 6 = - 8 + 16 - 14 + 6 = 0

Since f(- 2) = 0 then by the factor theorem x = - 2 is a root and (x + 2) a factor

Using synthetic division

- 2 | 1 4 7 6

- 2 - 4 - 6

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

1 2 3 0

Thus

f(x) = (x + 2)(x² + 2x + 3)

Solve x² + 2x + 3 using the quadratic formula

with a = 1, b = 2 and c = 3

x = (- 2 ± $\sqrt{2^2-(4(1)(3)}$ ) / 2

= ( - 2 ± $\sqrt{4-12}$ ) / 2

= ( - 2 ± $\sqrt{-8}$ ) / 2

= (- 2 ± 2i $\sqrt{2}$ ) / 2

= - 1 ± i $\sqrt{2}$

Hence roots are

{ - 2, - 1 + i $\sqrt{2}$ , - 1 - i $\sqrt{2}$ }

6 0

3 years ago