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4 years ago

1. if √16 = x, then x^2

1 answer:

4 0

1. A squares and square root cancels

2. CE square root of a perfect square is rational square root of non perfect squares are irrational

4. ✓16=4 ✓9 =3 therefore ✓10 will be between 4 and 3 which is 3.1 answer is C

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A function f(x) is described by the ordered pairs (x,y). If the given function is translated two units to the right and then ref

andrew11 [14]

Answer: The correct choice is answer D.

First, the first step of the transformation moves the unit 2 places to the right. The x-coordinate controls the movement left or right. Add 2 to the x-value moves it right 2 places.

Second, we have to reflect it over the x-axis. Taking the opposite of all of the y-values will reflect the shape over the x-axis. Therefore, we will use " - y" .

7 0

3 years ago

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If the sum of a number and its square is 182, what is the number ?

vivado [14]

Answer:

-14 or 13

Step-by-step explanation:

x + x^2 = 182

x^2 + x - 182 = 0

rearrange and solve by completing the square

x^2 + x = 182

x^2 + x + 1/4 = 182.25

(x + 1/2)(x + 1/2) = 182.25

(x + 1/2)^2 = 182.25

x + 1/2 = root 182.25

x = + or - root 182.25 - 0.5

x = + or - 13.5 - 0.5

x = 13 or x = - 14

5 0

3 years ago

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What is true about sides opposite congruent<br> angles within a triangle?

nignag [31]

Answer:

The converse of the base angles theorem is always true. The base angles theorem states that if two sides of a triangle are congruent the angles opposite them are also congruent. The converse of this statement is that if two angles in a triangle are congruent, then the sides opposite them will also be congruent

Step-by-step explanation:

8 0

2 years ago

Write an algebraic expression for the verbal description.

dimaraw [331]

Step-by-step explanation:

45X + 2000 = Y

Where X = Number of units

Y = Total Cost

3 0

3 years ago

NO LINKS!!! Please help me with these problems

nadezda [96]

<h3>Answers:</h3>

7) Center= (-1,2) Radius= $\boldsymbol{\sqrt{8}}$ Equation: $(x+1)^2+(y-2)^2 = 8$

8) Center= (3,13) Radius= 13 Equation: $(x-3)^2+(y-13)^2 = 169$

=========================================================

Explanation:

Problem 7

Let's find the distance from (-1,2) to (-3,4)

$(x_1,y_1) = (-1,2) \text{ and } (x_2, y_2) = (-3,4)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-1-(-3))^2 + (2-4)^2}\\\\d = \sqrt{(-1+3)^2 + (2-4)^2}\\\\d = \sqrt{(2)^2 + (-2)^2}\\\\d = \sqrt{4 + 4}\\\\d = \sqrt{8}\\\\$

This is the radius because it stretches from the center to a point on the circle, so $r = \sqrt{8}$

Squaring both sides will get us $r^2 = 8$

One useful template for a circle is the equation $(x-h)^2+(y-k)^2 = r^2\\\\$

(h,k) is the center

r is the radius

Let's plug in the given center (h,k) = (-1,2) and the r^2 value we found earlier.

$(x-h)^2+(y-k)^2 = r^2\\\\(x-(-1))^2+(y-2)^2 = 8\\\\(x+1)^2+(y-2)^2 = 8\\\\$

You can confirm this by using a tool like Desmos. See below.

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

Problem 8

The endpoints of the diameter are (-2,1) and (8,25)

The center is the midpoint of these endpoints.

The midpoint of the x coordinates is (-2+8)/2 = 3

The midpoint of the y coordinates is (1+25)/2 = 13

The center is (h,k) = (3,13)

Now find the distance from the center to one of the points on the circle, let's say to (8,25)

$(x_1,y_1) = (3,13) \text{ and } (x_2, y_2) = (8,25)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-8)^2 + (13-25)^2}\\\\d = \sqrt{(-5)^2 + (-12)^2}\\\\d = \sqrt{25 + 144}\\\\d = \sqrt{169}\\\\d = 13\\\\$

The radius is exactly 13 units.

So,

$(x-h)^2+(y-k)^2 = r^2\\\\(x-3)^2+(y-13)^2 = 13^2\\\\(x-3)^2+(y-13)^2 = 169\\\\$

is the equation of this particular circle.

Visual confirmation is shown below.

8 0

3 years ago

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