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3 years ago

What is the domain and range of g(x)= -|x+2| -1

Mathematics

1 answer:

solmaris [256]3 years ago

4 0

g(x)= -|x+2| -1

The domain is the input values, or x values

it is all real number

The range is the output values, or g(x)

the absolute value at is smallest is 0

0-1 is -1 this is the max since the absolute value is multiplied by -1

g(x) <=-1

the output is less than or equal to -1

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What is the equation of the circle whose diameter has endpoints (8,-2) and (-2,6)?

klemol [59]

Answer:

$(x-3)^{2} +(y-2)^{2}=41$

Step-by-step explanation:

step 1

Find the diameter of the circle

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

$A(8,-2)\\E(-2,6)$

substitute the values

$d=\sqrt{(6+2)^{2}+(-2-8)^{2}}$

$d=\sqrt{(8)^{2}+(-10)^{2}}$

$d=\sqrt{164}\ units$

$d=2\sqrt{41}\ units$

step 2

Find the center of the circle

The center is the midpoint of the diameter

The center is equal to

$C=(\frac{8-2}{2},\frac{-2+6}{2})$

$C=(3,2)$

step 3

Find the equation of the circle

The equation of the circle in center radius form is equal to

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

we have

(h,k)=(3,2)

$r=2\sqrt{41}/2=\sqrt{41}\ units$ ---> the radius is half the diameter

substitute

$(x-3)^{2} +(y-2)^{2}=(\sqrt{41})^{2}$

$(x-3)^{2} +(y-2)^{2}=41$

4 0

4 years ago

Solve Expression 12(3+5x)+1/4(16x-8)

Lynna [10]

Answer:

56x + 34

Step-by-step explanation:

12(3 + 5x) + 1/4(16x - 8)

First, use the distributive property. You will get:

(12)(3) + (12)(5x) + (1/4)(16x) - (1/4)(8)

Next, multiply the numbers. You will then have:

36 + 60x + 4x - 2

Now, rearrange the numbers. The variables go in the front. This is what it should look like:

60x + 4x + 36 - 2

Add 60x and 4x, then subtract 36 and 2. This is your answer:

56x + 34

4 0

3 years ago

PLEASEEEEE HELPPPPP Quick 15 points

zheka24 [161]

Answer:

Neither

Step-by-step explanation:

Since we only know the measure of the angles, we can only say the triangles are similar, not congruent. We need at least one side measurement on each triangle to determine if the triangles are congruent. And it would have to be the same side measurement. Then we could use ASA (Angle side Angle) or AAS ( Angle Angle side) to determine congruence.

The triangles are similar

62+39 +79 = 180

The three angles are the same

<A = 62 = <X = 62

<B = 39 = <Y = 39

<C = 79 = <Z = 79

This is shown by AAA similarity

5 0

3 years ago

Evaluate the expression for x=-6 4more than the product of-4 and the number

son4ous [18]

Answer:

Step-by-step explanation:

The product of -4 and the unknown number n is -4n.

4 more than the product of -4 and the unknown number n is -4n + 4.

Letting n = -6 results in the value -4(-6) + 4, or 24 + 4, or 28.

8 0

3 years ago

What is the vertex of Y equals X to the second power -4x-5

Fed [463]

Answer:

vertex = (2, - 9 )

Step-by-step explanation:

Given a quadratic in standard form : ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

$x_{vertex}$ = - $\frac{b}{2a}$

x² - 4x - 5 ← is in standard form

with a = 1, b = - 4, thus

$x_{vertex}$ = - $\frac{-4}{2}$ = 2

Substitute this value into the quadratic for corresponding value of y

(2)² - 4(2) - 5 = 4 - 8 - 5 = - 9

vertex = (2, - 9 )

5 0

3 years ago