Solve the linear equation 10x + 80 = 0 for x.

Mathematics

1 answer:

Kaylis [27]3 years ago

6 0

Rule: whatever you do to the left side, you must do on the right side. This means when you minus 80 on the left, you must minus 80 on the right as this continues to equate the two sides.

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The graph of the equation x^2+6x+y^2-16y=-9 is a circle. Choose True or False for each statement

BigorU [14]

Answer:

see the explanation

Step-by-step explanation:

we have

$x^2+6x+y^2-16y=-9$

Convert the equation of the circle in center radius form

Group terms that contain the same variable

$(x^2+6x)+(y^2-16y)=-9$

Complete the square twice. Remember to balance the equation by adding the same constants to each side

$(x^2+6x+9)+(y^2-16y+64)=-9+9+64$

$(x^2+6x+9)+(y^2-16y+64)=64$

Rewrite as perfect squares

$(x+3)^2+(y-8)^2=8^2$

The center of the circle is (-3,8)

The radius of the circle is 8 units

Verify each statement

A. The center of the circle is (3,-8).

False

The center of the circle is (-3,8)

B. The circle is tangent to the x-axis

True

The circle is tangent to x=5 and x=-11 and is tangent to y=0 and y=16

Remember that y=0 is the x-axis

C. The circle has a radius of 64

False

The radius of the circle is 8 units

7 0

3 years ago

The function g(x)=-(x)^2+5. The function f(x)=-g(x+2).

Vitek1552 [10]

Short Answer f(x) down 5 units, left 2 units and right side up from g(x)
Step One
Find out what -g(x+2) is.
There are two steps to this. The first is to deal with the minus sign
(g(x)) = - x^2 + 5. Be very careful what you do next.
Put brackets around both terms on the right.
g(x) = (-x^2 + 5) Now put the minus sign in front of g(x) and another one in front of the brackets.
-g(x) = - (-x^2 + 5) Remove the brackets.
-g(x) = x^2 - 5

Result
So far g(x) moves down 5 units and opens upward.

Step Two
The second step is to see what the x + 2 does.
-g(x + 2) = (x + 2)^2 - 5

The final result is that the graph opens upward, moves left 2 spaces and down 5.

There is a graph enclosed to show you the key steps.
The red graph is g(x) = x^2 - 5
The blue graph is g(x+2) = (x+2)^2 - 5