All categories

3 years ago

If f(x) = x2 - 2x and g(x) = 6x + 4, for which value of x does (f+g)(x) = 0?

Mathematics

2 answers:

madreJ [45]3 years ago

8 0

Answer:

x=-2

Step-by-step explanation:

f(x) = x^2 - 2x

g(x) = 6x + 4

Add them together

f(x) = x^2 - 2x

g(x) = 6x + 4

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

f(x) + g(x) =x^2 +4x+4

We want to find when this equals 0

0 =x^2 +4x+4

Factor

What two numbers multiply together to give us 4 and add together to give us 4

2*2 =4

2+2=4

0=(x+2) (x+2)

Using the zero product property

x+2 =0 x+2=0

x+2-2=0-2

x=-2

Law Incorporation [45]3 years ago

7 0

Answer:

-2

Step-by-step explanation:

Let's plug your functions f(x)=x^2-2x and g(x)=6x+4 into (f+g)(x)=0 and then solve your equation for x.

So (f+g)(x) means f(x)+g(x).

So (f+g)(x)=x^2+4x+4

Now we are solving (f+g)(x)=0 which means we are solve x^2+4x+4=0.

x^2+4x+4 is actually a perfect square and is equal to (x+2)^2.

So our equation is equivalent to solving (x+2)^2=0.

(x+2)^2=0 when x+2=0.

Subtracting 2 on both sides gives us x=-2.

You might be interested in

For which system of equations is (5, 3) the solution? A. 3x – 2y = 9 3x + 2y = 14 B. x – y = –2 4x – 3y = 11 C. –2x – y = –13 x

Alla [95]

The correct answer is:

D) $\left \{ {{2x-y=7} \atop {2x+7y=31}} \right.$ .

Explanation:

We solve each system to find the correct answer.

For A:
$\left \{ {{3x-2y=9} \atop {3x+2y=14}} \right.$

Since we have the coefficients of both variables the same, we will use elimination to solve this.

Since the coefficients of y are -2 and 2, we can add the equations to solve, since -2+2=0 and cancels the y variable:
$\left \{ {{3x-2y=9} \atop {+(3x+2y=14)}} \right. 
\\
\\6x=23$

Next we divide both sides by 6:
6x/6 = 23/6
x = 23/6

This is not the x-coordinate of the answer we are looking for, so A is not correct.

For B:
$\left \{ {{x-y=-2} \atop {4x-3y=11}} \right.$

For this equation, it will be easier to isolate a variable and use substitution, since the coefficient of both x and y in the first equation is 1:
x-y=-2

Add y to both sides:
x-y+y=-2+y
x=-2+y

We now substitute this in place of x in the second equation:
4x-3y=11
4(-2+y)-3y=11

Using the distributive property, we have:
4(-2)+4(y)-3y=11
-8+4y-3y=11

Combining like terms, we have:
-8+y=11

Add 8 to each side:
-8+y+8=11+8
y=19

This is not the y-coordinate of the answer we're looking for, so B is not correct.

For C:
Since the coefficient of x in the second equation is 1, we will use substitution again.

x+2y=-11

To isolate x, subtract 2y from each side:
x+2y-2y=-11-2y
x=-11-2y

Now substitute this in place of x in the first equation:
-2x-y=-13
-2(-11-2y)-y=-13

Using the distributive property, we have:
-2(-11)-2(-2y)-y=-13
22+4y-y=-13

Combining like terms:
22+3y=-13

Subtract 22 from each side:
22+3y-22=-13-22
3y=-35

Divide both sides by 3:
3y/3 = -35/3
y = -35/3

This is not the y-coordinate of the answer we're looking for, so C is not correct.

For D:
Since the coefficients of x are the same in each equation, we will use elimination. We have 2x in each equation; to eliminate this, we will subtract, since 2x-2x=0:

$\left \{ {{2x-y=7} \atop {-(2x+7y=31)}} \right. 
\\
\\-8y=-24$

Divide both sides by -8:
-8y/-8 = -24/-8
y=3

The y-coordinate is correct; next we check the x-coordinate Substitute the value for y into the first equation:
2x-y=7
2x-3=7

Add 3 to each side:
2x-3+3=7+3
2x=10

Divide each side by 2:
2x/2=10/2
x=5

This gives us the x- and y-coordinate we need, so D is the correct answer.

7 0

3 years ago

A T-shirt that usually cost $32 is on sale 1/4 off.What is the sale price??

olya-2409 [2.1K]

32/4 = 8
32 - 8 = 24 $

3 0

3 years ago

Read 2 more answers

BRAINLIEST QUESTION

Debora [2.8K]

Answer:

the answer is triangles ABC and DEC are similar

Step-by-step explanation:

angle C is a common angle for both triangles

angle D is equal to angle A ( corresponding angles)since they are parallel

angle B is also equal to angle B for the same reason as angle D and A

since the three angles of the two angles are equal they are similar

6 0

3 years ago

What is the relationship between ∠a and∠b? NO LINKS ! if you give me a link you're getting reported. Also the last option says n

oksano4ka [1.4K]

The answer would be B. As you can see Angle A and angle B are connected by that line and together they would equal 90 degrees like on the other side of line AB.

3 0

3 years ago

Complete the square for 3x^2-12x=9

larisa [96]

Answer:

The solutions are -0.65 and 4.65.

Step-by-step explanation:

3x^2 - 12x = 9

Divide both sides by 3

x^2 - 4x = 3

To make a square with "x^2 - 4x", you need to have a "+ 4" after it so it can be simplified as (x-2)^2. So add 4 to both sides.

x^2 - 4x + 4 = 7

(x-2)^2 = 7

x - 2 = (square root) of 7

x = 2 (+/-) (square root) of 7.

x = {-0.65, 4.65}

The solutions are -0.65 and 4.65.

hope this helps:)sorry if it doesnt

8 0

3 years ago

Read 2 more answers