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3 years ago

Given the function f(x) = -0.5|2x + 2| + 1, for what values of x is f(x) = 6?

Mathematics

1 answer:

Licemer1 [7]3 years ago

6 0

Answer:

<em>No values of x can make f(x)=6</em>

Step-by-step explanation:

Equation with Absolute Value

The absolute value of a number is always positive. That condition must be met when solving equations. Any condition that goes against the rule, must be discarded and not part of the solution.

The function provided in the question is:

$f(x) = -0.5|2x + 2| + 1$

We need to find the value(s) of x that make:

f(x)=6

It needs to solve the equation:

$-0.5|2x + 2| + 1=6$

Subtracting 1:

$-0.5|2x + 2| =6-1=5$

Dividing by -0.5:

$|2x + 2| =5/(-0.5)=-10$

We reach to this equation to solve:

$|2x + 2| =-10$

As stated above, the absolute value is always positive, and the equation forces the absolute value to be negative. There is no possible value of x that makes the absolute value negative, thus:

No values of x can make f(x)=6

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Solve for x; y=mx+b I can find x by_______________ on both sides of the equation PLZ Show your Work Thank You

amid [387]

Answer:

"subtracting b, then dividing by m"

Step-by-step explanation:

To solve for a particular variable, look a the operations that are being performed on that variable. Then "undo" those operations in reverse order.

Here, the operations done to x are ...

• multiply by m

• add b to the product

Using the above recipe, first we "undo" the additon of b. We accomplish that by subtracting b from both sides of the equation. This gives ...

y - b = mx + b - b

y - b = mx . . . . . . . . . simplify

Next, we "undo" the multiplicatin by m. We accomplish that by dividing both sides of the equation by m.

(y -b)/m = mx/m

(y -b)/m = x . . . . . . . . simplify

This is your solution for x:

x = (y - b)/m

We found it by subtracting b, then dividing by m on both sides of the equation.

6 0

4 years ago

For A (1, –1), B (–1, 3), and C (4, –1), find a possible location of a fourth point, D, so that a parallelogram is formed using

katrin [286]

The possible coordinates for the vertex D of the parallelogram could be (-4, 3)

It is given that A(1, –1), B (–1, 3), and C (4, –1) are the three vertices of the parallelogram.

Let us assume that the vertices are in the order A, C, B, and D where the coordinates of D are (a, b).

In this scenario, if we join AB and CD, they will become the diagonals of the parallelogram ABCD.

According to the properties of a parallelogram, diagonals bisect each other.

Hence, mid-point of AB = mid-point of CD

Now, according to the mid-point theorem, if mid-point of AB is given as (x,y), then,

x = (x₁ + x₂)/2 and y = (y₁ + y₂)/2

Here, for AC,

x₁ = 1, y₁ = -1

x₂ = -1, y₂ = 3

Then, x = ( 1 - 1)/2 and y = (-1 + 3)/2

(x, y) ≡ (0, 1) ............. (1)

Since (x, y) is also the mid-point of CD, we also have,

x₁ = 4, y₁ = -1

x₂ = a, y₂ = b

Then, x = (4 + a)/2 and y = (-1 + b)/2

(x, y) ≡ ((4 + a)/2, (-1 + b)/2) ................... (2)

From (1) and (2),

(4+a)/2 = 0 and (-1+b)/2 = 1

4+a = 0 and (-1+b) = 2

a = -4 and b = 3

Hence, the fourth vertex D of the parallelogram can be possibly located at (-4, 3)

Learn more about a parallelogram here:

brainly.com/question/1563728

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8 0

2 years ago

Can’t figure this out need help

Morgarella [4.7K]

i think D hope it helps

Step-by-step explanation:

1 7/8 the least because it farther from the line than 0

8 0

3 years ago

Read 2 more answers

Simplify and be granted 10 points! :0

babunello [35]

Answer:46

Step-by-step explanation:

5 0

2 years ago

Using f for the number of friends. Write an expression to represent how much Jack and Jenn will spend on breakfast if everyone g

antoniya [11.8K]

Answer:

$1.25f + $0.75f

Step-by-step explanation:

The cost of one bagel is $1.25 and cream cheese costs $0.75 per person. The total amount Jack and Jenn will spend on breakfast depends on the number of friends that eat breakfast.

to get the total amount spent on breakfast, multiply the cost of bagel by the number of friends and the cost of cream cheese by the number of friends. Add these numbers

The total amount spent on food = $1.25f + $0.75f

5 0

2 years ago