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3 years ago

How do I solve 3|x+10|=6

Mathematics

1 answer:

lianna [129]3 years ago

5 0

Answer:

x=-8 x=-12

Step-by-step explanation:

Divide 3 to both sides

|x+10|=2

Set x+10 to equal 2 and -2

x+10=2 x+10=-2

solve both equations

x=-8/-12

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Given h(t) = -2(t+ 5)^2 +4, find h(-8).

bekas [8.4K]

Answer:

Substitute -8 as x into the equation.

h(-8)=-2(-8+5)^2+4

h(-8)=-2(-3)^2+4

h(-8)=-2(9)+4

h(-8)=-18+4

h(-8)=-14

7 0

2 years ago

{4x-2y+5z=6 <br> {3x+3y+8z=4 <br> {x-5y-3z=5

lesya692 [45]

There are three possible outcomes that you may encounter when working with these system of equations:

one solution
no solution
infinite solutions

We are going to try and find values of x, y, and z that will satisfy all three equations at the same time. The following are the equations:

$4x-2y+5z = 6$
$3x+3y+8z = 4$
$x-5y-3z = 5$

We are going to use elimination(or addition) method

Step 1: Choose to eliminate any one of the variables from any pair of equations.

In this case it looks like if we multiply the third equation by 4 and subtracting it from equation 1, it will be fairly simple to eliminate the x term from the first and third equation.

So multiplying Left Hand Side(L.H.S) and Right Hand Side(R.H.S) of 3rd equation with 4 gives us a new equation 4.:

4. 4x-20y-12z = 20

Subtracting eq. 4 from Eq. 1:

(L.HS) : 4x-2y+5z-(4x-20y-12z) = 18y+17z

(R.H.S) : 20 - 6 = 14

5. 18y+17z=14

Step 2: Eliminate the SAME variable chosen in step 2 from any other pair of equations, creating a system of two equations and 2 unknowns.

Similarly if we multiply 3rd equation with 3 and then subtract it from eq. 2 we get:

(L.HS) : 3x+3y+8z-(3x-15y-9z) = 18y+17z

(R.H.S) : 4 - 15 = -11

6. 18y+17z = -11

Step 3: Solve the remaining system of equations 6 and 5 found in step 2 and 1.

Now if we try to solve equations 5 and 6 for the variables y and z. Subtracting eq 6 from eq. 5 we get:

(L.HS) : 18y+17z-(18y+17z) = 0

(R.HS) : 14-(-11) = 25

0 = 25

which is false, hence no solution exists

3 0

2 years ago

Determine the next step for solving the quadratic equation by completing the square.

Studentka2010 [4]

Answer:

The solutions are $x=\frac{1+\sqrt{7}}{2}$ and $x=\frac{1-\sqrt{7}}{2}$

Step-by-step explanation:

we have

$0=-2x^{2}+2x+3$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$-3=-2x^{2}+2x$

Factor the leading coefficient

$-3=-2(x^{2}-x)$

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

$-3-0.5=-2(x^{2}-x+0.5^{2})$

$-3.5=-2(x^{2}-x+0.5^{2})$

Rewrite as perfect squares

$-3.5=-2(x-0.5)^{2}$

$7/4=(x-0.5)^{2}$

square root both sides

$x-0.5=(+/-)\sqrt{\frac{7}{4}}$

$x-\frac{1}{2}=(+/-)\frac{\sqrt{7}}{2}$

$x=\frac{1}{2}(+/-)\frac{\sqrt{7}}{2}$

$x=\frac{1+\sqrt{7}}{2}$

$x=\frac{1-\sqrt{7}}{2}$

4 0

3 years ago

Samples of laboratory glass are in small, light packaging or heavy, large packaging. Suppose that 2% and 1%, respectively, of th

mixer [17]

Answer:

The solution is attached below:

6 0

3 years ago

The diagram below shows the graph of the quadratic function f (x) = ax² + 8x + c. calculate the value for each of the following.

Alexxandr [17]

Answer:

see explanation

Step-by-step explanation:

The y- intercept is at (0, 6) ⇒ c = 6

The x- coordinate of the vertex is at the midpoint of the zeros, that is

m = $\frac{-3-1}{2}$ = $\frac{-4}{2}$ = - 2

Since the zeros are x = - 3 and x = - 1 then the factors are (x + 3), (x + 1) and

f(x) = a(x + 3)(x + 1) = a(x² + 4x + 3)

Comparing with f(x) = ax² + 8x + 6 ⇒ a = 2

Thus

f(x) = 2x² + 8x + 6

Substitute m = - 2 into the equation for value of n

n = 2(- 2)² + 8(- 2) + 6 = 8 - 16 + 6 = - 2

Hence

c = 6, m = - 2, a = 2, n = - 2

3 0

2 years ago

Read 2 more answers