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Solve the equation. |x + 5| = 9 {–4, 14} {–14, 4} {4, 14} {–14, –4}

inna [77]

Answer:

{-14, 4}

Step-by-step explanation:

the absolute value function only makes sure that the result always has a positive sign.

so, (x + 5) must be either +9 or -9 to make the original equation true. the absolute value would turn both into +9.

so,

x + 5 = 9

x = 4

and

x + 5 = -9

x = -14

that gives us the correct set of solutions as indicated above.

6 0

3 years ago

The table represents a linear function. find the values of a,b, and c. Show your work.

viva [34]

Answer:

The values of a , b , c are ⇒ a = 1 , b = 10 , c = 9

Step-by-step explanation:

* Lets describe the meaning of the linear function

- Linear function is represented by a line graphically

- The equation of the line is y = mx + c, where m is the slope

of the line and c is the y-intercept (the point of intersection

between the line and the y-axis is (0 , c))

- m = change of y/change of x

- We can find m from any two points on the line

* Lets use m to find a, b and c

- Use the points (3 , 8) and (5 , 9) to find m

∵ m = (y2 - y1)/(x2 - x1)

∴ m = (9 - 8)/(5 - 3) = 1/2

- Find a by using points (a , 7) and (3 , 8) ⇒ (or (5 , 9))

∵ m = (8 - 7)/(3 - a) = 1/2

∴ 1/(3 - a) = 1/2 ⇒ by using cross multiplication

∴ 3 - a = 2 ⇒ subtract 3 from both sides

∴ -a = -1 ⇒ × -1 both sides

∴ a = 1

- Find b by using points (5 , 9) and (7 , b) ⇒ (or (3 , 8))

∵ m = (b - 9)/(7 - 5) = (b - 9)/2

∴ (b - 9)/2 = 1/2 ⇒ by using cross multiplication

∴ 2(b - 9) = 2 ⇒ open the bracket

∴ 2b - 18 = 2 ⇒ add 18 to both sides

∴ 2b = 20 ⇒ ÷ 2

∴ b = 10

- Find b by using points (5 , 9) and (c , 11) ⇒ (or (3 , 8))

∵ m = (11 - 9)/(c - 5) = 2/(c - 5)

∴ 2/(c - 5) = 1/2 ⇒ by using cross multiplication

∴ c - 5 = 4 ⇒ add 5 to both sides

∴ c = 9

* The values of a , b , c are ⇒ a = 1 , b = 10 , c = 9

6 0

3 years ago

write the slope - intercept equation of the line that passes through the point (6, "-1)" and has a slope of "-1/3"

TEA [102]

Answer:

y = - $\frac{1}{3}$ x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - $\frac{1}{3}$ , then

y = - $\frac{1}{3}$ x + c ← is the partial equation

To find c substitute (6, - 1 ) into the partial equation

- 1 = - 2 + c ⇒ c = - 1 + 2 = 1

y = - $\frac{1}{3}$ x + 1 ← equation of line

8 0

3 years ago

Question 3, help please!

White raven [17]

The answer is not defined.

Explanation:

The given matrix is $\left[\begin{array}{cc}{2} & {4} \\ {1} & {-6}\end{array}\right]+\left[\begin{array}{c}{1} \\ {0}\end{array}\right]$

The matrix $\left[\begin{array}{cc}{2} & {4} \\ {1} & {-6}\end{array}\right]$ has dimensions $2\times 2$

This means that the matrix has 2 rows and 2 columns.

Also, the matrix $\left[\begin{array}{l}{1} \\ {0}\end{array}\right]$ has dimensions $2\times1$

This means that the matrix has 2 rows and 1 column.

Since, the matrices can be added only if they have the same dimensions.

In other words, to add the matrices, the two matrices must have the same number of rows and same number of columns.

Since, the dimensions of the two matrices are not equal, the addition of these two matrices is not possible.

Hence, the addition of these two matrices is not defined.

4 0

3 years ago

How many x-intercepts would the function shown below have? <br> F(x) =x^2 (x^2+9) (x^2-3) (5x+1) ^2

-BARSIC- [3]

Step-by-step explanation:

step 1. x intercepts are where y = 0

step 2. y = 0 when factors are equal to zero

step 3. the x intercepts are 0, sqr(3), -sqrt(3), -1/5

step 4. answer: 4.

6 0

3 years ago