5k-3(2k-2/3)-9=0. Solve the equation

Sladkaya [172]

Answer:

x = 13

Step-by-step explanation:

Given that Δ NML and Δ PST are similar right triangles, we can set up the following proportional statement to establish their relationship:

$\frac{ML}{NM} = \frac{ST}{PS}$

$\frac{8}{10} = \frac{x - 1}{x + 2}$

Cross multiply:

8(x + 2) = 10 (x - 1)

8x + 16 = 10x - 10

Subtract 8x from both sides:

8x - 8x + 16 = 10x - 8x - 10

16 = 2x - 10

Add 10 to both sides:

16 + 10 = 2x - 10 + 10

26 = 2x

Divide both sides by 2:

$\frac{26}{2} = \frac{2x}{2}$

13 = x

Verify whether x = 13 is the correct value:

$\frac{ML}{NM} = \frac{ST}{PS}$

$\frac{8}{10} = \frac{x - 1}{x + 2}$

$\frac{8/2}{10/2} = \frac{4}{5}$

$\frac{x -1}{x+2} = \frac{13 - 1}{13 + 2} = \frac{12}{15} = \frac{12 / 3}{15 /3} = \frac{4}{5}$

This shows the proportional relationship between $\frac{ML}{NM} = \frac{ST}{PS}$ , and that ΔNML and ΔPST are indeed similar right triangles.

Therefore, the correct answer is x = 13.

4 0

3 years ago

Solve for w. −(1/4w 8) 8=3 w=52w=52 w=134w=134 w=−34w=−34 w=−12

prohojiy [21]

-(1/4 w + 8) + 8 = 3
-1/4 w - 8 = 3 - 8 = -5
1/4w = -8 + 5 = -3
w = 4 x -3 = -12
w = -12

8 0

3 years ago

If (5⁴)m = 5 ¹²,what is the value of m 2 3 5 8

Lapatulllka [165]

The correct answer is: [B]: " 3 " .
_______________________________________________
Note:
_______________________________________________
The question asks:
_______________________________________________
If (5⁴)ᵐ = 5¹² ; then what is "m" ?

Note the following property of exponents:
________________________________________________
(xᵃ)ᵇ = x⁽ᵃ*ᵇ⁾ ; a≠0 ; b ≠ 0 ;

Then, (5⁴)³ = 5⁽⁴ * ³⁾ = 5¹² .

So, "12 ÷ 4 = 3" .
________________________________________________
The answer is: "m = 3" ; which is: Answer choice: [B] .
________________________________________________

5 0

3 years ago

Solve for a and graph the solution on the number line below.

oksian1 [2.3K]

Solve for x and graph the solution on the number line below.

$-x-5 \geq 1 \text { or }-x-5 < -8$

$-x-5 \geq 1$

Add 5 to both sides

$-x-5+5 \geq 1+5$

Simplify

$-x \geq 6$

Multiply both sides by - 1 (reverse the inequality) $(-x)(-1) \leq 6(-1)$

Simplify

$x \leq-6$

$-x-5 < -8$

Add 5 to both sides

$-x-5+5 < -8+5$

Simplify

$-x < -3$

Multiply both sides by $-1$ (reversing the inequality)

$(-x)(-1) > (-3)(-1)$

Simplify

$x > 3$

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities, is at the core of social justice theories. However, because it frequently has diverse meanings to different individuals, it is prone to misunderstanding in public discourse. However, certain distinctions are universal.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Learn more about inequalities brainly.com/question/20383699

#SPJ9

7 0

1 year ago

What is the length of the hypotenuse of the triangle

user100 [1]

Answer: i think the answers D.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers