The answer is: [D]: " 24 + 2w " .
___________________________________________
Explanation:
___________________________________________
Given: The formula for the Perimeter of a rectangle:
___________________________________________
P = 2L + 2w ;

in which:
P = perimeter ;
L = length = 12 units (given);
w = width = unknown;
_______________________________________________________
Find the perimeter, "P", in terms of "w" ; since "w" (width) is unknown; and considering the answer choices given; along with the information provided in the problem, we only have enough information to solve for the perimeter, "P", in terms of "w" ;
_____________________________________________________
So, given the formula/equation for the perimeter, "P" :
_____________________________________________________
P = 2L + 2w ; we know that: " L = 12 units " ;
_____________________________________________________
P = 2*12 + 2w = 24 + 2w ; which is: "Answer choice: [D]" .
_____________________________________________________

7 0

2 years ago

4. If TV = 14x - 8, find TU. 9x+2 5

Musya8 [376]

Answer:

x = 3

Explanation:

The complete question is shown in the attached diagram

Collinear points are defined as points that lie on the same straight line

Since points U, T and V are given to be collinear, this means that these three points lie on the same straight line

Now, we are given that point U is between points T and V

This would mean that the length of segment TV can be written as the sum of the segments TU and UV

Therefore:

TV = TU + UV

We are given that:

TV = 14x - 8

TU = 9x + 2

UV = 5

Substitute with the givens in the above mentioned equation and solve for x as follows:

TV = TU + UV

14x - 8 = 9x + 2 + 5

14x - 8 = 9x + 7

14x - 9x = 7 + 8

5x = 15

x = 3

Hope this helps :)

5 0

3 years ago

Find the product of all positive integer values of $c$ such that $3x^2+7x+c=0$ has two real roots. I will award a lot of points

Agata [3.3K]

Answer: 24

Step-by-step explanation:

Let's find one solution:

3x² + 7x + c = 0

a=3 b=7 c=c

First, let's find c so that it has REAL ROOTS.

⇒ Discriminant (b² - 4ac) ≥ 0

7² - 4(3)c ≥ 0

49 - 12c ≥ 0

-12c ≥ -49

$c\leq\dfrac{-49}{-12}\quad \rightarrow c\leq \dfrac{49}{12}$

Since c must be a positive integer, 1 ≤ c ≤ 4

Example: c = 4

3x² + 7x + 4 = 0

(3x + 4)(x + 1) = 0

x = -4/3, x = -1 Real Roots!

You need to use Quadratic Formula to solve for c = {1, 2, 3}

Valid solutions for c are: {1, 2, 3, 4)

Their product is: 1 x 2 x 3 x 4 = 24

7 0

3 years ago

Select the correct answer.

Marrrta [24]

How many students are in the class? ( might say in a previous question )

5 0

2 years ago

Read 2 more answers