What is the area of the triangle in square yards?<br> 6 yd.<br> 15 3/4 yd.

-8z+(4.5)+3.5z+7y-1.5

bogdanovich [222]

Answer:

$\boxed{\sf{7y+3-4.5z}}$

Step-by-step explanation:

In order to combine like terms, you have to isolate x and y from one side of the equation.

$\sf{-8z+\left(4.5\right)+3.5z+7y-1.5}$

<u>First, thing you do is remove parentheses.</u>

$\Longrightarrow: \sf{-8z+4.5+3.5z+7y-1.5}$

<u>Solve.</u>

<u>Then, you combine like terms.</u>

$\Longrightarrow:\sf{-8z+3.5z+7y+4.5-1.5}$

<u>Add/subtract the numbers from left to right.</u>

-8z+3.5z=-4.5z

<u>Rewrite the problem down.</u>

$\Longrightarrow: \sf{-4.5z+7y+4.5-1.5}$

<u>Solve.</u>

4.5-1.5=3

$\Longrightarrow: \boxed{\sf{7y+3-4.5z}}$

<u>Therefore, the correct answer is 7y+3-4.5z.</u>

I hope this helps, let me know if you have any questions.

6 0

2 years ago

Directions: Using the digits 1 to 9, at most one time each, fill in the boxes to find the largest or smallest possible values fo

12345 [234]

9514 1404 393

Answer:

smallest: 8x -3 = 4; 1y +9 = 2. total = -49/8

largest: 1x -9 = 8; 2y +3 = 7. total = 19

Step-by-step explanation:

If we use variables to represent the box contents, we can write ...

ax -b = c
dy +e = f

Then the values of x and y are ...

x = (c +b)/a

y = (f -e)/d

For positive integer values of the variables, x will always be positive, and y may or may not be negative.

<h3>Smallest sum</h3>

For the sum to be the smallest, we must have x be as small as possible and the ratio (f-e)/d be as negative as possible.

x will be small for large 'a' and for (c+b) small. For y to be as negative as possible, we want 'd' and 'f' small and 'e' large. Best results are obtained for

8x -3 = 4 ⇒ x = 7/8
1y +9 = 2 ⇒ y = -7

For these coefficients, the sum is -6 1/8 = -49/8.

(note that the values of 'b' and 'c' can be swapped with no net effect)

<h3>Largest sum</h3>

For the sum to be the largest, we must have x as large as possible: (b+c) large and 'a' small. At the same time we must have y be positive and as large as possible: (f-e) positive and large, 'd' small. Best results are obtained for

1x -9 = 8 ⇒ x = 17
2y +3 = 7 ⇒ y = 2

For these coefficients, the sum is 19. Again, 'b' and 'c' can be swapped with no effect.

_____

<em>Additional comment</em>

These extreme values are verified by examination of the 60,480 possible permutations of the coefficients.

8 0

3 years ago

Read 2 more answers

What are the ordered pairs of the

9966 [12]

Start by writing the system down, I will use $y$ to represent $f(x)$

$y=x^2-5x+3\wedge y=-3$

Substitute the fact that $y=-3$ into the first equation to get,

$-3=x^2-5x+3$

Simplify into a quadratic form ( $ax^2+bx+c=0$ ),

$x^2-5x+6=0$

Now you can use Vieta's rule which states that any quadratic equation can be written in the following form,

$x^2+x(m+n)+mn=0$

which then must factor into

$(x+m)(x+n)=0$

And the solutions will be $m,n$ .

Clearly for small coefficients like ours $5,6$ , this is very easy to figure out. To get 5 and 6 we simply say that $m=3, n=2$ .

This fits the definition as $5=3+2$ and $6=2\cdot3$ .

So as mentioned, solutions will equal to $m=3, n=2$ but these are just x-values in the solution pairs of a form $(x,y)$ .

To get y-values we must substitute 3 for x in the original equation and then also 2 for x in the original equation. Luckily we already know that substituting either of the two numbers yields a zero.

So the solution pairs are $(2,0)$ and $(3,0)$ .