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Zielflug [23.3K]
2 years ago
15

If x = 9 and y = -3, evaluate the following expression: = 6x - 8y ​

Mathematics
1 answer:
masha68 [24]2 years ago
8 0

Answer: 78

Step-by-step explanation:

Step 1:

Substitute the variables in:

6(9) - 8(-3)

Step 2:

Multiply to get rid of the parentheses:

54 - -24 = 54 + 24 (the two negatives cancel out)

Step 3:

Add, and then you're done:

54 + 24 = 78

hope this helps :)

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PLEASE HELP ME!!!!!!!!!!
nikklg [1K]

Answer:

-7/10

Step-by-step explanation:

To find the slope of a line, you need to find the \frac{rise}{run} between two points. I will be using the points (-3, 5) and (7, -2).

\frac{rise}{run} = \frac{-2-5}{7-(-3)}

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8 0
3 years ago
In triangle abc, the perimeter is 36, and ab=ac. line ad is perpendicular to bc at the point d, and triangle abd's perimeter is
Musya8 [376]
Let x=ab=ac, and y=bc, and z=ad.

Since the perimeter of the triangle abc is 36, you have:

Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
(eq. 1) 2x + y = 36

The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.

Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).

The perimeter of the triangle abd is 30:

Permiter of abd = 30
ab + bd + ad = 30
x + y/2 + z =30
(eq. 2) 2x + y + 2z = 60

So, we have two equations on x, y and z:

(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60

Substitute 2x + y by 36 from (eq.1) in (eq.2):

(eq.2') 36 + 2z = 60

And solve for z:

36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12

The measure of ad is 12.

If you prefer a less algebraic reasoning:

- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).

- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:

ad = 30 - (36/2) = 30 - 18 = 12
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