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8090 [49]
3 years ago
6

If AD = 6x – 4 and AC = 4x – 3, find CD.

Mathematics
1 answer:
murzikaleks [220]3 years ago
8 0

Answer:

Since C is the mid point,

therefore, (6x - 4)/2 = 4x-3

=> 6x - 4 = 2X(4x-3) = 8x - 6

=> 6x - 8x = -6 + 4

=> -2x = -2

=> x = (-2)/(-2) = 1

Hence, CD = AC = 4x - 3 = 4X1 - 3 = 1

Step-by-step explanation:

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Suppose f(x, y) is a differentiable function of x and y and let g(r, s) = f (2rs, 8s − 2r). Use
worty [1.4K]

By the chain rule,

\dfrac{\partial g}{\partial r} = \dfrac{\partial f}{\partial r} \\\\ ~~~~~ = \dfrac{\partial f}{\partial x} \dfrac{\partial x}{\partial r} + \dfrac{\partial f}{\partial y} \dfrac{\partial y}{\partial r} \\\\ ~~~~~ = 2 s \dfrac{\partial f}{\partial x} - 2 \dfrac{\partial f}{\partial y}

where x(r,s)=2rs and y(r,s)=8s-2r.

If r=2 and s=1, then

x = 2\cdot2\cdot1 = 4

y=8\cdot1-2\cdot2 = 4

so that

g_r(2,1) = 2\cdot1 f_x(4,4) - 2 f_y(4,4) = 2\cdot2-2\cdot3 = \boxed{-2}

5 0
1 year ago
Using 5 letters followed by 2 ​digits, how many passwords are​ possible?
Deffense [45]
Since there is no condition whatsoever for this arrangement, I can consider the 2 digits and the 5 letters as 7 different objects.

Total permutation (with no repetition):
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Total permutation (WITH REPERTITION):

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6 0
3 years ago
Solve each system of inequalties by graphing.
nordsb [41]

Start by graphing each line.

• Because the first inequality is smaller than, it will have a dotted (- - -) line.

• Because the second inequality is smaller than or equal to, it will have a solid line (---).

Then, plug in points to see where your shading will go. If the statement is true (x = x), you will shade that area along the line.

y  < 3x + 2

(0)  < 3(0) + 2

0  <  2

0 is less than 2.

Do the same step for the other equation. Your solution to the problem is any point that lies between the shading from both inequalities (where the blue and red meet).

8 0
3 years ago
A deck of 38 cards contains 16 blue cards, 6 red cards, and 16 yellow cards. What is the probability of randomly drawing a blue
GalinKa [24]
The probability of drawing a blue card is equal to the quotient when the number of blue cards is divided by the total number of cards. This is, 16/38 which is also equal to 8/19. Thus, the probability of drawing a yellow card is 8/19. The answer is letter C. 
5 0
3 years ago
The ratio of the number of cups of blue paint to the number of cups of red paint that Lara mixed to make a shade of purple paint
Vikki [24]

Answer:

a

Generally given that the number of cups of blue to that of red paint is 3: 1 then the Lara mixed 3 cups of blue paint with 1 cup of red paint

b

The number is  x=  \frac{1}{3}

c

The price is P  = \$ 8

Step-by-step explanation:

From the question we are told that

   The ratio of  the number of cups of blue paint to the number of cups of red paint is  r  =  3: 1

Generally given that the number of cups of blue to that of red paint is 3: 1 then the Lara mixed 3 cups of blue paint with 1 cup of red paint

Given that  1 cup of  red paint  =>   3 cups of blue paint

                 x cup of  red paint  =>  1  cup of  blue paint

So

         x=  \frac{1 *  1}{3}

=>      x=  \frac{1}{3}

Generally the unit price of a cup of blue paint is mathematically represented as

     P  =  \frac{48}{6}

=>  P  = \$ 8

     

4 0
3 years ago
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