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3 years ago

Rewrite in simplest terms: -2(5d-9f)+7f-10(-9f-7d)−2(5d−9f)+7f−10(−9f−7d)

Mathematics

1 answer:

Bess [88]3 years ago

8 0

Answer:

= 5 ( 12d + 23f )

Step-by-step explanation:

-2(5d-9f)+7f-10(-9f-7d)

Open parenthesis

= -10d + 18f + 7f + 90f + 70d

Collect like terms

= -10d + 70d + 18f + 7f + 90f

= 60d + 115f

Factorise

= 5 ( 12d + 23f )

Therefore,

-2(5d-9f)+7f-10(-9f-7d) in its simplest form is 5 ( 12d + 23f )

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Suppose you pick two cards from a deck of 52 playing cards. What is the probability that they are both queens?

photoshop1234 [79]

Answer:

0.45% probability that they are both queens.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes

The combinations formula is important in this problem:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes

You want 2 queens. Four cards are queens. I am going to call then A,B,C,D. A and B is the same outcome as B and A. That is, the order is not important, so this is why we use the combinations formula.

The number of desired outcomes is a combinations of 2 cards from a set of 4(queens). So

$D = C_{4,2} = \frac{4!}{2!(4-2)!} = 6$

Total outcomes

Combinations of 2 from a set of 52(number of playing cards). So

$T = C_{52,2} = \frac{52!}{2!(52-2)!} = 1326$

What is the probability that they are both queens?

$P = \frac{D}{T} = \frac{6}{1326} = 0.0045$

0.45% probability that they are both queens.

4 0

3 years ago

From point A(3,-2), walk 4 spaces in the negative x direction, and 3 spaces in the positive y direction. Use a paper cutout to l

Zolol [24]

Answer: 3,-2Step-by-step explanation: ... Use a paper cutout to label the point you reach as. B. What are the coordinates of point B?

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

Answer all questions shown

FromTheMoon [43]

SOH CAH TOA

—>

Sin D = 13 sqrt3/26 = 0.76
Sin E = 13/26 = 0.47
Cos D = 13/26 = 0.87
Cos E = 13 sqrt3/26 = 0.64

7 0

2 years ago

If possible help me in this. I need to find the two odd numbers...

Lelechka [254]

Part (a)

Consecutive odd integers are integers that odd and they follow one right after another. If x is odd, then x+2 is the next odd integer

For example, if x = 7, then x+2 = 9 is right after.

<h3>Answer: x+2</h3>

========================================================

Part (b)

The consecutive odd integers we're dealing with are x and x+2.

Their squares are x^2 and (x+2)^2, and these squares add to 394.

<h3>Answer: x^2 + (x+2)^2 = 394</h3>

========================================================

Part (c)

We'll solve the equation we just set up.

x^2 + (x+2)^2 = 394

x^2 + x^2 + 4x + 4 = 394

2x^2+4x+4-394 = 0

2x^2+4x-390 = 0

2(x^2 + 2x - 195) = 0

x^2 + 2x - 195 = 0

You could factor this, but the quadratic formula avoids trial and error.

Use a = 1, b = 2, c = -195 in the quadratic formula.

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(1)(-195)}}{2(1)}\\\\x = \frac{-2\pm\sqrt{784}}{2}\\\\x = \frac{-2\pm28}{2}\\\\x = \frac{-2+28}{2} \ \text{ or } \ x = \frac{-2-28}{2}\\\\x = \frac{26}{2} \ \text{ or } \ x = \frac{-30}{2}\\\\x = 13 \ \text{ or } \ x = -15\\\\$

If x = 13, then x+2 = 13+2 = 15

Then note how x^2 + (x+2)^2 = 13^2 + 15^2 = 169 + 225 = 394

Or we could have x = -15 which leads to x+2 = -15+2 = -13

So, x^2 + (x+2)^2 = (-15)^2 + (-13)^2 = 225 + 169 = 394

We get the same thing either way.

<h3>Answer: Either 13, 15 or -15, -13</h3>

4 0

3 years ago

I need help with this question

aliya0001 [1]

Question 2. 2470, 2474
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3 years ago