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CaHeK987 [17]
2 years ago
9

3 times the sum of a number and 5 (Write this word expression as an algebraic expression. Use x as your variable.

Mathematics
1 answer:
enyata [817]2 years ago
6 0

Answer:

3(x+5)

Step-by-step explanation:

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Simplify completely: 8x+4/x^3+23÷4x^2-10x-6/9-x^2
Helen [10]

Answer:

The simplified form is: -x^2-2x+\frac{4}{x^3}+\frac{23}{4x^2}-\frac{2}{3}

Step-by-step explanation:

To simplify the expression given we, need to open the brackets, and if there is power term. Then we need to group all the like terms and then arrange in the descending order of powers of the given expression.

Now the expression that is given to us is:

8x+\frac{4}{x^3}+\frac{23}{4x^2}-10x-\frac{6}{9}-x^2

Here we will simplify it by grouping the like terms, as follows:

8x+\frac{4}{x^3}+\frac{23}{4x^2}-10x-\frac{6}{9}-x^2\\=-x^2+8x-10x+\frac{4}{x^3}+\frac{23}{4x^2}-\frac{6}{9}=-x^2-2x+\frac{4}{x^3}+\frac{23}{4x^2}-\frac{2}{3}

So this is the required simplified form.

7 0
3 years ago
What is the numerical probability of selecting a jury with 10 men and 2 women?
VladimirAG [237]

Answer:

Let E denote the event of choosing a jury with 10 men and 2 women.

The sample space for selecting 12 members from the pool contains 55C12 elements.

The number of ways of selecting 10 men and 2 women is 26C10  29C2.

The probability of event E =  

The probability of selecting a jury with 10 men and 2 women is 0.005 (0.5%).

Step-by-step explanation:

see the image :

3 0
2 years ago
Please help with any of this Im stuck and having trouble with pre calc is it basic triogmetric identities using quotient and rec
german

How I was taught all of these problems is in terms of r, x, and y. Where sin = y/r, cos = x/r, tan = y/x, csc = r/y, sec = r/x, cot = x/y. That is how I will designate all of the specific pieces in each problem.

#3

Let's start with sin here. \frac{2\sqrt{5}}{5} = \frac{2}{\sqrt{5}} Therefore, because sin is y/r, r = \sqrt{5} and y = +2. Moving over to cot, which is x/y, x = -1, and y = 2. We know y has to be positive because it is positive in our given value of sin. Now, to find cos, we have to do x/r.

cos = \frac{-1}{\sqrt{5}} = \frac{-\sqrt{5}}{5}

#4

Let's start with secant here. Secant is r/x, where r (the length value/hypotenuse) cannot be negative. So, r = 9 and x = -7. Moving over to tan, x must still equal -7, and y = 4\sqrt{2}. Now, to find csc, we have to do r/y.

csc = \frac{9}{4\sqrt{2}} = \frac{9\sqrt{2}}{8}

The pythagorean identities are

sin^2 + cos^2 = 1,

1 + cot^2 = csc^2,

tan^2 + 1 = sec^2.

#5

Let's take a look at the information given here. We know that cos = -3/4, and sin (the y value), must be greater than 0. To find sin, we can use the first pythagorean identity.

sin^2 + (-3/4)^2 = 1

sin^2 + 9/16 = 1

sin^2 = 7/16

sin = \sqrt{7/16} = \frac{\sqrt{7}}{4}

Now to find tan using a pythagorean identity, we'll first need to find sec. sec is the inverse/reciprocal of cos, so therefore sec = -4/3. Now, we can use the third trigonometric identity to find tan, just as we did for sin. And, since we know that our y value is positive, and our x value is negative, tan will be negative.

tan^2 + 1 = (-4/3)^2

tan^2 + 1 = 16/9

tan^2 = 7/9

tan = -\sqrt{7/9} = \frac{-\sqrt{7}}{3}

#6

Let's take a look at the information given here. If we know that csc is negative, then our y value must also be negative (r will never be negative). So, if cot must be positive, then our x value must also be negative (a negative divided by a negative makes a positive). Let's use the second pythagorean identity to solve for cot.

1 + cot^2 = (\frac{-\sqrt{6}}{2})^{2}

1 + cot^2 = 6/4

cot^2 = 2/4

cot = \frac{\sqrt{2}}{2}

tan = \sqrt{2}

Next, we can use the third trigonometric identity to solve for sec. Remember that we can get tan from cot, and cos from sec. And, from what we determined in the beginning, sec/cos will be negative.

(\frac{2}{\sqrt{2}})^2 + 1 = sec^2

4/2 + 1 = sec^2

2 + 1 = sec^2

sec^2 = 3

sec = -\sqrt{3}

cos = \frac{-\sqrt{3}}{3}

Hope this helps!! :)

3 0
3 years ago
Read 2 more answers
If there are 52 cards in a deck with four suits (hearts, clubs, diamonds, and spades), how many ways can you select 5 diamonds a
Luba_88 [7]

Answer:

12C5 *(12C3) = 792*220 =174240 ways

Step-by-step explanation:

For this case we know that we have 12 cards of each denomination (hearts, diamonds, clubs and spades) because 12*4= 52

First let's find the number of ways in order to select 5 diamonds. We can use the combinatory formula since the order for this case no matter. The general formula for combinatory is given by:

nCx = \frac{n!}{x! (n-x)!}

So then 12 C5 would be equal to:

12C5 = \frac{12!}{5! (12-5)!}=\frac{12!}{5! 7!} = \frac{12*11*10*9*8*7!}{5! 7!}= \frac{12*11*10*9*8}{5*4*3*2*1}=792

So we have 792 was in order to select 5 diamonds from the total of 12

Now in order to select 3 clubs from the total of 12 we have the following number of ways:

12C3 = \frac{12!}{3! 9!}=\frac{12*11*10*9!}{3! 9!} =\frac{12*11*10}{3*2*1}=220

So then the numbers of ways in order to select 5 diamonds and 3 clubs are:

(12C5)*(12C3) = 792*220 =174240 ways

3 0
3 years ago
Please Help! Will give BRAINLIEST!!!
Anestetic [448]

Answer:

about 200 people

4 0
3 years ago
Read 2 more answers
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