Evaluate the expression 2x - (4y - 3) + 5xz, when x = -3, y = 2, and z = ‐1.

Cos (72°) = x/20

x=cos(72°)×20

x=6.2

x≈6

Answer:

x=6

Step-by-step explanation:

Answer:

Step-by-step explanation:

The sides of a 30-60-90 triangle are in the ratio 1:√3:2

The side opposite the 30° angle is (12√6)÷2 = 6/√6.

The side opposite the 60° angle is √3×6/√6 = 6/√2 =3√2.

The sides of a 45-45-90 triangle are in the ratio 1:1:√2

The hypotenuse is 3√2, so the side opposite the 45° angle is 3.

x = 3

9514 1404 393

Answer:

  each is 55°

Step-by-step explanation:

The sum of angles in a trapezium is 360°, so the sum of the remaining two angles is 360° -250° = 110°. Each of those two equal angles will be ...

  110°/2 = 55°

Answer:The correct answer is  They wanted to impede the sale of alcohol.

Step-by-step explanation:

They had beliefs that alcohol was against Christianity and that it ruins families and since it ruins families it should be prohibited. They eventually managed to win enough support and ban all alcohol which lasted for a few years before the prohibition ended.

Answer:

[tex]Domain = (-\infty,-2)[/tex] --- quadratic function

[tex]Domain = (-2,6)[/tex] --- linear function

[tex]Domain = (6,\infty)[/tex] --- square root function

Step-by-step explanation:

Given

The attached graph

Required

The domain of each function

Starting from the left; the first function is the quadratic function.

The curve of the quadratic function stops at -2 So, the domain is:

[tex]Domain = (-\infty,-2)[/tex]

The straight line that starts at -2 and ends at 6 is a linear function.

So, the domain is:

[tex]Domain = (-2,6)[/tex]

Lastly, the square root function begins at 6. So, the domain is:

[tex]Domain = (6,\infty)[/tex]

Answer:

quadratic = (-∞,-2)

square root = (6,∞)

linear = (-2,6)

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

Using the division method, you find prime divisors that give integer quotients until the final quotient is a prime. For small divisors, it is beneficial to make use of divisibility rules. For larger ones, you just have to try the list of primes to see what you get.

The last two digits are divisible by 4, so the number can be divided by 2 twice (at least). We can keep dividing by 2 as long as the 1s digit is even.

  680624/2 = 340312

  340312/2 = 170156

  170156/2 = 85,078

  85078/2 = 42539

The next prime is 3. The divisibility rule for 3 is the sum of digits must be divisible by 3. 4+2+5+3+9 = 23, not divisible by 3.

The next prime is 5. For divisibility by 5, the number must end in 0 or 5. This is not divisible by 5.

The next prime is 7. For divisibility by 7, there are several possible rules you can use. One I find relatively easy to remember is to subtract double the 1s digit from the rest of the number and see if that is divisible by 7. Here, that gives ...

  4253 -2(9) = 4235; 423 -2(5) = 413; 41 -2(3) = 35 . . . divisible by 7

Continuing, we have ...

  42539/7 = 6077

There are additional divisibility rules for 11 and 13 that can be applied. For divisibility by 11, we can add pairs of digits: 77 +60 = 137, not divisible by 11.

For divisibility by 13, we can add 4 times the last digit to the rest:

  4253 +4(9) = 4289; 428 +4(9) = 464; 46 +4(4) = 62 . . . not divisible by 13

__

After this point, it is a matter of trying the primes one by one to see what the number may be divisible by. This "trial and error" will show you ...

  6077/59 = 103 . . . 103 is prime, so we're done

The final factorization is ...

  680624 = 2^4 · 7 · 59 · 103

__

As luck would have it, this is a perfect square, so we can immediately reduce the problem to something a little easier.

  √165649 = 407

We can see "immediately" that this is not divisible by 2, 3, 5, or 7. However, 04+07 = 11, so this is divisible by 11.

  407/11 = 37 . . . 37 is prime, so we're done

The final factorization is ...

  165649 = 11^2 · 37^2

_____

As you can probably tell, it is convenient to have a list of prime numbers available. Here is a list of the first few primes.

  2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59,

  61, 67, 71, 73, 79, 83, 89, 97, 101, 103

_____

Additional comment

If you start with the smallest primes, (2, 3, 5}, once you find a prime divisor, you only need to try primes greater than or equal to that one on the quotient. In any event, you only need to try primes up to the square root of the value you're trying to factor. If none of those work, then the number itself is a prime.

In the first problem, once we got to 6077, we would only need to try primes up to √6077 ≈ 77. That is, if 6077 turned out to be not divisible by any prime equal to 73 or less, then 6077 would be the last prime factor. (As we found, 6077 is composite, not prime, so using that number is just to illustrate the point regarding the largest value needed to be tested.)

Answer:

a. Set-builder form: {y | y is a natural number and 12 ≤ y ≤ 15}

Or

{y | y is a natural number and 11 < y < 16}

b. Rooster form: {3, 4, 5 ,6, ...}

Step-by-step explanation:

a. Rooster form: {12, 13, 14, 15}

All four numbers are natural numbers, therefore we would write this set of numbers in set builder form such that they will all have the same property. Thus:

Set-builder form: {y | y is a natural number and 12 ≤ y ≤ 15}

Or as

{y | y is a natural number and 11 < y < 16}

b. Set-builder form: {y | y is a natural number and y > 2}

Since natural numbers are positive integers, this tells us that all values of the set are not less than or equal to 2. Therefore, they are integers that range from 3 and above.

Thus:

Rooster form: {3, 4, 5 ,6, ...}

Answer:

B.

Step-by-step explanation:

Vertical line test is a test in which you draw a line that goes up and down through the function. If at any point it goes through the function twice, then the function is no longer a function. cheers

Answer: 9

Step-by-step explanation:

[tex] \frac{3}{5} \times 16.1 = 9.66[/tex]

Answer:

Sum of 6

Sum of 2 or 9

Sum (> 2 but < 5)

Step-by-step explanation:

We are given that :

Elena's probability of winning is 6 /36 = 1/6

And also that Martha's probability if winning is lower Than that of Elena ; Hence, Martha's outcome should be outcjnes whose probability is less than 1/6 (Elena's probability of winning)

Using a sample space that gives the sum of 2 dices.

Recall :

Probability = required outcome / Total possible outcomes

Total possible outcomes for a two dice throw = 6² = 36

Using the sample space attached, we can count the sums from the sample space :

To obtain a sum of 7 :

P(sum 7) = 6 /36 = 1/6

To obtain a sum of 6 :

P(sum 6) = 5 /36

Sum of 2 or 9:

P(sum of 2 or 9). = 5 / 36

Sum > 9 :

P(sum > 9). = 6/36

P Sum (> 2 but < 5) = 5 /36

Correct choices are probability values less than 6/36 which are :

Sum of 6

Sum of 2 or 9

Sum (> 2 but < 5)

Answer:

rolling a sum of 6

rolling a sum of 2 or a sum of 9

rolling a sum that is greater than 2 but less than 5

Step-by-step explanation:

Answer:

The length of a side of a cubic die of volume equal to 343/4 is 4.41 inches.

Step-by-step explanation:

The volume of a cube is given by:

[tex] V = l^{3} [/tex]

Where:

l: is the length =?  

V: is the volume = 343/4 in³

By solving the above equation for "l" we have:

[tex] l = (V)^{1/3} = (343/4 in^{3})^{1/3} = 4.41 in [/tex]

Therefore, the length of a side of a cubic die of volume equal to 343/4 is 4.41 inches.

None of the options are correct for the given volume.

I hope it helps you!                                

Recall that for |x| < 1, we have

[tex]\displaystyle \frac1{1-x} = \sum_{n=0}^\infty x^n[/tex]

Differentiating both sides gives

[tex]\displaystyle \frac1{(1-x)^2} = \sum_{n=0}^\infty nx^{n-1} = \sum_{n=0}^\infty (n+1)x^n[/tex]

and multiplying both sides by 8 gives the series for f(x) :

[tex]f(x)=\displaystyle \frac8{(1-x)^2} = \boxed{8\sum_{n=0}^\infty (n+1)x^n}[/tex]

and this converges over the same interval, |x| < 1, so that the radius of convergence is 1.

Answer:

Step-by-step explanation:

Answer:

3/8 x 5/8= 15/64

Step-by-step explanation:

Answer:

[tex]P(x=3)=0.2269[/tex]

Mean=2.1

Standard deviation=1.21

Step-by-step explanation:

We are given that

n=7

Probability of success, p=0.3

q=1-p=1-0.3=0.7

We have to find the probability of 3 success for the binomial experiment  and find the mean and standard deviation.

Binomial distribution formula

[tex]P(X=x)=nC_xp^{x}q^{n-x}[/tex]

Using the formula

[tex]P(x=3)=7C_3(0.3)^3(0.7)^{7-3}[/tex]

[tex]P(x=3)=7C_3(0.3)^3(0.7)^{4}[/tex]

[tex]P(x=3)=\frac{7!}{3!4!}(0.3)^3(0.7)^{4}[/tex]

[tex]P(x=3)=\frac{7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}(0.3)^{3}(0.7)^{4}[/tex]

Using the formula

[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]

[tex]P(x=3)=0.2269[/tex]

Now,

Mean, [tex]\mu=np=7\times 0.3=2.1[/tex]

Standard deviation, [tex]\sigma=\sqrt{np(1-p)}[/tex]

Standard deviation, [tex]\sigma=\sqrt{7\times 0.3\times 0.7}[/tex]

Standard deviation, [tex]\sigma=1.21[/tex]

Answer:

D

Step-by-step explanation:

It subtracts.

Answer:

so you need a khan academy account?

Answer:

B

Step-by-step explanation:

We want to find the value of:

[tex]\displaystyle |6-3i|[/tex]

Recall that given a complex number z in the form:

[tex]z=a+bi[/tex]

The absolute value of z will be given by:

[tex]\displaystyle |z| = \sqrt{a^2+b^2}[/tex]

We have the complex number:

[tex]6-3i[/tex]

Thus, a = 6 and b = -3.

Then its absolute value will be:

[tex]|6-3i|=\sqrt{(6)^2+(-3)^2}[/tex]

Evaluate:

[tex]\displaystyle |6-3i|= \sqrt{36+9}=\sqrt{45}=3\sqrt{5}[/tex]

Hence, our answer is B.

Answer:

y -2 = 0(x-1)

Step-by-step explanation:

Point slope form is

y -y1 = m(x-x1)  where m is the slope and (x1,y1) is a point on the line

y -2 = 0(x-1)

y-2 =0

Hi!

8 - 24 = -(24 - 8) = -16

Answer:

-16

Step-by-step explanation:

8-24=-16

Answer:

Function 

Step-by-step explanation:

) Domain is defined as the set of possible values of x where function is defined.

For domain, 

So, 

The value of x is define as 

The domain of the function is all real numbers except 

The range is defined as all the y values for every x.

So, The range of the function is all real numbers.

2) The general form of the cot function is 

Where, Period is 

On comparing, B=3

So, The period of the given function is 

3) Vertical asymptote is defined as the line which approaches to infinity but never touches the line.

The vertical asymptote is at  where function is not defined.

The two vertical asymptote is

Put n=0,

Put n=1,

So, The two vertical asymptote are 

Answer:

B.)

Step-by-step explanation:

took test

Answer:

y+10=2

y=-8

Step-by-step explanation:

y=2-10

y=-8

Answer:

h = 54.5

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin 35 = h/95

95 sin 35 = h

h=54.48976

Rounding to the nearest tenth

h = 54.5

Answer:

Step-by-step explanation:

[tex]sin 35/h = sin 90/95\\n=54.48976145\\54.5[/tex]

Answer:

15

Step-by-step explanation:

By order of operations, multiplication and division are done first, then the addition and subtraction. Remember, multiplication and division have the same precedence, as does addition and subtraction.

21*6 = 126

126/7 = 18

18 + 12 = 30

30 - 15 = 15

Answer:

15

Step-by-step explanation:

21 × 6 ÷ 7 + 12 - 15​

= 126 ÷ 7 + 12 - 15

= 18 + 12 - 15

= 30 - 15

= 15

hich theorem accurately completes Reason A

Answer:

Step-by-step explanation:

g(5) = 2 > 0

:::::

g(x) = 0 for x = -2, 2, 4

:::::

g(x) < 0 for  -3 ≤ x < -2

Answer:i need this too lol

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

124 * 11 = 1364

1364 + 328 = 1,692