Find all solutions to the equation in the interval [0, 2π). (3 points) cos 4x - cos 2x = 0 0, two pi divided by three. , four pi divided by three. pi divided by six , pi divided by two , five pi divided by six , seven pi divided by six , three pi divided by two , eleven pi divided by six 0, pi divided by three. , two pi divided by three. , π, four pi divided by three. , five pi divided by three. No solution

The probability that the next marble Kerry selects will be white is; D: 63%

The results of Kerry randomly selecting one marble from the bag out of 65 selections are;

Now, these numbers of marbles represents the amount of times the respective colors are gotten for every 65 selections. Thus;

P(next marble that Kerry selects will be white) = 41/65 * 100

P(next marble that Kerry selects will be white) ≈ 63%

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Answer:

1; solution is not extraneous

Step-by-step explanation:

the value 3=3 is true, meaning its not extraneous and also I got it correct on the test

The value of x is 1, and the solution is not extraneous.

Given that,

Equation; [tex]\sqrt{3x+6 } = 3[/tex]

We have to determine,

The value of x and identify if it is an extraneous solution.

According to the question,

Equation; [tex]\sqrt{3x+6 } = 3[/tex]

To find the value of the x following all the steps given below.

Squaring both the sides to solve the equation,

[tex]\sqrt{3x+6 } = 3\\\\(\sqrt{3x + 6 })^2= 3^2\\\\3x + 6 = 9\\\\3x = 9-6\\\\3x = 3\\\\x = \dfrac{1}{1}\\\\x = 1[/tex]

An extraneous solution is a root of a transformed equation that is not a root of the original equation.

Therefore, The solution is not extraneous.

Hence, The value of x is 1, and the solution is not extraneous.

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Answer:

8 and 23

Step-by-step explanation:

let the 1st equation be i and 2nd be ii

now putting the value of x in eqn ii, we get

12x -4×(3x-1) = 12

12x-12x+4=12

x=12-4

x=8

again,

y=3×8-1

y=23

Answer: the vertical line with the equation "x=-2"

Step-by-step explanation:

if you are perpendicular to the x axis, you will be looking for vertical lines that pass through (-2,-4)

the vertical line with the equation "x=-2" will pass though the point because (-2,-4) has an x coordinate of -2

Answer:

Its isosceles, so the the 2 sides other than st are equal. 2x+6=3x-6

Moves to one side. 12=x

x=12

Step-by-step explanation:

x=12

Step-by-step explanation:

You know that angles T and S are equal, meaning the lengths of the lines TV and SV are also equal. That means 2x+6=3x-6. You transfer the xs and get 6=x-6. You undo the negative 6, receiving 12=x.

Answer: 18 units

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

6 times 2 = 12

12+6=18

Answer:

p=1, q=5. (1, 5).

Step-by-step explanation:

8p+7q=43

2p-7=-q

------------------

q=-2p+7=7-2p

8p+7(7-2p)=43

8p+49-14p=43

8p-14p=43-49

-6p=-6

6p=6

p=6/6=1

2(1)-7=-q

2-7=-5=-q

q=5

Initially I had 48 tokens initially

Given that , For every 8 tokens you have your friend has 3

Then, let us assume that, we have 8n tokens. Then our friend will have 3n tokens

After you give half of your tokens to your friend Your friend now has 18 more tokens than you.  

We have to find how many tokens did you start with

Now, after giving away half of tokens we will have 8n/2 = 4n tokens

And our friend will have 4n + 3n = 7n tokens.

And according to given information

Friends tokens – my tokens = 18 tokens

7n – 4n = 18  

3n = 18  

n = 6

Then, I will have initially 8n = 8 x 6 = 48 tokens.

Hence, I had 48 tokens initially

Answer:

Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost for her pharmacy.

Step-by-step explanation:

Nancy counts 10 boxes of travoprost and the pharmacy needs 15 boxes to maintain a minimal level in the stock.

So, there is a need to order (15 - 10) = 5 boxes of travoprost.

Again, Nancy counts 3 boxes of latanoprost and the pharmacy needs to 12 boxes.  

So, there is a need to order (12 - 3) = 9 boxes of latanoprost.

Therefore, Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost for her pharmacy. (Answer)

Final answer:

Nancy needs to order 5 boxes of travoprost and 9 boxes of latanoprost to fulfill the pharmacy's minimal stock requirement.

Explanation:

Nancy needs to order more boxes of eye medication to meet the pharmacy's minimal stock levels. For travoprost, the pharmacy requires 15 boxes but currently has only 10 boxes. So, Nancy needs to order:

15 boxes (required amount) - 10 boxes (current amount) = 5 boxes of travoprost.

For latanoprost, the pharmacy needs 12 boxes, but only has 3 boxes in stock, meaning Nancy needs to order:

12 boxes (required amount) - 3 boxes (current amount) = 9 boxes of latanoprost.

Answer:

Step-by-step explanation:

1) 15%=15/100=3/20

2) 36%=36/100=9/25

3) 44%=44/100=11/25

4) 45%=45/100=9/20

5) 8%=8/100=2/25

6) 60%=60/100=6/10=3/5

Answer:

9

Step-by-step explanation:

The value of c is found by adding a (2) and b (7) together, which equals 9.

The question a + b = c is asking for the value of c when a is 2 and b is 7. To find c, we simply add the values of a and b together. In mathematics, this is known as solving for the unknown variable.

In this case:

a + b = c
2 + 7 = c
c = 9

Therefore, the value of c when a is 2 and b is 7 is 9.

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x = 1240-y can be used to model the situation where x is the amount earned in second week.

Step-by-step explanation:

Given,

Total amount earned = D =  $1240

Amount earned in first week = y = $480

Let,

x be the amount earned in second week.

Therefore,

Total amount earned = Amount earned in 1st week + 2nd week amount

D = x + y

1240 = x + y

Solving for x;

[tex]x= 1240- y [/tex]

x = 1240-y can be used to model the situation where x is the amount earned in second week.

Keywords: linear equation, subtraction

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Answer:

24.3

Step-by-step explanation:

Answer:

B. 1/2n - 3

Step-by-step explanation:

One way to get half a number is to multiply it by 1/2.

The phrase "a number less than an other number" often indicates subtraction.

[tex]\frac{1}{2}n-3[/tex]

Answer:1/2n-3

Step-by-step explanation:

because three less than half of a number means half minus three

Answer:

6

Step-by-step explanation:

Split the numerator/ denominator into like factors, that is

= [tex]\frac{72}{12}[/tex] × [tex]\frac{x^2}{x^2}[/tex] ← cancel to give 1

= 6 × 1

= 6

Answer:

Explanation:

The figure attached represents the situation.

The triangle on the left and the triangle on the right are similar triangles because they are right triangles and the marked angles are congruent.

The distance between the mirror and the basketball goal is represented by the unknown x.

By similarity:

Solving:

Thus, the mirror is 20/3 of feet, which is about 6.7 feet, from the basketball goal.

Answer:

(0,2)

Step-by-step explanation:

y-intercept: when x = 0

-3(0) + 12y = 24

12y = 24

y = 2

Answer:

W

Step-by-step explanation:

If its the graphs I got then yeah

The Graph that represents the inverse of function f is attached below.

Function is a type of relation, or rule, that maps one input to specific single output.

We have been given a function of x as; f(x) = 2x - 2

If function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

y = 2x - 2

x = 2y - 2

x + 2 = 2y

y = (x + 2)/2

It simply means, inverse of 'f' is undo operator, that takes back the effect of 'f' function here.

To Graph the inverse, Simply use a graphing calculator and the correct graph is attached below.

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Answer:

gl hf

Step-by-step explanation:

Answer:

ab² - b = b(ab -1)

Step-by-step explanation:

The variable b is common to both terms here.  Thus,

ab² - b = b(ab -1)

[tex](f o g)(x) = 245x^2+6\\(g o f)(x) = 5x^2+42\\ f(g(-4)) = 3926\\g(f(5)) = 917[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 5x^2+6\\g(x) = 7x[/tex]

So

[tex](f o g)(x) = 5(7x)^2+6\\= 5(49x^2)+6\\=245x^2+6\\(g o f)(x) = 7(5x^2+6)\\= 35x^2+42\\(fog(x))=245x^2+6f(g(-4)) = 245(-4)^2+6 \\=245(16)+6\\=3920+6\\=3926\\g(f(x)) = 35x^2+42\\g(f(5)) = 35(5)^2+42\\=35(25)+42\\=875+42\\=917[/tex]

Hence,

[tex](f o g)(x) = 245x^2+6\\(g o f)(x) = 5x^2+42\\ f(g(-4)) = 3926\\g(f(5)) = 917[/tex]

Keywords: functions, Function composition

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Answer:

The ratio of consonants to is 4:3. 4 consonants and 3 wolves.

Total amount of funds is $44.26 million.

Step-by-step explanation:

Given,

Donation received = $23.9 million

As it represents 54% of charity.

Let,

Total amount = x

Therefore,

54% of x = 23.9 million

[tex]\frac{54}{100}*x=23.9\\0.54x=23.9[/tex]

Dividing both sides by 0.54

[tex]\frac{0.54x}{0.54}=\frac{23.9}{0.54}\\x=\$44.26\ millions[/tex]

Total amount of funds is $44.26 million.

Keywords: percentage, division

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Answer:

C) 6(4m-n)

Step-by-step explanation:

Because 6(4m-n)=24m-6n.

Answer:

-4

Step-by-step explanation:

You can tell because every time the slope decreases by 5.

Answer:

-4

Step-by-step explanation:

Take the first two sets of points (-4,-2) and (-2,-10)

Then use the formula  Y2 - Y1 / X2 - X1  to find the slope

-10 + 2 / -2 + 4 = -8/2 which can be reduced to -4

Answer:

B

Step-by-step explanation

Answer:

Option B. a = −5, b = −9, c = 12

Step-by-step explanation:

The general form of the quadratic equation is as following

ax² + bx + c = 0

Where a, b and c are constants.

And the given equation is −5x2 − 9x + 12 = 0

Comparing the given equation to the general form

  ax² + bx + c = 0

−5x2 − 9x + 12 = 0

So, a = -5  , b = -9  and   c = 12

Identifying the values a, b, and c is the first step in using the Quadratic Formula to find solution(s) to a quadratic equation.

So, the answer is option B: a = −5, b = −9, c = 12

Answer:

361 sq, inches.

Step-by-step explanation:

Let us assume that the dimensions of the square picture are P in × P in.

So, the area of the picture alone is, A = P²

Now, if the photo has a frame of 1 inch wide, then the dimensions of the photo with frame are (P + 2) in × (P + 2) in.

So, the area of the photo with frame is A' = (P + 2)(P + 2) = (P + 2)²

Now, the area of the frame alone is 80 sq. inches.

Hence, A' - A = 80

⇒ (P + 2)² - P² = 80

⇒ 4P + 4 = 80

⇒ 4P = 76

⇒ P = 19 inches.

So, the area of the picture is = 19² = 361 sq. inches. (Answer)

361 sq, inches.

Step-by-step explanation: