If cos(x)= 2/3 and x is in quadrant I, then find exact values for (without solving for x): sin(2x) cos(2x) and tan(2x)

Answer:

X+1>12/3

X+1>4

X>4-1

X>3

let's go like the crab, go backwards, start at the last

if you don't have a Unit Circle, this is a good time to get one, there are many online.

Check the picture below.

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{6}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +6}{2}~~~ ,~~~ \cfrac{ y +7}{2} \right) ~~ = ~~\stackrel{midpoint}{(-5~~,~~-5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +6}{2}=-5\implies x+6=-10\implies \boxed{x=-16} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +7}{2}=-5\implies y+7=-10\implies \boxed{y=-17}[/tex]

A) x+2y=30

x=30-2y

B) x=8, y=11 and the solutions x and y represent the prices of tickets for students and non students.

An equation in French is defined as having one or more variables, whereas an equation in English is any well-formed formula consisting of two expressions combined with an equals sign.

Solving a variable equation includes determining which variables' values result in equality. Unknowns are the variables for which the equation must be solved, while equation solutions are the unknown values that satisfy the equality. An equation is a mathematical phrase with two equal sides separated by an equal sign. An equation is 4 + 6 = 10. We can see 4 + 6 on the left side of the equal sign and 10 on the right.

Given equations are:

2x + 3y = 49

x + 2y = 30

A) From eq 2,

x+2y=30

x=30-2y

B) x and y represents the prices of tickets for students and non students.

2(30-y)+3y=49

60-4y+3y=49

y=60-49

y=11

x=30-2y

x=30-2(11)

x=30-22

x=8

The solutions x and y represent the prices of tickets for students and non students.

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Part A: Probability that one of 400-page novels will have exactly one error-free page is 24.06%.

Part B.) No more than three pages contain errors: 40.06%.

The given data in the question-

The following is the probability mass function (PMF) for X:

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

Part A.) One of 400-page novels will have exactly one error-free page.

P(x = 1)  = ⁿCₓ . pˣ . qⁿ⁻ˣ

n = 400, x = 1

P(x = 1)  = ¹⁰⁰C₁ . (0.005)¹ . (0.995)¹⁰⁰ ⁻ ¹

P(x = 1)  =  0.2706

Thus,  probability that one of 400-page novels will have exactly one error-free page is 24.06%.

Part B.) No more than three pages contain errors.

P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)

P(x = 0)  = ¹⁰⁰C₀ . (0.005)⁰ . (0.995)¹⁰⁰ ⁻ ⁰

P(x = 0)  = 0.01346

P(x = 1)  = ¹⁰⁰C₁ . (0.005)¹ . (0.995)¹⁰⁰ ⁻ ¹

P(x = 1)  = 0.0270

P(x = 2)  = ¹⁰⁰C₂ . (0.005)² . (0.995)¹⁰⁰ ⁻ ²

P(x = 2)  = 0.00068

P(x = 3)  = ¹⁰⁰C₃ . (0.005)³ . (0.995)¹⁰⁰ ⁻ ³

P(x = 3)  = 0.0000027

Thus, P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)

P(x ≤ 3) =  0.01346 + 0.00068 + 0.00068 + 0.0000027

P(x ≤ 3) =  0.4060021

Consequently, the likelihood of at maximum three pages having typographical errors is 40.06%.

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Answer:

C.)

Step-by-step explanation:

1.) Since she does 8 vases in 2 hours, she would do 4 vases in 1 hour.

2.) By using this, we divide 50/4 to figure out the amount of hours. This is equal to 25/2, which is equal to 12.5.

3.) Now, check the options. C.) fits this situation the best. Therefore, C.) is the answer.

Answer:

a = b

b = a

Step-by-step explanation:

y=3

x=11

hence answer 25

3x+5y=48

2x-y=19

eliminate x to find y

(3x+5y=48)2

(2x-y=19)3

(6x + 10y. = 96)

- minus direct

(6x - 3y. = 57)

=

13y = 39

Note: (10y -(-3y)=13y)

divide by 13 to remain with y

y =3

substitute to any equation to get x lets pick second one

2x-(3)=19

2x-3=19

2x=19+3

2x/2=22/2. (to remain with x value)

x=11

therefore 2x+ y results to 2(11) +3=25

Answer:

2x + y = 25

Step-by-step explanation:

Given equations:

[tex]\begin{cases} 3x + 5y = 48\\\;\;2x-y=19\end{cases}[/tex]

Rearrange the second equation to isolate y:

[tex]\implies 2x-y=19[/tex]

[tex]\implies 2x-19=y[/tex]

Substitute the found expression for y into the first equation and solve for x:

[tex]\implies 3x+5y=48[/tex]

[tex]\implies 3x+5(2x-19)=48[/tex]

[tex]\implies 3x+10x-95=48[/tex]

[tex]\implies 13x=143[/tex]

[tex]\implies x=11[/tex]

Substitute the found value of x into the equation for y and solve for y:

[tex]\implies y=2x-19[/tex]

[tex]\implies y=2(11)-19[/tex]

[tex]\implies y=22-19[/tex]

[tex]\implies y=3[/tex]

Therefore, the solution of the given system of equations is:

To find the value of 2x + y, substitute the found values of x and y into the expression and solve:

[tex]\begin{aligned}\implies 2x+y&=2(11)+3\\&=22+3\\&=25\end{aligned}[/tex]

Therefore:

Answer:

f(1)=10

g(3)=2

f(1)+g(3)=12

f(10)-g(0)=104

Step-by-step explanation:

f(x)=10x

g(x)=2x-4

f(1)=10×1=10

g(3)=2×3-4=2

f(1)+g(3)=10+2=12

f(10)-g(0)=(10×10)-(2×0-4)=100+4=104

Answer:

28

Step-by-step explanation:

hope this helps if its wrong really sorry

The sequence of transformations that show figure A and figure B are congruent is: Translate figure A 4 units right and then reflect the image across the x-axis.

Translation refers to a type of transformation that involve a straight line movement.

Movements as seen in translation includes

The left and right movements are on the horizontal direction controlled by the x coordinate.

The object moved 4 units right then reflected over the x axis to have the mirror image below the x axis

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Answer:

k = 7

Step-by-step explanation:

given y varies jointly with x and w then the equation relating them is

y = kxw ← k is the constant of variation

to find k use the condition when y = - 42, x = 2 and w = - 3 , then

- 42 = k × 2 × - 3

- 42 = - 6k ( divide both sides by - 6 )

7 = k

constant of variation is k = 7

Answer:

7

Step-by-step explanation:

seven is the value e you would get

Answer:

2196 fish

Step-by-step explanation:

:)

Answer:

2196 fish

Step-by-step explanation:

your welcome

f\mathopen{}\mathclose{\left(6\right)}f(6)​ = (6-6)(something) + 22​ = 0(something) + 22​ = 22 which has a remainder of 22 when divided by x-6x-6​. f\mathopen{}\mathclose{\left(6\right)}f(6)​ = \boxed{22}.

The remainder theorem states that when a polynomial is divided by a linear term, the remainder equals the value of the polynomial at the root of the linear term. This theorem may be used to determine the roots of a polynomial by dividing it by a linear term and solving for the remainder. For instance, when the polynomial x3+x2-5x+6 is divided by (x2), the result is identical to the polynomial's value at x=2. After finding the remainder, we may determine that the polynomial's root is 2, which we can do by solving for the remainder. This theorem may also be used to discover the roots of higher degree polynomials by combining linear terms.

How to solve?

f\mathopen{}\mathclose{\left(x\right)}f(x)​ can be written as (x-6)(something) + 22​.  

f\mathopen{}\mathclose{\left(6\right)}f(6)​ = (6-6)(something) + 22​ = 0(something) + 22​ = 22​.

Therefore, f\mathopen{}\mathclose{\left(6\right)}f(6)​ = \boxed{22}.

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Answer: No solution

Step-by-step explanation:

[tex]\sqrt{x-3}=\sqrt{x} +3\\[/tex]

square both sides

x-3=x+9

x=x+12

0=12

0 does not equal 12, and therefor, there is no solution.

Answer:

Step-by-step explanation:

im not in 100th grade yet

Answer:

y = 2x - 4

Step-by-step explanation:

(3, 2) (1, -2)

m = y2-y1 / x2-x1

m = -2-2 / 1-3

m = -4/-2

m = 2/1

m = 2

y = 2x + b

2 = 2(3) + b

2 = 6 + b

b = -4

y = 2x - 4

Could you please give me brainliest for this? Thank you!

The side lengths of the triangle are 89 ft, 132 ft and 159 ft

The given parameters are

Angle, A = 34 degrees

Hypotenuse = 159 ft

The length BC is calculated as

sin(A) = BC/Hypotenuse

So, we have

BC = Hypotenuse * sin(A)

This gives

BC = 159 * sin(34 degrees)

Evaluate

BC = 89 ft

The length AC is calculated as

cos(A) = AC/Hypotenuse

So, we have

AC = Hypotenuse * cos(A)

This gives

AC = 159 * cos(34 degrees)

Evaluate

AC = 132 ft

Here, we have

Angle, A = 34 degrees

Because the triangle is a right triangle, we have

Angle, C = 90 degrees

The sum of angles in a triangle is 180

So, we have

Angle B = 180 - 90 - 34

Angle B = 56

This is calculated as

Area = 0.5 * BC * AC

So, we have

Area = 0.5 * 89 * 132

Evaluate

Area = 5874

Hence, the area is 5874 square units

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The solution to probability problem is the expected value for a person that buys one ticket is -$2.32

Probability is a measure of the likelihood or chance that a specific event will occur, expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

According to the given information:

To find the expected value, you need to multiply each possible outcome by its probability and then add them together.

In this case, there are two possible outcomes: either the person wins the laptop computer (with a probability 1/1500), or they don't win anything (with a probability 1499/1500).

So, the expected value can be calculated as:

E(x) = (1/1500)($1000) + (1499/1500)(-$3)

E(x) = $0.67 - $2.99

E(x) = -$2.32

So the expected value for a person that buys one ticket is -$2.32.

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Answer:

On (3,7) and (-2,7)

Step-by-step explanation:

Check the picture below.

let's take a looksie at that, notice, if we split the circle into 6 even pieces, we end up with six 60° angles at the center, namely six equilateral triangles as you see there.

now, if we run a dashed line as you see from a corner to the other to make the flatter triangle which is shaded, we end up cutting the equilateral triangle into two equal halves, each with 30° and 30° angles, because the dashed line intercepts the green line at 90°.

well, the flatter triangle from corner to corner, is spanning over two equilateral triangles, if it's owning half of one, it must be also owning half of the other.  What the dickens does that mean?  well, it means the area of the flatter triangle that's shaded, is really the same area as a "whole" of one of those equilateral triangles.

so hmmm we have three of those flatter triangles shaded hmm, so let's simply get the area of three of those equilateral triangles and sum them up.

[tex]\textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4} ~~ \begin{cases} s=side\\[-0.5em] \hrulefill\\ s=12 \end{cases}\implies A=\cfrac{12^2\sqrt{3}}{4}\implies A=36\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\large area of the shaded region}}{36\sqrt{3}~~ + ~~36\sqrt{3}~~ + ~~36\sqrt{3}}\implies 108\sqrt{3}\qquad \approx\qquad \text{\LARGE 187.1}[/tex]

Answer:

Slope- y=1/4x-6

Y intercept= (0,-6)

Hope this helps!

Answer:

Step-by-step explanation:

P = 2(L + W)

P = 34

L = W + 5

34 = 2(W + 5 + W)

34 = 2(2W + 5)

34 = 4W + 10

34 - 10 = 4W

24 = 4W

24/4 = W

6 = W <=== 6 meters wide

L = W + 5

L = 6 + 5

L = 11 <=== 11 meters long

If we want to translate (aka move) [tex]f(x) = x^2[/tex] down 5 units, we need to subtract 5 from the [tex]x^2[/tex].

          [tex]g(x) = x^2-5[/tex]

The [tex]k[/tex] in the [tex]a(x-h)^2 +k[/tex] form will always be the vertical translation component.  If you translate up, [tex]k[/tex] is positive.  If you translate down, [tex]k[/tex] is negative.

Answer:

Option 2 —› (56 - 42) / 7 = 2

Step-by-step explanation:

First you use PEMDAS to check.

P- parentheses

E- Exponents

M- Multiplication (can be switched with D)

D- Division (can be switched for M)

A- Addition

S- Subtraction

Now you need to solve each problem.

Option 1: INCORRECT

(56 - 42) / 7 = 5

(14) / 7 = 5

2 = 5

Option 2: CORRECT

(56 - 42) / 7 = 2

(14) / 7 = 2

2 / 2

I'll do the rest, so you can see how to solve.

Option 3: INCORRECT

56 - (42 / 7) = 2

56 - 6 = 2

50 = 2

Option 4: INCORRECT

(56 - 7) / 42 = 5

(49) / 42 = 5

1 1/6 = 5

We can use both according to the given information.

• In 2 triangles if 2 sides of a triangle and 2 sides of another triangle are equal and if any one angle is equal to the angle in another triangle then we use SAS congruence rule

• In 2 triangles if 3 sides are equal to the 3 sides of another triangle then we use SSS congruence rule

• We can also use RHS (Right angle Hypotenuse Side). It is for 2 right angle triangle.

Answer: neither

Step-by-step explanation:

To get rid of the fractions, we pick a useful number and multiply both sides of the equation by that number. The number is useful if multiplying eliminates all fractions.