Two forces act at a point in the plane. the angles between the two forces are given. fidn the magnitude of the resultant force

By expanding and simplifying the algebraic expression (y + 7)(y - 5), we have the result y² + 2y - 35

To expand an algebraic expression in brackets, we need to use the distributive property to make is easy for simplification, thus we expand and simplify the expression as follows:

(y + 7)(y - 5) = y(y - 5) + 7(y - 5) {distributive property}

(y + 7)(y - 5) = y² - 5y + 7y - 35

by simplification, we have;

(y + 7)(y - 5) = y² + 2y - 35

Therefore, the expansion and simplification of the algebraic expression (y + 7)(y - 5), gives the result y² + 2y - 35.

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Answer:

112 yards

Step-by-step explanation:

The center of the Ferris wheel is 61 yards above the ground and the radius is 51 yards. When Jack is at the 9 o'clock position, he is at a distance of 112 yards from the center of the Ferris wheel (51 yards from the center plus 61 yards above the ground). Let θ be the angle that Jack has swept out measured from the 9 o'clock position, in radians.

The function g that represents Jack's vertical distance above the ground in yards in terms of the angle θ is:

g(θ) = 61 + 51sin(θ)

where sin(θ) represents the vertical component of the distance Jack has traveled.

Note that when θ = 0, sin(θ) = 0, which means Jack is at the very top of the Ferris wheel, 112 yards above the ground. When θ = π/2, sin(θ) = 1, which means Jack is at the 12 o'clock position, 112 + 51 = 163 yards above the ground. Similarly, when θ = π, sin(θ) = 0, which means Jack is at the very bottom of the Ferris wheel, 112 yards above the ground.

The only graph that represents a function is: Graph D

A function is defined as a relationship or expression that involves one or more variables. It typically has a set of input and outputs.  Each input has only one output. The function is the description of how the inputs relate to the output.

A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.

From the graphs, we can see that:

Graph A has 2 outputs at x = -2

Graph B has 2 outputs at x = 0

Graph C has two outputs at x = -1

Graph D has a unique output for every input and as such it is a function

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Let's start by finding how many bags of lemons Rachel used on Monday. We know she used a whole number of bags plus a fraction, so we'll need to convert the mixed number to an improper fraction:

1 2/5 = 7/5

So Rachel used 7/5 bags of lemons on Monday.

On Tuesday, Rachel used 1 1/4 times as many lemons as on Monday. To find out how many bags of lemons that is, we can multiply the amount Rachel used on Monday by 1 1/4:

1 1/4 = 5/4

5/4 times 7/5 = 35/20 = 7/4

So Rachel used 7/4 bags of lemons on Tuesday, which is the same as 1 3/4 bags of lemons.

Therefore, Rachel used 1 3/4 bags of lemons on Tuesday.

Answer:250

Step-by-step explanation:

I think they just want you to multiply the 25 and the 10 (radius squared times the height)

Answer:

  58.85°

Step-by-step explanation:

You want to know the measure of the angle in the right triangle that has hypotenuse 29 and adjacent side 15.

The cosine function relates angles and sides by ...

  Cos = Adjacent/Hypotenuse

  cos(x) = 15/29

The inverse function is used to find the angle value:

  x = arccos(15/29) ≈ 58.85°

The value of x is about 58.85°.

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Probability of answering exactly 4 questions correctly = 0.206

P (More than 2) = 0.475

1.

ind P(4): Probability of answering exactly 4 questions correctly.

P(X=4) = (10C4) * (0.25^4) * (0.75^6)

10C4 = 10! / (4! * (10-4)!) = 210

P(X=4) = 210 * (0.25^4) * (0.75^6)

= 0.206

P(X=0) = (10C0) * (0.25^0) * (0.75^10) ≈ 0.056

P(X=1) = (10C1) * (0.25^1) * (0.75^9) ≈ 0.187

P(X=2) = (10C2) * (0.25^2) * (0.75^8) ≈ 0.282

Now, calculate P(X>2):

P(X>2)

= 1 - (P(X=0) + P(X=1) + P(X=2))

= 1 - (0.056 + 0.187 + 0.282)

= 1 - 0.525

= 0.475

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The minimum height of the second beaker must be approximately 13.5 inches to hold the solution without overflowing.

Now, For the minimum height of the second beaker, we need to find its volume first.

The volume of the first beaker is given by;

⇒ V₁ = πr₁²h₁

where r₁ is the radius and h₁ is the height.

Substituting the given values, we get:

V₁ = π(1.8)²(4.6)

V₁ ≈ 66.85 cubic inches

Since, the first beaker is filled to the top, its volume equals the volume of the solution.

Therefore, the volume of the solution is also 66.85 cubic inches.

To find the minimum height of the second beaker, we need to use the formula for the volume of a cylinder:

V₂ = πr₂²h₂

where r₂ is the radius and h₂ is the height of the second beaker.

We want to find h₂ such that V₂ is equal to 66.85 cubic inches.

Dividing both sides of the equation by πr₂², we get:

h₂ = V₂ / (πr₂²)

Substituting the given value for r₂, we get:

h₂ = 66.85 / (π(1.25)²)

h₂ ≈ 13.5 inches

Therefore, the minimum height of the second beaker must be approximately 13.5 inches to hold the solution without overflowing.

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The measure of the third outgoing current will be 0.5 amperes.

We know that,

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing currents measure 0.8 amps and 0.55 amps.

Then the measure of the third outgoing current will be

We know that the sum of the incoming current will be equal to the sum of the outgoing current at a junction.

Let the incoming current be I₁, I₂, and I₃. And the outgoing current is I₄, I₅, and I₆.

Then we have

I₁ + I₂ + I₃ = I₄ + I₅ + I₆

0.7 + 0.68 + 0.47 = 0.8 + 0.55 + I₆

1.85 = 1.35 + I₆

I₆ = 0.5

Thus, the measure of the third outgoing current will be 0.5 amperes.

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complete question:

The three incoming currents at a node in an electrical circuit measure 0.7 amps, 0.68 amps, and 0.47 amps two of the three outgoing current measure 0.8 amps and 0.55 amps find the measure of the third outgoing current

The percentage of Dinesh’s time spent on Project X is 36.90%.

We have,

From the table,

The total time spent on the X-project each week is given as:

= 23(1/3) + 16(1/3) + 9.33 + 4.20

= 23.33 + 16.33 + 9.33 + 4.20

= 53.19

This is the time spent on X-project for the month.

Now,

The total time spent on all the events in the table.

= 144.13

The percent of Dinesh’s time spent on Project X.

= 53.19/144.13 x 100

= 36.90%

Thus,

The percentage of Dinesh’s time spent on Project X is 36.90%.

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length LD = 6 units

length DF = 9 units

length HF = 6 units

length LH = 9 units

length L'D' = 2 units

length D'F' = 3 units

length H'F' = 2 units

length L'H' = 3 units

Dilation is the scaling of an object, where it gets bigger or smaller.

Scale factor = new dimension/old dimension

length LD = 15-9 = 6units

length DF = 6-(-3) = 9units

length HF = 15-9 = 6 units

length LH = 6-(-3) = 9 units

Since the scale factor is 1/3, we divide the preimage dimension by 3 to get the dimensions of the new image.

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Answer:0.98

2.17 are correct

Step-by-step explanation:

-u^2 - 4u + 4 = 0

Multiplying both sides by -1, we get:

u^2 + 4u - 4 = 0

Now we can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 4, and c = -4. Substituting these values, we get:

u = (-4 ± sqrt(4^2 - 4(1)(-4))) / 2(1)

u = (-4 ± sqrt(32)) / 2

u = (-4 ± 4sqrt(2)) / 2

u = -2 ± 2sqrt(2)

Therefore, either:

Based on the information, HH is a subset of Ha, which is a subset of aH, which is a subset of H, which is a subset of HH

It should be noted that to demonstrate this theory, we must show that each of these collections are components of the others and consequently all are equivalent.

At first, let's evaluate HH. As H is a subgroup of G, it is dependent on multiplication so for any two elements h1, h2 in H, the product h1h2 is also in H. Thus, every entity within HH can be expressed as the aggregate of h1h2 for certain elements h1, h2 from H. Since H is a subgroup, it is also subject to inverse property, so h2^-1h1^-1 remains inside H. Clearly, h1h2 thus translates to h'(h2^-1h1^-1)h'', where h', h'' are members of H.

This illustrates that every component of HH can be presented as h'h'' for a pair of h', h'' which exist in H, therefore approximating with accuracy the definition of H. Thus, we have demonstrated that HH is part of H.

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The correct option is D, the equation has two complex solutions.

Here we can see that we have the graph of a quadratic equation.

It opens upwards, and we can see that it has a vertex at (1, 4), which intercepts the y-axis at y = 5.

Now, we say that the solutions of a quadratic are the values of x such that the function becomes zero.

Particualrly, in this graph we can see that the graph never intercepts the x-axis, that means that this equation has no real roots.

Then the correct option is:

"Function f has exactly two complex solutions."

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The required mean will increase to about 12.6 when another student of age 15 joins the class, and the correct answer is C.

The original mean is the sum of the ages divided by the number of students:

Mean = (10 + 10 + 11 + 12 + 12 + 13 + 13 + 14 + 14 + 15) / 10

Mean = 124 / 10

Mean = 12.4

If another student of age 15 joins the class, the new sum of the ages is:

Sum = 10 + 10 + 11 + 12 + 12 + 13 + 13 + 14 + 14 + 15 + 15

Sum = 139

The new mean is the new sum of ages divided by the new number of students:

New mean = Sum / (Number of students + 1)

New mean = 139 / 11

New mean = 12.63636... or about 12.6 (rounded to one decimal place)

Therefore, the mean will increase to about 12.6 when another student of age 15 joins the class, and the correct answer is C.

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Answer: He would be spending $15.25 for each person including himself

Step-by-step explanation:

step 1. you need to find out how many people are getting food

step 2. divide that number (5) by how much the total cost is ($76.25) to get 15.25

False. When Jane turns left 40 degrees and walks 60 meters, she is farther away from her starting position than when she crossed the finish line.

If Jane turns left 90 degrees or 120 degrees, then she will also be farther away from her starting position than when she crossed the finish line. Turning left 90 degrees or 120 degrees will take her in a different direction, and thus she will be farther away from her starting position than when she crossed the finish line.

Therefore, the given statement is false.

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Answer:

(x²)³ - 1 = x^6 - 1

Step-by-step explanation:

To find (gof)(x), we first need to evaluate g(x), which is x², and then use the result as input to f(x), giving us f(g(x)).

So, we have:

g(x) = x²

f(g(x)) = f(x²) = (x²)³ - 1 = x^6 - 1

Therefore, (gof)(x) = g(f(x)) = (f(x))² = (x³ - 1)² = x^6 - 2x^3 + 1.

To find (fog)(x), we first need to evaluate f(x), which is x³ - 1, and then use the result as input to g(x), giving us g(f(x)).

So, we have:

f(x) = x³ - 1

g(f(x)) = g(x³ - 1) = (x³ - 1)² = x^6 - 2x^3 + 1

Therefore, (fog)(x) = f(g(x)) = (x²)³ - 1 = x^6 - 1.

Answer:

B.

Step-by-step explanation:

We can use the given formula to find the time it takes for the rocket to reach a height of 10 feet:

10 = -16t^2 + 22t + 6

Rewriting the equation in standard quadratic form:

16t^2 - 22t + 4 = 0

Using the quadratic formula:

t = (22 ± sqrt(22^2 - 4(16)(4)))/(2(16))

t = (22 ± sqrt(36))/32

t = 3/4 or 1/4

Since the rocket reaches a height of 10 feet at two different times (3/4 and 1/4 seconds), it must pass through that height twice during its flight. Therefore, the rocket will reach a height of 10 feet. The correct answer is B.

The sine of angle B is obtained dividing the length of the opposite side to angle B by the length of the hypotenuse.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined on the bullet points below:

The problem is incomplete, hence the general procedure to obtain the sine of angle B is presented.

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Answer:

  3013.5 cm³

Step-by-step explanation:

Given a ball with a circumference of 56.3 cm, you want to know its volume.

The formula for circumference is ...

  C = 2πr

Solving for radius, we get ...

  r = C/(2π) = 56.3 cm/(2π) ≈ 8.96042 cm

The volume of a sphere is given by ...

  V = 4/3πr³

  V = 4/3π(8.96042 cm)³ ≈ 3013.5 cm³

The ball's volume is about 3013.5 cubic centimeters.

__

Additional comment

Alternatively, we could use the formula ...

  V = C³/(6π²)

to get the same result.

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Answer: The point that satisfies the equation is E. (-3, -4).

Explanation:

To determine which point lies on the circle represented by the equation (x − 3)² + (y + 4)² = 6², we can substitute the coordinates of each point into the equation and see which one satisfies the equation.

A. (9, -2): (9 − 3)² + (-2 + 4)² = 6²

(6)² + (2)² = 36

36 + 4 = 40 ≠ 36

B. (0, 11): (0 − 3)² + (11 + 4)² = 6²

(-3)² + (15)² = 36

9 + 225 = 234 ≠ 36

C. (3, 10): (3 − 3)² + (10 + 4)² = 6²

(0)² + (14)² = 36

0 + 196 = 196 ≠ 36

D. (-9, 4): (-9 − 3)² + (4 + 4)² = 6²

(-12)² + (8)² = 36

144 + 64 = 208 ≠ 36

E. (-3, -4): (-3 − 3)² + (-4 + 4)² = 6²

(-6)² + (0)² = 36

36 + 0 = 36

The point that satisfies the equation is E. (-3, -4).

The measure of the missing dimension is 8 meters.

We are given that;

Volume= 2288 cubic meters

Height= 13meter

Length= 22meter

Now,

To find the width.

You can rearrange the formula to solve for width by dividing both sides by length and height:

Width = Volume / (length × height)

Plug in the given values:

Width = 2288 / (22 × 13)

Simplify:

Width = 2288 / 286

Width = 8

Therefore, by the given rectangular prism the answer will be 8 meters.

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The equation of smallest degree with integer coefficients will be f(x) = x^2 - (3 + √7)x + 3√7

It should be noted that to begin, let us establish the following:

x = √(8 - 1) which is equal to √7.

y = √(8 + 1) which is equivalent to √9. Therefore, y equals 3.

For the value of x, its conjugate coincides with √7; hence:

(x - x') × (x - y') = (x - √7)(x - 3)

Equation expansion yields:

f(x) = x^2 - (3 + √7)x + 3√7

By substituting for both values x and y in the equation above, we can show that f(x) satisfies the given specifications:

When x takes on a value of √7:

f(√7) = (√7)^2 - (3 + √7)√7 + 3√7 = 7 - 7 = 0

With an input value of 3:

f(3) = 3^2 - (3 + √7)(3) + 3√7 = 9 - 9 - 3√7 + 3√7 = 0

The lowest degree polynomial with rational coefficients having √(8 - 1) and √(8 + 1) as its roots is: f(x) = x^2 - (3 + √7)x + 3√7

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The required exact value of tan(5π/12) is (2 + √3) / 3.

We can use the half-angle identity for a tangent:

tan(x/2) = [1 - cos(x)] / sin(x)

to find the exact value of tan(5π/12), since 5π/12 is a half-angle of 5π/6.

First, we find the values of sin(5π/6) and cos(5π/6) using the unit circle:

sin(5π/6) = sin(π - π/6) = sin(π/6) = 1/2

cos(5π/6) = cos(π - π/6) = -cos(π/6) = -√3/2

Now we can use the half-angle identity for a tangent with x=5π/6:

tan(5π/12) = tan[(5π/6)/2] = [1 - cos(5π/6)] / sin(5π/6)

                = [1 - (-√3/2)] / (1/2)

               = (2 + √3) / 3

Therefore, the exact value of tan(5π/12) is (2 + √3) / 3.

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