Please helppp ASAP pleaee

The length s of the circular arc is; 27π/4

The formula for length of arc is;

L = (θ/ 360) * (2πr)

where;

θ is central angle

r is radius

From the diagram, we see that;

θ = 3π/4

r = 9

Now, 360 degrees in radians is 2π. Thus;

L = (3π/4)/(2π) * 2π(9)

L = (3π/4) * 9

L = 27π/4

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We can identify the extraneous solutions by checking if the solutions found by solving the equation make the denominator of the fraction equal to zero.

A rational equation is an equation that contains a fraction with a polynomial in the numerator and denominator.

To solve a rational equation, you can use the following steps:

Clear the fraction by multiplying both sides of the equation by the denominator of the fraction.

Solve the resulting equation for the variable.

Check your solutions by plugging them back into the original equation and making sure they are valid solutions.

Identify extraneous solutions by checking if the solutions found by solving the equation make the denominator of the fraction equal to zero. If it does, then the solutions are extraneous and should be rejected.

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After the time out each person scored 15 baskets.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Desiree's score was 20 points, and his score was 10 points. Desiree wanted to make the game fairer, so she called a time-out and modified the rules a bit. Desiree explained that for the rest of the game, she would get 3 points per basket, and Nick would get 4 points per basket.

The two equations can be written as:-

3D + 20 = 4N + 10

3D - 4N = -10

D + N = 30

Solve the above equations:-

3D - 4N = -10

4D  + 4N = 120

____________

7D = 110

D = 15

Hence, the score for each person would be 15.

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The required scale factor between the building and toy model is given as 900.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
The area of the front side of the toy building is 1 square foot.
The real building's front side has an area of 900 square feet.
The real buildings as a dilation of the toy,
Scale factor = 900 /1
Scale factor = 900

Thus, the required scale factor between the building and the toy model is given as 900.

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= (4x - y)/3 - (x + y)/2

= (4x - 3x - y + y)/6

= (x - y)/6

Answer:

18x+y

Step-by-step explanation:

[tex]4x-\frac{y}{3} - x + \frac{y}{2} \\\6(4x-\frac{y}{3} - x + \frac{y}{2})\\24x-2y-6x+3y\\18x+y[/tex]

I have no idea but I think this is what you're looking for

The Equation is x + 80 + 70 = 180 and the measure of x is 30 degree.

Horizontal Angles (Vertically Opposite Angles) The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles.

Angles that are vertically opposed to one another are equal. These are referred to as vertical angles at times.

Given:

Since x and y are vertical angles, they are the same.

Now,  the equation to solve for x would be:

x + 80 + 70 = 180

Now, solving for x we get

x + 150 = 170

x= 180- 150

x= 30

Hence, the measure of x is 30.

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Hank has to complete the job if he works t alone by 1/12 hours.

1/t+7+1/t

=1 /12

Hank can paint a kitchen in the same amount of time in half the time it takes Liya. They can finish the same task in 12 hours if they work together.

Through multiplication by 12t(t+7),

all denominators become equal to 1, 12t + 12(t+7) = t(t+7), and

t2 = -17t -84 = 0.

(tossing out a negative solution for unit measure)

(t + 4) (t -21) = 0 (Henry's time)

Likewise,

calculating 1/28 + 1/21 = 1/12

and 49/(28 21) = 1/12

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Answer:

Step-by-step explanation:

area of a circle formula is πr²

Find area of the larger and smaller circles and then subtract to find the shaded region. π = 3.14

area of the larger circle = π (11.5)²

                                      3.14 (132.25)

                                      415.265 units²

area of the smaller circle = π (5.5)²

                                           3.14(30.25)

                                           94.985 units²

subtract:   415.265 - 94.985 = 320.28 units²

The derivative of logₐ x (log x with base a) is 1/(x ln a).

Here, the interesting thing is that we have "ln" in the derivative of "log x". Note that "ln" is called the natural logarithm (or) it is a logarithm with base "e". i.e., ln = logₑ.

Further, the derivative of log x is 1/(x ln 10) because the default base of log is 10 if there is no base written.

The derivative of log x (base 10) with respect to x is denoted by d/dx (log x) or (log x)'. Thus,

d/dx(logₐ x) (or) (logₐ x)' = 1/(x ln a)

d/dx(log x) (or) (log x)' = 1/(x ln 10)

d/dx (logₐ x) = 1 / (x ln a)

Substitute a = e on both sides. Then we get:

d/dx (loge x) = 1 / (x ln e)

By the properties of natural logarithms, ln e = 1. So

d/dx (loge x) = 1 / (x · 1)

Thus, d/dx (loge x) = 1.

Replacing loge x with ln x back, we get d/dx (ln x) = 1/x.

Hence, the derivatives of logs are:

d/dx (logₐ x) = 1 / (x ln a) (this is the derivative of common logarithm)

d/dx (ln x) = 1/x (this is the derivative of natural logarithm)

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Answer: The complementary angle of 35° is 55°. true

Step-by-step explanation:

We can find the complementary angle of 35° using subtraction. We do this by subtracting 35° from 90°.

Answer:

A- TRUE

Step-by-step explanation:

subtract 35° from 90° to find complementary angle which is 55°.

The average rate of f(x) is -2.1 and The average rate of g(x) is -5.8

What is function ?

Function can be defined in which it relates an input to output.

Given ,

functions are ,

f(x) =  - 0.3 x²

g(x) = - 0.6 x²

and interval 2 <=  x  <= 5

So, the average rate  =  f ( 5 ) - f(2 )  /  5 - 2

= -0.3 * 5 * 5  +  0.3* 2 * 2 / 3

= -7.5 + 1.2 / 3

= -6.3 / 3

= - 2.1

So, the average rate of g(x)  =  f ( 5 ) - f(2 )  /  5 - 2

= -0.6 * 5 * 5  +  0.6* 2 * 2 / 3

= -15 + 2.4 / 3

= -17.4 / 3

= - 5.8

Therefore, The average rate of f(x) is -2.1 and The average rate of g(x) is -5.8

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Answer:

75 degrees

Step-by-step explanation:

Its an corresponding angle

The value of k If one root of the quadratic equation x²+ Kx-8=0 is - 4​ should be 2.

According to the question

Given that,

A quadratic equation x²+Kx-8=0 where one root is -4

If -4 is a root of the equation  x²+Kx-8=0 then if we put -4 in the pace of x we would get the final answer as 0 or in other words, -4 would satisfy the equation x²+Kx-8=0.

Hence,

⇒   x²+Kx-8=0.

⇒   (-4)²+ K(-4) - 8 = 0

⇒   16 -4k - 8 = 0

⇒   8 - 4k = 0.

-4k which is on the Left-Hand Side of the equation would be shifted to the Right-Hand Side of the equation and its sign would change from -4k to +4k.

⇒   8 = 4k.

⇒  k = 2.

Thus, The value of k If one root of the quadratic equation x²+ Kx-8=0 is - 4​ should be 2.

Which of the following is the value of k If one root of the quadratic equation x²+ Kx-8=0 is - 4​

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The final statement is: 1)50:40 2) 600:480

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"

Given here: The ratio of distance travelled between a cheetah and an impala as 5:4

Part 1) If the cheetah travels 50 feet then impala would travel 40 feet.

Part 2) If the impala travels 480 feet then the cheetah must travel 600 feet.

Hence, The required final ratios of distance travelled are 1) 50:40 and 2) 600:480

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Answr:

1.the y intercept is 4 as the base fee is $4

2.£28

3. 2(rate per mile driven)

Step-by-step explanation:

2.

2x7=14

14+4=28

The slope-intercept form of 3x 5y 10 0 is y = (3/5)x - (10/5).

This is a linear equation of the form y = mx + b, where m is the slope, and b is the y-intercept. In this equation, the slope m is equal to 3/5, and the y-intercept b is equal to -10/5. To calculate the slope (m), we need to divide the coefficient of x (3) by the coefficient of y (5). The answer is 3/5. To calculate the y-intercept (b), we need to divide the constant (10) by the coefficient of y (5). The answer is -10/5. Therefore, 3x 5y 10 0 written in slope-intercept form is y = (3/5)x - (10/5).The slope-intercept form of 3x 5y 10 0 is y = (3/5)x - (10/5).

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Complete question: What is the equation of the line represented by 3x + 5y = 10 in slope-intercept form?

Become familiar with the distance formula, a Pythagorean theorem application that can be used to determine the separation between two places.Height after three seconds is 144 feet

Become familiar with the distance formula, a Pythagorean theorem application that can be used to determine the separation between two places. To compute the separation between any two points, the Pythagorean theorem can be rewritten as d=((x 2-x 1)2+(y 2-y 1)2). Summary.The following literal equation relates the variables of distance, rate, and time:

distance=rate×timed=rt

You will have traveled 180 miles if, for instance, your speed is 60 mph and you drive for three hours.

Height after three seconds is 144 feet

H(t) =16 t²

Given

The phrase 16t power 2

Fixing (a)

As an algebraic expression, write.

Let H stand in for the height at time t.

We thus have:

H(t) =16 t²

The height after three seconds, for solving (b)

This suggests that:

t= 3

H(t) = 16 t2

H((3) = 16*32

H((3) = 16*9 H((3) = 144

by substituting 3 for t.

hence the height is 144 feet.

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So, the answer is $285,671.10 (Option b) that must be deposited earning 6.2% compounded yearly in order to make the annuity payment of $25,312 for 20 years.

The formula to determine the future value of an annuity is given by

FV = PV(1+r)^n + PMT( (1+r)^n - 1) / r

Where:

FV is the future value of the annuity

PV is the present value of the annuity

PMT is the payment made at the end of each period

r is the interest rate per period

n is the number of periods

We know that the payment made at the end of each period (PMT) is $25,312, the interest rate (r) is 6.2% and the number of periods (n) is 20.

We are looking for the present value of the annuity (PV)

So we can substitute the known values into the formula and solve for PV:

PV = PMT( (1+r)^n - 1) / (r (1+r)^n)

PV = $25,312 * ( (1+0.062)^20 - 1) / (0.062 (1+0.062)^20)

PV = $25,312 * (1.062^20 - 1) / (0.062 * 1.062^20)

PV = $25,312 * (1.062^20 - 1) / (0.062 * 1.062^20)

PV = $25,312 * (2.547 - 1) / (0.062 * 2.547)

PV = $25,312 * 1.547 / 0.157

PV = $285,671.10

Therefore, the answer is $285,671.10 (Option b) that must be deposited earning 6.2% compounded yearly in order to make the annuity payment of $25,312 for 20 years.

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Alvin's average paddling rate was 6.6 km/h.

We know that,

Speed= Distance/ Time  (solve for distance)

Distance = Speed × Time

To Campsite against the current,

Speed=r-y   ; speed=(r-3)

Time = 8 hours

Distance = (r-3)×8     (equation 1)

From Campsite with the current,

Speed = r + y   ; speed=(r+3)

Time = 3 hours

Distance = (r+3)×3        (equation 2)

Equating equation 1 and equation 2  because distance is same in both case,

(r+3)×3=(r-3)×8

3r+9=8r-24

8r-3r=24+9

5r=33

r=6.6 km/hour.

What does aptitude mean upstream and downstream?

Upstream/Downstream: In the case of water, downstream refers to the direction that follows the stream. Upstream refers to the direction that runs counter to the stream. Speed downstream equals (u + v) km/hr if a boat is moving at u km/hr in still water and v km/hr in a stream.

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The substitution method is one of the algebraic approaches to solving simultaneous linear equations. It applies to substitute the value of any one of the variables from one equation into the other equation.

The substitution method is a simple method to solve a system of linear equations algebraically and find the solutions of the variables. As the name implies, it applies to finding the value of the x-variable in terms of the y-variable from the first equation and then substituting the value of the x-variable in the second equation.

In this method, we can find the value of the y-variable by solving the equation. And then, we can substitute the value of y in any of the given equations to find the value of x. 

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If Marsha bought a new car for $21152.25 and picked cost is $2150 and sales tax is $1007.25 , then the base price of Marsha's car is $17995  .

the price that Marsha paid for the car is = $21152.25   ;

the picked cost for the car is = $2150  ;

the sales tax for the car is = $1007.25  ;

the formula to calculate the Marsha's car is = (Amount Paid) - (Picked Cost + Sales tax) ;

substituting the values ,

we get ;

= 21152.25 - (2150 + 1007.25 )

= 21152.25 - (3157.25)

= 17995 .

Therefore , the base price for the Marsha's car is $17995  .

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The length of c in the right angle triangle is 8.6 mm.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The sides of a right angle triangle c an be found using Pythagoras's theorem as follows:

Hence,

c² = a² + b²

Hence,

Therefore,

c² = 5² + 7²

c² = 25 + 49

c² = 74

square root both sides

c = √74

c = 8.60232526704

Therefore,

c = 8.6 mm

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Answer:14

Step-by-step explanation:

Mariah lost twice so that means she got -3 two times that goes the same for ryan he gets 7 points two times which equal 14

Answer: ryan would have 14 points and mariah would have -6 points

Step-by-step explanation:

The equation to represent the total cost as a function of the number of packages delivered is C(p) = 12.50 + 0.25p.

The revenue as a function of the number of packages delivered. is R(p) = 4.25p

a. i. The equation to represent the total cost, C, as a function of the number, p, of packages delivered is C(p) = 12.50 + 0.25p

ii. The revenue, R, as a function of the number, p, of packages delivered. is R(p) = 4.25p

b. The algebraic model for the profit function P(p) = R(p) - C(p) = 4.25p - (12.50 + 0.25p) = 4.00p - 12.50

c. i. C(p) has domain of all non-negative integers (p ≥ 0) and range of all real numbers greater than or equal to $12.50 (C(p) ≥ $12.50)

ii. R(p) has domain of all non-negative integers (p ≥ 0) and range of all real numbers greater than or equal to $0 (R(p) ≥ $0)

iii. P(p) has domain of all non-negative integers (p ≥ 0) and range of all real numbers (P(p) can be any real number)

Note: The domain of p is limited to 27 in this case as the maximum packages that can be delivered is 27.

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240 square feet is the area of a square mural. The approximate length of one side of the mural is between 15 and 16 feet.

The area of a square is described as the number of square units needed to fill a square. In general, the area is described as the territory occupied inside the boundary of a flat object or 2d figure. The calculation of area is done in square units, with the standard unit being square metres (m²).

The area of the square = (side)²

240 = (side)²

side = √240

side = 4√15

side = 15.49 feet

Hence, The approximate length of one side of the mural is between 15 and 16 feet.

Therefore, the correct option is (4).

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The constant of proportionality is 42 grams per egg

From the question, we have the following parameters that can be used in our computation:

The weight of 6 eggs is 252 g

The constant of proportionality can be calculated using

Constant = Weight/Number of eggs

Substitute the known values in the above equation, so, we have the following representation

Constant = 252/6

Evaluate

Constant = 42

Hence, the constant is 42 grams per egg

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Answer:

The Lawn Order lawnmower factory can produce 12 lawnmowers in 8 hours. This means that the factory's production rate is 12 lawnmowers per 8 hours. To find how many hours it will take the factory to produce 30 lawnmowers, we can use the formula:

Time = (quantity of work to be done) / (rate of work)

In this case:

Time = 30 lawnmowers / (12 lawnmowers per 8 hours)

To solve the equation we can multiply both sides by 8/12:

Time = (30 lawnmowers * 8 hours) / (12 lawnmowers)

The result is:

Time = 20 hours

So it will take the factory 20 hours to produce 30 lawnmowers.

Answer:

45 hours.

Step-by-step explanation:

The factory makes 12 lawnmowers in 8 hours. You would divide 12 by 8 to see how many they make in 1 hour. That would be 1.5 So, you multiply 1.5 by 30 to get 45.

The length of each leg is 8.46/√2 = 6 units.

In a 45-45-90 triangle, the ratio of the hypotenuse to each leg is √2: 1.

If the hypotenuse is 6 units, we can use this ratio to find the length of each leg.

6 (√2) = 6 * 1.41 = 8.46

So the length of each leg is 8.46/√2 = 6 units.

The hypotenuse is the longest side of a right triangle, and it is opposite the right angle. It is the side that is opposite the right angle and is opposite of the 90-degree angle. The two other sides of a right triangle are known as the legs. The length of the hypotenuse can be determined using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In other words, if a and b are the lengths of the legs, then the length of the hypotenuse c is given by [tex]c = √(a^2 + b^2).[/tex]

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Clare's account balance will be $25

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Since Clare has $150 in her bank account and She buys a bike for$200. That means she overdrew and she will have an overdraft of $50. That is:

account balance now = $150 - $200 = - $50

If she earns $75 next week and then deposits it in her account.

account balance =  - $50 + $75 = $25

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