Find the coordinate of the point P that divides each directed line segment in the given ratio. Round the

coordinate to the nearest tenth if necessary.

from K to L; 1 to 5

The coordinate of point P is

Using calculus,

For the parabola

.

.

Take the derivative of both sides

.

This is where the formula come from, you don't need to know where this came from.

The equation of the line

.

In this problem, we know that the coefficient of y is equal to 4p

So

.

.

.

.

.

For proof, let's graph this function

.

Now let's plug in the knowns to find the tangent line

If my work does not pop up, the answer is y=-x-3

The required equation of the tangent to the parabola at the given point y = -x - 3.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given expression,
x² = 12y

Comparing the above expression with the given expression,
P = 3

Now, we have p = 3 and (x₀, y₀) = (-6, 3)

So,
The equation of the tangent is given as,
y = -6/(2×3)x - 3
y = -x - 3

Thus, the required equation of the tangent to the parabola at the given point y = -x - 3.

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Answer: T = 0.25x + 50, where x represents the number of chirps in 1 minute.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The factored form of a polynomial function with roots r1 and r2 can be found by multiplying two linear factors (x - r1) and (x - r2).

Here are the steps to find the factored form of the polynomial function with roots 3i and 2:

Write the first linear factor: (x - 3i)

Write the second linear factor: (x - 2)

Multiply the two linear factors: (x - 3i)(x - 2)

Expand the product to find the polynomial function:

x^2 - (3i + 2)x + (3i * 2) = x^2 - 2x - 6i

And there you have it, the factored form of the polynomial function with roots 3i and 2 is x^2 - 2x - 6i.

Answer:

[tex]5b + 7p = 79[/tex]

[tex]7b + 5p = 77[/tex]

Answer:

If csc = 29/21, then the reciprocal of this is equal to the sine of the angle. So,

sin = 21/29.

Since cosine is less than 0, then the angle must be in the second or third quadrant, which means that the sine of the angle must be positive. So,

sin = 21/29, and cos = -√(1 - sin^2) = -√(1 - (21/29)^2)

Next, we can find the tangent by taking the ratio of sine to cosine:

tan = sin / cos = 21/29 / -√(1 - (21/29)^2) = -21/√(841 - 441)

Finally, we can find the cotangent by taking the reciprocal of the tangent:

cot = 1 / tan = -√(841 - 441) / 21

So, the remaining trigonometric functions are:

sin = 21/29

cos = -√(1 - (21/29)^2)

tan = -21/√(841 - 441)

cot = -√(841 - 441) / 21

It is possible to choose a and b such that the value of function(x) at any given point is equal to the limit of f(x) as x approaches any value. This guarantees that f is continuous throughout.

A function's limit as x approaches any value must match the value of f(x) at that moment in order for the function to be continuous everywhere. In order to ensure that this need is satisfied, the values of a and b that make up f(x), whether it be a linear equation, polynomial, or another sort of equation, must be chosen. Since the behaviour of the function varies smoothly as x approaches any value, this ensures that the function is continuous throughout. In other words, a and b values must be selected in a way that the function is continuous, i.e., defined and devoid of breaks or discontinuities.

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The complete question is

Find the values of a and b that make f continuous everywhere that f is continuous throughout.

Based on the information, it can be inferred that the area of the room is 121m².

To calculate the area of the room we must perform the following mathematical procedure:

1. Identify the length of the sides and the base.

2. multiply the length of a side by the base.

3. get the result of the area.

According to the above procedure, the area of the room would be:

According to the above, the area of the room would be 121m². The dimensions of the furniture in the room have no influence in this procedure.

Note: This question is incomplete because there is some information missing. Here is the complete information:

question:

Calculate the area of the room.

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The air speed of the plane to cover 360 miles against the wind and with the wind in the given time is equal to 200 miles per hour.

Let 'x' be the speed of the plane fly in still air.

And 'y' be the speed of the wind.

Speed against the wind = x - y

Speed with the wind = x + y

Total distance covered by plane = 360 miles

Time taken against the wind = 2 hours 15 minutes

                                               = 2 ( 1/4 ) hours

                                               = 9 / 4 hours

Time taken with the wind = 1 hour 30 minutes

                                          = 1 ( 1/2 ) hours

                                          = 3 /2 hours

Speed = distance / time

Against the wind :

x - y = 360 / (9 /4 )

⇒x - y = 160___(1)

With the wind:

x + y = 360 / (3 /2)

⇒x + y = 240 ___(2)

Add (1) and (2) we get,

2x = 400

⇒ x= 200miles per hour

⇒y = 40 miles per hour

Therefore, the air speed of the plane as per given condition is equal to 200miles per hour.

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The length is the unknown side increases while keeping the known side lengths fixed, the measurement of angle Z will increase. So, the triangle will not fit the given conditions anymore.

The properties of the triangle are: The sum of all the angles of a triangle (of all types) is equal to 180°. The sum of the length of the two sides of a triangle is greater than the length of the third side. In the same way, the difference between the two sides of a triangle is less than the length of the third side.

Given,  two sides and the angle opposite one of the sides. Under Sides, enter 9 for a and 6 for b. Under Angles, enter 30 for B.

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Complete question:

Depending on a given set of conditions and the properties of triangles, any of these four outcomes is possible when constructing triangles:

No triangles fit the condition.

One unique triangle fits the condition.

Two triangles fit the condition.

Infinitely many triangles fit the condition.

Complete the steps below to find the number of triangles that can be constructed based on the following conditions: one side measures 7 centimeters, another side measures 9 centimeters, and the angle between them measures 74°.

Part A

What does the dotted line in the diagram represent?

Part B

Now think about changing the triangle. What happens to angle Z if the unknown side length increases while keeping the known side lengths (XZ and ZY) the same? Will the triangle still fit the given conditions?

Part C

What happens to angle Z if the unknown side length decreases while keeping the known side lengths (XZ and YZ) the same? Will the triangle still fit the given conditions?

Part D

Based on your conclusions in parts B and C, can the length of the unknown side be changed in any way without changing the given conditions for the triangle?

Part E

You know the given conditions for the triangle are fixed. You also know the unknown side length is fixed. What does this tell you about the two angles adjacent to the unknown side?

Part F

From your conclusions in part E, how many triangles can be constructed based on the given conditions?

art G

Let c be the unknown side of the triangle. Use this triangle calculator to solve for c. Under Sides, enter 7 for side a and 9 for side b. Under Angles, enter 74 for angle C. Click Calculate once you have entered the information. What is the length of side c?

Part H

Now try to construct a triangle using a different set of measurements. This time, you’ll enter three angle measurements. Return to the Calculator tab, and click the Clear button to begin a new calculation.

Under Angles, enter 45 for A, 40 for B, and 95 for C. Then click Calculate. What happened? What message did the tool deliver? Explain the message in terms of the properties of a triangle and the given angles.

Part I

Click Clear in the tool to begin a new calculation. This time, you’ll check for valid triangles given two sides and the angle opposite one of the sides.

Under Sides, enter 9 for a and 6 for b. Under Angles, enter 30 for B. Then click Calculate. What happened? What message did the tool deliver? Click “Show other solution” in the tool and explain the message in terms of the angle measurements and the given information.

The old will Mr Lim be in 6 years time is 46 years old.

To make solving this problem easier, we need to consider the ages of Mr Lim and his son. For example by multiplying the number x.

Let:

Mr Lim's age = a

His son's age = b

So that,

The ratio of ages in the current year:

Mr Lim's age to his son's age = 5x : 2x

a : b = 5x : 2x

The ratio of ages in the four years ago:

Mr Lim's age to his son's age = 3x : x

(a - 4) : (b - 4) = 3x : x

[tex]\frac{a-4}{b -4} =\frac{3x}{x}[/tex]

[tex]\frac{5x-4}{2x -4} =\frac{3x}{x}[/tex]

[tex]\frac{5x-4}{2x -4} =\frac{3}{1}[/tex]

5x - 4 = 6x - 12

5x - 6x = -12 + 4

-x = -8

x = 8

So that we know the age of Pak Lim's and the age of his son's this year.

Mr Lim's age = 5x

                     = 5 × 8

                     = 40 years old

His son's age = 2x

                     = 2 × 8

                     = 16 years old

After that, we find Mr Lim's age 6 years from now by adding 6 years to this year's age.

Mr Lim's age be in 6 years time = 40 + 6

                                                    = 46 years old

So, the old will Mr Lim be in 6 years time is 46 years old.

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Answer:

[tex]x = \frac{5(6 + y)}{6} [/tex]

Step-by-step explanation:

[tex]1. \: 6x = 30 + 5y \\ 2. \: x = \frac{30 + 5y}{6} \\ 3. \: x = \frac{5(6 + y)}{6} [/tex]

There's your answer

Step-by-step explanation:

Since 4104 students are employed sophomores, juniors, or seniors, the total number of unemployed students is 11,989 - 4104 = 7885.

And since 745 students are employed freshman, the number of unemployed freshman is 7885 - 745 = 7140.

So, the total number of freshman is 745 + 7140 = 7885.

The Venn diagram would look like this:

[ Freshmen ] [ Sophomores, Juniors, Seniors ]

[ 7885 ] __________ [ 4104 ]

| 745 |

__________

[ 7140 ]

So, there are 7885 freshman.

Answer:

Step-by-step explanation:

The monthly payment on a loan and the total interest that will be paid during the term of the loan can be found using an amortization formula.

Here are the steps to find the monthly payment and total interest for the given loan conditions:

Convert the interest rate to a decimal: 7.5% = 0.075

Divide the interest rate by the number of periods (months) per year: 0.075 / 12 = 0.00625

Find the number of payment periods: 8 years * 12 months/year = 96

Calculate the monthly payment using the amortization formula:

Payment = Loan Amount * (Interest Rate / (1 - (1 + Interest Rate)^(-Number of Payments)))

Payment = $6,200 * (0.00625 / (1 - (1 + 0.00625)^(-96)))

Payment = $79.88

So, the monthly payment on the loan is $79.88.

Calculate the total interest paid over the term of the loan:

Total Interest = (Monthly Payment * Number of Payments) - Loan Amount

Total Interest = ($79.88 * 96) - $6,200

Total Interest = $7,538.88

So, the total interest that will be paid during the term of the loan is $7,538.88.

Answer:

Step-by-step explanation:

The current area is 60 sq. in. You wish to increase this area to 300 sq. in. by adding x in two dimensions: namely length and width.

These measurements would be 5 + x wide and 12 + x long.

(5 + x)(12 + x) = 300

x^2 + 17x + 60 = 300

Subtracting 300 from both sides and using the quadratic formula for

x^2 + 17x - 240 = 0,

we find that the one reasonable answer for the measure x is 9.2 inches.

The future value of this one-time investment of $1,000 in 5 years is equal to: A. $1,082.5.

Mathematically, future value can be calculated by using this formula:

F = P(1 + r)

Where:

Substituting the given parameters into the future value formula, we have the following;

Future value, F = 1,000(1 + 8.25/100)

Future value, F = 1,000(1 + 0.0825)

Future value, F = 1,000(1.0825)

Future value, F = $1,082.5.

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The required simplified expression of the given expression is [tex]{\frac{2}{x^5y^4}}$[/tex].

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here
When simplifying the expression 4x²y⁴/2x⁷y⁸, we can divide the numerator and denominator by the greatest common factor of each, which is x²y⁴. Doing so gives us:

[tex]$\frac{4x^2y^4}{2x^7y^8} = \frac{4}{2x^5y^4} = \frac{2}{x^5y^4} = \boxed{\frac{2}{x^5y^4}}$[/tex]

Thus, the required simplified expression of the given expression is [tex]{\frac{2}{x^5y^4}}$[/tex].

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The sample should be milled to a radius that is approximately 7.19 times its original radius in order to increase its work function by 2%.

The work function of a material is related to its surface area, and milling a sample into smaller nano-spheres increases its surface area. The increase in work function can be approximated by the following equation:

ΔW = kTln(A/A₀)

where ΔW is the change in work function, k is Boltzmann's constant, T is the temperature in Kelvin, A is the new surface area of the milled sample, and A₀ is the original surface area of the sample.

To find the size to which the sample should be milled to increase its work function by 2%, we need to rearrange the equation to isolate the new surface area:

A/A₀ = e^(ΔW/kT)

Plugging in the known values, we get:

A/A₀ = e^(0.02 * 5.1 eV / (8.62 * 10⁻⁵ eV/K * 300 K))

= 51.64

The new surface area is 5064% larger than the original surface area.

Since the sample is being milled into nano-spheres, the new surface area is proportional to the square of the radius. Let's call the original radius of the sample "r₀". Then the new radius is:

r = √(A/A₀) * r₀ = √(51.64) * r₀ = 7.19 * r₀

--The question is incomplete, answering to the question below--

"g a gold (au) macro scale sample has a work function of 5.1 ev. to what size should the sample be milled to increase its work function by 2 %? assume that the sample is milled into nano-spheres and give the size in terms of radius. What is the relation between the new radium and original radius?"

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Answer:

The grandfather is 72 years old and the granddaughter is 8 years old now.

Step-by-step explanation:

To calculate this, first calculate the grandfather's age in 8 years:

72 + 8 = 80.

Then, use the given information to calculate the granddaughter's age in 8 years: 8 + 8 = 16.

Finally, use the given information to calculate the grandfather's age now: 5 x 16 = 80, so 80/5 = 16, and 16 x 9 = 72.

The correct answer is option d. The length of the given hypotenuse  of a right triangle is 7 cm.

A right triangle has side lengths of 4 centimeters and 5 centimeters, so we can use the Pythagorean Theorem to find the length of the hypotenuse. The theorem states that in a right triangle, 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 this case, the hypotenuse c is given by

[tex]c^2 = 4^2 + 5^2[/tex]

= 16 + 25

= 41

so the length of the hypotenuse is c = √41 = 7 cm.

The answer is d. 7 cm.

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The probability of spinning a number greater than 4 on a spinner with 6 equal sections is 1 over 3. (option d)

A spinner with 6 equal sections has an equal probability of landing on any of the 6 sections. To find the probability of spinning a number greater than 4, we need to find the fraction of sections that meet this criterion. In this case, there are 2 sections that satisfy this condition (5 and 6).

Therefore, the probability of spinning a number greater than 4 is 2/6, or 1/3.

It's important to remember that when working with probability, the values can only be between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event. The probability of any event must be a number between 0 and 1, inclusive.

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By evaluating a proportional relation, we can see that if 10 fiction books are sold, then 13 non-fiction books are sold.

Here we know that 3 fiction books are sold for every 4 non-fiction books sold.

Then if x fiction books are sold, the number of non-fiction books sold are given by the proportional relation:

y = (4/3)*x

Here we know that 10 fiction books are sold, so x = 10, replacing that we will get:

y = (4/3)*10 = 40/3 = 13.33

So 13 non-fiction books are sold.

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Answer:

Step-by-step explanation:

One quarter = 1/4

1/4 of a number is 6.

We have to find that number by taking

6 times 4 = 24

So, we know that number is 24

What is one-third of the number?

1/3 of 24 = 8

So, the answer is 8.

Answer: 200 dollars more

Step-by-step explanation: I did 30% of 500 which is 150 that Noel has.

70% of 500 which is 350. 350-150 is 200

Frank has saved 200$ more than Noel

Answer: 200 dollars

The first step that we should do is divide 500 into 10 separate parts. Each part is 10 percent of the price. 500 divided by 10 is 50.

This means that Frank saved 50 x 7 and Noel saved 50 x 3.

50 x 7 is 350 and 50 x 3 is 150.

Frank saved 350 , while Noel saved 150.To check if we are correct we can add 350 and 150, which is 500 that brings us back to our original answer. Next we must subtract Franks total from Noel to figure out the difference.

350-150 is 200.

This means that Frank saved 200 more dollars than Noel.

I hope this helped & Good Luck <3 !!!

The right answer is option A, which reads "four times one-third" multiplied by the number of one-third cup servings in four cups.

You can multiply, reduce, add, or take this away in mathematics. An expression is put together as follows: Verb, numeric value, and math operator A mathematical formulation is composed of numbers, variables, and procedures (such as addition, subtraction, multiplication or division etc.) Opposing phrases and phrases is possible. An exponential function is any mathematical declaration that has variables, integers, or an mathematical operation. As an instance, the phrase 4m + 5 consists of both the terms 4m and 5, as well as the supplied equation's variable m, each of which is divided by the mathematical sign +.

given

the expression = "  number of one-third cup servings in 4 cups "

= four times one-third

= 4*1/3

The right answer is option A, which reads "four times one-third" multiplied by the number of one-third cup servings in four cups.

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Answer: 75.6, 14.4

Step-by-step explanation:

Note 2 angles are complementary if they adds up to 90 degrees. Lets set x to be the first angle.

x - (x - 61.2) = 90

Then we can know:

2x = 90 + 61.2;

2x = 151.2;

x = 75.6

Now we know the first angle is 75.6, we know the second angle is 75.6 - 61.2 = 14.4. Hope you find this helpful!

Answer & Explanation:

sin Θ = opp/hyp

cos Θ = adj/hyp

tan Θ = opp/adj

csc Θ = hyp/opp

sec Θ = hyp/adj

cot Θ = adj/opp

1.

sin Θ = opp/hyp = (8√2)/18 = (4√2)/9

cos Θ = adj/hyp = 14/18 = 7/9

tan Θ = opp/adj = (8√2)/14 =  (4√2)/7

csc Θ = hyp/opp = 18/(8√2) = (9√2)/(4√2√2) = (9√2)/8

sec Θ = hyp/adj = 18/14 = 9/7

cot Θ = adj/opp = 14/(8√2) = (7√2)/(4√2√2) = (7√2)/8

Therefore, Horatio can buy approximately 11.83 gallons of gas. However, since he cannot buy a fractional part of a gallon, the actual number of gallons he can buy is either 11 or 12 gallons.

An equation is a mathematical statement that shows the equality between two expressions. Equations are used to solve problems and find solutions to mathematical or real-world problems. They typically involve variables, which are symbols that represent unknown values, and constants, which are known values that are used in the equation. Equations can take many forms, but they generally follow the pattern: expression = expression. Equations are an important tool in mathematics, science, and engineering, and they can be used to model and analyze many different types of systems and processes.

Here,

Horatio has $230, but he wishes to save $160 and spend $24.95 on an oil change. So the amount of money he has left to spend on gas is:

$230 - $160 - $24.95 = $45.05

To find out how many gallons of gas Horatio can buy with $45.05, we can divide the amount of money by the price per gallon:

$45.05 ÷ $3.81/gallon ≈ 11.83 gallons

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Answer: (-4, 1)

Step-by-step explanation:

To solve graphically, change each equation into slope-intercept form

(y = mx + b)

3x + 4y = -8

+8 +8

3x + 4y + 8 = 0

-4y -4y

3x + 8 = -4y

Divide both sides by -4 to get y by itself

-3/4x - 2 = y or y = -3/4x - 2

Do the same for the other equation.

-x + y = 5

+x +x

y = 5 + x or y = x + 5

Plug in the equations graphically. The point at which the two lines intercept is your answer.

Answer:

Step-by-step explanation:

i have no clue to be honest