Prove the following:

The coordinates of point P are (-1, 1 8/11).

We have,

G(4, 4) and H(-7, 1)

m :n = 5:6

Using Section formula

x = (mx₂ + nx₁)/ (m+n) and y = (my₂ + ny₁)/ (m+n)

Here, x₁ = 4, y₁ = -7, x₂ = 4 and y₂ = -1

So, x = (5(-7) + 6(4))/ 11  and y = (5(-1) + 6(4))/ 11

x = -35+24/11 and y = -5 + 24/11

x = -11/11 and y = -19/11

x = -1 and y = 1 8/11

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Answer:

Step-by-step explanation:No, Lonnie is not correct. Step-by-step explanation: Because if we put 35 and 42 in rational form we can write it to its simple form by dividing it and after dividing we get the answer as 5 : 6. so that means Lonnie in incorrect.D

The three numbers are -2, 42 and 16 these we obtained by solving the equations

Let the three numbers x, y, and z. We know that:

x + y + z = 56 (Equation 1)

z - x = 44 (Equation 2)

x + y = 16 (Equation 3)

From Equation 3, we can solve for one of the variables in terms of the other:

y = 16 - x

Substituting this into Equation 1, we get:

x + (16 - x) + z = 56

Simplifying this equation, we get:

z = 40 - x (Equation 4)

Substituting Equation 4 into Equation 2, we get:

(40 - x) - x = 44

Simplifying this equation, we get:

40 - 2x = 44

Subtracting 40 from both sides, we get:

-2x = 4

Dividing both sides by -2, we get:

x = -2

z = 40 - (-2) = 42

Finally, using Equation 1, we can solve for y:

-2 + y + 42 = 56

y=16

Hence, the three numbers are -2, 42 and 16

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Answer:

perimeter = 84 feet

Step-by-step explanation:

using Pythagoras' identity in the right triangle to find a

a² + 35² = 37²

a² + 1225 = 1369 ( subtract 1225 from both sides )

a² = 144 ( take square root of both sides )

a = [tex]\sqrt{144}[/tex] = 12

then

perimeter = 35 + 37 + 12 = 84 feet

Answer:

9 pounds/135 cubic inches

= 1 pound/15 cubic inches

= .07 pounds/cubic inch

Suppose [tex]f(x) =8^{3x[/tex] and [tex]g(x) =8^{4x[/tex], function operations that are correct include the following:

A. (f + g)(x) = [tex]8^{3x} + 8^{4x}[/tex]

B. (f × g)(x) = [tex]8^{7x}[/tex]

C. (f - g)(x) = [tex]8^{3x} - 8^{4x}[/tex]

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:

(f × g)(x) = [tex]8^{3x+ 4x}=8^{7x}[/tex]

(f ÷ g)(x) = [tex]8^{3x- 4x}=8^{-x}[/tex]

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The most expensive car loan that Cindy can afford is $14,534.

The most expensive car loan is calculated by applying the following formula.

M.P = (Pr) / (1 - (1 + r)^(-n))

Where;

215 = (P x 0.00175) / (1 - (1 + 0.00175)^(-72))

215 = (P x 0.00175)/0.1183

(P x 0.00175) = 215 x 0.1183

P x 0.00175 = 25.44

P =  $14,534

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The painted area of the sign is approximately 324 square inches. This was calculated by finding the area of the pole, square signboard, and triangle portion of the signboard and adding them together.

To find the painted area, we need to find the area of the pole, the area of the square signboard, and the area of the triangular portion of the signboard.

Area of pole

The pole is a rectangular prism with height 60in and width 4in. Therefore, the area of the pole is:

60in x 4in = 240 sq. in.

Area of square signboard

The square signboard has a side length of 8in. Therefore, the area of the square signboard is:

8in x 8in = 64 sq. in.

Area of triangular portion of the signboard

The triangular portion of the signboard has a base of 8in and a height of 5in. Therefore, the area of the triangular portion of the signboard is:

(1/2) x 8in x 5in = 20 sq. in.

Total painted area

The total painted area is the sum of the area of the pole, the area of the square signboard, and the area of the triangular portion of the signboard. Therefore, the painted area is:

240 sq. in. + 64 sq. in. + 20 sq. in. = 324 sq. in.

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--The given question is incomplete, the complete question is given

" clara is running a bakery she has made a street sign to direct people to her bakery . She painted one of the post and sign. What is the painted area?8in,8in,5in, 60in, 4in "--

The probability that the sum of the numbers is even is,

⇒ P = 0.47

Since, We know that;

To have this kind of event you can have the following events, where

(d₁ ,d₂),  d1 is the number that appears uppermost on die 1 and d2 is the number that appears uppermost on dice 2:

(1, 1), (1, 3) , (1, 5), (2, 2), (2, 4) (2, 6) (3, 1) (3, 3) (4, 2) (4, 4) (4, 6), (5, 1) (5, 3), (5, 5) (6, 2) (6, 4) (6, 6)

And,  the total number of events is 36 since every dice have 6 numbers.

The probability is:

P(Event)=P(sum is even)/Total number of events

P = 17/36

P = 0.47

Thus, The probability that the sum of the numbers is even is,

⇒ P = 0.47

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Answer:

To determine the monthly deposit that Sophia must make in order to reach her retirement goal, we can use the formula for the future value of an annuity:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV = future value of the annuity (which is Sophia's retirement goal of $1,600,000)

P = monthly deposit

r = annual interest rate (which is 9%)

n = number of times interest is compounded per year (which is 12 for monthly compounding)

t = number of years until retirement (which is 65 - 28 = 37)

Substituting the given values, we get:

1600000 = P * ((1 + 0.09/12)^(12*37) - 1) / (0.09/12)

Simplifying and solving for P, we get:

P = 1600000 * (0.09/12) / ((1 + 0.09/12)^(12*37) - 1)

P ≈ $524.79

Therefore, Sophia must make a monthly deposit of approximately $524.79 in order to reach her retirement goal of $1,600,000.

Step-by-step explanation:

Answer: the answer is A=33∘, B=107.5∘, and C=39.5∘ is correct or c

Step-by-step explanation:

To find the angles of triangle ABC with side lengths a=12, b=21, and c=14, we can use the Law of Cosines and then apply the Law of Sines to find the remaining angles. Let's denote the angles as A, B, and C respectively.

According to the Law of Cosines:

c^2 = a^2 + b^2 - 2ab * cos(C)

Plugging in the given side lengths:

14^2 = 12^2 + 21^2 - 2 * 12 * 21 * cos(C)

196 = 144 + 441 - 504 * cos(C)

504 * cos(C) = 389

cos(C) = 389 / 504

C = arccos(389 / 504)

Using a calculator to find the approximate value of C, we get C ≈ 43.5°.

Answer:

To answer the question, you first need to understand what a net is. A net is a two-dimensional diagram that can be folded to form a three-dimensional object. In the context of this question, a net represents the unfolded and flattened-out shape of a flower box before it is assembled.

To draw a net that represents a flower box, you need to imagine what the box would look like if it were flattened out and unfolded. You can start by drawing a rectangle for the bottom of the box. Then draw four rectangles that represent the sides of the box. Each of the side rectangles should be the same length as the length of the bottom rectangle, and the width of each side rectangle should be the same as the height of the box.

Next, you need to label the net to indicate which sides will be connected to form the box. Label the edges of the rectangles with the corresponding letter to show how the box will be assembled. For example, label the top edge of the bottom rectangle as "A" and the bottom edge of one of the side rectangles as "B". Then, label the side edges of the side rectangle as "C" and "D".

To find the amount of material George needs for each box, you need to calculate the total surface area of the net. The surface area represents the amount of material needed to cover the entire box. You can find the surface area by calculating the area of each rectangle and adding them together.

In this case, the bottom rectangle has an area of 16 square inches, and each of the four side rectangles has an area of 8 square inches. Therefore, the total surface area of the net is:

16 + 4(8) = 48 square inches

This means that George needs 48 square inches of material to make one flower box.

You drew the net the way you did because it represents the flattened-out and unfolded shape of the flower box before it is assembled. Labeling the edges and rectangles helps to visualize how the box will be assembled and allows you to calculate the surface area needed to cover the entire box.  

have a good day and stay safe

The exact value of tan2θ in simplest radical form is  -21/√7.

The value of tan2θ is calculated as follows;

From Pythagorean identity, we know that;

sin² θ + cos² θ = 1

cos² θ is calculated as follows;

(3/4)² + cos² θ = 1

9/16 + cos² θ = 1

cos² θ = 1 - 9/16

cos² θ = 7/16

cos θ = √(7/16)

tan θ = sin θ / cos θ = 3/4 x 4/√7 = 3/√7

Now, we will find tan 2θ;

tan 2θ = 2tan θ / (1 - tan² θ)

tan 2θ = 2(3/√7) / (1 - (3/√7)²)

tan 2θ = (6/√7) / (-2/7)

tan 2θ = -21/√7

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The requried value of x that satisfies the problem is 4.5,

Let's start by finding the side length of the square tabletop, which is equal to the square root of its area. We have:

Area = 9x² - 30x + 25

Side length = √(Area) = √(9x² - 30x + 25)

To find x, we need to use the fact that the perimeter of the table top is 34 feet. The perimeter of a square is given by 4 times the length of one of its sides, so we can write:

Perimeter = 4 * Side length

34 = 4 * √(9x² - 30x + 25)

8.5 = √(9x² - 30x + 25)

9x² - 30x - 47.25 = 0

We can solve this quadratic equation by using the quadratic formula gives,

x = 4.5 and -1.16

Therefore, the value of x that satisfies the problem is approximately 4.5, since the other solution is negative and not meaningful in this context.

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Answer:

its not a function

Step-by-step explanation:

a)

The investment cost for replacing the 800 fixtures is $240,000.

b)

Annual utility cost savings is $57,600/year.

c)

Since the NPV is positive, the proposal should be accepted as it generates a positive return and is expected to be profitable.

We have,

a.

The investment cost for replacing the 800 fixtures is given as $300 per fixture, so the total investment cost would be:

Total Investment Cost = Number of fixtures x Investment cost per fixture

Total Investment Cost = 800 x $300

Total Investment Cost = $240,000

b.

To calculate the annual utility cost savings, we need to find the difference in the watt-hour consumption per fixture between HID and LED lighting, and multiply it by the number of fixtures, operating hours per day, operating days per year, and the metered utility rate per kilowatt-hour:

Energy consumption savings per fixture per hour = HID watt hour consumption - LED watt hour consumption

Energy consumption savings per fixture per hour = 500 watts/hr - 300 watts/hr

Energy consumption savings per fixture per hour = 200 watts/hr

Total energy consumption savings per hour for 800 fixtures:

= Energy consumption savings per fixture per hour x Number of fixtures

Total energy consumption savings per hour for 800 fixtures.

= 200 watts/hr x 800

Total energy consumption savings per hour for 800 fixtures.

= 160,000 watts/hr

Total energy consumption savings per year = Total energy consumption savings per hour x Operating hours per day x Operating days per year

Total energy consumption savings per year = 160,000 watts/hr x 10 hrs/day x 300 days/year

Total energy consumption savings per year = 480,000,000 watt-hours/year

Total energy consumption savings per year in kilowatt-hours (kWh):

= Total energy consumption savings per year / 1,000

Total energy consumption savings per year in kWh = 480,000,000 / 1,000

Total energy consumption savings per year in kWh = 480,000 kWh/year

Annual utility cost savings:

= Total energy consumption savings per year in kWh x Metered utility rate per kWh

Annual utility cost savings = 480,000 kWh/year x $0.12/kWh

Annual utility cost savings = $57,600/year

c.

To evaluate the proposal using net present value (NPV), we need to calculate the present value of the investment cost and the present value of the annual utility cost savings over a 15-year period.

Using the Present Value of the Ordinary Annuity formula with a 15-year life and 8% minimum rate of return, we get:

PV of Investment Cost = -$240,000 (negative because it's a cash outflow)

PV of Annual Utility Cost Savings = $514,883.81

NPV = PV of Annual Utility Cost Savings - PV of Investment Cost

NPV = $514,883.81 - (-$240,000)

NPV = $754,883.81

Therefore,

The investment cost for replacing the 800 fixtures is $240,000.

Annual utility cost savings is $57,600/year.

Since the NPV is positive, the proposal should be accepted as it generates a positive return and is expected to be profitable.

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The measure of the missing angle is 20 degrees.

The figure in the image is a right triangle.

To solve for the missing angle. we use trigonometric ratio.

Note: Tangent = Opposite / Adjacent

Plug in the values and solve for the angles:

tanθ = 8/20

Take the tan inverse

θ = tan⁻¹( 8/20 )

θ = 21.8°

θ ≈ 20°

Therefore, the angle is 20 degrees.

Option B)20° is the correct answer.

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Answer:

53

Step-by-step explanation:

20+8=28

90-28=62

62-9=53

90 angle!

To check if a solution is correct for a system of equations, we substitute the values of the solution into both equations and see if they are true.

Let's assume that the solution for the system of equations is (x,y) = (1,-1).

To check if this solution is correct for the first equation y = 2x - 3, we substitute x = 1 and y = -1:

-1 = 2(1) - 3

-1 = -1

Since -1 = -1, the solution (1,-1) satisfies the first equation.

To check if this solution is correct for the second equation y = -1/2x + 2, we substitute x = 1 and y = -1:

-1 = -1/2(1) + 2

-1 = 1

Since -1 is not equal to 1, the solution (1,-1) does not satisfy the second equation.

Therefore, the solution (1,-1) is not a solution for the system of equations y = 2x - 3 and y = -1/2x + 2.

The mistake is when you try to divide by X - 1, because you can't divide by zero.

Here we start by defining:

X = 1

The second step makes sense, we are adding the same value in both sides:

X + X = X + 1

2X = X + 1

Now subtract 2 in both sides:

2X - 2 = X + 1 - 2

2X - 2 = X - 1

Here is the mistake, you divide both sides by X - 1

But we already defined that X = 1

Then you are trying to divide by zero, and that opeartion is not defined, that is why you reach a false equation.

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Answer:5.08

4.34 are correct

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):

6u^2 - 3u - 8 = 0

We can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 6, b = -3, and c = -8. Substituting these values, we get:

u = (3 ± sqrt(9 + 192)) / 12

u = (3 ± sqrt(201)) / 12

Therefore, either:

The function type of f(x) = √3x + 2 is A. square root

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

f(x) = √3x + 2

In the above function, we have the notation √

The notation √ is a square root notation

This means that the function type of f(x) is A. square root

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The parent function is [tex]y = ab^x[/tex]

A function for the translation indicated is [tex]y = ab^{x+6} - 7[/tex].

In Mathematics and Geometry, the vertical translation a geometric figure or graph downward simply means adding a digit to the value on the y-coordinate of the pre-image or function.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

In this scenario, we can logically deduce that the graph of the parent function  was translated or shifted to the left (horizontally) by 6 units and downward (vertically) by 7 units;

[tex]y = ab^x[/tex]

[tex]y = ab^{x+6} - 7[/tex]

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Answer: C. V ≈ 635.2 cm^3.

Explanation: The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height (or slant height in this case).

Using the given values, we have:

V = (1/3)π(4.25 cm)^2(12 cm)

V ≈ 635.2 cm^3 (rounded to the nearest tenth)

Therefore, the answer is C. V ≈ 635.2 cm^3.

The dimension of the rectangle is 50 meters by 10 meters

The perimeter of a figure is the sum of all the external sides of the figure

The formula for calculating the perimeter of rectangle [tex]= 2(\text{l}+\text{w})[/tex]

If the length is 40 meters longer than the width, then:

[tex]\text{l} = 40 + \text{w}[/tex]

Substitute

[tex]120 = 2(40+2\text{w})[/tex]

[tex]60 = 40 + 2\text{w}[/tex]

[tex]30 = 20+ \text{w}[/tex]

[tex]\bold{w = 10 \ meters}[/tex]

Since [tex]\text{l} =40 + \text{w}[/tex]

[tex]\text{l} =40 +10[/tex]

[tex]\bold{l=50 \ meters}[/tex]

Hence the dimension of the rectangle is 50 meters by 10 meters

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The magnitude of the speed of the particle is determined as √ (17), m/s.

option A.

The speed of a particle is defined as the rate of change of the particle's displacement with time.

Mathematically, the formula for the speed of the a particle is given as;

v = dx/dt

where;

The speed of the particle is calculated as;

v = u + at

where;

at time, t = 0, the equation for the speed of the particle becomes;

v = u

v = i + 4j

The magnitude of the speed is calculated as follows;

v = √ (1² + 4²)

v = √ (17), m/s

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