Help me out please I beg you

Answer:x = midpoint_x - (midpoint_x - (-3)) * (sqrt(5)/6) = 19.5 - (22.5 * sqrt(5))/6 = 19.5 - 3.75sqrt(5)

Step-by-step explanation:To find the x-coordinate of the point that is 2/3 of the distance from (-3, 2) to (42, 32), we first need to find the coordinates of that point.

The distance between the two endpoints of the line segment is:

d = sqrt((42 - (-3))^2 + (32 - 2)^2) = sqrt(45^2 + 30^2) = 15sqrt(45)

The distance from (-3, 2) to the desired point is:

(2/3)d = (2/3)sqrt(45^2 + 30^2)

Let's call the desired point (x, y). We can use the midpoint formula to find the coordinates of the midpoint of the line segment:

midpoint = ((-3 + 42)/2, (2 + 32)/2) = (19.5, 17)

The midpoint is halfway between the two endpoints, so the distance from (-3, 2) to the midpoint is:

sqrt((19.5 - (-3))^2 + (17 - 2)^2) = sqrt(22.5^2 + 15^2) = 15sqrt(5)

To find the coordinates of the desired point, we can use similar triangles. The ratio of the distance from (-3, 2) to the midpoint to the distance from (-3, 2) to the desired point is:

15sqrt(5) / (2/3)sqrt(45^2 + 30^2) = 15sqrt(5) / 30sqrt(45) = sqrt(5)/6

The ratio of the distance from (42, 32) to the midpoint to the distance from (42, 32) to the desired point is the same:

15sqrt(5) / (2/3)sqrt(45^2 + 30^2) = sqrt(5)/6

The length of the third side is 14.4 units.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We find the third side of a triangle by using Pythagoras theorem.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

8²+12²=x²

64+144=x²

208=x²

Take square root on both sides

x=14.4

Hence, the length of the third side is 14.4 units.

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Answer:

3286714

Step-by-step explanation:

Let the digits of the number be :

Our given conditions :

Solving :

Solution :

So, the number is :

Answer:

$7.80

Step-by-step explanation:

Find the cost to download 1 song. Divide 6 from 4.68

4.68/6 = 0.78

Each song costs $0.78.

Find the amount 10 songs cost. Multiply 0.78 with 10:

10 x 0.78 = 7.80

$7.80 is your answer.

~

Hi

6 = 4.68

10 = X

X = 10*4.68 /6

X = 46.8/6

X = 7.8

We have to prove that triangles ABC and ADC are congruents.

We can draw a driagram of the triangles as:

As AB and AD are radius of the same circle, we have:

The same can be said for CB and CD, so:

Then, we have a shared side between the two triangle. Then, given the reflexive property we have:

Then, as we have 3 pair of congruent sides, by the SSS postulate, we can conclude that the triangles ABC and ADC are congruent. Then, all three pair of angles are also congruent.

NOTE:

If we just want to prove that the angles Then, we four right triangles (or a rhombus). Then, each angle of the erhombus is bisected.

The left angle at vertex D is complementary to the lower angle at A. The left angle at vertex B is complementary to the upper angle at A. As both angles at A are equal, The left angle at D and the left angle at B are complementary to the same angle.

Then, they have the same measure.

The same analysis can be done for the right angles.

Then, as both halves of the angles are equal, then the total angle

Answer:

There are 8568 ways to combine the shoes.

Step-by-step explanation:

In this case Connie wants to create smaller subsets from a larger group of things, therefore we must do a combination, which can be applied by using the following formula:

\(C_{(n,r)} = \frac{n!}{r!*(n - r)!}\)

In our case n = 18, which is the total number of shoes and r = 5, which is the subset she wants to create.

\(C_{(18,5)} = \frac{18!}{5!*(18 - 5)!} = \frac{18!}{5!*13!} = \frac{18*17*16*15*14*13!}{5!*13!}\\C_{(18,5)} = \frac{18*17*16*15*14}{5*4*3*2} = 8568\)

There are 8568 ways to combine the shoes.

The number of ways can she choose which shoes to take is 8,568.

Given that,

Based on the above information, the calculation is as follows:

\(= \frac{n!}{k!(n-k)!} \\\\= \frac{18!}{5!13!} \\\\= \frac{18\times 17\times 16\times\15\times \times 14}{5\times 4\times 3\times2\times 1}\)

= 8,568

Therefore we can conclude that The number of ways can she choose which shoes to take is 8,568.

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The simplified expression is  d/ c⁴.

To simplify the expression cd³ c⁻⁵ x d⁻², we can combine the variables with the same base (c and d) by adding their exponents:

Using the property of exponents as

When multiplying two exponential expressions with the same base, you can add the exponents. This can be expressed as follows:

aᵇ x aⁿ= aᵇ⁺ⁿ

When dividing two exponential expressions with the same base, you can subtract the exponents. This can be expressed as follows:

aᵇ / aⁿ= aᵇ⁻ⁿ

So, cd³ c⁻⁵ x d⁻²

= c¹⁻⁵ x d³⁻²

= c⁻⁴ x d¹

= dc⁻⁴

Again from the property of exponents

a⁻ᵇ = 1/aᵇ

So,  dc⁻⁴

= d/ c⁴

Therefore, the simplified expression is  d/ c⁴.

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Answer:

AB=BC,AM=MC

BM IAC , EF I BC

Step-by-step explanation:

AB

MA

B

F

с

A

Answer:

-10

Step-by-step explanation:

first you have to solve the parenthesis so you do -5(2+x)=(-5⋅2)+(-5⋅x). after that you get -10-5x and you have to add the 2x from the equation before. you add -5x and 2x because they are like terms. after that you get -3x and you get the equation -3x-10=20. after that you add 10 to both sides resulting in -3x=30. after that you divide both sides by -3 and you get x=-10 so the answer is -10

Answer:-10

Step-by-step explanation:

-5(2+x) + 2x =20

-10-5x+2x=20

-10-3x=20

-3x=30

X=-10

Answer:

10

Step-by-step explanation:

4y = 2x + 12

Divide both sides by 4:

y = ½ x + 3

This has a slope of ½ and a y-intercept of 3.

The other line has the same slope and a y-intercept of 30.

So the scale factor is 10.

Answer:1.4

Step-by-step explanation: first you add the amount of cups of each juice, when i did this I got 5.6 cups (1.5+2+2.1=5.6). Then you see she is making punch for herself and three friends, in total that’s 4 people, so I divided the amount of juice (5.6 cups) by the amount of people drinking it (4) to get a final answer of 1.4 (5.6/4).

Step-by-step explanation:

You must set up a proportion, it is called finding the geometric mean.

\( \frac{x}{4} = \frac{36}{x} \)

Then, you must cross multiply to get:

\( {x}^{2} = 144\)

Then, take the square root

\( \sqrt{ {x}^{2} } = \sqrt{144} \)

\(x = 12\)

If this answer helped you, I would greatly appreciate the brainliest :D

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Some things you can do to help you decide on a bank include:

When trying to locate a bank that offers competitive returns on savings and favorable borrowing costs, consider comparing interest rates.

To gather additional information about certain banks, why not solicit feedback from acquaintances? People who have personal experience with a particular bank can provide valuable insights into their satisfaction levels with regards to customer service, for example.

Finally, taking the time to visit branch offices can offer valuable clues regarding convenience level and overall atmosphere.

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Answer:

5 1/2- 1 2/7

11/2-9/7

(11×7-9×2)/14

59/14

4 3/14

140.55 pounds will be sold approximately each week at the optimal price of $0.67/lb.

To find the price elasticity of demand for bananas at $0.20/lb, we need to use the formula:

According to the given data:

E(p) = -p(q'/q(p))

where q' is the derivative of q(p) with respect to p.

First, we need to find q'(p):

\(q'(p) = -225e^(1.5(5-p))\)

Then, we can plug in the values:

E(0.20) = -0.20(q'(0.20)/q(0.20))

= \(-0.20(-225e^(1.5(5-0.20)) / 100e^(1.5(5-0.20)))\)

= 2.70

Therefore, the price elasticity of demand for bananas at $0.20/lb is 2.70.

To find the price elasticity of demand for bananas at $1/lb, we can use the same formula:

E(p) = -p(q'/q(p))

First, we need to find q'(p):

\(q'(p) = -225e^(1.5(5-p))\)

Then, we can plug in the values:

E(1) = -1(q'(1)/q(1))

= \(-1(-225e^(1.5(5-1)) / 100e^(1.5(5-1)))\)

= 0.68

Therefore, the price elasticity of demand for bananas at $1/lb is 0.68.

To find the price that maximizes revenue, we need to find the value of p that makes revenue, R(p), maximum.

Revenue is given by:

R(p) = pq(p)

= \(p100e^(1.5(5-p))\)

To maximize revenue, we need to find the critical point of R(p) by taking its derivative and setting it equal to zero:

\(R'(p) = 100e^(1.5(5-p)) - 150pe^(1.5(5-p)) = 0\)

Simplifying this expression, we get:

\(2e^(1.5(5-p)) - 3pe^(1.5(5-p)) = 0\)

2 = 3p

p = 2/3

Therefore, the price that maximizes revenue is $0.67/lb.

To find the maximum revenue per week, we can plug this price back into the revenue equation:

\(R(2/3) = (2/3)*100e^(1.5(5-2/3))\)

= $167.56

Therefore, the maximum revenue per week is $167.56.

To find how many pounds will be sold each week at the optimal price of $0.67/lb, we can plug this price back into the demand equation:

\(q(2/3) = 100e^(1.5(5-2/3))\)

= 140.55

Therefore, approximately 140.55 pounds will be sold each week at the optimal price of $0.67/lb.

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A unit rate of 4 deliveries per hour.

Rate is the special ratio in which two different terms are in different units.  a number, amount, or degree measured in relation to another object. a payment or charge that is calculated depending on another sum. more specifically: the premium per insurance unit. transitive verb rate.

Given that 16 deliveries are done in 4 hours. from that we can drive no. of deliveries in one hour. let's assume deliveries in one hour is x

For, x per hour =  16/4

x per hour is 4

Therefore the appropriate value for the unit rate of 4 deliveries per hour.

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The simplified expression of the radical expression ∛135a¹³ is (135a¹³)¹/³

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

A radical expression

The radical expression is given as

\sqrt[3]{135^{a13}}

Represent the expression properly

So, we have the following representation

∛135a¹³

Apply the exponent rule of indices

This gives

∛135a¹³ = (135a¹³)¹/³

135 and a¹³ are not perfect cube root expressions

This means that the expression cannot be further simplified

Hence, the solution is (135a¹³)¹/³

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Answer:

\(-3\frac{2}{10}\)

Or for a more simplified version:

\(-3\frac{1}{5}\)

Step-by-step Explanation:

Between each whole number, it is divided into 10 lines. And the dot is 2 to the left of -3. So the point is \(-3\frac{2}{10}\). Or for a more simplified version: \(-3\frac{1}{5}\).

Hope this helps! :)

Answer:

Step-by-step explanation:

As RS is a straight line sin ∠RUT = sin ∠SUT

line UT bisects ∠RTS

Let θ be ∠UTR and ∠UTS

Law of sines

Left side triangle

3x/sinθ = 40/sinRUT

sinRUT = 40sinθ / 3x

Right side triangle

(x + 2) / sinθ = 16 / sinSUT

(x + 2) / sinθ = 16 / (40sinθ / 3x)

(x + 2)(40sinθ / 3x)  = 16sinθ

(x + 2)(40sinθ)  = 48xsinθ

40xsinθ + 80sinθ = 48xsinθ

40x + 80 = 48x

80 = 8x

x = 10

Answer:

D. A pair of intersecting lines

Step-by-step explanation:

A conic section is a fancy name for a curve that you get when you slice a double cone with a plane. Imagine you have two ice cream cones stuck together at the tips, and you cut them with a knife. Depending on how you cut them, you can get different shapes. These shapes are called conic sections, and they include circles, ellipses, parabolas and hyperbolas. If you cut them right at the tip, you get a point. If you cut them slightly above the tip, you get a line. If you cut them at an angle, you get two lines that cross each other. That's what happened in your question. The plane cut the cone at an angle, so the curve is two intersecting lines. That means the correct answer is D. A pair of intersecting lines.

I hope this helps you ace your math question.

Answer:

For the first one: 6y + y^2

2nd one: 6y + 42

Answer:  a

Step-by-step explanation: hope it helps.

Answer:

y=5x+19

Step-by-step explanation:

y+1=-5(x+4)

y+1=-5x-20

Subtract 1 (like terms)

y=-5x-21

The responses to the questions involving the solution and equations of a straight line are;

6. The slope is -0.5

7. The equation is; y = x + 4

8. y = 7 - 0.25•x

9. The balance after m months is modeled by the equation;

B = 1,800 - 150•m

10. The slope is the monthly payment on the loan

6. The points on the graph in question 6 are; (0, 4), and (4, 2)

The slope is given by the ratio of the rise to the run of the graph as follows;

\(Slope = \frac{2 - 4}{0 - 4} = - 0.5\)

7. The equation in slope and intercept form is found as follows;

The given points are;

(-1, 3), and (-3, 1)

The slope and intercept form is presented as follows;

y = m•x + c

The point and slope form is presented as follows;

y - y1 = m•(x - x1)

Where m is the slope of the graph

m = (1 - 3)/(-3 - (-1)) = -2/-2 = 1

Which gives;

y - 3 = 1 × (x - (-1)) = x + 1

y = x + 1 + 3 = x + 4

The equation of the graph in slope and intercept form is; y = x + 4

8. The points are; (-4, 8), (4, 6)

Which gives;

m = (6 - 8)/(4 - (-4)) = -2/8 = -0.25

Therefore;

y - 8 = -0.25•(x - (-4)) = -0.25•x - 1

y = -0.25•x - 1 + 8 = -0.25•x + 7

9. The amount Zachary purchased the computer on loan = $1,800

The balance after 3 months = $1,350

The balance after 5 months = $1,050

Therefore;

The points on the graph of the equation that models the balance are therefore;

(0, 1,800), (3, 1,350), (5, 1,050)

Which gives;

B - 1800 = ((1,350-1,800)/(3-0))•(m - 0)

B - 1800 = -150•m

The equation that models the balance, B, after m months is therefore;

10. The slope, ((1,350-1,800)/(3-0)) = -150, signifies the amount by which the balance reduces each month, which is the same as the amount Zachary pays each month, (the monthly payment).

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The inverse of the divisor which can be used to complete the given equation would be 7/1.

The inverse of a divisor is defined as the changing of the numerator with the denominator when division is being carried out in fraction after which it can be multiplied to arrive at an answer.

The given fractions for division are as follows!

= 1/5 ÷ 1/7

= 1/5 × 7/1

= 7/5

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Answer:

10 + 9 + 0.06 = 19.06