Topic #2: Distance & Midpoint
9. Find ST if S(-3, 10) and T(-2, 3).

Answer:  L isn't the midpoint of segment MN.

Step-by-step explanation:

NL+LM=NM

6x-5+2x+3=4x+9

8x-2=4x+9

8x-2+2=4x+9+2

8x=4x+11

8x-4x=4x+11-4x

4x=11

Divide both parts of the equation by 2:

2x=5.5

NL=6x-5

NL=(2x)(3)-5

NL=(5,5)(3)-5

NL=16.5-5

NL=11.5

LM=2x+3

LM=5.5+3

LM=8.5

NL≠LM

Hence, L isn't the midpoint of segment MN.

In summary, based on the given lengths and mathematical reasoning, we have determined that point L is the midpoint of segment MN because the lengths of NL and LM are equal when x = 2.

We must compare the lengths of the two segments NL and LM and see if they are identical in order to establish whether point L is the midpoint of segment MN.

NL = 6x - 5

LM = 2x + 3

The lengths of NL and LM ought to be equal if L is the middle of segment MN. To put it another way, NL and LM ought to be equal.

Constructing the equation

6x - 5 = 2x + 3

Now, solve for x:

6x - 2x = 3 + 5

4x = 8

x = 2

As soon as we know the value of x, we can put it back into the NL and LM formulas to get their lengths at x = 2:

NL = 6x - 5 = 6 * 2 - 5 = 12 - 5 = 7

LM = 2x + 3 = 2 * 2 + 3 = 4 + 3 = 7

The lengths of NL and LM are both 7 units.

Point L is in fact the middle of segment MN because both segments NL and LM have similar lengths.

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Answer:

174 homes

Step-by-step explanation:

152+22

simplify to get your answer:

174

Answer:

20%

Step-by-step explanation:

Percentage discount on the cost of the sofa = 20%

Percentage discount = (Absolute discount / Cost price) × 100

Given,

             Cost price =  $600

Absolute discount  =  Cost price - Selling price

Absolute discount  =  $600 - $480

                                = $120

Percentage discount = (Absolute discount / Cost price) × 100

                                   = (120/600) × 100

                                   = 120/6

                                   = 20%

Hence, percentage discount on the cost of the sofa = 20% .

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Answer:

x < -7

Step-by-step explanation:

3(x-4)-2>5x

3x - 12 - 2 > 5x

3x - 14 > 5x

-2x > 14

x < -7

Answer: x<-7

Step-by-step explanation: 3(x-4)= 3x-12

3x-14>5x

5x-3x=2x

-14>2x

-14/2=-7

-7>x

Answer:

i think C

Step-by-step explanation:

tell me if i am wrong and hope you have a good day

Answer:

A

Step-by-step explanation:

The double dot plot shows the quiz scores for two different class periods, represented by the two sets of data points. Each data point represents the score of a single student on the quiz.

The first population, represented by the data points on the left side of the plot, appears to have a center at around 16-18 points and a variation that is more spread out. This suggests that the students in this class period had a wider range of quiz scores, with some students scoring higher and some scoring lower.

The second population, represented by the data points on the right side of the plot, appears to have a center at around 8-10 points and a variation that is more tightly clustered. This suggests that the students in this class period had a narrower range of quiz scores, with fewer students scoring higher and fewer scoring lower.

 Based on these observations, an inference that can be drawn about the two populations is that the class period with higher quiz scores had more students who performed well on the quiz, while the class period with lower quiz scores had fewer students who performed well on the quiz. This suggests that the level of student proficiency in the subject may vary across class periods, and that it may be important to consider this variability when designing instructional strategies.

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Answer:

3 upon 2. that's the answer ..

Answer: he would save15,000

Step-by-step explanation:

Answer:

B. 467

A yellow ball will be selected about 467 times.

The value of q is -27.

Recall Vieta's Formulas, which state that for a quadratic equation \(ax^2\) + bx + c = 0 with zeroes alpha and beta, the sum of the zeroes is equal to -b/a, and the product of the zeroes is equal to c/a.

In our equation \(x^2\) - 3x + q, the sum of the zeroes alpha and beta is -(-3)/1 = 3.

We are given that 2 alpha + 3 beta = 15. Substitute alpha = (15 - 3 beta)/2 into the equation.

Replace the value of alpha in the sum of zeroes equation: (15 - 3 beta)/2 + beta = 3.

Simplify the equation by multiplying both sides by 2: 15 - 3 beta + 2 beta = 6.

Combine like terms: 15 - beta = 6.

Subtract 15 from both sides: -beta = -9.

Multiply both sides by -1 to solve for beta: beta = 9.

Substitute the value of beta into the sum of zeroes equation: alpha = (15 - 3 * 9)/2 = -3.

Since we have the values of alpha and beta, we can find q using the product of the zeroes formula: q = alpha * beta = -3 * 9 = -27.

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The value of p in the given equation is -1.

Given is an equation p-3 = -4, we need to find the value of p,

So,

p-3 = -4

p = -4+3

p = -1

Hence, the value of p in the given equation is -1.

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The substitution effect is positive for goods that are complements, meaning that the quantity demanded of both goods increases as the price of one of the goods decreases.

If the price of B falls to $1, while the price of A and the consumer's income stay the same, the utility-maximizing combination of goods A and B will be represented by the consumer's indifference curve, which is tangent to the new budget constraint (given by the new relative price of B).

Explanation:

The substitution effect is a microeconomic concept that occurs when the price of a good increases or decreases, and consumers adjust their consumption of other goods. In this case, the price of good B falls to $1. However, the price of good A and the consumer's income remains constant.The utility-maximizing combination of goods A and B is represented by the consumer's indifference curve, which is tangent to the new budget constraint (given by the new relative price of B). Thus, the consumer will purchase a higher quantity of good B and a lower quantity of good A as a result of the fall in the price of B.

The substitution effect is generally so strong that it can often overcome the income effect. The income effect is a concept that refers to how consumers' income changes affect their purchasing decisions. The income effect can be positive or negative, depending on the type of good in question.A positive income effect means that an increase in income leads to an increase in demand for a good, while a negative income effect means that an increase in income leads to a decrease in demand for a good.The substitution effect is the change in quantity demanded of a good from a change in its relative price. The substitution effect is negative for goods that are substitutes, meaning that the quantity demanded of one good increases as the price of the other good increases.

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Answer:

18

Step-by-step explanation:

colored: white

3           :8

We have 48 white papers so multiply each side by 6

colored: white

3*6       :  8*6

18               48

There are 18 colored papers

Answer:

C)  18

Step-by-step explanation:

3/8 = c/48

cross-multiply to get:

8c = 144

c = 18

a. The number of Burger in the first case is 8.

b. The number of drinks will be 6 drinks.

c. The number of burgers is 0.

From the information, Chloe wants to buy food for her friends at the concession stand at a soccer game, the stand sells drinks for $4 and burgers for $3 and she has $32 to spend.

Let drinks = d

Let burger = b

For the first case, he has 2 drinks and need the number of burgers. This will be:

2($4) + 3b = 32

8 + 3b = 32

Collect like terms

3b = 32 - 8

3b = 24.

Divide

b = 24/3

b = 8

Number of Burger = 8 burger

For the second case, there are 4 burgers and we need to know the number of drinks. This will be:

4($3) + 3d = 32

12 + 3d = 32.

Collect like terms

3d = 32 - 12

3d = 20

Divide

d = 20/3 = 6

The number of drinks = 6

For the third case, there are 8 drinks. This will be:

8($4) + d + 32

32 + d = 32.

d = 32 - 32 = 0

The complete table will be:

Drinks Burgers

2. 8

6. 4

8. 0

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Complete question

Chloe wants to buy food for her friends at the concession stand at a soccer game. The stand sells drinks for $4 and burgers for $3. Chloe has $32 to spend and wants to spend it all.

The table shows different possible combinations of drinks and burgers that Chloe could order. Complete the table based on the information below.

Drinks Burgers

2

4

8

Theree numbers that follows given conditions are: 26, 19 and 38

Let a, b and c be three numbers.

We have been given the sum of three numbers is 83.

So, we get an equation a + b + c = 83              ............(1)

The third number is two times the second.

So, we get an equation,

c = 2b                              ...............(2)

The second number is seven less than the first.

So, we get an equation ,

b = a - 7                            

i.e., a = b + 7             ...............(3)

Substitute these values of a and c in equation (1)

b + 7 + b + 2b = 83

4b + 7 = 83

4b = 76

b = 19

Substitute this value of equation (2) and (3),

a = b + 7

a = 19 + 7

a = 26

and c = 2b

c = 2 * 19

c = 38

Therefore, the required numbers are: 26, 19 and 38

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The complete question is:

The sum of three numbers is 83. The third number is two times the second. The second number is seven less than the first. What are the numbers

To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.



To find the equation of a line parallel or perpendicular to a given line through a specific point, follow these steps:

1. Determine the slope of the given line. If the given line is in the form y = mx + b, the slope (m) will be the coefficient of x.

2. Parallel Line: A parallel line will have the same slope as the given line. Using the slope-intercept form (y = mx + b), substitute the slope and the coordinates of the given point into the equation to find the new y-intercept (b). This will give you the equation of the parallel line.

3. Perpendicular Line: A perpendicular line will have a slope that is the negative reciprocal of the given line's slope. Calculate the negative reciprocal of the given slope, and again use the slope-intercept form to substitute the new slope and the coordinates of the given point. Solve for the new y-intercept (b) to obtain the equation of the perpendicular line.

Remember that the final equations will be in the form y = mx + b, where m is the slope and b is the y-intercept.Therefore, To find the equation of a line parallel or perpendicular to a given line through a point, determine the slope and substitute the point's coordinates into the slope-intercept form.

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Answer:

$47.945

Step-by-step explanation:

Given the following

Original price = $43;

markup = 11.5%

Markup price = 11.5% of the original price

Markup price = 11.5% of $43

Markup price = 0.115×43

Markup price = $4.945

Retail price = original price+markup price

Retail price = $43+$4.945

Retail price = $47.945

a. The demand for central bank money is $400 billion.

b. The equilibrium interest rate is 0.02 or 2%.

c. The overall supply of money is $1,000 billion, which is equal to the overall demand for money at the interest rate found in part (b).

d. If central bank money is increased to $300 billion, it would not have an impact on the interest rate as long as the overall supply of money remains the same.

e. If the overall money supply increases to $3,000 billion, the impact on the interest rate cannot be determined without further information.

To calculate the answers, we will use the given information and equations:

a. The demand for central bank money (Md) is given by Md = $Y(0.8 - 4i). Given that nominal income (Y) is $5 trillion, we can substitute the values to find the demand for central bank money: Md = $5 trillion * (0.8 - 4i) = $4 trillion - $20 trillioni. Therefore, the demand for central bank money is $400 billion ($4 trillion * 0.1).

b. The equilibrium interest rate is determined by setting the demand for central bank money equal to the supply of central bank money. Since the supply of central bank money is $100 billion (the initial monetary base), we can equate it to the demand for central bank money: $100 billion = $4 trillion - $20 trillioni. Solving for i, we find the equilibrium interest rate to be 0.02 or 2%.

c. The overall supply of money is equal to the monetary base multiplied by the reserve-deposit ratio. Given that the monetary base is $100 billion and the reserve-deposit ratio is 0.1, the overall supply of money is $1,000 billion ($100 billion / 0.1). This is equal to the overall demand for money at the interest rate found in part (b), which ensures equilibrium.

d. Increasing central bank money to $300 billion does not impact the interest rate as long as the overall supply of money remains the same. Since the overall supply of money is determined by the monetary base and the reserve-deposit ratio, unless those factors change, the interest rate will remain unaffected.

e. Without further information on the changes in the reserve-deposit ratio or the demand for money, it is not possible to determine the impact on the interest rate when the overall money supply increases to $3,000 billion. Changes in either the reserve-deposit ratio or the demand for money can affect the equilibrium interest rate.

The demand for central bank money is $400 billion, and the equilibrium interest rate is 2%. The overall supply of money is $1,000 billion, which is equal to the overall demand for money at the equilibrium interest rate. Increasing central bank money without changing other factors does not impact the interest rate. The impact on the interest rate when the overall money supply increases to $3,000 billion cannot be determined without further information.

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Answer:

2^-2= 4^-1 =1\4

1\4=4

so I hope you get to it

Answer:

Inverse Property

When adding the additive

inverse to the number, the sum

is zero.

Step-by-step explanation:

When multiplying a number by

its reciprocal, the product is multiplicative inverse.

The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.

The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.

Given the production function q = 1000KL, we can differentiate it with respect to L:

d(q)/d(L) = 1000K

Therefore, the RTS of the isoquant for production level q is 1000K.

The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.

Labor cost = $20/hour

Capital cost = $40/machine/hour

Ratio of labor to capital cost = Labor cost / Capital cost

                              = $20/hour / $40/machine/hour

                              = 0.5

The ratio of labor to capital cost is 0.5.

To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.

Let C(K, L) be the total cost function.

The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:

C(K, L) = 40K + 20L

To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.

The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.

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On solving the provided question, we can say that random sample the conditions for interference are met.

selected at random (purely random, unpredictable). Every member of the population being polled ought to have an equal probability of getting chosen. She randomly selected 25 names from a pool of 250 employees as an example of a simple random sample. Since there are 250 of her employees in total, and each one has an equal probability of being chosen, the sample in this instance is random. Using simple random sampling, which is a form of probability sampling, researchers choose individuals at random from a population. There is an equal opportunity for selection for every person in the population.

Yes, the conditions for interference are met.

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Answer:

4x + 2.5y = 184

x = y - 6

Step-by-step explanation:

Let the number of smoothies sold by stand = x

And number of cones sold = y

If the selling price of each cone = $2.5

Selling price of the 'y' cones = $2.5y

Selling price of each smoothies = $4

Then sales of smoothies = $4x

If the total sales of one day = $184

Equation for this situation will be,

4x + 2.5y = 184 -------(1)

If the stand sold 6 less smoothies than the cones,

x = y - 6 -----(2)

Therefore, system of equations contains two equations (1) and (2).

Answer:

Step-by-step explanation:

kaja

Answer:

Rectangular pyramid : Faces, Vertices, Edges = 5 , 5 , 8 respectively

Step-by-step explanation:

Rectangular pyramid is a 3D shape, with base as rectangle & triangle face corresponding to each side of base (on the top)

Faces = 5 { 1 rectangular base face , 4 triangular faces above}

Vertices = 5 { 4 vertices of rectangle, 1 vertice on top - where triangles' tips intersect}

Edges = 8 {4 edges of rectangle at base , 4 edges of triangles above}

Answer:

b. 5, 5, 8

Step-by-step explanation:

i did the assignment and this was the correct answer <3

So the total amount received by Sohail is 100 * y². To get the precise amount, we must first determine the value of x.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Let's call the number of days Sohail was in town and cleaned the house "y". Then we can write:

y = x - 8 (since he was out of town for 8 days)

And the amount he was promised per day is 10, so the total amount promised is:

10 * y = 10 * (x - 8)

At the end of the break, his mother decided to square the amount due to him, so the final amount he received is:

(10 * y)² = (10 * (x - 8))²

Expanding the square and simplifying, we get:

100 * y²= 100 * (x - 8)²

So the final amount Sohail received is 100 * y². To find the exact value, we need to know the value of x.

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