Write the equation of the line which passes
through the point (2. −3) and has a slope of -2/5

A. 2x + 5y = 4
C. 2x+ 5y = −11
B. 2x+5y = −9
D. 2x-5y = −16

Show work for this question please & thank u

Answer:

k-4=c

Step-by-step explanation:

Answer:

sm\(prism M and Cylinder P\\\)\(Plato\)

Step-by-step explanation:

The required set of numbers 5, 9, 11, and 14 satisfies all the given conditions.

In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets; for instance, A = 1, 2, 3, 4 is a set.

a set of four whole numbers that satisfies the given conditions:

5, 9, 11, 14

To check that this set meets the requirements:

The range of the original set (12 - 4 = 8) increased by 2 to become 10 (14 - 4 = 10).

The mean of the original set ((4 + 9 + 10 + 12) / 4 = 8.75) remains the same in the new set ((5 + 9 + 11 + 14) / 4 = 8.75).

The median of the original set is 9.5 (the average of 9 and 10), and the median of the new set is 10 - 1 = 9.

Therefore, the set of numbers 5, 9, 11, and 14 satisfies all the given conditions.

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Answer:

(x - 4) * 2

Step-by-step explanation:

let x be the ? number

The given statement "2 is multiplied by the difference of a number and 4" can be written in the form of an expression as 2x-8.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given statement "2 is multiplied by the difference of a number and 4" can be written in the form of an expression as shown below. Therefore, the expression is,

2(x- 4)

Simplifying the expression,

= 2x - (2×4)

= 2x - 8

Hence, the given statement "2 is multiplied by the difference of a number and 4" can be written in the form of an expression as 2x-8.

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The length of the fence must be 618cm

The volume that it can hold is 1,909,620 cm³

First, the fence is just equal to the circumference of the cylinder, remember that the circumfernce of a circle of diameter D is:

C = П*D

Here we use П = 3, then:

C = П*206cm

C = 3*206cm = 618cm

Now the volume, for a cylinder of diameter D and height H, the volume is:

V = П*(D/2)²*H

Replacing the values that we know we will get:

V = 3*(206cm/2)²*60cm = 1,909,620 cm³

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Answer: $1346.40

Step-by-step explanation:

Volume of the pool is:

\((6)(8)(8)+\frac{1}{2}(6)(8)(6)=528\)

This has a cost of \((528)(2.55)=\boxed{\$1346.40}\)

The volume of the pool will be 528 cubic feet. Then the cost to fill the pool will be $1,346.4.

Let the prism with A is the base area and a height of H. Then the volume of the prism is given as

V = A × H

Then the volume of the pool will be

V = [(6 × 8) + (1/2 × 6 × 6)] × 8

V = (48 + 18) × 8

V = 66 × 18

V = 528 cubic feet

Then the cost to fill the pool will be

C = $2.55 × 528

C = $1,346.4

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Answer:

2x+3

Step-by-step explanation:

\((6x+6)+(-3-4x)=2x+3\)

Answer:

the correctanswer is 19

Answer:

3.188

Step-by-step explanation:

Given that :

Sample data: 26.5, 28, 30.2, 29.6, 32.3, 24.7

Sample standard deviation (s) = 2.728

Mean (mu) = 25

Tstatistic formula :

(x - mu) / (s/sqrt(n))

n = sample size = 6 ; s = 2.728 ; mu = 25

Sample mean (x) = (26.5 + 28 + 30.2 + 29.6 + 32.3 + 24.7) / 6

Sample mean (x) = 171.3 / 6 = 28.55

Tstatistic = (28.55 - 25) / (2.728 / sqrt(6))

Tstatistic = 3.55 / 1.1137013

Tstatistic = 3.1875692

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

Let A represent the number of students reading Accountancy, S represent the number of students reading Sociology, and F represent the number of students reading French.

Let X be the number of students reading all three.

From the information given:

A ∩ S = 19

A + S - 27 = 120 - 53 + 19 = 86 (number of students reading Accountancy or Sociology but not French)

S - A - X = 27

S + F - X = 53

F - X = 19

A - X = 86 - 19 = 67

Total = A + S + F - (A ∩ S) - (A ∩ F) - (S ∩ F) + X = 120

Solving, we get X = 6, A = 73, S = 52, F = 25.

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

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Answer: passes a horizontal AND vertical line test✅; no repeating x values✅

Step-by-step explanation:

To pass a line test, the function must pass BOTH the horizontal and vertical line test. If it only passes one but not the other, is it NOT a function.

Lastly, it can be a function if it has repeating y values.

The points (-3, 9), (-1, 1), (0, 0), (1, 1) and (3, 9) lie on the graph of the function y = x²

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation y = x²

When x = -3; y = (-3)² = 9

When x = -1; y = (-1)² = 1

When x = 0; y = (0)² = 0

When x = 1; y = (1)² = 1

When x = 3; y = (3)² = 9

The points (-3, 9), (-1, 1), (0, 0), (1, 1) and (3, 9) lie on the graph of the function y = x²

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The translation used to create the image of the second polygon is A, 7 units to the right.

To determine the translation used to create the image of the second polygon (A' B' C' D') from the original polygon (ABCD), compare the corresponding vertices.

Original polygon (ABCD):

A (-2, -1)

B (0, -4)

C (4, -4)

D (2, -1)

Image polygon (A' B' C' D'):

A' (5, -1)

B' (7, -4)

C' (11, -4)

D' (9, -1)

To find the translation, calculate the horizontal and vertical differences between the corresponding vertices.

Horizontal difference:

For point A: A'x - Ax = 5 - (-2) = 7

For point B: B'x - Bx = 7 - 0 = 7

For point C: C'x - Cx = 11 - 4 = 7

For point D: D'x - Dx = 9 - 2 = 7

Vertical difference:

For point A: A'y - Ay = -1 - (-1) = 0

For point B: B'y - By = -4 - (-4) = 0

For point C: C'y - Cy = -4 - (-4) = 0

For point D: D'y - Dy = -1 - (-1) = 0

From the calculations, see that the horizontal difference is 7 units for all the corresponding vertices, while the vertical difference is 0 units for all the corresponding vertices.

Therefore, the translation used to create the image of the second polygon is 7 units to the right.

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Mathematical form of the question:

Use the graph to answer the question.

Graph of polygon ABCD with vertices at A (-2, -1), B (0, -4), C (4, -4), D (2, -1). A second polygon A' (5, -1), B' (7, -4), C' (11, -4), D' (9, -1).

Determine the translation used to create the image.

7 units to the right

3 units to the right

7 units to the left

3 units to the left

if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

Calculating the loan amount for each brand by subtracting the down payment from the cash price:

Loan amount for Daewoo = RM1,899 - RM300 = RM1,599

Loan amount for Daikin = RM1,699 - RM300 = RM1,399

Loan amount for Mitsubishi = RM1,999 - RM300 = RM1,699

Calculating the interest charge for each brand:

Interest charge for Daewoo = Loan amount for Daewoo * Interest rate = RM1,599 * 0.04 = RM63.96

Interest charge for Daikin = Loan amount for Daikin * Interest rate = RM1,399 * 0.04 = RM55.96

Interest charge for Mitsubishi = Loan amount for Mitsubishi * Interest rate = RM1,699 * 0.04 = RM67.96

To find the monthly installment price, divide the total amount (cash price + interest charge) by the number of monthly installments:

Monthly installment price for Daewoo = (Cash price of Daewoo + Interest charge for Daewoo) / Number of monthly installments = (RM1,899 + RM63.96) / 18 ≈ RM107.22

Monthly installment price for Daikin = (Cash price of Daikin + Interest charge for Daikin) / Number of monthly installments = (RM1,699 + RM55.96) / 18 ≈ RM98.89

Monthly installment price for Mitsubishi = (Cash price of Mitsubishi + Interest charge for Mitsubishi) / Number of monthly installments = (RM1,999 + RM67.96) / 18 ≈ RM116.72

Therefore, if Jenny chooses to buy from Daikin, the monthly installment price would be approximately RM98.89, and the total installment price to be paid would be approximately RM1,779.98 (18 monthly installments * RM98.89).

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Answer:

62,500 pi

Step-by-step explanation:

diameter = radius + radius

d = 2r

r = d/2

A = 4pi r^2

= 4 pi (d/2)^2

= 4pi d^2/4

= 4pi* 250^2/4

= 4pi * 62,500/4

= 4pi * 15625

= 62,500 pi

Answer: Hello!

Step-by-step explanation: After measuring the two triangles I can conclude they are congruent!

Finn, tenth grader straight A student.

Have a great day.

Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

Based on the total costs of buying at the two stores, it is not worth the extra drive going to the store across town.

The total costs for buying 5 pounds of chicken at each store are added to the total gas costs to and from each location to determine the total costs of each option.

Based on the cost difference of $1 ($18.34 - $17.34), it is not advisable to travel across town just for 5 pounds of chicken, especially when you factor in the wear and tear of the car along the distance and the time difference.

The cost of a pound of chicken at a neighborhood store = $2.99

The cost of a pound of chicken at the store across town = $3.29

The number of pounds of chicken required = 5 pounds

The distance to and from the neighborhood store = 4.6 miles (2.3 miles x 2)

The distance to and from the store across town = 17.6 miles (8.8 miles x 2)

The total time to and from the neighborhood store = 14 minutes (7 x 2)

The total time to and from the store across town = 42 minutes (21 x 2)

The time difference = 28 minutes.

Car's mileage per gallon = 19 mpg

The cost of gas per gallon = $3.66

The total cost of buying at the neighborhood store = $17.34 ($3.29 x 5 + $3.66 x 4.6/19)

The total cost of buying at the store across town = $18.34 ($2.99 x 5 + $3.66 x 17.6/19)

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Weight of Omar after 4 weeks is 9.4375 pounds.

The same attribute is expressed using a unit conversion, but in a different unit of measurement.

For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

Weight of Omar at the time of birth = 8 pound 3 ounces

Weight gained by Omar in 4 weeks = 5 × 4 = 20 ounces

New weight of Omar

= (8 lb 3 ounces) + 20 ounces

= 8 lb + 23 oz

As, we know 16 ounces = 1 pound

23 ounces = 1.4375 pound

Now, total weight of Omar after 4 weeks = 8 lb + 23 oz

                                                                  ≈ 8 lb + (1.4375) lb

                                                                   ≈ 9.4375 pounds

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If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions. Use the sign of each side of your inequality to decide which of these cases holds. If the number on the other side of the inequality sign is positive, proceed to step 3.

Answer:

17.1

Step-by-step explanation

a^2+b^2=c^2

2^2 + 17^2 = c^2

4 + 289 = c^2

293 = c^2

square root of 293 or 17.1

First of all find the total area and then subtract the area of circle from the area of rectangle, It will be easier that way...

\(\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}\)

\( \qquad \bf \implies \: area = length \times breadth\)

\( \qquad \tt \blue\looparrowright \purple{area = 3 \times 4} \)

\( \qquad \tt \blue\looparrowright \purple{area = 12 \: {cm}^{2} } \)

\( \qquad \bf \implies \: area = \pi {r}^{2} \)

\( \qquad \tt \red\looparrowright \green{area = \frac{22}{7} \times {1}^{2} } \)

\( \qquad \tt \red\looparrowright \green{area = \frac{22}{7} \times 1} \)

\( \qquad \tt \red\looparrowright \green{area = 3.14 \: {cm}^{2} } \)

\( \qquad \bf \implies \: area =area \: of \: rectangle - area \: of \: circle\)

\( \qquad \tt \pink\looparrowright \orange{area = 12 - 3.14 } \)

\( \qquad \tt \pink\looparrowright \orange{area = 8.86} \)

➪ Thus, The area of the shaded region is 8.86 cm²...~

The integer that represents the submarine's position = -664 ft (option C)

To determine the submarine's position after ascension, we need to rewrite the statement in mathematical terms.

The initial position of the submarine = surface

The initial position of the submarine = 0 ft

The position after submerging and diving = -972 ft

Then it ascends = 308 ft

Since it is ascending, it means it is rising and this indicates a positive number (+308 ft)

The integer that represents the submarine's position = The position after submerging and diving + the number of ft it ascended

The integer that represents the submarine's position = -664 ft (option C)

Answer:

Options (2), (3), (5) and (6)

Step-by-step explanation:

Let the number of bicycles = x

and the number of treadmills = y

Since, number of new bicycles must be more than \(\frac{1}{3}\) times of new treadmills,

Inequality representing the statement will be,

x > \(\frac{1}{3}\)y

Each bicycle costs $340 and each treadmill costs $670.He must spend less than $5650,

Inequality will be,

340x + 670y < 5650

And the number of bicycles and treadmills should be greater than 0.

x > 0

y > 0

Therefore, constraints for this situation are,

Option (2)

Option (3)

Option (5)

Option (6)

Answer:

b

Step-by-step explanation:

840 different numbers can be created selecting 4 of the digits from the number

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

Number =  8712395

Digits = 4

The count of digits in the number is 7

Using the above as a guide, we have the following:

So, we have

Numbers = 7 * 6 * 5 * 4

Evaluate

Numbers = 840

Hence, 840 numbers can be formed

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