Solve this system.
Select one:

a.
No solution


b.
(4,-2)


c.
(5,10)


d.
Infinite solutions

The length of the base is 16 inches.

To find the length of the base of the triangular pane of glass, we can use the formula for the area of a triangle which is:

Area = (1/2) x base x height

We are given that the height of the pane is 32 inches and the area is 256 square inches. Substituting these values into the formula, we get:

256 = (1/2) x base x 32

To isolate the base, we can divide both sides by (1/2) x 32, which simplifies to 16. This gives us:

256 ÷ 16 = base

Simplifying the left side of the equation, we get:

16 = base

Therefore, the length of the base of the pane is 16 inches.

In summary, the triangular pane of glass has a height of 32 inches and an area of 256 square inches. To find the length of the base, we use the formula for the area of a triangle and solve for the base.

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Answer:

rita and john are susseful the job

js school

Answer is The smaller angle is 35°.

To solve for the acute angles in a right triangle when sin(5x)° = cos(3x + 2)°, we need to use trigonometric identities.

Recall that sin(x) = cos(90 - x) for any angle x. Using this identity, we can rewrite sin(5x)° as cos(90 - 5x)°.

Similarly, cos(x) = sin(90 - x) for any angle x. Using this identity, we can rewrite cos(3x + 2)° as sin(90 - (3x + 2))°, which simplifies to sin(88 - 3x)°.

Now we have cos(90 - 5x)° = sin(88 - 3x)°. Since these two expressions are equal, we can set them equal to each other and solve for x:

cos(90 - 5x)° = sin(88 - 3x)°

sin(5x)° = sin(88 - 3x)°

5x = 88 - 3x

8x = 88

x = 11

Therefore, the acute angles in the right triangle are 5x° and 90 - 5x°, or 55° and 35°. The smaller angle is 35°.

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Answer:

a. x = 68

b. x = 55

c. x = 18

Step-by-step explanation:

Formula

Inscribed angle = Central angle/2

a.

x = 136/2

x = 68

b.

x = ( 360 - 150 - 100 )/2

= 110/2

x = 55

c.

x = 18

Based on the equation, when Lisa sells 24 copies of Math is Fun, her total pay will be $3140.

The equation relating P to N is:

P = 1700 + 60N

This is because her base salary is $1700, and she earns an additional $60 for each copy of Math is Fun she sells.

In order to find her total pay if she sells 24 copies of Math is Fun, we simply need to substitute N = 24 into the equation:

P = 1700 + 60(24)

P = 1700 + 1440

P = 3140

Therefore, if Lisa sells 24 copies of Math is Fun, her total pay will be $3140.

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Using trigonometry, we can solve for the missing angles to find them as 18.43°, 45°, 45°, and 18.43°.

The sign is mounted on a sloped surface, which means that we'll need to use some trigonometry to find the missing angles.

Let's concentrate on the sign's upper right corner, where the letters x and y are absent from two perspectives. The magnitude of angle x may be determined using trigonometry.

Let's begin by sketching a right triangle that has an angle x. The triangle's two sides may be represented by the sign's vertical and horizontal lines, with the addition of a third side to join the top right corner of the sign to the sloping area below.

Since the sign is an octagon, we know that each interior angle is 135°. Therefore, the measure of angle y must be:

y = 180 - 135 = 45°

Now, let's look at the right triangle that includes angle x. We know that the hypotenuse of the triangle is the sloped surface of the sign, which has a length of 4.5 meters. We also know that the opposite side of the triangle is the height of the sign above the ground, which has a length of 1.5 meters.

Using trigonometry, we can find the measure of angle x by taking the inverse tangent of the opposite side over the adjacent side:

tan(x) = opposite/adjacent = 1.5/4.5 = 1/3

x = tan⁻¹(1/3) ≈ 18.43°

Therefore, the measure of angle x is approximately 18.43 degrees.

Hence, using trigonometry, we can solve for the missing angles to find them as 18.43°, 45°, 45°, and 18.43°.

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The mover is communicating that the weight of the table and 4 chairs combined, represented as t+4C, is greater than or equal to 100 pounds.

The expression t+4C represents the total weight of the table and 4 chairs. The mover's invoice states that this total weight is greater than or equal to 100 pounds, which means that the combined weight of the table and chairs is at least 100 pounds. Therefore, the correct answer is D, "The table and 4 chairs weigh at least 100 pounds."

To solve this mathematically, we can use algebraic inequalities. The inequality t+4C >_ 100 can be rearranged as t >_ 100-4C. This means that the weight of the table t must be greater than or equal to 100 minus four times the weight of a single chair C.

If each chair weighs less than 25 pounds, then the total weight of the table and 4 chairs combined will be at least 100 pounds. So D is correct answer.

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The arc measure of minor BC is 155°

An arc is a segment of a circle is defined by two endpoints and the set of points on the curve between them.

The length of an arc is a fraction of the circumference of the circle, and can be calculated using the angle between the two endpoints and the radius of the circle.

We can say that measure of arc BC is m∠ BPC. Also, arc AD is m∠ APD

By Vertical Angles Theorem. That is:

Provided AC and BD are diameters,

m∠ BPC = m∠ APD

m∠ BPC = 155°

Since m∠ BPC = 155°

Therefore, the arc measure of minor BC is 155°

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Complete Question

See attached image

Spencer will be on the phone for 56 minutes in total if he routes 28 calls.

Using unit rates, we can calculate how long Spencer will spend on the phone when routing 28 calls if he spent 10 minutes on the phone while routing 5 calls.

The amount of time spent on each phone call is the unit rate. In this instance, the unit fee is 10 minutes / 5 phone calls = 2 minutes each call.

In order to determine how much time Spencer will spend on the phone when routing 28 calls, we can use this unit rate as follows:

Therefore, Spencer will be on the phone for 56 minutes in total if he routes 28 calls.

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The price of a new ticket after reducing the ticket price by 25% is $6. Maddy will need to sell 400 more tickets this year to raise the same amount of money as last year.

Number of tickets sold = 1200

Cost of each ticket = $8

Part A:

If Maddy lowers ticket costs by 25%, The price of a new ticket will be:

Ticket price = $8 - (25% of $8)

Ticket price = $6

The New ticket price will be calculated by multiplying 0.75 for reducing the 25% tickets

New ticket price = $8 x 0.75 = $6

Part B:

To find how many tickets Maddy requires to sell to equal the same amount of money collected in the previous year:

Total revenue = total number of tickets x Ticket price

1200 tickets x $8 per ticket = $9,600

= $9,600 / $6

= 1,600

Total tickets need to sell = 1600-1200 = 400

Therefore we can conclude that Maddy will need to sell 400 more tickets this year.

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The lateral surface area of a cylinder is the area of the sides of the cylinder, not including the top or bottom. In the case of a can of beans, the label that wraps around the can represents this lateral surface area.

To find the lateral surface area of the can, we need to use the formula for the lateral surface area of a cylinder: LSA = 2πr*h, where r is the radius of the base of the cylinder and h is the height of the cylinder.

Since we are given the diameter of the can (7 cm), we need to divide it by 2 to get the radius: r = 7/2 = 3.5 cm. The height of the can is given as 11 cm.

Now we can plug these values into the formula to find the lateral surface area of the can: LSA = 2π(3.5)(11) ≈ 242.95 cm².

So the lateral surface area of the can of beans is approximately 242.95 cm². This is the area of the sides of the can that the label would wrap around.

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The volume of the prism in 120 cubic centimeter.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is a scalar quantity that characterizes the "size" or "capacity" of an object in three dimensions.

A prism is a three-dimensional geometric shape that has two parallel and congruent bases connected by lateral faces that are typically rectangular or parallelogram-shaped. Prisms are classified based on the shape of their base, such as rectangular prisms, triangular prisms, pentagonal prisms, hexagonal prisms, and so on. The lateral faces of a prism are perpendicular to the bases, and the bases are usually parallel to each other.

According to the given information:

Given the measures of prism is length = 8cm, breadth = 6 cm, height = 5 cm

The formula for volume of prism = 1/2 l*b*h

                                                      = 1/2 8*6*5

                                                      = 120 cubic centimeter

Hence the volume of prism is 120 cubic centimeter.

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The value is calculated by dividing the total number of occurrences by 200 favourable examples that do not possess a college degree is 0.33 is the determined probability value.

The favourable number of cases is 200.

The total number of cases is 600.

The calculation of the required probability is,

Probability = Favourable cases Total number of cases 200 600 = 0.33

Occurrences refer to events or incidents that happen in a particular time or place. These events can be both positive and negative and can occur in various contexts, such as personal experiences, historical events, natural phenomena, and scientific observations.

Occurrences can be significant or insignificant, depending on their impact on individuals or society as a whole. Some occurrences may be routine and expected, while others may be unexpected and unpredictable. The study of occurrences is important in many fields, including history, sociology, psychology, and environmental science. By analyzing past occurrences, researchers can gain insights into patterns of behavior and trends that can inform future decisions and policies.

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Complete Question:-

The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company does not have a college degree is:

The relative frequency of people who strongly agree with the statement "I feel respected by those I work for" is 0.312, or 31.2%.

This means that out of the 500 employees surveyed, 156 strongly agreed with the statement. To find the relative frequency, you simply divide the number of people who strongly agree by the total number of people surveyed (156/500).

This result suggests that the majority of employees feel respected by their employers, which is a positive sign for the workplace culture.

However, it's important to note that there are still a significant number of employees who either disagree or feel neutral about this statement, indicating that there may be room for improvement in terms of fostering a more respectful and supportive work environment.

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the partial derivative ∂z/∂y using implicit differentiation of e^z + sin(5x^2) + 2y = 0 is:
To calculate the partial derivative ∂z/∂y using implicit differentiation of e* + sin (5x^2) + 2y = 0, we first need to differentiate both sides of the equation with respect to y.

We get:

d/dy(e^z + sin(5x^2) + 2y) = d/dy(0)

Using the chain rule, the left-hand side becomes:

∂(e^z)/∂z * ∂z/∂y + ∂(sin(5x^2))/∂y + 2

We can simplify this by recognizing that ∂(sin(5x^2))/∂y = 0, since sin(5x^2) does not depend on y. Thus, we are left with:

∂(e^z)/∂z * ∂z/∂y + 2 = 0

Now, we need to solve for ∂z/∂y:

∂z/∂y = -2 / ∂(e^z)/∂z

To find ∂(e^z)/∂z, we differentiate e^z with respect to z, giving:

∂(e^z)/∂z = e^z

Substituting this into the expression for ∂z/∂y, we get:

∂z/∂y = -2 / e^z

Therefore, the partial derivative ∂z/∂y using implicit differentiation of e^z + sin(5x^2) + 2y = 0 is:

∂z/∂y = -2 / e^z

Note that we cannot simplify this any further without knowing the value of z.
To find the partial derivative ∂z/∂y using implicit differentiation for the equation e^z + sin(5x^2) + 2y = 0, we will first differentiate the equation with respect to y, treating z as a function of x and y.

Differentiating both sides with respect to y:

∂/∂y (e^z) + ∂/∂y (sin(5x^2)) + ∂/∂y (2y) = ∂/∂y (0)

Using the chain rule for the first term, we get:

(e^z) * (∂z/∂y) + 0 + 2 = 0

Now, solve for ∂z/∂y:

∂z/∂y = -2 / e^z

So, the partial derivative ∂z/∂y for the given equation is:

∂z/∂y = -2 / e^z

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After 2 hours, approximately 4.38 grams of Francium remain from the 480-gram sample.

What is Algebraic expression ?

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It may contain one or more terms, with each term separated by a plus or minus sign. Algebraic expressions are used in algebra to represent mathematical relationships and formulas.

a) To write an exponential function that models the mass of Francium remaining after t minutes, we can use the formula:

N = N0 * [tex](1/2)^{(t / t1/2)}[/tex]

where N is the amount remaining after time t, N0 is the initial amount, t1/2 is the half-life, and (t/t1/2) means raised to the power of t/t1/2.

In this case, the initial amount is 480 grams, the half-life is 22 minutes, and we want to find the amount remaining after t minutes. Therefore, the exponential function that models the mass of Francium remaining after t minutes is:

N = 480 * [tex](1/2)^{t/22}[/tex]

b) 2 hours is equal to 120 minutes. To find how many grams of Francium remain after 2 hours, we can substitute t = 120 into the exponential function we found in part a):

N = 480 *[tex](1/2)^{ (120 / 22) }[/tex] ≈ 4.38 grams

Therefore, after 2 hours, approximately 4.38 grams of Francium remain from the 480-gram sample.

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So, the answer is:
(a) f(x) does not exist at xa = 16.
(b) lim f(x) as x approaches 16 does not exist.
(c) None of the conditions for continuity are met at xa = 16.

To find the value of xa where the function is discontinuous, we need to look for any points where the function is undefined or where the left and right limits of the function are not equal.
(a) From the given information, we know that the function is undefined at xa = 16. So, this is the point of discontinuity.
(b) To find the left and right limits at xa = 16, we need to approach the point from both sides of the function. So,
lim f(x) as x approaches 16 from the left (denoted as lim-) = Im = 0
lim f(x) as x approaches 16 from the right (denoted as lim+) = Im = 16
Since the left and right limits are not equal, the limit as x approaches 16 does not exist. So,
lim f(x) as x approaches 16 (denoted as lim) does not exist.
(c) To determine which conditions for continuity are not met, we need to check if the function satisfies the three conditions for continuity at xa = 16.
i) The function must be defined at xa = 16. Since the function is undefined at xa = 16, this condition is not met.
ii) The left and right limits of the function must exist and be equal at xa = 16. Since the left and right limits are not equal, this condition is not met.
iii) The value of the function at xa = 16 must be equal to the limit of the function at xa = 16. Since the limit does not exist, this condition is also not met.
Therefore, none of the conditions for continuity are met at xa = 16.
So, the answer is:
(a) f(x) does not exist at xa = 16.
(b) lim f(x) as x approaches 16 does not exist.
(c) None of the conditions for continuity are met at xa = 16.
Note: The terms "discontinuous" and "continuity" are used throughout the explanation to describe the concept and the point of interest. The term "function" refers to the given function that we are analyzing.

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When the value of x is 7 the value of p will be equal to 8.

It is given that P varies inversely with x, so we can write that

p=k/x

where k is the proportionality constant.

here we can find the value of k by substituting the value of p and x with 7 and 8 in the relation that is given above, we get:

7=k/8

k=7*8

k=56

we the value of k to be 56 after putting the values in the relation.

Now if x is changed to 7, and k is equal to 56 we can get the value of p by putting the known values in the same relation.

p=k/x

p=56/7

p=8.

Therefore, when the value of x is 7 the value for p will be equal to 8.

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The new coordinate of the vertex after dilation is (-5, -3).

To find the new coordinate, you'll need to use the given scale factor of 1/3 and apply it to the original vertex coordinates (-15, -9). Here's a step-by-step explanation:

1. Identify the original vertex coordinates: (-15, -9).
2. Identify the scale factor for dilation: 1/3.
3. Apply the scale factor to the x-coordinate: (-15) * (1/3) = -5.
4. Apply the scale factor to the y-coordinate: (-9) * (1/3) = -3.
5. The new coordinates after dilation are (-5, -3).

By following these steps, you can find the new coordinates of the vertex after dilation at the origin using the given scale factor.

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lcmm,n∙gcdm,n=mn is verified for all three pairs of numbers. We can verify lcmm,n∙gcdm,n=mn for each pair of numbers as follows:

For 60 and 90:

lcm(60,90) = 180

gcd(60,90) = 30

180 * 30 = 5400

60 * 90 = 5400

Since both sides of the equation are equal to 5400, the equation is verified.

For 220 and 1400:

lcm(220,1400) = 3080

gcd(220,1400) = 20

3080 * 20 = 61600

220 * 1400 = 61600

Since both sides of the equation are equal to 61600, the equation is verified.

For 3273∙11 and 23∙5∙7:

lcm(3273∙11, 23∙5∙7) = 15015

gcd(3273∙11, 23∙5∙7) = 161

15015 * 161 = 2418315

3273∙11 * 23∙5∙7 = 2418315

Since both sides of the equation are equal to 2418315, the equation is verified.

Therefore, lcmm,n∙gcdm,n=mn is verified for all three pairs of numbers.

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The sample is being used with such referrals of a qualitative researcher studied women's decision to delay childbearing until their late 30s is Snowball, option C.

A non-probability sampling technique called snowball sampling entails the recruitment of new units by existing units to make up the sample. Research regarding people with certain characteristics who would be hard to find otherwise can benefit from snowball sampling (e.g., people with a rare disease).

Snowball sampling, sometimes referred to as chain sampling or network sampling, starts with one or more research participants. Following then, it proceeds based on recommendations from those individuals. This procedure is repeated until the required sample is obtained or a saturation point is reached.

The selection is based on a variety of factors, including:

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Complete question;

A qualitative researcher studied women's decision to delay

childbearing until their late 30s. Initial study participants

referred friends who had made similar decisions. What type

of sample is being used with such referrals?

A.Convenience

B.Volunteer

C.Snowball

D. Purposive

The predicted exam grade for 1 hour of studying is 66. Therefore the residual for 1 hours of studying can be calculated as Residual = Actual Exam Grade - 66.

To find the residual for 1 hour of studying, we first need to determine the predicted exam grade and compare it to the actual exam grade for that specific data point.

Using the line of best fit equation y = 6x + 60, we can find the predicted exam grade for 1 hour of studying:

y = 6(1) + 60
y = 6 + 60
y = 66

So, the predicted exam grade for 1 hour of studying is 66. To calculate the residual, you need the actual exam grade for 1 hour of studying. If that information is not provided, the residual cannot be calculated. If the actual grade is provided, subtract the predicted grade from the actual grade to find the residual:

Residual = Actual Exam Grade - Predicted Exam Grade

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57 students most likely got heads between 45 and 60 times.

To determine the number of students who got heads between 45 and 60 times, we'll use the normal distribution properties. First, we need to calculate the z-scores for 45 and 60:

Z = (X - μ) / σ

For 45 heads:
Z1 = (45 - 50) / 5 = -1

For 60 heads:
Z2 = (60 - 50) / 5 = 2

Next, we need to find the probability that a student falls between these z-scores. We can do this by looking up the z-scores in a standard normal distribution table or using a calculator. The probabilities corresponding to these z-scores are:

P(Z1) = 0.1587
P(Z2) = 0.9772

Now, subtract P(Z1) from P(Z2) to get the probability of a student's result falling between 45 and 60 heads:

P(45 ≤ X ≤ 60) = P(Z2) - P(Z1) = 0.9772 - 0.1587 = 0.8185

Finally, multiply this probability by the total number of students (70) and round to the nearest whole number:

Number of students = 0.8185 * 70 ≈ 57

So, approximately 57 students most likely got heads between 45 and 60 times.

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To find the value of a² + bc√(-d) when a = -3, b = 2, c = 100, and d = -2, follow these steps:

Step 1: Substitute the values into the expression.
a² + bc√(-d) = (-3)² + (2)(100)√(-(-2))

Step 2: Simplify the expression.
(-3)² + (2)(100)√(2) = 9 + 200√2

So, the value of a² + bc√(-d) when

a = -3,

b = 2,

c = 100,

d = -2 is 9 + 200√2.

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The derivative of the given function is f'(x) = 2(sec x * tan x) + sec^2 x. b) The critical numbers for the function are x = 0 and x = π.of the given function is f'(x) = 2(sec x * tan x) + sec^2 x.

The critical numbers for the function are x = 0 and x = π.

Derivative and critical numbers,

a) Find the derivative: We're given the function f(x) = 2 sec x + tan x.

To find its derivative, we need to find the derivatives of the individual terms (sec x and tan x) and then add them together.

The derivative of sec x is sec x * tan x. So, for the term 2 sec x, the derivative is 2 * (sec x * tan x).

The derivative of tan x is sec^2 x.

Now, we add both derivatives to find the derivative of f(x): f'(x) = 2(sec x * tan x) + sec^2 x

b) Find the critical numbers: Critical numbers are the points where the derivative of the function is either 0 or undefined.

To find the critical numbers, we'll set f'(x) equal to 0 and solve for x, as well as identify where the derivative is undefined.

First, let's set f'(x) to 0: 0 = 2(sec x * tan x) + sec^2 x

We need to solve this equation for x. It's a bit tricky, so let's rewrite the equation in terms of sin and cos: 0 = 2((1/cos x) * (sin x/cos x)) + (1/cos x)^2

Now let's simplify the equation: 0 = 2(sin x/cos^2 x) + 1/cos^2 x

To eliminate the denominators, we'll multiply through by cos^2 x: 0 = 2(sin x) + cos x

Now, we can use the unit circle to find the values of x in the interval 0 ≤ x ≤ 2π that satisfy this equation: For sin x = 0, x = 0, π For cos x = -2, there's no solution in the given interval because the range of cosine is -1 ≤ cos x ≤ 1.

Therefore, the critical numbers are x = 0 and x = π. Your answer:

a) The derivative of the given function is f'(x) = 2(sec x * tan x) + sec^2 x.

b) The critical numbers for the function are x = 0 and x = π.

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Answer:

156 bundles

Step-by-step explanation:

Total area of the roof = 2(70 x 30) = 4200 sf  

(4200 sf) / (27sf/bundle) = 155.56 ≈ 156 bundles

_______________________________

_______________________________

El intervalo correspondiente de millas que Juana puede manejar su nuevo auto está entre 10,000 y 14,000 millas.

Para determinar el intervalo correspondiente de millas que Juana puede manejar su nuevo auto, podemos resolver la fórmula del costo anual en términos de la variable m (millas recorridas por año). Dado que el costo anual está entre $6400 y $7100, podemos establecer la siguiente desigualdad:

6400 ≤ 0.35m + 2200 ≤ 7100

Restando 2200 en los tres lados de la desigualdad, obtenemos:

4200 ≤ 0.35m ≤ 4900

Dividiendo por 0.35 en los tres lados, obtenemos:

12000 ≤ m ≤ 14000

Por lo tanto, Juana puede manejar su nuevo auto en un intervalo de millas que va desde 12000 millas hasta 14000 millas por año.

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Using various laws of integers we can say that if a is a positive integer and b is a negative integer, statement A is False, B is True, C s True and D is false.

Here we are given that a is a positive integer while b is a negative integer.

A. The statement says that the difference (a - b) could be negative.

According to the subtraction law of integers, when a negative number is subtracted from a positive number, that is we have

2 - (-3)

Here the 2 minus signs will make a positive to give

2 + 3 = 5

Hence (a - b) will be a positive number since b is negative.

B.

The difference (b - a) cannot be positive.

Since a is positive and b is negative, according to the above example we will get

-3 - 2 = -5

Hence it is true that the difference (b - a) can't be positive.

C.

The sum (a + b) could be positive.

Here, we can see that a is a positive number while b is a negative number. In the light of above example, we will get

2 - 3 = -1

Here the sum is nagative as 3 > 2, but if we had

3 + (-2), then the answer would have been 1. Hence (a + b) can be positive. Hence the statement is true.

D.

The sum (b + a) must be negative.

Integers have commutative properties. Hence a + b = b + a

Hence if a + b can be positive, then b + a can also be positive.

Hence the statement is False.

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