Consider the following system of equations:
How many solutions does the system have?
-zero
-one
-two
-three
-four
-infinitely many

Answer:

8(x + 6) = 144

Step-by-step explanation:

We can start building this equation by making everything equal to 144 since the problem is representing the total number of apples:

? = 144

Next, we don't know how many apples are in each basket, so we can represent it with a variable, x.

Since 6 apples are added to each basket we will simply add 6 to the "x" amount of apples in each basket:

x + 6 = 144

Lastly, according to the scenario, we have 8 baskets, each holding "x" amount of apples plus the extra 6 that was added, so it will be multiplied:

8(x + 6) = 144

A geodesic is the shortest path between two points on a curved surface, such as a sphere. To find a geodesic, an integral is set up to determine the length of a path on the surface.

This integral is similar to the one used for flat surfaces but may be more complex and involve different coordinates depending on the nature of the curved surface. In the case of a sphere, spherical polar coordinates are commonly used.

The length of a path on a curved surface can be expressed using an integral similar to Equation (6.2) for flat surfaces. However, when dealing with a sphere, the integral may involve different coordinates, specifically spherical polar coordinates. Spherical polar coordinates consist of three components: radius (r), polar angle (θ), and azimuthal angle (φ). By expressing the path in terms of these coordinates, the integral can be set up to calculate the length of the geodesic.

To illustrate this, let's consider the example of finding the geodesic on the surface of a sphere. The integral would involve integrating the square root of the sum of squared differentials of the three spherical polar coordinates, weighted by the appropriate metric coefficients. The specific form of the integral would depend on the metric tensor associated with the spherical polar coordinate system. By minimizing this integral, the geodesic between two points on the sphere can be determined. In summary, finding the geodesic, or shortest path, between two points on a curved surface involves setting up an integral to calculate the path length. The integral is similar to the one used for flat surfaces but may be more complex and use different coordinates, such as spherical polar coordinates for a sphere. By minimizing the integral, the geodesic on the curved surface can be found.

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Researchers try to gain insight into the characteristics of a sample population by examining a sample of the population.

A sample is a subset of individuals or units taken from a larger population. Researchers use sampling methods to select a representative group of individuals from the population they are interested in studying. By studying the sample, researchers can make inferences and draw conclusions about the characteristics, behaviors, or trends that may exist within the entire population.

The goal of sampling is to obtain a sample that accurately represents the population in terms of its relevant characteristics. Researchers carefully select their samples to ensure that they are representative and minimize bias. This allows them to generalize the findings from the sample to the larger population with a certain level of confidence.

By examining a sample, researchers can collect data, analyze patterns, and draw conclusions about the population as a whole. This approach is more feasible and practical than attempting to study the entire population, especially when the population is large or geographically dispersed.

Therefore, researchers use samples to gain insight into the characteristics of a population, making option d. "Sample" the correct answer.

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Answer:

slop is 0.5 and intercept of y is -3

Answer:

½ is the slope,-3 is the intercept

Step-by-step explanation:

now to find the slope and intercept

we use the equation,

y=mx + c

where m is the slope

and c is the y intercept

so we compare 4y=2x-12 to the equation

but we first have to make y the subject of the equation in the question – 4y is already the subject –

y=2x-12/4

y=2x/4 -3

comparing...

we see that m is 2/4=½ c= -3

Answer:

lolololololololololololololololol

The cost of the most valuable watch is worth $177.

Let

x - y = 72

x + y = 282

y - (-y) = 282 - 72

y + y = 210

2y = 210

y = 210/2

y = $105

x - y = 72

x - 105 = 72

x = 72 + 105

x = $177

Therefore, the cost of the most valuable watch is worth $177.

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A cylinder with radius 1, height 1 in 1st octant of xyz-plane, center at origin, height from z=1 to z=2 and θ from 0 to π/2.

What is cylinder ?

A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.

The cylindrical coordinate conditions can be expressed mathematically as:

1≤r≤2

0≤θ≤π/2

1≤z≤2

These conditions define a cylinder with radius 1 and height 1 located in the first octant of the xyz-plane. The cylinder has its center at the origin (0,0,0) and its height extends from z = 1 to z = 2. The angle θ ranges from 0 to π/2, meaning that the cylinder is restricted to the first quadrant in the xy-plane.

A cylinder with radius 1, height 1 in 1st octant of xyz-plane, center at origin, height from z=1 to z=2 and θ from 0 to π/2.

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Answer:

\(\huge\boxed{\sf x = 5, \ y = 1/4}\)

Step-by-step explanation:

3x + 8y = 17 -----------------(1)

4x - 4y = 19 -----------------(2)

2(4x - 4y) = 19 × 2

8x - 8y = 38 ----------------(3)

3x + 8y + 8x - 8y = 17 + 38

3x + 8x = 55

11x = 55

x = 55/11

3(5) + 8y = 17

15 + 8y = 17

8y = 17 - 15

8y = 2

y = 2/8

\(\rule[225]{225}{2}\)

y varies directly with x, and the constant of variation is -10.

To determine whether y varies directly with x, we need to check if the equation can be written in the form y = kx, where k is the constant of variation.
In the given equation, y = -10x, we can see that y and x are directly proportional, since the equation can be written in the form y = kx.
To find the constant of variation, we compare the coefficients of x in both sides of the equation.

In this case, the coefficient of x is -10.
Therefore, the constant of variation is -10.
In conclusion, y varies directly with x, and the constant of variation is -10.

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Answer: EG = 80

Step-by-step explanation: A parallelogram is a quadrilateral with opposite sides parallel to each other.

The diagonals of a parallelogram bisect each other, which means, using the figure as example:

EJ = JG

So, to determine EG, first find w:

\(4w+4=2w+22\)

\(2w=18\)

w = 9

Substituting:

\(EJ=4w+4\)

\(EJ=4(9)+4\)

EJ = 40

Since each segment has the same measure:

EG = 2EJ

EG = 2(40)

EG = 80

The measure of EG is 80 units

Answer:

30 - 6{sqrt15}

Step-by-step explanation:

Answer: The correct answer is A :)

By applying the slope of a line and the y-intercept formula, the following are the answer to each table:

Slope of a line (gradient) shows the value or degree of incline on a straight line.

If it is known that two points are passed by a straight line, for example (x₁,y₁) and (x₂,y₂), then the gradient can be obtained by the formula:

m = ∆y/∆x

   = (y₂ - y₁) / (x₂ - x₁)

Y-intercept is the point where the line intersects the y-axis. It is the intersection of the function's graph with the y-axis when x = 0.

For every table, we pick 2 points to calculate the slope and y-intercept:

Table 1:

(x₁,y₁) and (x₂,y₂) = (-5,-4) and (0,-2)

m = (y₂ - y₁) / (x₂ - x₁)

   = (-2 + 4) / (0 + 5)

   = 2/5 (option S)

y-intercept is obtained when x = 0, thus (0,-2) is the y-intercept (option O)

Table 2:

(x₁,y₁) and (x₂,y₂) = (2,0) and (4,3)

m = (y₂ - y₁) / (x₂ - x₁)

   = (3 - 0) / (4 - 2)

   = 3/2 (option N)

y-intercept is obtained when x = 0, so we substitute this value into the formula given (x₂,y₂) = (4,3)

 m = (y₂ - y₁) / (x₂ - x₁)

3/2 = (3 - y₁) / (4 - 0)

  6 = 3 - y₁

  y₁ = -3

Thus, (0,-3) is the y-intercept (option K)

Table 3:

(x₁,y₁) and (x₂,y₂) = (1,-5) and (3,-3)

m = (y₂ - y₁) / (x₂ - x₁)

   = (-3 + 5) / (3 - 1)

   = 1 (option M)

y-intercept is obtained when x = 0, so we substitute this value into the formula given (x₂,y₂) = (3,-3)

m = (y₂ - y₁) / (x₂ - x₁)

1 = (-3 - y₁) / (3 - 0)

3 = -3 - y₁

 y₁ = -6

Thus, (0,-6) is the y-intercept (option B)

Table 4:

(x₁,y₁) and (x₂,y₂) = (1,3) and (3,1)

m = (y₂ - y₁) / (x₂ - x₁)

   = (1 - 3) / (3 - 1)

   = -1 (option A)

y-intercept is obtained when x = 0, so we substitute this value into the formula given (x₂,y₂) = (3,1)

m = (y₂ - y₁) / (x₂ - x₁)

-1 = (1 - y₁) / (3 - 0)

-3 = 1 - y₁

y₁ = 4

Thus, (0,4) is the y-intercept (option Q).

Table 5:

(x₁,y₁) and (x₂,y₂) = (1,3) and (2,6)

m = (y₂ - y₁) / (x₂ - x₁)

   = (6 - 3) / (2 - 1)

   = 3 (option P)

y-intercept is obtained when x = 0, so we substitute this value into the formula given (x₂,y₂) = (2,6)

m = (y₂ - y₁) / (x₂ - x₁)

3 = (6 - y₁) / (2 - 0)

6 = 6 - y₁

y₁ = 0

Thus, (0,0) is the y-intercept (option J)

Table 6:

(x₁,y₁) and (x₂,y₂) = (-6,6) and (0,3)

m = (y₂ - y₁) / (x₂ - x₁)

   = (3 - 6) / (0 + 6)

   = -1/2 (option F)

y-intercept is obtained when x = 0, thus, (0,3) is the y-intercept (option G)

Table 7:

(x₁,y₁) and (x₂,y₂) = (0,-5) and (2,0)

m = (y₂ - y₁) / (x₂ - x₁)

   = (0 + 5) / (2 - 0)

   = 5/2 (option E)

y-intercept is obtained when x = 0, thus, (0,-5) is the y-intercept (option L)

Table 8:

(x₁,y₁) and (x₂,y₂) = (0,1) and (3,3)

m = (y₂ - y₁) / (x₂ - x₁)

   = (3 - 1) / (3 - 0)

   = 2/3 (option H)

y-intercept is obtained when x = 0, thus, (0,1) is the y-intercept (option D)

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Answer:

If you count by 2's and 2 x 2 = 4

Step-by-step explanation:

Answer:

4 is a multiple of 2

Step-by-step explanation:

The reason it is because take a multiplication table for example. 1*2=2, 2*2=4, 3*2=6, 4*2=8, and so on.

Answer:

-10°F, -13°F, and -21°F

Step-by-step explanation:

we are looking for a temperature that is less than -8

-10°F, -13°F, and -21°F are all less than -8

Answer:

f-1 (x)

f-1 ×2 +7

f- 2 +7

f = + 5

The taxpayer who would most likely benefit from an installment sale is Allan, who sold a business use car at a net gain that was less than the amount of depreciation.

An installment sale is a transaction in which the sales price is received over a period of time that spans more than one tax year. Installment sales may have tax advantages, which is why taxpayers should consider them.

The taxable profit in an installment sale is not calculated using the entire sales price. Instead, it is calculated by applying the gross profit percentage to each installment's payments received during the year. In general, if an installment sale meets the definition, the taxpayer reports income from the sale as the payments are received, rather than in the year of sale.

However, in some situations, taxpayers might choose to report the entire profit from an installment sale in the year of sale. In such instances, an election to do so must be made.

The difference between the sales price and the adjusted cost basis of the asset is known as the gain. The gain is reduced by selling expenditures to arrive at the net gain. Net gain occurs when the sales price of a commodity is higher than its cost of acquisition and other fees or expenses related to its purchase and sale.

Depreciation is a term used in accounting and finance to describe the systematic decrease in the value of an asset over time due to wear and tear. It is an expense that lowers a company's net income and lowers the value of an asset on the balance sheet.

Hence, Allan, who sold a business use car at a net gain that was less than the amount of depreciation, will most likely benefit from an installment sale.

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Answer:

A=1 B=2 C=3   Domain: [2, infinity) Range: (neg. infinity, 3]

Step-by-step explanation:

a is rate B is Horitzontal shift C is vertical shift

Answer:

B. exponential; y = 89 • 0.62x

Step-by-step explanation:

Answer:

exponential; y = 89 • 0.62^x

...............................................................................................................................................

Answer:

Option B exponential y = 89 · 0.62x

Step-by-step explanation:

The table shows the estimated number of deer living in a forest over a five year period.

Year            Number of deers

0                     89

1                      55

2                     34

3                     21

4                     13

Now we have to find the model representing this situation. Difference in number of deer, in the forest.

We can see there is a common ratio between each successive term r =  = 0.618

r =  = 0.618

so it can be represented by an exponential model.

Option B is the answer.

...............................................................................................................................................

Answer: d, the diameter, is about 36.92 units

Step-by-step explanation:

         The c value is the circumference and we are being asked to solve for the diameter.

         We can take the value they give for the circumference, plug it into the circumference formula, and solve for d. Please note that the diameter is two times the radius, or r, so at the end I will multiply r by two.

C = 2πr

(116) = 2πr

18.46 ≈ r

r ≈ 18.46

-

18.46 * 2 = 36.92

     The missing measure is about 36.92 units.

The probability that calls to exactly two randomly selected households will both go unanswered is 0.1849

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

Probabiity of answering, p = 57%

This means that the probability that no one answers the call is

q = 1 - 57%

Evaluate

q = 43%

So, the probability that both calls will go unanswered is

P = q²

This gives

P = (43%)²

Evaluate

P = 0.1849

Hence, the probability is 0.1849

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Answer:

\(\textsf{D)} \quad (4 - (-6))^2+(3 - (-2))^2=\left(\sqrt{(4-(-6))^2+(-2-3)^2}\right)^2\)

Step-by-step explanation:

To find the length of p, subtract the x-coordinate of vertex Q from the x-coordinate of vertex R:

\(\implies p=x_R-x_Q\)

\(\implies p = 4 - (-6)\)

To find the length of q, subtract the y-coordinate of vertex P from the y-coordinate of vertex R:

\(\implies q = y_R-y_P\)

\(\implies q =3 - (-2)\)

To find the length of r, use the distance formula, where (x₁, y₁) = Q and (x₂, y₂) = P.

\(\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}\)

\(\implies r=\sqrt{(x_P-x_Q)^2+(y_P-y_Q)^2}\)

\(\implies r=\sqrt{(4-(-6))^2+(-2-3)^2}\)

Therefore, the equation that could be used to show p² + q² = r² is:

\((4 - (-6))^2+(3 - (-2))^2=\left(\sqrt{(4-(-6))^2+(-2-3)^2}\right)^2\)

Answer:

jjj

Step-by-step explanation:

Answer:

y = 2

x = -6

Step-by-step explanation:

Looking at the two equations, we notice right away that we can re-arrange the first equation to solve for x.

x + 4y = 2 becomes x = 2 - 4y

Now, we see that the second equation has an x in it. We replace the x in the second equation with the value of x we just found (using the first equation).

-x + y = 8 becomes -(2 - 4y) + y = 8

Simplify the left side!

1. Distribute the negative

        -2 +4y + y = 8

2. Simplify like terms

        -2 + 5y = 8

3. Move the -2 to the right side (changing its sign as we do so)

          5y = 8 + 2

          5y = 10

4. Divide both sides by 5

          y = 2

NOW TO FIND X

Since we have the value for y, we can plug it in an equation to find x. We will use the second equation.

-x + y = 8 becomes -x +2 = 8

1. Move the 2 to the right side:

-x = 8 - 2

-x = 6

2. Divide both sides by -1:

x = -6

Now we come to a very important step: we must check our answers. First, we will plug in our numbers for x and y into the first equation.

x + 4y = 2

(-6) + 4(2) = 2

-6 + 8 = 2

2 = 2

The variables hold true for that equation. Now we check them with the second equation!

-x + y = 8

-(-6) + 2 = 8

6 + 2 = 8

8 = 8

Both our answers are right!

Hope this helped!!!

The profit margins (return on sales) for each division are approximately :Division A = 10.85%,Division B = 9.11% and The calculations for the year would be:Net Income = $85,428,Return on Assets = 18.9%.

To compute the profit margins (return on sales) for each division, we divide the profit by the sales and multiply by 100 to express the result as a percentage.

For Division A:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($230,000 / $2,120,000) * 100

Profit Margin ≈ 10.85%

For Division B:

Profit Margin = (Profit / Sales) * 100

Profit Margin = ($34,700 / $381,000) * 100

Profit Margin ≈ 9.11%

To calculate the net income and return on assets for Polly Esther Dress Shops Inc., we use the given information.

Net Income = Profit Margin * Sales

Net Income = 7% * $1,220,400

Net Income = $85,428

Return on Assets = Profit Margin * Asset Turnover

Return on Assets = 7% * 2.7

Return on Assets = 18.9%

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Answer:

Step-by-step explanation:

-9 + b/4 >= -4

b/4 >= 5

b >= 20

the solution is d

Answer:

sorry only doing the ones im sure of

a)

FBC is half the circle, so the angle would = 180.

180 - 135 = 45, so thats the angle between BC

its a vertical angle, so it would be the same on the other side, between FE

the only angle left is betweeen DC, so add them all up and minus by 360

360 - 306 = 54

b)

a triangle's angles add up to 180, so

49 + 70 = 119

180 - 119 = 61

since this is an inscribed angle that isnt connected to the center, the arc will be double the angle

so ? = 122

d)

5(8) = 40

40/4 = 10

x = 10

f)

the rest of the circle is 243 bc 360-117=243

243 - 177 = 126

126/2 = 63

Answer:

Value of \(p-q=1\)

Step-by-step explanation:

We need to find \(p-q\)

\(p-q=14-13\\\\=1\)

\(\huge\boxed{\sf{Hello\:there!}}\)

We are asked to evaluate p-q.

Now, if we aren't given the value of every variable, evaluating this expression is impossible. However, we do have the value of p (14) and the value of q (13)

We plug these numbers instead of the variables:

p-q

p=14

q=13

14-13

1

Hence, the value of the expression is 1.

\(\huge\boxed{\sf{Hope\:it\:helps.\:Please\:mark\:Brainliest.}}\)

\(\huge\bold{Good\:luck!}}\)

\(\huge\mathfrak{LoveLastsAllEternity}\)

Given that `∥Ax∥ [infinity] =∥A∥ [infinity]⋅∥x∥ [infinity]`, we are to determine whether the statement is true or false. Answer: True

Explanation: First, let's recall the definition of the matrix norm:

Suppose `A` is a `m x n` matrix. Then, the norm of matrix `A`, denoted by `||A||`, is the maximum of the lengths of `Ax` over all `x` in `ℝ^n` with length `1`.i.e.,

`||A|| = sup_{x ≠ 0} ||Ax||/||x||`

The norm can also be written as:

`||A|| = max_{||x||=1} ||Ax||`

Now, coming back to the statement, we have

`∥Ax∥ [infinity] = ∥A∥ [infinity]⋅∥x∥ [infinity]`

We need to show that this statement is true.

To show this, we will use the definition of the matrix norm to prove it.

For any matrix `A` and a vector `x`, we can say that `||Ax||_∞ ≤ ||A||_∞ . ||x||_∞`.

Thus, we have `sup{ ||Ax||_∞/||x||_∞ } ≤ sup{ ||A||_∞ . ||x||_∞ / ||x||_∞ }`

i.e., `||A||_∞ ≤ sup{ ||Ax||_∞ / ||x||_∞ }`.

Since `||A||_∞` is less than or equal to some quantity and the definition of the norm also uses a supremum, we can say that `||A||_∞` is less than or equal to the norm.

Hence, we have `||A||_∞ ≤ ||A||`.

Similarly, we can show that `||x||_∞ ≤ ||x||`.

Hence, we can write `∥Ax∥ [infinity] / ∥x∥ [infinity] ≤ ∥A∥ [infinity]`

i.e., `∥Ax∥ [infinity] ≤ ∥A∥ [infinity] . ∥x∥ [infinity]`

Therefore, `∥Ax∥ [infinity] = ∥A∥ [infinity]⋅∥x∥ [infinity]` is true.

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True. the inequality ||Ax||∞ ≤ ||A||∞ ⋅ ||x||∞ holds true for any matrix A and vector x.

​

The statement is true. The infinity norm (also known as the maximum norm or supremum norm) of a matrix A is defined as the maximum absolute row sum of A, and the infinity norm of a vector x is defined as the maximum absolute element of x.

Therefore, the inequality ||Ax||∞ ≤ ||A||∞ ⋅ ||x||∞ holds true for any matrix A and vector x. This means that the infinity norm of the matrix-vector product is bounded by the product of the infinity norms of the matrix and the vector.

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