Which equation defines y as a linear function of x?
Select all that apply.
□ A. y = 3x² +7
□ B. x - 4y = 5
□ C. 5x² + y = 3
OD. 2(x+3y) = 6
O E. y = 5x - 3x + 4

a.(1) When both r and s are odd integers, the quadratic polynomial obtained by multiplying out (x - r)(x - s) will have a coefficient of 1 for x^2 term, and both the coefficient of x term and constant term will be odd integers.

(2) When both r and s are even integers, the polynomial obtained by multiplying out (x - r)(x - s) will also have a coefficient of 1 for x^2 term, but the coefficient of x term and constant term will be even integers.

(3) When one of r and s is even and the other is odd, the polynomial obtained by multiplying out (x - r)(x - s) will have a coefficient of 1 for x^2 term, the coefficient of x term will be an odd integer, while the constant term will be an even integer.

b. x^2 - 1253x + 255 cannot be written as a product of two polynomials with integer coefficients.

a. When both r and s are odd integers, the product (x − r)(x − s) will have a coefficient of 1 for x^2 term, and both the coefficient of x term and constant term will be odd integers. This is because the sum of two odd integers and the product of two odd integers is also an odd integer.

When both r and s are even integers, the product (x − r)(x − s) will also have a coefficient of 1 for x^2 term, but the coefficient of x term and constant term will be even integers. This is because the sum of two even integers and the product of two even integers is also an even integer.

When one of r and s is even and the other is odd, the product (x − r)(x − s) will have a coefficient of 1 for x^2 term, and the coefficient of x term will be an odd integer, while the constant term will be an even integer. This is because the sum of an odd and even integer is an odd integer, and the product of an odd and even integer is an even integer.

b. If x^2 - 1253x + 255 can be written as a product of two polynomials with integer coefficients, then we can write it as (x - r)(x - s) where r and s are integers. From part (a), we know that both r and s cannot be odd integers since the coefficient of x term would be odd, but 1253 is an odd integer. Similarly, both r and s cannot be even integers since the constant term would be even, but 255 is an odd integer. Therefore, one of r and s must be odd and the other must be even. However, the difference between an odd integer and an even integer is always odd, so the coefficient of x term in the product (x - r)(x - s) would be odd, which is not equal to the coefficient of x term in x^2 - 1253x + 255. Hence, x^2 - 1253x + 255 cannot be written as a product of two polynomials with integer coefficients.

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If the slope of the graph is increasing from positive x-axis to negative x-axis, then the function is not that decreasing. Therefore, Jonathan's statement is incorrect.

The function is decreasing on intervals where the slope is negative. In this case, since the slope is increasing from positive x-axis to negative x-axis, the function is decreasing on the interval where x is negative.

To determine this interval more precisely, we would need to find the x-value(s) where the slope changes sign from positive to negative. These x-values correspond to critical points, such as local maximums or minimums. The function is decreasing before a local maximum and after a local minimum.

Therefore, Jonathan's statement is not correct, and the function represented by the graph is decreasing on the interval where x is negative.

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a) The domain of the function is  [0, 7.1875], while the range is [0,23]. Considering the domain and the range, the graph of the function is given by the image presented at the end of the answer.

b) The trip had a duration of 5.1875 hours.

The function for this problem is defined as follows:

g(t) = 23 - 3.2t.

The domain is the set of input values that can be assumed by the function. The time cannot have negative measures, hence the lower bound of the domain is of zero, while the gas cannot be negative, hence the upper bound of the domain is given as follows:

23 - 3.2t = 0

3.2t = 23

t = 23/3.2

t = 7.1875 hours.

The range is given by the set of all output values assumed the function, which are the values of the gas, hence it is [0,23].

The graph is a linear function between points (0, 23) and (7.1875, 0).

At the end of the trip there were 6.4 gallons left, hence the length of the trip is obtained as follows:

23 - 3.2t = 6.4

t = (23 - 6.4)/3.2

t = 5.1875 hours.

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Answer:

Can you rephrase the question as it doesn't seem possible to solve. There may be a value missing.

In the given situation we know that the equation X²+6x=5 has (3) two real solutions.

In algebra, a real solution is just an answer to an equation that is a real number.

Discriminant b² - 4ac has zero value in the case of a single actual solution.

One solution, x = -1, exists for the equation x² + 2x + 1 = 0.

The Determinant Calculator on Cuemath can be used to determine the determinant of a quadratic equation.

Use the formula: b²-4ac

Insert values:

b²-4ac

6²-4(1)(5)

36-20

16

We know that:

If b²-4ac is > o (Two real solutions)

Therefore, in the given situation we know that the equation X²+6x=5 has (3) two real solutions.

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The points that lie on the line L with parametric form L(t) = (1, 3, 2) + t(-2, 1, -1) are (1, 3, 2), (-1, 4, 1), and (-3, 5, 0). So, the correct answer is C).

The parametric form of the line L can be written as:

L(t) = x0 + tv

where x0 = (1, 3, 2) and v = (-2, 1, -1)

To find which points lie on the line L, we can substitute different values of t into the parametric equation and see which points we get.

For t = 0, we have:

L(0) = x0 + 0v = (1, 3, 2) + 0(-2, 1, -1) = (1, 3, 2)

For t = 1, we have:

L(1) = x0 + 1v = (1, 3, 2) + (-2, 1, -1) = (-1, 4, 1)

For t = 2, we have:

L(2) = x0 + 2v = (1, 3, 2) + 2(-2, 1, -1) = (-3, 5, 0)

So the points that lie on the line L are (1, 3, 2), (-1, 4, 1), and (-3, 5, 0). So, the correct option is C).

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Answer:

n = 8

Step-by-step explanation:

We can find the slope using the slope formula which, which is

[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where x2, y2, x1, and y1 are a pair of coordinates and m is the slope.

We can allow (3, -2) to represent x2 and y2, and (n, 6) to represent x1 and y1:

[tex]8/5=\frac{-2-6}{3-n}\\ 8/5=\frac{-8}{3-n}\\ 8/5(3-n)=-8\\24/5-8/5n=-8\\-8/5n=-64/5\\n=8[/tex]

The R-square value informs us that whether the shift is in the morning or the evening and whether it is a weekday shift or weekend shift may account for 71% of the variability in the number of chairs generated.

The R-square statistic measures how much of the variance in the dependent variable in a regression model is accounted for by the independent variables. A better fit of the model to the data is indicated by higher values, which range from 0 to 1.

A value of 0 indicates that no variation is explained by the independent variables, while a value of 1 indicates that all variation in the dependent variable is explained by the independent factors.

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Answer:

slope = 5

slope = (y2 - y1) / (x2 - x1)

Using this formula, calculate the slope between pairs of points in the given set of data. For example, the slope between the first two points (-2, -12) and (-1, -7) is:

slope = (-7 - (-12)) / (-1 - (-2)) = 5 / 1 = 5

Calculate the slope between each pair of points as follows:

Between (-2,-12) and (-1,-7): slope = 5

Between (-1,-7) and (0,-2): slope = 5

Between (0,-2) and (1,3): slope = 5

Between (1,3) and (2,8): slope = 5

The volume of the solid bounded below by the cone z = √(x^2 + y^2) and bounded above by the sphere x^2 + y^2 + z^2 = 18 is 192π/3 cubic units

To find the volume of the solid bounded below by the cone z = √(x^2 + y^2) and bounded above by the sphere x^2 + y^2 + z^2 = 18, we can use a triple integral.

First, we need to determine the limits of integration. Since the solid is symmetric about the z-axis, we can use cylindrical coordinates.

The cone is given by z = √(x^2 + y^2), which in cylindrical coordinates becomes z = r. The sphere is given by x^2 + y^2 + z^2 = 18, which in cylindrical coordinates becomes r^2 + z^2 = 18.

Thus, the limits of integration are

0 ≤ r ≤ √(18 - z^2)

0 ≤ θ ≤ 2π

0 ≤ z ≤ √(r^2)

The integral to find the volume is

V = ∭ dV = ∫∫∫ dV

Using cylindrical coordinates, dV = r dz dr dθ, so the integral becomes

V = ∫₀²π ∫₀ᵣ√(18 - z²) ∫₀ᵣ r dz dr dθ

We can simplify this integral by first integrating with respect to z:

V = ∫₀²π ∫₀ᵣ√(18 - z²) r dz dr dθ

Using a trigonometric substitution u = z/√(18 - z²), we can simplify this to

V = ∫₀²π ∫₀¹ r√(18 - u²(18)) 18du dr dθ

V = 18∫₀²π ∫₀¹ r√(18(1 - u²)) du dr dθ

Using another substitution u = sin(θ), we can simplify this to:

V = 36∫₀²π ∫₀¹ r√(1 - u²) du dr dθ

This integral can be evaluated using the formula for the volume of a sphere of radius R

V = 36(4/3 π(√2)³)

V = 192π/3 cubic units

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The given question is incomplete, the complete question is:

Use a triple integral to find the volume of the solid bounded below by the cone z = √(x^2 + y^2 ) and bounded above by the sphere x^2 + y^2 + z^2 = 18

Step 1: Rearrange the equation √x +2y^2 = 15 to get x = (15 - 2y^2)^2.

Step 2: Substitute x = (15 - 2y^2)^2 in the equation √4x - 4y^2=6.

Step 3: Simplify the equation to get 4(15 - 2y^2)^2 - 4y^2 = 6.

Step 4: Solve for y^2 by rearranging the equation to get y^2 = (6 + 4(15 - 2y^2)^2)/8.

Step 5: Substitute y^2 = (6 + 4(15 - 2y^2)^2)/8 in the equation x = (15 - 2y^2)^2.

Step 6: Solve for x by rearranging the equation to get x = (15 - (6 + 4(15 - 2y^2)^2)/4)^2.

Step 7: Substitute y^2 = (6 + 4(15 - 2y^2)^2)/8 in the equation x = (15 - (6 + 4(15 - 2y^2)^2)/4)^2.

Step 8: Simplify the equation to get x = (15 - (6 + 60 - 8y^

V is 5.92 centimetres above the pyramid's base at its highest point.

A pyramid is a 3D pοlyhedrοn with the base οf a pοlygοn alοng with three οr mοre triangle-shaped faces that meet at a pοint abοve the base. The triangular sides are called faces and the pοint abοve the base is called the apex. A pyramid is made by cοnnecting the base tο the apex. Sοmetimes, the triangular sides are alsο called lateral faces tο distinguish them frοm the base. In a pyramid, each edge οf the base is cοnnected tο the apex that fοrms the triangular face.

Give the altitude the letter h. Next, we have:

tan(60) = h/2

Simplifying, we get:

h = 2 tan(60) = 2 √(3)

The Pythagorean theorem yields the following:

[tex]$\begin{align}{{V O^{2}+O F^{2}=V F^{2}}}\\ {{V O^{2}+1^{2}=6^{2}}}\\ {{V O^{2}=35}}\end{align}$[/tex]

Taking the square root of both sides, we get:

VO ≈ 5.92 cm

Rounding to three significant figures, we get:

VO ≈ 5.92 cm

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The maximum fuel cell area that can be operated at 1 A/cm^2 under the given conditions can be estimated using the equation A = I/(2FJ), where A is the maximum cell area, I is the current density (1 A/cm^2), F is the Faraday constant, and J is the current density per unit area. Assuming a stoichiometric number of 2 and substituting the given values, we get A = 0.029 m^2 or 290 cm^2.

Channel flow in fuel cells is almost always considered to be laminar because turbulent flow can cause mixing of the reactants and products, reducing the efficiency of the fuel cell. Laminar flow allows for efficient mass transport of the reactants and products to and from the electrode surface. Additionally, laminar flow reduces the likelihood of damage to the fuel cell due to erosion or corrosion caused by turbulent flow. However, the design of fuel cell flow channels can also affect the degree of turbulence and mixing, and optimizing this balance is an ongoing area of research.

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Answer:69

Step-by-step explanation: 32+420-90+09=69 pls mark it 5 stars

The equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 13xy is y = e^(13x^2/2).

To find an equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 13xy, we can use the method of separation of variables. Let's start by separating the variables:

dy/dx = 13xy

We can then rewrite this equation as:

dy/y = 13x dx

Integrating both sides of the equation gives:

ln|y| = 13x^2/2 + C

where C is the constant of integration.

To find C, we can use the fact that the curve passes through the point (0, 1). Substituting x=0 and y=1 into the equation above, we get:

ln|1| = 0 + C

C = 0

Substituting this value of C back into the equation gives:

ln|y| = 13x^2/2

Solving for y gives:

|y| = e^(13x^2/2)

Since the curve passes through the point (0, 1), we can take the positive branch of the absolute value to get:

y = e^(13x^2/2)

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Answer:

Step-by-step explanation:

To find the sum of the radii of the two types of cells in scientific notation, we need to add the two radii together. However, the radii are given in different orders of magnitude (exponents), so we need to convert one of the radii to match the order of magnitude of the other radius.

The radius of dish A cells is 5.1 x 10^-10 cm.

The radius of dish B cells is 4.1 x 10^-8 cm.

We can convert the radius of dish A cells to match the order of magnitude of dish B cells by multiplying it by 100 (10^2), which gives us:

5.1 x 10^-10 cm x 10^2 = 5.1 x 10^-8 cm

Now that both radii have the same order of magnitude (10^-8), we can add them together to get the total sum of the radii:

5.1 x 10^-8 cm + 4.1 x 10^-8 cm = 9.2 x 10^-8 cm

Therefore, the sum of the radii of the two types of cells, in scientific notation, is 9.2 x 10^-8 cm.

Answer:9.2 x 10^-8 cm.

Step-by-step explanation:

Answer:

124 and 125.97

Step-by-step explanation:

y

Answer:

In mathematics, an inequality is a statement that compares two values, indicating that they are not equal, and specifies the relationship between them. In other words, an inequality expresses a relative difference between two values or quantities, rather than an exact equality.

There are different types of inequalities, but the most common ones involve comparisons between numerical values or algebraic expressions using inequality symbols, such as:

Greater than: x > y (read as "x is greater than y")

Less than: x < y (read as "x is less than y")

Greater than or equal to: x ≥ y (read as "x is greater than or equal to y")

Less than or equal to: x ≤ y (read as "x is less than or equal to y")

Inequalities can also involve multiple variables and can be used to describe ranges of values or conditions that must be satisfied. For example, x + y > 5 is an inequality that describes a region of the xy-plane where the sum of x and y is greater than 5.

Inequalities are used extensively in many areas of mathematics, including algebra, calculus, and optimization, and also have applications in other fields such as economics, physics, and engineering.

Step-by-step explanation:

Answer

6255 pounds

8.34×750=6255lbs

The area οf the figure is 33 square yards.

A rectangle is a clοsed 2-D shape, having 4 sides, 4 cοrners, and 4 right angles (90°).The οppοsite sides οf a rectangle are equal and parallel. Since, a rectangle is a 2-D shape, it is characterized by twο dimensiοns, length, and width. Length is the lοnger side οf the rectangle and width is the shοrter side.

A crοssed rectangle is a crοssed (self-intersecting) quadrilateral which cοnsists οf twο οppοsite sides οf a rectangle alοng with the twο diagοnals (therefοre οnly twο sides are parallel). It is a special case οf an antiparallelοgram, and its angles are nοt right angles and nοt all equal, thοugh οppοsite angles are equal. Other geοmetries, such as spherical, elliptic, and hyperbοlic, have sο-called rectangles with οppοsite sides equal in length and equal angles that are nοt right angles.

Tο find the area οf the figure, we first find the area οf the rectangle (8 yds by 6 yds) and subtract the area οf the smaller rectangle (3 yds by 5 yds). The area οf the figure is:

Area = (8 yd)(6 yd) - (3 yd)(5 yd)

[tex]= 48 yd^2 - 15 yd^2[/tex]

[tex]= 33 yd^2[/tex]

Therefοre, the area οf the figure is 33 square yards.

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The original length of the reed is 3.83 nindas which can be calculated by using the information given in the question.

Area is a two-dimensional measurement of a surface or space. It is a measure of how much space is occupied by a two-dimensional object or surface. The area of a shape is determined by multiplying the length and width of the shape together.

Firstly, we need to calculate the width of the field. As the reed fits 30 times along the width, this implies that the width of the field is 30 times the length of the reed. Therefore, the width of the field is 30 x length of the reed.

Now, we need to calculate the area of the field. As the area of the field is given as 375 nindas², this implies that the area of the field is equal to 375 nindas².

We can substitute the width of the field (30 x length of the reed) into the equation for the area of the field, to yield: 375 nindas² = (30 x length of the reed) x length of the reed.

Solving for length of the reed, we get: length of the reed = (375/30)1/2 = 3.83 nindas.

Therefore, the original length of the reed is 3.83 nindas.

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Answer: At most 18 acute angles

Step-by-step explanation:

The sum of the interior angles of an n-sided polygon is (n-2) × 180 degrees. In a convex polygon, each interior angle is less than 180 degrees.

Let a₁, a₂, ..., a₁₁ be the interior angles of the 11-sided polygon. Then the sum of the interior angles is:

a₁ + a₂ + ... + a₁₁ = (11-2) × 180 = 1620 degrees

Since each angle is acute, we know that each angle is less than 90 degrees. Let A be the number of acute angles. Then the sum of the acute angles is at most:

A × 90

So we have:

a₁ + a₂ + ... + a₁₁ ≤ A × 90

Substituting the sum of the interior angles, we get:

1620 ≤ A × 90

Solving for A, we get:

A ≤ 18

Therefore, the polygon can have at most 18 acute angles.

Based on the graph given, the function is not continuous at x = 1.

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. A function is typically represented using functional notation as f(x), which means that the output value of the function f corresponds to the input value x.  Functions can take many forms and can be represented graphically or algebraically. They are used to describe many real-world phenomena, including physical systems, economic trends, and social behavior. Functions are important in mathematics because they provide a framework for understanding relationships between variables and for solving problems in various areas of mathematics, science, and engineering.

Here,

At x = 1, there is a "hole" or a point of discontinuity in the graph where the function is undefined. This is because the function has a removable discontinuity at x = 1, meaning that the limit of the function exists at x = 1 but the function is not defined at that point.

Therefore, the value of x at which the function is not continuous is: 1

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The product of the number 3/4 and 8 1/2 is 51/8.

A mixed number is one that has a fraction and a whole number, separated by a space. An example of a mixed number is 8 1/2. Contrarily, an improper fraction is one in which the numerator exceeds or is equal to the denominator. For instance, 17/2 is a bad fraction. An improper fraction is a fraction in which the numerator is more than or equal to the denominator, as opposed to a mixed number, which combines a whole number with a proper fraction.

The given numbers are 3/4 and 8 1/2.

Convert the mixed number to an improper fraction:

8 1/2 = (8 x 2 + 1) / 2 = 17/2

Then, we can multiply the fractions:

3/4 x 17/2 = (3 x 17) / (4 x 2) = 51/8

Hence, the product of 3/4 and 8 1/2 is 51/8.

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Answer:

Step-by-step explanation:

it is mable

Answer:

J. 500

Step-by-step explanation:

20 percent is 0.2 when multiplying.

0.2(0.2(x)) = 20

0.04(x) = 20

x = 500

Solution In the Attachment Above

The experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In other words, it is the ratio of the number of desired outcomes to the total number of outcomes.

The frequency of card 6 is 7 and the frequency of card K is 12. However, the card K is also counted in the total count for JQK, so we need to subtract 2 from the frequency of K to get the actual count of K.

Actual count of K = 12 - 2 = 10

Total count of 6 and K = 7 + 10 = 17

The experimental probability of drawing a K or 6 is the frequency of drawing K or 6 divided by the total number of draws:

Experimental probability = (frequency of K or 6) / (total number of draws)

Experimental probability = 17 / 100

Therefore, the experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

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Answer: The total number of ways the photography student can choose 4 photos out of 21 is given by the combination formula:

Step-by-step explanation: C(21, 4) = (21!)/((4!)(21-4)!) = 5985

Out of the 21 photos, 9 were photos of babies. The number of ways the student can choose 4 baby photos out of 9 is given by:

C(9, 4) = (9!)/((4!)(9-4)!) = 126

Therefore, the probability that all 4 photos chosen are of babies is:

P = (number of ways to choose 4 baby photos)/(total number of ways to choose 4 photos)

P = C(9, 4)/C(21, 4)

P = 126/5985

P ≈ 0.021

So, the probability that all 4 photos chosen are of babies is approximately 0.021 or 2.1%.

Answer: t = 1.8 seconds

Step-by-step explanation:

The function h(t) = 25t^2 - 81 gives the height of the rock (in feet) at time t seconds after it was dropped.

When the rock lands, its height is 0. So we can set h(t) = 0 and solve for t:

25t^2 - 81 = 0

Solving for t, we get:

t = ±√(81/25) = ±(9/5)

Since we are only interested in the time after the rock was dropped, we take the positive value:

t = 9/5 = 1.8 seconds

Therefore, the time between when the rock was dropped and when it landed is 1.8 seconds.

So the answer is: t = 1.8 seconds