Which of the following is NOT a term used to describe slope?
Unit Rate
Constant of Proportionality
Change in X over Change in Y
Rate of Change

The solution of the initial value problem y' = 2xy² ; y(1) = 1/2 is y(x) = -1/(x² - 3)

An initial value problem is a differential equation that contains the initial values of the variables of the differential equation.

Given the initial value problem

y' = 2xy² ; y(1) = 1/2

So, we solve the differential equation as follows

y' = 2xy²

dy/dx = 2xy²

Separing the variables, we have

dy/y² = 2xdx

Integrating both sides of the equation, we have

∫dy/y² = ∫2xdx

∫dy/y² = 2∫xdx

We know that ∫xⁿ = xⁿ⁺¹/(n + 1)

So, integrating the expressions, we have

y⁻²⁺¹/(-2 + 1) = 2x¹⁺¹/(1 + 1)

y⁻¹/(-1) = 2x²/2 + c

-y⁻¹ = x² + c

Given that y(1) = 1/2, substituting these into the equaqtion, we have

-y⁻¹ = x² + c

-(1/2)⁻¹ = 1² + c

-2 = 1 = c

c = -2 - 1

c = -3

So, -y⁻¹ = x² + c

-y⁻¹ = x² - 3

Dividing through by - 1, we have

y⁻¹ = -(x² - 3)

Taking the inverse of both sides, we have

y(x) = -1/(x² - 3)

So, y(x) = -1/(x² - 3)

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Answer:

C

Step-by-step explanation:

5-10x+25=0

5+25=10x

30=10x

x=3

Answer:

D is the answer because 4 goes into all of them.

Answer: the answer is x=−2

Answer:

the answer is x= -2

Step-by-step explanation:

negative two

Answer:

D

Step-by-step explanation:

the best answer may be D because 9/3 =3 3×5=15

Answer:

Step-by-step explanation:

A rotation is a transformation in a plane that turns every point of a figure through a specified angle and direction about a fixed point. The fixed point is called the center of rotation. The amount of rotation is called the angle of rotation and it is measured in degrees.

Therefore, the fixed point is called the center of rotation.

What are the angles?

Angles are formed when two lines intersect at a point. The measure of the 'opening' between these two rays is called an 'angle'.

A rotation means that the transformation in a plane that turns every point of a figure through a specified angle and direction about a fixed point.

So,the fixed point is called the center of rotation. The amount of rotation is called the angle of rotation and it is measured in degrees.

Hence, the fixed point is called the center of rotation. The amount of rotation is called the angle of rotation and it is measured in degrees.

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Answer:

False

Step-by-step explanation:

y=5x + 5

0=5 (5)+5

0=10+5

0≠15

False

Answer:

hope this helps

Step-by-step explanation:

Oh wait I think I know the answer, c.

Answer:

C

Step-by-step explanation:

angle DAB = angle CBA

angle DBA = angle CAB

line AB = line AB

Since we know that the two angles and 1 side are the same on both triangle ADB and BCA, the property is angle side angle

35kg - 3500g

3500g - 2500g

= 1000g

Answer:

1 : 14

Step-by-step explanation:

The measures must have the same units, that is both g or Kg

2500 g : 35 Kg

= 2500 g : 35000 g ( 1 Kg = 1000 g )

Divide both parts by 100

= 25 : 350 ( divide both parts by 25 )

= 1 : 14

Therefore, Chase ran 49/8 miles each day.

To find out how many miles Chase ran each day, we need to divide the total distance he ran (36 3/4 miles) by the number of days (6 days).

First, let's convert the mixed number into an improper fraction. 36 3/4 is equal to (4 * 36 + 3)/4 = 147/4.

Now, we can divide 147/4 by 6 to find the distance he ran each day:

(147/4) / 6 = 147/4 * 1/6 = (147 * 1) / (4 * 6) = 147/24.

Therefore, Chase ran 147/24 miles each day.

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 147 and 24 is 3.

So, dividing 147 and 24 by 3, we get:

147/3 / 24/3 = 49/8.

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Chase ran a total of 36 3/4 miles over six days. To find out how many miles he ran each day, simply divide the total distance (36.75 miles) by the number of days (6). The result is approximately 6.125 miles per day.

To solve this problem, you simply need to divide the total number of miles Chase ran by the total number of days. In this case, Chase ran 36 3/4 miles over six days. To express 36 3/4 as a decimal, convert 3/4 to .75. So, 36 3/4 becomes 36.75 miles.

Now, we can divide the total distance by the total number of days:

36.75 miles ÷ 6 days = 6.125 miles per day. So, Chase ran about 6.125 miles each day.

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The difference in the proportion of males and the proportion of females that smoke is 0.08

In a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.

The given parameters are:

                             Male           Female

Sample                  61                  48

Smokers               15                   8

The proportion is calculated using:

p = Smoker/Sample

So, we have:

Male = 15/61 = 0.25

Female = 8/48 = 0.17

The difference is then calculated as:

Difference = 0.25 - 0.17

Evaluate

Difference = 0.08

Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08

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Answer:

Step-by-step explanation:

You want values of ∆y and dy for y = x² -6x and x = 5, ∆x = dx = 0.5.

The value of dy is found by differentiating the function.

  y = x² -6x

  dy = (2x -6)dx

For x=5, dx=0.5, this is ...

  dy = (2·5 -6)(0.5) = (4)(0.5)

  dy = 2

The value of ∆y is the function difference ...

  ∆y = f(x +∆x) -f(x) . . . . . . . where y = f(x) = x² -6x

  ∆y = (5.5² -6(5.5)) -(5² -6·5)

  ∆y = (30.25 -33) -(25 -30) = -2.75 +5

  ∆y = 2.25

__

Additional comment

On the attached graph, ∆y is the difference between function values:

  ∆y = -2.75 -(-5) = 2.25

and dy is the difference between the linearized function value and the function value:

  dy = -3 -(-5) = 2.00

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Answer:

  see below

Step-by-step explanation:

It works well to think about what these compound inequalities mean. One way to do that is to graph them, or to imagine what the graph of them looks like.

Since the result is a single inequality (x < 2), the compound will be "and" with x < 2 being more restrictive, or will be "or" with x < 2 being the least restrictive of completely overlapping inequalities.

Of the choices offered, C is the one of interest.

_____

Comment on other choices

A has all real numbers as solutions except in the range 2 ≤ x ≤ 3.

B has no solutions

C simplifies to x < 2 . . . . the one we want

D simplifies to x < 4

Answer:

#7 can be simplified to -10 √15x -40 √5

#8 = -20 √6x +30x√2

#9 = 10x√6+3 √15xx

#10 = -20√6a -15 √2

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(4)=-3(4)+5 = -12+5=-7

The number of polynomials that can be formed with -2 and 5 as zeroes are more than 1.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.x² -3x - 7 is an illustration of a polynomial with a single indeterminate x.

Given that the zeros of a polynomial are -2 and 5.

The polynomial that has a and b as zeors is p(x) = k[x² + (a+b)x + ab].

where k is a real number.

The polynomial that has -2 and 5 zeros is

p(x) = k[x² + (-2 + 5)x + (-2)×5]

p(x) = k[x² + 3x - 10]

Where k is a real number.

The number of real numbers is infinity.

The number of polynomials is infinity.

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A line segment known as a perpendicular bisector divides a straight line segment into two congruent or equal pieces. At the exact midway of the line segment, they divide it. A perpendicular bisector turns the line segment it bisects 90 degrees.

A line that precisely divides a line segment connecting two locations in half at a 90 degree angle is known as a perpendicular bisector. Finding the midpoint and negative reciprocal of two points, then entering these solutions into the equation for a line in slope-intercept form, will get the perpendicular bisector of the two points.

The need for determining the perpendicular line is coordinates and a line equation. Think about a line with the equation axe + by + c = 0 and the coordinates (x1, y1). The slope should be a/b. The slopes should add up to -1 if one line is perpendicular to this one.

The line connecting the points of intersection of these arcs is Perpendicular bisector

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Answer:

Step-by-step explanation:

7 students from the Junior class.

6 students from the Senior class.

4 new members are to be chosen.

Required: Find the number of ways 4 new members can be chosen if 2 or fewer must be from the senior class. So, Therefore, the correct answer is 560 ways.

Answer:

y = -5x + 25

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The number 71.38 can be written in word form as "seventy-one and thirty-eight hundredths." The correct answer is option D.

In decimal notation, the number 71.38 can be broken down into its whole number and decimal parts. The whole number part is 71, and the decimal part is 0.38.

In a decimal number, the digits to the right of the decimal point represent fractions of a whole. Each digit to the right of the decimal point has a place value that is a power of 10.

In word form, the decimal part 0.38 is read as "thirty-eight hundredths." Therefore, when combined with the whole number 71, the correct word form is "Seventy-one and thirty-eight hundredths."

Therefore option D is the correct answer.

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It is not possible to answer the question with the given information.In geometry, a point is an exact position or location on a plane surface. Points are usually labeled with an uppercase letter.

Given:

AWXY had points at W(7,1), d. k = 3To find: The coordinates of point X and Y.The given points in the question are W(7,1) and d. The coordinates of the point d is missing, which makes it impossible to find the coordinates of the points X and Y.

In the coordinate system, the point is represented by its coordinates (x, y).

The coordinates are always listed in the order of the x-coordinate and then the y-coordinate.

To find the coordinates of X and Y, we need to have the coordinates of the point d as well. Please provide the complete question so that we can provide the solution.

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Let T: R3 → R3 be a linear transformation such that T(1,1,1) = (2,0,-1) T(0,-1,2)= (-3,2,-1) T(1,0,1) = (1,1,0) . The price of T(-2, 1, 0) is (-1, 1, 0).

To find the value of T(-2, 1, 0), we will use the linearity property of linear transformations.

Since T is a linear transformation, we will specify it as a linear mixture of its well-known foundation vectors: T(x, y, z) = a(1, 0, 0) + b(0, 1, 0) + c(0, 0, 1), where a, b, c are the coefficients.

We are given the values of T(1, 1, 1), T(0, -1, 2), and T(1, 0, 1), which permits us to form a machine of linear equations to clear up for the coefficients a, b, and c.

Using the given information, we have the following machine of equations:

2a + 0b - c = 1

-3a + 2b - c = 0

a + b + 0c = 1

Solving this machine of equations, we find a = 1/2, b = half, and c = 0.

Now, we will discover T(-2, 1, 0) by way of substituting the values into the expression for T:

T(-2, 1, 0) = (1/2)(-2, 1, 0) + (1/2)(0, 1, 0) + (0)(0, 0, 1)

Simplifying the expression, we get:

T(-2, 1, 0) = (-1, 1/2, 0) + (0, 1/2, 0) + (0, 0, 0)

T(-2, 1, 0) = (-1, 1, 0)

Therefore, the price of T(-2, 1, 0) is (-1, 1, 0).

None of the solution alternatives provided healthy this result, so the ideal alternative isn't always listed.

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The set of vectors {x, cos(x)} is linearly independent as per the concept of linearity of vectors.

To determine if the set of vectors {x, cos(x)} in F(-∞, ∞) is linearly dependent, we need to check if there exist scalars c1 and c2, not all zero, such that c1x + c2cos(x) = 0 for all values of x in the given interval.

Let's consider a specific value of x, say x = 0.

Plugging this value into the equation, we have c1(0) + c2cos(0) = 0. Since cos(0) = 1, the equation simplifies to c2 = 0.

Now, considering another specific value of x, say x = π/2, we have c1(π/2) + c2cos(π/2) = 0. Again, cos(π/2) = 0, so the equation simplifies to c1(π/2) = 0. This implies that c1 = 0.

Since c1 = c2 = 0, the only solution to the equation c1x + c2cos(x) = 0 for all x in F(-∞, ∞) is the trivial solution. Therefore, the set of vectors {x, cos(x)} is linearly independent.

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The complete question:

By using appropriate identities, where required, determine which of the following sets of vectors in F(-∞, ∞) are linearly dependent.

a. x, cosx

The given sequence is not an arithmetic sequence. Option B is correct.

Given the sequence below

-2, -8, -32, -128

The nth term of an arithmetic sequence is given as Tn = a + (n-1)d

The common difference is the difference between the preceding and the succeeding term.

First term = -2

Second term = -8

Common difference = -8 -(-2) = -6

d= -32 + 8 = -24

Since the values are not equal, hence the sequence is not an arithmetic sequence.

Hence the common difference of the sequence is 8

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The graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The inequality expression is given as

y ≤ 3/4x − 4

The inequality symbol in the above inequality expression is

≤

This implies that the inequality expression is a less than or equal to

When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line

Also, the inequality symbol implies that the bottom part is shaded

Hence, the graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)

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No, the F-test statistic cannot be less than 1 when it represents the larger of two sample variances.

The F-distribution is always a positive distribution with a range of values greater than zero. The F-test value is always greater than or equal to 0, but it is not always less than or equal to 1.

The numerator, representing the bigger sample variance, is always greater than or equal to the denominator, representing the smaller sample variance. Consequently, the F-ratio, which is the ratio of the larger to the smaller variance, is always greater than or equal to 1. Thus, an F-test statistic that is less than 1 is mathematically incorrect.

Therefore, an F-test statistic is always a positive number that is greater than or equal to zero and greater than or equal to 1. This is because the numerator of an F-distribution is always greater than or equal to the denominator.

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the given proportional relationship y=0.5x with proportional constant is 1/2.

what is proportional relationship?

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.

Given x and y will have a proportional relationship if the ratio of x to y will be equal for all given values.

For every 1 scoop of ice cream, cup of milk is needed 1/2, and for every 5 scoops of ice cream, 2 cups of milk 2 1/2 are needed.

So the equation will be y = kx

or y = 0.5(x)

Here proportional constant is 1/2 or 0.5.

For 18 scoops of icecream, milk will be needed is 18/2 = 9 cups of milk.

Hence, we can say that the given proportional relationship y=0.5x with a proportional constant is 1/2.

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Answer:

the answer is equals to:1.715

Lila's height is

Metre is the standard measure of height.

Fatima's height, F = 1.27m

Charlotte's height, C=0.89m

Lila is taller than Charlotte by half the difference between Fatima's height and Charlotte's height, so we can write

Lila's height, L = C+((F-C)/2)

L=0.89+((1.27-0.89)/2)=1.08

Hence, Lila is 1.08 metres tall.

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