Suppose the velocity of an object moving along a line is positive. Are​ position, displacement, and distance traveled​ equal? Explain.
A. ​Yes, if the velocity is positive then the​ displacement, distance​ traveled, and position of the object will be given by v'​(t).
B. No, the displacement and position of the object will be equal but since the initial position is not​ given, the distance traveled by the object may not be equal to the position and the displacement of the object.
C. ​No, the displacement and distance traveled by the object will be equal but since the initial position is not​ given, the position of the object may not be equal to the distance traveled and the displacement of the object.
D. Yes, if the velocity is positive then the​ displacement, distance​ traveled, and position of the object will be given by Integral from a to b v left parenthesis t right parenthesis dt∫abv(t) dt.

The value of length of pen should always be greater than 5 feet.

Rectangle:

                Rectangle is a special kind of parallelogram in which opposite sides are equal and adjacent sides are perpendicular to each other.It contains of length and breadth,The area of rectangle is given by,

                  Area = length x breadth

Now as per question,

A family wants to build a pen for their new puppy.

They want's the area of the pen to be more than 225 square feet.

width of the pen is = 25 feet

let,

     The length of the pen is \(x\) feet.

Area of pen = length * width

                    = \(x\) * 25

                    = 25x

According to the question,

                        Area of pen > 225 square feet

                         25x > 225

                            x >225/25

                             x > 5 feet

Thus,

        The value of length should always be greater than 5 feet.

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Answer:

Step-by-step explanation:

Angles formed when we turn clockwise in the given directions,

a) N to E → 90°

b). W to NE → (90° + 45°) = 135°

c). SE to NW → 180°

d). NE to N → 360° - 45° = 315°

e). W to NE → 90° + 45° = 135°

f). S to SW → 45°

g). S to SE → 360° - 45° = 315°

h). SE to SW → 180°

i). E to SW → 90° + 45° = 135°

Answer:

B. >

Step-by-step explanation:

Yes, you got it correct! Anything with a "-" is always less than a "+". Look at it this way:

I have 11 dollars (+11) and you owe me one dollar (-1). Now which is better?

Hope this helps

~R3VO

The given equation can be solved for the value of x and y

i.e. x = (3y - 7)/4 & y = (4x + 7)/3.

What is the linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We have,

The equation 4x=3y-7

So, here we can solve this equation for the x as well as y equals,

Firstly we will solve for x:

4x = 3y - 7

dividing the whole equation by 4 we get,

4x/4 = (3y - 7)/4

x = (3y - 7)/4

Similarly, we will solve for y:

4x = 3y - 7

3y = 4x + 7

dividing the whole equation by 3 we get,

3y/3 = (4x + 7)/3

y = (4x + 7)/3

Hence, the given equation can be solved for the value of x and y

i.e. x = (3y - 7)/4 & y = (4x + 7)/3

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Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Answer:  C

Step-by-step explanation:

Reflection across x = -1

The simplest way to calculate the new coordinates is to draw x = -1, count how many units away the point is from x = -1, then count the same number of units from x = -1 in the OPPOSITE direction to find the reflection. (see attachment)

J = (0, 0) is 1 unit to the right of x = -1

J' = (-2, 0) is 1 unit to the left of x = -1

K = (1, 4) is 2 units to the right of x = -1

K' = (-3, 4) is 2 units to the left of x = -1

L = (3, 3) is 4 units to the right of x = -1

L' = (-5, 3) is 4 units to the left of x = -1

Reflection across x-axis

Change the sign of the y-value:  (x, y) → (x, -y)

J' = (-2, 0)           J'' = (-2, 0)

K' = (-3, 4)           K'' = (-3, -4)  

L' = (-5, 3)            L' = (-5, -3)

Answer:

\(the \: number \: is \: 96\)

Explanation:

\(let \: the \: number \: be \: = \: x \)

\( \frac{x}{2} + x = 144\)

\(2( \frac{x}{2} ) + 2(x) = 2(144)\)

\(x + 2x = 288\)

\(3x = 288\)

\( \frac{3x}{3} = \frac{288}{3} \)

\(x = 96\)

Answer:

C

Step-by-step explanation:

because it is asking to find the number of classes held during the weekday zumba class.

weekday class = 30 minutes

Saturday= 45 minutes

total = 165  

The transformation will map ΔABC onto image ΔA'B'C' is, a reflection in the line y = x. So Option C is correct

In mathematics, the triangle is a type of polygon which has three sides and three vertices. the sum of all the interior angles of the triangle is 180°

If anyone of the triangle is 90° then it is called as right angle triangle

Given that,

Two triangles,

First,   ΔABC

Whose coordinates are A(1,3), B(1, 6), C(4, 6)

Second,  ΔA'B'C'

Whose coordinates are A'(3, 1), B'(6, 1), C'(6, 4)

There is only one transformation is  possible,

Which is a reflection in the line  y = x

Because,  the distance of the points will be equal from the line y = x

In comparison of corresponding points

Hence, the transformation is a reflection in the line y = x

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Randomization test is a test in which there is no assumption of restriction for sampling population. It is also sometimes termed as permutation tests. Here we need not take assumptions for the data as in parametric test.

It permit us to check whether there is difference in the observed data from a random distribution created by reordering our observed data. If it is not random, then it should occur more or less frequently than we expect under this distribution. If there is no pattern, then it should be just as likely as any other pattern generated by reordering the data.

In the example of checking two shoe material type for 10 boys, as randomization test don't estimate parameters we don't have to choose samples randomly.

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The value of P and Q such that: PAQ = CF (A), the canonical form of A. \((i) P = \left[\begin{array}{ccc} 1 & 0 & 0 \\ -1 & 1 & 0 \\ -1 & 0 & 1 \end{array}\right]\)

\((ii) Q = \left[\begin{array}{cccc} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right]\)

\((iii) HF(A) = \left[\begin{array}{cccc} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]\)

\((iv) CF(A) = \left[\begin{array}{cccc} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]\),

(v) The rank of A, Rnk(A) = 3.

(vi) Yes, PAQ = (HF(A))Q = CF(A).

The values of P and Q such that PAQ equals the canonical form CF(A) of matrix A, we need to perform a sequence of matrix operations. Let's break down the steps and find the values:

To obtained matrix P, we perform row operations on matrix A to obtain its Hermite Form (HF(A)). The row operations must be done in a way that only swaps rows, multiplies a row by a nonzero scalar, and subtracts a multiple of one row from another row.

\(A = \left[\begin{array}{cccc} B_{12} &B_{22} & 1 & 1\\1 & B_{23} & B_{33} & 1 \\ 1 & 1 &B_{34} & B_{44}\end{array}\right] \\\)

To determine the matrices P and Q, we need to find the pivot positions in the matrix A by applying row operations. Let's perform the row operations:

Row 2 = Row 2 - Row 1

Row 3 = Row 3 - Row 1

The resulting matrix after the row operations is:

\(A = \left[\begin{array}{cccc} B_{12} &B_{22} & 1 & 1 \\ 0 & B_{23}-B_{12} & B_{33}-1 & 0 \\ 0 & 0 &B_{34}-1 & B_{44}-1 \end{array}\right]\)

Now, let's determine the matrices P and Q:

(i) P will be the product of the elementary row operations performed on A:

\(P = \left[\begin{array}{ccc} 1 & 0 & 0 \\ -1 & 1 & 0 \\ -1 & 0 & 1\end{array}\right]\)

(ii) Q will be the identity matrix of the appropriate size:

\(Q = \left[\begin{array}{cccc} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right]\)

(iii) This matrix is already in its Hermite Form (HF(A)), as it is in reduced row echelon form with leading entries in each row.

Therefore, the Hermite Form (HF(A)) of matrix A is:

\(HF(A) = \left[\begin{array}{cccc} B_{12} &B_{22} & 1 & 1\\0 & B_{23}-B_{12} & B_{33}-1 & 0 \\ 0 & 0 &B_{34}-1 & B_{44}-1\end{array}\right]\)

\(HF(A) = \left[\begin{array}{cccc} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]\)

(iv) The canonical form (CF(A)) of matrix A will be:

\(CF(A) = \left[\begin{array}{cccc} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]\)

(v) To determine the rank of matrix A (Rnk(A)), we count the number of linearly independent rows or the number of nonzero rows in the Hermite Form (HF(A)) of matrix A.

From the previously calculated Hermite Form (HF(A)):

\(HF(A) = \left[\begin{array}{cccc} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0\end{array}\right]\)

We can see that there are three nonzero rows in HF(A). Therefore, the rank of matrix A (Rnk(A)) is 3.

(vi) The matrices P and Q that satisfy PAQ = CF(A) are:

\(P = \left[\begin{array}{ccc} 1 & 0 & 0 \\ -1 & 1 & 0 \\ -1 & 0 & 1 \end{array}\right]\)

\(Q = \left[\begin{array}{cccc} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{array}\right]\)

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Answer:

400

Step-by-step explanation:

Profit = 1000

Ratio Rachel : Martin = 7 : 3

Profit Rachel = 7/10 x 1000 = 700

Rachel spend : save = 4 : 3

Rachel spend = 4/7 x 700 = 400

Answer:

Angle 6 = 140°

Step-by-step explanation:

Angle 5 = 40°

Angles 5 and 6 are supplementary (Their sum is equal to 180°)

180 - 40 = 140°

Angle 6 = 140°

Hope this helps. Have a nice day.

Answer:

Step-by-step explanation:

∠6 = 180 - 40

∠6 = 140°

see image below.

A function assigns the values. The value of f(1.6) and f(-3.3) is -2.2 and -16.9, respectively.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function f(x) = 3(x-3) + 2, now to know the value of f(1.6) and f(-3.3), subtitute the value of x as 1.6 and -3.3, respectively.

f(x) = 3(x-3) + 2

f(1.6) = 3(x-3) + 2

        = 3(1.6 - 3) + 2

        = 3(-1.4) + 2

        = -2.2

f(-3.3) = 3(x-3) + 2

          = 3(-3.3 - 3) + 2

          = 3(-6.3) + 2

          = -18.9 + 2

          = -16.9

Hence, the value of f(1.6) and f(-3.3) is -2.2 and -16.9, respectively.

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Answer: 118

Step-by-step explanation:

Answer:

3 parallelograms

Step-by-step explanation:

Answer:

90meters/60seconds = 1.5meters per second

Step-by-step explanation:

The correct option is option B that is the unit rate at which Darrell walks is 1.5 meters per second.

What is the unit rate ?

An unit rate is a ratio that is used for comparing two different kinds of quantities which have different units.

It is given that Darrell is walking for a distance of 90 meters in time 60 seconds. We have to find the unit rate at which Darrell is walking.

So , to find out the unit rate we must divide the distance travelled by Darrell by the time taken to travel that distance.

i.e.,

The unit rate is given by :

Unit rate = Distance travelled in meters / Time taken in seconds

or

Unit rate = 90 meters / 60 seconds

or

Unit rate = 1.5 meters per second.

Therefore , the correct option is option B that is the unit rate at which Darrell walks is 1.5 meters per second.

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\(-9^2=-(9^2)=-81\), whereas \((-9)^2=9^2=81\).

This is because of the order of operations.

100x + 200y < 3100 inequality can be used to describe the situation.

According to the question

Dixon orchards has purchased land on which to plant lime and orange trees.

Each lime tree requires 100 square feet of area.

Each orange tree requires 200 square feet of area.

Dixon orchards determines that they have no more than 3,100 square feet of land on which to plant the lime and orange trees.

If x represents the number of lime trees and y represents the number of orange trees.

Inequality:

lime tree requires 100 square feet of area that means100x

orange tree requires 200 square feet of area that means 200y

They have no more than 3,100 square feet of land

Rewrite the inequality

100x + 200y < 3100

Therefore,

100x + 200y < 3100 inequality can be used to describe the situation.

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The alternative and hull hypotheses is H₀: P=0.03, H₁: P≠0.03.

Given that,

According to a representative of the Ohio Department of Education, 3% of graduating high school seniors in Ohio have dropped out in recent years. Out of the 600 pupils enrolled, 30 students from Podunk High School dropped out of school last year.

We have to find is there enough data to say that this school's dropout rate is higher than the state average. Using symbols and words, state the alternative and hull hypotheses.

We know that,

n is 600,

3% Ohio high school seniors dropout.

30 dropout out of 600 in Podunk high school.

Here,

H₀: μ₁=μ₂  vs   H₁:μ₁≠μ₂

In coordinates,

H₀⇒ dropout number is equal for both schools.

H₁⇒ dropout number not equal for both schools.

H₀: P=0.03, H₁: P≠0.03.

Therefore, The alternative and hull hypotheses is H₀: P=0.03, H₁: P≠0.03.

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Answer:

39

Step-by-step explanation:

5x+9

5(6)+9

30+9

39

Answer:

39

Step-by-step explanation:

first 5 times 6 since x=6. that equals 30. 30 plus 9 is 39.

hope this helps :)

(a) M = ∬[R] ρ(x, y) dA. (b) x = (1/M) * ∬[R] x * ρ(x, y) dA y = (1/M) * ∬[R] y * ρ(x, y) dA. (c) The moment of inertia (I_x) about the x-axis can be found using the following integral expression: I_x = ∬[R] y^2 * ρ(x, y) dA

To set up integral expressions for the mass, center of mass, and moment of inertia about the x-axis, let's consider an object with density function ρ(x,y) in a region R on the xy-plane.

(a) The mass (M) of the object can be found using the following integral expression:
M = ∬[R] ρ(x, y) dA

(b) To find the center of mass, we need to find the coordinates (x, y) using the following integral expressions:
x = (1/M) * ∬[R] x * ρ(x, y) dA
y = (1/M) * ∬[R] y * ρ(x, y) dA

(c) The moment of inertia (I_x) about the x-axis can be found using the following integral expression:
I_x = ∬[R] y^2 * ρ(x, y) dA

These integral expressions provide a foundation for finding the mass, center of mass, and moment of inertia about the x-axis for a given object with a specified density function ρ(x, y) in the region R. To evaluate these expressions, you'll need to know the density function and region for the specific problem you're working on.

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The postfix expression of "7+5-3*2(6*7)/4" is "7 5 + 3 2 * 6 7 * 2 * - 4 /". Evaluating the postfix expression gives the result of the expression. The prefix expression for the given infix expression is "/ - + 7 5 * 3 * 2 ( * 6 7 ) 4".

To convert the infix expression "7+5-3*2(6*7)/4" into postfix expression, we follow the rules of operator precedence and associativity. The postfix expression is obtained by placing operators after their operands.

The postfix expression for the given infix expression is:

"7 5 + 3 2 * 6 7 * 2 * - 4 /"

To evaluate the postfix expression, we use a stack data structure. We scan the postfix expression from left to right and perform the corresponding operations.

Starting with an empty stack, we encounter the operands "7" and "5". We push them onto the stack. Then we encounter the operator "+", so we pop the last two operands from the stack (5 and 7), perform the addition operation (7 + 5 = 12), and push the result back onto the stack.

We continue this process for the remaining operators and operands in the postfix expression. Finally, after evaluating the entire expression, the result left on the stack is the final answer.

To convert the infix expression into prefix expression, we follow similar rules but scan the expression from right to left. The prefix expression is obtained by placing operators before their operands.

The prefix expression for the given infix expression is:

"/ - + 7 5 * 3 * 2 ( * 6 7 ) 4"

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Answer:

6y=12x+18

Step-by-step explanation:

Y=Mx+b

Answer:

if an input produces more than one output, the table does not represent a function. In this case, table D is not a function. the x value 0 has three different output values, -1, 4, and 6; the input 2 also has three different output values.

Answer:

$17.5 differnce

Step-by-step explanation:

20% tip on is $57.49

20% tip off is $39.99

tip on vs off when a tip is on means its