\(\sf\large\green{\underbrace{\red{Question*}}}:\)
Solve for y
\( \frac{y}{3} > 7 - \frac{y}{2} \)
​

Answer: 57

Step-by-step explanation: 86 + 37 = 123, then subract 123 from 180

A nameless polynomial p(x), or simply "some polynomial p whose variable is x," serves as the foundation of the Remainder Theorem. The Theorem then talks about dividing that polynomial by some linear factor, x a, where an is just a number.

Examples :

Factor 4x² - x - 3 :  (4x + 3 ) (x - 1)

4x² - x - 3

=(4x² + 3x) + (-4x -3)

Factor out x from 4x² + 3x : x(4x + 3 )

Factor Out -1 from -4x -3: -(4x + 3)

=x(4x + 3) - (4x +3)

Factor out common team (4x + 3): (4x + 3) (x - 1)

=(4x + 3) (x - 1).

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The equation to determine the length and width of the rug is

28 = w² + 12w

Since, the shape of the rug is rectangle, therefore area of rectangle has been used to obtain the solution.

What is a rectangle?

Rectangle is a flat, two-dimensional shape, having four sides and vertices with opposite sides being equal and parallel. We may easily represent a rectangle in an XY plane by using its length and breadth as the arms of the x and y axes, respectively.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

We are given a rectangular rug with an area of 28 square feet.

Also, the rug is 12 feet longer than it is wide.

So,

Let 'l' be the length of the rug and 'w' be the width of the rug

As given, Length is 12 feet longer than its width

Therefore, l = w + 12

We know Area of rectangle = Length * Width and area is given to be 28 square feet.

So,

⇒28 = (w + 12)w

⇒28 = w² + 12w

Hence, the equation to determine the length and width of the rug is

28 = w² + 12w.

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Question: Tammy has a rectangular rug with an area of 28 square feet. The rug is 12 feet longer than it is wide.

Create an equation to determine the length and the width of the rug.

Answer:

the answer is 5

Step-by-step explanation:

³√125 or this can also be written as 125^⅓

it means cube root of 125

And the cube root of ³√125 is 5

then the cube of 5³ is 125

If the expression AXB is defined, and A is a 3X5 matrix, then the dimension of B could be 5XN.

“N” could be the any number as in order to do any multiplication, the number of columns of first matrix and the number of rows of second matrix should be same in order to perform the multiplication between those matrices.

A matrix is a collection of integers that are organized in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. If the matrix has m rows and n columns, it is referred to as a "m by n" matrix, abbreviated "mXn."

A matrix A multiplied by a matrix B yields a matrix C only when the number of columns in the first matrix A equals the number of rows in the second matrix B. To find the element cij, which is in the product's ith row and jth column, multiply the first element in the ith row of A by the first element in the jth column of B, the second element in the row by the second element in the column, and so on until the last element in the row is multiplied by the last element in the column; the sum of all these products yields the element cij.

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The perimeter of a rectangle is equal to 30.

The rectangle is a quadrilateral.  The classification for quadrilaterals is given by the length of sides and angles. For a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

A rectangle is a geometric figure that has 4 sides called: length and width (W). Due to its characteristics, the rectangle presents two length (L) and two widths (W).

The perimeter is the sum of all sides of a geometric figures. For a rectangle, the perimeter is 2L+2W.

The area for a rectangle is given by A=L*W.

The question gives:

From the area, you can find the width, see below.

A=L*W

A=2W*W

50=2W²

25=W²

5=W

If W=5, from condition length = 2*W, you can find the length. See

L=2*W

L=2*5

L=10

Therefore, the perimeter will be:

P=2L+2W

P=2*10+2*5

P=20+10

P=30

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Answer:

The groups have no common factor and can not be added up to form a multiplication. Final result : 9x8 + 6x4y + 12x4 + y2 ...

Step-by-step explanation:

so did u understand

Answer:

(-3/2, -13/2)

Step-by-step explanation:

To solve the system of equations graphically, we need to plot the two equations on the same set of axes and find the point of intersection.

To plot the first equation y = x - 5, we can start by finding the y-intercept, which is -5. Then, we can use the slope of 1 (since the coefficient of x is 1) to find other points on the line. For example, if we move one unit to the right (in the positive x direction), we will move one unit up (in the positive y direction) and get the point (1, -4). Similarly, if we move two units to the left (in the negative x direction), we will move two units down (in the negative y direction) and get the point (-2, -7). We can plot these points and connect them with a straight line to get the graph of the first equation.

To plot the second equation y = -x - 8, we can follow a similar process. The y-intercept is -8, and the slope is -1 (since the coefficient of x is -1). If we move one unit to the right, we will move one unit down and get the point (1, -9). If we move two units to the left, we will move two units up and get the point (-2, -6). We can plot these points and connect them with a straight line to get the graph of the second equation.

The point of intersection of these two lines is the solution to the system of equations. We can estimate the coordinates of this point by looking at the graph, or we can use algebraic methods to find the exact solution. One way to do this is to set the two equations equal to each other and solve for x:

x - 5 = -x - 8 2x = -3 x = -3/2

Then, we can plug this value of x into either equation to find the corresponding value of y:

y = (-3/2) - 5 y = -13/2

So the solution to the system of equations is (-3/2, -13/2).

Answer:

60%

Step-by-step explanation:

The student covers a total distance of 22.05 kilometers in a week's time, walking between the park and the house each day.

To find the total distance covered by the student in a week's time, we need to calculate the distance covered in one round trip (from the house to the park and back) and then multiply it by the number of round trips in a week.

Given that the difference between the park and house is 1 kilometer and 575 meters, we can convert it to a total distance of 1.575 kilometers.

In a round trip, the student covers twice the distance between the park and the house, which is 1.575 kilometers * 2 = 3.15 kilometers.

Now, we need to determine how many round trips the student makes in a week. Let's assume the student makes one round trip each day.

Since there are 7 days in a week, the total distance covered by the student in a week's time is 3.15 kilometers * 7 = 22.05 kilometers.

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Answer:

126

Step-by-step explanation:

Answer:

The median or Answer d

Step-by-step explanation:

i just do it already

Using the Pigeonhole Principle, it can be shown that in a set of n positive integers, none exceeding 2n, there is at least one integer that divides another integer.

We can prove this statement by contradiction using the Pigeonhole Principle.

Suppose we have a set of n positive integers, none of which exceed 2n, and assume that no integer in the set divides another integer.

Consider the prime factorization of each integer in the set. Since each integer is at most 2n, the largest prime factor in the prime factorization of any integer is at most 2n.

Now, let's consider the possible prime factors of the integers in the set. There are only n possible prime factors, namely 2, 3, 5, ..., and 2n (the largest prime factor).

By the Pigeonhole Principle, if we have n+1 distinct integers, and we distribute them into n pigeonholes (corresponding to the n possible prime factors), at least two integers must share the same pigeonhole (prime factor).

This means that there exist two integers in the set with the same prime factor. Let's call these integers a and b, where a ≠ b. Since they have the same prime factor, one integer must divide the other.

This contradicts our initial assumption that no integer in the set divides another integer.

Therefore, our assumption must be false, and there must be at least one integer in the set that divides another integer.

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Answer:

Between 1 and 2, the graph goes over 4 and down 1, so the slope is -1/4

Between 0 and 1, the graph goes over 4 and down 2, so the slope is -2/4 = -1/2

We can see a trend here. For each unit interval farther to the left, the slope doubles. So, we have ...

1 ≤ x ≤ 2 : -0.25

0 ≤ x ≤ 1 : -0.5

Step-by-step explanation:

The statement If a simple random sample is chosen with replacement, each individual has the same chance of selection on every draw is True.

If a simple random sample is chosen with replacement, it means that after each selection, the chosen individual is placed back into the population before the next selection is made. In this case, each individual in the population has the same chance of being selected for every draw.

The process of replacing the selected individual ensures that the selection probabilities remain constant throughout the sampling process. As a result, each individual has an equal probability of being chosen on each draw, making the statement true.

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Explanation:

The blue rectangle has area of 4a^2*6a^2 = 24a^4

The red rectangle has area 4a^2*9a = 36a^3

The green rectangle has area 4a^2*3 = 12a^2

The total area is 24a^4 + 36a^3 + 12a^2

Answer:

x=29

Step-by-step explanation:

we know that opposite angles are equal, so therefore 3x+2=89.

Subtract 2 from both sides, and you have 3x=87

divide the 3 over, and you get x=29

Hope that helps!!!

The system is inconsistent for values of a equal to √(13) or -√(13).

The correct answer is not listed in the given options.

The determinant of the coefficient matrix to determine whether the system is inconsistent or not.

If the determinant is zero, then the system has no unique solution and is inconsistent.

Otherwise, the system has a unique solution.

The coefficient matrix of the system is:

[1  2  3]

[3  5  4]

[2  3  a²]

The determinant of this matrix is given by:

det = 1 × (5 × a² - 12) - 2 × (3 × a² - 8) + 3 ×(3 × 3 - 2 × 5)

   = 5a² - 12 - 6a² + 16 + 9

   = -a² + 13

Therefore, the system is inconsistent when the determinant is zero, i.e., when:

-a² + 13 = 0

a² = 13

a = ±√(13)

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The system is inconsistent for a = ±1, and the correct answer is C. a = 1.

To determine the value of a that makes the given system of linear equations inconsistent, we need to check if the system has no solutions or infinitely many solutions. If the system has a unique solution, it is consistent.

To solve the system, we can use Gaussian elimination to transform the system into row echelon form. The augmented matrix for the system is:

[1 2 3 | 1]

[3 5 4 | a]

[2 3 a^2| 0]

First, we can use row operations to eliminate the entries below the first entry in the first column. We can subtract 3 times the first row from the second row and subtract 2 times the first row from the third row to get:

[1 2 3 | 1]

[0 -1 -5 | a-3]

[0 -1 a^2-6| -2]

Next, we can use row operations to eliminate the entry in the second row and third column. We can subtract the second row from the third row to get:

[1 2 3 | 1]

[0 -1 -5 | a-3]

[0 0 a^2-1 | a-1]

Now, we can see that the system will have no solutions if a^2 - 1 = 0 and a - 1 ≠ 0. This simplifies to a = ±1.

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Answer:

C = 4 memory cards.

Step-by-step explanation:

256 × 4 = 1024

1024 + 105 = 1129 GB

She needs 4 memory cards.

Nancy needs to buy 4 memory cards.

Given that Nancy needs at least 1000 gigabytes of storage to take pictures and videos on her upcoming vacation, and she checks and finds that she has 105 GB available on her phone, and she plans on buying additional memory cards to get the rest of the storage she needs, and the cheapest memory cards she can find each hold 256 GB and cost $ 10, and she wants to spend as little money as possible and still get the storage she needs, to determine how many memory cards to buy, the following calculation must be performed:

So if Nancy buys 3 cards she will still be short on gigabytes. Therefore, she must buy 4 memory cards.

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The answer to the trigonometry question in the picture attached is:

   = cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

Simplify 1-csc θ as follows:

1 - csc θ = (1 - csc θ)(1 + csc θ) / (1 + csc θ)

= 1 - csc^2 θ / (1 + csc θ)

= 1 - 1/sin^2 θ / (1 + 1/sin θ)

= 1 - sin^2 θ / (sin θ + 1)

= (sin θ - sin^2 θ) / (sin θ + 1)

Simplify 1+csc θ as follows:

1 + csc θ = (1 + csc θ)(1 - csc θ) / (1 - csc θ)

= 1 - csc^2 θ / (1 - csc θ)

= 1 - 1/sin^2 θ / (1 - 1/sin θ)

= 1 - sin^2 θ / (sin θ - 1)

= (sin θ + sin^2 θ) / (sin θ - 1)

Substitute the above simplifications in the expression cos θ/(1-csc θ) * 1+csc θ/(1+ csc θ) to get:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

Simplify the expression by canceling out the sin^2 θ terms:

cos θ / (sin θ - sin^2 θ) * (sin θ + sin^2 θ) / (sin θ + 1)

= cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

Simplify further by factoring out common terms in the numerator and denominator:

cos θ / (sin θ - sin^2 θ) * (1 + sin θ) / (sin θ + 1)

= cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

Finally, simplify the expression by factoring out a sin θ term from the denominator:

cos θ * (1 + sin θ) / [(sin θ - sin^2 θ) * (sin θ + 1)]

= cos θ * (1 + sin θ) / [sin θ * (1 - sin θ) * (sin θ + 1)]

= cos θ / [sin θ * (1 - sin θ)] * (1 + sin θ)

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Answer:Yes, because ∛84 = ∛(2 × 2 × 3 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 84 is an irrational number.

Step-by-step explanation:

Answer: i think so

Step-by-step explanation:

Answer:

The increase is 88.1% B

Step-by-step explanation:

2.22 = (x/100)(1.18)

x = 2.22(100)(1.18)

x = 188.1%

2.22=(188.1/100)(1.18)

2.22=2.22

Answer:

16

Step-by-step explanation:

5(4)=20 so you multiply 4(4) and you get 16

Answer:

17 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = (1, - 2 ) and (x₂, y₂ ) = (9, 13 )

d = \(\sqrt{(9-1)^2+(13-(-2))^2}\)

   = \(\sqrt{8^2+(13+2)^2}\)

   = \(\sqrt{64+15^2}\)

   = \(\sqrt{64+225}\)

   = \(\sqrt{289}\)

   = 17

Answer:

The number of women teachers attending the lecture is 1.

Step-by-step explanation:

Denote the variables as follows:

M = men

W = women

T = teacher

The data provided is:

n (M) = 23

n (W) = 29

n (T) = 4

n (M ∪ T) =  24

Compute the number of men teachers as follows:

\(n(M\cap T)=n(M)+n(T)-n(M\cup T)\)

               \(=23+4-24\\=3\)

Compute the number of women teachers as follows:

        \(n(T)=n(M\cap T)+n(W\cap T)\)

             \(4=3+n(W\cap T)\)

\(n(W\cap T)=1\)

Thus, the number of women teachers attending the lecture is 1.

Answer:

D

Step-by-step explanation:

We can substitute y = 2x + 1 in the second equation

2x + 1 = -7x + 8

Add 7x to both sides

9x + 1 = 8

Subtact 1 from both sides

9x = 7

x = 7/9

Substituing x in the first equation

y = 14/9 + 1

x rounds to 0.8

y rounds to 2.5

The critical value at the 0.010 significance level with 6 degrees of freedom are ±3.7074

The dataset is given as:

21.1, 25.1, 26.1, 27.1, 24.1, 31.1, and 31.1

The sample mean is:

\(\bar x = 22.1\)

The significance level is

α = 0.010

Start by calculating the degrees of freedom using:

df = n - 1

Where n represents the sample size (n = 7)

So, we have:

df = 7 - 1

df = 6

Using the table for t critical values for a two-tailed test, we have:

Critical value = ±3.7074

Hence, the critical value at the 0.010 significance level with 6 degrees of freedom are ±3.7074

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Answer:

D

Step-by-step explanation:

The matrix of the relation r={(1,2),(2,3),(3,4),(4,5)} on the set x={1, 2, 3, 4, 5}; ordering of x:1,2,3,4,5 is as follows.

\($$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}$$\)

A relation is a set of ordered pairs.

The matrix of a relation is constructed by using its ordered pairs with their respective values as its entries, and its rows and columns by its domain and range, respectively.

So, the relation r is given as{(1,2),(2,3),(3,4),(4,5)}

The elements in the rows of the matrix correspond to the elements of x, while the elements in the columns of the matrix correspond to the elements of x as well, in that order.

So, the matrix of r on x can be written as:

\($$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix}$$\)

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