The width of a rectangle is 6n - 2.5 feet and the length is 2.5 + 8 feet. Find the perimeter of the rectangle.

Answer:

No solutions

Step-by-step explanation:

6x+2y=20

-3x-y=-4 (by rewriting)

So

6/-3 = 2/-1≠20/-4

-2=-2≠-5

So it has no solutions

Answer:

x = 256

Step-by-step explanation:

-5/8x = -160

Multiply each side by -8/5 to isolate x

-8/5*-5/8x = -160*-8/5

x = 256

Answer:

-0.1

Step-by-step explanation:

just did it

The common difference in the given sequence is 0.1, gotten by subtracting second term from the first term

A common difference is a value that describes the step or the diference between two items in a sequence, it is also a value that follows a pattern.

Common difference can either by whole numbers or decimal.

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Student Reading Art Math Writing

Bill X O X X
Sally O O X O
Bob X X O X
Sue X X X X

Based on the information given, Sally's favorite subject is either art or writing, but since she likes reading better than art, her favorite subject must be writing. Bob's favorite subject is math and Sue doesn't like any of the subjects listed, so we can mark X's for all subjects for her.

Bill's favorite subject cannot be math, so we mark an X for math. BII (assuming this is a typo and should be Bill) prefers writing to art, so we mark an O for writing and an X for art.

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Answer:

The factors are;

(x + 4) , (x + 1) and (2x-1)

Step-by-step explanation:

Given the zeros, we want to get the factors

To get the zeros, we simply equate the factors to zero and solve for x

so for x = 1/2

we can have x - 1/2 = 0

multiply through by 2

= 2x - 1

for x = -4

x + 4

for x = -1

x + 1

So the factors are;

(x + 1) , (x + 4) and (2x-1)

Answer:

x-3+2x+3+2x = 5x

x+8+4x-3x-4 = 2x+4

4x+x-11-5X+25+4x = 4x+14

3x+5-2x-5x+9+8x = 4x+14

5+9x-7-4X-3x+6 = 2x+4

6x-9-5x+4-x+5x+5 = 5x

Step-by-step explanation:

Simplified by adding like terms

Answer: The answer is 0 because if it was negative, there are no solutions and if the discriminant is equal to zero we have a solution. can you give me brainliest

Step-by-step explanation:

The general solution of the given system of equations is x₁(t) = C₁e^t + C₂e^(4t) and x₂(t) = -C₁e^t + C₂e^(4t), where C₁ and C₂ are arbitrary constants. We need to find the eigenvalues and eigenvectors of matrix A.

To find the general solution, we can start by writing the system of equations in matrix form:

dx/dt = A  x

where

A = [[1, 1], [5, 3]]

x = [x₁, x₂]

To solve this system, we need to find the eigenvalues and eigenvectors of matrix A.

First, we find the eigenvalues λ by solving the characteristic equation |A - λI| = 0, where I is the identity matrix:

|A - λI| = |[1-λ, 1], [5, 3-λ]| = (1-λ)(3-λ) - (5)(1) = λ² - 4λ - 2 = 0

Solving the quadratic equation, we find two eigenvalues: λ₁ ≈ 5.73 and λ₂ ≈ -0.73.

Next, we find the corresponding eigenvectors by solving the equation (A - λI)v = 0 for each eigenvalue:

For λ₁ ≈ 5.73, we have (A - λ₁I)v₁ = 0, which gives:

[1-5.73, 1][v11, v12] = [0, 0]

[-4.73, -4.73][v11, v12] = [0, 0]

Solving the above system, we find an eigenvector v₁ = [1, -1].

Similarly, for λ₂ ≈ -0.73, we have (A - λ₂I)v₂ = 0, which gives:

[1+0.73, 1][v21, v22] = [0, 0]

[1.73, 1.73][v21, v22] = [0, 0]

Solving the above system, we find an eigenvector v₂ = [1, -1].

The general solution is then given by x(t) = C₁e^(λ₁t)v₁ + C₂e^(λ₂t)v₂, where C₁ and C₂ are arbitrary constants.

Substituting the values, we get x₁(t) = C₁e^(5.73t) + C₂e^(-0.73t) and x₂(t) = -C₁e^(5.73t) - C₂e^(-0.73t).

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Let's find the magnitude of each component:

Let:

 \((x1,y1)=(4,4)\)

\((x2,y2)=(-12,8)\)

     \(u=ax+by\)

  \(||u||=\sqrt{a^2+b^2}\)

So, let's find a and b:

\(a=|x2-x1|=|-12-4|=|-16|=16\)

       \(b=|y2-y1|=|8-4|=|4|=4\)

so:

\(||u||=\sqrt{16^2+4^2}\)

   \(||u||=\sqrt{272}\)

 \(||u||\thickapprox16.492\)

And the direction is:

         \(\theta=180-\text{tan}^{-1}\huge \text(\dfrac{b}{a}\huge \text)\)

        \(\theta=180-\text{tan}^{-1}\huge \text(\dfrac{4}{16}\huge \text)\)

\(\theta\thickapprox180-\text{tan}^{-1}\huge \text(\dfrac{4}{16}\huge \text)\thickapprox165.964\)

Answer:

(-2,1)

Step-by-step explanation:

Substitute the value of y (x+3) from one equation into the second equation (2x+5)

X+3 = 2x + 5

add -2x to both sides

-x+3=5

add -3 to both sides

-x=2

x=-2

substitute -2 for x in either equation to find y.

y=-2+3

y=1

Check your answer by substituting x and y into either equat to make sure it equals.

y=x+3

1=-2+3

1=1

or

y=2x+5

1=2(-2)+5

1=-4+5

1=1

Answer: 50

Step-by-step explanation:

Answer:

Option A

Step-by-step explanation:

Median of a trapezoid is parallel to both the bases and measure of median equals to half of the sum of bases.

By this property,

QR = \(\frac{1}{2}(PM+ON)\)

\((x+15)=\frac{1}{2}[(9x-42)+(30)]\)

2x + 30 = 9x - 12

9x - 2x = 30 + 12

7x = 42

x = 6

Option A is the correct option.

Answer:

6

Step-by-step explanation:

Answer: 12.5

Step-by-step explanation:

Answer:-1.5

Step-by-step explanation:

First, -3/4 = -0.75

Second, -0.75 divided by 2 is -1.5

The equation of the line passing through the points (4,-3) and (-5,2) is y = -1/3x - 7/3. The equation of the line passing through the point (-2,7) with a y-intercept of -1 is y = 2x + 5.

1. To find the equation of the line passing through the points (4,-3) and (-5,2), we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line. First, we calculate the slope:

m = (y2 - y1) / (x2 - x1) = (2 - (-3)) / (-5 - 4) = -5/9.

Using one of the given points, (4,-3), we substitute the values into the point-slope form:

y - (-3) = (-5/9)(x - 4).

Simplifying the equation gives us:

y + 3 = (-5/9)x + 20/9.

Rearranging the equation to the slope-intercept form, y = mx + b, where b is the y-intercept, we get:

y = -5/9x - 7/3.

2. For the line passing through the point (-2,7) with a y-intercept of -1, we can directly write the equation in slope-intercept form, y = mx + b. The slope, m, is calculated by comparing the given point with the y-intercept:

m = (y2 - y1) / (x2 - x1) = (-1 - 7) / (0 - (-2)) = -8/2 = -4.

Substituting the values into the slope-intercept form and solving for the y-intercept, we have:

7 = -4(-2) + b,

7 = 8 + b,

b = -1.

Thus, the equation of the line is y = -4x - 1 + 1, which simplifies to y = -4x + 5.

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Answer:

∠L=23°

Step-by-step explanation:

(6x-5)+(x+9)=(9x-24) (ext angle of triangle)

   6x-5+x+9=9x-24

           7x+4=9x-24

          7x-9x=-24-4

              -2x=-28

               2x=28

                 x=28÷2

                   =14

Hence, ∠L = (x+9)°

                  = (14+9)°

                  = 23°

Answer:

30x-35

Step-by-step explanation:

Ok so you have a problem: 5 * ( 6 x - 7 )

The problem tells you to apply the distributive property and simplify it to remove parenthesis.

To simplify the expression using the distributive property, you need to multiply the number outside the parentheses by each term inside the parentheses:

5(6x-7) = 30x - 35

Therefore, 5(6x-7) simplifies to 30x - 35.

Brainliest? This took a long time to explain :)

Answer: x=9

Step-by-step explanation:

The bottom triangle that has a 40° is an isosceles triangle, therefore the other angle at the bottom right is also 40°. This leaves the top angle to be 100°.

180=40+40+x

180=80+x

x=100

Now, to find ∠2, you can tell it is a supplementary angle. Therefore, the 2 angles add up to 180°

180-100=∠2

80°=∠2

The problem states that ∠2 is 9x-1. We know that ∠2 is 80°. We can solve for x.

80=9x-1

81=9x

x=9

The correct response is d) All the above. The arithmetic mean is equal to the median, the median is equal to the mode, and the mode is equal to the arithmetic mean.

If the data are graphed symmetrically, the distribution demonstrates 0% skewness regardless of how long or fat the tails are. When the median of a data set is utilized, 50% of the data points in the collection have values lower than or equal to the median, and 50% of them have values greater than or equal to the median. The middle score in the set is known as the median. The first step in calculating the median is to order the data points from smallest to greatest. The median in an odd-numbered set will be the value that falls exactly in the middle of the list. You must determine the average of the two middle numbers in a set of even numbers. The average is determined by summing up each value individually and dividing that sum by the total number of observations.

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Answer:  8 days

Step-by-step explanation:

Given, At Sami's Shoe Warehouse, it takes 4 over 5 of a day to complete 1 over 10 of an order of sneakers.

i.e. \(\dfrac{4}{5}\) x  (1 day) = \(\dfrac{1}{10}\) x (an order of sneakers)

Multiply 10 on both the sides , we get

\(\dfrac{4}{5}\times10\) x  (1 day) = \(\dfrac{1}{10}\times10\) x (an order of sneakers)

⇒\(4\times2\) x  (1 day) = an order of sneakers

⇒\(8\) x  (1 day) = an order of sneakers

i.e. Time to complete an order of sneakers = 8 days

Hence, it will take 8 days to complete the entire order of sneakers.

Answer: 8 days total

Step-by-step explanation:

page 1:

\(-\frac{8}{3} m = 6\)

\(-8m = 6(3)\)

\(-8m = 18\)

\(m = \frac{18}{-8}\)

\(m = -\frac{9}{4}\)

\(m = -2\frac{1}{4}\)

page 2:

7)

\(0.8x = 19\)

\(x = 19/0.8\)

\(x = 23.75\)

8)

\(0.12x = 1\)

\(x = 1/0.12\)

\(x =\)\(\frac{25}{3}\)

\(x = 8\frac{1}{3}\)

5)

3.3(x+4)

3.3x + 13.2

b.

\(9-5\:\frac{1}{2}x-3\left(-2x+1\right)\)

\(9-\frac{11}{2}x-3\left(-2x+1\right)\)

\(6x-\frac{11}{2}x+9-3\)

\(x\frac{1}{2}+6\)

\(\frac{1}{2}x+6\)

c.

\(2.2(3.1+x)+3x\)

\(6.82+2.2x+3x\)

\(6.82+5.2x\)

page 3:

1.

3/4 x = 60

x = (60*4)/3

x = 80

2.

2/5 x =42

x = (42*5)/2

x =105

3.

3/5 y = 40

y = (40*5)/3

y = \(\frac{200}{3}\)

y = \(66\frac{2}{3}\)

4.

\(-\frac{8}{3}m =6\)

\(m = \frac{6*3}{-8}\)

\(m = -\frac{9}{4}\)

\(m = -2\frac{1}{4}\)

5.

\(\frac{5}{6} x =4\)

\(x = \frac{4*6}{5}\)

\(x =4.8\)

6.

\(\frac{5}{3} x =12\)

\(x = \frac{12*3}{5}\)

\(x =7.2\)

Answer:

Step-by-step explanation:

-8/3m =  6

divide both sides by -8/3

m = 6/(-8/3)

m= -2.25

2. 0.8x = 19

x= 19/0.8

x= 23.75

3. 0.12x = 1

x= 1/0.12

x= 8.333333

3/4x = 60

x = 60*(3/4)

x = 45

SORRY I COULDN'T ANSWER EVERYTHING THE QUESTIONS WERE ALOT, BUT WITH MY EXPLANATIONS YOU CAN ANSWER ALL OF THEM. NO SWEAT

The variation equation is y = (4/3)x. This equation tells us that if x increases (or decreases) by a certain factor, y will increase (or decrease) by the same factor multiplied by 4/3. For example, if x doubles, y will also double, since 2 times 4/3 is 8/3.

When two variables are said to vary directly, it means that if one variable increases (or decreases) by a certain factor, the other variable will increase (or decrease) by the same factor. In mathematical terms, this can be represented as:

y = kx

where k is the constant of variation.

Now, let's use the given information to find the constant of variation and the variation equation. We know that y is 20 when x is 15, so we can plug these values into the equation:

20 = k(15)

Simplifying this equation, we can divide both sides by 15:

20/15 = k

We can simplify the fraction on the left side to get:

4/3 = k

So the constant of variation is 4/3. Now we can use this value to write the variation equation:

y = (4/3)x

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The correlation coefficient measures the strength and direction of the linear relationship between two variables. The value of the correlation coefficient ranges from -1 to 1.

Among the given options, the correlation coefficient that represents the weakest correlation between two variables is:

C. 0.02

A correlation coefficient of 0.02 indicates a very weak positive or negative linear relationship between the variables, as it is close to zero. In comparison, options A (-0.10) and D (0.10) represent slightly stronger correlations, while option B (-1.00) represents a perfect negative correlation.

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In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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Answer:

1500 * 0.07 = 105

105 + 1500 = 1605

Step-by-step explanation:

296 hot lunches were sold on Friday.

The number of hot lunches sold on Friday can be calculated by multiplying the total number of hot lunches by the relative frequency on Friday:

Hot lunches sold on Friday = 1,350 * 0.22 = 296

Relative frequency is a measure of the number of times an event occurs in a sample, expressed as a proportion of the total number of events. To find the number of hot lunches sold on Friday, we multiply the total number of hot lunches sold in the week by the relative frequency of Friday. This gives us the number of hot lunches sold on Friday, which is 296 in this case. Understanding relative frequency is important in statistics as it helps to summarize data and understand the distribution of events.

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AB is the answer. :)

Given the following expression:

You need to remember that, by definition:

In this case, you can identify that:

Then, substituting values and evaluating, you get the following:

The answer is:

The equation shows that the number of injuries is directly proportional to the number of workers involved in the fast food chains.

The relationship between the number of adult workers and the number of teenage workers injured in these fast food chains can be expressed using an algebraic equation.

Let the number of adult workers be represented by the variable 'A' and the number of teenage workers be represented by the variable 'T'.Let 'I' represent the number of injuries.

We can assume that the number of injuries is proportional to the number of workers involved in the fast food chains.

So, the relationship between the number of adult workers and the number of teenage workers injured in these fast food chains can be represented using the following algebraic equation:

\($\frac{I}{A+T} = k$$\)

where 'k' is the proportionality constant.

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