What is the slope, x-intercept, and y-intercept of -8x + 2y = 16

With a step by step

No, the vector [1] is not in the column space of matrix a = [2 0 2 1 3].

The column space of a matrix is the set of all linear combinations of its columns. To determine if [1] is in the column space of a, we need to check if there exists a linear combination of the columns of a that equals [1].

Let c1, c2, c3, c4, and c5 be constants such that

c1[2] + c2[0] + c3[2] + c4[1] + c5[3] = [1].

This simplifies to 2c1 + 2c3 + c4 + 3c5 = 1.

There is no solution to this equation, since the left-hand side is always even (due to the presence of even coefficients) and the right-hand side is odd. Therefore, [1] is not in the column space of a.

No, [1] is not in the column space of the matrix a.

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(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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(a) For y''+4y=sin2t+(2t+1)cos2t+tsint, we need to find a particular solution Y(t) using the method of undetermined coefficients.

Since the right-hand side of the equation contains sin(2t), cos(2t), and tsin(t), we can assume that the particular solution has the form:

Y(t) = A sin(2t) + B cos(2t) + Ct sin(t) + Dt cos(t) + Et + F

where A, B, C, D, E, and F are undetermined coefficients to be determined.

(b) For y''-4y'+4y=t^2(e^(2t)-1), we need to find a particular solution Y(t) using the method of undetermined coefficients. Since the right-hand side of the equation contains t^2e^(2t) and t^2, we can assume that the particular solution has the form:

Y(t) = (At^2 + Bt + C)e^(2t) + Dt^2 + Et + F

where A, B, C, D, E, and F are undetermined coefficients to be determined.

(c) For y''+2y'+2y=3e^(-t)+2e(-t)cos(t)+4(t^2)e^(-t)sin(t), we need to find a particular solution Y(t) using the method of undetermined coefficients. Since the right-hand side of the equation contains e^(-t), e^(-t)cos(t), and t^2e^(-t)sin(t), we can assume that the particular solution has the form:

Y(t) = Ae^(-t) + (Bt + C)e^(-t)cos(t) + (Dt + Et^2) e^(-t)sin(t) + F

where A, B, C, D, E, and F are undetermined coefficients to be determined.

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Step-by-step explanation:

since f'(x) = 2f(x) and f(3) has no term of x (so, there must be a constant that eliminates x for x = 3), we get

f(x) = x²/9 × c

c = m×e^n

f(1) = 1/9 × m×e^n = 5

=> m×e^n = 45

f(3) = 9/9 × m×e^n = 45

m = 45

n = 0

Answer:

Step-by-step explanation:

17

Answer:

Step-by-step explanation:

The first one is correct.

Answer:

The firest one( 2x + 8y ≤ 140 )

Step-by-step explanation:

Answer:

first box: right 4, up 6

second box: left 4, up 6

third box: right 6, down 4

Step-by-step explanation:

Answer:The first one is to the right 4 up 6

Second one is left four up 6

Last one is right 6 down 4

Step-by-step explanation:

Answer: 14 Units

Step-by-step explanation: Subtract (10-2) and (11-5)

Answer:

Step-by-step explanation:

2 π + ( π - \(\frac{\pi }{4}\) ) = \(\frac{8\pi +4\pi -\pi }{4}\) = \(\frac{11\pi }{4}\)

Answer:8

Step-by-step explanation: isaid it is

if we take 34000(origin amount) to be the 100%, what is 6200 off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 34000 & 100\\ 6200& x \end{array} \implies \cfrac{34000}{6200}~~=~~\cfrac{100}{x} \\\\\\ \cfrac{ 170 }{ 31 } ~~=~~ \cfrac{ 100 }{ x }\implies 170x=3100\implies x=\cfrac{3100}{170}\implies x\approx 18.24\)

The missing values are derived from the graph as follows:

3 ) 7, 14, 21, 28, 35

4) 3, 7, 10, 14, 17

5) 1, 21, 10, 49, 19

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

In order to solve for the above values, the best way is to spot the function that exists in the graph which is given as:

F(y) = 3.5x

In the first table, where x = 2

y= 3.5 *2

= 7

This iteration goes on and on and is consistent for all the values.

In the second table,

Where F(y) is known, for example 10.5, then x is derived as:

10.5 = 3.5x (divide both sides by 3.5)

x = 3

This iteration goes on and on and is consistent for all the values.

In the third table, we simply swap the values back and forth using the function F(y) = 3.5x to derive all values.

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When solving a system of linear equations by substitution, normally, we want to try to solve for the easiest one to get to or we choose a variable with unit coefficient.

A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

A constant component of a word as opposed to a variable. a measurement of some property or characteristic using a number (as of a substance, device, or process)

There are many factors, it is all a matter of preference, normally, we want to try to solve for the easiest one to get to

example;

if we have

(x-3)^2+y=9

we would solve for y because it is less tricky or we choose a variable with unit coefficient.

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The nearest whole number, the estimated time required by the 50th unit is 47 minutes.Therefore, the correct option is b. 48 minutes.

Given the 13th unit requires 87 minutes and 26th unit requires 64 minutes.To find the estimated time required by the 50th unit, we need to use the equation of the linear equation of the line.Let's find the value of m (slope).`m = (64 - 87)/(26 - 13)m = -23/13`Let's find the value of b (y-intercept).`b = 87 - (-23/13) × 13b = 87 + 23b = 110`

Therefore, the equation of the line can be written as:y = -23/13 x + 110Let's substitute the value of x as 50 and find the value of y (time required by the 50th unit).`y = -23/13 × 50 + 110y = 47.31`Rounded to the nearest whole number, the estimated time required by the 50th unit is 47 minutes.Therefore, the correct option is b. 48 minutes.

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Answer: North 136.81 mph

               East: 375.88 mph

Step-by-step explanation:

Hi there,

First you are going to want to set up a triangle based on the given information. You are giving a bearing for the degrees of the triangle, so the angle for the triangle you are going to solve will be 20 degrees.

You can use either Law of Sines or SOHCAHTOA to solve, but since you are setting up a right triangle I would use SOHCAHTOA. You are trying to find the vertical and horizontal components so start with sine to find the y-value. It should look like:

sin(20)=(opposite side of the given angle/400)

It will be travelling North at 136.81 mph

Similarly, we now need to find the horizontal component. Start by using cosine. It should look like

cos(20)=(side adjacent to the given angle/400)

It should be traveling East at 375.88 mph

Hope this helps.

The north component is 137.64 mi/h and the east component is 123.12 mi/h.

To find the north and east components of the velocity, we can use trigonometry.

The velocity can be divided into two components: one in the north direction and one in the east direction. The north component is given by:

North component = Velocity x sin(θ)

where θ is the angle between the velocity vector and the north direction.

Similarly, the east component is given by:

East component = Velocity x cos(θ)

where θ is the angle between the velocity vector and the east direction.

In this case, the angle between the velocity vector and the north direction is (90° - 70°) = 20° (since the direction is given as "n 70° e", which means 70° east of north). Therefore:

North component = 400 x sin(20°) = 137.64 mi/h

The angle between the velocity vector and the east direction is 70°. Therefore:

East component = 400 x cos(70°) = 123.12 mi/h

Rounding to two decimal places, the north component is 137.64 mi/h and the east component is 123.12 mi/h.

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The best measure of center for this data is the median, and its value is 3.

Option B is the correct answer.

We have,

From the line plot,

The median is the best measure of center for this type of data, as it is not affected by outliers.

To find the median, we need to arrange the data in order from least to greatest:

1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 10

Since there are 15 data points,

The median is the middle value, which is 3.

Therefore,

The best measure of center for this data is the median, and its value is 3.

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Let's simplify the expression step by step: Expand the squared term:

(x - 3y)² = (x - 3y)(x - 3y) = x² - 6xy + 9y²

Expand the second term:

3(x + y)(x − 4y) = 3(x² - 4xy + xy - 4y²) = 3(x² - 3xy - 4y²)

Expand the third term:

x(3x + 4y + 3) = 3x² + 4xy + 3x

Now, let's combine all the expanded terms:

(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)

= x² - 6xy + 9y² + 3(x² - 3xy - 4y²) + 3x² + 4xy + 3x

Combining like terms:

= x² + 3x² + 3x² - 6xy - 3xy + 4xy + 9y² - 4y² + 3x

= 7x² - 5xy + 5y² + 3x

The simplified form of the expression is 7x² - 5xy + 5y² + 3x.

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Answer:

6 hours

Step-by-step explanation:

8+5=12

12/2=6

It takes40/ 13 or approximately 3.1 hours to do the job with both printers working on it.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given:

It takes an old printer 8 hours to print all the pictures for the yearbook.

A modern printer can do the same job in 5 hours.

If both work together,

it will take,

x(1/8 + 1/5) = 1

x(8 + 5)/40 = 1

8x + 5x = 40

x = 40/13

x = 3.07

x = approximately 3.1 hours.

Therefore, the work will be done in 40/13 hours.

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Answer:

Simplified: 2x/15 + 5y/8

Step-by-step explanation:

Simplify the expression.

Answer:

Answer: 2x/15 + 5y/8

Step-by-step explanation:

Just Simplify the expression dude.

Answer:

4 1

Step-by-step explanation:

4 and 1

4 is alternate interior angle

1 is corresponding angle

The expression which represents either the length or width is (x+3). The correct answer is option (c).

Given that the area of a rectangle which is given as x²+5x+6.

We have to find which expression represents either the length or width.

We are given an expression for the area. But we also know that the area of a rectangle is length times width. So the expression we were given, x²+5x+6 must be equal to the length of the rectangle times its width.

So, will find the factoring the expression we can see expressions for the length and the width.

Factoring x²+5x+6 we get (x+2)(x+3).

One of these factors is the width and the other is the length.

Hence, the expression represents either the length or width of the rectangle when the area of a rectangle is given as x²+5x+6 is (x+3).

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The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45

We have to given that;

One bag contains 3 red lollipops and 2 green lollipops.

And, The other bag contains four purple lollipops and five blue lollipops.

Hence, The probability of choosing a green lollipop is,

P₁ = 2 / 5

And, The probability of choosing a purple lollipop is,

P₂ = 4 / 9

Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,

P = P₁ ×  P₂

P = 2/5 × 4/9

P = 8/45

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Answer:

Step-by-step explanation:

To analyze the equation -12 + x + 10x² + 3x³ = 0, we can determine the number of complex roots, the possible number of real roots, and the possible rational roots.

Number of Complex Roots:

The equation is a polynomial of degree 3 (highest power of x is 3), so it can have up to 3 complex roots. However, we need to evaluate the discriminant to determine the nature of the roots more precisely.

Possible Number of Real Roots:

The possible number of real roots can be determined by analyzing the signs of the coefficients. Counting the sign changes in the coefficients when arranged in descending order, we can identify the potential number of positive and negative real roots.

In this case, we have the coefficients: 3, 10, 1, -12.

- The number of sign changes is 2, indicating there are 2 or 0 positive real roots.

- We can also check the number of sign changes when considering f(-x) (replacing x with -x) to find the number of negative real roots. In this case, there is 1 sign change, indicating there is 1 negative real root or an odd number of negative real roots.

Possible Rational Roots:

According to the Rational Root Theorem, any rational root of the equation must be of the form p/q, where p is a factor of the constant term (-12) and q is a factor of the leading coefficient (3).

The factors of -12 are ±1, ±2, ±3, ±4, ±6, and ±12.

The factors of 3 are ±1 and ±3.

Therefore, the possible rational roots can be expressed as:

±1/1, ±1/3, ±2/1, ±2/3, ±3/1, ±3/3, ±4/1, ±4/3, ±6/1, ±6/3, ±12/1, ±12/3.

Simplifying these fractions, we have:

±1, ±1/3, ±2, ±2/3, ±3, ±1, ±4, ±4/3, ±6, ±2, ±12, ±4.

These are the possible rational roots of the equation -12 + x + 10x² + 3x³ = 0.

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Answer:

Let s = Susan's sales and y = Yvette's sales.

s = $105 + 6y

s + y = $1,960

$105 + 6y + y = $1,960

$105 + 7y = $1,960

7y = $1,855

y = $265, s = $105 + 6($265) = $1,695

Yvette's sales = $265

Susan's sales = $1,695

Susan's sales were $1175, and Yves's sales were $185. Susan's sales were determined by multiplying Yves's sales by six and adding $105. Together, their sales amounted to $1960.

Let's assume Yves's sales to be Y. According to the given information, Susan's sales were $105 more than six times Yves's sales, which can be represented as 6Y + $105. Additionally, we know that together their sales amounted to $1960. Therefore, we can form the following equation:

6Y + $105 + Y = $1960

Combining like terms, we get:

7Y + $105 = $1960

Subtracting $105 from both sides of the equation, we have:

7Y = $1960 - $105

7Y = $1855

Dividing both sides by 7, we find:

Y = $1855 / 7

Y ≈ $264.29

Since sales cannot be in fractional amounts, we can round Y to the nearest whole number, which is $264. Now we can determine Susan's sales by multiplying Yves's sales by six and adding $105:

S = 6Y + $105

S = 6 * $264 + $105

S = $1584 + $105

S = $1689

Therefore, Susan's sales were $1689, and Yves's sales were $264.

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Answer:

a)It is a vertical line with an undefined slope

b)It is a vertical line with an undefined slope

c)7/4

d)-7/4

Step-by-step explanation:

The formula for gradient of a line is given as;

m=Δy/Δx

where Δy = y₂-y₁   and Δx=x₂-x₁

For L₁

x=2

It is a vertical line with an undefined slope

For L₂

x=-3

It is a vertical line with an undefined slope

For L₃

The points on the line are : (0,-3)  and (4,4)

m= Δy/Δx

m= 4--3/4-0

m=7/4

For L₄

The points on the line are : (0,-3) and (-4,4)

m=Δy/Δx

m=4--3/-4-0

m=7/-4

m= - 7/4

The answer is 4/15

2/5 * 2/3 = 2 · 2/5 · 3 = 4/15

Multiply the numerators and denominators together. Keep the result fraction to the smallest possible denominator GCD(4, 15) = 1. It cannot further simplify the fraction result by canceling in the following intermediate step.

In other words, two fifths times two thirds equals four fifteenths.

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Answer:

5/3

Step-by-step explanation:

"of" means times so so so often. It is not a hard math rule/definition. But more like a soft English-Math translation.

So, "2/5 of what"

means 2/5x (but make sure the 2/5 is a fraction beside the x, NOT the x on the bottom with the 5)

"is" means equals.

2/5x = 2/3

Multiply both sides by 5/2.

5/2 • 2/5x = 2/3•5/2

x = 2/3 • 5/2

x = 5/3

You get 5/3 either by "cancelling" the 2's OR by

fraction multiplication where you times top×top and bottom×bottom and simplify.

x = 10/6

x = 5/3

2/5 of 5/3 is 2/3.

The "what" in the question is 5/3.

The critical value of the correlation coefficient for a two-tailed test at alpha = 0.05 with a sample size of n = 23 is approximately plus/minus 0.497.

To understand why this is the case, we need to consider the distribution of the correlation coefficient, which follows a t-distribution. In a two-tailed test, we divide the significance level (alpha) equally between the two tails of the distribution. Since alpha = 0.05, we allocate 0.025 to each tail.

With a sample size of n = 23, we need to find the critical t-value that corresponds to a cumulative probability of 0.025 in both tails. Using a t-distribution table or statistical software, we find that the critical t-value is approximately 2.069.

Since the correlation coefficient is a standardized measure, we divide the critical t-value by the square root of the degrees of freedom, which is n - 2. In this case, n - 2 = 23 - 2 = 21.

Hence, the critical value of the correlation coefficient is approximately 2.069 / √21 ≈ 0.497.

Therefore, the correct answer is A. Plus/minus 0.497.

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Answer:

\(-2 \geq w \geq 2\)

Step-by-step explanation:

Given

\(|-w| \geq 2\)

Required

Solve for w

\(|-w| \geq 2\)

In absolution functions;

\(|-w| = |w|\)

So, the given expression can be rewritten as

\(|w| \geq 2\)

Removing the absolute sign, will gibe

\(w \geq 2\) or \(w \leq -2\)

When the second inequality os rewritten, it gives

\(w \geq 2\) or \(-2 \geq w\)

Reorder both inequalities

\(-2 \geq w\) or \(w \geq 2\)

Lastly, both inequalities are combined

\(-2 \geq w \geq 2\)

The number of gigabytes that Sydney can use while staying within her budget is less than 2.9 gigabytes.

How to illustrate the information?

From the information, Sydney pays a flat cost of $35.50 per month and $5 per gigabyte. She wants to keep her bill under $50 per month.

The inequality that can be used to determine x x, the number of gigabytes Sydney can use while staying within her budget will be:

35.50 + 5x < 50

Collect like terms

5x < 50 - 35.50

5x < 14.50

x < 14.50 / 5

x < 2.9

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