find k so that a and b will be orthogonal

The system of equations containing equations  y = 5/2 x + 2 and 2y = 5 x + 4 will have infinitely many solutions.

What is system of equations?

A finite collection of equations for which we searched for the common solutions is referred to in mathematics as a system of equations, sometimes known as a set of simultaneous equations or an equation system. Similar to single equations, a system of equations can be categorized. In everyday life, systems of equations are used to model problems when the unknown values can be represented by variables.

Given equations:

y = 5/2 x + 2

2y = 5 x + 4

We will use the substitution method, to get the values of x and y:

2 ( 5/2 x + 2 ) = 5 x + 4

5 x + 4 = 5 x + 4

0 · x = 0

x , y ∈  R

Therefore, this system of equations will have infinitely many solutions.

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Complete question

How many solutions does the following system of equations have?

y = 5/2x + 2,

2y = 5x + 4.

The the expression is in the required form. Thus, A = 211, B = 1, and C = 1. We use the properties of logarithms to rewrite the expression 21619 log 211 in a form with no logarithm of a product, quotient, or power. is in the required form. Thus, A = 211, B = 1, and C = 1. We use the properties of logarithms to rewrite the expression 21619 log 211 in a form with no logarithm of a product, quotient, or power.

To rewrite the expression 21619 log 211 in a form with no logarithm of a product, quotient or power using the laws of logarithms; it is best to express it in exponential form and then separate it into logarithms.21619 log 211Let's express this expression in exponential form.

We know that log a b = c if a = b.

Using this property, we can write,

\(21619 log 211 = 211^(21619)\)

Now let's separate this exponential expression into logarithms.

\(z1y19 log A log(z)+ Blog(y) + Clog(z) 211\)

Now, we have the value of

\(211^(21619)\)

so we can substitute this value in the above expression to get,

\(z1y19 log A log(z)+ Blog(y) + Clog(z) 211z1y19 log A + log(z^z1y19) + Blog(y) + log(z^C) 211\)

Now we use the property that

log a^n = nlog a to split the logs into their coefficients.

\(z1y19 log A + z1y19 log(z) + Blog(y) + Clog(z).\)

Now, the expression is in the required form. Thus, A = 211, B = 1, and C = 1. We use the properties of logarithms to rewrite the expression 21619 log 211 in a form with no logarithm of a product, quotient, or power.

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Answer:

second number = - 28

Step-by-step explanation:

let the first number be x and the second number y , then

x + y = - 18 , that is

10 + y = - 18 ( subtract 10 from both sides )

y = - 28 , that is

the second number is - 28

Answer:

Step-by-step explanation:

The equation that represents the situation is -28 + 10 = -18

The second number is -28.

The height is changing at the rate of 1/20in per minute in the given right cylindrical tank.

So, the changing the rate of the height:

Calculate height as follows:

Therefore, the height is changing at the rate of 1/20in per minute in the given right cylindrical tank.

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To solve this problem first we hace to name the variable so y will be the earnings and x will be the number of bracelets she sell so the equation will be:

So if y is equal to 101 we can solve the equation for x so:

Answer:

3.5m

Step-by-step explanation:

Volume of pyramid = lwh÷3

25.77 = [(4.7)² × x] ÷ 3

25.77 × 3 = 22.09x

77.31 = 22.09x

x = 77.31 ÷ 22.09

= 3.49

= 3.5m

The three solutions of the equation y = -2x - 1 are (–2, 3), (1, –3), and (2, –4).

To find the solutions, we substitute different values of x into the equation and solve for y.

For the first solution, when x is –2, we have y = -2(-2) - 1 = 3. Therefore, the first solution is (-2, 3).

For the second solution, when x is 1, we have y = -2(1) - 1 = -3. Thus, the second solution is (1, -3).

For the third solution, when x is 2, we have y = -2(2) - 1 = -4. Hence, the third solution is (2, -4).

These three points satisfy the equation y = -2x - 1, and therefore, they are the solutions of the equation. They represent coordinate pairs (x, y) where the equation holds true.

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Answer:

18 pounds

Step-by-step explanation:

assuming a 3:4 rate

24 Euros is

24/4 * 3 = 18 pounds

The solution is £ 18

The value of €24 in pounds is 18 pounds or £ 18

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the value of £3 be = €4

So , the equation will be

The value of €1 = £ ( 3/4 )

So , the value of €24 is calculated by the equation

The value of €24 in pounds = value of €1 x 24

Substituting the values in the equation , we get

The value of €24 in pounds = £ ( 3/4 ) x 24

The value of €24 in pounds = £ 3 x 6

The value of €24 in pounds = £ 18

Therefore , the value of €24 in pounds is £ 18

Hence , The value of €24 in pounds is 18 pounds or £ 18

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The arithmetic sequence with a first term of 14, a common difference of 3, and the 14th term being 42 can be described by the formula: aₙ = 14 + (n - 1) * 3.

In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. The general formula for the nth term of an arithmetic sequence is given as aₙ = a₁ + (n - 1) * d, where aₙ represents the nth term, a₁ is the first term, n is the position of the term in the sequence, and d is the common difference.

Given that a₁₄ = 42 and d = 3, we can substitute these values into the formula to find the nth term. Plugging in the values, we have a₁₄ = 14 + (14 - 1) * 3, which simplifies to 14 + 13 * 3, resulting in a₁₄ = 14 + 39 = 53. Therefore, the 14th term of the arithmetic sequence is 42.

To graph the first six terms of the sequence, we can substitute n = 1, 2, 3, 4, 5, and 6 into the formula. The corresponding terms are as follows:

a₁ = 14 + (1 - 1) * 3 = 14

a₂ = 14 + (2 - 1) * 3 = 17

a₃ = 14 + (3 - 1) * 3 = 20

a₄ = 14 + (4 - 1) * 3 = 23

a₅ = 14 + (5 - 1) * 3 = 26

a₆ = 14 + (6 - 1) * 3 = 29

Plotting these values on a graph, we would have the following points: (1, 14), (2, 17), (3, 20), (4, 23), (5, 26), and (6, 29). Connecting these points would result in a straight line with a positive slope, representing the arithmetic sequence.

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a. x=5

b. y=x

c. y=0

d. y=x-7

Answer:

10/ 3

Step-by-step explanation:

3 × (48 xy) × 5/ (54 x y) × 4

3 × 48x y x 5/ 54 xy × 4

12 × 5/ 18

2 × 5 / 3

10/ 3

hope it helps!

Given that line AC is perpendicular to the circle centered at O with a radius of 1 unit, and the length of AC is 1.5 units, we can find the length of segment AB using the Pythagorean theorem.

Let's denote the length of segment AB as x.

Since AC is a diameter of the circle, its length is twice the radius, which is 2 units. However, in this case, the length of AC is given as 1.5 units.

Now, we have a right triangle formed by segments AO, OB, and AB. AO and OB are both radii of the circle, each measuring 1 unit.

Applying the Pythagorean theorem, we can write the equation: AO^2 + OB^2 = AB^2.

Substituting the known values, we get: 1^2 + 1^2 = AB^2.

Simplifying, we have: 1 + 1 = AB^2.

This gives us: AB^2 = 2.

Taking the square root of both sides, we find: AB = √2 units.

Therefore, the length of segment AB is approximately 1.41 units.o\(\)

The distribution will keep the same shape as the original, the standard deviation will be 1 and it will have a mean 0

Standard Deviation: the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range

it is asked that, to describe what happens to the mean, the standard deviation, and the shape of a distribution when all of the scores are transformed into z-scores

Every score stays in the exact same position relative to every other score in the distribution. Mean - when raw scores are transformed into z-scores, the mean will always = 0. The standard deviation - when any distribution of raw scores is transformed into z-scores the standard deviation will always = 1

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Answer:

1. 14ftx23ft=322ft

2. 26inX18in= 468in

Step-by-step explanation:

The linear inequalities are a ≤ 2j+3 , j≥14 ,a≤35 , Therefore Option C is the correct answer.

Inequality can be defined as a mathematical statement where the algebraic expression are equated by an inequality Operator , < , > ,<> etc.

It is given in the question that

Anna is no more than 3 years older than 2 times jamie’s age.

Let Anna's age be a and Jamie's age is j

then

a ≤ 2j+3

jamie is at least 14 and anna is at most 35

j≥14

a≤35

The linear inequalities are a ≤ 2j+3 , j≥14 ,a≤35

Therefore Option C is the correct answer.

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Answer:

b

Step-by-step explanation:

Answer:

scale factor(k)=23

A(x,y)=A'(kx,ky)

Let's do by using this formula

C(9,0)=C'(kx,ky)(here x=9 and y=0)

C(9,0)=(23*9,23*0)

C(9,0)=(207,0)

A(0,3)=A'(kx,ky)(here x=0 and y=3)

A(0,3)=A'(23*0,23*3)

A(0,3)=A'(0,69)

Step-by-step explanation:

sorry i dont know how to do B no

Answer:

$8.70

Step-by-step explanation:

Answer:

The best chart to show how your department's expenses compare to the total company's expenses, and hopefully save employee jobs, would be:

Pie Chart

Step-by-step explanation:

Answer:

can't see, the pic is too blurry

The question is an illustration of sequence and pattern

The cell entries that complete the table are 0.08 and 400

The table entries are given as:

Day     Avi's rule      Benita's rule

1             0.01              100

2            0.02             200

3            0.04            300

4

From Avi's rule, we can see that:

The new elements are generated by multiplying the current element by 2.

So, the entry that fills the missing blank in Avi's rule is:

\(Avi = 2 * 0.04\)

\(Avi = 0.08\)

From Benita's rule, we can see that:

The new elements are generated by adding 100 to the current element.

So, the entry that fills the missing blank in Benita's rule is:

\(Benita = 100 + 300\)

\(Benita = 400\)

So, the complete table is:

Day     Avi's rule      Benita's rule

1             0.01              100

2            0.02             200

3            0.04            300

4            0.08           400

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Step-by-step explanation:

A  =  S + 2

L = A + 10 =   S+2   + 10  = S + 12

S  = S

Summed , they equal 83

S+2     +  S+12   + S  = 83

3S = 69

S = 23  messages  

Answer:

1600

Step-by-step explanation:

(20 x 16)5

=320 x 5

=1600

The general solution is (2/3)x³ - xy² + 3x + C1(y) + (7/3)y³ - xy² + 2y + C2(x).

To determine whether the given differential equation is exact, we need to check if the partial derivatives of the equation with respect to x and y are equal.

Given differential equation: (2x² − 2xy + 3) dx + (7y² − x² + 2) dy = 0

Taking the partial derivative with respect to x:

∂/∂x(2x² − 2xy + 3) = 4x - 2y

Taking the partial derivative with respect to y:

∂/∂y(7y² − x² + 2) = 14y - 0 = 14y

Since the mixed partial derivative (∂²/∂x∂y) is not equal to the difference between the two partial derivatives (∂/∂y(4x - 2y) - ∂/∂x(14y)), the given differential equation is not exact.

To proceed, we can check if the equation can be made exact by multiplying an integrating factor.

Dividing both sides of the equation by (4x - 2y), we get:

[(2x² − 2xy + 3)/(4x - 2y)] dx + [(7y² − x² + 2)/(4x - 2y)] dy = 0

Comparing this with the form M(x, y) dx + N(x, y) dy = 0, we have:

M(x, y) = (2x² − 2xy + 3)/(4x - 2y)

N(x, y) = (7y² − x² + 2)/(4x - 2y)

To find the integrating factor (μ), we can use the formula:

μ = e^(∫(∂M/∂y - ∂N/∂x) dx)

Calculating the values:

∂M/∂y = (-2x + 2)/(4x - 2y)

∂N/∂x = (-2x + 7)/(4x - 2y)

∂M/∂y - ∂N/∂x = [(-2x + 2)/(4x - 2y)] - [(-2x + 7)/(4x - 2y)]

             = (-2x + 2 + 2x - 7)/(4x - 2y)

             = (-5)/(4x - 2y)

∫(-5)/(4x - 2y) dx = -5ln|4x - 2y|

Therefore, the integrating factor (μ) is μ = e^(-5ln|4x - 2y|) = 1/(|4x - 2y|^5).

Now, multiply the entire equation by the integrating factor:

1/(|4x - 2y|^5) [(2x² − 2xy + 3) dx + (7y² − x² + 2) dy] = 0

Simplifying the equation, we get:

(2x² − 2xy + 3)/(|4x - 2y|^5) dx + (7y² − x² + 2)/(|4x - 2y|^5) dy = 0

Now, we need to check if this new equation is exact.

Taking the partial derivatives with respect to x and y, we find that they are equal.

Since the equation is now exact, we can find the solution by integrating the equation.

Integrating (2x² − 2xy + 3)/(|4x - 2y|^5) with respect to x,

and integrating (7y² − x² + 2)/(|4x - 2y|^5) with respect to y.

To integrate the given differential equation with respect to x and y, we treat it as a function of two variables and integrate each term separately.

Integrating with respect to x:

∫ (2x² - 2xy + 3) dx = (2/3)x³ - xy² + 3x + C1(y)

Integrating with respect to y:

∫ (7y² - x² + 2) dy = (7/3)y³ - xy² + 2y + C2(x)

Where C1(y) and C2(x) are arbitrary functions of y and x, respectively.

Combining the results, we have the general solution:

(2/3)x³ - xy² + 3x + C1(y) + (7/3)y³ - xy² + 2y + C2(x) = C

Where C is the constant of integration.

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The margin of error for the number of animals housed daily is approximately 2.246.

To calculate the margin of error for the number of animals housed daily, we need to use the formula for the margin of error in estimating the population mean:

Margin of Error = Critical Value * Standard Error

First, let's find the critical value corresponding to a 99 percent confidence level. Since the sample size is 29, we have (n - 1) degrees of freedom, which is 28. Using a t-distribution table or a statistical calculator, the critical value for a 99 percent confidence level with 28 degrees of freedom is approximately 2.756.

Next, we need to calculate the standard error, which is the standard deviation of the sample divided by the square root of the sample size:

Standard Error = Standard Deviation / √(Sample Size)

Standard Error = 4.4 / √(29) ≈ 0.815

Now, we can calculate the margin of error:

Margin of Error = Critical Value * Standard Error

Margin of Error = 2.756 * 0.815 ≈ 2.246

Therefore, the margin of error for the number of animals housed daily is approximately 2.246. This means that if we construct a 99 percent confidence interval, we can expect the estimated mean number of animals housed daily to be within 2.246 units of the sample mean.

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Answer:

Distance = \(\sqrt{(1-5)^{2} + (5-2)^{2} }\) units

               = \(\sqrt{(-4)^{2} + (3)^{2} }\) units

               =\(\sqrt{25}\) units

               = 5 units

The equation of a quadratic equation with a vertex and a point is

y = 1/4 (x - 11)² + 2

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 6 is an equation.

We have,

Vertex = (11, 2)

Point = (9, 3)

The equation of a quadratic equation with a vertex and a point is

y = a (x - h)² + k

Where (h, k) is the vertex and (x, y) is the point.

Now,

(11, 2) = (h, k)

(9, 3) = (x, y)

Substitute.

y = a (x - h)² + k

3 = a (9 - 11)² + 2

3 = a x 4 + 2

3 = 4a + 2

3 - 2 = 4a

a = 1/4

Now,

The equation of a quadratic equation is y = 1/4 (x - 11)² + 2.

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The expression for  d=rt in terms of the time is t = d/r; t = 5.

Therefore,

In the equation d=rt

                          t = d/r

when distance is 40 and the rate is 8

                          t = d/r

Replace d with 40 and rate with 8

                          t = 40/8

                          t = 5

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Answer:

Step-by-step explanation:

object       X-axis            Y-axis             y = x               y = -x

(0,6)          (0 , -6)            (0,6)                (6 ,0)             (-6 ,0)

(-3 , 5)       (-3, -5)            (3 , 5)              (5 , -3)           (-5 , 3)

(-4 , -6)      (-4 , 6)           (4 , -6)              (-6,-4)           (6 , 4)

(8,-3)         (8 , 3)             (-8,-3)              (-3, 8)           (3 , -8)

(0,3)           (0 ,-3)           (0 ,3)                ( 3, 0)          (-3 , 0)

(0, -9)          (0 , 9)           (0 ,9)              (-9 , 0)         ( 9 , 0)

(5,0)           (5, 0)              (-5,0)             (0 , 5)           (0 , -5)  

(-2,0)           (-2,0)            (2,0)               (0, -2)         (0,2)

(-7 , 8)        (-7 , -8)          (7 , -8)             (8, -7)           (-8,7)

(12 , -6)      (12, 6)           (-12,-6)              (-6,12)          (6 ,-12)

When a point is reflected over x-axis, x-coordinate remains same and y-coordinate  change to its opposite sign.

When a point is reflected over y-axis, y-coordinate remains same and x-coordinate  change to its opposite sign.

When a point is reflected over y = x axis, x-coordinate and y-coordinate change their places.

When a point is reflected over y = -x axis, x-coordinate and y-coordinate change their places and are negated

Answer:

350x⁶+1360x⁵-1337x⁴-7618x³-5517x²+1620x+1836