How do I solve −6 + 9(8 − 2b) using distributive property or combining like terms.

Answer:

x= -10

y= -4

Step-by-step explanation:

Given data

3x+1=8y----------------1

11y-3x=-11--------------2

rearange

3x-8y=-1------------------1

-3x+11y=-11---------------2

add 1 and 2

3x-8y=-1------------------1

-3x+11y=-11---------------2

0+ 3y= -12

y= -12/3

y= -4

put y= -4 in 2

11y-3x=-11

11(-4)-3x=-11

-44-3x=-11

-44+11=3x

-33= 3x

x= -33/3

x= -10

Answer:

f(3) = 7

Step-by-step explanation:

Using the recursive formula and f(1) = - 3 , then

f(2) = f(1) + 5 = - 3 + 5 = 2

f(3) = f(2) + 5 = 2 + 5 = 7

Answer:

-13 + 25 = 12

Step-by-step explanation:

You get 12 because 13 is a negative so subtract 25 from 13 and that turns 13 into 0 so 0 + 12 = 12

Sorry if my explanation didn't make sense.

The first-order partial derivatives of the function \(z = e^{(-x^5 - y^3)}\) are:

∂z/∂x =\(-5x^4 e^{(-x^5 - y^3)}\)

∂z/∂y = \(-3y^{2} e^{(-x^5 - y^3)}\)

In the given function, \(z = e^{(-x^5 - y^3)}\). To find the first-order partial derivatives, we differentiate the function with respect to each variable while treating the other variable as a constant.

For the partial derivative with respect to x (∂z/∂x), we apply the chain rule. The derivative of the exponential function \(z = e^{(-x^5 - y^3)}\) is \(e^{(-x^5 - y^3)}\), and we multiply it by the derivative of the exponent \((-x^5 - y^3)\) with respect to x, which is\(-5x^4\).

Similarly, for the partial derivative with respect to y (∂z/∂y), we again apply the chain rule. The derivative of \(e^{(-x^5 - y^3)}\) is \(e^{(-x^5 - y^3)}\), and we multiply it by the derivative of the exponent \((-x^5 - y^3)\)with respect to y, which is\(-3y^2\).

These partial derivatives represent the rates of change of the function z with respect to x and y, respectively. They provide valuable information about the direction and magnitude of the function's change when the input variables x and y are varied.

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Answer:

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

i think

Answer:

The equation of line is as follows:

Slope-intercept form: \(y = 7x-5\)

Standard Form: \(-7x+y = -5\)

Step-by-step explanation:

Given that

Slope of line: 7

Point : (1,2)

Slope-intercept form of equation of line is given by:

\(y = mx+b\)

Here m is the slope and b is y-intercept.

Putting the value of slope

\(y = 7x+b\)

To find the value of b, we have to put the point in the equation

\(2 = 7(1) +b\\2 = 7+b\\2-7 = b\\b = -5\)

So the equation will be:

\(y=7x-5\)

The standard form of equation of line is:

\(Ax+By = C\)

To convert the equation in standard form, subtracting 7x from both sides

\(y-7x = 7x-5-7x\\-7x+y = -5\)

Hence, the equation of line is as follows:

Slope-intercept form: \(y = 7x-5\)

Standard Form: \(-7x+y = -5\)

The equation of a line in slope-intercept and standard form through (1, 2), slope = 7 is  7x - y = 5.

To find the equation of a line in slope-intercept and standard form.

First, we can write the equation in point-slope form. The point-slope formula states:

(y − y₁) = m (x − x₁)

Where m is the slope and

(x1, y1) is a point the line passes through.

Substituting the values from the problem gives:

(y − 2) = 7(x − 1)

Now, we need to convert to standard form.

The standard form of a linear equation is:

Ax + By = C

where, if at all possible,

A, B, and C are integers, and A is non-negative, and, A, B, and C have no common factors other than 1

We convert as follows:

y − 2 = (7 × x) − (7 × 1)

y − 2 = 7x − 7

−7x + y − 2  = − 7

Adding 2 in both side.

−7x + y − 2 + 2 = − 7 +2

-7x + y = -5

7x - y = 5

Therefore,  the equation of a line in slope-intercept and standard form is 7x - y = 5.

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Answer:

400 + 16 x

Step-by-step explanation:

hope this helps

The content dimension of a message deals with the what of a message, while the relational dimension of a message deals with the how of a message is the correct answer.

Content dimensions is a generic concept to have multiple variants of a content node. It involves the information being explicitly discussed. The content repository supports any number of dimensions. The content dimension is the meaning of the actual message itself.

"Relational dimension of communication is a concept in which we have similar weight and impact as that of the message. This concept deals with the quality or nature of the relationships and networks."

Hence we can conclude that the content dimension of a message deals with the what of a message, while the relational dimension of a message deals with the how of a message is the correct answer.

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Answer:

209

Step-by-step explanation:

You would first create an explicit formula for the provided sequence.

The basic explicit formula for arithmetic sequences is \(a_{n} = d(n-1) + a_{1}\), where an is the number of the term, d is the number you are adding or subtracting by, n the location of the term, and a1 is the first number.

We would then substitute the values given into the formula.  

We are trying to solve the value of the 52nd term. This makes n = 52. The first number of the sequence is 5, so a1 is 5. Finally, d is 4 because we are adding 4 to each number in the sequence.

Therefore, our resulting equation would be \(a_{n} =4(52-1)+5\), which equals 209.

Answer: B(0,-6); C(-2,0)

Step-by-step explanation:

A was translated 4 units to the right (x) and 5 units down (y)

Do the same for the other points

B(-4+4, -1-5)                        C(-6+4, 5-5)

B(0, -6)                                C(-2, 0)

Answer:

1/5=0.2

0.3=3/10

1/2=0.5

7/10=0.7

3/4=0.75

W={a, b, c, d}

n(W) =4

No of subsets =2^n=2^4=16

The subsets are

{a, b};

{a, c};

{a, d};

{b, c};

{b, d};

{c, d};

{a};

{b};

{c};

{d};

{a, b, c};

{a, b, d};

{a, c, d};

{b, c, d},

{a, b, c, d};

{0}

Your Welcome

Step-by-step explanation:

your answer is 8.9 and minus 11 by 3 means your answer is A

The vertex of the parabola represented by the equation -3x² - 12x - 23 = y - 8 is (-2, -63).

To find the vertex of the parabola using completing the square, we can rewrite the equation in the form:

\(y = a(x - h)^2 + k\)

Where (h, k) represents the coordinates of the vertex.

Let's complete the square for the given equation:

\(-3x^2 - 12x - 23 = y - 8\)

First, we'll move the constant term to the right side of the equation:

\(-3x^2 - 12x = y - 8 + 23\\-3x^2 - 12x = y + 15\)

Next, we'll factor out the coefficient of \(x^2 (-3)\) from the first two terms:

\(-3(x^2 + 4x) = y + 15\)

To complete the square, we need to take half of the coefficient of x (4), square it (16), and add it inside the parentheses. However, since we added it inside the parentheses, we need to subtract 16 * (-3) from the right side to maintain the equality:

\(-3(x^2 + 4x + 4) = y + 15 - 16 * (-3)\\-3(x + 2)^2 = y + 15 + 48\\-3(x + 2)^2 = y + 63\\\)

Now, we can rewrite the equation in the vertex form:

\(y = -3(x + 2)^2 - 63\)

Comparing this with the vertex form equation: \(y = a(x - h)^2 + k\), we can see that the vertex is at the point (-2, -63).

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The vertex of the parabola is (-2, -19).

To find the vertex of the parabola given by the equation \(-3x^2 - 12x - 23 = y - 8\), we can complete the square. The general form of a quadratic equation is \(y = ax^2 + bx + c,\) where (h, k) represents the vertex of the parabola.

First, let's rewrite the equation in the standard form:

\(-3x^2 - 12x + 15 = y.\)

Now, we can complete the square. To do this, we need to take half of the coefficient of x (-12) and square it: \((-12/2)^2 = 36.\)

Add 36 to both sides of the equation: \(-3x^2 - 12x + 15 + 36 = y + 36.\)

Simplify: \(-3x^2 - 12x + 51 = y + 36.\)

Now, we can rewrite the equation in vertex form by factoring the left side: \(-3(x^2 + 4x - 17) = y + 36.\)

Next, we complete the square within the parentheses:

\((x + 2)^2 = -3(y + 19).\)

Now, the equation is in the form \((x - h)^2 = 4p(y - k)\), where (h, k) represents the vertex. In this case, the vertex is (-2, -19).

Overall, the process involves rewriting the equation in standard form, completing the square, and then rearranging the equation to match the vertex form. This allows us to identify the vertex of the parabola.

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Answer:

The surface area of the triangular prism is 223.789 cm^2.

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

cross section area multiply by length.

i.e

(1/2*4*6) *12

The calculated value of x in the circle is 59

From the question, we have the following parameters that can be used in our computation:

The circle

The measure of angle at the center of the circle is calculated as

Center = 2 * 31

So, we have

Center = 62

The sum of angles in a triangle is 180

So, we have

x + x + 62 = 180

This gives

2x = 118

Divide by 2

x = 59

Hence, the value of x is 59

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The inequality of the graph from the boundary line is y ≤ x - 3

From the question, we have the following parameters that can be used in our computation:

Boundary line: y = x  - 3

This means that

The inequality can be any of the following

y > x - 3

y < x - 3

y ≥ x - 3

y ≤ x - 3

In this case, we make use of y ≤ x - 3

So, we plot the graph

See attachment for the graph of the inequality expression y ≤ x - 3

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Answer:

9.3 ft

Step-by-step explanation:

Answer:

The answer to your problem is, 63

Step-by-step explanation:

How to find area of a trapezoid:

Area = \(\frac{a+b}{2}\)h

Base = 10

Height = 7

Base = 8

We would need to use our formula to find our answer:

Area = \(\frac{a+b}{2}\)h  = \(\frac{10+8}{2}\)×7 =

18 / 2 = 8

8 x 7

= 63

Thus the answer to your problem is, 63

The population after one hour is 997.

Bacterial population:

The rate of exponential growth of a bacterial culture is expressed as generation time, also the doubling time of the bacterial population. Generation time (G) is defined as the time (t) per generation (n = number of generations).

Therefore the equation is:

G = t/n

Here we have to find the population after one hour.

It is given the rate as:

dP/ dt = 1000- 6t

The population after 1 hour if given by:

P = \(\int\limits^1_0 {1000- 6t} \, dt\)

So we have to use the differential.

P = \([1000 - 3t^{2} ]_{0}^{1}\)  

  = 997

Therefore 997 is the population.

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The series converges for values of x within the interval (-√2/2, √2/2), the radius of convergence, R, is √2/2. The interval of convergence, I, is (-√2/2, √2/2).

To find the radius of convergence, R, of the series, we can use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms in a series is L, then the series converges if L < 1 and diverges if L > 1.

Let's apply the ratio test to the given series:

aₙ = x⁴ⁿ / (n (ln n)⁸)

First, let's find the ratio of consecutive terms:

|rₙ| = |(\(x^{4(n+1)}\)/ ((n+1) (ln(n+1))⁸)) * ((n (ln n)⁸) / x⁴ⁿ)|

|rₙ| = |(x⁴ / (n+1)) * ((ln n)⁸ / (ln(n+1))⁸)|

Now, let's simplify the expression:

|rₙ| = (x⁴ / (n+1)) * ((ln n)⁸ / (ln(n+1))⁸)

Taking the limit as n approaches infinity:

\(lim_{n- > oo}\) |r_n| = \(lim_{n- > oo}\) [(x⁴ / (n+1)) * ((ln n)⁸ / (ln(n+1))⁸)]

Using L'Hôpital's rule to evaluate the limit:

\(lim_{n- > oo}\) [(x⁴ / (n+1)) * ((ln n)⁸ / (ln(n+1))⁸)]

= \(lim_{n- > oo}\) [(4x⁴ / (n+1)) * ((ln n)⁷ / (ln(n+1))⁷ * (1 / (n+1)) / (1 / (n+1))]

= 4x⁴ * \(lim_{n- > oo}\) [((ln n)⁷ / (ln(n+1))⁷ * (1 / (n+1)) / (1 / (n+1))]

= 4x⁴ * \(lim_{n- > oo}\) [(ln n)⁷ / (ln(n+1))⁷]

Now, let's consider the limit as n approaches infinity for the expression inside the parentheses:

\(lim_{n- > oo}\) [(ln n)⁷ / (ln(n+1))⁷]

Since the limit of the logarithm ratio as n approaches infinity is 1:

\(lim_{n- > oo}\) [(ln n)⁷ / (ln(n+1))⁷] = 1

Substituting this back into the previous limit:

\(lim_{n- > oo}\) |rₙ| = 4x⁴ * 1 = 4x⁴

According to the ratio test, the series converges if |rₙ| < 1. Therefore, we have:

4x⁴ < 1

Solving for x:

x⁴ < 1/4

Taking the fourth root of both sides:

x < (1/4)¹

x < 1/√2

x < √2/2

Since the series converges for values of x within the interval (-√2/2, √2/2), the radius of convergence, R, is √2/2. Therefore:

R = √2/2

The interval of convergence, I, is (-√2/2, √2/2), which can be represented in interval notation as:

I = (-√2/2, √2/2)

The complete question is:

Find the radius of convergence, R, of the series.

\(\sum_{n=2}^{oo} x^{4n}/[n(In n)^8]\)

R =?

Find the interval, I, of convergence of the series. (Enter your answer using interval notation.)

I =?

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The required bearing angle of town B from Thomas is 75°.

We have,

Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.

Given that

Thomas is facing towards town A, which is at a bearing of 300°.

Implies that town A is 300° from north.

If Thomas turns 135° clockwise, then he faces towards town B,

The bearing angle will be 300+135 = 435°

Since, one complete round makes angle 360°, therefore

The required bearing angle = 435 - 360 = 75

The bearing angle of town B from Thomas is 75°.

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The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true so, here The probability of the type I error.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true so, here The probability of the type I error.

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Answer:

20400RS

Step-by-step explanation:

Given, Kitchen Size = 15ft * 12ft wall height to be tiled = 5 ft so area of focer walls

= 2* 15+2*5*12

= 150+120=170ft.

Rate is 120/ sq*ft here rate

= 120*170

= 20400RS

Answer:

the answer is in the picture

Step-by-step explanation:

Answer:

11025

Step-by-step explanation:

100+5÷100=1.05 squared

10000x1.05squared=11025

Answer:

Amount = 11205

CI = 1205

Step-by-step explanation:

\(a = p(1 + \frac{r}{n} ) {}^{nt} \)

Here,

p = 10000

r = 5% = 5/100 = 0.05

n = 1

t = 2

\(a = 10000(1 + \frac{0.05}{1} ) {}^{1 \times 2} \)

\(a = 10000(1.05) {}^{2} \)

\(a = 10000(1.1025)\)

\(a = 11205\)

C.I = a - p

C.I = 11205 - 10000

C.I = 1205

Answer:

2

Step-by-step explanation:

Both point a and b have an x value of -2 so to find the distance between the two points we simply have to find the horizontal distance. We can do this by subtract the y value of the first point by the y value of the second point.

Point A y value : 2

Point B y value : 0

Distance between Point A and Point B : 2 - 0 = 2 units

The equation of the plane passing P (1,2,1) and orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is -3x-2y-z+8=0.

Equation of plane passing through (x1,y1,z1) is given by

A(x-x1)+B(y-y1)+C(z-z1)=0

where, A, B, and C are direction ratios

In the question, it is given that the plane passes through (1,2,1)

So, the equation of the plane will be in the form,

A(x-1)+B(y-2)+C(z-1)=0

It is also given that the plane is perpendicular to give 2 planes.

So, their normal to the plane would be perpendicular to the normal of both planes.

So, the required normal is a cross-product of the normals of planes

x-y-z-10=0 and x-2y+z-2=0

i.e,

-3i-2j-k=0

so, the direction ratios,

A=-3, B=-2, C=-1

putting the direction ratios in the previous equation of the plane,

-3(x-1)-2(y-2)-1(z-1)=0

-3x+3-2y+4-z+1=0

-3x-2y-z+8=0

is the required equation of the plane

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