Solve 4x+5y=13 for y

9514 1404 393

Answer:

  39 units

Step-by-step explanation:

The angle markings tell you this is an equilateral triangle, so all sides are the same length.

  10x -11 = 2x +29

  8x = 40

  x = 5

Then the side length is ...

  2x +29 = 2·5 +29 = 39

The length of side KL is 39 units.

Answer:

(1,3), (2,2), (3,1), (4,0), (-1,5), (-2,6), (-3,7), (-4,8), (-5,9), & (-6,10)

Step-by-step explanation:

First, solve to alter the equation into a slope form instead of in standard form.

x+3y=12

Because x represents the slope, we need to transfer it to the other side of the equation. By subtracting it, it'll allow the equation to only have 3y on the left side of the equation and x will become negative x which will be added on to the 12 on the right side.

x+3y=12

-x       -x

+3y=-x+12

3y=-x+12

Next, you would divide the 3 underneath the y and the number 12 to allow the 3y to become y because y needs to be isolated in order for the slope intercept formula to work.

3y divided by 3 equals 3 and 12 divided by 3 is 4.

3y/3=-x+12/3

The final equation would look as follows:

y=-x+4

Hence, the y-intercept is 4 and the slope is -1.

You would then plot the origin coordinate of (0,4) and either go down one and right one or up one and left one; either way, you'll receive a negative slope looking like this: \

Some points on the graph would be: (1,3), (2,2), (3,1), (4,0), (-1,5), (-2,6), (-3,7)

Hope this helps.

Answer:

It's A

Step-by-step explanation:

y/x

it's starting point is 5 and it goes up 1 and over 2

1 is on the y-axis and 2 is on the x-axis and it is y over x so the answer is 1/2x+5

NOTE:I MAY NOT BE ACCURATE BUT IM PROBABLY IT COULD BE WRONG BUT IF U REALLY ARE STUCK ON A QUESTION THEN CHOOSE A

Answer:

144m^3

Step-by-step explanation:

ANSWER

k = 7

EXPLANATION

The unknown variable in this equation is k,

To find its value, first, we have to combine like terms. This means that on the left side of the equation, we have to combine the coefficients of k,

And then, divide both sides by 6,

Hence, the value of k is 7.

Answer: B (The cost of a notebook is $0.75, and the cost of a folder is $0.25.)

Step-by-step explanation:

No need for explanation. i know i’m right!!

Answer:

If you have the radius:

You can use the Circumference which us equal to:

\(circumference = 2 \times \pi \times \: r\)

Then substitute:

\( arc = \frac{31}{360} \times 2 \times \pi \times r\)

The we have shown that S is a subspace of Rn and that x + y ∈ S.

Suppose ~u1, ~u2, . . . , ~uk∈Rnand let S = span( ~u1, ~u2, . . . , ~uk). Suppose ~x, ~y ∈S.(d) Show that ~x + ~y ∈S.The solution is given as follows.The problem statement is given below.Suppose u1, u2, . . . , uk∈Rnand let S = span(u1, u2, . . . , uk). Suppose x, y ∈S. Show that x + y ∈S.To prove that x + y ∈ S, we must first prove that S is a subspace of Rn. We can then show that x + y is a linear combination of vectors in S, so it must be in S.Let's get started with the proof.Let S = span{u1, u2, . . . , uk} be a subspace of Rn. Then u1, u2, . . . , uk are linearly independent, which implies that they span S. Thus, any vector in S can be written as a linear combination of u1, u2, . . . , uk.Suppose x, y ∈ S. Then x = a1u1 + a2u2 + . . . + akuk, and y = b1u1 + b2u2 + . . . + bkuk, for some scalars a1, a2, . . . , ak and b1, b2, . . . , bk.Now we can show that x + y is a linear combination of vectors in S, so it must be in S.x + y = (a1 + b1)u1 + (a2 + b2)u2 + . . . + (ak + bk)ukSince a1, a2, . . . , ak and b1, b2, . . . , bk are scalars, (a1 + b1), (a2 + b2), . . . , (ak + bk) are also scalars. Thus, x + y is a linear combination of u1, u2, . . . , uk, and hence x + y ∈ S. Therefore, we have shown that S is a subspace of Rn and that x + y ∈ S.

Learn more about Subspace

brainly.com/question/30318872

#SPJ11

y'' - y' + (1/4)y = 0 .

This the correct / main answer .

Explanation:

To solve the differential equation by undetermined coefficients, we first find the general solution to the homogeneous equation:

y'' - y' + 1/4 y = 0

The characteristic equation is r^2 - r + 1/4 = 0, which has roots r = 1/2 ± i/2. Therefore, the general solution to the homogeneous equation is:

y_h = c_1 e^(x/2) cos(x/2) + c_2 e^(x/2) sin(x/2)

To find a particular solution to the non-homogeneous equation, we guess a form for y_p based on the right-hand side of the equation. In this case, since the right-hand side includes the term ex/2, we guess that y_p takes the form:

y_p = A x e^(x/2)

where A is a constant to be determined.

We now substitute this guess into the differential equation to find A:

y_p'' - y_p' + 1/4 y_p = 8 + ex/2

Differentiating y_p twice, we get:

y_p'' = (1/4 + 1/2x + 1/4x^2) A e^(x/2)

y_p' = (1/2 + 1/2x) A e^(x/2)

Substituting these expressions into the differential equation and simplifying, we get:

(1/4 + 1/2x + 1/4x^2) A e^(x/2) - (1/2 + 1/2x) A e^(x/2) + 1/4 (A x e^(x/2)) = 8 + ex/2

Simplifying further, we get:

(1/4)x^2 A e^(x/2) = 8

Solving for A, we get:

A = 32 / (x^2 e^(x/2))

Therefore, the particular solution is:

y_p = 32x / (x^2 + 4) e^(x/2)

The general solution to the non-homogeneous equation is the sum of the homogeneous and particular solutions:

y = y_h + y_p

 = c_1 e^(x/2) cos(x/2) + c_2 e^(x/2) sin(x/2) + 32x / (x^2 + 4) e^(x/2)

Hence, the correct  answer is:

y(x) = yp(x) + yc(x) = 28 + yc(x)

where yc(x) is the complementary solution obtained by solving the homogeneous equation:

y'' - y' + (1/4)y = 0.

To know more about homogenous equation , refer here :

https://brainly.com/question/30624850#

#SPJ11

To find the Maclaurin series of the function f(x) = (6x^2)e^(-7x), we can use the formula for the Maclaurin series of e^x and multiply it by 6x^2. The Maclaurin series of e^x is  e^x = ∑n=0[infinity] (1/n!) x^n

Multiplying by 6x^2, we getx

6x^2 e^x = ∑n=0[infinity] (6/n!) x^(n+2)

Now, we substitute x with -7x to get the Maclaurin series of f(xx

f(x) = (6x^2)e^(-7x) = 6x^2 e^x(-7x) = ∑n=0[infinity] (-42/n!) x^(n+2)

Therefore, the Maclaurin series of f(x) is

f(x) = ∑n=0[infinity] (-42/n!) x^(n+2)

To find the Maclaurin series of the function f(x) = (6x^2)e^(-7x), we can use the formula for the Maclaurin series of e^x and multiply it by 6x^2. The Maclaurin series of e^x is:

e^x = ∑n=0[infinity] (1/n!) x^n

Multiplying by 6x^2, we get:

6x^2 e^x = ∑n=0[infinity] (6/n!) x^(n+2)

Now, we substitute x with -7x to get the Maclaurin series of f(x):

f(x) = (6x^2)e^(-7x) = 6x^2 e^x(-7x) = ∑n=0[infinity] (-42/n!) x^(n+2)

Therefore, the Maclaurin series of f(x) is:

f(x) = ∑n=0[infinity] (-42/n!) x^(n+2)

To find the Maclaurin series of the function f(x) = (6x^2)e^(-7x), we can use the formula for the Maclaurin series of e^x and multiply it by 6x^2. The Maclaurin series of e^x is e^x = ∑n=0[infinity] (1/n!) x^n

Multiplying by 6x^2, we get

6x^2 e^x = ∑n=0[infinity] (6/n!) x^(n+2)

Now, we substitute x with -7x to get the Maclaurin series of f(x)x

f(x) = (6x^2)e^(-7x) = 6x^2 e^x(-7x) = ∑n=0[infinity] (-42/n!) x^(n+2)

Therefore, the Maclaurin series of f(x) is

f(x) = ∑n=0[infinity] (-42/n!) x^(n+2)

To know more about the Maclaurin series refer here

https://brainly.com/question/31745715

SPJ11

The given expression ((y-b)²/(y-b+1)+(y-b)/(y-b+1) after being reduced to a polynomial, can be represented as y-b.

In order to reduce the given equation to a polynomial, we are required to simplify and combine like terms. First, we can simplify the expression in the numerator by expanding the square:

((y-b)²/(y-b+1) = (y-b)(y-b)/(y-b+1) = (y-b)²/(y-b+1)

Now, we can combine the two terms in the equation by finding a common denominator:

(y-b)²/(y-b+1) + (y-b)/(y-b+1) = [(y-b)² + (y-b)]/(y-b+1)

Next, we can combine the terms in the numerator by factoring out (y-b):

[(y-b)² + (y-b)]/(y-b+1) = (y-b)(y-b+1)/(y-b+1)

Finally, we can cancel out the common factor of (y-b+1) in the numerator and denominator to get the polynomial:

(y-b)(y-b+1)/(y-b+1) = y-b

Therefore, the equation ((y-b)²)/(y-b+1)+(y-b)/(y-b+1)  after being simplified, is equivalent to the polynomial y-b.

Learn more about polynomials :

https://brainly.com/question/30127172

#SPJ4

The polygon will have 9 sides.

The required polygon is a nonagon.

A polygon is named on the basis of the number of sides it has, as a polygon having 5 sides is a pentagon, a polygon having 6 sides is a hexagon, a polygon having 7 sides is a heptagon, and so on., and the addition of their interior angles is (n - 2) 180°.

To identify the polygon, we need to know the number of sides of the polygon. We know that the sum of internal angles of an n - sided polygon is

(n - 2) 180°.

For the given polygon, the internal angles added up to 1260 degree. Equate  (n - 2) 180° to 1260 degree and solve the resulting equation for n.

(n - 2) 180° = 1260°

n - 2 =  1260°/ 180°

n - 2 = 7

n = 7 + 2

n = 9

The given polygon will have 9 sides.

=> The required polygon is a nonagon.

Learn more about Polygon at:

https://brainly.com/question/24464711

#SPJ4

The probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

To find the probability that a randomly selected carton has a puncture or a smashed corner, we can use the formula:

P(puncture or smashed corner) = P(puncture) + P(smashed corner) - P(puncture and smashed corner)

where P(puncture) is the probability of a carton having a puncture, P(smashed corner) is the probability of a carton having a smashed corner, and P(puncture and smashed corner) is the probability of a carton having both a puncture and a smashed corner.

Substituting the given probabilities into the formula, we get:

P(puncture or smashed corner) = 0.03 + 0.06 - 0.014

P(puncture or smashed corner) = 0.076

Therefore, the probability that a randomly selected carton has a puncture or a smashed corner is 0.076, or 7.6%.

To learn more about probability from the given link:

https://brainly.com/question/30034780

#SPJ1

Answer:

C. 1,120 cubic inches

Explanation:

To find the total volume, we will divide the solid as follows:

The edge with a length equal to 10 in was calculated as:

18 in - 8 in = 10 in

Because 18 in is the length of the largest height of the figure and 8 in is the length of the smaller height.

Now, the volume of a rectangular prism can be calculated as:

Volume = Length x Width x Height

So, the volume of solid 1 is equal to:

V₁ = 12 in x 4 in x 10 in

V₁ = 480 in³

In the same way, the volume of solid 2 is equal to:

V₂ = 20 in x 4 in x 8 in

V₂ = 640 in³

Therefore, the total volume of the solid is the sum of both parts. Then:

V₁ + V₂ = 480 in³ + 640 in³

V₁ + V₂ = 1120 in³

So, the answer is C. 1,120 cubic inches

The correct option would be -4...4.

The expression (randgen.nextInt(9) - 4) uses a random number generator object named randgen to generate a random integer between 0 (inclusive) and 9 (exclusive) using the nextInt() method.

By subtracting 4 from this random integer, we determine the range of possible values for the expression.

Since the original random integer ranges from 0 to 8, subtracting 4 shifts the range to -4 to 4. This means that the possible values for (randgen.nextInt(9) - 4) can be any integer between -4 and 4, inclusive.

In other words, the expression can yield values such as -4, -3, -2, -1, 0, 1, 2, 3, and 4. These values cover a total of nine integers, including both positive and negative numbers.

Therefore, the correct option is -4...4, which represents the range of possible values for the expression (randgen.nextInt(9) - 4).

Learn more about random integer

brainly.com/question/31474611

#SPJ11

Answer:

9 dollars

Step-by-step explanation:

do 14 - 23

The z-score for a data value of 119 is equal to -1.4.

The z-score is a numerical measurement used in statistics to determine the sample data value's relationship to the mean of a group of values, measured in terms of standard deviation from the mean. It is measured as the difference of the sample data value and the sample mean over the standard deviation, such that

z-score = (x – μ) / σ

where x = sample data value

μ = mean

σ = standard deviation

Based on the problem, the sample data value is 119, the mean is 133, and the standard deviation is 10. Substitute these values into the equation and solve for the z-score.

z-score = (x – μ) / σ

z-score = (119 - 133) / 10

z-score = -14 / 10

z-score = -1.4

Learn more about z-score here: brainly.com/question/17489087

#SPJ4

The running distance is 4.23 miles, the swimming distance is 1.98 miles and the cycling distance is 35.64 miles.

Each racer travels the same distance and the sum of the distances travelled (\(x\)), in miles. By definition of average speed (\(v\)), in miles per hour, we get the following system of equations:

Amanda

\(t_{A} = \frac{x_{R}}{v_{A, R}}+\frac{x_{S}}{v_{A,S}}+\frac{x_{C}}{v_{A,C}}\) (1)

Where:

Bryce

\(t_{B} = \frac{x_{R}}{v_{B, R}}+\frac{x_{S}}{v_{B,S}}+\frac{x_{C}}{v_{B,C}}\) (2)

Where:

Corey

\(t_{C} = \frac{x_{R}}{v_{C, R}}+\frac{x_{S}}{v_{C,S}}+\frac{x_{C}}{v_{C,C}}\) (3)

Where:

If we know that \(t_{A} = 2.7\,h\), \(v_{A,R} = 10\,\frac{mi}{h}\), \(v_{A,S} = 4\,\frac{mi}{h}\), \(v_{A, C} = 20\,\frac{mi}{h}\), \(t_{B} = 3.27\,h\), \(v_{B,R} = 7.5\,\frac{mi}{h}\), \(v_{B,S} = 6\,\frac{mi}{h}\), \(v_{B,C} = 15\,\frac{mi}{h}\), \(t_{C} = 1.833\,h\), \(v_{C,R} = 15\,\frac{mi}{h}\), \(v_{C,S} = 3\,\frac{mi}{h}\) and \(v_{C,C} = 40\,\frac{mi}{h}\), then the solution of the linear system of equations is:

\(\frac{x_{R}}{10} + \frac{x_{S}}{4} + \frac{x_{C}}{20} = 2.7\) (4)

\(\frac{x_{B}}{7.5}+\frac{x_{S}}{6} +\frac{x_{C}}{15} = 3.27\) (5)

\(\frac{x_{R}}{15}+\frac{x_{S}}{3} +\frac{x_{C}}{40} = 1.833\) (6)

\(x_{R} = 4.23\,mi\), \(x_{S} = 1.98\,mi\), \(x_{C} = 35.64\,mi\)

The running distance is 4.23 miles, the swimming distance is 1.98 miles and the cycling distance is 35.64 miles.

We kindly invite to check this question on systems of linear equations: https://brainly.com/question/20379472

Answer:

-3

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

it would be 20 too but there is no opition for this  i hope i helped

The z-score corresponding to an observation is -1.64 and option b is the correct answer.

The relationship between a value and a group of values' mean is described statistically by the Z-score. Standard deviations from the mean serve as the unit of measurement for Z-score. The score for a data point is equal to the mean score if the Z-score is 0. A result that deviates by one standard deviation from the mean is indicated by a Z-score of 1.0.

The z-score is given by the following formula:

z = 4.5 - 5.7/ 0.61

z = -1.64

Hence, the z-score corresponding to an observation is -1.64 and option b is the correct answer.

Learn more about z-score here:

https://brainly.com/question/15016913

#SPJ4

The values for x, y, and z are 95, -9, and -21, respectively, resulting in a three-digit number: 95-9-21 = 95921.

To solve the system of equations:

x + 3y - 2z = 1

2x + y + 3z = 20

2x - 2y + z = 6

By the use of the method of Gaussian elimination or matrix algebra. Here, the Gaussian elimination:

1. Multiply equation 1 by 2 and subtract equation 3:

2(x + 3y - 2z) - (2x - 2y + z) = 2 - 6

2x + 6y - 4z - 2x + 2y - z = -4

8y - 5z = -4

2. Multiply equation 1 by 2 and subtract equation 2:

2(x + 3y - 2z) - (2x + y + 3z) = 2 - 20

2x + 6y - 4z - 2x - y - 3z = -18

5y + z = -18

3. Rearrange equation 2:

2x + y + 3z = 20

2x + 2y + 6z = 40

4. Subtract equation 3 from equation 2:

(2x + 2y + 6z) - (5y + z) = 40 - (-18)

2x + y + 5y + 6z - z = 58

2x + 6y + 5z = 58

Now we have a new system of equations:

8y - 5z = -4

5y + z = -18

2x + 6y + 5z = 58

We can solve this system using any method of our choice. In this case, solving the system yields:

x = 95

y = -9

z = -21

Therefore, the values for x, y, and z are 95, -9, and -21, respectively, resulting in a three-digit number: 95-9-21 = 95921.

To learn more about Gaussian elimination from the given link

https://brainly.com/question/30528045

#SPJ4

Answer:

D.  x>[4]

Plzzzzz give me Brainliest!!!!!  

Answer:

D. x > 4

Step-by-step explanation:

You have to do the opposite operations to get the variable on one side of the equation by itself.

4 - x + 4 = 8 - 4

x = 4

You only switch the comparison sign if you mutliply or divide by negative numbers when you do opposite operations to get the variable on one side of the equation by itself.

I hope this helps!

Answer:

y = -X + 3

Step-by-step explanation:

X + Y = 3

Y = -X + 3 (in the form of Y = mX + c, where m is the gradient of the graph and c is the y intercept of the graph)

Through observation,

gradient = -1

y-intercept = 3

The correct answer is D) 0.2693.To calculate the probability that the height of a randomly selected student is between 164 and 174, we can use the standard normal distribution.

Given that the height follows a standard normal distribution with a mean (μ) of 161 and a standard deviation (σ) of 5, we need to convert the given range to z-scores.

The z-score formula is:

z = (x - μ) / σ

where x is the observed value, μ is the and σ is the standard deviation.

For the lower boundary of 164:

z1 = (164 - 161) / 5 = 0.6

For the upper boundary of 174:

z2 = (174 - 161) / 5 = 2.6

Now, we need to find the probability that the z-score falls between z1 and z2, which represents the area under the standard normal curve between these z-scores.

Using a standard normal distribution table or a statistical software, we can find the corresponding probabilities:

P(z1 < z < z2) = P(0.6 < z < 2.6)

Using the standard normal distribution table or a calculator, we find that the probability is approximately 0.2693.

Therefore, the correct answer is D) 0.2693.

Learn more about probability here: brainly.com/question/31828911

#SPJ11

Answer:

[C] 3 3/4 Miles

Step-by-step explanation:

Given:

Zoe jogs 3/4 of a mile every 1/5 of an hour.

How many miles does Zoe jog per hour?

[A] 3/20 Miles

[B] 4/15 Miles

[C] 3 3/4 Miles

[D] 6 2/3 Miles

Solve:

Since, Zoe jogs 3/4 of a mile every 1/5 hour. And 5/5 = 1 hour.(Also known as 60 minutes) Which means 1/5 is 12 minutes. In order to find how much Zoe jogs per hour, we have to multiply.

Knowing that;

1/5 = 12 minutes

2/5 = 24 minutes

3/5 = 36 minutes

4/5 = 48 minutes

5/5 = 60 minutes (1 Hour)

Hence, 3/4 Multiply by 5.

3/4 × 5 = 3.75 = 15/4 = 3 3/4

As a result, Zoe jogs 3 3/4 miles per hour.

RevyBreeze

The graph of the parabola given below.

Here, we have,

Here we have the function:

g(x) = (15x)^2

Notice that this is a contraction of scale factor 15 of the function f(x) = x^2

To graph this, we can just evaluate the function in 3 points, the vertex and two other ones.

for x = 0.

g(0) = (15*0)^2 = 0

So we have the point (0, 0).

Evaluating in x = 1 and x = -1 (give the same value) we get:

g(±1) = (±15)^2 = 225

So we have the points (1, 225) and (-1, 225).

Now we can just connect these 3 points with a parabola.

If you want to learn more about parabolas:

brainly.com/question/4061870

#SPJ1

The Taylor series formula in summation notation f(t) = Σ[n=0 to infinity] { (1/n!)f^n(a)(t-a)^n } where f^n(a) denotes the nth derivative of f(t) evaluated at t = a.

Since the functions f(t) and g(t) have not been given in the question, I cannot provide a specific answer to this question. However, I can provide a general approach to finding the power series expansion of a function about a point.

To find the power series expansion of a function f(t) about a point t = a, we can use the Taylor series formula:

f(t) = f(a) + f'(a)(t-a) + (1/2!)f''(a)(t-a)^2 + (1/3!)f'''(a)(t-a)^3 + ...

where f'(a), f''(a), f'''(a), ... are the first, second, third, and higher-order derivatives of f(t) evaluated at t = a.

To find the first four nonzero terms of the power series expansion, we can calculate the values of f(a), f'(a), f''(a), and f'''(a) at t = a, substitute them into the Taylor series formula, and simplify the resulting expression. The first four nonzero terms will be the constant term, the linear term, the quadratic term, and the cubic term.

To find the general term of the power series expansion, we can write the Taylor series formula in summation notation:

f(t) = Σ[n=0 to infinity] { (1/n!)f^n(a)(t-a)^n }

where f^n(a) denotes the nth derivative of f(t) evaluated at t = a. The general term of the power series expansion is given by the expression in the curly braces. We can use this expression to find any term in the series by plugging in the appropriate values of n and f^n(a).

Learn more about Taylor series here

https://brainly.com/question/28168045

#SPJ11

Graph of given system of equations is shown in figure with intersection point (2, 4).

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equation is,

⇒ 2x + y = 8

⇒ - x + 2y = 6

By solving both equation , we get;

⇒ (x, y) = (2, 4)

Thus, The graph of system of equation intersect on point (2, 4).

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1