A triangle has the following side lengths: 6ft, 8ft, and 10ft. Is this a right triangle?

How did you know that the triangle is or is not a right triangle?

The optimal solution is x1 = 4, x2 = 0, x3 = 1, w = 0, and the minimum value of the objective function is 0.

To solve this linear programming problem using the Simplex method, we first need to convert it into standard form by introducing slack variables.

Our problem can be rewritten as follows:

Minimize w = 9x1 + 6x2

Subject to:

x1 + 2x2 + x3 = 5

2x1 + 2x2 + x4 = 8

x1 + 2x2 + 2x3 = 6

where x1, x2, x3, and x4 are all non-negative variables.

Next, we set up the initial simplex tableau:

Basic Variables x1 x2 x3 x4 RHS

x3 1 2 1 0 5

x4 2 2 0 1 8

x5 1 2 2 0 6

z -9 -6 0 0 0

The last row represents the coefficients of the objective function. The negative values in the z-row indicate that we are minimizing the objective function.

To find the pivot column, we look for the most negative coefficient in the z-row. In this case, the most negative coefficient is -9, which corresponds to x1. Therefore, x1 is our entering variable.

To find the pivot row, we calculate the ratios of the RHS values to the coefficients of the entering variable in each row. The smallest positive ratio corresponds to the pivot row. In this case, the ratios are:

Row 1: 5/1 = 5

Row 2: 8/2 = 4

Row 3: 6/1 = 6

The smallest positive ratio is 4, which corresponds to row 2. Therefore, x4 is our exiting variable.

To perform the pivot operation, we divide row 2 by 2 to make the coefficient of x1 equal to 1:

Basic Variables x1 x2 x3 x4 RHS

x3 0 1 1 -1 1

x1 1 1 0 1/2 4

x5 0 1 2 -1 2

z 0 -3 9 9/2 -18

We repeat the process until all coefficients in the z-row are non-negative. In this case, we can stop here because all coefficients in the z-row are non-negative.

Therefore, the optimal solution is x1 = 4, x2 = 0, x3 = 1, w = 0, and the minimum value of the objective function is 0.

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Answer:

2<y<6

Step-by-step explanation:

12 < 8y-y^2

y^2 -8y +12 <0

(y-6)(y-2)<0

y < 6

y < 2

 2.       6

-       -        +

-       +.       +

+.      -         +

2<y<6

Answer: 5

Step-by-step explanation: You have to do rise overrun which is \(\frac{5}{1}\), which equals 5.

Answer:

The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept.

Step-by-step explanation:

i hope the above help you find it

all the best mate !

Answer:

a) (x-2)² = 25

b) 7 and -3

Step-by-step explanation:

Given the expression 24 = x^2 - 4x + 3

Rewrite

x^2 - 4x + 3 - 24  = 0

x^2 - 4x - 21 = 0

Add 21 to both sides

x^2 - 4x - 21 + 21 = 0 + 21

x^2 - 4x = 21

Add the square of the half of coefficient of x to both sides

constant to add = (-4/2)² = (-2)²

x^2 - 4x + (-2)²  = 21 + (-2)²

(x-2)² = 21 + 4

(x-2)² = 25

Hence the rewritten form of the equation is (x-2)² = 25

Calculate the value of x

(x-2)² = 25

Square root both sides

√(x-2)² = ±√25

x - 2 = ±5

x= ±5 + 2

x = 5 +2 and-5+2

x = 7 and -3

Hence the solutions to the equation are 7 and -3

Answer:

1) (x-2)^2=25

2)x=2 plus or minus 5

Step-by-step explanation:

i got it right on khan

Answer: 860 buttons

Step-by-step explanation: 688/12 = 57.3333333...

                         57.3333... multiplied by 15 is equal to (860 buttons)

The equation for the diameter is d = 8.65 ± 0.05.

The minimum possible diameter of the soccer ball is 8.60 inches and maximum possible diameter of the soccer ball is 8.70.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Given that,

diameter of soccer ball = 8.65 inches

Also, there is an allowable margin of error = 0.05 inch.

The equation for the diameter of the new soccer ball can be written as,

d = 8.65 ± 0.05

The minimum possible diameter of the soccer ball can be

= 8.65-0.05

= 8.60 inches

The maximum possible diameter of the soccer ball can be

= 8.65 + 0.05

= 8.70 inches

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Answer:

8 cm and 10 cm

Step-by-step explanation:

Hello, I can help you with this.

Step 1

According to the question there are two rectangles A and B,

Rectangle A is a scale drawing of Rectangle B and has 25% of its area

in other words

\(Area_{A}=0.25*Area_{B} (Equation\ 1)\\\)

Step 2

Let

Rectangle A

length (1)= 4 cm

length (2)= 5 cm

\(Area_{A}=4\ cm * 5\ cm\\Area_{A}=20\ cm^{2}\)

put this value into equation 1

\(Area_{A}=0.25*Area_{B} (Equation\ 1)\\\\20\ cm^{2} =0.25*Area_{B} \\divide\ each\ side\ by\ 0.25\\\frac{20\ cm^{2} }{0.25}=\frac{0.25}{0.25}*Area_{B}\\ Area_{B}=80\ cm^{2}\)

Now, we know the area of rectangle B, to know its length we need to formule other equation

Step 3

\(Area_{B}=80\ cm^{2}\\length (1B)*length (2B)=80\ cm^{2} (equation\ 2)\\\)

the ratio between the lengths must be constant, so the ratio of A must be equal to ratio in B, then

\(\frac{length(1A)}{length(2A)}=\frac{length(1B)}{length(2B)} \\\\\\frac{4}{5}= \frac{length(1B)}{length(2B)}\\0.8=\frac{length(1B)}{length(2B)}\\length(1B)=0.8*length(2B) (Equation 3)\)

Step three

using Eq 1 and Eq 2 find the lengths

put the value of length(1B) into equation (2)

\(length (1B)*length (2B)=80\ cm^{2} (equation\ 2)\\\(0.8*length(2B)) (*length (2B)=80\ cm^{2} \\\\0.8*(length (2B))^{2} =80\ cm^{2}\\(length (2B))^{2} =\frac{80\ cm^{2}}{0.8} \\(length (2B))^{2}=100\\\sqrt{(length (2B))^{2}}=\sqrt{100\ cm^{2}} \\ length (2B)=10\ cm\)

Now, put the value of length(2B) into equation 3 to know length (1B)

\(length(1B)=0.8*length(2B)\\length(1B)=0.8*10\ cm\\length(1B)=8 cm\)

I really hope this helps you, have a great day.

The congruence angle and congruence side of both triangles are:

<A= <D

<B= <E

<C= <F

AB= DE

AC= DF

BC = EF

When two angles and one triangle's involved side are equal to two angles and the other triangle's included side, two triangles are said to be congruent. When all three sides of one triangle match the length of all three sides of the other, two triangles are said to be congruent.

Given:

We have the Triangles with some equal parts mention.

So from both triangles the congruent angles are:

<A= <D

<B= <E

<C= <F

and, Congruent sides are:

AB= DE

AC= DF

BC = EF

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Answer:

I can explain.  The answer is A

Step-by-step explanation:

Think of it this way: when you write a mixed number, the fraction is out of 100.    If the denominator is 8, find 1/8 of 100 by doing 100 divided by 1/8.  This gives you 12.5.  The entire fraction is 2/8, so we need to multiply 12.5 by 2, since it's only 1/8.  12.5 x 2 gives us 25.  In the decimal, this would be equal to .25.  A is the only answer that represents the mixed number as a decimal correctly.

A congruent rectangle is a rectangle that has the same size and shape as another rectangle. In other words, two rectangles are congruent if they have the same length and width.

Since the rectangle is 4 inches by 7 inches, one of the dimensions represents the length and the other represents the width. The length and the width can be interchanged to form a different rectangle with the same area.

Since the rectangle is congruent to the 4-inch by 7-inch rectangle, the length and width of the rectangle are either 4 inches or 7 inches. Therefore, the length of segment JM can be either 4 inches or 7 inches.

So, there are two possible values for the length of segment JM: 4 inches and 7 inches.

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The actual calculation depends on the specific vector field you are working with. You need to substitute the appropriate expressions for P and Q into the integrals and evaluate them accordingly.

To evaluate the line integral around the clockwise-oriented triangle with corners at the origin (0,0), (1,0), and (0,1), we need to sketch the vector field and the triangle and then calculate the integral.

Next, let's assume there is a vector field defined over the plane. Since you haven't provided the vector field explicitly, let's use a general notation and consider a vector field F = (P, Q), where P and Q are functions of x and y.

To calculate the line integral, we need to parameterize the triangle. We can divide the triangle into three line segments and parametrize each segment separately.

Line segment from (0,0) to (1,0):

Let's parameterize this segment as r(t) = (t, 0), where 0 ≤ t ≤ 1.

Line segment from (1,0) to (0,1):

Let's parameterize this segment as r(t) = (1 - t, t), where 0 ≤ t ≤ 1.

Line segment from (0,1) to (0,0):

Let's parameterize this segment as r(t) = (0, 1 - t), where 0 ≤ t ≤ 1.

Now, we can calculate the line integral for each segment and sum them up:

Line integral along the first segment:

\(\int(0 to 1) P(t, 0) dt + \int(0 to 1) Q(t, 0) dt\)

Line integral along the second segment:

\(\int(0\: to \:1) P(1 - t, t) dt + \int(0 \:to\: 1) Q(1 - t, t) dt\)

Line integral along the third segment:

\(\int(0 \:to \:1) P(0, 1 - t) dt + \int(0\: to \:1) Q(0, 1 - t) dt\)

Finally, the total line integral around the triangle is the sum of these three line integrals:

Total Line Integral = Line integral of segment 1 + Line integral of segment 2 + Line integral of segment 3

Please note that the actual calculation depends on the specific vector field you are working with. You need to substitute the appropriate expressions for P and Q into the integrals and evaluate them accordingly.

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Answer: (x-6)= -5

(x+4)= -1

Step-by-step explanation:

The reminders when Polynomial P(x) is divided by (x -6) and (x +4) are -5 and -1 respectively.

An algebraic equation that has more than two terms, particularly the accumulation of numerous phrases that each include a different power of the same variable (s).

Given, P(x) is a polynomial. Here are a few values of P(x).

P(-6) = 3, P(-4) = -1, P(4) = 2, and P(6) = -5

The remainder theorem says that:

“When a polynomial p(x) is divided by (x−a), the remainder is p(a).

Since, p(6) is -5 and p(-4) is -1

Thus, the remainder when P(x) is divided by (x – 6) is -5

the remainder when P(x) is divided by (x + 4) is -1

Therefore, When Polynomial P(x) is divided by (x -6) and (x +4) the reminders would be -5 and -1 respectively.

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Answer:

y=-1/5x+1

Step-by-step explanation:

divide both sides by 5: 1/5x+y=1

subtract 1/5x so y is alone since slope-intercept has y=mx+b: y=-1/5x+1

The slope-intercept form of the line x + 5y = 5 is y = - (1/5)x - 1.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, An equation of a line in the standard form x + 5y = 5.

We know the equation of the slope-intercept of the line is y = mx + b.

Therefore, The slope-intercept form of the equation x + 5y = 5 is,

5y = - x - 5.

y = - (1/5)x - 1.

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Answer:

Multiply what?

Step-by-step explanation:

The equation 2 - 3(x + 4) = 3(3 - x) has no solution for x

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

2 - 3(x + 4) = 3(3 - x)

Open the brackets

So, we have

2 - 3x - 12 = 9 - 3x

Evaluate the like terms

So, we have

-10 = 9

The above equation is false

Hence, the equation has no solution

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The verbal description matches option D; Gene earns 2% interest after depositing $150 into his account.

The function is a type of relation, or rule, that maps one input to specific single output.

The function given;

f(x) = 0.02 x +150

Gene earns 2% interest after depositing $150 into his account.

Thus, this verbal description matches the function given as it represents, the total account balance Gene.

Hence, Option D is the correct answer.

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The implicit differentiation of the given function is dy/dx = ((-4x-8y))/((8x +12y+ 13)).

In implicit differentiation, each side of an equation with two variables (usually x and y) are differentiated by treating one of the variables as a function of the other. The technique of implicit differentiation enables the determine the derivative of y with respect to x without having to solve the given equation for y. The chain rule must be used whenever the function y is being differentiated because of the assumption that y may be expressed as a function of x.

In order to find the differentiate implicitly,

d/dx  (2x^2+8xy+6y^2+13y-2)=0

4x + 8y + 8xdy/dx + 12ydy/dx + 13dy/dx = 0

dy/dx (8x + 12y + 13) = -4x -8y

dy/dx = ((-4x-8y))/((8x +12y+ 13))  

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Answer:

4h+1.5

Step-by-step explanation:

Considering a growth factor of 10, the values of the exponential function are given as follows:

An exponential function is a function in which when the input x is increased by one, the output y is multiplied by the growth factor.

From the table given in the problem, the growth factor is of 8, meaning that when the input variable representing the number of hours is increased by one, the output is always multiplied by 8.

For the second table, which we have to fill, the growth factor is of 10, meaning that for each hour, the number of bacteria is given by the number of bacteria in the previous hour multiplied by 10, then:

And so on...

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2.15 is  value of binomial distribution and 2.15 is value of standard deviation.

In statistics, what is a binomial distribution?

The possibility that a variable would take one of two independent values under a certain set of factors or assumptions is expressed by the statistical distribution known as the binomial distribution.

                                 As an illustration, there are only two conceivable results from tossing a coin: heads or tails, and there are only two outcomes from taking a test: success or failure. The term "binomial probability distribution" is sometimes used to describe this distribution.

Given that,

p = 0.2

q = 1 - p =1-0.2=0.8

n = 29

Using binomial distribution,

  Standard deviation = σ = √n * p * q

                                          = √29 * 0.2 * 0.8 = 2.15

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The complete question is -

Find the standard deviation, σ, for the binomial distribution which has the stated valuesof n and p. Round your answer to the nearest hundredth.

n = 29; p = 0.2

σ = 2.15

σ = 6.27

σ = -0.26

σ = 5.42

Answer:

4(3+1/4c-1/2d)

12+c-2d

Let me know if this helps!

Answer:

The answer is true......

The cost of each large smoothie (y) is $7.

To find the cost of a small smoothie (x) and the cost of a large smoothie (y), we can set up a system of equations based on the given information.

Let's denote the cost of a small smoothie as x and the cost of a large smoothie as y.

We can establish two equations:

Equation 1: 10y + 5x = 65 (The girls soccer team paid $65 for 10 large smoothies and 5 small smoothies.)

Equation 2: 14y + 3x = 77 (The boys soccer team paid $77 for 14 large smoothies and 3 small smoothies.)

To solve this system of equations, we can use various methods such as substitution or elimination.

Let's solve it using the elimination method:

Multiply Equation 1 by 2 to eliminate the x term:

20y + 10x = 130

Now we have:

20y + 10x = 130

14y + 3x = 77

Subtracting Equation 2 from Equation 1, we get:

(20y + 10x) - (14y + 3x) = 130 - 77

6y + 7x = 53

We now have two equations:

6y + 7x = 53

14y + 3x = 77

Solving this system of equations will give us the values of x and y, representing the cost of a small smoothie and a large smoothie, respectively.

To find the cost of each large smoothie, we can substitute the value of y back into either of the original equations.

Let's use Equation 1:

10y + 5x = 65

10(3) + 5x = 65 (substituting y = 3)

30 + 5x = 65

5x = 65 - 30

5x = 35

x = 35/5

x = 7

The cost of each large smoothie (y) is $7.

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A.  To ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02, at least 7976 voters should be polled.

b. We find the z-score corresponding to a cumulative probability of 0.95 to be approximately 1.96.

n > 2401

a) Using the Chebyshev inequality, we can determine the minimum number of voters that should be polled to ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02.

The Chebyshev inequality states that for any random variable X with mean μ and standard deviation σ, the probability of X deviating from the mean by k standard deviations is at least 1 - 1/k^2.

In this case, we want the relative frequency estimate to deviate from 0.20 by less than 0.02, which means we want the difference to be within 0.02 standard deviations of the mean. Since the relative frequency estimate is a sample proportion, its standard deviation can be approximated by sqrt(p(1-p)/n), where p is the true proportion (0.20) and n is the sample size.

We can set up the inequality as follows:

1 - 1/k^2 ≥ 0.95

Solving for k:

1/k^2 ≤ 0.05

k^2 ≥ 1/0.05

k^2 ≥ 20

Taking the square root of both sides:

k ≥ sqrt(20)

k ≥ 4.47

To ensure that the difference between the relative frequency estimate and 0.20 is within 0.02, we need k standard deviations to be less than 0.02. So, we have:

k * sqrt(p(1-p)/n) < 0.02

4.47 * sqrt(0.20(1-0.20)/n) < 0.02

Simplifying:

sqrt(0.20(1-0.20)/n) < 0.02/4.47

sqrt(0.16/n) < 0.00448

0.4/sqrt(n) < 0.00448

sqrt(n) > 0.4/0.00448

sqrt(n) > 89.29

n > 89.29^2

n > 7975.84

Therefore, to ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02, at least 7976 voters should be polled.

b) Using the central limit theorem, we can determine the minimum number of voters that should be polled to ensure that the probability is at least 0.95 that the sample mean differs from 0.20 by less than 0.02.

According to the central limit theorem, the sample mean follows a normal distribution with mean μ and standard deviation σ/sqrt(n), where σ is the population standard deviation (unknown in this case), and n is the sample size.

To ensure that the difference between the sample mean and 0.20 is within 0.02, we can set up the following inequality:

z * (σ/sqrt(n)) < 0.02

Since the population standard deviation σ is unknown, we can use a conservative estimate by assuming the worst-case scenario, which is p(1-p) = 0.25. Therefore, σ = sqrt(0.25) = 0.5.

Using the standard normal distribution table, we find the z-score corresponding to a cumulative probability of 0.95 to be approximately 1.96.

1.96 * (0.5/sqrt(n)) < 0.02

0.98/sqrt(n) < 0.02

sqrt(n) > 0.98/0.02

sqrt(n) > 49

n > 49^2

n > 2401

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Step-by-step explanation:

25 min. to get to the library

1-hour story = 60 min.

25 min. to go back home

25 + 25 + 60 = 110 min.

110. min = 1.83333 hrs.

9:15 am + 1.83333 = 10.98333 am

98 - 60 = 38

60 = 1 hr. -----> 60 + 60 = 120 minutes -----> 2 hrs.

11: 38 am

Brainlist Pls!

Answer:

B trust

Step-by-step explanation:

Trust☑️

Answer:

below

Step-by-step explanation:

f(x) = x² is not linear because it is not a straight line and does not have a constant slope.

The function shows an example of a quadractic function.

Best of Luck!

Answer:

no because the parenthesizes means your multiplying

Step-by-step explanation:

The distance bewteen the points (-3,5) and (3,1) in a simple radical form is 2√13.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

From the graph;

Point A: (-3,5)

x₁ = -3

y₁ = 5

Point B: (3,1)

x₂ = 3

y₂ = 1

Plug the given values into the distance formula and simplify.

\(d = \sqrt{( x_2 - x_1)^2 + (y_2 -y_1 )^2} \\\\d = \sqrt{( 3-(-3))^2 + (1 -5)^2} \\\\d = \sqrt{( 3+ 3)^2 + (1 -5)^2} \\\\d = \sqrt{( 6)^2 + (-4)^2} \\\\d = \sqrt{36 + 16} \\\\d = \sqrt{52}\\\\d = 2\sqrt{13}\)

Therefore, the distance between the points is 2√13.

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From the information provided, Kelly is using an average of 4 packs of notebook paper per month.

To find the rate at which Kelly is using notebook paper, we need to determine the amount of notebook paper she is using per unit of time.

First, let's convert the fraction of a year that Kelly used the notebook paper into a decimal. The fraction 1/6 can be converted to a decimal by dividing the numerator by the denominator,

so 1/6 = 0.1667.

Next, let's convert the amount of notebook paper Kelly used into a decimal. The fraction 2/9 can be converted to a decimal by dividing the numerator by the denominator, so 2/9 = 0.2222.

Now we can calculate the total amount of notebook paper Kelly used in the first 1/6 of the year.

To do this, we multiply the number of packs of notebook paper by the amount of notebook paper in each pack:

3 packs × 0.2222 notebook paper per pack = 0.6667 notebook paper.

Finally, we can divide the total amount of notebook paper used by the number of months to find the average rate of usage per month: 0.6667 notebook paper / 0.1667 months = 4 notebook paper per month. So Kelly is using an average of 4 packs of notebook paper per month.

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