Which of the following sets of numbers could represent the three sides of a triangle O (6,8,14} O {11, 14, 22} O {13, 20, 34) O {13, 20, 35} ​

Using common factor method, sum of the given expressions is 17.14m + 9.37

what is common factor ?

In mathematics, a common factor is a factor that two or more numbers have in common. For example, the numbers 12 and 18 have common factors of 1, 2, 3, and 6. The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers.

In algebra, we often use the term "common factor" when referring to expressions. When two or more algebraic expressions have a factor in common, we can use the distributive property to factor out the common factor.

According to the question:
To add the expressions (5.19+4m)+(4.18+3.95m), we can first group the like terms:

(5.19 + 4.18) + (4m + 3.95m)

9.37 + 7.95m

So, the sum of the expressions is:

(5.19+4m)+(4.18+3.95m) = 9.37 + 7.95m

Now, we can use the distributive property to factor out a common factor of m from 7.95m:

9.37 + 7.95m = 4m + (5.19 + 7.95)m

We can factor out a common factor of 1 from (5.19 + 7.95)m:

4m + (5.19 + 7.95)m = (4 + 5.19 + 7.95)m

Adding the coefficients, we get:

4 + 5.19 + 7.95 = 17.14

Therefore, the sum of the expressions is:

(5.19+4m)+(4.18+3.95m) = (4m+5.19)+(3.95m+4.18)= 17.14m + 9.37.

To know more about common factor visit:
https://brainly.com/question/29014674
#SPJ1

Answer:

(8,-43)

(4,-22)

Step-by-step explanation:

In order for the ordered pair to be a solution of the inequality, you must be able to plug in the y-value of the ordered pair and it must be less than or equal to 0.

For example:

(4,-22)

x=4 ; y=-22

Plug y into the inequality

y≤0

-22≤0

Since the statement is true, I know that (4,-22) must be a solution to the inequality.

Another way to solve this problem is by graphing. If an ordered pair is in the shaded region, it is a solution to the inequality. Attached is a graph of both the inequality and ordered pairs plotted.

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

Answer:

Step-by-step explanation:

To determine whether each ordered pair is a solution to the inequality y ≤ 0, we need to check if the y-coordinate of each pair is less than or equal to zero.

Let's check each ordered pair:

(8, -43):

The y-coordinate is -43. Since -43 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(4, -22):

The y-coordinate is -22. Since -22 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(-3, 25):

The y-coordinate is 25. Since 25 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

(-7, 45):

The y-coordinate is 45. Since 45 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

So, the solutions to the inequality y ≤ 0 are:

(8, -43) and (4, -22).

Wouldn't the answer be 1 and 4?

Answer: (2,144)

Step-by-step explanation:

\((\stackrel{a}{-3\sqrt{3}}~~,~~\stackrel{b}{-9}) \\\\[-0.35em] ~\dotfill\\\\ r=\sqrt{a^2 + b^2}\implies r=\sqrt{(-3\sqrt{3})^2 + (-9)^2}\implies r=\sqrt{108}\implies r=6\sqrt{3} \\\\[-0.35em] ~\dotfill\)

\(\theta =\tan^{-1}\left( \cfrac{b}{a} \right)\implies \theta = \tan^{-1}\left( \cfrac{-9}{-3\sqrt{3}} \right) \\\\\\ \theta = \tan^{-1}(\sqrt{3})\implies \theta = \begin{cases} \frac{\pi }{3}\\[1em] \frac{4\pi }{3} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill~\left( 6\sqrt{3}~~,~~\frac{\pi }{3} \right)\hspace{5em}\left( 6\sqrt{3}~~,~~\frac{4\pi }{3} \right)~\hfill~\)

The new annual output from the turbine is 1122kw to give a percentage of 87

Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

Data;

This can be represented mathematically as

87 / 100 = y - 600/ 600

We can solve for y

0.87 = y - 600 / 600

x = 1122kw

The new annual output from the turbine is 1122kw

Learn more on percentage here;

https://brainly.com/question/843074

#SPJ1

The similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other. When two shapes are similar, one can be obtained from the other by uniformly scaling (enlarging or reducing) the shape.

Given that the shape EFGH is a smaller shape of JKLM, and they are similar, then:

the measure of angle Z is equal to 65°

the side EF corresponds to JK and side FG corresponds to KL, so:

8/20 = 11/x

x = (11 × 20)/8 {cross multiplication}

x = 27.5

the side EF corresponds to JK and EH corresponds to JM, so:

8/20 = y/30

y = (30 × 8)/20 {cross multiplication}

y = 12

Therefore, the similar shapes EFGH and JKLM have the measurement of angle Z equal to 65°, the length x = 27.5 and the length of y = 12

Read more about similar shapes here: https://brainly.com/question/21823811

#SPJ1

The maximum height reached by each stone is 40.5 meters.

The height of each stone above the ocean is given by the function:

h = -2t² + 2t + 40

This is a quadratic function in standard form, with a = -2, b = 2, and c = 40.

The maximum height reached by the stone occurs at the vertex of the parabolic curve described by this function.

The t-coordinate of the vertex is given as:

t = -b / 2a

Substitute the values of a and b,

t = -2 / (2×(-2)) = 0.5

So the maximum height is reached 0.5 seconds after the stone is thrown.

To find the maximum height, substitute the value of t into the function:

h = -2(0.5)² + 2(0.5) + 40 = 40.5 meters

Therefore, the maximum height reached by each stone is 40.5 meters.

Learn more about the maximum height here:

https://brainly.com/question/15025354

#SPJ1

Using Cramer's rule for first-order condition:

Using Hessian for the second-order condition, critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

(a) Using Cramer's rule for the first-order condition:

To optimize the function y, find the critical points where the gradient is equal to zero. The gradient of y is given by:

∇y = [6x₁ - x₂ - 3x₃ - 5, -x₁ + 12x₂ + 2x₃ - 4, 2x₂ + 8x₃ + 2 - 3x₁]

Setting the gradient equal to zero:

6x₁ - x₂ - 3x₃ - 5 = 0 (1)

-x₁ + 12x₂ + 2x₃ - 4 = 0 (2)

2x₂ + 8x₃ + 2 - 3x₁ = 0 (3)

Using Cramer's rule to solve this system of linear equations, the determinant of the coefficient matrix is:

|A| =

| 6 -1 -3 |

|-1 12 2 |

|-3 2 -3|

|A| = 444

The determinant of the matrix obtained by replacing the first column of A with the constants on the right-hand side of the equations is:

|A₁| =

| 5 -1 -3 |

| 0 12 2 |

| 0 2 -3|

|A₁| = -149

The determinant of the matrix obtained by replacing the second column of A with the constants is:

|A₂| =

| 6 5 -3 |

|-1 0 2 |

|-3 0 -3|

|A₂| = -138

The determinant of the matrix obtained by replacing the third column of A with the constants is:

|A₃| =

| 6 -1 5 |

|-1 12 0 |

|-3 2 2|

|A₃| = -278

Therefore, using Cramer's rule:

x₁ = |A₁|/|A| = -149/444

x₂ = |A₂|/|A| = -69/222

x₃ = |A₃|/|A| = 139/444

(b) Using the Hessian for the second-order condition:

To check whether the critical point found in part (a) is a maximum, minimum or saddle point, we need to use the Hessian matrix evaluated at the critical point. The Hessian of y is given by:

(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

Evaluating H(y) at the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444):

H(y) =

| 6 0 -3 |

| 0 12 2 |

|-3 2 8 |

The eigenvalues of H(y) are 2, 6, and 18, which are all positive. Therefore, H(y) is positive definite, and the critical point is a minimum.

Therefore, the critical point (x₁, x₂, x₃) = (-149/444, -69/222, 139/444) is the unique minimum of y.

Find out more on first-order condition here: https://brainly.com/question/31451579

#SPJ1

Answer:

The 95% CI is   \(2.108 < \mu < 2.892\)

Step-by-step explanation:

From the question we are told that

   The  population mean \(\mu = 2.5\)

    The standard deviation is  \(\sigma = 0.8\)

Given that the confidence level is  95% then the level of confidence is mathematically evaluated as

          \(\alpha = 100 - 95\)

   =>  \(\alpha = 5\%\)

  =>    \(\alpha = 0.05\)

Next we obtain the critical value of  \(\frac{\alpha }{2}\) from the normal distribution table, the values is  \(Z_{\frac{\alpha }{2} } = 1.96\)

Generally the margin of error is mathematically evaluated as

          \(E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }\)

here we would assume that the sample size is  n =  16 since the person that posted the question did not include the sample size

  So    

               \(E = 1.96* \frac{0.8}{\sqrt{16} }\)

               \(E = 0.392\)

The  95% CI is mathematically represented as

              \(\= x -E < \mu < \= x +E\)

substituting values

              \(2.5 - 0.392 < \mu < 2.5 + 0.392\)

substituting values

              \(2.108 < \mu < 2.892\)

Answer:

The 95% confidence interval of mean wake time for a population with treatment is between 86.2401 and  108.7599 minutes.

This interval contains the mean wake time before treatment and which does not prove to be effective

Step-by-step explanation:

GIven that :

sample size n = 17

sample mean \(\overline x\) = 97.5

standard deviation \(\sigma\) = 21.9

At 95% Confidence interval

the level of significance ∝ = 1 - 0.95

the level of significance ∝ =  0.05

\(t_{\alpha/2} = 0.025\)

Degree of freedom df = n - 1

Degree of freedom df = 17 - 1

Degree of freedom df = 16

At ∝ =  0.05 and df = 16 , the two tailed critical value from the t-table \(t_{\alpha/2 , 16}\) is :2.1199

Therefore; at 95% confidence interval; the mean wake time is:

= \(\overline x \pm t_{\alpha/2,df} \dfrac{s}{\sqrt{n}}\)

= \(97.5 \pm 2.1199 \times \dfrac{21.9}{\sqrt{17}}\)

= 97.5 ± 11.2599

= (86.2401 , 108.7599)

Therefore; the mean wake time before the treatment was 104.0 min

The 95% confidence interval of mean wake time for a population with treatment is between 86.2401 and  108.7599 minutes.

This interval contains the mean wake time before treatment and which does not prove to be effective

The surface area of the largest size sphere that can fit in this box is 400π

What is the surface area of the sphere?

The surface area of a sphere is the space that the sphere's outer surface occupies. A sphere is a circle in three dimensions. A circle is a two-dimensional (2D) shape, whereas a sphere is a three-dimensional (3D) shape, which is the difference between the two.

Here, we have

The diameter of the biggest sphere will be equal to the side of the sphere.

radius = 20/2

​ = 10

The surface area of the sphere = 4πr²

=4π(10)²

= 400π

Hence, the surface area of the largest size sphere that can fit in this box is 400π.

To learn more about the surface area of the sphere from the given link

https://brainly.com/question/1293273

#SPJ1

Answer: 18.78 cubic feet

Step-by-step explanation:

The detailed analysis is attached below.

The steps in solving the given expression shows that the result is:

0.92 * 10²

The expression is given as:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

The steps that Maggie followed are:

Step 1: Rewrite the given expression:

6.89 * 10⁻⁴/(7.5 * 10⁻⁶) = 0.92 * 10¹

Step 2: Divide the coefficients:

The coefficient of the numerator (6.89) is divided by the coefficient of the denominator (7.5) to get:

6.89 / 7.5 = 0.9186667.

Step 3: Divide the powers of 10:

This is done by subtracting the exponent of the denominator 10⁻⁶ from the exponent of the numerator 10⁻⁴ to get: 10²

Step 4: Combine the results:

This gives:

0.9186667 * 10²

Step 5: Simplify the coefficient:

She rounded the coefficient (0.9186667) to two decimal places, resulting in 0.92.

Read more about  Laws of Exponents at: https://brainly.com/question/11761858

#SPJ1

A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is known as an algebraic expression.

910x − 2

simplify | 910 x - 2

2 (455 x - 1).

To Learn more About Algebraic Expression, refer To:

https://brainly.com/question/4344214

#SPJ1

Answer:

Step-by-step explanation:

B im pretty sure hope its right

Answer:

Marissa buys 5 bottles of soda which cost X, she also buys a 9 dollar meal. If her total cost was 44 dollars, how much does each bottle cost?

Step-by-step explanation:

Answer:

there was was 5 fish in the tank and a shipment of x amount plus nine recent babies were born? equaling to 44 in total?

Step-by-step explanation:

Answer:

To solve for y in the equation:

3y - 1/3 = 5

First, we need to isolate the term containing y by adding 1/3 to both sides of the equation:

3y - 1/3 + 1/3 = 5 + 1/3

Simplifying the left-hand side:

3y = 5 + 1/3

Next, we need to isolate y by dividing both sides of the equation by 3:

3y/3 = (5 + 1/3)/3

Simplifying the right-hand side by finding a common denominator:

3y/3 = (15/3 + 1/3)/3

3y/3 = 16/3

Simplifying the left-hand side:

y = 16/9

Therefore, the solution to the equation 3y - 1/3 = 5 is y = 16/9.

Step-by-step explanation:

Answer:

24 feet

Step-by-step explanation:

9×2=18

18+6=24

24-18=6

1. Convert 2 feet, 9 inches to feet: 2.75 feet, since 9 inches is 3/4 of a foot.

2. Set up a ratio for the man comparing height to shadow length:

    6 feet / 2.75 feet

3. Set this ratio equal to a simlar ratio for the pole:

    \(\dfrac{6 \text{ feet}}{2.75 \text{ feet}} =\dfrac{x \text{ feet}}{15 \text{ feet}}\)

4. Solve the equation by multiplying by 15 on both sides of the equation:

    \(15 \cdot \dfrac{6 }{2.75 } =x\)

or x ≈ 32.727272... or x ≈ 33 to the nearest foot

Answer:

16291.8

Step-by-step explanation:

271.53×60

Multiply 271.53 and 60 to get 16291.8.

16291.8

I'm putting here a picture of the working out

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

For more question on expression

https://brainly.com/question/1859113

#SPJ8

Answer:

Step-by-step explanation:

Here we need to write the equations that passes through the point (4 , 3) and is parallel to the given line and perpendicular to it. So lets get started,

a)

First we calculate the slope of the given line by using any two points on the given line by the help of the formula:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

we take the points (1 , 6) and (2 , 2) i chose these two you can choose any other two doesn't matter so now we calculate the slope,

\(m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{2-6}{2-1}\\\\m=\frac{-4}{1}\\\\m=-4\)

now since our slope is -4 and the line is parallel to the given line so the line that we need in part a would also have the same slope by the law parallel lines have same slope/gradient.

\(m_1=m_2\)

so the slope/gradient of our new line that we need which passes through the point (4,3) is -4

Now using the point slope form formula:

\(y-y_1=m(x-x_1)\)

we have our point (4,3) which corresponds to \((x_1,y_1)\) and m which corresponds to -4 , so now

\(y-y_1=m(x-x_1)\\y-3=-4(x-4)\\y-3=-4x+16\\y=-4x+19\)

sow our new line in part a is

\(y=-4x+19\)

b)

In this part we need a line that is perpendicular to the given line which means we use the formula to calculate the slope of the perpendicular line which is:

\(m_1m_2=-1\)

where \(m_1=-4\) the slope of our given line so the slope of the perpendicular line is,

\(m_1m_2=-1\\-4m_2=-1\\\\m_2=\frac{1}{4}\)

so using the point (4,3) and the new slope 1/4 we find the equation of the perpendicular line again by using the point-slope form formula:

\(y-y_1=m(x-x_1)\\y-3=\frac{1}{4}(x-4)\\\\4y-12=x-4 \\4y=x+8\\\\y=\frac{x+8}{4}\\\\y=\frac{x}{4}+2\)

I have attached of the graphs as well you can check it out for better understanding.

Using the normal distribution and the central limit theorem, it is found that the sample of 36 Great Basin rattlesnakes is more likely to be shorter than 29.65 inches.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For the Sample of 36 Great Basin rattlesnakes:

Then:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{29.65 - 32.3}{0.88}\)

\(Z = -3.01\)

For the Sample of 100 Southern Pacific rattlesnakes:

Then:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{29.65 - 32.2}{0.795}\)

\(Z = -3.33\)

Due to the higher z-score, the random sample of 36 Great Basin rattlesnakes is at a higher percentile, hence it is more likely to be shorter than 29.65 inches,

To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213

First of all, we would calculate the predetermined overhead rate by using this formula:

Predetermined overhead rate = Manufacturing overhead/Direct material costs

Predetermined overhead rate = $2,342,400/$1,464,000

Predetermined overhead rate = 1.6 per DM $.

Next, we would calculate the overhead applied by using this formula:

Overhead applied = Job × DM cost

For job 0701, we have:

Overhead applied = 76,000 × 1.6

Overhead applied = $121,600.

For job 0702, we have:

Overhead applied = 104,000 × 1.6

Overhead applied = $166,400.

For job 0703, we have:

Overhead applied = 135,000 × 1.6

Overhead applied = $216,000.

For job 0704, we have:

Overhead applied = 67,000 × 1.6

Overhead applied = $107,200.

For the overapplied manufacturing overhead for year 1:

Less applied overhead = $1,630,000 × 1.6

Less applied overhead = $2,608,000.

Overapplied manufacturing overhead = Actual overhead cost - Less applied overhead

Overapplied manufacturing overhead = $2,480,000 - $2,608,000

Overapplied manufacturing overhead = $128,000.

Read more on overhead cost here: brainly.com/question/26475885

#SPJ1

b. four fifths plus two fourths

Step-by-step explanation: Change the fractions to their equivalents in 20ths-- like finding the common denominator.

Divide the original denominator into 20, then multiply the result by the original numerator to get the new numerator.

4/5  20/5 = 4    4×4 = 16   so 4/5 is equivalent to 16/20

2/4   20/4 = 5    5×2 = 10   so  2/4 is equivalent to 10/20  

Add:    16/20 + 10/20 = 26/20

brainliest me

The result of the unknown variable x is equivalent to 7

Linear equations are equation that has a leading degree of 1. Given the expression below:

5(3x − 15) + 16 = 5x + 11

Expand the expression

5(3x) - 5(15) + 16 = 5x + 11

15x - 75 + 16 = 5x + 11

15x - 5x - 59 - 11 = 0

10x - 70 = 0

10x = 70

Divide both sides by 10

10x/10 = 70/10

x = 7

Hence the value of x makes the equation true is 7

Learn more on linear equation here: https://brainly.com/question/2030026

#SPJ1

Answer:

infinitely many solutions (infinite solutions)

Step-by-step explanation:

2y - 8 = 6x

   +8    +8

-------------------------------

2y = 6x + 8

\(\frac{2y}{2}\) = \(\frac{6x}{2}\) + \(\frac{8}{2}\)

-------------------------------

y = 3x + 4

Because 3x + 4 = 3x + 4, there are infinitely many solutions to this system of equations. This is because they're the exact same equations. Any substitution for x will give you a true statement to y when compared to the other equation.  

Answer:

\(x=5\)

Step-by-step explanation:

The perimeter of a figure is the sum of all its sides.

The sides are x, (x+3), and (2x). The perimeter is 23, so the sum of the expression equates to 23. Thus:

\(x+(x+3)+(2x)=23\)

Combine like terms:

\(4x+3=23\)

Subtract 3 from both sides:

\(4x=20\)

Divide both sides by 4:"

\(x=5\)

And we're done!