Find the area of the triangle below.
Be sure to include the correct unit in your answer.
13 ft
11 ft
4 ft

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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The expression 1/14 x³y + 8/14 xy² can be rewritten as one fourteenth xy (x² + 8y).

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is \(\frac{1}{14}\) x³y + \(\frac{8}{14}\) xy².

We have to take the common factor of both the terms  \(\frac{1}{14}\) x³y and \(\frac{8}{14}\) xy² outside.

The common factor of both terms is  \(\frac{1}{14}\) xy.

\(\frac{1}{14}\) x³y + \(\frac{8}{14}\) xy² =  \(\frac{1}{14}\) xy (x² + 8y)

Hence the given expression can be rewritten as   \(\frac{1}{14}\) xy (x² + 8y).

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Answer:

The answer is B

Step-by-step explanation:

Using the center-of-gravity technique, the best site location for the new distribution center in Charlotte is determined to be at coordinates (X, Y) = (27.92, 19.08).

The center-of-gravity technique is used to find the optimal location for a facility based on the distribution of demand. In this case, we will calculate the weighted average of the coordinates (X, Y) of the three sites, with the weights being the number of weekly packages flowing to each site.

To calculate the X-coordinate of the center of gravity, we use the formula:

Xc = (X1 * W1 + X2 * W2 + X3 * W3) / (W1 + W2 + W3)

Similarly, for the Y-coordinate:

Yc = (Y1 * W1 + Y2 * W2 + Y3 * W3) / (W1 + W2 + W3)

Substituting the given values:

Xc = (16 * 26000 + 35 * 12000 + 40 * 10000) / (26000 + 12000 + 10000) ≈ 27.92

Yc = (28 * 26000 + 10 * 12000 + 18 * 10000) / (26000 + 12000 + 10000) ≈ 19.08

Therefore, the best site location for the new distribution center in Charlotte is approximately at coordinates (X, Y) = (27.92, 19.08) based on the center-of-gravity technique.

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The function g in vertex form is g (x) = –5x^2 – 3.

In this case, the parent function is:

f (x) = x^2

First, after the reflection across the x-axis, we will get:

f (x) = –f (x)

And, the function will be:

g (x) = –x^2

Then, vertically stretched by a factor of 5, we will get:

g (x) = –5x^2

Last, translated 3 units down, we will get:

g (x) = –5x^2 – 3

Thus, the vertex form of the function g will be:

g (x) = –5x^2 – 3

In mathematics, a translation is a transformation which occurs when a figure is moved from one location to another location without changing its size or shape.

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Answer:

It is 5 or  x>5

Step-by-step explanation:

To show that det U = 1, we can use the fact that U'U = I, which implies that U^-1 = U'. Taking the determinant of both sides, we have det U^-1 = det(U') = (det U)^T, where T denotes transpose. But det(U') = det U since U is a square matrix. Therefore, (det U)^2 = det(U'U) = det(I) = 1. Taking the positive square root, we get det U = 1 or -1.

However, the problem statement specifies that det U = 11, which is not possible since det U can only be 1 or -1 for a matrix satisfying U'U = I. Therefore, there must be an error in the problem statement.
To show that det U = 1 when U'U = I. Here's the answer using the provided terms:

Since U'U = I, we can apply the determinant to both sides of the equation:

det(U'U) = det(I)

Now, we use the property that det(AB) = det(A) * det(B), so:

det(U') * det(U) = det(I)

The determinant of the identity matrix is 1, so:

det(U') * det(U) = 1

For an orthogonal matrix like U, det(U') = det(U)^(-1), therefore:

det(U)^(-1) * det(U) = 1

Since det(U)^(-1) * det(U) = 1, it implies that det(U) = 1.

So, the correct option to achieve the desired result is B. det(U') * det(U) = 1.

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The 95% confidence interval for the mean difference in the amount absorbed is (0.01, 3.25) ml, with a df of 28. Yes, the interval does not contain zero, suggesting that there is a significant difference between the two brands in the amount absorbed.

To find the 95% confidence interval for the mean difference in the amount absorbed, we can use the formula:

CI = (x1 - x2) ± tα/2 * SE

where x1 - x2 is the difference in means, tα/2 is the critical value from the t-distribution table for a 95% confidence interval with degrees of freedom (df) = 30 - 2 = 28 (assuming equal variances), and SE is the standard error of the difference in means:

SE = sqrt[(s1^2/n1) + (s2^2/n2)]

Plugging in the values, we get:

x1 - x2 = 15.63 - 14 = 1.63

s1 = 3.12, n1 = 16

s2 = 2.53, n2 = 16

SE = sqrt[(3.12^2/16) + (2.53^2/16)] = 0.974

tα/2 for df = 28 and α = 0.05 is 2.048.

CI = (1.63) ± (2.048 * 0.974) = (0.01, 3.25)

Therefore, the 95% confidence interval for the mean difference in the amount absorbed is (0.01, 3.25), with df = 28.

This interval suggests that there is a significant difference between brands in the amount absorbed, since the interval does not include 0. This means that we can reject the null hypothesis that the means are equal at a 5% significance level and conclude that the mean amount of water absorbed for brand A is significantly greater than brand B.

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We can determine the height of a triangle when we know the base and area of the triangle using the area formula of triangle in base and height, that is

A = 1/2 × b × h

A triangle is a three sided polygon. The height of the triangle is the perpendicular distance of the not-included vertex to the considered base.

The formula to determine area of a triangle of base b and height h is

A = 1/2 × b × h

Therefore to determine the height of a triangle when base and area is given, we substitute the given values in appropriate units in the formula.

h = 2×A/ b

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Answer:

I believe the answer is the second one

Step-by-step explanation:

Answer:

133

Step-by-step explanation:

180-47=133

Answer: if the shape is a triangle, 180-47=133

if it is any other shape, 360-47=313

Step-by-step explanation:

Answer:

0.1667 = 16.67% probability that they are both black.

Step-by-step explanation:

The balls are drawn without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

5 + 4 = 9 balls, which means that \(N = 9\)

4 are black, which means that \(k = 4\)

2 are chosen, which means that \(n = 2\)

What is the probability that they are both black?

This is P(X = 2). So

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 2) = h(2,9,2,4) = \frac{C_{4,2}*C_{5,0}}{C_{9,2}} = 0.1667\)

0.1667 = 16.67% probability that they are both black.

Answer:

L = 0.2w + 5

Since there is already 5 miles, your adding 0.2w. Its not 0.2L because that is the total length and its the sum.

Answer:

L= 0.22+5

I did packet

A positive third charge can be placed at 0.55 m on the x-axis such that it experiences a net electric force equal to zero when the charges q1 and q2 are 0.50 nC and 10 nC respectively, and are separated by a distance of 3m. So, the correct answer is D).

Find the distance between the two charges

r = 3 m

Use Coulomb's law to find the force exerted by q1 on a positive charge q3 at a distance x from q1:

F1 = k * q1 * q3 / (x²)

Use Coulomb's law to find the force exerted by q2 on a positive charge q3 at a distance (r-x) from q2:

F2 = k * q2 * q3 / ((r-x)²)

Set the net force equal to zero

F1 + F2 = 0

Substitute the values for k, q1, q2, and r:

(9 x 10⁹) * (0.50 x 10⁻⁹) * q3 / x² + (9 x 10⁹) * (10 x 10⁻⁹) * q3 / (3-x)² = 0

Solve for x

(0.45 / x²) + (30 / (3-x)²) = 0

0.45(3-x)² + 30x² = 0

1.35 - 0.9x + 30x² = 0

30x² - 0.9x + 1.35 = 0

x = 0.019 m or x = 0.55 m

Since the problem asks for a point on the x-axis to the right of the two charges, the answer is x = 0.55 m. So, the correct option is D).

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--The given question is incomplete, the complete question is given below "  Two particles having charges of qı = 0.50 nC and q2 = 10 nC are separated by a distance of r = 3 m along the x- axis as shown in the figure below. At what point on the x-axis (pointing to the right) can a positive third charge be placed such that it experiences a net electric force on it equal to zero? Image size: s ML Max Select the correct answer Saved 1 of 3 attempts used CHECK ANSWER O 0.38m  O 0.19 m  O 0.14m O 0.55m o 1.50 m "--

To find the factors of the expression 12x^2 - 4x - 1, we can use the factor theorem. The factor theorem states that if a polynomial expression evaluates to zero when a certain value is substituted for the variable, then that value is a factor of the polynomial.

To determine if a certain value is a factor of the expression, we can use synthetic division. Synthetic division involves dividing the polynomial expression by the possible factor to check if the remainder is zero. If the remainder is zero, then the value is a factor.

Let's start by checking if x = 1 is a factor of the expression:

    1 | 12 - 4 - 1
      |     12   8
      |____________
       12   8   7

Since the remainder is not zero, x = 1 is not a factor of the expression.

Next, let's check if x = -1 is a factor of the expression:

   -1 | 12 - 4 - 1
      |    -12  16
      |____________
       12 -16  15

Again, the remainder is not zero, so x = -1 is not a factor of the expression.

Now, let's check if x = 2 is a factor of the expression:

    2 | 12 - 4 - 1
      |     24 40
      |____________
       12  20 39

Once again, the remainder is not zero, so x = 2 is not a factor of the expression.

Finally, let's check if x = -2 is a factor of the expression:

   -2 | 12 - 4 - 1
      |    -24 56
      |____________
       12 -28 55

As we can see, the remainder is not zero, so x = -2 is not a factor of the expression.

After checking all the possible factors, we can conclude that none of the values tested (1, -1, 2, -2) are factors of the expression 12x^2 - 4x - 1.

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The given limit is evaluated by dividing numerator and denominator by x and then applying L'Hopital's rule. The limit converges to e^(3/2) as x approaches infinity.

We can evaluate the given limit by dividing both the numerator and denominator by x and then using L'Hopital's rule

lim x → ∞ (xe^(3/2) - x) = lim x → ∞ x(e^(3/2) - 1/x)

Taking the derivative of both the numerator and denominator with respect to x, we get

lim x → ∞ (e^(3/2) - 1/x)

Since the limit of 1/x as x approaches infinity is 0, we get

lim x → ∞ (e^(3/2) - 1/x) = e^(3/2)

Therefore, the limit of (xe^(3/2) - x) as x approaches infinity is e^(3/2).

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--The given question is incomplete, the complete question is given

" Evaluate the limit. (If you need to use -60 or co, enter -INFINITY or INFINITY.) lim x approaches to infinity (xe^3/2 – x)"--

Answer:

A and C

Step-by-step explanation:

Answer:

6x-1

Step-by-step explanation:

I dont know  how to explain but it is correct

Answer:

6x – 1

Step-by-step explanation:

Answer:

the answer is 20 hope this helps :)

Step-by-step explanation:

Answer:

18.84.

Step-by-step explanation:

Radius times 2 is diameter. 6 feet is diameter. Circumference is diameter times pi.

6 × 3.14 = 18.84

Answer:18.5

Step-by-step explanation:

Okay if it's a square that means four sides.so you would take 74 divide it by four and get the final answer of 18.5

\((\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{10}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{4}}}\implies \cfrac{9}{3}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{3}(x-\stackrel{x_1}{4}) \\\\\\ y-1=3x-12\implies y=3x-11\)

The price we have to pay for the disc after 10% discount is 1467 dollars.

Percentage is the value per hundredth.

According to the given question we bought a disc which costs 1630 dollars there's a 10% discount we have to find how much i have to pay.

10% of 1630 dollars will be

= (10/100) × 1630 dollars.

= 16300/100 dollars.

= 163 dollars.

So, the price we have to pay for the disc after 10% discount is

= (Total amount - Discount amount)

= ( 1630 - 163 ) dollars.

= 1467 dollars.

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The speeding cost extra $0.38025 per minute in fuel. The speeding saves the company $2 per minute in tech pay.

Gas is $5 a gallon. The vehicle gets 20 mpg. Tech makes $30 an hour. He speeds 15 mph over the speed limit. The speeding increases the fuel cost by 30%.To calculate the cost per minute of speeding in fuel, we need to first calculate how much fuel the car uses per minute. The vehicle gets 20 miles per gallon of fuel. Thus, it uses 1 gallon of fuel every 20 miles. Suppose the speed limit is 55 mph. When Tech speeds at 15 mph over the speed limit, his speed becomes 70 mph.  At 70 mph, the car travels 1.17 miles in a minute [(70 miles/hour) x (1 hour/60 minutes)].Thus, the car uses 1/20 gallons of fuel to travel 1 mile, so it uses 1.17/20 = 0.0585 gallons of fuel in a minute.

When the speeding increases the fuel cost by 30%, the cost of fuel per gallon becomes $5.00 × 1.3 = $6.50.

Therefore, the cost per minute of speeding in fuel is: Cost per minute of speeding in fuel = 0.0585 gallons × $6.50 per gallon= $0.38025

Thus, the speeding cost extra $0.38025 per minute in fuel.

To calculate how much money per minute does the speeding save the company in tech pay, we need to calculate the difference in Tech's pay between his regular pay and overtime pay. Overtime pay = Regular pay + (Pay rate x 1.5)Tech's regular pay is $30 an hour, and he is speeding, so he will reach the destination faster. Assuming the destination is 30 minutes away, his regular pay would be: Regular pay = ($30/hour) x (0.5 hours) = $15

If he is driving 15 mph over the speed limit, he would reach the destination in 25 minutes instead of 30. Thus, his overtime pay would be: Overtime pay = $30 + ($30 × 1.5) = $30 + $45 = $75

Therefore, speeding saves the company $75 - $15 = $60 per half hour or $2 per minute ($60 ÷ 30).

Thus, the speeding saves the company $2 per minute in tech pay.

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The COP value for the vapor compression refrigeration cycle is:COP = Heat Absorbed/ Work DoneCOP = 187.8 KJ/kg / 187.8 KJ/kgCOP = 1

The coefficient of performance (COP) of a refrigeration system is a ratio of the quantity of heat removed from the cold space to the quantity of work delivered to the compressor. The COP of the system is generally high when the difference between the evaporator and condenser temperatures is high.

The vapor compression refrigeration cycle is widely used in refrigeration systems, and it comprises four processes:

Compression (1-2)

Rejection of heat (2-3)

Expansion (3-4)

Absorption of heat (4-1)

Given the information,

Th = 10°C, and Tc = -20°C

Calculating COP for vapor compression refrigeration cycle:

COP = Desired Output / Required Input

We can rewrite this as COP = Heat Absorbed / Work Done

To solve this question, we need to calculate the Heat Absorbed and Work Done.

The COP for the vapor compression refrigeration cycle is given by

COP = (Heat Absorbed) / (Work Done)

Let the value of heat absorbed = QL and work done = W

Compression Process:

Heat Rejected (QH) = Work Done (W) + Heat Absorbed (QL)

1-2 - Heat is absorbed from the evaporator and compressed by the compressor. The refrigerant is thus transformed from low pressure and low temperature (1) to high pressure and high temperature (2) by the compressor. It is an adiabatic process since no heat is exchanged between the refrigerant and the surroundings.

Hence, QH = W + QL

Heat Absorbed (QL) = QH - W

Heat Absorbed (QL) = 294.1 - 106.3 = 187.8 KJ/kg

Heat Absorbed (QL) = 187.8 KJ/kg

Expansion Process:

Heat Extracted (QC) = 0

3-4 - The refrigerant, which is a two-phase mixture, expands and loses pressure and temperature. The work input to the expansion valve is minimal. The process is adiabatic; thus, no heat is exchanged between the refrigerant and the surroundings. This point marks the beginning of the process of vaporization.

Hence, Heat Extracted (QC) = 0

Heat Extracted (QC) = 0

Heat Extracted (QC) = 0

Heat Extracted (QC) = 0

Heat Absorbed (QL) = Heat Extracted (QC)

Heat Absorbed (QL) = 0

Work Done (W) = Heat Absorbed (QL) + Heat Extracted (QC)

W = 187.8 + 0

W = 187.8 KJ/kg

Thus, the COP value for the vapor compression refrigeration cycle is:

COP = Heat Absorbed / Work Done

COP = 187.8 KJ/kg / 187.8 KJ/kg

COP = 1.

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The function y = 2.5x + 500 represents the total number of miles if the motor car race is 500 miles long, option (d) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

y represents the number of miles a motor car has left to go in the race

x represents the number of laps completed by the motor car

The total number of miles if we consider only circular speedways = 2.5x

The total number of miles:

y = 2.5x + 500  (because 500 is the constant)

Thus, the function y = 2.5x + 500 represents the total number of miles if the motor car race is 500 miles long option (d) is correct.

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