please help................

1. For Joshua's triangle; the distance of the green side of the triangle d₃ is 5.

2. For Murney's triangle, the perimeter of the triangle is 12.

3. For Grace, Abby and Chris's triangle, the perimeter of the triangle is 5 + √17 +  4√2.

4. For Chloe's triangle, the perimeter of the triangle is 11 + √65.

The distance of the triangles is calculated as follows;

For Joshua's triangle;

The length of d₁, d₂, and d₃ is calculated as follows;

d₁ = √ [(3 - 2)² + (2 - 0)²] = √5

d₂ = √ [(-1 - 3)² + (4 - 2)²] = 2√5

d₃ = √ [(-1 - 2)² + (4 - 0)²] = 5

The distance of the green side of the triangle d₃ = 5

For Murney's triangle, the perimeter of the triangle is calculated as;

BC = √ [(4 - 4)² + (6 - 2)²] = 4

AC = √ [(1 - 4)² + (2 - 2)²] = 3

AB = √ [(4 - 1)² + (6 - 2)²] = 5

Perimeter = 4 + 3 + 5 = 12

For Grace, Abby and Chris's triangle, the perimeter of the triangle is calculated as;

AC = √ [(-3 - 2)² + (2-2)²] = 5

BC = √ [(1 - 2)² + (2 + 2)²] = √17

AB = √ [(1 + 3)² + (2 + 2)²] = 4√2

Perimeter = 5 + √17 +  4√2

For Chloe's triangle, the perimeter of the triangle is calculated as;

AC =  √ [(-3 - 4)² + (2-2)²] = 7

BC =  √ [(4 - 4)² + (6-2)²] = 4

AB =  √ [(4 + 3)² + (6-2)²] = √65

Perimeter = 7 + 4 + √65 = 11 + √65

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The probability of being a senior is the total number of seniors divided by the total number of students.

The probability of a student walking given that they are seniors can be calculated using Bayes' theorem. Bayes' theorem is a formula that relates conditional probabilities to their inverses. The formula is: P(A|B) = P(B|A) P(A) / P(B)where P(A|B) is the probability of event A given that event B has occurred. In this case, A is "walking" and B is "senior." P(B|A) is the probability of being a senior given that the student is walking, P(A) is the probability of walking, and P(B) is the probability of being a senior. We can also represent the above formula in the form of a tree diagram, where P(walk | senior) is one branch of the tree.

The probability of being a senior is represented by the root of the tree, while the probability of walking is represented by a branch from the root. The probability of walking given that the student is a senior is calculated by dividing the probability of a senior walking by the probability of being a senior. The probability of walking can be calculated by adding up the probabilities of walking for each grade level and dividing by the total number of students.

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Answer:

3.486 feet (1.06 m) or 3 feet (0.91 m) five inches

Step-by-step explanation:

17 percent of 4.2 is 0.714 and 4.2–0.714 is 3.486

Step-by-step explanation:

Answer: 11 1/3 (eleven and one third)

Step-by-step explanation:

Answer:

132.84 is the answer as volume is area times length

Answer: -3/2

Step-by-step explanation:

To find the slope of the line perpendicular to the given one, we first need to change the equation to y=mx+b to find the original slope.

\(6x-9y=216\)             [subtract both sides by -6x]
\(-9y=-6x+216\)        [divide both sides by -9]
\(y=\frac{2}{3} x-24\)

Now we know slope is 2/3. The slope of the perpendicular line is the opposite sign and reciprocal of the slope.

Opposite would make it -2/3.

Reciprocal would be -3/2.
So the slope is -3/2.

Answer:

X>-4

Y>-18

X>-7

I hope this helps

ANSWER

The equation of the line tangent to the function at the given point is:

STEP-BY-STEP EXPLANATION

The given equation is:

Step 1: Determine the 1st derivative of the equation

Step 2: To determine the slope (m) of the tangent line, insert the x-value (1) into the equation 2

Step 3: use the point-slope formula to determine the equation of the line tangent to the given function at x = 1

Hence, The equation of the line tangent to the function at the given point is:

=======================================================================

1. Take 1st derivative

2. insert the x-value (-1) to determine the slope (m)

3. Now, determine the equation of the line tangent at (-1,3)

Answer:

6:2

Step-by-step explanation:

Answer:6:2 I hope this is helpful

Step-by-step explanation:

6 apples to 2 mangos is 6:2

To match decimal values with their corresponding hexadecimal values, we need to convert the decimal numbers into their hexadecimal equivalents using division and remainders.

To match each decimal value on the left with the corresponding hexadecimal value, we need to convert the decimal numbers into their hexadecimal equivalents.

Here are a few examples:

1. Decimal 10 = Hexadecimal A

To convert 10 to hexadecimal, we divide it by 16. The remainder is A, which represents 10 in hexadecimal.

2. Decimal 25 = Hexadecimal 19

To convert 25 to hexadecimal, we divide it by 16. The remainder is 9, which represents 9 in hexadecimal. The quotient is 1, which represents 1 in hexadecimal. Therefore, 25 in decimal is 19 in hexadecimal.

3. Decimal 128 = Hexadecimal 80

To convert 128 to hexadecimal, we divide it by 16. The remainder is 0, which represents 0 in hexadecimal. The quotient is 8, which represents 8 in hexadecimal. Therefore, 128 in decimal is 80 in hexadecimal.

Remember, the hexadecimal system uses base 16, so the digits range from 0 to 9, and then from A to F. When the decimal value is larger than 9, we use letters to represent the values from 10 to 15.In conclusion, to match decimal values with their corresponding hexadecimal values, we need to convert the decimal numbers into their hexadecimal equivalents using division and remainders.

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The coordinates of the center is (32, 40.5).

length of the radius of the circle is 73 units.

The coordinates of the center is solved using the formula for midpoints expressed as

Midpoint x-coordinate = (x₁ + x₂) / 2

Midpoint y-coordinate = (y₁ + y₂) / 2

Plugging in the values:

x₁ = 8 and y₁ = 13

x₂ = 56 and y₂ =68

Midpoint x-coordinate

= (8 + 56) /2

= 64/2

= 32

Midpoint y-coordinate

= (13 + 68) /2

= 81/ 2

= 40.5

distance formula will be used to find the length of the radius of the circle

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Plugging in the values:

= √[(56 - 8)² + (68 - 13)²]

= √(48² + 55²)

= √(2304 + 3025)

= √5329

= 73

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Answer:

The change in latitude, Δφ, from Liverpool to Melbourne is 91.22° south

The change in longitude, Δλ, from Liverpool to Melbourne is 147.95° East

Step-by-step explanation:

The parameters given are;

The latitude of Liverpool is 53.41°

The longitude of Liverpool is -2.99°

The latitude of Melbourne is -37.81°

The longitude of Melbourne is 144.96°

The change in latitude from Liverpool to Melbourne = Δφ

Δφ = 53.41° - (-37.81°) = 53.41° + 37.81° = 91.22°

The change in latitude, Δφ, from Liverpool to Melbourne = 91.22° south

The change in longitude from Liverpool to Melbourne = Δλ

Δλ = -2.99° - 144.96°  = -147.95°

Therefore the change in longitude from Liverpool to Melbourne = 147.95° East.

Answer:

the difference in latitude is 91.22°

the difference in longitude is 147.95°

Explanation:

For Liverpool, London. The latitude is 53.41°, longitude is -2.99°

For  Melbourne, Australia. The latitude is -37.81°, longitude is 144.96°

The negative or positive magnitude of their values shows their position on either sides of the origin of the latitude (equator) and the origin of the longitude (prime meridian).

The latitude measures the relative position of a point, north or south of the equator (latitude 0°). The longitude measures the relative position, east or west of the prime meridian (longitude 0°)

the difference in latitude is 53.41° - (-37.81°) = 53.41° + 37.81° = 91.22°

the difference in longitude = 144.96° - (-2.99°) = 144.96 + 2.99 = 147.95°

Answer:

each person would get about 1 4/10 slices

The value of probability of 65 ≤ X ≤ 74 is 0.0808.

Based on the information given, we can use the properties of the standard normal distribution to find the values of Z associated with the probabilities given.

Hence, By Using a standard normal distribution table, we find that;

P(Z ≤ -1.67) = 0.0421

And, P(Z ≥ 0.86) = 0.1298.

So, We can then use these Z values to standardize the random variable Y and find its mean and standard deviation:

Z₁ = (66 - μ) / σ = -1.67

Z₂ = (81 - μ) / σ = 0.86

Solving for μ and σ, we get:

μ = 73.5,  σ = 5

Now that we know the mean and standard deviation of Y, we can use them to find the probability of 65 ≤ X ≤ 74.

For this, we once again standardize the random variable Y:

Z₃ = (65 - 73.5) / 5 = -1.7

Z₄ = (74 - 73.5) / 5 = 0.1

Using a standard normal distribution table, we find that;

P(-1.7 ≤ Z ≤ 0.1) = 0.0808.

Therefore, the probability of 65 ≤ X ≤ 74 is 0.0808.

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Answer:

Step-by-step explanation:

Let the horizontal distance is x

Use tangent to solve this:

The weight in pounds of the fourth dog, is 55 lbs.

What is weight?

The force exerted on an object by gravity is known as its weight. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.

As given, Ben is walking with three dogs that weigh an average of 75 pounds each. Ben begins to walk with a fourth dog, and the average weight of the dogs decreases to 70 pounds.

The total weight of the first three dogs is 225 pounds.

This amount, plus the weight of the fourth dog, divided by total number of dogs, is the new average weight:

\(\frac{d+225}{4} = 70\\d + 225 = 280\\d = 280 - 225\\d = 55 lbs\)

Therefore, the weight of the fourth dog is 55 lbs.

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The length of y is given as follows:

y = 7.8 cm.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

In the context of this problem, we have that y is the hypotenuse, while 6.1 cm is the side length adjacent to the angle of 39º, hence:

cos(39º) = 6.1/y

y = 6.1/cosine of 39 degrees

y = 7.8 cm.

6.1 cm is adjacent to the angle of 39º, while y is the hypotenuse.

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Answer:

X = 208

Step-by-step explanation:

Answer:

yes its X-squadrant

Step-by-step explanation:

The value of an invertible matrix p and a matrix of the form c is

\(C=\left[\begin{array}{cc}6+4i&0\\0&6-4i\end{array}\right]\)

What is an invertible matrix?

If a matrix meets the necessary requirements, it is said to be invertible because a matrix inversion operation can be performed on it. Any given square matrix A of order n × n is referred to be invertible if another n × n square matrix B exists such that,

AB = BA = In

B = A⁻¹

Where In is an identity matrix of order n × n.

As given,

\(\left[\begin{array}{cc}7&-17\\1&5\end{array}\right]\)

And 6 + 4i, 6 - 4i are eigen values of A.

Also given that eigen vector corresponding to λ = 6 + 4i is

\(\left[\begin{array}{c}4-i\\-i\end{array}\right]\)

And eigen vector corresponding to λ = 6 + 4i is

\(\left[\begin{array}{c}4+i\\i\end{array}\right]\)

Suppose that,

\(P=\left[\begin{array}{cc}4-i&4+i\\-i&i\end{array}\right]\)

The P diagonal A into diagonal from given by

\(P^-^1AP=C\\\\\)

\(C=\left[\begin{array}{cc}6+4i&0\\0&6-4i\end{array}\right]\)

Hence, the value of an invertible matrix p and a matrix of the form c has been obtained.

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The solution to the equation x² = 6x - 9 is x = 3.

To solve the equation x² = 6x - 9 using the quadratic formula, we need to rewrite the equation in standard form (ax² + bx + c = 0).

Given equation:

x² = 6x - 9

Move all terms to one side to obtain:

x² - 6x + 9 = 0

Now we can identify a, b, and c for the quadratic formula, where a = 1, b = -6, and c = 9.

The quadratic formula states that the solutions for x can be found using the equation:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values of a, b, and c into the quadratic formula:

x = (-(-6) ± √((-6)² - 4(1)(9))) / (2(1))

x = (6 ± √(36 - 36)) / 2

x = (6 ± √0) / 2

Since the discriminant (√(b² - 4ac)) is zero, there is only one solution for x.

x = 6 / 2

x = 3

Therefore, the solution to the equation x² = 6x - 9 is x = 3.

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Answer:

5/12 gallons

Step-by-step explanation:

Answer:

1 Gallon

Step-by-step explanation:

Okay, This is easy!

She is using 1/6 gallon of Lemonade and 1/4 of fruit juice. All we need to do is simply add them together and we get 1/10. 1/10 is the same as 1 Gallon.

Hope this helps,

PumpkinSpice1♥

0.0912   is the probability that the score will be 120 or higher .

What is probability explain with an example?

Zlower = X₁ - μ/σ  = 120 - 100/15  = 1.33

the probability is compared as

                    Pr ( X ≥ 120 ) = Pr(X - 100/15 ≥ 120 - 100/15)

                                         = Pr(Z ≥ 120 - 100/15

                                          = Pr( Z ≥ 1.33)

                                          = 0.0912

Since 0.0912 > 0.05 i.e. this IQ score is not unusual and hence I can believe the claim.

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Answer:

Step-by-step explanation:

You want to know the number of panels and posts needed for a 40 ft fence comprised of 8 ft panels, with a post between panels and at each end of the fence.

The number of panels needed is ...

  (40 ft)/(8 ft/panel) = 40/8 panels = 5 panels

The 5 panels will have 2 ends and 4 spaces, requiring 2 + 4 = 6 posts.

  o ---- o ---- o ---- o ---- o ---- o

Answer:

27 years

Step-by-step explanation:

Given that :

Town A:

Initial population = 14280

Rate = increase by 160 per year

Let t = time in years

Population is thus :

14280 + 160t - - - (1)

Town B:

Initial population = 24000

Rate = decrease by 200 per year

P = 24000 - 200t - - - (2)

Equate both equations :

14280 + 160t = 24000 - 200t

160t + 200t = 24000 - 14280

360t = 9720

t = 9720 / 360

t = 27

In 27 years

Answer:

The mean is 47

Step-by-step explanation:

First, you want to add up all of the numbers.

47 + 25 + 43 + 33 = 148

Now, you want to divide what you got by how many numbers there are.

148/4 = 37

The mean is 47

   Mean of the terms given in the data set as {47, 25, 43, 33} (four terms) will be 37.

          Mean = \(\frac{\text{Total of the terms in a data set}}{\text{Numbers of the terms}}\)

Total of the terms given in the the data set = 47 + 25 + 43 + 33

                                                                        = 148

Number of terms in the data set = 4

Substitute these values in the expression of the mean,

Mean = \(\frac{148}{4}\)

          = 37

      Therefore, mean of the data set given in the question is 37.

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Answer:

y=3x-15

Step-by-step explanation:

y-y1=m(x-x1)

y-9=3(x-8)

y=3x-24+9

y=3x-15

Answer:

Step-by-step explanation:

Notice that ∠5 is an internal angle, because it's between the parallels.

∠1  and ∠5 are corresponding angles, becasue they are at the same side of the transveral, and one is internal and the other external. So, ∠1 = 62°.

∠2 and ∠1 are supplementary angles, because they are on a straight angle, so if ∠1 = 62°, then ∠2 = 180° - 62° = 118°.

∠3 and ∠1 are vertical angles, because they have a vertex in common only. So, they are congruent, which means ∠3 = 62°.

Finally, ∠4 and ∠2 are vertical angles, so they are congruent. ∠4 = 118°.

Answer:

\(31.98\)

Step-by-step explanation:

Given the following question:

41% of 78

In order to find the answer, we will use the formula to calculate percentages and solve.

\(\frac{p\times n}{100}\)
\(\frac{41\times78}{100} =41\times78=3198\div100=31.98\)
\(=31.98\)

41% of 78 is indeed "31.98."

Hope this helps.

Answer:

The awnser to this equation is 120 cents

The cost of using a 200-watt television for 30 days, turned on for 2 hours per day, would be $1.20.  

To calculate the cost of using a 200-watt television for 30 days with 2 hours of daily usage at 10 cents per kilowatt-hour, we need to find the total energy consumption and then multiply it by the cost per kilowatt-hour.

First, let's find the total energy consumption:

1. Daily energy usage: 200 watts * 2 hours = 400 watt-hours
2. Monthly energy usage: 400 watt-hours * 30 days = 12,000 watt-hours

Now, we need to convert watt-hours to kilowatt-hours:
3. Monthly energy usage in kilowatt-hours: 12,000 watt-hours / 1,000 = 12 kWh

Finally, let's calculate the cost:
4. Cost of using the television for 30 days: 12 kWh * 10 cents per kWh = 120 cents

So, the cost of using a 200-watt television for 30 days with 2 hours of daily usage at 10 cents per kilowatt-hour is 120 cents.

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