What a thrill! I'm parasailing at an elevation of five hundred sixty feet above the beautiful deep blue sea. But wait! Suddenly, I feel myself being reeled in several minutes too early and I'm sinking at the rate of one point nine feet per second and I keep sinking at this rate! I want my money back!

The elevation is now one hundred seventy-nine point seven yards. How long have I been plummeting downward?

Answer:

y-1= -1/3(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-1=m(x+3)

the slope is rise over run

the slope is -1/3

Answer:

y - 1 = 3/2 (x + 3)

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (-3, 1), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point and m is the slope of the line.

First, let's calculate the slope of the given line using the two points (-2, -4) and (2, 2):

slope = (y₂ - y₁) / (x₂ - x₁)

= (2 - (-4)) / (2 - (-2))

= 6 / 4

= 3/2

Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope (m) of the new line is also 3/2.

Now we can substitute the values into the point-slope form using the point (-3, 1):

y - 1 = (3/2)(x - (-3))

y - 1 = (3/2)(x + 3)

The equation in point-slope form of the line parallel to the given line and passing through the point (-3, 1) is:

y - 1 = 3/2 (x + 3)

Answer:

918.60

Step-by-step explanation:

dont mind my handwriting

The answer is 840.

I hope am right

The linear and exponential equations for the amount of money in the banks indicates;

TCF Bank Equation

y = 100·x + 1000

Well Fargo Bank Equation

y = (1.06)ˣ

The number of years it will take for both accounts to have the same amount of money is about 17 years

An exponential equation is an equation of the form; y = a·bˣ, where the input variable, x is an exponent.

The equation for calculating the amount in each bank, based on the details are;

TCF Bank;

Amount invested = $1,000

Amount added each year = 100·x

Well Fargo Bank Equation

The percentage of the amount earned as interest each year = 6% = 0.06

The exponential equation for compound interest amount is; y = 1000·(1 + 0.06)ˣ

Therefore; y = 1000·(1.06)ˣ

When the amount in the two accounts have the same amount of money, we get;

1000·(1.06)ˣ = 100·x + 1000

Therefore; (1.06)ˣ = (100·x + 1000)/1000 = 0.1·x + 1

(1.06)ˣ = 0.1·x + 1

Solving the above equation using the substitution method and graphing indicates that we get;

x = 0, and x ≈ 17.125732

Therefore, it takes about 17 years for the two accounts to have the same amount of money

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Answer:

492 yd^2

Step-by-step explanation:

Way 1: 250 + 242 = 492

Way 2: 800 - 132 - 176 = 492

The decimal representation of the given sequence is 4,063.21.

The given sequence can be interpreted as follows: "63 ones, 21 hundredths, 4 thousand." To convert this sequence into decimal form, we need to understand the place value of each digit.

Starting from the left, we have "63 ones." This means we have 63 units, which can be represented as 63.

Next, we have "21 hundredths." Since there are two digits after the decimal point, the number becomes 0.21.

Finally, we have "4 thousand." Considering the place value, 4 thousand would be written as 4,000.

Putting it all together, we have 63 + 0.21 + 4,000, which equals 4,063.21. Therefore, the decimal representation of the given sequence is 4,063.21.

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The solution to the inequality equation \(x^{2}\) – 9x < –18 is 3 < X < 6

Inequality equation means a mathematical expression in which the sides are not equal to each other

\(x^{2}\) – 9x < –18

Rewrite in standard form

x^2 -9x +18 < 0

Factorise the equation

\(x^{2}\)  - 3x -6x +18 < 0

x (x - 3) - 6 (x - 3) < 0

(x - 3) ( x- 6) < 0

(x - 3) < 0

x < 3

( x- 6) < 0

x < 6

3 < X < 6

Therefore, the solution to the inequality is 3 < X < 6

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The data-set with the given features is presented as follows:

4, 4, 7, 8, 12.

The mode of 4 means that the element that appears the most times is of 4, which appears two times.

The median of 7 means that the middle element, which is the third element, is of 7.

The mean of 7 means that the sum of the five elements divided by 5 has a result of 7.

The range of 8 means that the largest element is of 8 + 4 = 12, as the range is the difference between the highest and the lowest value of the data-set.

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If α is an ordinal and β ∈ α, then β satisfies all three properties of an ordinal. Therefore, β is also an ordinal.

To prove the statement "If α is an ordinal and β ∈ α, then β is an ordinal," we need to demonstrate that if α is an ordinal and β is an element of α, then β satisfies the three properties of an ordinal:

Well-Ordering: Every element of β is strictly well-ordered by the membership relation ∈. This property holds because α is an ordinal and satisfies the well-ordering property, and β being an element of α inherits this property.

Transitivity: For any two elements γ and δ in β, if γ ∈ δ and δ ∈ β, then γ ∈ β. Since β is an element of α and α is transitive, the transitivity property carries over to β.

Trichotomy: For any two elements γ and δ in β, either γ ∈ δ, δ ∈ γ, or γ = δ. Again, this property is inherited from α, as β is an element of α.

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Answer:

24

Step-by-step explanation:

The formula for area of any triangle is (length * width) * 1/2. This makes the angle of 90 degrees irrelevant.

6 x 8 = 48

48 / 2 = 24

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

\(\qquad \sf  \dashrightarrow \: f(x) = 2 {x}^{2} - 2x - 4\)

\(\qquad \sf  \dashrightarrow \: f(3) = 2(3) {}^{2} - 2(3) - 4\)

\(\qquad \sf  \dashrightarrow \: f(3) = 2(9) {} - 6- 4\)

\(\qquad \sf  \dashrightarrow \: f(3) = 18{} - 10\)

\(\qquad \sf  \dashrightarrow \: f(3) = 8\)

Answer and Explanation:

Given:

The box plot showing the data for the number of the tickets sold, in hundreds as shown below;

Recall that a box plot is generally given as below;

If we compare the above with the given box plot we can see that the;

Minimum Value = 100

First Quartile(Q1) = 300

Median = 400

Third Quartile (Q3) = 600

Maximum Value = 900

Q1(first quartile) is at 300 and the median, which is the middle number is at 400. Note that the Q1 represents the value under which 25% of the data points are found when they are arranged in increasing order. So 25% of the data are below 300 and are between the first quartile and the median.

25% of the data is between 300 and 400. TRUE

Recall that the interquartile range(IQR) is the difference between the third quartile and the first quartile, so we'll have;

So the IQR is 300 and not 800.

The interquartile range is 800. FALSE

As earlier mentioned above, the median is 400. TRUE

As earlier mentioned above, the first quartile is 300. TRUE

Note that the range is the difference between the maximum value and the minimum value, so we'll have;

So we can see from the above that the range is 800 and not 300.

The range is 300. FALSE

Note that 25% of the data are between Q1 and the median and 25% of the data are also between the median and the Q3, so we have that 50% of the data are between Q1 and Q3

50% of the data are between 300 and 600. TRUE

The minimum value is 100. TRUE

The maximum value is 9. FALSE

Both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

In triangle JKL, if angle J is less than 90 degrees, then angle K and angle L are both acute angles.

An acute angle is defined as an angle that measures less than 90 degrees. Since angle J is given to be less than 90 degrees, it is an acute angle.

In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle J is less than 90 degrees, the sum of angles K and L must be greater than 90 degrees in order to satisfy the condition that the angles of a triangle add up to 180 degrees.

Hence, both angle K and angle L must be acute angles, measuring less than 90 degrees, in order to satisfy the conditions of the given triangle.

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Answer:

1 1/2

Step-by-step explanation:

5 1/3÷3 5/9=

16/3÷32/9=

16/3×9/32=

144/96=

1 1/2

Answer:

780

Step-by-step explanation:

Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

Answer:

\(x^{2}-\frac{3}{2} x-\frac{7}{16} =0\)

Step-by-step explanation:

\(\begin{cases}\alpha -\beta =2\\ \alpha^{2} -\beta^{2} =3\end{cases}\)

\(\Longleftrightarrow \begin{cases}\alpha -\beta =2&\\ \left( \alpha +\beta \right) \left( \alpha -\beta \right) =3&\end{cases}\)

\(\Longleftrightarrow \begin{cases}\alpha -\beta =2&\\ \alpha +\beta =\frac{3}{2} &\end{cases}\)

Then

2α = 2 + 3/2 = 7/2

2β = (3/2) - 2 = -1/2

Then

Then

α = 7/4

β = -1/4

Then

a quadratic equation with root α and β can be :

\(\left( x+\frac{1}{4} \right) \left( x-\frac{7}{4} \right) =0\)

\(\Longrightarrow x^{2}-\frac{3}{2} x-\frac{7}{16} =0\)

Answer:

Price of each item is $1.17

Step-by-step explanation:

so the 3 case of items was $1.17

\(\huge\mathcal {♨Answer♥}\)

(01)

(02)

(03) Yes, The xavier is correct.

8.953 > 8

8.953 < 9

8.953 is bigger than 8 and smaller than 9.

9.000 - 8.953 = 0.047

(04)

(05)

(06)

(07)

(08)

☆...hope this helps...☆

_♡_mashi_♡_

9514 1404 393

Answer:

  54°, 90°, 108°, 126°, 162°

Step-by-step explanation:

The sum of angles in a pentagon is 180°(5 -2) = 540°.

The sum of ratio units is 3 +5 +6 +7 +9 = 30. So, each "ratio unit" stands for ...

  540°/30 = 18°

Then the angles are found by multiplying the given ratios by 18°:

  3 : 5 : 6 : 7 : 9 = 54° : 90° : 108° : 126° : 162°

Answer:

$15.00 per day and $0.22 per mile.

Step-by-step explanation:

To determine the daily fee and mileage fee charged by Best Rentals, we can set up a system of equations based on the given information.

Let's assume the daily fee is represented by "d" and the mileage fee is represented by "m."

For Mateo:

3d + 300m = 111.00

For Dara:

5d + 600m = 207.00

Now we can solve this system of equations to find the values of "d" and "m."

Multiplying the first equation by 2 to eliminate "m," we get:

6d + 600m = 222.00

Subtracting the second equation from this equation, we have:

(6d + 600m) - (5d + 600m) = 222.00 - 207.00

d = 15.00

Substituting the value of "d" into the first equation, we can solve for "m":

3(15.00) + 300m = 111.00

45.00 + 300m = 111.00

300m = 111.00 - 45.00

300m = 66.00

m = 0.22

Therefore, Best Rentals charges $15.00 per day and $0.22 per mile.

The graph shows the function g(x) as

\(g(x)=x^{1/3}-3\)

Given, that the function f(x)

\(f(x)=x^{1/3}\)

the graph shows a function g a transformation of f(x).

As, the graph of f(x) shifted 3 units downwards to get this function in the graph.

we know, that when a graph of a function is shifted 'a' units upwards or downwards then we add or subtract 'a' to the function respectively.

because the graph is shifted 3 units downwards.

Hence, the function g(x) can be defined as

\(g(x)=x^{1/3}-3\)

So, the graph shows the function g(x) as

\(g(x)=x^{1/3}-3\)

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Answer:

a

Step-by-step explanation:

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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Answer:

It's 117

Step-by-step explanation:

The first team has a total of 515 and the second 398

so you subtract 398 from 515 and you will get 117

Answer:

-22=22

Step-by-step explanation:

3,5-5,7=

-22/22

The equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

To find the equation of the line passing through the midpoint R and the points P and Q, we first need to find the coordinates of the midpoint R. The midpoint coordinates can be found by taking the average of the x-coordinates and the average of the y-coordinates of P and Q.

The x-coordinate of the midpoint R is (3 + (-5)) / 2 = -1/2.

The y-coordinate of the midpoint R is (5 + 7) / 2 = 6.

So, the coordinates of the midpoint R are (-1/2, 6).

Next, we can use the two-point form of the equation of a line, which states that the equation of the line passing through points (x₁, y₁) and (x₂, y₂) is given by:

(y - y₁) = (y₂ - y₁) / (x₂ - x₁) \(\times\) (x - x₁)

Substituting the coordinates of R (-1/2, 6) and P (3, 5) into the equation, we have:

(y - 6) = (7 - 5) / (-5 - 3) \(\times\)(x - (-1/2))

Simplifying the equation:

(y - 6) = (2 / -8) \(\times\)(x + 1/2)

(y - 6) = -1/4 \(\times\)(x + 1/2)

4(y - 6) = -x - 1/2

Therefore, the equation of the line passing through R and PQ is 4(y - 6) = -x - 1/2.

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Solve e from the equation by substraction 96 to both sides of the equal sign: