show the work for 6 4/5 - 2 1/3=

Answer:

A, C and D are true statements.

Step-by-step explanation:

Megan constructed triangle ABC.

In Megan’s triangle, m∠A is represented by x°.

Therefore, ∠A = x°

For m∠B is 4 times greater than m∠A

Therefore, ∠B = 4x°

For m∠C is 30° less than 5 times m∠A.

Therefore, ∠C = 5x°-30°

ABC is a triangle.

Sum of all angles of a triangle is 180°. Angle sum property of triangle.

m∠A + m∠B + m∠C = 180°

x° + 4x° + 5x°-30° = 180°

x° = 15°

True Statements are:

A) m∠A = x°

C) m∠B = (4x)°

D) m∠C = (5x – 30)°

Answer: B

Step-by-step explanation:

A = lw

A = (8.5m)(4.5m)

A = 38.25m^2

Answer:

important thing this is 1245386536789854

The difference in overall gain between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price is $239.50.

To determine the difference in overall gain or loss between selling stock A at the current day's high price or low price and selling stock B at the current day's high price or low price, we need to calculate the selling prices of the stocks.

Stock A:

High price = $105.19

Low price = $103.25

Close price = $103.38

Stock B:

High price = $145.18

Low price = $143.28

Close price = $144.05

The investor purchased 50 shares of stock A at $90 per share and 75 shares of stock B at $145 per share.

To calculate the selling prices, we need to multiply the number of shares by the respective selling price.

Selling price of stock A at the high price: 50 shares \(\times\) $105.19 = $5,259.50

Selling price of stock A at the low price: 50 shares \(\times\) $103.25 = $5,162.50

Selling price of stock B at the high price: 75 shares \(\times\) $145.18 = $10,888.50

Selling price of stock B at the low price: 75 shares \(\times\) $143.28 = $10,746.00

Now, let's calculate the difference in overall gain or loss:

Difference in overall gain = Selling price at the high price - Selling price at the low price

= ($5,259.50 + $10,888.50) - ($5,162.50 + $10,746.00)

= $16,148.00 - $15,908.50

= $239.50

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We can actually get the line of best fit. This is a line closest to all the data points. The least squares regression is applied for better accuracy.

If the line of best fit is drawn, then the slope can be determined and the point slope formula would be written as

y - y1 = m(x - x1)

Based on a system of equations, the number of children (and adults) that attended the amusement park on that particular day is:

Children = 10,000

Adults = 20,000.

A system of equations is two or more equations solved concurrently or simultaneously.

A system of equations can be solved by graphing, matrix, elimination, and substitution methods.

The cost per child = $10

The cost per adult = #20

The total number of children and adults who attended on the da = 30,000

The total revenue generated by the park from tickets = $500,000

Let the number of children = x

Let the number of adults = y

x + y = 30,000 ... Equation 1

10x + 20y = 500,000 ... Equation 2

Multiply Equation 1 by 10:

10x + 10y = 300,000 ... Equation 3

Subtract Equation 3 from Equation 2:

10x + 20y = 500,000

-

10x + 10y = 300,000

10y = 200,000

y = 20,000

x = 30,000 - y

= 10,000

Check:

x + y = 30,000 ... Equation 1

10,000 + 20,000 = 30,000

10x + 20y = 500,000 ... Equation 2

100,000 + 400,000 = 500,000

Thus, using a system of equations, we can conclude that 10,000 children attended with 20,000 adults.

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The final rule for g(x) is g(x) = 3|3x| + 12.

To stretch the graph of f(x) = −|3x| − 4 vertically by a factor of 3, we multiply the function by 3. This will result in a vertical stretching of the graph.

So, the rule for g(x) is g(x) = 3f(x).

Now, let's find the expression for g(x) using the given function f(x) = −|3x| − 4:

g(x) = 3f(x)

g(x) = 3(-|3x| - 4)

g(x) = -3|3x| - 12

This is the expression for g(x), which represents the transformed graph.

To reflect the graph of g(x) across the x-axis, we change the sign of the function. This means that the negative sign in front of the absolute value will become positive, and the positive sign in front of the constant term will become negative.

Therefore, the final rule for g(x) is g(x) = 3|3x| + 12.

Now, let's consider the graph of g(x). The graph will have the same shape as f(x), but it will be stretched vertically by a factor of 3 and reflected across the x-axis.

The original graph of f(x) = −|3x| − 4 is a V-shaped graph that opens downward and passes through the point (0, -4). The transformed graph of g(x) will have a steeper V-shape, opening downward, and passing through the point (0, 12) instead of (0, -4).

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The Statements which are true are;

Inverse Operations:

Operations said to be inverse if both operations are complementary.

Ultimately,

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The amount that she owes after she factors in interest will be $33,455.64.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Rita necessities to apply for a line of credit for another vehicle. Her advance is $25,000. The financing cost on the advance is 6% and is accumulated yearly. She intends to take care of the advance in 5 years.

Then the amount is given as,

A = $25,000 x (1 + 0.06)⁵

A = $25,000 x (1.06)⁵

A = $25,000 x 1.3382

A = $33,455.64

The amount that she owes after she factors in interest will be $33,455.64.

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Answer:

π/10

Step-by-step explanation:

α=-19π/10=-19π/10+2π=(-19π+20π)/10=π/10

The net to compute the surface area of the three-dimensional figure is 166 square units.

We have,

the surface area of the three-dimension figure:

The surface area is the area calculated for the three-dimensional object. As the three-dimensional object is made up of 2D faces, the surface area is the sum of the areas of all the faces of the figure.

A cuboid is a three-dimensional figure having length, width, and height. The surface area of a cuboid can be calculated by adding together the areas of the six faces.

For the given cuboid, length l = 8 , width w = 5 and height h = 5.

The surface area of the figure is given by;

SA = 2 (lw+lh+wh)

    =70 + 56 + 40

    = 166

Hence, the net to compute the surface area of the three-dimensional figure is 166 square units.

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Answer:30

Step-by-step explanation:

Let's use v1(t) and v2(t) to represent the speed of the first and second runners, respectively, at time t. The functions v1 and v2 must both be continuous in the time variable t, hence this assumption must be made.

So, their difference, a(t), is similarly a continuous function in the variable t, with the formula a(t) = v1(t)-v2(t).  

Now, using the principle of contradiction, one may demonstrate that t1, t2, such that a(t1) is less than or equal to 0 and a(t2) is higher than or equal to 0, exist because the overall average speed of both runners is identical.

Now, we may utilize the continuous function a's Intermediate Value Property to locate a t0 between t1 and t2, where a(to)=0 and the runners are moving at the same speed at this point.

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Explanation:

First, we need to find what is the total number of values in the data. So, taking into account the height of the bars, we can calculate the size of the data as follows:

6 + 2 + 3 + 5 + 4 + 4 = 24

Where each number in the sum is the height of each bar.

Then, the position of the median can be calculated using the following equation:

Where n is the size of the data.

Finally, the value in position 12.5 is in the interval 90 - 119

Because, there are 6 values in 0- 29, there are

From the given expression, the factors are x+1 and x - 5 and the zeros of the function is equivalent to -1 and 5

Factorisation is defined as the breaking or decomposition of an entity. Given the quadratic equation below;

y=x² - 4x - 5

Factorize

y = x^2 - 5x + x - 5

y = x(x - 5) + 1(x - 5)

y = (x+1)(x-5)

From the given expression, the factors are x+1 and x - 5 and the zeros of the function is equivalent to -1 and 5

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Answer:

1. 4

Step-by-step explanation:

(-3, 6) and (-3, 10)

|-3 - 3| = 0, |6 - 10| = 4

4² + 0² = 16, \(\sqrt{16}\) = 4

(4, -5) and (-2, -5)

|4 - -2| = 6, |-5 - 5| = 0

6² + 0² = 36, √36 = 6

(6, 4) and (6, -1)

|6 - 6| = 0, |4 - -1| = 5

5² + 0² = 25, √25 = 5

(-9, 1) and (-4, 1)

|-9 - -4| = 5, |1 - 1| = 0

5² + 0² = 25, √25 = 5

Answer:

Drag each set of coordinates to the correct location on the table.

Calculate the distance between the pairs of coordinates, and classify them according to the distance between them.

(3, 4) and (2, 1)

(3, 7) and (5, 2)

(5, -2) and (3, 3)

(-2, 3) and (1, 2)

(-4, -2) and (-3, 1)

(4, -1) and (-1, 1)

Step-by-step explanation:

After the translation vertically downward by 7 units, we get the function g(x) is g(x)=x².

The given function is h(x)=x²+7.

The graph of h is translated vertically downward by 7 units, it becomes the graph of a function g.

The new graph of g(x) will have the same shape as the graph of h(x), but it will be shifted down by 7 units. This means that the equation for g(x) can be obtained by subtracting 7 from h(x):

g(x) = x² + 7 -7 = x²

Therefore, after the translation vertically downward by 7 units, we get the function g(x) is g(x)=x².

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Answer:

A student who runs 3/4 mile in 6 minutes is faster than a student who runs 1/2 mile in 5 minutes because when you simplify both fractions to per minute, the student who ran 3/4 mile in 6 minutes (1/8 mile per min) ran faster than the student who ran 1/2 mile in 5 minutes (1/10mile in 1 min).

Step-by-step explanation:

\(\frac{3/4mile}{6min}\) divided by 6 to get per min =

1/8 mile per min

The disadvantages of the mode are: For many sets of data there is no mode.

The mode is a measure of central tendency that represents the most frequently occurring value in a dataset.

However, one of the disadvantages of the mode is that for many sets of data, there may not be a distinct mode. In such cases, the data may have a uniform distribution where all values occur with equal frequency, or it may have multiple modes with similar frequencies.

The mode is not affected by extremely large or small values. It only considers the frequency of values and not their magnitude. Therefore, extreme values do not influence the mode.

The statement that the mode can only be computed for interval-level data or higher is incorrect. The mode can be computed for any type of data, including nominal, ordinal, interval, and ratio data. It is applicable to categorical as well as numerical data.

The main disadvantage of the mode is that for many datasets, there may not be a distinct mode.

The correct option is: For many sets of data there is no mode.

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The coordinates of the reflected point P' will be (4, -3).

When a point is reflected over the x-axis, its y-coordinate changes sign.

In this case, the point P has coordinates (4,3).

To reflect it over the line x=3, we need to keep its x-coordinate the same and change its y-coordinate to its opposite.

So, the x-coordinate of the reflected point will still be 4, but the y-coordinate will become -3.

Therefore, the coordinates of the reflected point P will be (4, -3).

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Answer:

Step-by-step explanation:

Therefore, we need 17 towels of brand C to clean a single sq ft

Brand A:

we add up all the sq ft cleaned by brand a

0.75+1.50+2.25=4.5

and we add up all paper towels used in total

6+13+20=39

now

to clean 4.5 square ft, we need 39 towels. how many we need to clean a single square foot?

4.5 sq ft ___________39 towels

1 sq ft_____________A

and A= 1 sq ft * 39 towels / 4.5 sq ft

and that gives us 8.6 towels, so we need 9 towels to clan a square foot with the brand A

now we repeat this with bran b and c

brand B:

0.75+1.75+2=4.5 sq ft

9+22+25= 56 towels

4.5 sq ft________56 towels

1 sq ft__________B

B= 1 sq ft * 56 towels / 4.5 sq ft = 12.4

so we need 13 towels of brand B

at last

brand C:

1+1.75+2.5=5.25 sq ft

17+29+41= 87 towels

5.25 sq ft________87 towels

1 sq ft__________C

C= 1 sq ft * 87 towels / 5.25 sq ft = 16.57 towels

Therefore, we need 17 towels of brand C to clean a single sq ft

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Here is one: (14, 48, 50)

The surface area of the vase is 168.4 square inches.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that has two congruent circular bases connected by a curved surface.

The surface area of the cylindrical vase can be found using the formula SA = B + Ph, where B is the area of the base, P is the perimeter of the base, and h is the height of the vase. Since the vase has a circular base, the area of the base can be found using the formula for the area of a circle: B = πr², where r is the radius of the base.

The diameter of the vase is 4.3 inches, so the radius is half of that, or 2.15 inches. The area of the base is therefore:

B = πr² = 3.14 * (2.15)² ≈ 14.46 square inches.

The perimeter of the base is the circumference of the circle, which can be found using the formula C = 2πr:

P = 2πr = 2 * 3.14 * 2.15 ≈ 13.53 inches.

Now we can use the formula SA = B + Ph to find the surface area of the vase:

SA = B + Ph = 14.46 + 13.53 * 11 ≈ 168.39 square inches.

Rounding to the nearest tenth of a square inch, the surface area of the vase is approximately 168.4 square inches.

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a.The Industry Average Salary is $55,680. b.The Firm A's Average Salary is $51,718.40 .c. Firm B's average salary is approximately 112.27% of Firm A's average salary.

a. To determine the industry average salary, we can use the information that the industry average salary is 96% of Firm B's average salary. Firm B's average salary is $58,000. Therefore, we can calculate the industry average salary as follows:

Industry Average Salary = 96% of Firm B's Average Salary

= 0.96 * $58,000

= $55,680

b. Firm A's average salary is stated as 93% of the industry average salary. To calculate Firm A's average salary, we can multiply the industry average salary by 93%:

Firm A's Average Salary = 93% of Industry Average Salary

= 0.93 * $55,680

= $51,718.40

c. To express Firm B's average salary as a percentage of Firm A's average salary, we can divide Firm B's average salary by Firm A's average salary and multiply by 100:

Percentage = (Firm B's Average Salary / Firm A's Average Salary) * 100

= ($58,000 / $51,718.40) * 100

≈ 112.27%

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Answer:

Step-by-step explanation:

3x  +  5  +  x  -  25  =  180

4x  -  20  =  180

4x  =  200

x  =  50

The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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Answer:

The answer is 55, you can figure this out as each number is increasing by 10

a_n=-5+10n

hope it helps

Answer:

2√2 units.

Step-by-step explanation:

To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of points A and B into the formula, we have:

d = sqrt((1 - 3)^2 + (3 - 5)^2)

  = sqrt((-2)^2 + (-2)^2)

  = sqrt(4 + 4)

  = sqrt(8)

  = 2sqrt(2)

Therefore, the length of the line joining points A and B is 2√2 units.

Answer:

16,000 ft = 3.03 miles

16,000 ft = 5,333 yards

16,000 ft= 16,000 ft

Answer:
- Foot---Miles: 16,000ft = 3.03 Miles.
- Foot---Yard: 16,000ft = 5,333 Yards.
- Foot---Foot: 16,000ft = 16,000 Foot.

Step-by-step explanation:

- 16,000 ÷ 5,280 = 3.0303030303 ---- 3.03

- 16,000 ÷ 3 = 5333.33333333 ----- 5,333

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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