what is one and half right angle​

The surface areas are given as;

a.  2700 cm²

b. 280. 6 cm²

c. 815. 3 cm²

The formula for calculating the surface area of a cuboid is expressed as;

Surface area (SA) = 2lw+2lh+2hw

Such that l is the length, w is the width and h is the height

Substitute the values, we have;

a. Surface area = 2(25×25) + 2(4 ×25) + 2(25 ×25)

expand the bracket, we have;

Surface area = 1250 + 200 + 1250

Surface area = 2700 cm²

b. Surface area of the pyramid = √3/ 2a²

Substitute the value

Surface area = √3 /2 × 18²

Find the square, we have;

Surface area = 280. 6 cm²

c. The total surface area to be painted ;

= 675 + √3/4a²

= 675 + 140.3

= 815. 3 cm²

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The simplified expression is 1,675,616. the value of the expression is 1,675,616.

To find the simplified expression and the value of 6 raised to a power, follow the steps given below:

Step 1: Simplify the expression Firstly, the simplified expression is obtained by using the rule of exponents, which states that if a number raised to a power is multiplied by the same number raised to another power, then the resulting power is the sum of the two powers.

6 raised to the power of 2 is 6 × 6 = 36.6 raised to the power of 3 is 6 × 6 × 6 = 216.6 raised to the power of 4 is 6 × 6 × 6 × 6 = 1296.6 raised to the power of 5 is 6 × 6 × 6 × 6 × 6 = 7776.

Step 2: Find the value of the expression

From these results, it can be seen that when 6 is raised to an even power, the resulting number is even, and when 6 is raised to an odd power, the resulting number is odd. This is because 6 is an even number.

In general, if a number is even, then the result obtained when it is raised to an even power is even, and the result obtained when it is raised to an odd power is odd.

If a number is odd, then the result obtained when it is raised to any power is odd. 6 raised to the power of 8 can be written as 6 raised to the power of 4 raised to the power of 2, as shown below 6 raised to the power of 8 = (6 raised to the power of 4) raised to the power of 2= 1296 raised to the power of 2= 1,675,616

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The time needed to travel 1386 miles is given as follows:

t = 33 hours.

Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

The motorist travels 210 miles in 5 hours, hence the velocity is given as follows:

v = 210/5

v = 42 miles.

Then the time needed to travel 1386 miles is given as follows:

42 = 1386/t

42t = 1386

t = 1386/42

t = 33 hours.

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Answer:

A ≈ 199.98

Step-by-step explanation:

the area (A) of Δ ABC can be calculated as

A = [tex]\frac{1}{2}[/tex] ab sinΘ ( substitute values for a, b and Θ )

  = [tex]\frac{1}{2}[/tex] × 25 × 33 × sin29°

  = 12.5 × 33 × sin29°

  ≈  199.98 ( to 2 decimal places )

Step-by-step explanation:

To calculate your monthly take-home pay, you can use the following formula:

```

Monthly take-home pay = (Regular hourly rate x 40 hours x 5 days) + (Regular hourly rate x 8 hours x 2 Saturdays x 4 weeks) x 2 - Deductions

```

Where:

- Regular hourly rate = $15.20

- Deductions = 29% of gross pay

First, let's calculate the gross pay for one month:

```

Gross pay = (Regular hourly rate x 40 hours x 5 days) + (Regular hourly rate x 8 hours x 2 Saturdays x 4 weeks) x 2

= ($15.20 x 40 x 5) + ($15.20 x 8 x 2 x 4) x 2

= $3,424

```

Next, let's calculate the deductions:

```

Deductions = Gross pay x 29%

= $3,424 x 0.29

= $992.96

```

Finally, let's calculate the monthly take-home pay:

```

Monthly take-home pay = Gross pay - Deductions

= $3,424 - $992.96

= $2,431.04

```

Therefore, your monthly take-home pay is **$2,431.04**.

The maximum number of tables the restaurant can have is 37. This ensures that the total number of people seated at the tables (37 * 4 = 148) is less than the legal limit of 150 people in the restaurant at one time.

To find the maximum number of tables the restaurant can have, we need to solve the inequality 4t < 150.

Dividing both sides of the inequality by 4, we have:

t < 150/4

Simplifying the right side, we get:

t < 37.5

Since the number of tables must be a whole number, we can conclude that the maximum number of tables the restaurant can have is 37.

Let's verify this by substituting t = 37 into the original inequality:

4t < 150

4(37) < 150

148 < 150

Since 148 is less than 150, the inequality holds true. However, if we increase the number of tables to 38, we get:

4(38) < 150

152 < 150

In this case, 152 is not less than 150, so the inequality is no longer satisfied.

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A 16 ounce bottle of spring water is $2.08. A 20 ounce bottle of fresh water is $2.40 Therefore, this statement "A 20 ounce bottle of fresh water is $2.40" is true.

To determine which statement is true, let's compare the prices of the two water bottles:

16 ounce bottle of spring water: $2.08

20 ounce bottle of fresh water: $2.40

To find the price per ounce for each water bottle, we can divide the total price by the number of ounces:

Price per ounce of spring water: $2.08 / 16 ounces = $0.13 per ounce

Price per ounce of fresh water: $2.40 / 20 ounces = $0.12 per ounce

Comparing the prices per ounce, we can see that the price per ounce of fresh water ($0.12) is less than the price per ounce of spring water ($0.13).

Therefore, the statement "A 20 ounce bottle of fresh water is $2.40" is true.

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The value of x in the similar shapes is 10

From the question, we have the following parameters that can be used in our computation:

The similar shapes

On the shapes, we have

x/20 = 5/10

Multiply through the equation by 20

So, we have

x = 20 * 5/10

Evaluate

x = 10

Hence, the value of x is 10

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The domain and the range of the function are

From the question, we have the following parameters that can be used in our computation:

The graph

The graph is a piecewise function

When combined gives an absolute function

The rule of a function is that

The domain is the set of all real numbers

This means that the input value can take all real values

However, the range is greater than the constant term

In this case, it is 0

So, the range is y > 0

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Question

The graph represents the piecewise function:

f(x) =

What is the domain and range of the function

The missing angle measurements are:

Angle G = 66.67 degrees

Angle H = 113.32 degrees

Angle Z = 66.68 degrees

Angle I = 66.68 degrees

Let's analyze the given information and solve for the missing angle measurements:

From the diagram, we can see that angle H and angle G are adjacent angles, and the line segment HG acts as a transversal. We are given that the measure of angle G is 2x, and we need to find the missing angle measurements, which are the measures of angle H, angle Z, and angle I.

Since angle G and angle H are adjacent angles, their measures add up to 180 degrees. So we can set up the equation:

2x + (4x - 20) = 180

Simplifying the equation:

6x - 20 = 180

Next, we solve for x:

6x = 200

x = 200/6

x = 33.33

Now that we have found the value of x, we can substitute it back into the original equation to find the measures of the missing angles:

Angle G = 2x = 2(33.33) = 66.67 degrees

Angle H = 4x - 20 = 4(33.33) - 20 = 133.32 - 20 = 113.32 degrees

Angle Z = 180 - Angle H = 180 - 113.32 = 66.68 degrees

Angle I = Angle Z = 66.68 degrees

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Answer:

f(g(x)) = f((x^2/3)

(x^2/3)^3

continue solving

The equivalent fractions with a denominator of 12 are

To rewrite each fraction with a denominator of 12, we need to find an equivalent fraction that has 12 as its denominator.

3/4 can be rewritten as (3/4) * (3/3) = 9/12.

5/3 can be rewritten as (5/3) * (4/4) = 20/12.

Therefore, the fractions with a denominator of 12 are:

3/4 = 9/12

5/3 = 20/12

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complete questions

Rewrite each fraction with a denominator of 12.

3/4

5/3

The volume of the rectangular prism with a length of 9m, width of 12m, and height of 5m is 540 cubic meters.

To find the volume of a rectangular prism, we multiply its length, width, and height.
Given that the length is 9m, the width is 12m, and the height is 5m, we can calculate the volume as follows:

Volume = Length x Width x Height

Substituting the given values:

Volume = 9m x 12m x 5m

To perform the multiplication, we can multiply the numerical values first and then consider the units:

Volume = (9 x 12 x 5) m³

Multiplying the numbers:

Volume = 540 m³

Therefore, the volume of the rectangular prism with a length of 9m, width of 12m, and height of 5m is 540 cubic meters.

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The relation of a line graph is visualized by drawing lines between all of the points on a grid is false.

A line graph is a type of graph that uses lines to connect data points. The points are typically plotted on a grid, but the lines do not need to connect all of the points. In fact, it is often more helpful to only connect the points that are relevant to the data that you are trying to visualize.

For example, when graphing temperature over time, there is only need to connect the points that represent the temperature at each hour. There is no need to connect the points that represent the temperature at midnight, 2am, 4am, etc.

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Complete question:

The relation of a line graph is visualized by drawing lines between all of the points on a grid. Is this true or false? Explain your answer.

The coordinates of A' and B' include the following:

A' (4, 7).

B' (10, 9).

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 2 centered at the point (6, 3) by using the following mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate A', we have;

Coordinate A' = (5, 5)  →  (2(5 - 6) + 6, 2(5 - 3) + 3)

Coordinate A' = (5, 5)  →  (2(-1) + 6, 2(2) + 3)

Coordinate A' = (5, 5)  →  (-2 + 6, 4 + 3)

Coordinate A' = (5, 5)  →  (4, 7)

For coordinate B', we have;

Coordinate B' = (8, 6)  →  (2(8 - 6) + 6, 2(6 - 3) + 3)

Coordinate B' = (5, 5)  →  (2(2) + 6, 2(3) + 3)

Coordinate B' = (5, 5)  →  (4 + 6, 6 + 3)

Coordinate B' = (5, 5)  →  (10, 9)

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Therefore, if the time is between 8:00 a.m. and 3:00 p.m., then people may make withdrawals or deposits at the bank.

This conclusion is based on the given premises that the bank is open during the time between 8:00 a.m. and 3:00 p.m. and that when the bank is open, people may make withdrawals or deposits. By combining these premises with modus ponens (a valid form of deductive reasoning), we can infer that if the time is within the bank's operating hours, then people may make withdrawals or deposits at the bank.

It will take the ball 2.12s to the nearest hundredth to hit the ground.

Quadratic formula is a formula that gives the solutions of the general quadratic equation ax² + bx + c = 0 and that is usually written in the form

x = (-b ± √(b2 − 4ac))/(2a)

From the question, the initial height, h, of the ball is 40 ft

When the ball hits the ground, the height, h, is zero

The equation h = - 16t² + 15t + 40 becomes

0 = - 16t² + 15t + 40

16t² - 15t - 40 = 0

Solving the quadratic equation by formula method for t,

t = (-b ± √(b² - 4ac)) / (2a)

Where, a = 16, b = -15, and c = -49

Substitute these values into the quadratic formula,

t = (15 ± √2785) / 32

Therefore, the possible values of t are:

t = (15 + √2785) / 32

t = (15 - √2785) / 32

Which implies t = 2.12 or t = - 1.18

Since time, t, cannot be negative, t = 2.12s to the nearest hundredth.

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The price has increased by approximately

To calculate the percentage increase, we use the following formula:

Percentage Increase = ((New Value - Old Value) / Old Value) * 100

given data:

New Value = $119

Old Value = $85

Percentage Increase = (($119 - $85) / $85) * 100

= ($34 / $85) * 100

≈ 40%

Therefore, the price has increased by approximately 40%.

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The equivalent expression to [tex]3\sqrt{6}[/tex] is given as follows:

[tex]\sqrt{54}[/tex]

Two expressions are defined as equivalent expressions when they have the same result.

The expression for this problem is given as follows:

[tex]3\sqrt{6}[/tex]

For the equivalent expression, we can move the outer term 3 inside the root, with it being squared, as follows:

[tex]3\sqrt{6} = \sqrt{3^2 \times 9} = \sqrt{54}[/tex]

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The significant numbers in 420 are 4 and 2.

Significant numbers are digits that is nonzero or, when zero, followed either by a nonzero digit or by further zeros and then a nonzero digit.

Significant numbers are digits 1 to 9

All zeros between integers are significant.

Zero’s preceding the first integers are insignificant.

Zero’s after the decimal point are significant.

Zeroes used for spacing the decimal point are not significant.

Therefore, it can be concluded that there are 2 significant numbers in 420 which are 4 and 2.

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The coordinates of C are (121/6, -47/15).Therefore, the answer is (121/6, -47/15 )Answer: (121/6, -47/15)

The given points are A (-2, 1) and B (3, 4).

We need to determine the coordinates of point C in the fourth quadrant such that m∠CAB=90° and AB=AC.

In order to determine the coordinates of point C,

The slope of ABThe slope of the line passing through A(-2, 1) and B(3, 4) is given bym = (y₂ - y₁) / (x₂ - x₁)m

= (4 - 1) / (3 - (-2))m

= 3 / 5

The mid-point of A and BMid-point of A and B is given by the following formula:

Mid-point = ((x₁ + x₂)/2, (y₁ + y₂)/2)

Mid-point of AB is: ((-2 + 3) / 2, (1 + 4) / 2)

= (1/2, 5/2)

The slope of the line perpendicular to AB

The slope of the line perpendicular to AB is given by the following formula: m₁ * m₂ = -1

Where m₁ is the slope of AB and m₂ is the slope of the line perpendicular to ABm₁ = 3 / 5m₂ = - 5 / 3 (as the line is perpendicular to AB and the product of slopes of two perpendicular lines is -1)

The mid-point and the slope of the line perpendicular to AB to find the coordinates of C

Let the coordinates of C be (x, y)We know that AC = AB and we know the coordinates of A (-2, 1) and mid-point of AB (1/2, 5/2).

Simplifying this equation, we get:

15b = 47b = 47 / 15

Substituting this value of b in the equation we got earlier:

a = (70 + 20b) / 8

= (70 + 20(47/15)) / 8

= 121 / 6

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Given statement solution is:- The statement that best explains whether the data in the table represents a linear or nonlinear function is:

The table represents a nonlinear function because the graph does not show a constant rate of change.

When x increases from -1 to 0, y changes from 2.5 to 2, which is a rate of change of -0.5. These varying rates of change indicate a nonlinear relationship between x and y.

The statement that best explains whether the data in the table represents a linear or nonlinear function is:

The table represents a nonlinear function because the graph does not show a constant rate of change.

In the given table, the values of y do not change at a constant rate as x increases or decreases. For example, when x increases from -4 to -1, y changes from 4 to 2.5, which is a rate of change of -1.5. However, when x increases from -1 to 0, y changes from 2.5 to 2, which is a rate of change of -0.5. These varying rates of change indicate a nonlinear relationship between x and y.

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We can solve for x:

20z + 16x = 360°

16x = 360° - 20z

x = (360° - 20z)/16

Quadrilateral ABCD is given with the measures of angles:

m∠A = 10z

m∠B = 8x

m∠C = 10z

m∠D = 8x

The sum of the measures of the angles of a quadrilateral is 360°:

m∠A + m∠B + m∠C + m∠D = 360°

Substituting the given angle measures:

(10z) + (8x) + (10z) + (8x) = 360°

Combine like terms:

20z + 16x = 360°

Given the equation from step 4, we can solve for x:

20z + 16x = 360°

16x = 360° - 20z

x = (360° - 20z)/16

Reasons:

Step 1: The given angles are labeled with their corresponding measures.

Step 2: The sum of the measures of the angles of a quadrilateral is a geometric property.

Step 3: Substitution of the given angle measures into the equation for the sum of angles.

Step 4: Combining like terms by adding the coefficients of z and x.

Step 5: Solving the equation for x by isolating it on one side.

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The volume of water required to fill up the tank is: 540 cm³

The formula for the volume of a cuboid is:

Volume = Length * Width * Height

Thus:

Volume of bigger tank = 15 * 15 * 12

Volume = 2700 cm³

Now, we are told that it is 4/5 filled with water.

Thus, volume needed to fill up the tank is:

¹/₅ * 2700

= 540 cm³

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Answer:

The rational zeros theorem states that all possible rational zeros of a polynomial with integer coefficients are of the form p/q, where p is a factor of the constant term, and q is a factor of the leading coefficient.

In this case, the constant term is -7 and the leading coefficient is 9. Thus, the possible rational zeros are:

p/q = ±1, ±7, ±9

Answer:

Step-by-step explanation:

The description that does NOT guarantee that a quadrilateral is a parallelogram is:

While it is true that consecutive angles in a parallelogram are supplementary (their sum is 180 degrees), the converse is not true. In other words, having consecutive angles that are supplementary does not necessarily imply that the quadrilateral is a parallelogram.

There are other types of quadrilaterals, such as trapezoids or irregular quadrilaterals, that can also have consecutive angles that are supplementary.

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Answer:

look below

Step-by-step explanation:

formula A=1/3 Bh

1/3 ×8×5×5

8x5x5=200

200/3=66.66666 round to 66.77cubic metets