Using a pencil, pair of compasses, ruler and protractor, construct a triangle with angles 71° and 36° and side between of 6cm. Measure the length of the other side adjacent to the 71° angle

Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)

9514 1404 393

Answer:

  x = 5

Step-by-step explanation:

The arc subtended by the marked angle is ...

  360° -226° = 134°

The measure of the marked angle is half this, so we have ...

  15x -8 = 134/2

  15x = 75 . . . . . . . add 8

  x = 5 . . . . . . divide by 15

Answer:

-5,0

Step-by-step explanation:

Answer: If we resolve, 10 to the power of 5 means 100,000.

Step-by-step explanation:

Answer:

,mnl.khvmfjdrykytdd7ir rvrtuy

Step-by-step explanation:

The pre-image of the point is A ( -1 , 9 )

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

Given data ,

To determine the coordinates of the pre-image point A, we need to reverse the translation by moving left 4 units and down 5 units from the image point B(3, 14).

Moving left 4 units from B(3, 14) means subtracting 4 from the x-coordinate:

x-coordinate of A = 3 - 4 = -1

Moving down 5 units from B(3, 14) means subtracting 5 from the y-coordinate:

y-coordinate of A = 14 - 5 = 9

Hence , the coordinates of the pre-image point A are (-1, 9)

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Answer:

The green room is 12 (4x3)

The yellow room is 9 (3x3)

The red room is 12 (2x6)

Step-by-step explanation:

Answer:

32 :P

Step-by-step explanation:

10x2 is 20, 6x2 is 12, and 12+20=32

The Operating income is $172,500.

To calculate the margin of safety, contribution margin ratio, and operating income, we need to use the given information.

a. Margin of Safety:

Margin of Safety = Actual Sales - Break-even Sales

Given that the break-even point is at $750,000 in sales revenue and actual sales are $1,100,000, we can calculate the margin of safety:

Margin of Safety = $1,100,000 - $750,000 = $350,000

Therefore, the margin of safety is $350,000.

b. Margin of Safety as a Percentage of Sales:

Margin of Safety Percentage = (Margin of Safety / Actual Sales) * 100

Using the values from the previous calculations:

Margin of Safety Percentage = ($350,000 / $1,100,000) * 100 = 31.82%

Therefore, the margin of safety expressed as a percentage of sales is approximately 31.82%.

c. Contribution Margin Ratio:

Contribution Margin Ratio = (Contribution Margin / Sales) * 100

To calculate the contribution margin, we need to subtract variable costs from sales:

Contribution Margin = Sales - Variable Costs = $1,100,000 - $645,000 = $455,000

Using the values, we can calculate the contribution margin ratio:

Contribution Margin Ratio = ($455,000 / $1,100,000) * 100 = 41.36%

Therefore, the contribution margin ratio is approximately 41.36%.

d. Operating Income:

Operating Income = Sales - Variable Costs - Fixed Costs

Using the values provided:

Operating Income = $1,100,000 - $645,000 - $282,500 = $172,500

Therefore, the operating income is $172,500.

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The value of m∠Q as shown in the right-angled triangle below is 62.59°.

The Formula used is:

m∠Q = cos⁻¹(s/r)........................ (1)

Where:

s = 29 m

r = 63 m

Now, Substitute these values into equation 1

m∠Q = cos⁻¹(29/63)

m∠Q = cos⁻¹(0.46)

m∠Q = 62.59°

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Answer:

11

Step-by-step explanation:

The statement about probability that is correct would be that the probability of landing on yellow is less than the probability of landing on blue. That is option B.

Probability is defined as the total number of possible outcome of an event.

The repeated colour which are numbered from 1 to 8 are as follows:

Therefore, the probability of landing on yellow is less than the probability of landing on blue because 1/4 is less than 3/8.

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Answer: B: The probability of landing on yellow is less than the probability of landing on blue.

Step-by-step explanation:

Answer:

can you explain the question better

Answer:

100x

Step-by-step explanation:

Answer: 2 times

Step-by-step explanation:

You need to move the digit to the digit of the two in the number of 3.254 then see how many times you took

The approximate area of the mulch around the merry-go-round is 126.228 feet².

Diameter of the merry go round = 10.4 feet

Radius is half of the diameter.

Radius of the merry go round = 10.4/2 = 5.2 feet

Before the piece can be installed, a solid circular pad of mulch must be put down which extends 3 feet beyond the edge of the merry-go-round.

Radius of the merry go round with mulch = 5.2 + 3 = 8.2 feet

Total area of the merry go round with the mulch is,

Area = π (8.2)² = 67.24π feet²

Area of the merry go round = π (5.2)² = 27.04π feet²

Area of the mulch = 67.24π feet² - 27.04π feet² = 40.2π = 126.228 feet²

Hence the required area is 126.228 feet².

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Applying the slope formula, the slope of the line is determined as: 2.

The slope of a line on a coordinate plane can be described as the steepness of the line, which is determined by finding the ratio of the rise of the line to the run of the line.

How to Find the Slope of a Line?

Using any two points on a line, use the formula below to find the slope of a line:

Slope (m) = y2 - y1/x2 - x1

Therefore, using, two points on the given line:

(0, -3) = (x1, y1)

(2, 1) = (x2, y2)

Plug in the values

Slope (m) = (1 -(-3))/(2 - 0)

Slope (m) = 4/2

Slope (m) = 2

Thus, applying the slope formula, the slope of the line is determined as: 2.

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From trigonometric ratio, we used the tangent of the angle to determine that the flagpole is leaning by an angle of 47.12°

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

In the question, we can assume the point of view and the flagpole makes a right angle triangle.

Since we have the opposite and adjacent, we can find the acute angle by using the tangent of the angle

tanθ = opposite / adjacent

tan θ = 14 / 13

θ = tan⁻¹(14/13)

θ = 47.12°

The flagpole is leaning with an acute angle of 47.12 degrees

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Answer:

180 gallons

Step-by-step explanation:

The smaller container has 150 gallons.

Now the large container is filled with the 4/5 of the smaller container.

So if the full volume of the small container is 150 gallons so the 4/5 of it can be calculated as, 4/5*150=120 gallons.

Answer:

hoi

Step-by-step explanation:

Answer:

35 degrees

Step-by-step explanation:

Answer:

A'O

Step-by-step explanation:

Since A' is just a 180-degree rotation around point O, it didn't change the length at all. Therefore the answer must be A'O.

Answer:

Step-by-step explanation:

To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.

Given:

y = -3a + 3

a = -5x + 1

Substituting the value of "a" in the first equation:

y = -3(-5x + 1) + 3

Now, let's simplify this expression:

y = 15x - 3 + 3

y = 15x

Therefore, y can be expressed as a function of x as:

y = 15x

Answer:

x = 0 , x = 2

Step-by-step explanation:

3x² = 6x ( subtract 6x from both sides )

3x² - 6x = 0 ← factor out 3x from each term

3x(x - 2) = 0

equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 2 = 0 ( add 2 to both sides )

x = 2

solutions are x = 0 , x = 2

Answer:

3000 - 18*x

Step-by-step explanation:

if "a certain number of minutes" = x then

water remains in the container  = 3000 - 18*x

Answer:

y = 3000 - 18x

Step-by-step explanation:

To describe the scenario of a garden watering bucket with 3000 milliliters of water and a leak of 18 milliliters per minute, we can create a function.

Let's denote the number of minutes as 'x' and the amount of water remaining in the container as 'y'. The function can be represented as:

y = 3000 - 18x

In this function, 3000 represents the initial amount of water in the container, and 18x represents the amount of water leaked after x minutes.

Therefore, the function that describes the scenario is:

Answer:

\(x\geq 7\\\)

\(x\) ∈ \([7,\) ∞ \()\)

Step-by-step explanation:

In this problem, one is given the following function,

\(f(x)=(x-7)^2\)

The problem asks one to find the interval for which the function is one-to-one and non-decreasing.

A one-to-one function is when every element in the range corresponds to every element in the range. Moreover, no element in the range will correspond to more than one element in the domain. In essence, every input pairs to only one output, and every output pairs to only one input. In a quadratic equation (an equation with a term to the second degree (exponent of (2)), half of the graph will form a one-to-one function. This is because when one has the full graph, for every output there are two inputs. However, with half of the graph, there is only one input for every output. Therefore, a function with a domain of all values less than the (x-coordinate) of the vertex will form a one-to-one function. The same conclusion can be drawn for any value greater than the (x-coordinate) of the vertex.

The given function is in vertex form. This means that one can find the vertex using the given information. The general format for the vertex form of a quadratic equation is as follows,

\(y=k(x-h)^2+k\)

Where vertex is the following,

\((h,k)\)

Applying this logic here, one can state that the vertex of the given equation (\(f(x)=(x-7)^2\)) is as follows,

\((7, 0)\)

Since the coefficient of this equation is positive (no coefficient means that it is (1)) outside of it, one can conclude that the graph of the equation is increasing after the (x) value of (7). Therefore, the function is one-to-one and increasing on the interval (\(x\geq 7\\\)).

Answer:

The answer is f−1(x)=1x13

Step-by-step explanation: hi

Answer:

The calculated t- value = 1.09 > 3.19 at 0.025 level of significance

Null hypothesis is rejected

There is sufficient evidence to support the claim that the bags are underfilled

Step-by-step explanation:

Step(i):-

Given the mean of the Population(μ)  = 419 grams

The sample size 'n' =19

Given mean of the sample x⁻ = 412

Given variance of the sample S² = 784

                                                 S = √784 = 28

Step(ii):-

Null hypothesis: H₀: There is no sufficient evidence to support the claim that the bags are underfilled.

Alternative hypothesis: H₁:

There is sufficient evidence to support the claim that the bags are underfilled.

Test statistic

                     \(t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }\)

                    \(t = \frac{412 -419}{\frac{28}{\sqrt{19} } }\)

                   t = -1.09

                 |t| = |-1.09|

Degrees of freedom   ν = n-1 = 19-1 =18

t₀.₀₂₅ =  3.19

Final answer:-

The calculated t- value = 1.09 > 3.19 at 0.025 level of significance

Null hypothesis is rejected

There is sufficient evidence to support the claim that the bags are underfilled

The measure of the missing side length x in the right triangle is 1.5.

The figure in the image is a right triangle having one of its interor angle at 90 degree.

From the diagram;

Let angle θ = 30 degree

Opposite angle θ = x

Hypotenuse = 3

To solve for the missing side length x, we use the trigonometric ratio.

Note that: sine = opposite / hypotenuse

Hence:

sin( θ ) = opposite / hypotenuse

Plug in the values:

sin( 30 ) = x / 3

x = sin( 30 ) × 3

x = 1.5

Therefore, the value of x is 1.5.

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