Which of the following statements are true about the right triangle? Select all that apply.

If 6 times the 6th term of an A.P is equal to 9 times the 9th term, then 15th term of the A.P. is -2d with d as the common difference.

Let's call the common difference of the arithmetic progression (A.P.) "d". The nth term of an A.P. is given by the formula T = a + (n - 1)d, where a is the first term and n is the term number.

Using this formula, we can write two expressions for the 6th and 9th terms:

T₆ = a + (6 - 1)d = a + 5d

T₉ = a + (9 - 1)d = a + 8d

According to the problem, 6 times the 6th term of the A.P. is equal to 9 times the 9th term, so we can write the following equation:

6T₆ = 9T₉

Substituting the expressions for T₆ and T₉, we get:

6(a + 5d) = 9(a + 8d)

Expanding and solving for a, we get:

6a + 30d = 9a + 72d

Subtracting 6a from both sides:

24d = 3a + 72d

Subtracting 72d from both sides:

-48d = 3a

Dividing both sides by 3:

-16d = a

So, the first term of the A.P. is -16d.

To find the 15th term, we can use the formula for the nth term:

T₁₅ = a + (15 - 1)d = -16d + 14d = -2d

So, the 15th term of the A.P. is -2d.

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Answer:

42.9

Step-by-step explanation:

tan 40 = 36/x

so x = 36/tan 40 =36/0.84 =42.9

The option that is correct is ' This polynomial could be factored by finding the GCF, then by grouping or using the perfect squares method. (optionA)

Factoring a polynomial is expressing the polynomial as a product of two or more factors; it is somewhat the reverse process of multiplying. To factor polynomials, we generally make use of the following properties or identities; along with other more techniques. Distributive Property: ab+ac=a(b+c)

To factorize the expression 2x3 + 4x2 + 2x

Let's factor out the Greatest common factor which is 2x

2x( x²+2x+1)

2x( x² +2x + 1)

Therefore the factors of 2x³ + 4x²+ 2x are 2x and x²+2x+1)

Therefore the expression can be factored by finding the GCF and then grouping or using perfect square method.

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Answer:

Step-by-step explanation:

One half ÷ 3 = 1/2 ÷ 3

To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. So,

1/2 ÷ 3 = 1/2 x 1/3 = 1/6

Therefore, one half ÷ 3 is equal to one-sixth.

Hi there, here's your answer.

Given:

A circle with center O.

A, B, C and D lie on the circumference of the circle.

AC is the diameter of the circle.

∠DCA = 33° and ∠BCA = 31°

To find:

∠DAB

Solution:

Since AC is a diameter, ∠CDA and ∠CBA will be equal to 90° (Angles in a semi-circle)

Now, ∠BCD = ∠DCA + ∠BCA

∴ ∠BCD = 33° + 31° = 64°

Now, ∠BCD + ∠CDA + ∠DAB + ∠ ABC = 360° (Angle-sum property of a quadrilateral)

Substituting the values of the angles:

64° + 90° + 90° + ∠DAB = 360°

Or

244° + ∠DAB = 360°

Therefore ∠DAB = 360° - 244° = 116°

Hope it helps!

The percentage of the ratio 13:20 is approximately 39.39%.

What is the percentage?

In mathematics, a percentage is a way of expressing a number as a fraction of 100. Percentages are often used to represent proportions, rates, or changes in quantities. The word "percent" means "per hundred," so a percentage is equivalent to the corresponding fraction multiplied by 100.

To find the percentage of a ratio, we need to convert the ratio to a fraction and then multiply by 100 to express it as a percentage.

The ratio 13:20 can be written as a fraction by dividing the first term by the sum of the terms

13 / (13 + 20) = 13/33

To express this fraction as a percentage, we multiply by 100:

(13/33) x 100 = 39.39%

The grid can be shaded as below:

Therefore, the percentage of the ratio 13:20 is approximately 39.39%.

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Answer:

4 hours

Step-by-step explanation:

By adding the x's on the graph, they practiced 2/4 + 3/4 + 3/4 + 1 + 1 hours, which is 4 hours

The graph of the first function is y = √(x - 5).

The graph of the second function is y =  |x - 1| + 4.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

The graph of the first function is f(x) = y = √x.

Now, f(x - 5) would be the same function shifter 5 units to the right,

f(x) = √(x - 5).

The graph of the second function is  a modulus function shifted up 2 units and to right by 1 unit g(x) = |x - 1| + 2 and again g(x) + 2 =  |x - 1| + 4.

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The process of simplifying square roots involves finding an equivalent expression for the square root that has smaller or more manageable numbers inside the root sign.

This can be achieved by using prime factorization, the properties of square roots, and rationalizing the denominator. The final result should be in the simplest form possible, without any radicals in the denominator, or any perfect square factors in the numerator.

A square root is a number that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 x 3 = 9. The symbol for square root is √. For example, √9 = 3.

The square root of a number can be either positive or negative, but for most purposes, the positive square root is used.

Additionally, there are also square roots of expressions, not just numbers, which can be simplified using similar methods

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The frequency tree will be:

Tree imagination attached as image below.

This question can be answered by calculating the ratio of boys to girls and the number of people with and without vouchers.

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Answer:

(i) 90°

(ii) 10 cm

Step-by-step explanation:

What is a Rhombus?

A rhombus is a special parallelogram  that has all four sides equal. But unlike a square, the angles are not right angles

Properties of a rhombus

We are given AC = 16 cm, BD = 12 cm
Using property 3, we see that

AO = CO = AB/2 = 16/2 = 8 cm

BO = DO =12/2 = 6 cm

m∠AOB = 90°  Answer (i)

(ii) Since m∠AOB  = 90°, ΔAOB is a right triangle with AB as the hypotenuse and AO, BO as the legs of the right triangle

By the Pythagorean Theorem
AB² = AO² + BO²

AB² = 8² + 6²

AB² = 64 + 36

AB² = 100

AB = √100 = 10 cm   Answer (ii)

Answer:

Step-by-step explanation:

You have a rhombus ABCD with diagonals AC = 16 cm and BD = 12 cm. You want the magnitude of central angle AOB, and the length of one side, AB.

The diagonals of a rhombus bisect each other and cross at right angle. They divide the figure into four (4) congruent right triangles.

The central angle AOB has magnitude 90°.

Each of these right triangles will have leg lengths of 6 cm and 8 cm, which you recognize as having the ratio 3 : 4. These are the leg lengths of a 3:4:5 right triangle. In this rhombus, those right triangles have lengths 6 cm : 8 cm : 10 cm. The side AB of the rhombus is 10 cm.

__

Additional comment

If you don't remember the 3-4-5 right triangle, you can use the Pythagorean theorem to find the hypotenuse of the triangle with legs 6 cm and 8 cm:

  c² = a² +b²

  c² = 6² +8² = 36 +64 = 100

  c = √100 = 10

The side AB is 10 cm long.

Answer: The cubic parent function f(x)=x^3 has been transformed to form the function g(x)=-2(x+4)^3-5 in the following ways:

Vertical scaling: The function has been vertically scaled by a factor of -2, which means that the height of the function has been multiplied by -2.

Horizontal shift: The function has been horizontally shifted 4 units to the right. This is because the expression inside the parenthesis (x+4) can be seen as shifting the graph 4 units to the right.

Vertical shift: The function has been vertically shifted down by 5 units. This is because the constant term -5 has been added to the expression, which moves the graph down by 5 units.

So, the parent function f(x)=x^3 has been transformed by a vertical scaling by -2, followed by a horizontal shift 4 units to the right, and finally a vertical shift 5 units down to form the function g(x)=-2(x+4)^3-5.

After solving the fraction answer is 4 7/12 but the Susi's answer is 5 7/1. So the Susi's answer is wrong.

The given expression is 8 1/3- 3 3/4

We first solve that expression.

We convert mixed fraction into improper fraction.

After conversion we equal the denominator of of both fraction.

Then we subtract the fraction.

After solving we check Susi's answer is right or wrong.

To convert 8 1/3 into improper fraction we multiply 8 and 3 then we add 1 in the answer of multiplication of 8 and 3.

8 1/3 = 25/3

To convert 3 3/4 into improper fraction we multiply 3 and 4 then we add 3 in the answer of multiplication of 3 and 4.

3 3/4 = 15/4

Now the expression is:

= 25/3 - 15/4

Multiply and divide by 12 on both side

= 25/3 × 12/12 - 15/4 × 12/12

= (25 × 4)/12 - (15 × 3)/12

= 100/12 - 45/12

= (100 - 45)/12

= 55/12

= 4 7/12

The simplified answer of given expression is 4 7/12 but the Susi's answer is 5 7/1. So the Susi's answer is wrong.

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The fraction in simplest form for 3/4 divided by 6 2/3 is 5/9. To get this fraction, the numerator 3/4 is multiplied by the reciprocal of 6 2/3 which is 9/6. This results in 5/9.

To solve 3/4 divided by 6 2/3, the first step is to convert 6 2/3 into an equivalent fraction with a denominator of 4. To do this, the numerator of 6 2/3 is multiplied by 4/4 which results in 25/4.  The next step is to take the reciprocal of the denominator 25/4. The reciprocal is 4/25. This can be done by flipping the numerator and denominator of 25/4. The final step is to multiply 3/4 by 4/25. The fraction in simplest form for 3/4 divided by 6 2/3 is 5/9. This results in the fraction 5/9. Therefore 3/4 divided by 6 2/3 is equal to 5/9 in simplest form.

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Five general things we get from natural resources are food, energy, raw material, medicine, leisure, recreation.

Resources refer to the materials, substances, and energy sources that exist in the environment and can be used to produce goods and services. They can be natural, such as minerals, water, forests, and wildlife, or human-made, such as technology, infrastructure, and knowledge. The term "resources" also encompasses the availability and accessibility of these materials, as well as the ability to use and manage them sustainably.

Food: Natural resources such as crops, fisheries, and livestock provide us with a source of nutrition.

Energy: Resources such as coal, oil, natural gas, and hydroelectric power are used to produce energy for heating, transportation, and other forms of electricity.

Raw Materials: Natural resources such as minerals, metals, and forests provide the raw materials needed to manufacture a wide range of products, including construction materials, electronics, and consumer goods.

Medicines: Many natural resources, such as plants and minerals, have medicinal properties that can be used to treat and prevent diseases.

Leisure and recreation: Natural resources like parks, forests, lakes, and beaches provide opportunities for outdoor recreation and leisure activities, contributing to our mental and physical well-being.

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Answer:

6(2x + 3y)

Step-by-step explanation:

             Two x plus three = 2x + 3y

      Six times of (2x + 3y) = 6 *(2x + 3y)

The trigonometric ratios for each triangles are:

Please note that all angles B are the right angle, then:

cos B = 1; sin B = 0; tan B = -

The trigonometric ratio of sin, cos, tan, can be formulated as:

(please refer to the attached triangle below for reference)

cos A = side adjacent to A / Hypotenuse

Cos A = b/c

Sin A = side opposite to A / Hypotenuse

Sin A = a/b

Tan A = Side opposite to A / Side adjacent to A

Tan A = a/b

From these formulas, we can find that:

Triangle 1

Cos A = 40/50 = 4/5

Sin A = 30/50 = 3/5

Tan A = 30/40 = 3/4

Cos C = 30/50 = 3/5

Sin C = 40/50 = 4/5

Tan C = 40/30 = 4/3

Triangle 2

Cos A = 27/45 = 3/5

Sin A = 36/45 = 4/5

Tan A = 36/27 = 4/3

Cos C = 36/45 = 4/5

Sin C = 27/45 = 3/5

Tan C= 27/36 = 3/4

Triangle 3

Cos A = 15/17

Sin A = 8/15

Tan A = 8/15

Cos C = 8/17

Sin C = 15/17

Tan C = 15/8

Please note that all angle B on the three triangles are all a right angle, then:

Cos B = 1

Sin B = 0

Tan B = -

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The equation of line in standard form and slope intercept form is,

⇒ y - 5 = - x

⇒ y = - x + 5

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, 5) and (5, 0).

Now,

Since, The equation of line passes through the points (0, 5) and (5, 0).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (0 - 5) / (5 - 0)

m = - 5 / 5

m = - 1

Thus, The equation of line with slope - 1 is,

⇒ y - 5 = - 1 (x - 0)

⇒ y - 5 = - x

⇒ y = - x + 5

Therefore, The equation of line passes through the points  (0, 5) and

(5, 0) will be;

⇒ y - 5 = - x

⇒ y = - x + 5

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y= (1/9)x + b,  plug in the point to solve for b

5= (1/9)(-4) + b

b = 5 + 4/9 = 49/9

y= (1/9)x + 49/9

9y = x + 49

The variance is 4.93 and the expected value of the number of seniors receiving the award is 10.91.

Let X represent the total number of seniors who will be honored. Using parameters n = 20 and p = 60/110, where n is the number of trials and p is the likelihood that a trial would succeed, we can represent X as a binomial random variable (i.e., a senior receiving the award).

X's anticipated value is determined by:

E(X) = np = 20 * 60/110 = 10.91

The formula for X's variance is:

Var(X) = np(1 - p) = 20 x 60 x 50 x 110 = 4.93

As a result, the variance is 4.93 and the expected value of the number of seniors receiving the award is 10.91.

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Based on the information presented, the ratio represents 8th-grade baseball players to total athletes.

A ratio is a mathematical expression that shows the proportion or the number of a specific element in a category compared to the number of another element in the same category. For example, if you count the animals on a farm the ratio of cows to chickens can be 5:7, which means that for every 5 cows there are 7 chickens.

here, we have,

What does the ratio 5:73 mean?

5 : This is the number of baseball players who are in 8th-grade

73: This is the total of players. You get this number if you add all the numbers given.

Based on this, this ratio is comparing the number of baseball players and total players, which means the meaning of this ratio is " the ratio of 8th grade baseball players to total athletes".

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Based on the information provided, it can be concluded that by 10:00 p.m. the temperature was 1°.

First, let's list the information provided:

8:00 a.m. = -3

1:00 p.m. = +14

10:00 p.m. = - 10

Based on this, let's calculate the temperature by 10:00 p.m.

-3 + 14 = 11° by 1:00 p.m.

This means the temperature at 1:00 p.m. was 11° grades. Now, let's calculate the temperature at 10:00 p.m.

11 -10 = 1° by 10:00 p.m

This means that by 10:00 p.m. the temperature was 1°.

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The most appropriate measure for the typical value of the average salary paid to nfl players is mean.

The most appropriate measure for the spread of these salaries is IQR

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply said, the mean is the average of the values in the given collection. It indicates that values in a certain data collection are distributed equally.

The three most often employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to get the mean.

The difference between the third and the first quartile is defined by the interquartile range. The partitioned values known as quartiles divide the whole series into four equally sized segments. There are so three quartiles.

The first quartile, also known as the lower quartile, is marked by Q1, the second quartile by Q2, and the third quartile, sometimes known as the upper quartile, is denoted by Q3. The lower quartile less the higher quartile equals the interquartile range.

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Answer:

Step-by-step explanation:

1/2*2cosx*sinx

= sin2x/2

The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units

We can find the intersection point between these two lines;

y = 3x - 6

y = -2x + 8

Set these two equations equal to each other.

3x - 6 = -2x + 8

5x - 6 = 8

Add 6 to both sides of the equation.

5x = 14

Divide both sides of the equation by 5.

x = 14/5  

Find the y-value where these points intersect by plugging this x-value back into either equation.

y = 3(14/5) - 6

Multiply and simplify.

y = 42/5 - 6

Multiply 6 by (5/5) to get common denominators.

y = 42/5 - 30/5  

Subtract and simplify.

y = 12/5

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

(I) 0 = 3x - 6  

Add 6 both sides of the equation.

6 = 3x

x = 2  

Set the second equation equal to 0.

(II) 0 = -2x + 8

Add 2x to both sides of the equation.

2x = 8

Divide both sides of the equation by 2.

x = 4

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

Formula for the Area of a Triangle:

A = 1/2bh

Substitute 2 for b and 14/5 for h.

A = (1/2) · (2) · (12/5)

Multiply and simplify.

A = 12/5

The area of the region is 12/5 units

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Answer: 10

Step-by-step explanation:

ex: reciprocal of 2 would be 1/2 because 2 can be written as 2/1; you just switch the demoninator and numerator

Answer: (1,2.5), (2, 3.5), (3, 4.5)

Step-by-step explanation: The question states that the frame is one and a half inches wider than the picture, so the equation would be f = p+ 1.5. Add 1.5 to each value of p to find the value of f