What is the slope of the line in the graph?A. 1 B. 2C. 0 D. -2

Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

Area = 1/2*b*h

\(1 \times 2 \times b \times h\)

The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)

To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:

1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).

2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).

3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:

\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).

4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).

This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)

This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.

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The lengths of the two legs of the right triangle are 58 and 839, in increasing order.

We have,

The formula given is incorrect.

The correct formula for Pythagorean triples with a given integer z is:

(z² - 1², 2z, z² + 1²)

Using this formula, we can find the two legs of the right triangle with hypotenuse 29 as follows:

z² + 1² = 29²

z² + 1 = 29²

z² = 29² - 1

z² = 840

z = √840

z = 28.98

Since z must be an integer, we can try integer values close to 28.98 to find one that works.

Trying z = 29,

a = z² - 1² = 840 - 1 = 839

b = 2z = 58

c = z² + 1² = 840 + 1 = 841

Therefore,

The lengths of the two legs of the right triangle are 58 and 839, in increasing order.

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The angle measure of x is 115°.

A parallelogram is a four-sided shape with two sets of parallel sides, which means that opposite sides are both parallel and have equal length. Parallelograms also have opposite angles with the same measure, and their diagonals intersect at the midpoint and bisect each other. This results in the parallelogram being divided into two triangles that are congruent. Examples of parallelograms include rectangles, squares, and rhombuses, and they are commonly used in both geometry and everyday life, particularly in the design of buildings and other structures.

We can call this figure ACDEF. Let us join CB.

Now we can see that BDEF is a parallelogram. Opposite angles of a parallelogram are equal, hence ∠DBF = ∠DEF = x°

And also consider the triangle ABC,

∠BAC = 50°

∠ABC = 180 - ∠DBF = 180° - x° (linear pair)

∠ACB = 180 - ∠ACD = 180° - x° (linear pair)

We know that all the angles of a triangle adds up to 180°.

Using this we can find x°:

∠BAC + ∠ABC + ∠ACB = 180°

50° + 180° - x° + 180° - x° = 180°

-2x° + 410 = 180°

-2x° = 180° - 410° = -230°

x° = -230/ -2

x ° = 115°

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Answer:

Step-by-step explanation:

The answer is in the attachment.

Besides this, there are more rules of trichotomy.

Answer:

Let us consider any two numbers 6 and 9 then we have the relation.

\( \gray{ \frak{9 > 6 \: \: \: or \: \: \: 6 < 9}}\)

Rule 1.

Adding 2 on both sides then;

\( \frak{ \gray{9 + 2 > 6 + 2 \: \: \: or \: \: \: 6 + 2 < 9 + 2}}\)

\(\frak{ \gray{ \therefore \: 11 > 8 \: \: \: or \: \: \: 8 < 11}}\)

Both are true for addition.

Thus,when equal number is added to both sides of trichotomy symbol,the symbol remains the same.

Rule 2.

Subtracting 2 on the both sides then,

\(\frak{ \gray{9 - 2 > 6 - 2 \: \: \: or \: \: \: 6 - 2 < 9 - 2}}\)

\(\frak{ \gray{\therefore \: 7 > 4 \: \: \: or \: \: \: 4 < 7}}\)

Both are true for subtraction.

Thus,when equal number is subtracted to both sides of trichotomy symbol,the symbol remains the same.

Rule 3.

Multiplying both sides by 2 then,

\(\frak{ \gray{9 \times 2 > 6 \times 2 \: \: \: or \: \: \: 6 \times 2 < 9 \times 2}}\)

\(\frak{ \gray{ \therefore \: 18 > 12 \: \: \: or \: \: \: 12 < 18}}\)

Both are true for multiplication by positive numbers.

But if we multiplied by -2 then there will be,

\(\frak{ \gray{ - 18 > - 12 \: \: \: or \: \: \: - 12 < - 18}}\)

These are not true.

To be true,there must be:

\(\frak{ \gray{ - 18 < - 12 \: \: \: and \: \: \: - 12 > - 18}}\)

Thus,when both sides of trichotomy symbol are multiplied by equal positive number then the symbol remains the same.When both sides of trichotomy symbols are multiplied by equal negative numbers then the symbol changes as follows:

'<' Changes to'>' and '>' Changes to'<'.

Similarly check for division then get the same result as in multiplication.

Thus,when both sides of trichotomy symbol are divided by an equal positive number, the symbol remains the same.When both sides of trichotomy symbol are divided by an equal negative number,the symbol '<' is changed to'>' or '>' is changed to'<'.

\(\boxed{\frak{\gray{BrainlyFairy}}}\)

Answer: D) 54 inches = 1 1/2 yards

explanation: 1 1/2 yards = 54 inches.

Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

The function has no hole.

Given the function expressed as:

Note that for any function to have a hole, there must be a common factor at both numerator and denominator of such function, if there is no common factor then the function has no hole.

According to the function given, you can see that there is no common factor at both the numerator and the denominator. Therefore we can conclude that the given function has no hole.

The area of the rhombus, obtained from the dimensions, of the diagonals, found from the trigonometric of sines of the angle can be presented as follows;

Area = 8·√3

The area of a plane figure is the two dimensional space occupied by the figure on a plane.

The measure of the angle ABC, m∠ABC = 60°

The length of the segment AE = 2 units

The diagonals of a rhombus bisect each other at right angles, and the right angles through which they pass, therefore;

BE = ED, m∠AEB = 90°

m∠ABE = 30°

sin(30°) = AE/AB

sin(30°) = 2/AB

AB = 2/(sin(30°)) = 4

AB = 4

BE = √(4² - 2²) = √(12) = 2·√3

Therefore; AC = 2 + 2 = 4

BD = 2·√3 + 2·√3 = 4·√3

The area of a rhombus = (1/2) × The product of the length of the diagonals

Therefore;

Area of the rhombus = (1/2) × (4·√3) × 4 = 8·√3

The area of the rhombus = 8·√3

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We need to find two relations, and use them to find the value of y when z = 15.

We will see that the value of y in that case is 4,860.

We know that y  varies inversely with the square of  x, also y  is also proportional to the cube of  z

Then we can write:

y = k/x^2

y = c*z^3

We also know that:

When x = 3, y = 80.

Replacing that in the first equation to find the value of k:

80 = k/3^2

80 = k/9

80*9 = k = 720

We also know that when x = 2, z = 5

From the first relation we have:

y = 720/2^2 = 720/4 = 180

Now we replace this in the equation of y and z:

y = c*z^3

180 = c*5^3

180 = c*125

180/125 = c = 1.44

Now we need to calculate y when z = 15, then we just need to replace z by 15 in the equation for y and z:

y = 1.44*(15)^3 = 4,860.

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a) Composite function fog(x) = 3/(x+3)

b) Domain of fog(x) in interval notation = (-∞,-3)∪(-3,∞)

A function is a process or a relation that associates each element 'a' of a set A , to a single element 'b' of another set B.

Given functions,

f(x) = x/(x+2)

g(x) = 6/x

a) (fog)(x) = f(g(x))

= f(6/x)

= (6/x)/((6/x) + 2)

= 6/x((6/x) + 2)

= 6/(6 + 2x)

= 3/(x+3)

fog(x) = 3/(x+3)

b) Domain of (fog)(x)

y = 3/(x+3)

For domain y = 0

⇒ x+3  = 0

⇒ x  = -3

But the function gets undefined for x = -3

So, Domain x ≠ -3

⇒ x > -3 or x < -3

Domain set Interval Notation : (-∞,-3)∪(-3,∞)

Hence, value of composite function

fog(x) = 3/(x + 3)

Domain of fog(x) : (-∞,-3)∪(-3,∞)

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Answer:

The probability is    \(P( \= X > 268 ) =0.35376\)

Step-by-step explanation:

From the question we are told that

   The mean is  \(\mu = 266\)

    The standard deviation is  \(\sigma = 16\)

Generally the standard error of mean is mathematically represented as

        \(\sigma_{\= x} = \frac{\sigma}{\sqrt{n} }\)

=>     \(\sigma_{\= x} = \frac{16}{\sqrt{9} }\)

=>     \(\sigma_{\= x} = 5.33\)

Generally the probability that the average pregnancy length for nine randomly chosen women exceeds 268 days is mathematically represented as

        \(P( \= X > 268 ) = P (\frac{ \= x - \mu }{ \sigma_{\= x}} > \frac{268 - 266}{5.33 } )\)

\(\frac{\= X -\mu}{\sigma_{\= x} }  =  Z (The  \ standardized \  value\  of  \ \=  X )\)  

          \(P( \= X > 268 ) = P (Z > 0.3752 )\)

From the z table  the area under the normal curve to the right  corresponding to  0.3752  is

P (Z  >  0.3752)   =    0.35376

So  

       \(P( \= X > 268 ) =0.35376\)

Answer:

6

Step-by-step explanation:

Answer:i dont know

Step-by-step explanation:

Answer: 55.2 in

Step-by-step explanation:

1ft = 12 in

41.4/9 = 4.6 ft

4.6 x 12 = 55.2 in

Answer:

\(3\sqrt{22}\)

Step-by-step explanation:

The product of roots with the same index is equal to the root of the product \(3\sqrt{11*2}\)

Multiply

The area of the circle is 254. 502 square units

The formula for area of a circle is expressed as;

Area = πr²

Where;

r is the radius of a circle

Note that the radius of a circle with an inscribed triangle is expressed as;

Radius = ABC/4A

Where;

A, B and C are the sides of the inscribed triangle

Radius = 6 × 6 × 6 / 4(6)

Radius = 216/ 24

Radius = 9 units

Now, substitute the value of the radius into the formula

Area = 3. 142 × (9)²

Area = 3. 142 × 81

Area = 254. 502 square units

Thus, the area of the circle is 254. 502 square units

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Answer:

6/5

Step-by-step explanation:

rise/run

Answer:

Step-by-step explanation:

To completely solve the problem, Karim should convert the product back into standard decimal notation.

We cannot directly apply the product of powers property because the binomial is not raised to a power itself.

(1) To convert a number from scientific notation to standard decimal notation, we multiply the coefficient (0.0258) by 10 raised to the power of the exponent (-8).

0.0258 × \(10^{-8\)  = 0.0258 × 0.00000001

                         = 0.000000000000258

(2) The product of powers property states that when you raise a term with an exponent to another exponent, you can simplify it by multiplying the exponents.

In the expression \((3z + y)^3\), we have a binomial term (3z + y) raised to the power of 3. This is not a situation where we can directly apply the product of powers property because the binomial is not raised to a power itself.

To simplify the expression, we need to expand it using the binomial theorem or by applying the concept of binomial expansion.

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Given:

Radius, r=5m

Central angle is 145 degrees.

To find the area of the sector:

The area of the sector formula is,

On substitution we get,

Hence, the area is 31.6468 sq. m.

Answer:

(x + 1 s 1) n (x + 12 1)

(x +1<1) n (x + 1 > 1)

Step-by-step explanation:

Just simplify each the statements.

Then compare and and see if the statements are contradictory and therefore FALSE, if so, then there is no solution.

(x + 1<-1) n (x + 1< 1)

(x <-2) n (x < 0) which is true, so there is a solution.

(x + 1 s 1) n (x + 12 1)

this doesn't make sense so there is no solution.

(x +1<1) n (x + 1 > 1)

(x < 0) n (x > 0)

This is not possible, the statements are contradictory and therefore FALSE, so there is no solution.

Answer:

116°

Step-by-step explanation:

You just add angle FUV and angle TUF together bc they make up the angle TUV

Answer:

116

I'm not gonna explain it but yeah it's 116

Answer:

slope = 3

Step-by-step explanation:

rise/run = 3/1 = 3

Answer:

x = 19

Step-by-step explanation:

So cos and sin are closely related, but they are not equal. In order for these two to be equal to each other, the angles (in the parenthesis by the cos and by the sin) have to be complementary. That is, they have to add up to 90°

Use this idea to set up an equation.

x + 16 + 3x - 2 = 90

Combine like terms.

4x + 14 = 90

Subtract 14.

4x = 76

Divide by 4.

x = 19

x = 19

If you are kooking for the angles:

x + 16

= 19 + 16

= 35

and

3x - 2

= 3(19) - 2

= 57 - 2

= 55

Check: 35 + 55=90

Also,

cos35 = sin55

True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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Answer:

approximately 4 Tbsp. of powdered milk to 1 cup of water

Step-by-step explanation:

Answer:

....................

The amount of water tank  with water after 10 minutes will be 4950 liters.

To solve this problem, we need to keep track of the net flow of water into the tank over the course of 10 minutes. The tap filling water adds water to the tank, while the tap emptying water removes water from the tank.

Let's calculate the net flow rate of water per minute:

Flow rate = (filling tap flow rate) - (emptying tap flow rate)

Flow rate = 40 L/min - 25 L/min

Flow rate = 15 L/min

Now, we can calculate the net flow of water over 10 minutes:

Net flow of water = (flow rate) * (time)

Net flow of water = 15 L/min * 10 min

Net flow of water = 150 L

Therefore, over the course of 10 minutes, the net flow of water into the tank is 150 liters.

Initially, the tank had 4800 liters of water. Adding the net flow of water, we can determine the final amount of water in the tank:

Final amount of water = (initial amount of water) + (net flow of water)

Final amount of water = 4800 L + 150 L

Final amount of water = 4950 L

After 10 minutes, there will be 4950 liters of water in the tank.

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