Simplify this fraction 20/48

Pythagorean theorem is represented by triangle B.

In this question we find four cases of triangle, of which we must determine what triangle can be explained by Pythagorean theorem. This theorem offers a relationship between the three sides of the triangle:

r² = x² + y²

Where:

Please notice that hypotenuse is the longest side of the triangle. Graphically speaking, there is a right triangle, that is, a triangle with one right angle. Then, triangle B express the relationship according to Pythagorean theorem.

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The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

3/2

Step-by-step explanation:

Simplify the following:

((4 + 1/5)×5)/14

((4 + 1/5)×5)/14 = ((4 + 1/5)×5)/14:

((4 + 1/5)×5)/14

Put 4 + 1/5 over the common denominator 5. 4 + 1/5 = (5×4)/5 + 1/5:

(((5×4)/5 + 1/5) 5)/14

5×4 = 20:

((20/5 + 1/5)×5)/14

20/5 + 1/5 = (20 + 1)/5:

(((20 + 1)/5)×5)/14

20 + 1 = 21:

(21/5×5)/14

21/5×5 = (21×5)/5:

((21×5)/5)/14

((21×5)/5)/14 = (21×5)/(5×14):

(21×5)/(5×14)

(21×5)/(5×14) = 5/5×21/14 = 21/14:

21/14

The gcd of 21 and 14 is 7, so 21/14 = (7×3)/(7×2) = 7/7×3/2 = 3/2:

Answer:  3/2

The decimal equivalent of the largest Absolute value, 987654321, is 987,654,321.  the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.

The largest and smallest absolute values using the digits 1 to 9, we need to arrange them in a way that maximizes or minimizes the resulting number. Let's consider the boxes as placeholders for the digits.

To determine the largest absolute value:

We place the digit 9 in the leftmost box, as it is the largest digit among 1 to 9. Then we arrange the remaining digits, 8, 7, 6, 5, 4, 3, 2, and 1, from largest to smallest in the remaining boxes. This gives us the number 987654321, which is the largest possible number using the given digits. Therefore, the largest absolute value is 987654321.

To determine the smallest absolute value:

We place the digit 1 in the leftmost box, as it is the smallest digit among 1 to 9. Then we arrange the remaining digits, 2, 3, 4, 5, 6, 7, 8, and 9, from smallest to largest in the remaining boxes. This gives us the number 123456789, which is the smallest possible number using the given digits. Therefore, the smallest absolute value is 123456789.

To find the decimal equivalent of these numbers, we simply read the digits from left to right. The decimal equivalent of the largest absolute value, 987654321, is 987,654,321. The decimal equivalent of the smallest absolute value, 123456789, is 123,456,789.

Thus, the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.

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Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².

To convert the acceleration from meters per second squared (m/s²) to inches per second squared (in/s²), we need to use the conversion factor between the two units.

1 meter is equal to 39.37 inches.

To convert the units, we can set up the following conversion factor:

1 m/s² = (39.37 in/m)^2 = 1550.0031 in/s²

Now, we can multiply the given acceleration in m/s² by the conversion factor to obtain the acceleration in in/s²:

Acceleration in in/s² = 9.81 m/s² * 1550.0031 in/s²

Acceleration in in/s² ≈ 15222.7568 in/s²

Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².

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Answer:

3 1/4 ÷ 2 2/3 = 3 1/8

Answer:

The answer is 3 1/8. Hope this helps :)

Step-by-step explanation:

Answer:

y = 0.6x + 12.5

The courier service had to travel 18 miles

Step-by-step explanation:

Create an equation where y is the cost to deliver a package, and x is the number of miles traveled.

Since the service charges $0.60 per mile, the cost can be represented by $0.60x.

There is a flat rate of $12.50, so this will be added to 0.60x.

Then, set this equal to y. Using this, create an equation:

y = 0.6x + 12.5

Find how many miles the courier service had to travel by plugging in 23.30 as y, and solving for x:

y = 0.6x + 12.5

23.3 = 0.6x + 12.5

10.8 = 0.6x

18 = x

So, the courier service had to travel 18 miles.

Answer :

square of 5 is 25 .

Answer:

\(7 > \frac{u}{2} \\ 7 \times 2 > \frac{u}{2} \times 2 \\ 14 > u \\ u < 14\)

The probability that Kate chooses a two-digit number or a prime number randomly from the month of August is 7/31.

Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.

Kate is randomly choosing a date in the month of August. This date must be a two-digit number or a prime number.

The two digit prime numbers are 7(11,13,17,19,23,29,31). Thus, the probability is,

\(P=\dfrac{7}{31}\)

Hence, the probability that Kate chooses a two-digit number or a prime number randomly from the month of August is 7/31.

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The circumference of a circle with diameter 6cm is 18.85 cm.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that diameter of a circle is 6 cm.

We need to find the circumference  of circle with diameter 6 cm.

The formula to find circumference of circle=2πr

Radius=Diameter/2

=6/2=3 cm

Circumference of circle=2×3.14×3

=18.85

Hence, the circumference of a circle with diameter 6cm is 18.85 cm.

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Answer:

Step-by-step explanation:

18.8

Answer:

4 months

Step-by-step explanation:

Leslie's equation: y = 15x + 20

Rashad's equation: y = 10x + 40

you can put them both in a table or substitute each answer option for x in both equations and see when they're equal

if you substitute 4 for x, both equation equal 80

The domain of the square root function is x greater-than-or-equal-to 0, since the function is defined for all non-negative x-values or x-values greater than or equal to zero.

The domain of the square root function graphed below can be determined by looking at the x-values of the points on the graph.

From the given information, we can see that the curve starts at (0, -1) and goes through (1, -2) and (4, -3).

The x-values of these points are 0, 1, and 4.

Since the square root function is defined for any non-negative x-values or x-values more than or equal to zero, its domain is x greater-than-or-equal-to 0.

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An absolute value is the numerical value of a number without consideration of its sign. It can be represented graphically by a straight line known as a number line. Absolute value equations are equations that include absolute values of variables or unknown quantities. The following are examples of how to write an absolute value equation in the form |x-c|=d to fit the provided solution sets:

Example 1:

Solution set: {x|x≤-3 or x≥1}
Absolute value equation: |x-(-1)|=4
Explanation: -1 is the midpoint of the two ranges (-3 and 1) in the solution set. |x-(-1)|=|x+1| is the absolute value expression for the midpoint -1. The distance d from -1 to the solutions' furthest endpoints, 1 and -3, is four, hence the value of d in the absolute value equation is 4.
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F ∩ H = [4, 9)

FUH= ∞

Generally, To find the intersection of F and H, denoted as F ∩ H, we need to identify the values that are in both sets F and H.

From the definitions of F and H, we have:

F = {v | v=4 or v>4}

H = {v | v<9}

The values that are in both F and H are those that satisfy both conditions, i.e., v=4 or v>4 and v<9. This is equivalent to just the condition v=4, since any value that satisfies v<−4 will also satisfy v>4 and v<9.

Therefore, F ∩ H = {v | 4}.

In interval notation, we can write this as:

F ∩ H = [4, 9)

To find the union of F and H, denoted as F ∪ H, we need to identify all the values that are in either set F or set H or both.

From the definitions of F and H, we have:

F = {v | v=4 or v>4}

H = {v | v<9}

this denotes

F=  {v | v=4> x > ∞}

H = {v |-∞ <v<9}

FUH= ∞

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Answer:

12 x 9 (12 on the top and bottom and 9 on the sides)

Step-by-step explanation:

100 km = 2 units, or 2 boxes

450 x 2/100 = 900/100 = 9

(not sure if this would help or not)

Answer: 13.3333333333333333333333334

Step-by-step explanation:

8/300 x 500

Answer:

4.24 is the answer

Answer:

Step-by-step explanation:

To find the number that Grace thought:

We'll represent the unknown number as "x."

"Added 7": This can be represented as (x + 7).

"Multiplied by 3": This becomes 3 * (x + 7).

"Took away 5": This is represented as 3 * (x + 7) - 5.

"Divided by 4": This gives (3 * (x + 7) - 5) / 4.

"To give an answer of 7": The equation is (3 * (x + 7) - 5) / 4 = 7.

Now we can solve for x:

(3 * (x + 7) - 5) / 4 = 7

Multiply both sides by 4 to eliminate the denominator:

3 * (x + 7) - 5 = 28

Simplify the left side:

3x + 21 - 5 = 28

Combine like terms:

3x + 16 = 28

Subtract 16 from both sides:

3x = 12

Divide both sides by 3:

x = 4

Therefore, the number that Grace thought of is 4.

The simplified form of the rational expression \((7x)/(14x^6)\) is \(1/(2x^6).\)

To simplify the rational expression \((7x)/(14x^6)\), we can begin by simplifying the numerator and denominator separately.

In the numerator, 7x, we can see that both 7 and x have a common factor of 7. So, we can rewrite the numerator as 7 × x = 7x.

In the denominator, \(14x^6\), we can see that both 14 and x^6 have a common factor of \(2x^6\).

So, we can rewrite the denominator as

\(14 \times x^6 = 2 \times 7 \times x^6 = 2 \times 7x^6.\)

Now, we can simplify the rational expression by canceling out the common factors in the numerator and denominator:

\((7x)/(14x^6) = (7x)/(2 \times 7x^6) \\= (7x)/(2 \times 7 \times x^6) \\= (cross(7x))/(2 \times cross(7) \times x^6) \\= 1/(2x^6)\)

Therefore, the simplified form of the rational expression\((7x)/(14x^6)\) is \(1/(2x^6).\)

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The trigonometric identity cos a(2sec a + tan a)(sec a - 2tan a) = 2cos a - 3tan a

Trigonometric identities are equations that contain trigonometric ratios.

Given the trigonometric identity cos a(2sec a + tan a)(sec a - 2tan a) = 2cos a - 3tan a, we need to show that Left hand side (L.H.S) equals Right hand side (R.H.S). We proceed as follows

L.H.S =  cos a(2sec a + tan a)(sec a - 2tan a)

Expanding the brackets, we have that

cos a(2sec a + tan a)(sec a - 2tan a) =  cos a(2sec² a -  4tan asec a + tan a sec a - 2tan² a)

= cos a(2sec² a -  3tan a sec a - 2tan² a)

Now using the trigonometric identity 1 + tan² a = sec² a, we have that

cos a(2sec² a -  3tan a sec a - 2tan² a) = cos a(2(1 + tan² a) -  3tan a sec a - 2tan² a)

= cos a(2 + 2tan² a -  3tan a sec a - 2tan² a)

Collecting like terms in the equation, we have that

= cos a(2 + 2tan² a - 2tan² a -  3tan a sec a)

= cos a(2 + 0 -  3tan a sec a)

= cos a(2 -  3tan a sec a)

Expanding the bracket, we have that

= 2cos a -  cos a × 3tan a sec a

=  2cos a -  cos a × 3tan a/cos a  (since sec a = 1/cos a)

= 2cos a - 1 × 3tan a

= 2cos a - 3tan a

= R.H.S

So, since L.H.S = R.H.S,

cos a(2sec a + tan a)(sec a - 2tan a) = 2cos a - 3tan a

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Answer:

x

=

3

2

−

y

2

Step-by-step explanation: just write them in order sorry for how i rote it

Answer:

2

Step-by-step explanation:

7.9-5.9= 2.0 the answer would be 2

Answer:

Step-by-step explanation:

X * 3^2 +2 = 47

X * 9 + 2 = 47

9X = 47 - 2

9x = 45

x = 45 : 9

X = 5

Answer:

tobe specific, it is 53.33%, but if you want just a whole #, it is 53%

Answer:

53.33%

Step-by-step explanation:

or 53% if rounded to the nearest whole

a) Yes , the variable y varies directly with x

b) The constant of variation is k = 1/3

c) The function rule is given by the equation y = x/3

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be A

Now , the values of x are in set P = { 57 , 63 , 66 }

The values of y are in the set Q = { 19 , 21 , 22 }

a)

From the data set of P and Q , we can see that when the value of y increase the value of x also increases

Therefore , the value of variable y varies directly with x

And , y ∝ x

b)

The value of variable y varies directly with x

And , y ∝ x

So , y = kx

Substituting the value for x and y from the data set , we get

The equation will be

y = kx

19 = 57k

Divide by 57 on both sides of the equation , we get

k = 19 / 57

k = 1/3

Therefore , the constant of variation k is 1/3

c)

The function rule is given by the equation

y = kx

Substituting the value for k in the equation , we get

y = ( 1/3 ) x

y = x/3

Hence ,

a) Yes , the variable y varies directly with x

b) The constant of variation is k = 1/3

c) The function rule is given by the equation y = x/3

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Answer:

its six hundred men

Step-by-step explanation:

its Six hundred men, six hundred men under my command

With only one goal in mind

Make it back alive to our homeland

Six hundred men, six hundred miles of open sea

But the problem's not the distance

It's what lies in between

And Ithaca's waiting Ithaca's waiting

My kingdom is waiting The kingdom is waiting

Penelope's waiting for me

So full speed ahead, full speed ahead

Answer:    x=67

Step-by-step explanation:

All of the angles add up to 180 for a triangle

38 + 75 + x = 180               >combine like terms (the numbers)

113 + x = 180                       >subtract 113 from both sides

x=67

Answer:

Step-by-step explanation:

We know that,

\( \sf \: By \: Using \: Angle \: sum \: property \: of \: triangle\)

\( \large \sf \: → x +38° + 75° = 180°\)

\( \large \sf \: → x + 113 = 180°\)

\( \large \sf→ x = 180°- 113°\)

\( \boxed{\large \bf→ x = 67° }\)