What is another name for AÉ?

The length of PR is 12cm using the Pythagorean theorem.

So, Pythagorean formula: [tex]c^{2} ={a^2+b^2}[/tex]

Now, insert the values in the formula as follows:

[tex]c^{2} ={a^2+b^2}\\37^{2} ={35^2+PR^2}\\37^{2} - 35^2={PR^2}\\PR^2 = 1369 - 1225\\PR^2 =144\\\\PR\sqrt{144} \\PR = 12\\[/tex]

Therefore, using the Pythagorean theorem the length of PR is 12cm.

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If 6 different colored tiles are available to make a pattern in a row of floor tile. The number of  possible different 4-color patterns that are possible if no colors may be repeated is: 360.

Given:

Different colored tiles=6

Different color patterns=4

There are 6 different colored tiles if one colored tiles is pick there will be 5 colored tiles, if two colored tiles is pick there will be 4 colored tiles, if  three colored tiles is pick there will be only 3 colored tiles left.

Hence,

Possible different color patterns=(6×5×4×3)

Possible different color patterns=360 ways

Therefore If 6 different colored tiles are available to make a pattern in a row of floor tile. The number of  possible different 4-color patterns that are possible if no colors may be repeated is: 360.

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If you randomly choose two cards from a thoroughly shuffled deck and if you put the first card back in the deck before you draw the second then the probability that the first card is an ace and the second card is a king is 0.59%.

The probability that the first card is an ace and the second card is a king can be calculated as follows,

Initially, divide the expected outcomes by the total possible outcomes

As a deck has a total of 52 cards, the total possible outcomes are considered to be 52

A deck consists of 4 aces and 4 king cards

Hence,

the probability that the first card is an ace = 4 / 52

the probability that the second card is a heart = 4 / 52

The probability that the first card is an ace and the second card is a heart can be determined by multiplying the probability of an ace with the probability of heart,

Probability = (4/52)(4/52)

Probability = 0.0059

Converting into percentage,

Probability = 0.0059 × 100

Probability = 0.59%

Hence the probability that the first card is an ace and the second card is a king is calculated to be 0.59%.

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Answer to this question is:

Domain of given function is [0,∞),{x|x≥0}

Range of given function is (-∞,0],{y|y≤0}

Inverse of given function is x²

The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.

This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.

When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.

Interval Notation: [0,∞)

Set-Builder Notation:{x|x≥0}

The set of all valid y values constitutes the range.

Interval Notation:(-∞,0]

Set-Builder Notation:{y|y≤0}

For calculation of inverse:

∴Domain of given function is  [0,∞),{x|x≥0}

Range of given function is (-∞,0],{y|y≤0}

Inverse of given function is x²

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When a number is 3 times a first number. A third number is 100 more than the first number and the sum of the three numbers is 450, the numbers are 70, 170 and 210.

Let the first number = x

Second number = 3x

Third number = x + 100

Sum = 450

The numbers will be:

x + 3x + x + 100 = 450

5x + 100 = 450

5x = 450 - 100

5x = 350

Divide

x = 350 / 5

x = 70

First number = 70

Second number = 3x = 3 × 70 = 210

Third number = x + 100 = 70 + 100 = 170

Therefore, the numbers are 70, 170 and 210.

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One number is 3 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 450 , find the numbers.

Salma bought 32 ounces of strawberries and the price in dollars per ounce of each strawberries is 0.45

In this question, Salma bought two pounds of strawberries for $14.40

We need to find the price, in dollars per ounce of strawberries

We know that 1 pound = 16 ounces

2 pounds of strawberries = 2 × 16 ounces of strawberries

                                          = 32 ounces of strawberries

By unitary method, the required price is,

14.40 ÷ 32 = 0.45 dollars per ounce

Therefore, Salma bought 32 ounces of strawberries and the price in dollars per ounce of each strawberries is 0.45

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Answer:

The answer is 17/9.

Step-by-step explanation:

5 2/3 = 17/3

3 = 2 3/3

17/3 / 9/3

17/3 * 3/9

= 17/9

i) y = 5x + 6

Gradient = 5 and intercept = 6

ii) y = 5 - 6x

Gradient = -6 and Intercept = 5

1)(bi)x + y = 6

Gradient = - 1 and intercept = 6

ii) 5y = 10x + 5

Gradient = 2 and Intercept = 1

iii) 6x - 10y = 2

Gradient = 0.6 and intercept = - 0.2

2)ai) 4x + y + 2 = 0

The line that depicts it is line A

ii) 4x + 2y = 8

The line that depicts it is line C

iii) 2x - 4y = 8

The line that depicts it is line B

1a) The general equation for a line in slope intercept form is;

y = mx + c

where;

m is slope or gradient

c is y-intercept

i) y = 5x + 6

Gradient = 5 and intercept = 6

ii) y = 5 - 6x

y = -6x + 5

Gradient = -6 and Intercept = 5

1)(bi)x + y = 6 can be rearranged in slope intercept form as;

y = -x + 6

Gradient = - 1 and intercept = 6

ii) 5y = 10x + 5

y = 2x + 1

Gradient = 2 and Intercept = 1

iii) 6x - 10y = 2

10y = 6x - 2

y = 0.6x - 0.2

Gradient = 0.6 and intercept = - 0.2

2)ai) 4x + y + 2 = 0

y = -4x - 2

Slope = -4 and intercept = -2 and the line that depicts it is line A

ii) 4x + 2y = 8

y = -2x + 4

Slope = -2 and intercept = 4 and the line that depicts it is line C

iii) 2x - 4y = 8

y = 0.5x - 2

Slope = 0.5 and intercept = -2 and the line that depicts it is line B

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The simplified form is = 3.53553

Simplify is to make something less complicated or much less cluttered. An instance of simplification is when you provide an explanation for a difficult math idea in truly smooth phrases for a kid to understand. An example of simplifying is whilst you chop out a whole lot of the activities that were making you busy and careworn. To turn out to be less difficult.

The phrase simplifies the approach to make something simpler to do or understand. So, by lowering or simplifying the fractions approach we make the fraction as simple as viable. We do this by dividing the numerator and the denominator via the biggest range that may divide into each number precisely.

Converting mixed numbers to an improper fraction,

[tex]5^{1}. 0.5^{1/2}[/tex]

= 5* 0.70710

= 3.53553

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The road was 9.62 miles long after rebuilding.

The road was initially 3.7 miles long

After a rebuild it was 2.6 miles as long

The new length can be calculated by multiplying the initial length which is  3.7 by 2.6

= 3.7 × 2.6

= 9.62

Hence, after the rebuild the road was  9.62 miles long

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p(rolling an 8) with one regular die if we roll the die just once is 0.

A regular die has 6 sides. One each side, a unique number is written from 1 to 6. Thus, when a regular die is rolled, the outcomes can be-

1, 2, 3, 4, 5, 6

Thus, the sample space = { 1, 2, 3, 4, 5, 6 }

The probability of getting any one of the numbers will be 1/6 as total number of outcomes are 6.

Now, we need the probability of rolling a 8.

As we can see 8 is not a value in the sample space.

Thus, P(rolling an 8) will be ⇒ 0/6 = 0. That is, 8 will never be rolled.

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The equivalent expression of the expression given as −3/4÷(−8/12) is 9/8

The expression is given as

−3/4÷(−8/12)

Rewrite the expression properly as

−3/4 ÷ (−8/12)

Express the expression as a product

So, we have

−3/4 ÷ (−8/12) = −3/4 x −12/8

Divide the common multiples

So, we have

−3/4 ÷ (−8/12) = −3/4 x −3/2

Evaluate the products

−3/4 ÷ (−8/12) = 9/8

Hence, the equivalent expression of the expression given as −3/4÷(−8/12) is 9/8

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Answer:

supplementary means the angles add upto 180 degrees. The name for 2 anglew which add upto 90 degrees is "complimentary".

The linear equation passing through (1, 4) and (6, -1) is y = -x + 5.

Linear equation can be represented in slope intercept form.

The line passes through the points (1, 4) and (6, -1).

The equation of the line can be represented as follows:

y = mx + b

where

Therefore, let's find slope using (1, 4) and (6, -1)

m = -1  - 4 / 6 - 1

m = - 5 / 5

m = -1

Therefore, let's find the y-intercept using (1, 4)

y = -x + b

4 = -1 + b

b = 4 + 1

b = 5

Therefore, the linear equation passing through (1, 4) and (6, -1) is y = -x + 5.

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Answer:

57.79

Step-by-step explanation:

Substitute: 63.5-5.71

Calculate the difference: 57.79

Answer: 57.79

Nine hundred Fifty-Six and three hundreths

900 + 50 + 6 + 3/100

956.03

900+ 50+ 6+ .03

For the pair of functions, (g⁰f)(x) is - 6 x ² - 3 x + 22 and (f ⁰g)(x) is - 18 x ² + 7 x - 5

The given questions asks to find (g⁰f)(x) and (f ⁰g)(x), that is, function of g in terms of f(x) and function of f in terms of g(x).

To find : (g⁰f)(x)

Step 1 : Write g (x)

=> g (x) = - 3x -1

Step 2 : Put f (x) in place of x in g (x)

=> g (f(x) = -3 ( 2 x ² + x - 7 ) + 1

=> g (f(x) = - 6 x ² - 3 x + 21  + 1

=> g (f(x) = - 6 x ² - 3 x + 22

=> (g⁰f)(x) = - 6 x ² - 3 x + 22

Similarly,

To find : (f ⁰g)(x)

Step 1 : Write f (x)

=> f (x) = 2 x ² + x - 7

Step 2 : Put g (x) in place of x in f (x)

=> f (g(x) = 2 ( -3 x - 1 ) ² + x - 7

=> f (g(x) = 2 - ( 9 x ² + 1 + 3 x ) + x - 7

=> f (g(x) = - 18 x ² + 2 + 6 x + x - 7

=> f (g(x) = - 18 x ² + 7 x - 5

=> (f ⁰g)(x) = - 18 x ² + 7 x - 5

Therefore, we get for the pair of functions, (g⁰f)(x) as - 6 x ² - 3 x + 22 and (f ⁰g)(x) as - 18 x ² + 7 x - 5

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The missing value of direct variation is 32

The direct variation property states that , whenever the division of values of two quantities is a constant value then there is same variation between these two corresponding values. Or we can also say that if the divisible  nature of two corresponding values is constant, then one quantity is directly varies with second quantity.

Let say if x and y are two values and k is a constant value, then

According to direct variation

k = y / x or y = k x

In the given question,

Take the order pair (4,1.5)

As it is an direct variation, we can substitute it

y=k x  

1.5 = k × 4

K=0.375

Now find the direct variation equation

y=k x

put value of 2nd pair and k in the eq.

12 = 0.375 × x

x = 32

Therefore, missing value is 32

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Answer:

Step-by-step explanation:

Answer:Of(x)=

O F¹(x) =

Of(x)=

2

4x-3

Or¹(x)=2x-3

=

2

Step-by-step explanation:

Which function below is the inverse of f(x) = 4x-3? (1 point)

Answer:

Y = - 2

Step-by-step explanation:

Answer:Vamos a convertir 420 kcal/h a una tasa de cal/min con estas tasas de conversion: Hay 60min en 1h Hay 1000cal en 1 kcal entonces 1000 x 420 = 420000 / 60 = 7000

Answer:

-15+x+11y

Step-by-step explanation:

How to Solve

-15+x-y+12y  < ------ Subtract the values -5 and -10

-15+x+11y    <  -----   Combining like terms -y−y and 12y12y

For the pair of functions, (g⁰f)(x) is 4 x ² - 7 and (f ⁰g)(x) is 16 x ² + 8 x - 1

The given questions asks to find (g⁰f)(x) and (f ⁰g)(x), that is, function of g in terms of f(x) and function of f in terms of g(x).

To find : (g⁰f)(x)

Step 1 : Write g (x)

=> g (x) = 4 x + 1

Step 2 : Put f (x) in place of x in g (x)

=> g (f(x) = 4 ( x ² - 2 ) + 1

=> g (f(x) = 4 x ² - 8 + 1

=> g (f(x) = 4 x ² - 7

=> (g⁰f)(x) = 4 x ² - 7

Similarly,

To find : (f ⁰g)(x)

Step 1 : Write f (x)

=> f (x) = x ² - 2

Step 2 : Put g (x) in place of x in f (x)

=> f (g(x) = ( 4 x + 1 ) ² - 2

=> f (g(x) = 16 x ² + 1 + 8 x -2

=> f (g(x) = 16 x ² + 8 x - 1

=> (f ⁰g)(x) = 16 x ² + 8 x - 1

Therefore, we get for the pair of functions, (g⁰f)(x) as 4 x ² - 7 and (f ⁰g)(x) as 16 x ² + 8 x - 1

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If the function be f(x) = 1.5 x² - 4 then the inverse of the function is [tex]f^{-1}[/tex](x) = 3x - 4

An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by f-1 or F-1 if the function is denoted by ' f ' or ' F '.

Let the given function be f(x) = 1.5 x² - 4

To find the inverse of the function

[tex]f^{-1}[/tex](x)

To differentiate f(x) with respect to x

[tex]f^{-1}[/tex](x) = 2x(1.5) - 4

simplifying the above equation, we get

[tex]f^{-1}[/tex](x) = 3x- 4

Therefore, the inverse of f(x) = 3x - 4

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Adding the additive inverse of B (that is, “-B” which must exist in every Vector Space . A+B-B = 0 -B A= -B

What is magnitude vector?

The magnitude of a vector is the square root of the scalar product of that vector by itself.

l A l  = [tex]\sqrt{A . A}[/tex]

l B l = [tex]\sqrt{B . B}[/tex]

l A + B l  = [tex]\sqrt{( A + B ) . ( A + B ) } = \sqrt{AA + AB + BA + BB}[/tex]

l A + B l = [tex]\sqrt{l A l^{2} + l B I ^{2} + 2 .l A l l B l cos (angle) }[/tex]

In case |A+B| = |A| + |B|

That is the same as the condition that the squares are equal.

l A + B l² = ( l A l + l B l)² =  l A l²  + l B l²  + 2|A||B|

|A||B| cos(angle)=|A||B|

|A||B|[cos(angle)−1]=0

This happens if and only if :

Either |A| or |B| or [cos(angle) - 1] must be zero.

In case |A| and |B| are not zero then cos(angle) = 1, that is : angle = 0

That means B = c*A where c is a positive constant. And, also when either A or B (or both) are the zero vector.

The second question is easier:

|A+B| = 0 implies A+B must be the zero vector.

A+B = 0

then, adding the additive inverse of B (that is, “-B” which must exist in every Vector Space)

A+B-B = 0 -B

A= -B

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Answer:

See attached graph for the rotated figure

The incorrect image point from the choices given is the first choice  T'(-3, -2). T' should have coordinates (-3, 2)

Step-by-step explanation:

When a point A(x, y) on the XY coordinate system is rotated 180° (either clockwise or anticlockwise) the coordinates of the new point A' will be (-x, -y). Thus the new coordinates will be the negative of the original coordinates

Looking at the figure and following the above rule we get the following results for original and rotated coordinates by 180°

Original Coordinates(x, y)             Rotated 180 Coordinates (-x, -y)

K(-1, -1)                                                 K'(1, 1)                          (-1 becomes 1)
P(0, -1)                                                 P'(0, 1)                           (0 stays at 0)
T(3, -2)                                                T'(-3, 2)
Q(0, -4)                                                Q'(0, 4)

To get the rotated image draw the new point coordinates and connect them