Identify each function or situation as an example of exponential growth or decay. What is the y -intercept?

a. y=3(4x)

Answer:

cos (-1 • 0^2) = 1

Step-by-step explanation:

Plug in the value x=0

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:

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

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 angle of ∠FEG is 58 degrees

The angle DEF is a right angle.

Therefore,

∠DEF = 90°

Hence,

∠FEG + ∠GED = ∠DEF

∠FEG  = 5x - 22

∠GED = 2x

∠DEF = 5x - 22 + 2x

90 = 5x + 2x - 22

90  = 7x - 22

90 + 22 = 7x

112 = 7x

divide both sides by 7

x = 112 / 7

x = 16

∠FEG  = 5x - 22

∠FEG  = 5(16) - 22

∠FEG  = 80 - 22

∠FEG  = 58°

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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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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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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.

The surface area of the triangular prism is 136 cm square.

The surface area of a triangular prism can be found as follows;

Therefore,

surface area of a triangular prism = (perimeter of the triangle × height of prism) + (2 × base area)

Hence,

perimeter of the triangle = 5 + 5 + 6

perimeter of the triangle = 16 cm

height of prism = 7 cm

base area = 1 / 2 bh

base area =  1 / 2 × 4 × 6

base area = 24 / 2

base area = 12 cm²

Therefore,

surface area of a triangular prism = (16 × 7) + (2 × 12)

surface area of a triangular prism = 112 + 24

surface area of a triangular prism = 136 cm²

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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:

4.35

Step-by-step explanation:

Answer:

4.35 kilo

Step-by-step explanation:

The translation rule that maps ABC to  A'B'C' is (x, y) ⇒ (x + 3, y + 6)

Transformation is the movement of a point around the coordinate plane. Types of transformations are rotation, translation, reflection and dilation.

Translation is the movement of a point either up, down, left or right in the coordinate plane.

The translation rule that maps triangle ABC to angle A'B'C' is (x, y) ⇒ (x + 3, y + 6)

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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)

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 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:

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

Answer:

Y = - 2

Step-by-step explanation:

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

Nine hundred Fifty-Six and three hundreths

900 + 50 + 6 + 3/100

956.03

900+ 50+ 6+ .03

Answer:

P [tex]\leq[/tex] 6

Step-by-step explanation:

Set up Equation:

17.50 + 36.25(p) [tex]\leq[/tex] 235

Simplify Expression to Solve for how many people can go the park, using inverse operations.

36.25(p) [tex]\leq[/tex] 235 - (17.50)

36.25(p) [tex]\leq[/tex] 217.5

p [tex]\leq[/tex] 217.5/36.25

p [tex]\leq[/tex] 6

Therefore, no more than six people can attend the amusement park.

Answer:

Distributive property is the answer

Expression as a single natural logarithm is 2.48490664979.

ln 3+ ln 4

ln (3×4)

ln(12) =2.48490664979

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

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The nine thousand one hundred ninety-one in number form is 9191

nine thousand one hundred ninety-one in number form is written as

9000+100+90+1=9191

Numbers may be represented in language with range phrases. more universally, person numbers may be represented through symbols, called numerals;

for example, "five" is a numeral that represents the wide variety five. As handiest a fairly small wide variety of symbols may be memorized, primary numerals are commonly organized in a numeral system, which is an organized way to represent any quantity.

The maximum commonplace numeral device is the Hindu–Arabic numeral machine, which allows for the illustration of any quantity the use of a mixture of ten fundamental numeric symbols, called digits

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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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Answer:

57.79

Step-by-step explanation:

Substitute: 63.5-5.71

Calculate the difference: 57.79

Answer: 57.79

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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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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Answer:

Step-by-step explanation:

Answer:

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