When Heather started a new job, her mom made this statement.

If Heather doesn't put money into a savings account each month, then Heather won't be able to take a vacation next summer.

The length of side AB rounded to 3 significant figures is 8.86 cm.

The figure on the image is a right triangle.

From the image;

using the trigonometric ratio, we determine the length of side AB.

Sine = Opposite / Hypotenuse

sin( 41 ) = AB / 13.5

AB = sin( 41 ) × 13.5

AB = 8.86 cm

Therefore, the side AB has a length of 8.86 cm.

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The equation for the line that passes through the points (-6,-9) and (2,3) is y = 3x/2 - 6..

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Based on the information provided, we can logically deduce the following data points on the line:

At point (-6, -9), a linear equation of this line can be calculated in slope-intercept form as follows:

y + 9 = (3 + 9)/(2 + 6)(x + 6)

y = 12/8(x + 2) - 9

y = 3/2(x + 2) - 9

y = 3x/2 - 6.

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Answer:

x= -13

Step-by-step explanation:

10-7x=101

-10      -10

_________

-7x=91

/-7   /-7

_________

x=    -13

The values of x in the circles and secant lines are 7 in all cases

To calculate x, we make use of the intersecting secant line theorem which stated that

a * c = b * d

Using the above as a guide, we have the following:

Shape (7)

4 * (4 + 2x) =3 * (3x + 1)

This gives

16 + 8x = 9x + 9

Collect and evaluate the like terms

x = 7

Shape (8)

20 * (20 + x) = 15 * (15 + 3x)

This gives

400 + 20x = 225 + 45x

Collect and evaluate the like terms

x = 7

Shape (9)

6 * (6 + 4) = 5 * (5 + x)

This gives

60 = 25 + 5x

Collect and evaluate the like terms

x = 7

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Answer:

3/7 + 1/3 = 1621 ≅ 0.7619048

Spelled result in words is sixteen twenty-firsts.

Step-by-step explanation:

Answer:

7/21

Step-by-step explanation:

The variance is the correct option of property of Poisson distribution.

The Poisson distribution has the property that its mean is equal to its variance. This means that the average number of occurrences, represented by λ, is equal to the spread of the distribution.

The Poisson probability is calculated as P (x, λ) = (e^-λ * λ^x) / x! where e is approximately equal to 2.71828. The mean, represented as E(X), is equal to the variance, V(X). In a Poisson distribution, λ is the expected value of the distribution.

When certain conditions are met, there is a table available to make calculating probabilities easier using the Poisson distribution.

In Poisson distribution, the mean is known as E(X) = λ.

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The transformation will be R(T(ABC )), A" ( 1, 1), B"(1, 6) and C"(-3, 2).

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

R(x, y) = (–x, –y) and T(x, y) = (x + 5, y + 1).

The coordinates are A (–4, –2), B (–6, –7), and C (–2, –3).

So, After the T rule the coordinates will be

A' ( -1, -1), B'(-1, -6) and C'(3, -2).

Also, the transformation will be R(T(ABC )),

A" ( 1, 1), B"(1, 6) and C"(-3, 2).

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Considering the distributive property, the factored expression is given as follows:

3/4(x + 3).

The expression for this problem is defined as follows:

3/4x + 9/4.

The common factor to both terms of the expression is given as follows:

3/4, as 3 x 3/4 = 9/4.

Hence the factored expression is given as follows:

3/4(x + 3).

Applying the distributive property, multiplying the outer term 3/4 by both of the inner terms and combining them, we go back to the original expression.

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The justification of each step in solving the system of equations is below;

5x - y = 3

x + 2y = 5

multiply equation (1) by 2 (Multiplication Property of Equality)

10x - 2y = 6

x + 2y = 5

Add both equations (Addition Property of Equality)

11x = 11

divide both sides by 11

x = 1

Substitute x = 1 into (Substitution Property of Equality)

5x - y = 3

5(1) - y = 3

5 - y = 3

-y = 3 - 5

-y = -2

y = 2

Hence, the steps involved in solving the equation are; Multiplication Property of Equality, Addition Property of Equality, Substitution Property of Equality.

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Answer:

I'm not an expert, but I would choose option A

The area of the prism A before dilation is 75 m²

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

Given that, a triangular prism B is the image of triangular prism A after dilation by a scale factor of 1/5, the surface area of triangular prism B is 3 m²,

Since, the dilation transformation gives similar figures,

We know that, in solids that are similar, the ratio of their surface areas is equal to the square of the ratio of their scale factor.

Let the area of Prism A be x,

Therefore,

(1/5)² = 3/x

x = 75

Hence, the area of the prism A before dilation is 75 m²

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The rational functions that have an oblique asymptote are:

are:

f(x) = x^2 + 1/X

f(x) =4x^2 - 6/x + 1

f(x) =x^5/x^3 +1

f(x) =x² +2/ x^2+ 3x

The concept that will be used here is finding the function one after the other.

The first function:

f(x) = x^2 + 1/X

The degree of numerator is seen to be 2, which can be considered to be  is greater than the degree of denominator which is one, the, we can consider this function as oblique asymptote.

Second function:

f(x) =4x^2 - 6/x + 1

The degree of numerator which can be seen to be 2 is greater than the degree of denominator which is 1 and can be considered as  an oblique asymptote.

Third function:

f(x) =-x/x^2

The degree of numerator can be seen as 1 which can be considered to be less than the degree of denominator which is 2, and we can not considere this as  an oblique asymptote.

The fourth function:

f(x) =x^5/x^3 +1

The degree of numerator can be seen as 5 which can be considered to begreater than the degree of denominator which is 3 and this  function can be considered to be an oblique asymptote.

Fifth option:

f(x) =x² +2/ x^2+ 3x

The degree of numerator can be seen as 3 which can be considerd to be  greater than the highest degree of denominator which is seen as 2 and can be considered to be  oblique asymptote.

Therefore, the 1st, 2nd, 4th, and 5th options are correct.

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missing options:

f(x) = x^2 + 1/X

f(x) =4x^2 - 6/x + 1

f(x) =-x/x^2

f(x) =x^5/x^3 +1

f(x) =x² +2/ x^2+ 3x

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{Original equation: }\large\boxed{\rm{2x = -12}}[/tex]

[tex]\large\text{Divide 2 to both sides:}[/tex]

[tex]\large\boxed{\rm{\dfrac{2x}{2}= \dfrac{-12}{2}}}[/tex]

[tex]\large\text{Cancel out: }\boxed{\rm{\dfrac{2}{{2}}}}\large\text{ because it give you 1.}[/tex]

[tex]\large\text{Keep: }\large\boxed{\rm{\dfrac{-12}{2}}}\large\text{ because it give you the x-value.}[/tex]

[tex]\large\boxed{\rm{x = \dfrac{-12}{2}}}[/tex]

[tex]\large\boxed{\rm{x =-6}}[/tex]

[tex]\huge\text{Therefore, your answer should be:}\\\\\\\huge\boxed{\mathsf{x = -6}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

190

Step-by-step explanation:

For every one of the 20 people, they shake hands with 19 others.

However, if A shakes hands with B, we double count because B shakes hands with A. Therefore we do 20*19/2 = 190.

If the schoolyard is 114 centimeters wide in the drawing, then the actual schoolyard is 57 meters wide.

In mathematics, a scale refers to the relationship between the size of an object in a drawing or model compared to its actual size in the real world. Scales are often expressed as ratios, where the first number represents the size in the drawing or model and the second number represents the actual size.

The scale used in the drawing is 2 centimeters to 1 meter, which means that for every 2 centimeters in the drawing, there is 1 meter in the actual schoolyard. To find the actual width of the schoolyard, we need to divide the width in the drawing by the scale factor:

114 centimeters / 2 centimeters/meter = 57 meters

Therefore, the actual schoolyard is 57 meters wide.

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The following information of each of the following arithmetic series is shown below:

Case 15

f(1) = 3, Common difference: 5, f(n) = 3 + 5 · (n - 1), f(20) = 98

Case 16

f(1) = 28, Common difference: - 6, f(n) = 28 - 6 · (n - 1), f(20) = - 86

Case 17

f(1) = 37, Common difference: - 10, f(n) = 37 - 10 · (n - 1), f(20) = - 153

Case 18

f(1) = - 8, Common difference: 9, f(n) = - 8 + 9 · (n - 1), f(20) = 163

In this problem we find six cases of arithmetic series, that is, set of numbers generated by a linear expression of the form:

f(n) = a + d · (n - 1)

Where:

The common difference of any arithmetic series is the difference between two consecutive elements of the series.

Now we proceed to determine the find the explicit formula for each arithmetic series:

Case 15

First value: 3

Common difference: 8 - 3 = 5

Explicit expression: f(n) = 3 + 5 · (n - 1)

Value of the 20th term of the arithmetic series: f(20) = 3 + 5 · (20 - 1) = 98

Case 16

First value: 28

Common difference: 22 - 28 = - 6

Explicit expression: f(n) = 28 - 6 · (n - 1)

Value of the 20th term of the arithmetic series: f(20) = 28 - 6 · (20 - 1) = - 86

Case 17

First value: 37

Common difference: 27 - 37 = - 10

Explicit expression: f(n) = 37 - 10 · (n - 1)

Value of the 20th term of the arithmetic series: f(20) = 37 - 10 · (20 - 1) = - 153

Case 18

First value: - 8

Common difference: 1 - (- 8) = 9

Explicit expression: f(n) = - 8 + 9 · (n - 1)

Value of the 20th term of the arithmetic series: f(20) = - 8 + 9 · (20 - 1) = 163

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Answer:

The first table is linear.  The other are not linear.

Step-by-step explanation:

See the attached graph. The tables should have a constant rate of change between the numbers.  The first table have value of y that are related to -3x (the value of y shifts by -3 for each 1 increase in x.  The other tables don't have predictable rate of change.

The number of robberies in Colorado Springs per year is a ratio variable is 1/2

Ratio variables are a type of continuous variable in which the values have a meaningful order and can be compared in terms of their size.

In terms of mathematical expression, the number of robberies in Colorado Springs per year can be represented by the variable x.

The value of x can range from 0 to infinity, with 0 implying the absence of robberies and any value greater than 0 representing the number of robberies that have occurred. The mathematical expression for this ratio variable would be:

=> x = number of robberies in Colorado Springs per year.

Where the value of 4 and 2, then it can be written as,

=> 2/4 = 1/2

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Answer:

(x + 10)/4 = 7

Step-by-step explanation:

Break the sentence into segments:

let the number be x

Answer:

the graph of an exponential function f(x) = bx approaches , but does not cross the x-axis.

the x-axis is a horizontal asymptote

The percentage change in the price of coffee is 10%.

The price of coffee at the dining common last year = $2.00

The price of coffee at the dining common current year = $2.20

To know the change in the price of the coffee from last year to the current year's price we can do subtraction.

So, the change in price = $2.20 - $2.00.

To convert the difference into a percentage divide the difference by the actual price and then multiply by 100

(($2.20 - $2.00) / $2.00) * 100% = 10%

So, the percentage change in the price of coffee is 10%

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Note that the amount of kinetic energy an object has directly depends upon the object's mass and velocity. (Option B and D)

Kinetic energy is the energy an object possesses due to its motion. It is calculated as the product of the object's mass and its velocity squared, thus the more massive an object is and the faster it moves, the more kinetic energy it has.

Factors such as density and shape do not affect an object's kinetic energy directly. Velocity is, in essence, a vector quantity. It is the pace at which distance changes. It is the displacement rate of change. A moving object's speed can never be negative. A moving object's velocity can be zero.

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Full Question:

Select each correct answer.

If an object is moving, the amount of kinetic energy it has directly depends upon which of the following factors?

the object's density

the object's mass

the object's shape

the object's velocity

Answer:

22.3 x 1.8 = 40.14

Step-by-step explanation:

22.3

x  1.8  

________

1784

2230

________

40.14

Answer:

40.14

Step-by-step explanation:

22.3

× 1.8  ← Forget about the decimal places and multiply by the one's place.

1 7 8 4

2 2 3 0 ← Put a 0 to hold the one's place and multiply 223 by ten's place.

4 0 . 1 4 ← Add those 2 numbers and keep 2 decimal places.

The results of the exponent expressions are;

5) 8

6) 125

7) 1

8) 1

9) 1/36

10) 1

11) 1/16

12) -27

13) 5 1/4

14) 1/243

15) 1/125

We know that the laws of exponents are also called the laws of indices these are the laws that can be used when we are trying to sort out a mathematical problem that involves the expoennets.

In this case we can see that we can use the laws of the exponents to determine the simple values of each of the expressions as we have been able to show above and then know what then value of the exponent is.

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The ladder reaches up to a height of 2√209 feet.

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

From the given information, we can form a right angled triangle, with the hypotenuse being equal to 30 foot and base equal to 8 feet.

We have to find the altitude.

Using Pythagoras theorem,

Altitude² = Hypotenuse² - Base²

              = 30² - 8²

              = 900 - 64

              = 836

Altitude = √836 = 2√209 feet

Hence the height on the building that the ladder reaches is 2√209 feet.

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Answer: 30

Step-by-step explanation: If you divide your area (1800) by 60 you'll get your width which is 30. To check your answer you can multiply 30 by 60 and you will get 1800.

The sum of two numbers is 13 more than twice the first number. Their difference is 14 less than twice the second number. Then each of these numbers are 1/2 and 13 1/2.

Create equations from statements

Suppose: x = the first number

                y = the second number

x + y = 2x + 13

⇔ y + x - 2x = 13

⇔ y - x = 13

⇔ y = x + 13    ... (1)

y - x = 2y - 14

⇔ y - 2y - x = -14

⇔ -y - x = -14  ... (2)

Solve the system of equations

-y - x = -14

- (x + 13) - x = -14

-x - 13 - x = -14

-2x = -1

  x = 1/2

y = x + 13

y = 1/2 + 13

y = 13 1/2

So, each of these numbers are 1/2 and 13 1/2.

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Answer:

Step-by-step explanation:

Oscar needs to ship 24 rock CDs,and 56 pop CDs. He can pack only one type of CD in each box, and he must pack the same number of CDs in each box. What is the greatest number of CDs Oscar can pack in each box?