Evelyn is getting older and feels like she should donate her collection of stuffed animals to children who are less fortunate. She has 18 stuffed cats and 12 stuffed dogs, which she wants to divide into identical groups, with no stuffed animals left over. What is the greatest number of groups Evelyn can place her stuffed animals into?

Answer:

The transformation from the parent function is a translation of 3 units left, a vertical stretch of scale factor 2, and a reflection in the x-axis.

Step-by-step explanation:

Given function:

[tex]\text{g}(x) = -2|x+3|[/tex]

Parent function:

[tex]\text{f}(x) = |x|[/tex]

A parent function is the simplest form of a family of functions.

The graph of g(x) is related to the graph of f(x) by a series of transformations.  To determine the series of transformations, work out the steps of how to go from f(x) to g(x).

Transformations

For a > 0

[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]

[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]

[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]

[tex]-f(x) \implies f(x) \: \textsf{reflected in the $x$-axis}[/tex]

[tex]f(-x) \implies f(x) \: \textsf{reflected in the $y$-axis}[/tex]

Step 1

Translation left by 3 units:

[tex]\implies f(x+3) =|x+3|[/tex]

Step 2

Stretch in the direction of the y-axis (vertically) with scale factor 2:

[tex]\implies 2f(x+3) =2|x+3|[/tex]

Step 3

Reflection in the x-axis:

[tex]\implies -2f(x+3) =-2|x+3|[/tex]

Conclusion

The transformation from the parent function is a translation of 3 units left, a vertical stretch of scale factor 2, and a reflection in the x-axis.

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The correct expansion of log₄√t/s is 1/2 log₄(t/s).

Logarithms is another way of writing exponents. Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only. Understanding logs is not so difficult. To understand logarithms, it is sufficient to know that a logarithmic equation is just another way of writing an exponential equation.

Logarithm and exponent are inverse forms of each other. One can understand this from the section below. Initially, a mathematician named John Napier introduced logarithms for making calculations in a simple way and this concept is quickly adopted by other scientists, engineers, etc.

Given that, log₄√t/s and we have to expand this logarithmic function having base 4 accordingly. So, let's proceed to solve this logarithmic expansion.

log₄√t/s = log₄((t/s)^(1/2))

= log₄((t/s)^(1/2))

Apply log rule, logₐ(xᵇ) = b.logₐ(x), assuming x ≥ 0

= 1/2 log₄(t/s)

Hence, log₄√t/s = 1/2 log₄(t/s) is the correct expansion.

Therefore, 1/2 log₄(t/s) is the required answer.

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When -46 decreased by the difference between -23 and -61, the number becomes -18.

Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign that is used to represent subtraction is -.

According to mathematical rules, when two negative signs are multiplied by each other, the number becomes positive.

The difference between -23 and -61: -61 - (-23)

-61 + 23 = -38

-46 - (-38)

-46 + 28 = -18

Here is the complete question:

-46 decreased by the difference between -23 and -61. What is the value of the number?

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Answer: x=0

Step by step explanation:

1/3 (9x+3) =3x+1

=3x+1=3x+1

=3x-3x=1-1

=0x=0

So x=0

I hope this helps you! Have a nice day!!!!

The required value of x using the properties of exponents and logarithm is 6.362.

What are the various properties of the logarithm?

Out of several properties of logarithms, some of the main properties are given below:

Product Rule

log (ab) = log a + log b

Change of base

log ₇ x = log x / log 7

Power Rule

log a² = 2 log a

Quotient Rule

log (a / b) = log a - log b

Solving the given equation for x

We are given a logarithmic expression: log (1 + 3x) = 3

On applying exponent both sides, we get,

e^[log (1 + 3x)] = e^3

Using the properties of exponents and logarithm, we get,

1 + 3x = 20.0855

3x = 19.0855

x = 6.362

Hence, the required value of x can be 6.362.

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Answer: f(-2) = - 4

Step-by-step explanation:

Answer: Distance point is 8.

Step-by-step explanation:

You would do 2 by the power of 2 and double that (8)

Answer:

the answer is 1

Step-by-step explanation:

trust mehhhh

The fourth point of the parallelogram is (10, -3).

What is Parallelogram?

A Parallelogram is a quadrilateral with opposite sides parallel.

Given that;

Three points of a parallelogram are (4,3), (-4,3) and (2,-3).

Now, Take Two points at one diagonal of parallelogram are (4, 3) and

(2, -3).

Let fourth point of a parallelogram is (x, y).

Take (-4,3) and (x, y) on the another diagonal of a parallelogram.

Since, Midpoint of both diagonal is same.

Hence, Midpoint of (4, 3) and (2, -3) is calculated as;

(4+2/2, 3+(-3)/2) = (6/2, 0/2) = (3, 0)

So, Midpoint of (4, 3) and (2, -3) = (3, 0)

And, Midpoint of (-4,3) and (x, y)  = (-4+x/2, 3+y/2)

Since,  Midpoint of both diagonal is same.

Hence, (-4+x/2, 3+y/2) = (3, 0)

Equating coordinates we get;

⇒-4+x/2 = 3

⇒ -4 + x = 6

⇒ x = 6 + 4

⇒ x = 10

And, 3+y/2 = 0

    ⇒3 + y = 0

    ⇒y = -3

So, The fourth point of the parallelogram is (10, -3).

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Answer: he was faster the second time

Step-by-step explanation:

1/15 is a smaller fraction and 1/12, 1/15 of an hour is 4 minutes and 1/12 of an hour is 5 minutes, so he took it in 4 minutes the second time which was quicker

Answer:15 spoonfuls

Step-by-step explanation:

Answer:

Heya, your answer would be 52 horses, and 42 chickens.

Step-by-step explanation:

By doing the long, long and I mean long process of adding 2 + 2 or 4 + 4 (due to the fact chickens have 2 legs and horses have 4), we get to 52 horse legs, and 62 chicken legs.

Adieu

Answer:

There are 9 horses and 29 chickens.

Step-by-step explanation:

a = animals

a = 38

h = horses

c = chickens

l = legs

l = 94

Equation 1: h + c = 38

Horses have 4 legs. Chickens have 2 legs.

Equation 2: 4h + 2c = 94

Manipulate the equations so that one of the coefficients are the same.

We will multiple Equation 1 by 2 so that both equations have 2c.

Equation 1: 2h + 2c = 76

Equation 2: 4h + 2c = 94

Subtract Equation 1 from Equation 2.

Equation 2 - Equation 1

(4h + 2c) - (2h + 2c) = 94 - 76

(4h - 2h) + (2c - 2c) = 94 - 76

2h = 18

h = 9

Substitute h into either equation to solve for c.

Equation 1: 2h + 2c = 76

Equation 1: 2(9) + 2c = 76

Equation 1: 18 + 2c = 76

Equation 1: 2c = 76 - 18

Equation 1: 2c = 76 - 18

Equation 1: 2c = 58

Equation 1: c = 29

Equation 2: 4h + 2c = 94

Equation 2: 4(9) + 2c = 94

Equation 2: 36 + 2c = 94

Equation 2: 2c = 94 - 36

Equation 2: 2c = 58

Equation 2: c = 29

There are 9 horses and 29 chickens.

Interest accrued at the end of the month is $1.41.

Credit cards impose interest on any sums that you don't pay by the due date each month. Interest accrues everyday when you hold a balance from month to month based on the so-called Daily Periodic Rate (DPR). DPR is only another term for your daily interest charge.

Step 1: Make the initial payment of $882 ($1,032 - $150).

Step 2: $882 times 1.00938 is $890.27

Step 3: Pay $1,032 multiplied by 1.00938 ($1,041.68) at the conclusion.

Step 4. $1,041.68 - $150= $891.68

The interest for the first month is $1.41.

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Step-by-step explanation:

500.000 evvie was on the digit card

Given that Point T is on line segment SU, T is collinear with S and U, and the numerical length of SU is 24.

Since Point T is on line segment SU, then S, T, and U are collinear.

Collinear points refers to the points that lies on the same straight line.

IF S, T, and U are collinear, then the sum of the numerical length of ST and the numerical length of TU is equal to the numerical length of SU.

ST + TU = SU

Given:

ST = 3x + 2

TU = 3x + 4

SU = 5x + 9

Substitute the expressions in the equation and solve for x.

ST + TU = SU

3x + 2 + 3x + 4 = 5x + 9

3x + 3x - 5x = 9 - 2 - 4

x = 3

Substitute the value of x in the expression for SU.

SU = 5x + 9

SU = 5(3) + 9

SU = 24

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Answer: Using a property of operations, what can you say about the sum of two expressions, Then the temperature changed more on Day 2.

Step-by-step explanation:

Using a property of operations, what can you say about the sum of the two expressions.

Let us assume the table of values is : Sunrise (F) = -11.31 -7.69

                                                              Sunset (F) = 13.49 25.25

           Day 1 and Day 2

Sunrise Temperature (F) = -11.31 -7.69         (eq-1)

Sunset Temperature (F) = 13.49 25.25        (eq-2)

The sum of the two equations are:

Sunrise Temperature (F) = -11.31 -7.69

                                    (F) = -19

Sunset Temperature (F) = 13.49+  25.25

                                   (F) = 38.74

Which day saw the greatest variation in temperature? Describe your thinking. To do this, we only compute the absolute difference in daily temperatures between the times of sunrise and sunset.

So, we can write

Day 1 = |-11.31 - 13.49|

Day 1 = 24.8

Day 2 = |-7.69 - 25.25|

Day 2 = 32.94

 So,      32.94 is greater than 24.8

 Therefore,     Day 2 is greater than the Day 1

Hence, the temperature changed more on Day 2.

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The coordinate of point C from the given expression is (2, 4)

The formula for calculating the midpoint of coordinates is given by the equation shown below:

Midpoint = {(x₁+x₂)/2, (y₁+y₂)/2}

Given the following parameters

Midpoint = M(5, 2)

B(8, 0)

Required

Coordinate point C

Substitute the given parameters

5 = (8+x₂)/2

5(2) = 8+x₂

10 = 8+x₂

x₂ = 2

Similarly

2 = (0+y₂)/2

2(2) = 0+x₂

4 = 0 +y₂

y₂ = 4

Hence the coordinate of point C from the given expression is (2, 4)

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Answer:

Rate of change in y is -6

-3-6 = -9

-9-6=-15

-15-6=-21

Rate of change in x is 1

1+1=2

2+1= 3

3+1 = 4

4-1=5

........And so on

The transformation of pentagon Q to pentagon Q' is a clockwise rotation of 180° about the origin.

A transformation is a general term for four specific ways to manipulate the shape or position of a point, a line, or a geometric figure.

We have,

Coordinates of a pentagon Q.

(2, 4), (3, 7), (7, 5), (5,4), and (4,2).

Coordinates of pentagon Q'.

(-2, -4), (-3, -7), (-7, -5), (-5,-4), and (-4,-2).

We see that the coordinates of each point of the pentagon Q have changed their position as negative coordinates in pentagon Q'

The coordinates of pentagon Q are in (x, y) which can be assumed to be in the first quadrant of the coordinate plane.

The coordinates of pentagon Q' are in (-x, -y) which is in the 3rd quadrant.

From the first quadrant to 3rd quadrant there is a rotation of 180°.

Thus the transformation of pentagon Q to pentagon Q' is a clockwise rotation of 180° about the origin.

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Answer: Graph A represents the given inequality 3y−5x>−6. Option A is correct.

From the graphs, the graph is to choose which best describes the inequality 3y−5x>−6

Step-by-step explanation: hope this helps

Graph A represents the inequality 3y - 5x≤-6. Correct option is A. The inequality 3y - 5x ≤ -6 represents a linear inequality in two variables, y and x.

To graph this inequality, we can rearrange it into slope-intercept form (y = mx + b), where m is the slope, and b is the y-intercept.

Let's rearrange the given inequality:

3y - 5x ≤ -6

First, add 5x to both sides of the inequality:

3y ≤ 5x - 6

Now, divide both sides by 3 to isolate y:

y ≤ (5/3)x - 2

Now, you have the inequality in slope-intercept form:

y ≤ (5/3)x - 2

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The percent error is 56. 9%

Percent error is defined as the difference between the estimated value and the actual value in comparison to the actual value.

The formula for percent error is expressed as;

Percent error = [tex]\frac{|VA - VE|}{VE}[/tex] × 100/1

Where;

Substitute the values

Percent error = | 612 - 390| / 390 × 100/ 1

Percent error = 222/ 390 × 100/ 1

Percent error = 0. 56 × 100

Percent error = 56. 9%

Thus, the percent error is 56. 9%

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[tex]25^{2x+1}=144[/tex] => x = 0.272, by properties of logarithm.

Given: [tex]25^{2x+1}=144[/tex]

Taking logarithm on both sides:

log ([tex]25^{2x+1}[/tex]) = log (144)

=> (2x + 1) log (25) = log (144) (As [tex]log_b(a)^m = m (log_b(a))[/tex])

=> 2x + 1 = [tex]\frac{log144}{log25}[/tex]

=> 2x + 1 = [tex]\frac{2.158}{1.397}[/tex]

=> 2x + 1 = 1.544

=> 2x = 0.544

=> x = 0.272

Hence, [tex]25^{2x+1}=144[/tex] => x = 0.272, by properties of logarithm.

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The dimensions of the drawing of the rectangular plot using the scale of 1in.:5yd is; 24 inches by 10.6 inches

We are told that the dimensions of the rectangular plot of land is 120yd x 53yd.

Now, you want to draw this rectangular plot on a scale of 1 inch : 5 yards. This means that 1 inch will represent 5 yards.

Thus, for the side of 120 yards, using the scale gives us;

1/5 * 120 = 24 inches

For the side of 53 yards, using the scale gives us;

1/5 * 53 = 10.6 inches

Thus, the dimensions of the drawing of the rectangular plot using the scale of 1in.:5yd is; 24 inches by 10.6 inches

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The total revenue the previous year is $20,000

This year the total revenue of the small  business is $14,200

This amount is 29% less than the total revenue in the previous year

Therefore the total revenue in the previous year can be calculated as follows

100 - 29

= 71

= 71/100

= 0.71

Total revenue= 14,200/0.71

= 20,000

Hence the total revenue the previous year is $20,000

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Answer:

Step-by-step explanation:

no because perenthesis

Answer:

No it is not equivalent because the parenthesis

Step-by-step explanation: When it comes to parenthesis you have to do the problem in them, so you would do 33x33 rather than the whole problem at once. no idea if that makes sense bff it sounded right in my head

For the system of equations 4 x+2 y = 4 and 6 x+2 y = 8, the solution is (2, - 2).

We are given the system of equations as:

4 x+2 y = 4    … (1)

6 x+2 y = 8    … (2)

We need to solve it to find the value of x and y.

Subtracting equation (1) form equation (2), we get that:

6 x - 4 x + 2 y - 2 y = 8 - 4

Combining the like terms, we get that:

2 x = 4

x = 4 / 2

x = 2

Now put it in equation (1) to get the value of y

4 (2) + 2 y = 4

8 + 2 y = 4

2 y = - 4

y = - 2

(x, y) = (2, - 2)

Therefore, we get that, for the system of equations 4 x+2 y = 4 and 6 x+2 y = 8, the solution is (2, - 2).

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Rollercoaster Car is at 4 m above the ground by using integer concept.

As per the question statement, Rollercoaster Car that goes above and below the ground.

Before solving the question, we need to know the concept of integer operations on a number line.

Here the car is [tex]1 meter[/tex] above the ground level and then goes 4 meter down.

So the position is [tex]1-4=-3 meter[/tex] or 3 meter below the ground level.

Now it rises 13 meter above the ground. So now the position is [tex]-3+13 = 10 meter[/tex] or 10 meter above the ground.

Now it again falls by 6 meter so position is [tex]10-6 = +4 meters[/tex] or 4 meters above the ground.

Therefore the final position is 4 meters above the ground level.

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Answer:

Step-by-step explanation:

Can somebody simplify this?

(−8) × (-6) − (−5)² =

48 - 25 =

23