Student Name: davidmontague
Distributive Property Using Area
You have just used the distributive property to write these products as a sum. If drawing rectangles
helps you, feel free to use that visual aid to rewrite the following expressions as a sum. 2 points each
5
14. 8(y + 2)
16. a(a + 3)
18. 2m(m + 4)
13. 5(m-2);
15.-3(m + 4)
17. h(h-2).
19.-2(z-8)
20. -4x(x - 10)

The actual roller coaster is 204 ft tall.

Given that, the length of the model roller coaster is 4 ft and the scale factor is 1/51.

The scale factor is defined as the number or the conversion factor which is used to change the size of a figure without changing its shape. It is used to increase or decrease the size of an object.

Let the length of the actual roller coaster be x.

We know that Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Now, 1/51 = 4 / x

⇒x=204 ft

Therefore, the actual roller coaster is 204 ft tall.

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The perimeter of the regular polygon is 232

The side lengths of the regular polygon are given as

4/3x - 1/3 and x + 7

The sides of regular polygon are equal

So, we have:

4/3x - 1/3 = x + 7

Multiply both sides by 3

4x - 1 = 3x + 21

Collect like terms

4x - 3x = 1 + 21

Evaluate the like terms

x = 22

Substitute x = 22 in x + 7

Side = 22 + 7

Side = 29

The perimeter of the regular polygon is calculated as:

Perimeter = Number of sides x Side length

So, we have

Perimeter = 8 * 29

Evaluate

Perimeter = 232

Hence, the perimeter of the regular polygon is 232

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Answer:

(x^2+2x-15) units

Step-by-step explanation:

Area=LW

=(x+5)(x-3)

=x^2-3x+5x-15

(x^2+2x-15) units

After differentiating the function f(x)=3 - 2 x ², we get the result as d y / d x = - 4 x

Differentiation is a process applied to a function which finds the function's rate of change compared to the rate of change of the independent variable.

We are given the function as:

f(x)=3 - 2 x ²

We need to find d y / d x

For this we need to differentiate the function with respect to x.

Differentiating the function with respect to x, we get that:

d y / d x = ( 0 ) - 2 ( 2 x ) ( 1 )

d y / d x = 0 - 4 x

d y / d x = - 4 x

Therefore, after differentiating the function f(x)=3 - 2 x ², we get the result as d y / d x = - 4 x

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We get the length of the arc that subtends a central angle of 1 radians as 6 miles with radius as 6 miles also.

We are being asked to solve for the length of the arc of a circle.

For this, we are given that:

A radius of around 6 miles.

And a central angle that is subtended by the arc which is equal to 1 radians.

In order to solve for this, we need to use the length of the arc formula.

The formula is:

s = r θ

Where r =  is the radius

and

θ = is the subtended central angle given in radians

Now, by substituting the values in the formula, we get that:

s = 6 mi (1 rad) = 6 miles

Therefore, we get the length of the arc that subtends a central angle of 1 radians as 6 miles with radius as 6 miles also.

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Answer:

Option B. is correct.

Step-by-step explanation:

arctan(y) = tan - 1(y) = x+ kπ

for k = {...,-2,-1,0,1,2,...}

➫ e.g tan(45°) = 1

➫ and that would mean the arctangent of 1 is 45 degrees(We represent this in π/? form)

arctan(1) = tan-1(1) = 45° = -π/4

Hope this helps!

The number of columns is in the title floor before the change in layout is 10

Given that A rectangular tiled floor is composed of 70 square tiles. The rectangular floor is rearranged so that 2 tiles are removed from each columns and 4 tiles are added to each row. After the change in layout, the floor will still have 70 tiles, and still be rectangular asked to find the number of columns in  the tile floor before the change in layout.

Let's assume the number of rows is x

The number of columns will be [tex]\frac{70}{x}[/tex]

After the changing, the rows can be x+4

The number of columns will be  [tex]\frac{70}{x}[/tex]-2

The equation will be (x+4)([tex]\frac{70}{x}[/tex]-2)=70

⇒[tex]x^{2} +4x-140=0[/tex]

⇒x=10

Therefore,The number of columns is in the title floor before the change in layout is 10

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Answer:

5.

Step-by-step explanation:

5 is in the hundred thousand place because starting from the right it goes ones, tens, hundreds, thousands, then thousands, and hundred thousand meaning 5 would be in that place.

Answer: Idrissa collected 240 pennies

Step-by-step explanation:

2400/5=480

h(x) is a translation upwards of 2 units of f(x), and the new range of the function h(x) will be [2, ∞)

We know that f(x) is the parent absolute value function:

f(x) = |x|

It is transformed so we get:

h(x)=  |x| + 2

Remember that a vertical translation of N units is written as:

h(x) = f(x) + N

Then h(x) is a translation upwards of 2 units of f(x), and the new range of the function h(x) will be [2, ∞)

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Solution,

Given,

A = 39

B = 8

b = 5

A = h(B+b)

Now,

A = h(B+b)

Putting the given values,

39 = h(8+5)

or, 39 = h×13

or, 39÷13 = h

or, 3 = h

or, h = 3

Therefore,the value of h is 3

Answer: z=8

Step-by-step explanation:

5.3=z-2.7

5.3+2.7=z-2.7+2.7    ==> remove the 2.7 in 'z-2.7' to single out the variable z.

z=5.3+2.7

z=8

z = 8 ✅

Step 1:

Add 2.7 to both sides

5.3 = z - 2.7

5.3 + 2.7 = z - 2.7 + 2.7

      ⬆️                   ⬆️

Step 2:

Simplify

5.3 + 2.7 = z - 2.7 + 2.7

  ( = 8 )   ⬇️     ( = 0 )

    ⬇️     ⬇️

      8      = z

Answer:

This point would affect the mean more because the median is less sensitive to outliers.

Step-by-step explanation:

Hope this helps!

The class boundaries are:

1 58000 but less than 88,000

2 88,000 but less than 118,000

3 118,000 but less than 148,000

4 148,000 but less than 178,000

5 178,000 but less than 208,000

6 208,000 but less than 238,000

The class interval width for the distribution that we have here is given as $30000.

The six midpoints and the class boundaries are:

238,000 - 58,000= 180000

180000 / 6 = 30000

1 58000 but less than 88,000

2 88,000 but less than 118,000

3 118,000 but less than 148,000

4 148,000 but less than 178,000

5 178,000 but less than 208,000

6 208,000 but less than 238,000

238,000 - 58,000= 180000

180000 / 6 = 30000

width = 30000

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The coordinates of C' after a reflection across the line y = -2 are (3, -2).

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

Given that the verticles of ABC are A(-4,5,)B(-2,4), and C(-3,2). If ABC is reflected across the line y = - 2 to produce the image ABC, then we need to find the coordinates of the vertex C.

Let (x, y) represent the coordinate of the point C

x-coordinate value:

The line y = -2 is parallel to the x-axis, therefore the x-value will remain the same following a reflection across the x-axis.

Taking the point C' as the image of the corresponding point C(-3,2), we need that the x-coordinate of the point C' is also 3

x = 3

y-coordinate value:

The difference between the coordinate of the pre-image and the reflecting line is same as difference between the reflecting line and the coordinates of the image.

Therefore, the coordinates of the point C' is (x, y) = (3, -2)

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1. No, the set of data does not represent a function.

A function relates an input to an output. It is like a machine that has an input and an output. And the output is related somehow to the input.

We are given with (1,4), (2, 4), (3, 5), (2, 2)

This is because every output of this data does not have unique input.

4 and 2 have the same input i.e. 2.

2. Yes, the set of the data represents a function.

We are given with (10, 5), (12, 5), (7, 12), (12, 2)

It is a function as every input has a single output.

So, (10, 12, 07) are the elements of the domain and (2, 5, 7, 12) is the range of the function.

3. Yes, it is a function as every input of this data represents the single and unique output.

We are given with  (0, 0), (5, 4), (4, 5), (1, 0)

It has its unique elements and domain (0,1,4,5) and range is from (0, 1, 2, 3, 4, 5).

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Answer:  The combined amount of raisin and oatmeal cookies sold=80. Step-by-step explanation: Let x be the combined amount of raisin and oatmeal cookies sold.

Step-by-step explanation: i really hope this helps but lmk if i am wrong have a good day/night (: <3

The simplified expression represents how much Meera spends giving directions is D. 6a + 2r.

A simplified expression is a mathematical expression that has completed the mathematical operations of adding, subtracting, multiplying, and dividing with the known values.

Given a simplified expression, the work left would be to fill in the independent variables.

The total time spent answering phone calls = a

The total time spent responding to emails = r

The total time spent giving directions = 4a + 2(a + r) = 6a + 2r

Thus, we can conclude that Meera spends six times the amount she spends answering the phone and two times the time she spends responding to emails to give directions.

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Answer: the answer is C. 10.16

Step-by-step explanation: on the right each value is going up by 2.54 cm so for the forth row on the right you just need to multiply 2.54 x 4 which equals 10.16

hope this helps

8A = [tex]2^{n + 3} * 3 * 5^{m}[/tex] is  a product of powers of its prime factors of Polynomials.

What is Polynomials ?

Given -  [tex]2^{n} * 3 * 5^{m}[/tex]

The numbers 2, 3 and 5 are already prime numbers.

Multiplying 8 on both sides

8 × A = [tex]2^{n} * 3 * 5^{m} * 8[/tex]

Expressing 8 as the product of prime numbers

8A = [tex]2^{n} * 3 * 5^{m} * 2 * 2 * 2[/tex]

8A = [tex]8A = 2^{n} * 3 * 5^{m} * 2^{3}[/tex]         (When the base is same, the power is added)

Adding the power of base 2, we add n and 3

8A = [tex]2^{n + 3} * 3 * 5^{m}[/tex]

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Step-by-step explanation:

SUPPLEMENTARY because they are on a staright line and add up to 180°

[tex]76 + (2x + 4) = 180 \\ 2x + 76 + 4 = 180 \\ 2x = 180 - 76 - 4 \\ 2x = 100 \\ \frac{2x}{2} = \frac{100}{2} \\ x = 50[/tex]

x=50°

Answer:

B. SAS

Step-by-step explanation:

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

Answer:

28

Step-by-step explanation:

4 x 7 = 28

Answer:

4

Step-by-step explanation:

the coefficient is usually a constant factor for a variable.

so, the answer here is 4.

The correct scientific notation of [0.789×(10⁵)] is 78900.

As per the question statement, we are provided with a multiplication of a decimal number and an exponential number.

We are required to determine its correct scientific notation.

A decimal number, say 0.059, can be expressed as a multiplication of a decimal number and an exponential number, such as [5.9×(10)⁻²].
But in our case, after performing the multiplication of the given values, we get, [tex][0.789*10^{5}]=(\frac{789}{1000}*100000)=(789*100)=78900[/tex]

And 78900 is not a decimal value. Hence, the correct scientific notation of [0.789×(10⁵)] is 78900.

[Note: Here, we need to know the procedure to convert a decimal into a fraction, using which we converted 0.789 into [tex]\frac{789}{1000}[/tex]. First, we will need to eliminate the decimal point and consider the digits in the same order as a complete number which will be our numerator. Secondly, we will use (10ⁿ) as the denominator, where "n" is the number of digits to the right side of the decimal point in the original decimal number. Thus, 0.789 can be written as [tex]\frac{789}{1000}[/tex], as there are three digits to the right of the decimal point in 0.789]

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Answer:

414/3

Step-by-step explanation:

If she has 414 inches of ribbon and uses 3 inches for each bow then that means that you would have to divide 414 by 3 in order to find the amount of bows that Jesse could make

Answer:

Chen family used the sprinklers for 25 hours

Aoki family used the sprinklers for 40 hours

Step-by-step explanation:

Let C be the number of hours the Chen family used the sprinklers and let A be the number of hours the Aoki family used the sprinklers

Total hours used

=> C + A = 65 (1)

Total water usage for Chen family = 40C  (40 L per hour x no. hour)
Total water usage for Aoki family = 25C    (25 L per hour x no. hours)

Total used by both families = 2000 L

So
40C + 25A = 2000           (2)

Therefore we have two equations in 2 variables which can be solved simultaneously

Multiply (1) by 25:
==> 25C + 25A = 25 x 65
==> 25C + 25A = 1,625   (3)

Subtract (3) from (2) to eliminate the A term:
(2) - (3) ==>
40C + 25A - (25C + 25A ) = 2000 - 1625

40C + 25A - 25C - 25A = 375
40C - 25C = 375
15C = 375
C = 375/15

C = 25
So the Chen family used the sprinklers for 25 hours

Since C + A = 65
A = 65 - C
==> A = 65 - 25
A = 40
The Aoki family used the sprinklers for 40 hours