1.8.7 Check Your Understanding
Amala is copying XY.
After drawing an arc with the compass from the first point of the construction, the next step is [DROP DOWN 1].
Drop Down 1
Y
pick a point on the arc that will be the second endpoint of the new segment
Select a Value
adjust the compass width to equal the length of XY
use a straightedge to draw a line segment from the new points
pick a point on the arc that will be the second endpoint of the new segment

Simplified expression for [tex] \frac{1}{( {5n⁴})^{- 3} } [/tex] is 1/125n¹².

As per the rule of exponents, the powers will be multiplied. Representing the mentioned rule in the form of example -

[tex]( {{a}^{m} })^{n} = {{a}^{m} }^{ \times n} [/tex]

Another rule of exponent to be used in the question is : [tex] {a}^{ - x} = \frac{1}{ {a}^{x} } [/tex]

Now, simplifying the expression mentioned in question as per the above written rule.

Rewriting the equation according to second rule.

Value = [tex] \frac{1}{( {5n⁴})^{ 3} } [/tex]

Now, solving the equation by taking cube according to first rule

Value = 1/125n¹²

Thus, the simplified expression is 1/125n¹².

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The possible change in volume (in mm3) resulting from the error in measuring the radius is 32. 06 mm³

The formula for volume of a sphere is expressed by;

Volume = 4/3 πr³

Where;

From the information given, we have that the measured radius is 5 mm, with a possible measurement error of 0.1 mm

Then, radius  a = 5mm

Radius b = 5 + 0. 1 = 5. 01mm

Now, substitute the values into the formula

Volume, v = 4/ 3 (3.14)(5)³

expand the bracket

Volume, v = 4/ 3 (392.5)

Volume, v = 523. 3 mm³

For radius of 5.01mm

Volume =  4/ 3 (3.14)(5.1)³

expand the bracket

Volume = 4/3 (416.52)

Volume = 555. 4 mm³

The change in volume = 555. 4 - 523. 3 = 32. 06 mm³

Hence, the change in volume is 32. 06 mm³

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The associative property can be applied to addition and multiplication.

When more than two numbers are added together or multiplied, the outcome is always the same, regardless of how the numbers are arranged. This is known as the associative property.

For example,

2 × (7 × 6) = (2 × 7) × 6

2 + (7 + 6) = (2 + 7) + 6

Associative Addition Property

The associative feature of addition states that the total sum of the numbers will not change no matter how they are arranged. This may be stated as follows:

(x + y) + (z + y) = x

Associative Multiplication Property

The idea behind the associative property for multiplication is that no matter how the numbers are arranged, the result will always be the same. This may be stated as follows:

P = (q)/(r) = (q)/(r)

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Given expression:

[tex]7p+\frac{q}{3}[/tex]  , given that p = 6 and q = 12.

Here, we need to substitute the values of p and q in the given expression to  obtain the value of the expression.

On substitution, the expression becomes,

[tex]7X6+\frac{12}{3}[/tex]  ,

Here we use BODMAS rule ( Brackets, Orders, Division, Multiplication, Addition, Subtraction) , hence initially we do the division operation, then the multiplication operation and at last the addition operation,

= 7x6 + 4 =  42 + 4 = 46.

Hence, option D) 46 is the correct option.

These type of expressions can be solved by simply substituting the given values of the variables such as p, q and so on.

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Answer:

-21/2

Step-by-step explanation:

-5-2= - 7

7-4=3(+, - = -)

-7×3/2= - 21/2

Answer:

672 sq km

Step-by-step explanation:

Area of a regular polygon
[tex]A = \dfrac{P}{2} \times a[/tex]

P = perimeter of the polygon

a = apotherm which is defined as
The distance from the center of a regular polygon to the midpoint of a side.

The given polygon has 8 sides and each side is 12 km
So the perimeter P = 12 x 8 = 96 km

The apotherm is given as 14 km

So area
[tex]A = \dfrac{96}{2} \times 14 = 672 \text { sq km}[/tex]

Answer: your answer in in the screenshot

Step-by-step explanation:

Answer:

A goes to K. C goes to M. B goes to L.

Step-by-step explanation:

:)

Answer:

Step-by-step explanation:

13

The determined value of the number of nickels and the number of dimes that Grayson has is

This is further explained below.

Generally, The following phrase represents Jayden's complete financial worth:

Nickels are worth $0.05 each.

The dime value is equal to $0.10

The total value is equal to the sum of the values of the nickels and dimes.

where;

[tex]1.20= (0.05*2 x) +(0.1*x)[/tex]

0.1 x+0.1 x=1.2

0.2 x=1.2

[tex]x=\frac{1.2}{0.2}[/tex]

x=6

y=2

In conclusion, the Total number of dimes=6

Total number of nickels=12

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Recall that the ratio 9:8 can be written as follows:

therefore, when 64 is increased in the ratio 9:8 we get:

Answer: 72.

Answer:

72

Step-by-step explanation:

Since X : 64 = 9 : 8

Then we know X/64 = 9/8

Multiplying both sides by 64 cancels on the left64 × (X/64) = (9/8) × 64

X = (9/8) × 64Then solving for X X = 64 × (9/8)X = 72

Therefore 72 : 64 = 9 : 8

The approximate value of the expression given will be equal to -6.3.

An approximation may be defined bringing the value of a certain entity which is almost similar, but not exactly equal to the correct value. The expression can be written as −12 + √32. The value of √32 can be written as 5.656. Since, after decimal 6 to the right of 5 is greater than 5 so to the nearest tenth, we can write as 5.66. Therefore, √32 = 5.66

For the required value of the expression we can write,

−12 + √32

Putting the value of √32 = 5.66 in the expression we get

-12 + √32 = -12 + 5.66

After solving we get

⇒ -12 + √32 = -6.34

To the nearest tenth it will be -6.3.

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Answer:

$2.39, hope this helps,

Step-by-step explanation:

1.50+0.89=2.39

Answer: $2.39

Step-by-step explanation: 0.89 + 1.50

0.8 + 1.5 = 2.3

89 + 50 = 139

2.39

Seven people sharing the rent would make the cost $120 per person.

When two quantities are inversely proportional, that is, when an increase in one causes a decrease in the other and vice versa, they are said to be inversely proportional.

The general equation for inverse variation is y = k/x, where k is the proportionality constant and x and y are two variables.

Given:

The price paid by Four friends on a ski trip to share the rent of a cabin = $210

The cost per person varies inversely with the number of persons.

Let the cost be C and the number of persons be n,

C ∝ 1/n

So, the equation becomes, k = Cn.

Putting the values in the equation we obtain the value of k,

k = 210×4 = 840

We have to find the number of people sharing the rent that would make the cost $120 per person.

Using the equation,

k = Cn

840 = 120 × n

n = 840/120 = 7

Therefore, seven people sharing the rent would make the cost $120 per person.

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The number 27 is a natural number, whole number, rational, real and an integer .

The number 27

And this number is a natural number and thus it is a natural number and a rational number too.

This is also an integer .

Reason: Natural number : A natural number is one that naturally and frequently appears. It is a whole, non-negative number as a result. N, the collection of natural numbers, can be defined in one of two ways: N = {0, 1, 2, 3, ...}

whole number: the sum of all natural numbers plus zero. neither a decimal nor a fraction. {0, 2, 3, 4, 5 6, 7, 8, 9, 10, 11 …} Integer. 0, the negative, or a counting number.

Rational number: A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0. Some of the examples of rational numbers include 1/3, 2/4, 1/5, 9/3, and so on.

Real number: Rational, irrational, entire, and natural numbers are all examples of real numbers. Negative, positive, and zero numbers are all examples of integers.

Integer : An integer, pronounced is a whole number that can be positive, negative, or zero and is not a fraction.

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Answer: y = 4x-1

Step-by-step explanation:

1) Choose two points for the later equation.

For this example, I will use (-1,-5) and (2,7)

2) Place it in a rise/run equation. (y/x)

[tex]\frac{y2-y1}{x2-x1} \\\\\frac{7-(-5)}{2-(-1)} \\\\\frac{12}{3} \\\\4[/tex]

The Slope is 4.

3) Find the y-intercept

So, we can place a given point and slope into a y=mx+b function.

[tex]y=4x+b[/tex]

Next, we can substitute the point and slope.

[tex]7 = 4(2)+b\\7=8+b\\-1=b[/tex]

4) Finally, place it all in slope intercept form

y = 4x-1

Based on the price of the cell phone in November and December, the price of the cell phone in March was $39

To find the price of the cell phone in March, you need to first find the price of the cell phone in November.

The price of the cell phone in November was $25 more than the price in December:

= 25 + 53

= $78

The price in November was double the price in March so the price in March was:

= 78 / 2

= $39

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The Supplement postulate can be used to prove that the angles ∠CAB and ∠CAD are supplementary.

According to the Supplement Postulate, two angles are supplementary if they create a linear pair.

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When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative

What is the explanation?

U(2, 7) → U'(-7, 2)

V(10, 7) → V'(-7, 10)

W(2, 3) → W'(-3, 2)

Step-by-step explanation:

From the picture attached,

Coordinates of the vertices of the given triangle,

U → (2, 7)

V → (10. 7)

W → (2, 3)

Since rule for the coordinates of a point P(x, y) after a rotation of 90° counterclockwise about the origin is,

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1 2/3 divided by 4/5

= 5/3 ÷ 4/5

make common denominators:

[tex]\frac{25}{15} /\frac{12}{15}[/tex]

invert one and multiply across:

[tex]\frac{25}{15} * \frac{15}{12}[/tex]

= 375/180

reduce:

25/12 or 2 1/12

By the analysis of the graph, the constant of proportionality is 2.

By analyzing the graph given we can infer that  If five rooms are reserved, he must provide ten towels.

So x is the number booked and y is the number of towels, Then

x is directly proportional to y,

The given graph is linear in nature, as we increase x, there will be a significant increase increase in y, The constant of proportionality(k) tells us how much y will change when x changes.

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

Now, 10= k *5

        [tex]k =\frac{10}{5} \\k =2[/tex]

Hence, the constant of proportionality k is 2.

and the equation of the given graph is y = 2x

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Answer:

Your missing number is -87.5.

Step-by-step explanation:

You want to follow reverse order of operations to isolate your variable x

First, you plug in y= 700 to get::

700 = (24x)/7 +1000

Then subtract 1000 from both sides to get:

-300 = (24x)/7

Then multiply both sides by 7 to get:

-2100 = 24x

Then, divide by 24 to get:

-87.5 = x

Thus, your answer x= -87.5

The values of the following functions are:-

f(-4) = 20

f(2) = -1

f(6) = 11

f(0) = -5

Given that ,

          -3x + 8, -6 ≤ x ≤ -3

f(x) =   [tex]x^2-5[/tex],  -2 ≤ x ≤ 3

          (1/2)x + 8 , 5  ≤ x  ≤10

We have to find the values of f(-4) , f(2),  f(6) and, f(0).

As, -6 < 4 < -3

So, we will write,

f(-4) = -3(-4) + 8 = 12 + 8= 20

As, -2 < 2 < 3

So, we will write,

f(2) = [tex](2)^2-5[/tex] = 4 - 5 = -1

As, 5 < 6 < 10

So, we will write,

f(6) = (1/2)(6) + 8 = 3 + 8 = 11

As, -2 < 0 < 3

So, we will write,

f(0) = [tex](0)^2-5[/tex] = 0 - 5 = -5

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ok

MPG = 66.8

The output value of f( 38 ) in the function f( x ) = x/2 is 19.

A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.

Given the data in the question;

To determine the output value of f( 38 ), replace all the occurrence of x with 38 in the function and simplify.

f( x ) = x/2

f( 38 ) = 38/2

Divide 38 by 2

f( 38 ) = 38/2

f( 38 ) = 19

Therefore, the output value is 19, this forms an ordered pair of ( 38,19 ).

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The Item would cost if he had not used the coupon 41.05, this is the amount where he is not availing the offer percent.

Felipe has a limited time period to use the 40 percent off coupon on a single item. First, we suppose he avail the 40 percent coupon in the given mean time which is 47:17 then that single item would have cost the Felipe

According to the question, the item have cost if he had not used the coupon, so let the value of the single item is x

x × 40 % = $ 16.42

x × [tex]\frac{40}{100}[/tex] = $ 16.42

40 × x = 16.42 × 100

x =    [tex]\frac{16.42 * 100}{40}[/tex]

x = $ 41.05

The Item would cost if he had not used the coupon 41.05, this is the amount where he is not availing the offer percent.

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Answer:

A = (1, 1)

B = (3, 2)

C = (2, 4)

Step-by-step explanation:

Vertices of the triangle:

Mapping rule for a 90° clockwise rotation about the origin:

(x, y) → (y, -x)

Therefore:

Mapping rule for a reflection in the x-axis:

(x, y) → (x, -y)

Therefore:

Therefore, the coordinates of the new triangle are: