How many diagonals can be drawn from one vertex of a hexagon

The scale factor used to find the dimensions of the scale drawing is 1/12. This is found by dividing the dimensions of the drawing by the dimensions of the actual flower bed, confirming both scale factors for length and width are equal.

The student is asking about determining the scale factor used to create a scale drawing from the actual dimensions of an object, which in this case is a flower bed. To find the scale factor, we compare the dimensions of the drawing with those of the actual object. For the given dimensions of the drawing, which are 3 inches by 7 inches, and the actual dimensions being 36 inches by 84 inches, we can find the scale factors for the length and width separately and confirm they are the same.

For the length, the scale factor is calculated as:
Scale factor for length = Length of drawing / Length of actual object
Scale factor for length = 3 inches / 36 inches = 1/12

For the width, the scale factor is calculated as:
Scale factor for width = Width of drawing / Width of actual object
Scale factor for width = 7 inches / 84 inches = 1/12

Thus, the scale factor for the scale drawing is 1/12. This means that each unit of measurement in the drawing represents 12 units in the actual flower bed.

We see that both of them cost equal.

(  As they are approximately of the same cost in cents)

1)

            12 oz for $ 5.28

This means that the rate of 1 oz is:

      $ 5.28/12= $ 0.44

Also we know that 1 dollar= 100 cents.

This means that:   $ 0.44= 44 cents.

Hence, cost of 1 oz is: 44  cents.

2)

                     18 oz for  $ 7.96

This means that the rate of 1 oz is:

      $ 7.96/18= $ 0.4422 cents

Also we know that 1 dollar= 100 cents.

This means that:   $ 0.4422= 44.22 cents.

Hence, cost of 1 oz is: 44  cents.

        Both are of same cost.

To find the perpendicular components of a displacement vector with a magnitude of 20 meters, use trigonometry and the Pythagorean theorem.

The question asks for the perpendicular components of a displacement vector with a magnitude of 20 meters. Perpendicular components of a vector can be determined using trigonometry. Let's assume the vector has components Ax and Ay.

Using the Pythagorean theorem, Ax^2 + Ay^2 = 20^2. Since the components are perpendicular, we can set up a right triangle and solve for the components using the sine and cosine functions. For example, if one component is Ax = 10 meters, the other component Ay can be calculated using Ay = sqrt(20^2 - 10^2) = 10*sqrt(3) meters. Similarly, if one component is Ay = 10 meters, the other component Ax can be calculated using Ax = sqrt(20^2 - 10^2) = 10*sqrt(3) meters.

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Caroline saves the amount of $180 in 12 months which is determined by the proportion of the given rate.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other. Proportions are represented by the symbols "::" or "=".

We have been given that Caroline saves $45 in 4 months.

To determine the time takes her to save $180

Let the number of months takes her to save $180 would be x

As per the given condition, we can write a proportion as

4 months : $45 = x months : $45

⇒ 4 / 45 = x / 180

Apply the cross-multiplication operation,

⇒ 4 × 180 = x × 45

⇒ 540 = 45x

⇒ x = 540 / 45

⇒ x =12

Therefore, Caroline saves the amount of $180 in 12 months.

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we know that

if two lines are perpendicular, then the product of their slopes is equal to minus one

so

[tex]m1*m2=-1[/tex]

Step 1

Find the slope of the given line

we have

[tex]3y=-4x+2[/tex]

Solve for y

Divide by [tex]3[/tex] both sides

[tex]3y/3=(-4x+2)/3[/tex]

[tex]y=-\frac{4}{3}x+ \frac{2}{3}[/tex]

the slope of the given line is [tex]m1=-\frac{4}{3}[/tex]

Step 2

Find the slope  of a line that is perpendicular to the given line

we have

[tex]m1=-\frac{4}{3}[/tex]

[tex]m1*m2=-1[/tex]

[tex]m2=-1/m1[/tex]

substitute the value of m1

[tex]m2=-1/(-4/3)=\frac{3}{4}[/tex]

therefore

the answer is

the slope is [tex]\frac{3}{4}[/tex]

The slope of a line that is perpendicular to a line of the given equation is [tex]\frac{3}{4}[/tex]

Given the following equation;

To find the slope of a line that is perpendicular to a line of the given equation:

In Mathematics, the slopes of two lines are said to be perpendicular when the product of these slopes is equal to negative one (-1).

Mathematically, this is given by:

[tex]m_1 \times m_2 = -1[/tex]   ...equation 1.

First of all, we would determine the slope of the given equation:

[tex]3y =-4x +2\\\\y = \frac{-4x}{3} + \frac{2}{3}[/tex]

Slope, [tex]m_1[/tex] = [tex]\frac{-4}{3}[/tex]

Substituting slope 1 into eqn 1, we have:

[tex]\frac{-4}{3} \times m_2 = -1\\\\-4m_2 = -3\\\\m_2 = \frac{3}{4}[/tex]

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Joe used 1/5 of the timber for the first garden and 3/8 for the second garden. After converting these fractions to have a common denominator, we found that 23/40 of the timber was used. Therefore, 17/40 of the timber remains for the third garden.

The student is asking how much of the timber remains after Joe has used some for two gardens. Joe uses 1/5 of the wood for the first garden and 3/8 for the second garden. To solve this, we first add the fractions of wood used for both gardens to find out the total used fraction:

1/5 + 3/8

To add these fractions, we first need to find a common denominator, which in this case is 40. So we convert the fractions:

8/40 + 15/40} = 23/440

Now we subtract the used fraction from the total amount of timber, which is 1:

1 - 23/40 = 40 / 40 - 23 / 40= 17 / 40

Thus, 17/40 of the wood remains for the third garden.

Answer:

8.3% or 0.083  

Step-by-step explanation:

In the question we are given that:

The original price of bed = 1200$

The price of the bed after the discount = 1100$

Money saved = The original price of bed - The price of the bed after the discount = 1200$ - 1100$ = 100$

Percentage of original price = [tex]\frac{\text{Money saved}}{\text{Original price}}\times 100[/tex] = [tex]\frac{100}{1200}\times 100[/tex] =  8.3333..%

If we want to write the answer in the form of nearest tenths, then our percentage becomes 8.3%.

The decimal expansion can be written as 0.083.

Answer:

The answer is C.

Step-by-step explanation:

I just did it and is was marked right.

The value of the variables 'x' and 'y' will be 1 and 2, respectively. Then the value of the expression y / x will be 2.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of equations is given below.

3x + 5y = 13          ...1

6x + 7y = 20        ...2

Multiply the equation 1 by -2, then we have

6x + 7y = 20            ...2

- 6x - 10y = - 26          ...3

Add both equations, then we have

- 3y = - 6

y = 2

Then the value of the variable 'x' will be given as,

3x + 5(2) = 13

3x = 3

x = 1

The value of the expression y / x will be given as,

y / x = 2 / 1

y / x = 2

The value of the variables 'x' and 'y' will be 1 and 2, respectively. Then the value of the expression y / x will be 2.

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Answer:

infinite

Step-by-step explanation:

same line

Answer: C) Yes, the figure can be rotated 180°.

Step-by-step explanation:

Here,the given figure is a rectangle, and we know that a rectangle has order of rotational symmetry of 2.

The 180° and 360° rotations will map it onto itself.

So, from the given options, the right answer is C) Yes, the figure can be rotated 180°.