Parallelograms partner challenge

Step-by-step explanation:

Given that , the scale on map is 1 : 320000.

Its means that if the scale shows 1 unit  then actual length is 320000 units

So If the  shows 1  cm then the actual distance = 320000 cm

                                                                              =[tex]\frac{320000}{100000}[/tex] km = 3. 2 km

Answer:

48.5 gal/min

Step-by-step explanation:

I used a ratio to solve this problem.

If 97 gallons flow in 2 minutes, the ratio is 97/2

To find the flow per one minute, the ratio is x/1

You can then cross multiply to get 97=2x

When solved, this gives you 48.5 gal/min.

To check, you can multiply x2.

The wheel covered 785 feet in one complete turn

Solution:

Given that, The first Ferris wheel was built in 1893 in Chicago

Diameter of wheel = 250 feet

Let us find the radius of wheel

[tex]Radius = \frac{diameter}{2}\\\\Radius = \frac{250}{2}\\\\Radius = 125[/tex]

Thus radius of wheel is 125 feet

We have to find the distance covered in one complete turn

The number of feet the wheel rotated in one turn is equal to its circumference

The circumference of circle is given as:

[tex]C = 2 \pi r[/tex]

Where, "r" is the radius and [tex]\pi[/tex] is a constant equal to 3.14

Substituting the values we get,

[tex]C = 2 \times 3.14 \times 125\\\\C = 785[/tex]

Thus the wheel covered 785 feet in one complete turn

Answer:

B

Step-by-step explanation:

Substitute the value of (2,1) into the equations, and you find that only B works.

Answer:

d) 1998 to 2000

Step-by-step explanation:

Consumer price index (CPI) is an economic indicator that shows the average change in prices of items, goods and services. Basically, if CPI is increasing over a period of time that means that there is inflation, and if it decreases that means that there is deflation (lowering of prices).

Now, looking at our table, we see that:

- 1992-1994: CPI increased from 44.3 to 58.2 -> inflation

- 1994-1996: CPI increased from 58.2 to 65.9 -> inflation

- 1996-1998: CPI increased from 65.9 to 70.4 -> inflation

- 1998-2000: CPI decreased from 70.4 to 69.1 -> deflation

Answer:

The correct answer is D. 1998 to 2000

Step-by-step explanation:

Answer:

I believe the answer to this question is: 1 x 10^21 equal to 1000000000000000000000.

Answer:5y+5

Step-by-step explanation:

2+y+y+y+y+y+3

Collect like terms

y+y+y+y+y+3+2

5y+5

Answer:

[tex]y = f(x) = \frac{1}{5}x + 1[/tex]

Step-by-step explanation:

The function notation of a linear function is given by y = f(x) = ax + b.

Now, the given equation is - x + 5y = 5

So, we have to arrange it for the function notation.

Now, - x + 5y = 5

⇒ 5y = x + 5

⇒ [tex]y = \frac{1}{5}(x + 5)[/tex]

⇒ [tex]y = \frac{1}{5}x + 1[/tex]

Therefore, the function notation of the given equation will be

[tex]y = f(x) = \frac{1}{5}x + 1[/tex] (Answer)

Answer:

answer is c i did the test

Step-by-step explanation:

Answer:

A function and its inverse

Step-by-step explanation:

The property (fg)(x)= x holds for a function and its inverse.

For instance:

Let

[tex]f(x) = 2x[/tex]

and

[tex]g(x) = \frac{x}{2} [/tex]

These two functions are inverse of each other.

[tex]f(g(x)) = 2( \frac{x}{2} ) = x[/tex]

The correct pair is B: [tex]\(f(x)=\frac{2}{x}\) and \(g(x)=\frac{2}{c}\)[/tex], satisfying [tex]\((f \circ g)(x)=x\).[/tex]

To find which pairs of functions satisfy the condition [tex]\((f \circ g)(x) = x\),[/tex] let's compute [tex]\(f(g(x))\)[/tex] for each pair of functions and see if it equals [tex]\(x\).[/tex]

A. [tex]\(f(x) = x^2\) and \(g(x) = \frac{1}{x}\):[/tex]

[tex]\[f(g(x)) = f\left(\frac{1}{x}\right) = \left(\frac{1}{x}\right)^2 = \frac{1}{x^2}\][/tex]

[tex]\(f(g(x)) \neq x\),[/tex] so option A is not correct.

B. [tex]\(f(x) = \frac{2}{x}\) and \(g(x) = \frac{2}{c}\):[/tex]

[tex]\[f(g(x)) = f\left(\frac{2}{c}\right) = \frac{2}{\frac{2}{c}} = c\][/tex]

[tex]\(f(g(x)) = x\)[/tex] if [tex]\(c = x\).[/tex] So, option B is correct.

C. [tex]\(f(x) = \frac{x - 2}{3}\) and \(g(x) = 2 - 3x\):[/tex]

[tex]\[f(g(x)) = f(2 - 3x) = \frac{(2 - 3x) - 2}{3} = \frac{-3x}{3} = -x\][/tex]

[tex]\(f(g(x)) \neq x\)[/tex], so option C is not correct.

D. [tex]\(f(x) = \frac{1}{2x - 2}\) and \(g(x) = \frac{1}{2x + 2}\):[/tex]

[tex]\[f(g(x)) = f\left(\frac{1}{2x + 2}\right) = \frac{1}{2\left(\frac{1}{2x + 2}\right) - 2}\][/tex]

[tex]\[= \frac{1}{\frac{1}{x + 1} - 2}\][/tex]

[tex]\[= \frac{1}{\frac{1 - 2(x + 1)}{x + 1}}\][/tex]

[tex]\[= \frac{1}{\frac{-2x - 1}{x + 1}}\][/tex]

[tex]\[= \frac{x + 1}{-2x - 1}\][/tex]

[tex]\(f(g(x))\)[/tex] does not simplify to [tex]\(x\)[/tex], so option D is not correct.

Thus, the correct answer is option B: [tex]\(f(x) = \frac{2}{x}\) and \(g(x) = \frac{2}{c}\).[/tex]

Complete Question:

For which pairs of functions is (fg)(x)=x?

A. f(x)=x^2 and g(x)=1/x

B.f(x)=2/x and g(x)=2/c

C. f(x)=x-2/3 and g(x)=2-3x

D. f(x)=1/2x-2 and g(x)=1/2x+2

Answer:

Step-by-step explanation:

The amount of simple interest is ...

  I = Prt = $218·0.06·7 = $91.56

The total account balance is this amount added to the original deposit:

  $218.00 + 91.56 = $309.56

Answer:

Total cost of painting the pyramid including the base = 19,200

Total cost of painting the pyramid excluding the base = 12,000

Step-by-step explanation:

Data provided in the question:

Height of the doll = 8 cm

Slant height of the pyramid, s = 5 cm

Base dimensions = 6 × 6

Cost of painting = 200 per cm²

Now,

Area of the base = 6 × 6 = 36 cm²

Area of the Pyramid = Area of the base + [tex]\frac{1}{2} \times P\times s[/tex]

here,

P is the perimeter of the base = 4 × side

= 4 × 6

= 24 cm

Thus,

Area of the Pyramid = 36 + [tex]\frac{1}{2} \times24\times 5[/tex]

or

Area of the Pyramid = 36 + 60 = 96 cm²

Total cost of painting the pyramid including the base = 96 cm² × 200

= 19,200

Total cost of painting the pyramid excluding the base = 60 cm² × 200

= 12,000

The probability that John will practice his trombone is 34%.

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Given that,

If it rains ​tomorrow, the probability is 0.9. If it does not rain ​tomorrow, there is only a 0.5 chance. And, the chance of rain tomorrow is 70​%.

Calculation of probability:

= 0.9 (0.1) + 0.5 (0.5)

= 0.34

= 34%

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The probability that John will practice his trombone is 0.7 or 70%, calculated using the law of total probability considering the two scenarios of snow and no snow.

To calculate the probability that John will practice his trombone, we need to consider two scenarios: one where it snows and one where it does not. We can solve this by using the law of total probability.

Let's denote the probabilities as follows:
P(Snow) is the probability it will snow, which is given as 0.5.
P(Practice|Snow) is the probability John will practice given that it snows, which is 0.9.
P(Practice|No Snow) is the probability John will practice given that it does not snow, which is 0.5.

The total probability that John will practice is:

P(Practice) = P(Snow) * P(Practice|Snow) + P(No Snow) * P(Practice|No Snow)
          = 0.5 * 0.9 + 0.5 * 0.5
          = 0.45 + 0.25
          = 0.7

Therefore, the probability that John will practice his trombone is 0.7 or 70%.

Answer:

16.75

Step-by-step explanation:

7.5+9.25=16.75

Line up the digits and use traditional algorithm.

Final answer:

To find the difference between 83456 and 728.88, subtract the second number from the first, resulting in the answer 82727.12.

Explanation:

To find the difference between the two numbers 83456 and 728.88, we simply subtract the second number from the first:

Write the numbers in a vertical column, aligning the digits by place value.

Perform the subtraction, starting from the rightmost digits (the ones place) and moving to the left, borrowing as needed.

Subtract each digit in the smaller number from the corresponding digit in the larger number.

83456
-  728.88
_______
82727.12

The difference is 82727.12.

Answer:

The value of given expression is 3.8.

Step-by-step explanation:

Given:

[tex]1.8+0.5(y+6)-2^3[/tex]

We need to find the simplified value of given expression using y =14

Solution:

Now we will substitute y =14 we get;

[tex]1.8+0.5(y+6)-2^3\\\\1.8+0.5(14+6)-2^3[/tex]

Now using PEDMAS we will first solve the parenthesis we get;

[tex]1.8+0.5\times20-2^3[/tex]

Now we will solve the exponent function we get;

we know that;

[tex]2^3=8[/tex]

So we can say that;

[tex]1.8+0.5\times20-8[/tex]

Now we will solve the multiplication operation.

[tex]1.8+10-8[/tex]

Now we will perform addition operation.

[tex]11.8-8[/tex]

And finally we will perform subtraction operation.

3.8

Hence The value of given expression is 3.8.

Answer:

D(-6,-4)

Step-by-step explanation:

-5x + y = 26

2x - 7y = 16

-5x/-5 = 26-y/-5

x = -26/5 + y/5

2(-26/5 + y/5) = 7y = 16

-52/5 + 2y/5 = 16 + 52/5

-33y/5 = 80/5 + 52/5

-33y/5 = 132/5

-33y = 132

y = -4

2x - 7(-4) = 16

2x + 28 = 16

2x = -12

x = -6

Answer:

1. 192 books.  

2. 96 books.  

3. 24 books.

Step-by-step explanation:

1. Let's find the volume of each book and the volume of the box, this way:

Volume of a book = 4 * 6 * 1 = 24 inches ³  

Volume of the box = 24 * 24 * 8 = 4,608 inches ³

2. If Hardy fills the box completely, what is the greatest number of books that fit into the box?

Greatest number of books = Volume of the box/Volume of a book

Greatest number of books = 4,608/24

Greatest number of books = 192

3. If Hardy fills the box completely with the least number of layers, there will be (blank) books on the bottom layer.

The height of the box is 8 inches, so it can only can hold 2 or 8 layers of books, since the books are 4 * 6 * 1 inches.  

Greatest number of layers = Height of the box/Width of a book  

Greatest number of layers = 8/1 = 8  

Minimum number of layers = Height of the box/Height of a book  

Minimum number of layers = 8/4 = 2  

Upon saying that, we have:  

Number of books per layer = Greatest number of books/Minimum number of layers  

Number of books per layer = 192/2 = 96

4. To fill the box completely, Hardy places 8 layers of books in the box. There are (blank) books in each layer.

Number of books per layer = Greatest number of books/Number of layers

Number of books per layer = 192/8  

Number of books per layer = 24

Note: Same answer to question 14559894, answered by me today.

Final answer:

The greatest number of books Hardy can fit into the box is 192. With the least number of layers and the box completely filled, there would be 24 books on the bottom layer. And if there are 8 layers of books in the box, there would be 24 books in each layer.

Explanation:

Hardy is packing books into a box and wants to maximize the number of books while also considering different arrangements. The dimensions of each book are 4 inches by 6 inches by 1 inch, and the dimensions of the box are 24 inches by 24 inches by 8 inches. The volume of a book is 4in x 6in x 1in = 24in³, and the volume of the box is 24in x 24in x 8in = 4,608in³. Therefore, the greatest number of books that fit into the box is the volume of the box divided by the volume of one book, which gives us 4,608in³ / 24in³ = 192 books.

If Hardy fills the box completely with the least number of layers, he would place the books so that the largest book dimensions are aligned with the box's. This means laying the books down in layers where each layer measures 24in by 24in. Since each book has a 6-inch side, we can fit four books along the width of the box (24in / 6in = 4 books), and similarly, we can fit six books along the length of the box (24in / 4in = 6 books), resulting in 4 x 6 = 24 books on the bottom layer.

If Hardy fills the box completely with 8 layers of books, he is dividing the height of the box by the height of a book (8in / 1in = 8 layers). In this case, since there are 24 books per layer (as calculated previously), and there are 8 layers, it means there are still 24 books in each layer.

Answer:

The points (12,3), (-2,-5) and (1,15) through which the line can pass.

Step-by-step explanation:

A line passes through the point (0, –1) and has a positive slope.

(i) The slope of the line passing through the points (0,-1) and (12,3) will be

[tex]\frac{- 1 - 3}{0 - 12} = \frac{1}{3} > 0[/tex]

(ii) The slope of the line passing through the points (0,-1) and (-2,-5) will be

[tex]\frac{- 1 + 5}{0 + 2} = 2 > 0[/tex]

(iii) The slope of the line passing through the points (0,-1) and (- 3,1) will be

[tex]\frac{- 1 - 1}{0 + 3} = - \frac{2}{3} < 0[/tex]

(iv) The slope of the line passing through the points (0,-1) and (1,15) will be

[tex]\frac{- 1 - 15}{0 - 1} = 16 > 0[/tex]

(v) The slope of the line passing through the points (0,-1) and (5,-2) will be

[tex]\frac{- 1 + 2}{0 - 5} = - \frac{1}{5} < 0[/tex]

Therefore, the points (12,3), (-2,-5) and (1,15) through which the line can pass. (Answer)

Answer:

A, B, D

Step-by-step explanation:

just took it on edg

Answer:

x ≈ 745.5 ft

Step-by-step explanation:

The angle at the lower right of the triangle is 28° ( alternate angle )

Using the sine ratio in the right triangle

sin28° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{350}{x}[/tex]

Multiply both sides by x

x × sin28° = 350 ( divide both sides by sin28° )

x = [tex]\frac{350}{sin28}[/tex] ≈ 745.5 ft ( to the nearest tenth )

Answer:

(-2,5) and (7,23)

Step-by-step explanation:

we have

[tex]y=x^{2} -3x-5[/tex] ---> equation A

[tex]y=2x+9[/tex] ---> equation B

Solve the system by graphing

Remember that the solution of the system is the intersection point both graphs

Using a graphing tool

The intersection points are (-2,5) and (7,23)

see the attached figure

therefore

The solutions are (-2,5) and (7,23)

The solution points are [tex](-2,5)[/tex] and [tex](7,23)[/tex].

It is given equations are,

Explanation:

From the given graph it is clear that the curve and line intersect each other at two points. These points are the solutions for the given system of equations.

The graph of line and curve intersect each other at [tex](-2,5)[/tex] and [tex](7,23)[/tex].

Thus, the solution points are [tex](-2,5)[/tex] and [tex](7,23)[/tex].

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Answer:

i) the value of a = 0 is non-permissible

ii) the value of b = 0 is non-permissible

Step-by-step explanation:

i) the given expression is [tex]\frac{5a^{2} + 80a }{50ab^{2} }[/tex]

ii) if a = 0 then the expression will become infinity hence the value of a = 0 cannot be used

iii) if b = 0 then the expression will become infinity, hence the value of b = 0 also cannot be used.

iv) In the numerator of the expression if it is factorized we get 5a[tex]\times[/tex] ( a + 16)

    if a = -16 then the value of the expression becomes zero.

Answer:

The slope of the line passing through the given points (-2,-7) and (9,-7) is m=0

Step-by-step explanation:

Given that the line passing through the points (-2,-7) and (9,-7)

To find the slope of the line passing through the points :

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] be the given points (-2,-7) and (9,-7) respectively

Substitute the points in the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{-7-(-7)}{9-(-2)}[/tex]

[tex]=\frac{-7+7}{9+2}[/tex]

[tex]=\frac{0}{11}[/tex]

Therefore m=0

Therefore Slope m is 0

Therefore the slope of the line passing through the given points (-2,-7) and (9,-7) is m=0

Answer:

14

Step-by-step explanation:

12+b=26

b=26-12

b=14

Answer:14

Step-by-step explanation:You first want to do 12+12 because that =24 and then keep on adding until u get 26

The number of batches of cookies made is [tex]7\frac{1}{2}[/tex]

Solution:

Given that, baker has 10 cups of sugar to make cookies

Each batch calls for [tex]1\frac{1}{3}[/tex] cups of sugar

To find: Number of batches of cookies can be made

From given information,

Total number of cups of sugar = 10

Cups of sugar for 1 batch = [tex]1\frac{1}{3} = \frac{3 \times 1 + 1}{3} = \frac{4}{3}[/tex]

Therefore, number of batches of cookies can be made is found by dividing the total number of cups of sugar by cups of sugar for 1 batch

Thus we get,

[tex]\text{Number of batches of cookies can be made} = \frac{\text{Total number of cups of sugar}}{\text{Cups of sugar for 1 batch}}[/tex]

Substituting the values, we get

[tex]\text{Number of batches of cookies can be made} = \frac{10}{\frac{4}{3}}\\\\\text{Number of batches of cookies can be made} = 10 \times \frac{3}{4}\\\\\text{Number of batches of cookies can be made} = \frac{15}{2}\\\\\text{In mixed form, we get }\\\\\rightarrow \frac{15}{2} = 7\frac{1}{2}[/tex]

Thus number of batches of cookies made is [tex]7\frac{1}{2}[/tex]

The expression 1/4x + 19/4 can be factored by taking out the common factor of 1/4, resulting in the completely factored form (1/4)(x + 19).

The student has asked to factor the expression 1/4x + 19/4 completely. To begin with, we note that both terms in the expression share a common factor of 1/4. Thus, we can factor out this common factor. The expression becomes:

(1/4)(x + 19)

The 1/4 is factored out, and we are left with the binomial x + 19 inside the parentheses. This is the completely factored form of the expression. Remember that factoring is essentially reversing the distribution process. In this case, we took out the common factor of 1/4 that was distributed across the x and 19.

Answer: 18cm

Step-by-step explanation:

Let original drawing's base be b.

We are using scale factor of 0.4, so

0.4 of b = 7.2cm

0.4 × b = 7.2cm

b = (7.2/0.4)cm

b = 18cm

The base of the original drawing must be 18 cm.

Option B is the correct answer.

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

Scale factor = 0.4.

From the figure,

Original height = 25.6 cm

Original base = b cm

Scale height.

= 25.6 x 0.4

= 10.24 cm

Scale base = 7.2 cm

Now,

Original base.

b x 0.4 = 7.2

b = 7.2 / 0.4

b = 18 cm

Thus,

The base of the original drawing must be 18 cm.

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Answer:

B is the answer to the equation