Solve (2/3)-(1/x)=5/6

Triangles ade and bef are similar due to equal angles. The ratio of their areas (9:1) means their sides have a ratio of 3:1. Using the properties of parallelograms, the parallelogram's area will be double the area of triangle ade, or 18 square units.

In the given problem, we have a parallelogram abcd and we're asked to find its area. Given the properties of a parallelogram, we know that angle bad equals angle bef. This leads to the conclusion that triangle ade is similar to triangle bef since their angles are the same. As the ratio of their areas is 9:1, it's clear the ratio of their sides is 3:1, since the ratio of the areas of similar figures is the square of the ratio of their corresponding sides.

The parallelogram's area will be double the area of triangle ade, thanks to the properties of a parallelogram (it's made up of two congruent triangles). Therefore, the area of the parallelogram is 18 square units. The important steps here were recognizing the similar triangles and knowing how to calculate a parallelogram's area.

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Answer: D. The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r+t=20 and 5r+5t=150.

Step-by-step explanation:

Let 'r' represents the number of roast beef sandwiches it provides and 't' represents the number of tuna sandwiches.

Then, the total number of roast beef sandwiches and tuna sandwiches is equal to the number of employees :

[tex]r+t=20[/tex]....................(1)

Also, the cost of each roast beef sandwich and cost of each tuna sandwich is same as $5.

If company wants to use the entire budget of $150, then we have another equation :-

[tex]5r+5t=150\\\5(r+t)=150[/tex]

If we divide 5 on both sides we get

[tex]r+t=30[/tex].............................(2)

When we compare equation (1) and (2) we get 20=30 but it is not possible therefore the system has no solution.

Therefore, the correct statement is "The company cannot provide lunch for all 20 employees and use the entire budget because there is no solution to the system of equations r+t=20 and 5r+5t=150."

divide 21 3/4 by 1 1/3 = 16 5/16

 she can make 16 dresses

Solving a system of equations to help a company plan revenue and production constraints.

The system of equations:

20b + 30h = 275 (total revenue equation)

8b + 9h = 53 (total boxes equation)

By solving these equations simultaneously, the company can determine the number of cow bells and air horns to produce to make $275 while satisfying the box constraint.

The solution would be like this for this specific problem:

Given:

46547 17395 25765 11325 14071 61688

You want two-digit numbers between 01 and 50, so break it up into chunks of two and eliminate any string that is not between 01 and 50.

So, the numbers from the string are:

46 54 71 73 95 25 76 51 13 25 14 07 16 16 88

Eliminated numbers:

54 71 73 95 25 76 51 88

Numbers remaining:

46 25 13 14 07 16

So, the 2 contestants from a game show out of a pool of 50 would be 46 and 25 (since these are the possible contestants based from the given).

Answer:

1 radien = 57.3 degrees

Step-by-step explanation:

1 radien = 57.3 degrees

The student is trying to find the 4th term in a mathematical sequence where the first term is 13 and the rule for each term is to add 5. Thus, the 4th term of this sequence is 28.

The student is asking about a mathematical sequence where the first term is 13 and the term to rule is 'take away -5', or in other words, add 5 (since subtracting a negative number is the same as addition). So, to find the nth term of this sequence, you subtract (or add in this case) -5 to the first term, and continue in the sequent term.

Using these rules, here are the first four terms of the sequence: 1st term - 13. 2nd term [tex]- 13 + 5 = 18[/tex]. 3rd term [tex]- 18 + 5 = 23[/tex]. 4th term[tex]- 23 + 5 = 28.[/tex]

So, the 4th term in this sequence is 28.

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1st number can be 0-9 = 10 numbers

2nd number can be 0-9 = 10 numbers

3rd number can be 0-9 = 10 numbers

10 * 10 * 10 = 1000 combinations

Answer:

Property's actual area  = 6400 m²

Step-by-step explanation:

Scale = 1 : 500

Side on map = 16 cm

Side of property = scale x side on map = 16 x 500 = 8000 cm

Area of property = 8000 x 8000 = 64000000 cm²

Area of property = 6.4 x 10⁷ cm² = 6.4 x 10³ m²

Property's actual area  = 6400 m²

To convert 0.36 repeating into a fraction, we get [tex]\frac{4}{11}[/tex].

To convert the repeating decimal 0.36 repeating (written as 0.363636...) into a fraction, follow these steps:

⇒ 100x = 36.363636...

⇒ 100x - x = 36.363636... - 0.363636...

⇒ 99x = 36

⇒ x = [tex]\frac{36}{99}[/tex]

⇒ x = ([tex]\frac{36}{99}[/tex]) / ([tex]\frac{99}{9}[/tex]) = [tex]\frac{4}{11}[/tex]

Therefore, the fraction equivalent of 0.36 repeating is [tex]\frac{4}{11}[/tex].

Hence, the volume of pyramid is:

3x^2 cm^3

We know that a volume(V) of a oblique square pyramid with height 'h' and base area A is given by the help of formula:

[tex]V=\dfrac{1}{3}\times (Ah)[/tex]

Now, according to the ques we have:

The base edge of an oblique square pyramid is represented as x cm.

The height is 9 cm.

Hence, the base area (A) is calculated as:

[tex]A=x^2[/tex]

( Since the base is in the shape of a square and we know that the area of square with side length s is given as:

[tex]Area=s^2[/tex] )

So, the volume of the pyramid is calculated as:

[tex]V=\dfrac{1}{3}\times (x^2\times 9)\\\\V=3x^2 \ cm^3[/tex]

Hence, the volume of pyramid is:

3x^2 cm^3

A pyramid is a solid shape with several triangles and a base. The volume of the pyramid in terms of x is 3x^2 cm3

The volume(V) of an oblique square pyramid with height 'h' and base area A is expressed according to the formula:

V = Bh/3

B is the base area = x * x = x^2

h is the height = 9cm

Substitute

V = x^2*9/3

V = 3x^2cubic cm

Hence the volume of the pyramid in terms of x is 3x^2 cm3

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37-3 = 34

34/2 = 17

Michael drove 17 hours

Sarah drove 20 hours  (17+3)

For the table, y = 25x.
When x = 12, y = 25*12 = 300

For the graph, y = 30x
When x = 12, y = 30*12 = 360

When x = 12, the value of y on the graph is 60 more than its value in the table.

Answer:

The correct option is C. The value of y be on the graph than is 60 more than the y value in the table when x = 12.

Step-by-step explanation:

If a line passing through two points then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

From the given table it is clear that the line passing thought the points (4,100) and (5,125).

[tex]y-100=\frac{125-100}{5-4}(x-4)[/tex]

[tex]y-100=25(x-4)[/tex]

[tex]y-100=25x-100[/tex]

[tex]y=25x[/tex]

The value of this function at x=12 is

[tex]y=25(12)=300[/tex]

From the given table it is clear that the line passing thought the points (0,0) and (2,60).

[tex]y-0=\frac{60-0}{2-0}(x-0)[/tex]

[tex]y=30x[/tex]

The value of this function at x=12 is

[tex]y=30(12)=360[/tex]

The difference between y value in the graph and in the table at x=12 is

[tex]360-300=60[/tex]

The value of y be on the graph than is 60 more than the y value in the table when x = 12. Therefore the correct option is C.

you would need a function to determine whether to use a formula for 1 or 2 nights or a formula for more than 2 nights

T(x)={a if x <_ 2, b if x > 2}

 if it's 2 nights or less use option a, a = 75x

 if its longer than 2 days use option b, b= 50x + 50

Answer:

t = 75x  {x ≤ 2}

t = 150 + 50x {x > 2}

Step-by-step explanation:

A hotel chain charges $75 per night for first two nights.

If the number of nights of the stay are x then charges for x nights

= 75x where x ≤ 2

If the stay is for than 2 nights then charges for x nights

= Charges for two first 2 nights(@$75 per night) + charges for other than initial 2 nights (@$50 per night)

= (75×2) + 50x where x > 2

Therefore total cost of the hotel if represented by t then the function will be

t = 75x  {x ≤ 2}

t = 150 + 50x {x > 2}

Answer: false

Step-by-step explanation:

Answer:

The correct answer is [tex]y = \frac{10}{9}(x+3)^2+2[/tex]

Step-by-step explanation:

The correct answer to the question is not provided in the options listed below.

In order to find the equation of the quadratic function that you're looking for, you should identify the two points the parabola passes through: the vertex (that is point (-3,2)) and the y-intercept (the point (0,12)).

As we are given the vertex of the quadratic function, we can use the completed square form:  [tex]y=a(x-h)^2+k[/tex], where h and k are, respectively, the x and y coordinates of the vertex.

As (-3,2) is the vertex, we have:

[tex]y=a(x+3)^2+2[/tex]

Now, as the graph passes through the point (0,12), we can replace x=0 and y=12 in the formula above in order to find the value of a. Then, we make a the subject of the equation:

[tex]12=a(0+3)^2+2[/tex]

[tex]12=9a+2[/tex]

[tex] 10=9a[/tex]

[tex] \frac{10}{9}=a[/tex]

So, the equation of the parabola is [tex]y=\frac{10}{9}(x+3)^2+2[/tex].

Solution:

Cost of apartment(Ben + Housemates) = $ 563 per month

Amount paid by Ben per month = $ 215

Yes, Accommodation provided by someone for fixed amount is an essential Expense.

All the three statements regarding Ben who pays $ 215 per month are true.

a. It cannot be eliminated in a later budget, in order to save money.

b. Living expenses have a higher priority than any other type of expense.

c. The spender controls the amount of the rent by choice of apartment.

The equation y = ax represents a straight line with slope a. If a is negative, the line slopes downward to the right, not down and to the left.

The equation y = ax describes the graph of a line. The & in the equation appears to be a typo and should likely refer to a. The constant a represents the slope of the line. When the slope a is negative, the line slopes downward as it moves to the right on a coordinate plane. This is because a negative slope indicates that as the independent variable (usually the x-axis) increases, the dependent variable (y-axis) decreases. A line with a negative slope is straight, and its steepness depends on the absolute value of the slope a. Thus, the line goes down and to the left.

Answer: The correct option is 4, i.e., translation.

Explanation:

It is given that the triangle DEF is congruent to GHJ by the SSS theorem.

From the given figure it is noticed that the triangle DEF and GHI are isosceles triangle.

Reason for correct option:

In transition the side and angles of the shape are not effected and the figure transfers from one place to another place without making any other change.

Since the both triangle are congruent and the position of all sides and angles are same, therefore option 4 is correct.

Reason for incorrect option:

In dilation the size of the figure is either stretched or compressed according to the scale factor k. But in the given figure the size of both triangles are same it means option A is incorrect.

In reflection the distance of all the point in preimage and all the image are same from the central line. Any central line does not exist in given figure. SO, the option B is incorrect.

In rotation the side length and angles are not affected but the position are not same, therefore the option C is incorrect.

Answer: Translation

Step-by-step explanation:

Given: Triangle DEF is congruent to GHJ by the SSS theorem.

From the given picture two sides of both triangles are equal therefore, the triangle DEF and GHI are isosceles triangle.

We know that a transition is a kind of rigid motion used in geometry to trace a function that moves an object a particular distance that maps produces images.

Since the both triangle are congruent and just position of triangle GHJ is shifted to the right and down.

Therefore, the  transition is rigid transformation which is required to map DEF onto GHJ

Answer: 4

Step-by-step explanation: