A 12 foot piece of sting is cut into two pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.The shorter piece is how many feet long?The longer piece is how many feet long?

Answer:

36x-6=0

36x-6+6=0+6

36x=0+6

36x=6

x=6÷36

x=6

The surface area of a triangular box when the triangles and rectangles are added together is 3345cm².

An material's surface area is an indication of how much space it takes up overall. The overall amount of space together around three-dimensional shape is its surface area. The total surface area of a two half shape is referred to as its surface area. By summing the regions of each face, one can determine the surface area of either a cuboid of six rectangular faces. Alternatively, you can name the frame's dimensions using the following formula: Surface (SA) = 2lh, 2lw, and 2hw. The total size of the area occupied by the surface of a muti form is measured as land area (a three-dimensional shape is a shape that has height, width, and depth).

given

Area= Height × (1/2)base.

Area= 13cm ×7.5 cm

Therefore the area of the triangle is equal to 97.5cm².

The surface area of the two triangles = 195cm².

The total surface area = add the triangles with the rectangles which is equal to 3150cm² +195cm² = 3345cm².

The surface area of a triangular box when the triangles and rectangles are added together is 3345cm².

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a) The break-even point for the division is: 4000 units

b) The level of sales for 10% profit is: 4681 units

The break-even point is defined as the point at which total cost and total revenue are equal, meaning there is no loss or gain for your small business. In other words, you've reached the level of production at which the costs of production equals the revenues for a product.

a) We are told that:

Selling price for income tax app = $8

Monthly fixed cost = $20000

Variable cost producing each app = $3

Thus:

8x = 3x + 20000

5x = 20000

x = 4000 units

b) 8x = 1.1(3x + 20000)

8x = 3.3x + 22000

4.7x = 22000

47x =220000

x = 4681 units

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Missing questions are:

(a) Find the break-even point for the division.

(x,y)=

(b) What should be the level of sales in order for the division to realize a 10% profit over the cost of making the income tax apps? (Round your answer up to the nearest whole number.)

0.07x+0.11(3x+24000)=27040

we will solve for x

x=61,000 [ investment at 7%]

Investment at 11% = 3x + 24000

= 3(61000)+24000

= 207000 [ investment at 11%]

1. Relation 1 is a function

2. Relation 2 is a function

3. Relation 3 is not a function

4. Relation 4 is a function

From the question, we have the following parameters that can be used in our computation:

The relations (1) to (4)

Relation (1)

This relation is a function

This is because each range value point to unique domain values

Relation (2)

This relation is a function

This is because each range value point to unique domain values

Relation (3)

This relation is not a function

This is because domain values w have different range values.

Relation (4)

This relation is a function

This is because each range value point to unique domain values

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Answer:

Step-by-step explanation:

Which tables give sets of values that satisfy the linear function y = 2x – 6

Answer: \(129.42m\)

Step-by-step explanation:

We can use a trigonometric function to find x.

In this case, sine works.

\(sin=\frac{opposite}{hypothenuse}\)

Solve for hypothenuse.

\(hypothenuse=\frac{opposite}{sin}\)

\(h=\frac{120}{sin68}\)

\(h=129.42m\)

Answer:

Final mixture is 120 gm

x = 10%      then   (120-x) = 25%

.25(120-x)    + .1 (x)    =  .15 (120)       solve for x= 10% amount

                                                                 then  25% amount = 120-x

Step-by-step explanation:

Answer:

(r+21 ) / 4

Step-by-step explanation:

as we can see DF = FM
and DF = 4R ,  FM =r+21

so,
4R = r+21
=> R= (r+21)/4

Answer:

D

Step-by-step explanation:

1 + 4x and 57° are corresponding angles and are congruent , so

1 + 4x = 57 ( subtract 1 from both sides )

4x = 56 ( divide both sides by 4 )

x = 14

Answer: A

Step-by-step explanation:

Replace x by 3, and y by 2

Answer:

Step-by-step explanation:

x = 3 , y = 2

• Y= x - 1

• 2 = 3-1

• 2 = 2

Answer:

25× 1/10 = 5/2

Step-by-step explanation:

5/2 or 2.5 lies between 2 and 3

Answer:

Step-by-step explanation:

To find the area of the shaded region, we need to first find the x-coordinates of the points where the two functions intersect. We can set f(x) = g(x) and solve for x:

x^4 - 12x^3 + 48x^2 = 44x + 105

x^4 - 12x^3 + 48x^2 - 44x - 105 = 0

We can use a numerical method, such as the Newton-Raphson method, to approximate the roots of this equation. Using a graphing calculator or computer algebra system, we can find that the roots are approximately:

x = -1.932, x = 0.695, x = 4.149

Note that the root x = -1.932 is outside the given interval [3, 4], so we can ignore it.

The shaded region is bounded by the x-axis, the line y = 340, and the graphs of f(x) and g(x) between x = 3 and x = 4. To find the area of this region, we can integrate the difference between the two functions over this interval:

A = ∫3^4 [g(x) - f(x)] dx

A = ∫3^4 [44x + 105 - (x^4 - 12x^3 + 48x^2)] dx

A = ∫3^4 [-x^4 + 12x^3 - 48x^2 + 44x + 105] dx

We can integrate term by term using the power rule:

A = [-x^5/5 + 3x^4 - 16x^3 + 22x^2 + 105x]3^4

A = [-1024/5 + 192 - 192 + 22 + 105] - [-81/5 + 108 - 192 + 66 + 105]

A = 347.2

Therefore, the area of the shaded region is approximately 347.2 square units.

Answer:

2z+6 or 2(z+3) are the equivalent expressions

Step-by-step explanation:

z+(z+6)

opening the brackets

z+z+6

=2z+6

or if we take 2 as common the answer is

=2(z+3)

i hope this will help you :)

Answer:

Given that the expression is z+(z+6)

The equivalent expression to the give expression

From the given expression z+ (z+6)

z+ (z+6)

=z+z+6

Adding the like terms

=2z+6

Taking the common term 2 outside of the above expression

=2(z+3)

Therefore z+ (z+6)  =2(z+3)

Therefore the other given optional expressions are not equivalent to the given expression.

The option 2(z+3) is correct and it is the equivalent expression.

Hence the given expression z+ (z+6)  is equivalent to the expression 2(z+3)

The probability of rolling a number less than 15 and rolling an even number is;  7/20

We are told that the single die has 20 sides.

There are 14 numbers less than 15. Thus;

On the first roll, probability of rolling a number less than 15 is 14/20.

Now, there are 10 even numbers in a 20 side die. Thus, probability of rolling an even number on the second roll is; 10/20

Thus;

probability of rolling a number less than 15 and rolling an even number = 14/20 * 10/20 = 7/20

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Answer:

x = 0.1

Step-by-step explanation:

1/x - x/6 = 2/3

1/ x - 6/x = 2/3

6/x = 2/3

6x = 2/3

x = 0.1

Answer:

x = 0.2

Step-by-step explanation:

1/x - x/6 = 2/3

=> 1/x - x = 2/3 * 6

=> 1/x - x = 12/3

=> 1/x - x = 4

=> 1/x - x/1 = 4 (x = x/1 )

=> 1 - x/1 = 4 * x

=> -x/1 = 4x - 1

=> -x/1 -4x = -1

=> -5x/1 = -1

=> x = -1/-5

=> x = 0.2 (Because negative / negative = positive)

If I am wrong please tell me.

If my answer helped, kindly mark me as the brinliest!!

Thanks!!

Answer:

The first answer is correct.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

12 liters per minute.

Step-by-step explanation:

41litres-5litres=36

If 36litres are filled up within 3 min,how many litres will be filled within 1 min

1/3×36=12

=12 litres per min

Point d is at (5, -5), which is five units to the right of the origin on the x-axis and five units below the origin on the y-axis. Similarly, point e is at (7, 3), point f is at (-1, 5), and point G is at (-3, -3).

The given points, d (5, -5), e (7, 3), f (-1, 5), and G (-3, -3) form quadrilateral DEFG. To plot these points, we can first draw the x and y axes on a graph paper.

Then, we can plot each point by locating its x-coordinate on the x-axis and its y-coordinate on the y-axis.

After plotting the points, we can click on the "Graph Quadrilateral" button to see the quadrilateral DEFG. It should be a closed shape with four sides, connecting the four points in the given order.

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The 1 in y = 1/7x+1, is the y-intercept. Its coordinates are (0,1). 1/7 means you are going up 1 and to the right 7, since it's positive.

On a graph, it looks like the graph above.

The answer is in the picture.

I hope this helped

The percentage of apartments in the building are that are small is 80%.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

So the percentage actually means a part per 100.

Percentage is usually denoted by the symbol '%'.

Given that,

The ratio of small apartments to regular apartments is 16 to 4.

Total apartments = 16 + 4 = 20

Number of small apartments = 16

Number of regular apartments = 4

Percentage of small apartments = (16 / 20) × 100

                                                      = 0.8 × 100

                                                      = 80%

Hence 80% of the apartments are small.

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Answer: The graph has a line of symmetry at y = 0.

Step-by-step explanation:

I suppose that this refers to the function:

f(x) = IxI

The parent absolute value function.

Remember how this works:

IxI = x if x ≥ 0

IxI = -x if x ≤ 0.

Let's analyze the sentences:

1) "The x- and y-intercepts are (0,0)"

This is true, when x = 0 we have:

y = f(0) = I0I = 0

So the point (0, 0) is the only x-intercept and the only y-intercept.

2) "Domain: (-∞,∞); Range: [0,∞)"

This is also true, we clearly do not have any restriction in the domain.

And when looking at the range, we can see that the possible values of y are always positive or zero.

3) "(0, 0) is the minimum point."

Now, as x increases in the positive range, also does the value of y.

And as x decreases in the negative range, as the absolute value changes the sign, we will also have an increase in the value of y.

Then we have that (0, 0) must be the minimum.

4) "The graph has a line of symmetry at y = 0."

This is false.

The real line of symmetry is at x = 0, y = 0 corresponds to the x-axis, and as the graph opens up, we can not have symmetry about any line parallel to the x-axis.

Answer:

B.

Step-by-step explanation:

The graph has a line of symmetry at y = 0.

Answer:

He says that because he thinks ur cheating for attention. When they say you 'let the whole world know' that you`re unloyal and can be with any guy, without a care, it`s an insult.

Answer:

it means that he was dating another person while already dating

Step-by-step explanation:

it like when ur dating 2 people at one time without the other person knowing

Answer: 10.98 meters

Step-by-step explanation:

Answer:

\(\frac{75}{100}\)

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

2.04 is neither greater nor less than 2.040

but 2.04 is equal to 2.040.

\(2.04=2.040\)

Answer:

the answer is the 3rd one

Step-by-step explanation:

Answer:

1681

Step-by-step explanation:

In a four digit perfect square, the first two digits and last two digits taken seperately are also perfect squares.

Therefore, the answer is 1681 because 1681=41*41 and

16=4*4 and 81=9*9