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Solve the equation
3x-2
4
-
2x-5
3
=
1+x
6

A forest is decreasing in size by 60 hectares every 3 years. In 7 years, the forest will have decreased by 140 hectares.

Using the Unitary Method:

∵ In '3' years, a forest decreased in size by '60' hectares

∴ In '1' year, a forest will be decreased in size by '20' hectares

Every year 20 hectares is decreased. Considering a regular trend in the decrement of forest area, the time span of '7' years will diminish 'to 140' hectares.

The 'Unitary Method' is also known as the 'Mango Method'. It establishes a relation between given data. The relation is used to predict results in different conditions. The Unitary Method is always used for regular trends.

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1. 2 ² x 5b³ =   20b³

2. (3a²) ² x 2 (b ²) ³ = 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex] 5d

3. 15d ³ divided by 3d ² = 5d

What is Operations?

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's acuity is determined by the number of operands.

The given problems are:

1. 2 ² x 5b³

2. (3a²) ² x 2 (b ²) ³

3. 15d ³ divided by 3d ²

1. 2 ² x 5b³

  = 4 x 5b³

  = 20b³

2. (3a²) ² x 2 (b ²) ³

  By the exponent rule:
         [tex](x^{n} )^m[/tex] = [tex]x^{n * m}[/tex]

                   = [tex]x^{nm}[/tex]

∴ 3[tex]a^{2*2}[/tex] x 2[tex]b^{2*3}[/tex]

= 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex]

3. 15d ³ divided by 3d ²

    15d ³ ÷ 3d ²

By the exponent rule:

         [tex]a^{m}[/tex]÷[tex]a^{n}[/tex] = [tex]a^{m-n}[/tex]

∴  5[tex]d^{3-2}[/tex] = 5[tex]d^{1}[/tex]

              = 5d

Hence, The solutions are 20b³, 3[tex]a^{4}[/tex] x 2[tex]b^{6}[/tex] and 5d

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The measure of the angle is calculated using the attached figure.

What is an angle?

An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are known as dihedral angles. An angle defined by two intersecting curves is the angle of the rays lying tangent to the respective curves at their point of junction. Angle can also refer to the measurement of an angle or of a rotation. This measurement is the length of a circular arc divided by its radius. The arc is centered at the vertex in the case of a geometric angle.

From figure,

angle x = 180° - 110° = 70° (linear pair)

angle y = 37° (alternate interior angles)

Measure of angle 1 = 70° + 37° (exterior angle in a triangle is equal to the sum of opposite interior angles)

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We will use simple division to solve the problem. The number of representatives attended from each country is 706.

In the given question we know that a political gathering in South America was attended by 8475 people and each 12 territories of South America were equally represented. We need to find out how many representatives attended from each country. Inorder to find the number of representatives we can divide 8475 by 12.

number of representatives= 8475/12 =706

Therefore number of representatives from each country is 706.

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Answer:

1.5 m/s

Step-by-step explanation:

Distance = 6.8×1609.344 = 10943.5392

time=2×60×60 = 7200

velocity= distance/time = 10943.5392/7200= 1.51 m/s

Answer:

x = 1, y = 1

Step-by-step explanation:

This Question involves the concept of Solving Simulteanous Equations.

Simulteanous Equations are 2 sets of equation with 2 unknownes to solve. Methods used are Substitution and Elimination methods, use either to solve unless question specify a method.

Example:

2x + 4y = 67

3x + 9y = 90

We are given the 2 equations:

y = 2x - 1 (Equation 1)

2x + y = 3 (Equation 2)

We are asked to use the Substitution Method.

We first substitute Equation 1 to Equation 2 to find the value of x.

2x + (2x - 1) = 3

2x + 2x - 1 = 3

4x - 1 = 3

4x = 3 + 1

4x = 4

x = 4 ÷ 4 = 1

Now we can substitute x into Equation 1 to find the value of y.

y = 2(1) - 1

y = 2 - 1 = 1

Based on the lengths of the sides of the triangle, we can infer that this is NOT a right triangle.

A right angled triangle would obey the Pythagoras Rule which is that the square of the hypotenuse (longest side) will be the sum of the squares of the other sides of the triangle.

This means that for this to be a right triangle, it needs to obey the function:

45 ² = 35 ² + 30 ²

Solving gives:

2,025 ≠ 2, 125

This shows that the triangle is not a right triangle.

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It is not a right-angle triangle since 2125 ≠ 2025 meant that it did not conform to Pythagoras' theorem's specifications.

This kind of query creates a right-angled triangle that Pythagoras' theorem can resolve.

In a right-angled triangle, the square of the greatest side is equal to the sum of the squares of the smaller two sides.

Given, There are three sides to a triangle, each measuring 30 kilometers, 35 kilometers, and 45 kilometers.

∴ 30² + 35² = 45².

900 + 1225 = 2025.

2125 ≠ 2025.

Due to the fact that it didn't meet the requirements of Pythagoras' theorem, it is not a right-angle triangle.

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Answer:

Step-by-step explanation:

-3x – 10 = 32 Help me I need the answer

-3x – 10 = 32

-3x = 32 + 10

-3x = 42

x = 42 :(-3)

x = - 14

-----------------

check

-3 × (-14) - 10 = 32                      (remember pemdas)

42 - 10 = 32

32 = 32

the answer is good

The equivalent expression of the expression given as [tex]\frac{\frac{3}{x - 2} - 5}{2 - \frac{4}{x - 2}}[/tex] is (13 - 5x)/(2x - 8)

From the question, the expression is given as

[tex]\frac{\frac{3}{x - 2} - 5}{2 - \frac{4}{x - 2}}[/tex]

Take the LCM of the fractions in the above expression

So, we have

[tex]\frac{\frac{3 - 5x + 10}{x - 2}}{\frac{2x - 4 - 4}{x - 2}}[/tex]

Evaluate the like terms of the expressions

So, we have

[tex]\frac{\frac{13 - 5x}{x - 2}}{\frac{2x - 8}{x - 2}}[/tex]

Divide the common factor x -2 in the expression

So, we have

[tex]\frac{13 - 5x}{2x - 8}[/tex]

Rewrite as

(13 - 5x)/(2x - 8)

The expression cannot be further simplified

Hence, the solution is (13 - 5x)/(2x - 8)

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The rate of change are:

a. 3 ft/min

b. 0.5 ft/min

c. -2.2 ft/min

The formula for finding the rate of change of a relationship is given as:

Rate of change = Change in y/change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

a. (2, 8) = [tex](x_1, y_1)[/tex]

(5, 17) = [tex](x_2, y_2)[/tex]

Rate of change = (17 - 8)/(5 - 2)

Rate of change = 9/3

Rate of change = 3 ft/min

b. (3.4, 6.8) = [tex](x_1, y_1)[/tex]

(7.2, 8.7) = [tex](x_2, y_2)[/tex]

Rate of change = (8.7 - 6.8)/(7.2 - 3.4)

Rate of change = 1.9/3.8

Rate of change = 0.5 ft/min

c. (3/2, - 3/4) = [tex](x_2, y_2)[/tex]

(1/4, 2) =  [tex](x_2, y_2)[/tex]

Rate of change = (2 - (-3/4))/(1/4 - 3/2)

Rate of change = 11/4 / -5/4

Rate of change = 11/4 × -4/5

Rate of change = -11/5 = -2.2 ft/min

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In the two triangles FIH and GHI

IH is a common side

FI = GH

The angles are between the equal sides

Then the two triangles are congruent by SAS postulate

The answer is A

Solution

Transform figure using the rule (x , y) = (-x , y - 8)

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.

The Null hypothesis will be expressed as u = 0.79 whereas the Alternative hypothesis will be expressed as. u > 0.79

The null hypothesis (H0) may be used to show that there exists no significant variation between variables or that a single variable is not different than its mean. While an alternative Hypothesis (Ha) is a theory that attempts to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean. According to the question we can say that the

Null hypothesis (H0): u = 0.79

Alternative hypothesis (Ha): u > 0.79

Where u may be called as the proportion of their reader that owns a personal computer.

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          An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power. Alternatively put, none of the exponents can be greater than 1. As an illustration, while x is a variable raised to the first power, x2 is a variable raised to the second power. An illustration of a constant is 5.

The number of deposits will change at a 100 percent rate.

Given that, consider the image of the linear function's graph.

Currently, the graph's two points are (3, 350) and (2, 250).

Rate of change is therefore equal to (250 - 350) / (2 - 3)

= -100/-1

 = 100.

The rate of change will therefore be 100 in relation to the number of deposits.

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A linear function is a function in which we add multiple of a constant.

Given data:

We have

Clearly, we have add multiples of 480 to 18,250.

So, the given function represents a linear function.

So, the correct option is (a).

Solving those simple linear equations, by isolating the variable, and combining like terms.

1.3x-4=23

3x -4=23

3x=27

x=9

2) 9-4x=17

-4x =17-9

-4x=8

4x=-8

x=-2

3) 6(x-7)=36 Distributing the factor

6x -42=36

6x=36+42

6x=78

x=13

4) 2(x-5)-8=34 Distributing the factor

2x -10-8=34

2x -18=34

2x=52

x=26

The value of interior angle is 60.

What is triangle?

A triangle is a simple polygon with 3 sides and 3 interior angles. It is one of the basic shapes in geometry in which the 3 vertices are joined with each other and it is denoted by the symbol.

What is interior angle?

In a triangle, there are three interior angles at each vertex. The sum of those interior angles is always 180°. The bisectors of these angles meet at an point known as incenter. As the sum of interior angles of a triangle is 180°, there is only one possible right angle or obtuse angle possible in each triangle.

The sum of interior angle is 180

Given angles is 30, 90, x.

Therefore, sum is given by

90 + 30 + x = 180

120 + x = 180

x = 180-120

x = 60

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Answer:7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

420÷60 is the same as 42÷6.

42 goes into 6, 7 times:

6, 12, 18, 24, 30, 36, 42.

Therefore, 420÷6 is 7.

Please use a calculator next time.

Three pairs of siblings from different families can be seated in two rows of three chairs so that siblings may not sit next to each other in the same row, and no child may sit directly in front of their sibling in 96 ways.

There are 3 pairs of siblings. We can name them as a₁, a₂, b₁, b₂, c₁ and c₂, a total of 6 children.

There are 2 rows of 3 seats each.

We will try to find the number of ways each seat can be filled.

So considering the first seat in first row, it can be filled in 6 different ways. Because any one from 6 children, say a₁, can be seated.

Now for the second seat in first row can only be filled by one of b₁, b₂, c₁ or c₂ because the first seated child a₁ along with the sibling a₂ of the same cannot be seated in the second seat. So in 4 different ways.

For the third seat remaining in the first row, one out of the remaining  pair of siblings c₁ or c₂ can be seated. This can be done in 2 ways.

Now after filling the first row in this manner, the second row can be filled in only 2 ways.

So total number of ways the children can be seated = 6 x 4 x 2 x 2 = 96 ways

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Answer:

1,730

Step-by-step explanation:

173x10 (pieces)= 1730

Answer:

Step-by-step explanation:

You want the range of amounts of 60% solution that can be added to a 40% solution to achieve 30 kg of a solution that lies in the range of 46% to 50%.

Let x represent the mass in kg of 60% solution added. The fraction of the total solution that is glucose will be ...

  0.46 ≤ (0.60x +0.40(30 -x))/30 ≤ 0.50

Multiplying by 30 and simplifying the inequality, we have ...

  13.8 ≤ 0.20x +12 ≤ 15

  1.8 ≤ 0.2x ≤ 3 . . . . . . . . subtract 12

  9 ≤ x ≤ 15 . . . . . . . . . . divide by 0.2

The least amount of 60% solution that should be added is 9 kg. The greatest amount is 15 kg.

__

Check

  9 kg of 60% +21 kg of 40% has 5.4 +8.4 = 13.8 kg of glucose, the minimum.

  15 kg of 60% +15 kg of 40% has 9 +6 = 15 kg of glucose, the maximum.

(The minimum and maximum values are seen in the solutions steps after the initial multiplication by 30.)

Answer:

x = 7.5

Step-by-step explanation:

[tex] \frac{6}{15} = \frac{3}{x} [/tex]

cross multiply expressions

6x = 45 divide both sides by 6

x = 7.5

Answer: $31,200 per year

Step-by-step explanation:

The question tells us that they are working 40 hours a week and making 15 dollars an hour. We can find out how much they make a week and then multiply by 52 (number of weeks in a year) to find the amount they make in a year.

Per week:

15 * 40 = $600

Per Year:

600 * 52 = $31,200

Answer:

$31,285.74 per year

Step-by-step explanation:

What we know:

- $15 per hour

- 40 hour weeks

- 52.1429 weeks per year

What we need to find out:

- How much money per year

Step 1: Multiply for how much made per week

We know that we need $15 dollars for 40 hours so we start with multiplying them together to see how much we make a year.

40 x 15 = $600 per week

Step 2: Now multiply the amount of weeks a year by the amount made per week

So now we know that we make $600 per week now we have to multiply the amount of weeks in a year by the money made per week so.

52.1429 x 600 = $31,285.74 per year. So the house keeper makes $31,285.74 per year.

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Answer:

1/5

Step-by-step explanation:

"percent" means "per hundred"

(because cent means hundred like years in a century or cents in a dollar)

anyway

20% means

20 per 100

write it as 20/100



Now simplify it.

20/100

= 2/10

= 1/5

Answer:

12

Step-by-step explanation:

You have 15 pencils in your pencil case.1/5 of the pencils are green. How many are not green?

= 1 - 1/5

= 5/5 - 1/5

= 4/5

This means that 4/5 of the 15 pencils are not green. So:

4/5 * 15 = 12 pencils are not green.

Account balance after 2 years $441.

Based on the given condition, here the details:

P = $400

r = 5 % = 0.05

n = 1

t = 2

Formulate and substitute all above:

F = P · (1 + [tex]\frac{r}{n}[/tex][tex])^{nt}[/tex]

F = 400. 1 + [tex]\frac{0.05}{1}[/tex])²

F = $441

From this as general, account balance is:

A checkbook, a savings account, or an investment account, for example, has a balance that shows how much money is available in the account. This is also called the current account value. The current value of account balances is shown by financial institutions on both paper statements and online tools.

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Answer:

The exact answer would be:

[tex]\sqrt{39}[/tex] + [tex]\sqrt{7}[/tex] + [tex]\sqrt{46}[/tex]  an approximate answer to the nearest whole number would be 7

Step-by-step explanation:

To find the missing side we would use the Pythagorean Theorem.

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] =[tex]c^{2}[/tex]

[tex]\sqrt{7} ^{2}[/tex] + [tex]b^{2}[/tex] = [tex]\sqrt{46} ^{2}[/tex]

7 + [tex]b^{2}[/tex] = 46  Subtract 7 from both sides

[tex]b^{2}[/tex] = 39

[tex]\sqrt{b^{2} }[/tex] = [tex]\sqrt{39}[/tex]

b = [tex]\sqrt{39}[/tex]

The perimeter, the distance around the triangle, is [tex]\sqrt{39}[/tex] + [tex]\sqrt{7}[/tex] + [tex]\sqrt{46}[/tex]

After performing some mathematical operations, we know that the total cost of 8 popcorn bags and 5 drinks is $53.

So, the total cost:

Cost of a total of 8 bags of popcorn and 5 drinks:

Therefore, after performing some mathematical operations, we know that the total cost of 8 popcorn bags and 5 drinks is $53.

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The correct question is given below:

Zahra and some friends are going to the movies. At the theater, they sell a bag of popcorn for $3.50 and a drink for $5. How much would it cost if they bought 8 bags of popcorn and 5 drinks?