Bunting has been hung in a straight line
between a wall and a house, as shown
below.
Calculate the height, p, of the house.
Give your answer in metres to 2 d.p.
36°
2.64 m
5.47 m
Not drawn accurately

The given number 2/3 belongs to the subset of rational numbers.

All numbers on the number line, from negative to plus infinity, are considered to be real numbers. They are breaking up into the following groups:

1. We can count the components of a set using natural numbers.

2. Natural numbers and their opposites in the negative, such as zero, are known as integers.

3. Fractions can be used to express rational numbers.

4. Non-periodic infinite decimals are indicative of irrational quantities.

The answer to the given question is : It belongs to the rational numbers because it is a fraction.

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Answer:

[tex]a.[/tex] [tex]\frac{49}{50}[/tex]

[tex]b.[/tex] [tex]8[/tex]

Step-by-step explanation:

[tex]a.[/tex]  [tex]\frac{1}{2} +\frac{2}{5} +\frac{2}{25}[/tex]

To solve this, we must first find the LEAST COMMON MULTIPLE (LCM).

To find the LCM, we must list the multiples of the denominators, then find the smallest multiple that all three numbers have in common.

2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

25: 25, 50

The LCM is 50.

Now that we have found the LCM, we will change the fractions so that all three have a denominator of 50.

To do this, we multiply the numerator and the denominator by the same number.

[tex]\frac{1}{2} *\frac{25}{25} =\frac{25}{50}[/tex]

[tex]\frac{2}{5} *\frac{10}{10} =\frac{20}{50} \\[/tex]

[tex]\frac{2}{25} *\frac{2}{2} =\frac{4}{50}[/tex]

Now that all fractions have the same denominator, we can add them. Remember, when adding fractions, the denominators stay the same. Only add the numerators.

[tex]\frac{25}{50} +\frac{20}{50} +\frac{4}{50} \\\\=\frac{49}{50}[/tex]

_______________________________________________________

[tex]b.[/tex]  [tex]\frac{2}{3} *\frac{30}{7} *\frac{14}{5}[/tex]

To multiply fractions, multiply the numerators, then the denominators. Lastly, simplify the product.

[tex]2*30*14=840\\3*7*5=105[/tex]

[tex]\frac{840}{105} =\frac{8}{1}[/tex]

Mr mole descend at the rate of 2.3 meters per minutes.

A rate in mathematics is the comparison of two related values expressed in dissimilar units.

The given equation to represent the position of Mr. Mole is

A = -2.3 t - 7

where A denotes the depth and t is the time.

Now the rate can be found out by dividing the change in depth by the change in time.

Differentiating we get

ΔA = -2.3 Δt

or, ΔA / Δt = -2.3

hence the rate of the mole is 2.3 meters per minutes.

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We get PQR≅ ABC by using the Pythagorean theorem. Consequently, we would have: ∠ACB = ∠PRQ = 90°.

According to the Pythagorean Theorem, the square of a right triangle's longest side (hypotenuse) is always equal to the sum of the squares of its other two sides (legs).

Knowing that PQR is a right triangle, the following follows:

x² + y² = PQ²

Additionally, we are informed that x² + y² = PQ² , therefore by substitution, we get  [tex]Z^{2} = PQ^{2}[/tex] Both triangles have corresponding congruent sides since  , ΔPQR ≅ΔABC.

We can deduce the following from the congruent triangles' corresponding parts: ΔACB = ΔPRQ = 90°.

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Based on the number of bags of leaves that Finn emptied and the number of bags remaining, the total number of bags that Nora and Finn filled up is 11 bags.

Finn and his sister, Nora, have been racking leaves and they raked enough to fill up a certain number of bags.

Out of these bags, Finn emptied 4 bags to be able to make a leaf pile. Nora then stopped him from emptying the other 7 bags.

The total number of bags of leaves raked by Nora and Finn is:

= Number of bags remaining + Number of bags emptied by Finn

= 7 + 4

= 11 bags of leaves

Remaining part of question:

How many bags of leaves were raked by Finn and Nora?

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Answer:

1. P

2. U

3. K

4. A

5. M

6. C

7. E

8. J

9. L

10. I

Answer:

A. 6.5 liters

B. 26 servings

Step-by-step explanation:

Part A:

(4 × 1.5) + (2 × .25) = 6.5 liters

Part B:

6.5 liters ÷ .25 liters/serving = 26 servings

The equation would be y = 16/9x which represents the algebraic relationship between x and y which is the correct answer would be an option (A).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Given that x and y vary directly and y = 32 when x = 18

Direct variation equation can be written as:

y = kx where "k" is a constant.

Substitute the values of y = 32 and x = 18 in the direct variation equation and solve for k:

⇒ 32 = k(18)

⇒ k = 32/18

⇒ k = 16/9

The direct variation equation :

⇒ y = 16/9x

Therefore, the equation would be y = 16/9x which represents the algebraic relationship between x and y.

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By using the concept of composite solid, the volume of the entire figure is equal to 566 cubic centimeters.

In this question we find a composite solid formed by the following components:

Please notice that the volume of a prism is equal to the product of the area of the transversal area and the height of the prism. Now we proceed to determine the volume of the entire figure:

V = V₁ + V₂ + 2 · V₃    

V = (19 cm) · (2 cm) · (7 cm) + (10 cm) · (4 cm) · (7 cm) + 2 · [(1 / 2) · (5 cm) · (4 cm)]

V = 566 cm³

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Using algebraic expression and equation, the hotel charge before tax in each city is $5749.60 and $6249.60, respectively.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

Let x = hotel charge before tax in the first city

If the hotel charge before tax in the second city was $500 higher than in the first, then

hotel charge before tax in the second city = $500 + x

If the tax in the first city was 6.5% and the tax in the second city was 6% and the total hotel tax paid for the two cities was $748.7, then

x(0.065) + ($500 + x)(0.06) = $748.7

Solving for x,

x(0.065) + ($500 + x)(0.06) = $748.7

0.065x + $30 + 0.06x = $748.7

0.065x + 0.06x = $748.7 - $30

0.125x = $718.7

x = $5749.60

hotel charge before tax in the first city = $5749.60

hotel charge before tax in the second city = $500 + x

hotel charge before tax in the second city = $500 + $5749.60

hotel charge before tax in the second city = $6249.60

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Y-b=m (x-a)

y- 4= -5 (x+2)

y- 4= -5x -10

y = -5x -6

Answer:

the vertical line is:

x = 5

The horizontal line is:

y = -9

Step-by-step explanation:

A vertical line has a fixed x-value, while a horizontal line has a fixed y-value.

Then we can write a vertical line as:

x = a

and a horizontal line as

y = b

Then, if we want a vertical line that passes through the point (5, -9), remember that the x-vale will be fixed, then we fix the x-value at the same x-value of the point, which we know that is 5, then the vertical line that passes through the point (5, -9) is:

x = 5

Step-by-step explanation:

Answer: 31, 34, 17

Step-by-step explanation:

The angle between the line PT and the plane PQRS is 63.4°

In this question, we have been given a rectangular based pyramid PQRST.

A pyramid has height of 10 cm.

We need to find the angle between the line PT and the plane PQRS.

We know that the angle made by triangular plane TPS with the rectangular plane PQRS is same as the angle between the line PT and the plane PQRS.

If we draw a perpendicular through point T and intersects the plane PQRS at point M.

Let R be the midpoint of side PS

Consider a right triangle RMT.

We need to find angle TRM.

Here, MT = 10 cm, MR = 5 cm (1/2 × length of the rectangle)

Consider the tangent of the angle TRM

tan(∠TRM) = TM / RM

tan(∠TRM) = 10 / 5

∠TRM = tan^(-2)[2]

∠TRM = 63.4°

Therefore, the angle between the line PT and the plane PQRS is 63.4°

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Answer:

15 percent change

Step-by-step explanation:

1) 500 - 425 = 75

2) 75 / 500 = 0.15

3) 0.15 * 100= 15

Answer:

[tex]-2(x+5) = -2x -10[/tex]

Step-by-step explanation:

Hi there,

For us to answer the question we have to check if whether the end product on the both LHS and RHS are equal or not , so lets take each equation is whether both the sides are similar or not :

First eq :-

[tex]-2(x-5) = -2x + 5\\giving\\-2x+10\neq -2x+5[/tex]

Since it is not equal it is incorrect.

Second eq:-

[tex]-2(x+5) = -2x-5\\giving\\-2x-10\neq -2x-5[/tex]

Since it is not equal it is incorrect.

Third eq:-

[tex]-2(x+5) = -2x -10\\giving\\-2x-10=-2x-10\\[/tex]

Now we got the equation that equals both in LHS and RHS.

So our Answer is

[tex]-2(x+5) = -2x -10[/tex]

Hope this helped you out if so do mark me as the brainliest,

a fellow mate,

cheers!

Answer:

7. 45

8. 19

9. 15

10. 24

11. 23

12. 6

13. 8

14. 15

15. 12

16. 3

17. 26

18. 12

19. 21

20. 34

21. 2

hope this helps!:)

Using an assumed value that the octagon must fit inside an 11 inch square space, tthe length of each side of the octagon would be 8.23 inches.

Since an assumed side of the square is 11 inches

Here, y is the two equal sides of the right-angle triangle

So y + x + y = 11

Using Pythagoras's theorem for the right angle triangle

y² + y² = x²

2y² = x²

y² = (x²)/2

y = x /√2

So substitute the value of y = x /√2 in the equation

x /√2 + x + x /√2 = 11

2x /√2 + x = 11

2x /√2 + x√2 /√2 = 11

x[2/√2 + √2 /√2] = 11

x[(2 + √2) /√2] = 11

x(2 + √2) = 11√2

x = 11√2/(2 + √2)

x = 15.5563/3.4142 = 12.1421

Round to the nearest hundredth of an inch

x = 12.1

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Based on the number of houses in the neighborhood and those that have a chain-link fence and a privacy fence, the number of houses with no fence in the backyard are 28 houses

First, find the number of houses in the neighborhood that have a chain-link fence:

= Number of houses x Proportion with a chain-link fence

= 80 x 1/4

= 20 houses

Then find the number of houses in the neighborhood that have a privacy fence:
= Number of houses x Proportion with a privacy fence

= 80 x 2/5

= 160 / 5

= 32 houses

The number of houses in the neighborhood that have no fence is:

= Total number of houses - Houses with a chain-link fence - Houses with a privacy fence

= 80 - 20 - 32

= 28 houses with no fence

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The new conditional statement that follows from the pair of true statement is If 4x + 5 = 13; then -5x = -10

The law of Syllogism states that if the following two statements are true:

Statement 1: If x , then y

Statement 2: If y , then z

Then we can derive a third true statement:

Statement 3: If x , then z

From the given;

Statement 1: If x , then y

If 4x + 5 = 13; then x = 2

Statement 2: If y , then z

If x = 2; then -5x = -10

Statement 3: If x , then z

If 4x + 5 = 13; then -5x = -10

In conclusion, according to the law of Syllogism, the statement that follows from the pair of true statement is If 4x + 5 = 13; then -5x = -10

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Answer:

-4 11/15

Step-by-step explanation:

The total attendance at the food festival from 2014 to 2017 is 16648.

It should be noted that a graph is simply used in Mathematics to illustrate the information given for a data.

In this case, the graph shows the attendance for the years that are given. Therefore, the total attendance at the food festival from 2014 to 2017 will be:

= 2118 + 3391 + 4785 + 6354

= 16648

The attendance is 16648.

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The total cost for the items which the Tiny family purchased is $41.6 × 10⁻⁶ while their change is equal to $45.84 × 10⁻⁵.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In order to determine the total cost, we would add all of the costs incurred by Tiny family as follows:

Total cost = 1.3 × 10⁻⁵ + 2.1 × 10⁻⁵ + 7.6 × 10⁻⁶

Total cost = (1.3 + 2.1) × 10⁻⁵ + 7.6 × 10⁻⁶

Total cost = 3.4 × 10⁻⁵ + 7.6 × 10⁻⁶

Total cost = $41.6 × 10⁻⁶

Next, we would calculate the change as follows:

Change = Amount paid - Total cost

Change = $5.0 x 10⁻⁴ - $41.6 × 10⁻⁶

Change = $45.84 × 10⁻⁵

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The solution of this absolute value equation is f<3

Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.

On subtracting 7 from both sides

=6|-f + 3| + 7 - 7 > 7 - 7

=6|-f + 3| > 0

Now diving both sides by 6

|-f + 3| > 0

Now, this results in two condition

1.) -f+3>0

So,

f<3

2.) -(-f+3)<0

So,

3-f<0

f<3

Therefore, f can accept any value that satisfies the equation f<3.

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Answer:

y = (3/2)x + 3

Step-by-step explanation:

Comment

The general equation is

y = mx + b

Finding m

The equation for the slope is

m = (y2 - y1)/(x2 - x1)

Givens

y2 = 3

y1 = 0

x2 = 0

x1 = - 2

m = (3 - 0)/(0 - -2)

m = 3 / 2

m = 3/2

Finding b

b is the y intercept which is (0,3)

x = 0

y = 3

3 = 0*3 + b

b = 3

So the equation is

y = (3/2) x + 3

The rule of g(x) after the transformation is g(x) = 3(x + 4)^2 + 3(x + 4)

The function is given as

f(x) = x^2 + x

The transformations are given as:

The rule of the above transformations are :

When the above transformations are combined, we have

This means that

g(x) = 3f(x + 4)

So, we have

g(x) = 3(x + 4)^2 + 3(x + 4)

Hence, the function g(x) is g(x) = 3(x + 4)^2 + 3(x + 4)

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Answer:

I am stuck on it too can some one help me please.

Answer:

Formula for gradient is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2), where x and y are the coordinates of the points.

(k-4)÷(0-1) = 9

k-4 = 9(0-1)

k-4 = -9

k = -5