Pythagorean theorem and its converse
problem 3:

leg:16

leg:x

hypo:27

problem 4:

leg:12.8

leg:5.3

hypo:x

problem 5

18 <--------->

`20

x'

The area of the figure given is 49 square feet's.

       ∫dA = ∫∫F(x, y) dx dy

       A =  ∫∫F(x, y) dx dy

Given is a figure as shown in the image attached.

We can write the area of the figure as -

A = A{T} + A{R}

A = (4 x 10) + (1/2 x 6 x 3)

A = 40 + 9

A = 49 square feet's

Therefore, the area of the figure given is 49 square feet's.

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Answer:

  10.35 kg

Step-by-step explanation:

Given a bag of sugar weighs 3.45 kg, you want the weight of 3 bags.

The weight of 3 bags will be three times as much as the weight of one bag:

  3 × 3.45 kg = 10.35 kg

Three such bags weigh 10.35 kg.

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Answer:

40000

hope this helped

Step-by-step explanation:

Answer:

40000

Step-by-step explanation:

Answer:

d. x les-than-or-equal-to 3 Graph B

Graph B expressed as follows; The graph on the coordinate plane, a line goes through (0, 3) and (4, 5). Another line goes through (1, 0.5), and (4, 6.5). The lines intersect at (3, 4.5)

Step-by-step explanation:

The given inequality is expressed as follows;

0.5·x + 3 ≥ 2·x - 1.5

Let y₁ = 0.5·x + 3, and y₂ = 2·x - 1.5, we get;

For x = -1, 0, 1, 2, 3, 4, 5, 6

y₁ = 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6

y₂ = -3.5, -1.5, 0.5, 2.5, 4.5, 6.5, 8.5, 10.5

From the given data, the lines intersect at (3, 4.5)

The graph on the coordinate plane, a line goes through (0, 3) and (4, 5). Another line goes through (1, 0.5), and (4, 6.5). The lines intersect at (3, 4.5)

Please find attached the required inequality created with MS Excel

Therefore, we have;

3 + 1.5 ≥ 2·x - 0.5·x

4.5 ≥ 1.5·x

∴ 3 ≥ x

x ≤ 3

Therefore, with (typographical) correction, the best option is x les-than-or-equal-to 3 Graph B

Answer:

D

Step-by-step explanation:just took the test

Answer:

4n -13

Step-by-step explanation:

notice that the difference between the adjacent terms is 4.

nth term is given by:

nth term = first term + (n-1) × difference -n is any number

= -9 + (n-1) × 4

= -9 + 4n -4

= 4n -13

Answer:

4

Step-by-step explanation:

Half means 1/2

Half of 8

= 1/2 x 8

= 8/2

= 4

Hence, half of 8 is 4.

Answer: 4

Step-by-step explanation:4 + 4 is 8 half of 4 is eight.

A scatter plot which represents relationship between the time (in hours) and height (in meters) has been plotted in the image attached below.

In this scenario, the time (in hours) would be plotted on the x-axis (x-coordinate) of the scatter plot while the height (in meters) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

From the scatter plot (see attachment) which models the relationship between the time (in hours) and height (in meters), a linear equation for the line of best fit is given by

y = -0.29x + 0.52

In conclusion, we can reasonably infer and logically deduce that the scatter plot indicates an inverse relationship between the time (in hours) and height (in meters).

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Answer:

2.7n + 6.6 or 6.6 + 2.7n

Step-by-step explanation:

Algebraic Expressions are just like Numerical Expressions but instead of numbers, alphabets are used, these alphabets can also be used as variables. (BODMAS rule applies to Algebraic Expressions as well.)

Eg. 45x + 31x(2) = 45x + 62x = 107x

Given from the question:

[tex]0.3(9n + 22) \\ = 2.7n + 6.6 \: or \: 6.6 + 2.7n[/tex]

Answer:

- 1/2

Step-by-step explanation:

y2 - y1 / x2 - x1

6 - 12 / 4 - (-8)

-6 / 12

= -1/2

Answer:

Step-by-step explanation:

[tex]6\cdot6+5\cdot(6\cdot7)+6\cdot4+2\cdot(\frac12\cdot6\cdot4)=36+210+24+24=294\,cm^2[/tex]

Answer:

10

Step-by-step explanation:

divide 12.5 by 5 to get the ratio of enlargement, then multiply 2 by that ratio to get x

if you have any questions, leave them in the comments and i will try to answer them, if this helped, pls give brainliest

Answer:

[tex]m = \frac{4}{5} [/tex]

Step-by-step explanation:

The slope of a graph is also known as its gradient, which is the steepness of the graph.

If we are given two points on the line, we can find the slope by taking rise/ run, which is the ratio of the change in y-coordinate against the change in the x-coordinate. This can also be written as a formula:

[tex]\boxed{slope = \frac{y1 - y2}{x1 - x2} }[/tex]

☆ (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate

In this question, we are given the equation of the line. This equation is already in the slope-intercept form (y= mx +c) since the coefficient of y is 1 and all the other terms are on the other side of the equal sign. In the slope-intercept form, m is the slope while c is the y-intercept.

m= ⅘ since the coefficient of x is ⅘ in the given equation (when the equation is in the slope-intercept form).

If the number of dragons in Westeros rose by a shocking 15% this year if there were 300 dragons in the previous year, then there will be a total of 345 dragons in this year.

The percentage increase in the number of dragons in Westeros rose = 15%

The total number of dragons in Westeros rose in previous year = 300

So, for calculating the total number of dragons in Westeros rose in this year we will first find the value of 15% of 300 and then add it to 300.

So, finding the value of 15% of 300

As we know, for removing the percentage sign we will divide the given number by 100

So, the value of 15% of 100 = (15/100)*300 = 45

So, the value of the total number of dragons in Westeros rose in this year will be 300+45 = 345

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The correct question may be like:

If the number of dragons in Westeros rose by a shocking 15% this year if there were 300 dragons in the previous year, then what will be a total of dragons in this year?

Answer:

The KOT club has 5 pledges and can send between 2 and 4 pledges to work at Goodwill on Helping-Out Day. This can be done in 10 different ways

Step-by-step explanation:

The probability the coin comes up all heads or all tails after 4 tosses is 1/8

The value of the odds is given as

Odds = 1 : 7

Represent the odds as a fraction

So, we have the following representation

Odds = 1/7

To convert the odds to probability, we make use of the following equation

Probability = Odds/(1 + Odds)

Substitute the known values in the above equation, so, we have the following representation

Probability = (1/7)/(1/7 + 1)

Evaluate the sum

Probability = (1/7)/(8/7)

Evaluate the quotient

Probability = 1/8

Hence, the probability is 1/8

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Answer:

You add the powers, so (X^3)(x^-17)=x^n n= (3+-17) Meaning n=-14

Step-by-step explanation:

Answer:

4382 contains 4 significant figures, 4382 round to 1 significant figure is 4000.

Answer:

10,000

Step-by-step explanation:

10 x 10 x 10 x 10

Answer:

81 times its common sense but you dont have nun.

Answer:

1) b   2) b

Step-by-step explanation:

1) Both expressions have (x+6). Rearrange them and you'll have one expression as (x+6) and the other as (5ab-4).

2) (4b - 7x)(a + b) factors to be 4ba + 8b - 7ax - 14x, which can be rearranged to 4ab - 7ax + 8b - 14x

Question 1

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

Explanation:

Note how we have (x+6) show up twice. What we can do is erase both copies to end up with 5ab-4. Then stick parenthesis around that to get (5ab-4). Effectively what is going on here is that we're pulling out the GCF (x+6).

Lastly, tack on the (x+6) we erased earlier to get the factorization of (5ab-4)(x+6). Because multiplication can be done in any order, this means it's the same as (x + 6)(5ab - 4)

We can use the distribution method, the box method, or FOIL to expand that factorization back out and help confirm we have the correct answer.

===========================================================

Question 2

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

Explanation:

We'll use the factor by grouping method.

Pair up the terms, then factor each grouping pair. From there, you'll follow the ideas mentioned in problem 1 to finish things off.

This is what the steps could look like:

4ab - 7ax + 8b - 14x

(4ab - 7ax) + (8b - 14x) ... pair up terms

a(4b - 7x) + 2(4b - 7x) ... factor out GCF from each group

(a + 2)(4b - 7x) ... use the trick done in problem 1

(4b - 7x)(a + 2) .... the order of multiplication doesn't matter

You can use the distribution method, FOIL method, or box method to help confirm the answer.

Answer:

y = 15x - 19

Step-by-step explanation:

In order to pass through both (-2, 11) and (1, -34), then the equation must be y = 15x - 19. Hope this helps!

Answer:it is c

Step-by-step explanation:

The sequence of transformations maps quadrilateral ABCD onto quadrilateral EFGH is Reflection across the x-axis, translation 6 units left

Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.

A reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to be a reflection of the other figure, then every point in a figure is at equidistant from each corresponding point in another figure.

According to the question

Quadrilateral ABCD  

A(1,1) , B(2,3) , C(4,3) , D(5,1)

Quadrilateral EFGH

E(-5,-1) , F(-4,-3) , G(-2,-3) , H(-1,-1)

As we can that  

Quadrilateral ABCD and EFGH have opposite sign coordinates

i.e Reflection across the x-axis,

and difference between x axis of Quadrilateral ABCD and EFGH  is 6

|-5 - 1 |  = 6  ( as distance is always +ve)

therefore,

translation 6 units left

Hence, the sequence of transformations maps quadrilateral ABCD onto quadrilateral EFGH is Reflection across the x-axis, translation 6 units left

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Answer: 43.2°

In the given diagram, we are given the hypotenuse and opposite side from the angle x. This means that we need to use the sine ratio. When finding the angle in this triangle, we need to use [tex]sine^{-1}[/tex], not just sine. (This applies for other problems that require you to solve for the angle. The equation should be [tex]sine^{-1}(\frac{5}{7.3} )[/tex]. Calculate the equation with your calculator to get 43.2

Answer:

Below

Step-by-step explanation:

csc x = 1/sinx    

so    sinx ( 1 + cscx )

     = sinx ( 1 + 1/sinx)

      = sinx + sinx /sinx

      = sin x + 1              Done .

The amount of money saved by Andre in 40 weeks is $1280.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.

Given is Andre saves up the same amount of money each week.

We can write the equation, equating the total amount of money saved and the number of weeks as follows. Assume the equation to be -

y = mx + c

Then -

m = (288 - 224)/(9 - 7)

m = 64/2

m = 32

Now -

y = 32x + c

For the point (7, 224), we can write -

224 = 32 x 7 + c

c = 0

For {x} = 48, we can write the amount of money saved as -

y = 32 x 40

y = 1280

Therefore, the amount of money saved by Andre in 40 weeks is $1280.

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Ratios express the relationship between two or more quantities, they can be expressed in different forms such as 6:12, 42:12 and 3:1, 10:10, 100:10, and 10:1, 24:36 and 2:3.

1. 6 Weeks to 12 days:

2. 10 decimeters to 10 centimetres:

3. 4 days to 36 hours:

4. 4 months to 8 weeks:

5. 30 seconds to 6 minutes:

6. 24 girls to 16 boys:

7. 12 mangoes to 36 fruits:

8. 2 years to 36 months:

9. 45 points to 9 games:

10. 468 students for 9 classrooms:

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Answer: r = 5

Step-by-step explanation:

Using Pythagoras we can find the length of the diameter

d^2 = (3 - -5)^2 + (-8 - -2)^2

= 8^2 + (-6)^2

= 64 + 36

= 100

This means d = 10 and r = 5