Explain how you would estimate the area of the figure below.
(Each square represents 1 square foot)

Answer:

  Triangles I and III are right triangles, because they are similar to a 3-4-5 right triangle.

Step-by-step explanation:

The Pythagorean theorem tells you of the relationship between the sides of a right triangle. A set of integer side lengths that satisfies the Pythagorean theorem is called a Pythagorean triple. There are an infinite number of these, and there are formulas for finding them.

The smallest Pythagorean triple is {3, 4, 5}, and it is generally the first one you learn about. It is special for a variety of reasons. One of them is that it is the only Pythagorean triple that is an arithmetic sequence. Any multiple of a Pythagorean triple is also a set of side lengths that will form a right triangle.

__

If we multiply the {3, 4, 5} triple by 2/10, we get {6/10, 8/10, 1}, which matches the side lengths of Triangle I in your list. Multiplying by 1/13 gives {3/13, 4/13, 5/13}, which matches the side lengths of Triangle III in your list. That means both Triangles I and III are right triangles.

__

The Pythagorean theorem tells you that a right triangle with sides a, b, and hypotenuse c will satisfy the relation ...

  c² = a² +b²

If the triangle is isosceles, such that a=b, then the hypotenuse will be ...

  c² = a² +a² = 2a²

  c = a√2

In reduced terms, the sides of an isosceles right triangle have the ratios ...

  {1, 1, √2}

That is, there is no rational Pythagorean triple that describes an isosceles triangle. Triangle II cannot be a right triangle.

_____

Additional comment

Just so that you can see {3, 4, 5} is a Pythagorean triple, we show you ...

  5² = 3² +4²   ⇔   25 = 9 + 16

Other small integer triples that may be seen in math problems are ...

  {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}, {11, 60, 61}, {12, 35, 37}

Answer:

x=y+9

Step-by-step explanation:

so what we do here is take x-9 and add 9 to both sides giving us y+9=x all we do is put x first and y+9 last and we have the inverse

Answer:

6√5

Hope this helps :)

Answer:

[tex]3[/tex]

hope this helps

Answer:

Step-by-step explanation:It’s actually the fourth one because all of them equal 2187 the only one is the last one because it equals 1/2187

Answer:

Yes, because the linear function  x - y = 5 is a function

Step-by-step explanation:

x - y = 5  can look like   y = x - 5  with slope 1 and y-intercept -5

so this is a function  which makes set K a function.

Answer:

4x2+216x-684x

Step-by-step explanation:

solnA) The dimensions of the table are in inches

Let

x=the thickness of the border

we know that the table and the border must have an area of 3,276 square feet

convert the dimensions of the table to feet

remember that; 1ft =12in

36in=3ft

72in=6ft

i.e; 3,276 = (6+12x)*(3+2x)

solve for x

3276=6×3+ 6×2x +2x×3+ 4x²

3276=18+12x+6x+4x²

4x²+18x+18-3276=0

4x²+18x-3258

solnB) The dimensions of the table are in feet

Let

x=the thickness of the border

we know that the table and the border must have an area of 3,276 square feet

i.e 3,276 = ()×()

solve for x

3,276 = 72×36 + 72×2x + 2x×36 + 4x²

3,276 = 2,592 + 144x + 72x + 4x²

4x² + 216x + 2,592 + 3276 = 0

4x²+216× - 684= 0

therefore; the quadratic equation can be used to determine the thickness of the border =

4x² + 216x - 684 = 0

Answer:

The answer is 32

Step-by-step explanation:

hope this helps

Answer:

$32

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Since we want to test if it is a right triangle, we can use Pythagorean Theorem

a^2+b^2=c^2

where a and b are the legs, and c is the hypotenuse.

In the given triangle, 23 and 26 are the legs, since they are shorter sides.  42 is the hypotenuse, since it is the longest side.

Therefore, a is 23, b is 26 and c is 42. Substitute these values into the equation

23^2+26^2=42^2

Evaluate the exponents

529+676=1764

Add 529 and 676

1205=1764

This statement is not true, 1205 is not equal to 1764. Therefore this is not a right triangle.

Answer:

C

Step-by-step explanation:

Calculate the distance d using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (8, 3) and (x₂, y₂ ) = (3, 1)

d = [tex]\sqrt{(3-8)^2+(1-3)^2}[/tex]

  = [tex]\sqrt{(-5)^2+(-2)^2}[/tex]

  = [tex]\sqrt{25+4}[/tex]

  = [tex]\sqrt{29}[/tex] → C

Answer:

D

Step-by-step explanation:

The fourth graph makes sense, and follows Deepak's equation. To check if a graph follows an equation, all you have to do is substitute the values of x and y into the equation and see if they follow the equation.

Answer:

it would be the last one

Step-by-step explanation:

Answer:

10 cm, 14 cm, 23 cm

Step-by-step explanation:

Answer:

10 cm, 14 cm, 23 cm

Step-by-step explanation:

Answer:

-10 > (-4x - 6) > -22

Step-by-step explanation:

Given inequality is 5 < 2x + 3 < 11

Now we will multiply this inequality by (-2) resulting,

5(-2) > (2x + 3)(-2) > 11(-2)

-10 > (-4x - 6) > -22 (Sign of inequality gets reversed when the inequality is multiplied or divided by a negative number)

Therefore, the possible range of (-4x - 6) is between -22 and -10.

Answer:

x = 1

Step-by-step explanation:

Download photomath and you can find out.

Answer:

Part A: What is the y-intercept for f(x)? Write your answer as a fraction.

-1/3

Part B: What is the x- intercept for f(x)?

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Part C: Find f(-1)

-1

Step-by-step explanation:

Hope this helps those on Section 7 Topic 4

Answer:

41 Units

Step-by-step explanation:

You have to use Pitagora.

Diagonal (d) = √9²+40² = √1681 = 41

The length of a diagonal is 41 units.

Using Pythagorean theorem formula

Diagonal (d) =√width²+length²

Let plug in the formula

Diagonal (d)=9²+40²

Diagonal (d) =81+1600

Diagonal (d)=√1681

Diagonal (d) =41 units

Inconclusion the length of a diagonal is 41 units.

Learn more about length of a diagonal here:https://brainly.com/question/23008020

Answer:A

Step-by-step explanation:

The cost function for Natalie's clothing store per month is C = 10.25n + 725.

The cost function for Natalie's clothing store per month can be calculated by adding up all the costs she incurs. This includes the cost of the gym shorts, the cost of the boxes for the shorts, the cost of the bags, and the monthly expenses for rent, electricity, and advertising.

The cost of each pair of shorts is $7, the cost of each box is $3, and the cost of each bag is $0.25. The monthly expenses are $650 for rent, $55 for electricity, and $20 for advertising.

Therefore, the cost function for Natalie's clothing store per month can be expressed as: C = 7n + 3n + 0.25n + 650 + 55 + 20, where n represents the number of gym shorts sold.

Simplifying the expression, we get: C = 10.25n + 725

https://brainly.com/question/31952319

#SPJ2

Answer:

y = -2

Step-by-step explanation:

2y + 10 = -3y

subtract 2y from both sides

10 = -5y

divide by -5 for both sides

-2 = y

Answer:

the answer is D

Step-by-step explanation:

12 times 5 equals 60 1 times 15 eqauls 15 60+15=75

Answer:D

Step-by-step explanation:12 senior tickets times 5 dollars each equal $60 plus 15 dollars for one child ticket equal $75

11 child tickets times 15 dollars each equal $165 plus 5 dollars for 1 senior ticket equal $170

Answer:

age of Sam= 15 years

age of Nina  = 25 years

Step-by-step explanation:

Let  Nina's age be X years

Let  Sam's age be Y years

Five years ago Nina's age will be X- 5 years

Five years ago Sam's age will be Y- 5 years

Given in question

Five years ago, Nina was twice as old as Sam

writing it mathematically using X and Y we have

Nina's age = 2 * Sam's age

X- 5 = 2 *(Y- 5)

X = 2 *(Y- 5) + 5 = 2Y - 10 + 5 = 2Y - 5  _________________equation A

__________________________________________________________

Five years in future Nina's age will be X+ 5 years

Five years ago Sam's age will be Y+ 5 years

Given in question

In five years, she will be 1.5 times as old as Sam

writing it mathematically using X and Y we have

Nina's age = 1.5 * Sam's age

X+5 = 1.5 *(Y+ 5)

X = 1.5*(Y+5) -5 = 1.5Y +7.5 - 5 = 1.5Y +2.5  _________________equation B

_______________________________________

in equation A we have X = 2Y - 5

in equation B we have X = 1.5Y + 2.5

equating equation A and B  we have

2Y - 5 = 1.5Y +2.5

=> 2Y - 1.5Y = 2.5 + 5

=> 0.5Y = 7.5

=> Y = 7.5/0.5 = 15

from equation A we have

X = 2Y - 5  (substituting the value of Y = 15 in equation we have)

X = 2*15 - 5 = 25

Therefore age of Sam= 15 years

age of Nina  = 25 years

Answer:

Nina's 25 and Sam's 15

Step-by-step explanation:

Answer:

He sees the future as a test.

He sees his program as a challenge.

He says his program depends on the actions

of the people of the US.

Step-by-step explanation:

i think it's tho i hope this help

The reasons why Johnson's Speech is similar to Kennedy's Speech is because;

A: He sees the future as a test.

B: He sees his program as a challenge.

C: He says his program depends on the actions

John F. Kennedy and Lyndon B, Johnson were former Presidents of the USA and they delivered speeches on civil rights. Now, both Kennedy and Johnson were effective in their speeches by utilizing their credibility as Presidents to back up the statistical and logical evidence.

Now, although  Kennedy was more effective in delivering his speech due to his use everyday situations to appeal to the audience’s emotion, there were some similarities between his speech and that of Johnson and they are;

Read more about similar speeches at; https://brainly.com/question/25887038

Answer:

it would be 0.000088 hope this helps also is it just 4 or is it 4.10

Step-by-step explanation:

Answer:

35.2%

Step-by-step explanation:

Add all of the passengers up for the total.

10 + 81 + 14 + 57 = 162

The fraction for how many Coach passengers that did not check their bags is:

57/162

Simplify to a decimal and multiply by 100 to get percent.

Answer: 41.3

Step-by-step explanation:

Answer:

0, 1, 2

Step-by-step explanation:

Hi there!

A quadratic function can have either 0, 1 or 2 x-intercepts. This means that the graph of a quadratic function can intercept the x-axis 0, 1 or 2 times.

Attached are some graphical representations of all three cases.

I hope this helps!

Answer:

20 minutes

Step-by-step explanation:

2 feet below sea level  is -2

The opposite is 2 feet above sea level +2

They are +2 ft at 20 minutes

Answer:

C

Step-by-step explanation:

2 feet below sea level: depth = +2

Opposite: -2

Time: at 50 minutes

Work Shown:

5(3-x) < -2x+6

15-5x < -2x+6 .... distribute

15-5x+5x < -2x+6+5x ... adding 5x to both sides

15 < 3x+6

15-6 < 3x+6-6 ... subtracting 6 from both sides

9 < 3x

3x > 9 ... flip both sides of inequality, flip the inequality sign

3x/3 > 9/3 ... dividing both sides by 3

x > 3

Notice that when going from 3x > 9 to x > 3, the inequality sign does not flip. The sign only flips if you divided both sides by a negative number.

Answer:

maybe D

Step-by-step explanation:

I'm thinking D because if do

[tex] - 6 - 4 = - 10[/tex]

but also it doesn't make 16 when you do

[tex]4 \times 6 = 24[/tex]