Six right triangles are shown. Each side of each triangle is also the side of a square.

Answers

Answer 1

The area of the small triangle in six right triangles are shown is 1/25 units² and the area of the small square is 1 units².

What is the area of square?

Area of square is the square of its sides length. It can be given as,

A=a^2

Here, (a) is the length of the side of the square

The legs of the smallest triangle is 1-1 units long. Thus, the area of this triangle is,

[tex]A=\dfrac{1\times1}{2}\\A=\dfrac{1}{2}\rm\; unit^2[/tex]

The area of small squares with side 1 is,

[tex]A=1^2\\A=1 \rm \;unit^2[/tex]

Pythagoras theorem says that in a right angle triangle, the square of the hypotenuse side is equal to the sum of the square of other two legs of the right angle triangle.

The hypotenuse side length of this triangle is,

[tex]h=\sqrt{1^2+1^2}\\h=\sqrt{2}[/tex]

Thus, the area of the square with √2 side is,

[tex]A=\sqrt{2}^2\\A=2\rm\; unit^2[/tex]

Similarly, the area of all the squares and triangle with the different sides can be found out.

Thus, the area of the small triangle in six right triangles are shown is 1/25 units² and the area of the small square is 1 units².

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Related Questions

on the same coordinate plane mark all points (x y) that satisfy the rule y=3x-2 SHOW GRAPH

Answers

The equation y = 3x - 2 is a linear equation

Points (0,2), (1,1) and (2,4) are on the line y = 3x - 2

How to determine the points?

The rule is given as:

y = 3x - 2

Set x = 0

y = 3(0)- 2 = -2

Set x =1

y = 3(1)- 2 = 1

Set x = 2

y = 3(2)- 2 = 4

The above means that (0,2), (1,1) and (2,4) are on the line y = 3x - 2

See attachment for the graph of the line y = 3x - 2

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If mMVUW=(4x+6)° and mWUT=(6x+10)°, what is the measure of WUT

Answers

As ray UW bisects ( divides the angles into two equal parts )

WUT = WUV

6x - 10° = 4x + 6°

6x - 4x = 6° + 10°

2x = 16°

x = 16° ÷ 2 = 8°

Putting the value of x in the Angle WUT

6 × 8° - 10° = 48° - 10° = 38°

A cereal box has a height of 32 centimeters. It has a base with an area of 160 square centimeters.
What is the volume, In cubic centimeters, of the cereal box?

Answers

Answer:

You would multiply 160 by 32 and get an answer of 5120 centimeters cubed.

Step-by-step explanation:You would multiply 160 by 32 and get an answer of 5120 centimeters cubed.

The triangle circumscribes the circle. What is the perimeter of the triangle?

Answers

Answer:

P = 72 ft

Step-by-step explanation:

the perimeter P is the sum of the 3 sides.

Tangents to a circle from an external point are congruent , then

side 24 = 15 + 9

side 21 = 9 + 12

Third side = 12 + 15 = 27 ft

P = 24 + 21 + 27 = 72 ft

Factor 64r^2 −9s^2 ANSWER ASAP I WILL GIVE BRAINLEST

.

Answers

(8r+3s)(8r-3s) dont have working but noticed that it is the difference of two squares

need help please will mark branliest

whats the perimeter of triangle

side is x+1
side is x+1
base is 2x+2

2.whats the perimeter of rectangle

length is x
width is x+3

Answers

Triangle - 4x+3
Rectangle is 4x+6
To get perimeter of some thyroid add all the sides together

The answers are
Perimeter of triangle:6x+6
Perimeter of rectangle:4x+6

Find the slope of the line that is parallel and perpendicular to the following equation.
-4x - 4y = 16

Answers

Answer:

Slope of the line that is parallel: -1

Slope of the line that is perpendicular: 1

Step-by-step explanation:

For the parallel line:

Rewrite your equation to slope-intercept form: y = mx + b

y = mx + b

m = slopeb = y-intercept (when x = 0)

-4x - 4y = 16 <== add 4x to both sides

+4x +4x

-4y = 4x + 16 <== divide both sides by -4

/-4 /-4

y = -x - 4

The slope of the line that is parallel to this line is -1 (invisible 1 in front of x).

For the perpendicular line:

*Perpendicular lines have negative reciprocals*

Steps:

1. Take your original slope (-1)

2. Flip it (-1/1)

3. Change the sign (1)

For a slope of -1, the reciprocal would be: 1

Hope this helps!

-4x-4y=16

Convert to y=mx+b form

-4y=4x+16y=-x-4

Slope:-

m=-1

Parallel lines have equal slope

Perpendicular line's slope=1

What are the domain, range, and asymptote of h(x) = (1.4)x + 5?

domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5
domain: {x | x > 5}; range: {y | y is a real number}; asymptote: y = 5
domain: {x | x > –5}; range: {y | y is a real number}; asymptote: y = –5
domain: {x | x is a real number}; range: {y | y > –5}; asymptote: y = –5

Answers

Answer:

The answer is

→ A.) Domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5

Step-by-step explanation:

For every real x, (1.4)x is always positive, therefore the range would be y > 0, but (1.4)x + 5 adds 5 to every integer in the original range. This suggests that the real range is y | y > 5, or all positive values bigger than 5.

This is the sole choice for the range that A has, therefore, it should. (The other two characteristics hold true, as can be any real integer and lim h(x) = 5 x, implying that y = 5 is a horizontal asymptote of h(x).)

Therefore, A.) Domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5 is your answer.

Hope this helped! :^)

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Submitted on 4/20/2022 at 1:37 PM

(To avoid plagarism, by users whom decide to copy.)

Domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5. Option A is correct.

The given function is [tex]h(x)=1.4^x+5[/tex].

The domain of a function is the set of all valid inputs (x-values) for which the function is defined.

In this case, there are no restrictions on the base (1.4) raised to any real exponent, and thus, the domain includes all real numbers.

Therefore, Domain: {x | x is a real number}

The range of a function is the set of all possible output (y-values) that the function can produce.

In this case, the base (1.4) raised to any real exponent will always be positive, and when you add 5 to a positive number, you get values greater than 5.

Hence, the range consists of all real numbers greater than 5.

Therefore, Range: {y | y > 5}.

An asymptote is a line that a function approaches but never crosses.

For this exponential function, there are no vertical asymptotes since it is defined for all real numbers.

However, there is a horizontal asymptote. As the value of x approaches negative or positive infinity, the function h(x) will approach 5.

Therefore, Asymptote is y = 5.

Hence, option A is correct, domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5.

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A stadium can seat `16000` people at full capacity.if there are `13920` people in the stadium, what percent of the stadium is full?

Answers

Answer:

87%

Step-by-step explanation:

13920/16000=0.87=87%

2-root3/root3. Rationalize the following equation

Answers

Answer:

-1/3

Step-by-step explanation:

Multiply by root 3 on the top and bottom. Root 3 times root 3 is 3. 2-3 is -1.

Which equation represents the line shown in the graph below

Answers

Answer:

b: y = 2x + 5

Step-by-step explanation:

you can find this out by first looking at what the slope is

the slope is rise over run which is 2

then you can see that the y intercept is 5

y = 2x + 5

1. Two numbers have a product of 12 but their sum is -7 what are the numbers.
2. The sum of two numbers is 1 but their product is -30 what are the numbers.

Answers

Answer:

1. (-3) and (-4)

2. (-5) and 6; vise versa

Answer:

Step-by-step explanation:

hello :

1)Two numbers have a product of 12 but their sum is -7 :

means : xy=12 ....(*)

x+y = -7 ....(**)

solve this system : use (**) you have x = -y-7 put this value in (*)

so : (-y-7)y = 12

-y²-7y-12 = 0

y² +7y+12=0 a=1 b=7 and c= 12

the discriminant delta =b²-4ac delta = 7²-4(1)(12) = 1

y1 = (-7-1)/2 = -4 and y2 = (-7+1)/2 =-3

but x= -7-y

if :y = - 4 x= -7-(-4) =-3

if : y=-3 x = -7-(-3) =-4

2) same method : xy=-30

x+y=1

The hypotenuse of a right triangle measures 4 cm and one of its legs measures 3 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

Answers

Applying the Pythagorean theorem, the measure of the other leg, to the nearest tenth, is: 2.6 cm.

What is the Pythagorean Theorem?

In a right triangle, where the lengths of its two legs are a and b, and the hypotenuse length is c, the Pythagorean theorem states that: c² = a² + b².

Given the following parameters of the right triangle:

c = 4 cma = 3 cmb = ? (other leg)

Apply the Pythagorean theorem:

b = √(4² - 3²)

b = 2.6 cm (nearest tenth)

Thus, applying the Pythagorean theorem, the measure of the other leg, to the nearest tenth, is: 2.6 cm.

The points on the graph are given as:

(x,y) = (0,0) and (4,11)

The equation of the graph is then calculated using:

y = (y₁/x₁) * x

This gives

y = (11/4) * x

Evaluate

y = 11x/4

Hence, the equation that represents the graph is y = 11x/4

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WHOEVER HELPS ME WITH THESE 4 QUESTIONS WILL GET 60 POINTS AND RIGHT AWNSERS I WILL RATE U BRAINLIEST thank u so much and pls hurry up i only have 7 min left! ( pls good explanation)

Answers

34) to get 16 points he will have to answer 5 questions
35) to get 128 points answer 8 questions
36) 256 points: 9 questions
37) 512 points: 10 questions

Answer:

34) 5 questions

35) 8 questions

36) 9 questions

37) 10 questions

Step-by-step explanation:

We could create an exponential function for this scenario, but it is quicker and easier to simply list the potential scores.

We are told that the initial score is 1.

We are told that the the score doubles each time.

Therefore, the scores in sequence are:
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 ... etc.

34) 16 is the 5th term in the sequence, so 5 questions

35) 128 is the 8th term in the sequence, so 8 questions

36) 256 is the 9th term in the sequence, so 9 questions

37) 512 is the 10th term in the sequence, so 10 questions

Triangle JKL has vertices J(-4, 4), K(-1, 3), and
L(-2, 1). Graph the figure and its rotated image after a
clockwise rotation of 90° about the origin. Then give the
coordinates of the vertices for triangle J'K'L'.
K
o

NO LINKS

Answers

Answer:

J(0,6)

K(-1,3)

L(-3,4)

Step-by-step explanation:

Hello everyone i need help with the following question?

If x=3 and y=67

what is 6x × 8y + 27x - 6y + 3=

Answers

Answer:

9330

Step-by-step explanation:

6x × 8y + 27x - 6y + 3 = 18 × 536 + 81 - 402 + 3 =

But better to get hurt by the truth than comforted with a lie.How could you relate with this ? Which statement about the interference behavior of electromagnetic radiation seen in the double-slit test experiment is true? (1 point)O Waves that make up the radiation collide with each other so that they add together or cancel each other out.O Particles that make up the radiation collide with each other so that they add together or cancel each other out.O Particles that make up the radiation collide with each other and scatter randomly.O Waves that make up the radiation do not interact with each other. A politician takes an SRS of 75 citizens in a county to see what proportion of citizens sampled are satisfied withtheir standard of living. Suppose that 80% of the 118,000 citizens in the county are satisfied with theirstandard of living.What are the mean and standard deviation of the sampling distribution of the proportion of citizens who aresatisfied with their standard of living? Refer to the illustrations showing a sarcomere in two different stages What does Stage 2 represent? a muscle that is rotating a muscle that is fully at rest a muscle that is fully contracted Last week, Riley worked 7.5 hours per day for 3 days and earned a total of $306.45. What was Riley's hourly rate of pay last week? Graph the solution to this inequality on the number line.1/4x 2 < 1 1/2 find the slope and y-intercept of the line y=7x-9 Hold fast to dreamsFor if dreams dieLife is a broken-winged birdThat cannot fly.Hold fast to dreamsFor when dreams goLife is a barren fieldFrozen with snow.- Langston Hughes Assume the following information: April 1 Inventory 3 units at cost of $20 April 10 purchase 5 units at cost of $20 April 12 sale 6 units Using the perpetual inventory system, what is the amount of cost of goods sold How long does the shingles vaccine remain effective. 28. Pay attention to the height data (cm) of the following 10 students! 155, 153, 153, 160 157, 155. 160, 155, 150, 155 The data mode is Your :A. 150 B. 153 C. 155 D. 157 Given the function f(x)=2x+1/x and f(1/x)=f(x).Find the value of xR correct to 3 significant figures.x=2.83x=0.382x=1x=2.83I NEED A QUICK ANSWER PLSSS 3/4 of ... is 12 I neeed your help please help me pls help me to answer this You have a cup of lemonade. Each ice cube has a length of 2 cm, a width of 1 1/4 cm and a height of 3 cm. What is the volume of one of the ice cubes? Show your steps and Explain how you used math to come to your decision. / 100 points if you answer and ill give you brianliest and 5 stars\ what is -4/3x < -8 equal? What cell structure is best represented by the image? A. a permeable exoskeleton B. a waterproof nuclear envelope C. a non-permeable cell wall D. a selectively permeable membrane Solve for the missing angle labeled "?".9) MI115SUP47RQA) 47B)65C) 68D)133 HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP The blue dot is at what value on the number line? -3 -1