Triangle ABC is a right triangle. The length of one of the legs is 12 centimeters, and the length of the hypotenuse is 20 centimeters. What is the length of the other leg?​

Answers

Answer 1

Answer: 16 centimeters

Step-by-step explanation:

    We will use the Pythagorean theorem to solve. The c variable is the hypotenuse, the a and b variables are the legs.

a² + b² = c²

12² + b² = 20²

144 + b² = 400

b² = 256

b = [tex]\sqrt{256}[/tex]

b = 16

          The length of the other leg is 16 centimeters.

Answer 2

Answer:

The other leg is 16 cm long.

Explanation:

Use the Pythagorean theorem:

[tex]c^2=a^2+b^2[/tex],

where:

[tex]c[/tex] is the hypotenuse, and [tex]a[/tex] and [tex]b[/tex] are the other two sides (legs).

Let [tex]a=12[/tex] [tex]cm[/tex]

Rearrange the equation to isolate [tex]b^2[/tex]. Plug in the values for [tex]a[/tex] and [tex]c[/tex], and solve.

[tex]b^2=c^2-a^2[/tex]

[tex]b2=(20 cm)^2-(12 cm)^2[/tex]

Simplify.

[tex]b^2=400 cm^2-144cm^2[/tex]

[tex]b^2=256 cm^2[/tex]

Take the square root of both sides.

[tex]b=\sqrt{256cm^2}[/tex]

Simplify.

[tex]b=16[/tex] [tex]cm[/tex]


Related Questions

Ms. Bell's mathematics class consists of 11 sophomores, 7 juniors, and 13 seniors. How many different ways can Ms. Bell create a 3-member committee of juniors if each junior has an equal chance of being selected?

Answers

Answer:

35 ways

Step-by-step explanation:

Seven juniors to choose three from

  7 C 3 = 7! / ( 4! 3!) = 35

Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-response question. There are 15 questions on the test and the students have been given 55 minutes to complete it

Answers

Let

x------> the number of multiple choice question

y------> the number of free response question

we know that

-----> equation A

-----> equation B

Substitute equation B in equation A

Find the value of x

therefore

the answer is

the number of multiple choice question are

the number of free response question are

Find the gradient of the curve y =2x³-7x+4when x=-2

Answers

By applying concepts from vectorial calculus, we conclude that the gradient of the one variable function y = 2 · x³ - 7 · x + 4 when x = -2 is equal to 17.

How to find the gradient of a function

A gradient is a generalization of the tangent curve used for multivariate function, that is, a function with more than one variable. In this case we have a function with one variable, which means that the gradient is equal to the slope:

[tex]\nabla f = \frac{df}{dx}[/tex]     (1)

Now we proceed to calculate the gradient of the curve:

[tex]\nabla f = 6\cdot x^{2}-7[/tex]

[tex]\nabla f = 6\cdot (-2)^{2}-7[/tex]

[tex]\nabla f = 17[/tex]

By applying concepts from vectorial calculus, we conclude that the gradient of the one variable function y = 2 · x³ - 7 · x + 4 when x = -2 is equal to 17.

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Quadrilateral ABCD below is a parallelogram. Use the figure to select the best answer from the choices provided. If AD = 3x + 5, AB = 7x – 3, and BC = 8x – 10, what is the value of x? Select the best answer from the choices provided. A. 2 B. 3 C. 7 D. 8

Answers

Answer: 3

Step-by-step explanation:

Opposite sides of a parallelogram are congruent, so AD=BC.

[tex]3x+5=8x-10\\5=5x-1015=5x\\x=\boxed{3}[/tex]

Look at the pattern below.
step 1 step 2 step 3 step 4
How many squares will be in the pattern at the 8th step?
Choose 1 answer:
8 squares
12 squares
B

Answers

There will be 36 squares in the 8th step of the pattern

How to determine the number of squares?

The pattern and the squares are represented as:

Pattern   Squares

1                 1

2                3

3               6

4             10

This can be rewritten as:

Pattern   Squares

1                 1

2                1 + 2

3                1 + 2 +3

4                1 + 2 + 3 +4

So, the number of squares on the 8th pattern is:

8th pattern = 1 + 2 + 3 +4 + 5 + 6 + 7 + 8

Evaluate

8th pattern = 36

Hence, there will be 36 squares in the 8th step

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Expand and simplify
(5x + 2)(x + 2)

Answers

Answer:

5x²+12x+4

Step-by-step explanation:

5x²+10x+2x+4

5x²+12x+4

Answer:

[tex]5x^{2}+12x+4[/tex]

Step-by-step explanation:

Use the FOIL method to expand.

5x*x+

2*x+

5x*2+

2*2

which is

5x^2+2x+10x+2

combining the two x s we get

5x^2+12x+4


28. Which of the following is the correct measure of
angle ABC?

A. 30°
B. 88°
C. 132°
D 44°

Answers

Answer:

D) 44°

Step-by-step explanation:

According to the diagram we observe:

∠ACD is the exterior angle of triangle ABC.

As we know the exterior angle is same as the some of the remote interior angles.

It can be shown as:

m∠ACD = m∠CAB + m∠CBA

Substitute the values and solve for x:

5x - 18 = 3x - 2 + x + 145x - 18 = 4x + 125x - 4x = 12 + 18x = 30

Find the measure of m∠ABC:

x + 14 = 30 + 14 = 44

The matching answer choice is D.

Don’t know how to solve

Answers

Answer:

Hi,

Step-by-step explanation:

I don't know the name in Enghish but in French it is "une règle de 3"

(may be linear rule)

arc length= 2*π*r/360*100=50*π/9

area= π*r²*100/360=250*π/9

Solve the equation. 5/x+3 + 4/x+2 = 2
Please explain this step by step

Answers

Answer:

Step-by-step explanation: If I have to Write In Slope- Intercept form, This Is how I explain it.

Since x = −3 is a vertical line, there is no y-intercept and the slope is undefined.

Slope: Undefined

y-intercept: No y-intercept

this is a lot more clear​

Answers

i agree it is much more clear

kadeem has 58m of fencing to build a four-sided fence around a rectangular plot of land. the area of the land is 204 square meters. solve the dimensions of the field. (length and width)

Answers

I’m not quite sure what you mean so do this equation



64837//294738383&38373736

The dimensions of the rectangular plot of the land is 17 × 12 square units.

What is perimeter?

The perimeter of a shape is the distance around the shape. It is the total length of the shape's sides.

What is the formula for the perimeter of rectangle?

Perimeter of rectangle = 2( length + width)

What is area?

The area can be defined as the space occupied by a flat shape or the surface of an object.

What is formula for the area of rectangle?

Area of rectangle = length × width

According to the given question.

Let the length and width of the rectangular plot be x and y respectively.

Kadeem has 58m of fencing.

Perimeter of the rectangular plot of land = 58m

⇒ 2(length + width) = 58

⇒ x + y = 29...(i)

Also, area of plot land = 204 square units.

⇒ x × y = 204

⇒ x × (29 - x) = 204

⇒ [tex]29x -x^{2} = 204[/tex]

⇒ [tex]x^{2} -29x + 204=0[/tex]

⇒ [tex]x^{2} -12x -17x +204=0[/tex]

⇒ [tex]x(x-12)-17(x -12)=0[/tex]

⇒ [tex](x -12)(x -17) = 0[/tex]

⇒ x = 12 or x = 17

When, [tex]x = 12[/tex]

[tex]y = 29-12 = 17m[/tex]

And when, [tex]x = 17[/tex]

[tex]y = 29 - 17 = 12m[/tex]

Hence, the dimensions of the rectangular plot of the land is 17 × 12 square units.

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8. Jaime has 20 min to get to her after- school job. Despite her best efforts, she is
frequently late and has recorded her travel time (in minutes) as {18, 20, 22, 27, 16, 23, 25,
26, 19, 28). Her boss has told her that unless she shows more consistency, she will lose her
job. Over the next two weeks, Jaime records her travel time: (22, 20, 22, 24, 24, 23, 25, 21,
19, 21). Should Jaime lose her job? Use statistics (mean and standard deviation) to justify
your answer. [8 marks]

Answers

The calculation of the mean shows that Jamie should not lose her job as she was faster after the talk from the boss.

How to calculate the mean?

The mean of the travel time in the first scenario will be:

= (18, 20, 22, 27, 16, 23, 25,26, 19, 28)/10

= 224/10

= 22.4

She she shows consistency, the mean will be:

= (22, 20, 22, 24, 24, 23, 25, 21, 19, 21)/10

= 221/10

= 22.1

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11+7+(75÷(16+9))+4x(20÷10)+(28-27)


by the way the x in 4x is not a variable it means multiplication

Answers

Answer:

30

Step-by-step explanation:

What is the measure of AT in 0 below?
A
123
0
97⁰
T
ASAPP!!

Answers

If an angle is a central angle, meaning that it goes through the center, then its corresponding arc has the same measure.

AOT is a central angle, which means that AT will have the same measure.

AOT = 97, AT = 97

Answer: A, 97

Hope this helps!

Can you please help me with this

Answers

Answer:

  dilation by a factor of 1/3 about the origin

Step-by-step explanation:

Each side of triangle B is 1/3 the length of the corresponding side of triangle A. This tells you dilation using a scale factor of 1/3 is involved.

Lines joining corresponding points of triangles A and B converge on the origin. This tells you the center of dilation is the origin.

The one transformation that maps A to B is ...

  dilation by a factor of 1/3 about the origin

_____

Additional comment

No rotation, reflection, or translation are needed, since the triangles have the same orientation, and dilation fully accounts for their relative position.

ASAP!
What is the value of x, given that the two prisms are similar?
5
20
2 25
1.5
A. 2
OB. 10
OC. 2.5
OD. 1.5
3
1
1

Answers

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. The value of x is 10. Thus, the correct option is B.

What are Similar Figures?

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".

Since the two prisms are similar, their sides will be in a common ratio. The value of the common ratio will be,

Common ratio = 4/2 = 5/2.5 = 3/1.5 = 2

Since the common ratio of every side is equal to 2, the value of x can be written as,

Common Ratio = 20/x = 2

20/x = 2

x = 10

Hence, the value of x is 10. Thus, the correct option is B.

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What is the sum of the first 6 terms of the sequence defined by an = 3n - 2?

Answers

Answer:

51

Step-by-step explanation:

when n=1

t 1=1

when n=2

t2=4

as first term is 1 and second term is 4 so the common difference is 3 ,for 6 term if you put this in formula for sum to the n term you will get 51

t1 =1

d=3

n=6

than S6=51

An unusual number cube (with 6 sides) has the numbers 2, 2, 4, 4, 6, and 6 on its faces.
It is rolled once.
Match the outcome to its probability.

Answers

Answer:

1. P(2 or 4) - 2/3

2. P(multiple of 2) - 1

3. P(multiple of 3) - 1/3

4. P(odd prime numbers) - 0

Step-by-step explanation:

Hope this helps

P(2 or 4) = 2/3

p(multiple of 2) =  1

p(multiple of 3) = 1/3

P(odd prime numbers) = 0

What are the probabilities?

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

P(2 or 4) = (number of sides that have a value of 2 / total number of sides) + (number of sides that have a value of 2 / total number of sides) = 2/6 + 2/6 = 2/3

p(multiple of 2) = number of sides that are a multiple of 2 / total number of sides

6/6 = 1

p(multiple of 3) = number of sides that are a multiple of 3/ total number of sides

= 2/6 = 1/3

P(odd prime numbers) = number of odd prime numbers / total number of sides  = 0

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what is the simplified forom of i^14

Answers

Answer:

i4=1

Step-by-step explanation:

Explanation: Rewrite i14 as (i4)3×i2 . If i=√−1, then i2=−1 . From here (i2)2=(−1)2 , so i4=1

HELP PLEASEEE!!!!1!!!!

Answers

Answer: 1. Dilation.

Step-by-step explanation: All of these transformations do not change the shape's form except for a dilation. It is nessacary to change the shape, so it is a dilation.

The function ((-1,2),(9-1),(-8,5),(2,-8)(?,9)has the same set for its domain and range.

Find the missing value from the function. The missing value is _____.

Answers

Answer:  5

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

Explanation:

The range is {2, -1, 5, -8, 9} which sorts to {-8, -1, 2, 5, 9}. This is the set of y coordinates of the points given. Each point is of the form (x,y).

Since the domain and range are the same set in this case, we must have those value mentioned as x coordinates of the points.

The domain is the set of x coordinates of the points given.

The values -8, -1, 2, and 9 are already used as x coordinates. The only thing missing is the 5.

The input of a function can also be identified as the ____?

Answers

Answer:

Domain of the function

Step-by-step explanatio

Simplify the expression. Write your answer as a power.
8¹⁰x8⁴
The simplified expression is

Answers

Answer:

[tex]8^{14}[/tex]

Step-by-step explanation:

When we multiply exponents with the same base, the product it the base to the power of the exponents added together. In this case, the base will remain as 8 and the exponent will be 10 + 4 = 14. Therefore, the answer is [tex]8^{14}[/tex].

Answer:

[tex]\large\boxed{\sf \sf 8^{14}}[/tex]

Explanation:

[tex]\rightarrow \sf 8^{10} \ \ x \ \ 8^4[/tex]

apply exponent rule: [tex]\sf \bf a^b\cdot \:a^c=a^{b+c}[/tex]

[tex]\rightarrow \sf 8^{10+4}[/tex]

[tex]\rightarrow \sf 8^{14}[/tex]

Independent Assessment 2
Directions: Use the data in the line graph below to answer the following questions.
Pieces of Bibingka Sold Per Day
60
50
40
30
20
10
0
Monday
Tuesday Wednesday Thursday
1. How many bibingka were sold on
Tuesday and Wednesday?
2. What days have the same number of
bibingka sold?
3 How many more bibingka were sold
on Monday than on Wednesday?
4. What is the average pieces of
bibingka sold for the first three days?
5. In your opinion, what other kind of rice
cake do you prefer to sell? Give your
reason
Pieces of Bibingka Sold
Friday
0000
Answer
Answer
Answer
Answer
Answer

Answers

Answer:

are you from Philippines?

Step-by-step explanation:

because I want to know gehe

Which of the following equations has infinitely many solutions?

A.
4x + 5(2x + 6) = 14x + 30

B.
5x + 2 = 2x + 6

C.
4(x + 5) + 2 = 6x + 4(x + 2)

D.
4x + 5 = 2

Answers

The equation that has infinitely many solutions is A. 4x + 5(2x + 6) = 14x + 30

How to determine the equation?

An equation with infinitely many solutions is represented as:

ax + b = ax + b

This means that both sides of the equation must be the same.

Next, we test the options:

4x + 5(2x + 6) = 14x + 30

Open the bracket

4x + 10x + 30 = 14x + 30

Evaluate the like terms

14x + 30 = 14x + 30

Both sides of the equation must be the same.

Hence, the equation that has infinitely many solutions is A. 4x + 5(2x + 6) = 14x + 30

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Question 27(Multiple Choice Worth 1 points)
(01.05 LC)
Which calculation can be used to find the value of p in the equation p³= 8?
Op=√8
Op=3•√8
Op=2•√8
Op=√8

Answers

Answer:

Option 1 ========>  p = ∛8

Step-by-step explanation:

In order to make p the subject we would need to cube root both sides and would therefore get :

∛(p³) = ∛8

p = ∛8

Just a side not but you wrote the first option wrong but it's fine as you attached an image.

Hope this helped and have a good day

The calculation p=∛8  can be used to find the value of p in the equation p³= 8

What is Expression?

An expression is combination of variables, numbers and operators.

The given equation is  p³= 8

p to the power of three equal to eight

p is the variable in the given equation

We have to find the value of p from the equation

Take cube root on both the side

∛ p³= ∛8

On left hand side the cube will be cancelled and left with p

p=∛8

Hence, p=∛8 calculation can be used to find the value of p in the equation p³= 8

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Which of the following inequalities is graphed on the coordinate plane?
A. y > 30 +5
B. y ≤ 3r +5
C. y < 3x + 5
D. > 31 +5

Answers

Based on the scenario above, the inequalities that can be graphed on the coordinate plane is y < 3x + 5.

What is the inequalities about?

In graphing inequalities, one can graph inequality on the coordinate plane.

Note that the solutions for a linear inequality can be seen in the area of the coordinate plane. The boundary line used are  > ,<, ≥ and ≤.

Note also that the  inequalities graphed on the coordinate plane known to be y < 3x + 5 is shown in the image attached. When you look at option A, B and D, you will see that they are incomplete and missing some values but option C gave the correct example of an inequalities.

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You have a 3-gallon and a 5-gallon jug that you can fill from a fountain of water. The problem is to fill one of the jugs with exactly 4 gallons of water. How do you do it?

Answers

Answer:

See below

Step-by-step explanation:

Fill the 5   and pour into the 3    ....this will leave 2 gal in the 5 bucket

  empty the 3 bucket and put that 2 gallon in to it.....

      then fill the 5 bucket again......pour 1 gallon into the 3 gallon bucket to fill it....then there will be 4 gallons left in the 5 bucket

Three times the sum of a number and 3 is 3 less than the number times 5. Find the
number.

Answers

Answer:

3 * (x + 3) = x * 5 - 3

Which of the statements are true about the function f given by f(x) = 100-e? Select all that apply.
a The values of increase when x increases.
b The value off when x = 5 is less than 1.
d
e The value of is never 0.
E
The value of f when x=-1 is a little less than 40.
The y-intercept of the graph off is at (0, 100).

Answers

From the above function, it is clear that the value of f is never 0. Hence the statement that is true is (Option E), See explanation of same below.

What is the explanation for the above function?

Note that the function is related to Euler's number which is depicted as:
e ≈ 2.7182. The function is given as:

f(x) = 100 * [tex]e^{-x}[/tex]

Assuming x = -2, we'd have:

100 * 2.7182[tex]^{-2}[/tex]

= 271.82[tex]^{-2}[/tex]

= 0.00001353354

Hence, even when x tends < 0 the function f(x) thus, is never 0. See the attached graph for confirmation.

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