Mathematics High School

What is the side length b in the triangle below

Answers

Answer 1

12^2 +b^2 = 20^2 because of the Pythagorean theorem
144 + b^2 =400
B^2 =256
B=16

Answer 2

Answer:

Option B : 16

Step-by-step explanation:

Refer the attached file

Given :

In ΔABC , AB = b , BC = 12 , AC= 20

To Find : value of b i.e. Length of AB

Solution:

Since we are given a right angles triangle so we can use Pythagoras theorem i.e.

[tex](Hypotenuse)^{2} =(Perpendicular)^{2} +(Base)^{2} [/tex] ---(a)

Now in a given triangle AB is Perpendicular , BC is Base and AC is Hypotenuse.

So, putting values in (a)

[tex](AC)^{2} =(AB)^{2} +(BC)^{2} [/tex]

[tex](20)^{2} =(b)^{2} +(12)^{2} [/tex]

[tex]400 =(AB)^{2} +144 [/tex]

[tex]400-144 =(b)^{2} [/tex]

[tex]256 =(b)^{2} [/tex]

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

[tex]16=b[/tex]

Thus the value of b is 6

Hence Option B is correct.

Related Questions

BRAINLIESTTTTTTTTTTT!!

1. For the following system, if you isolated x in the second equation to use the Substitution Method, what expression would you substitute into the first equation?

2x + y = 8
−x − 3y = −12

3y + 12
−3y + 12
3y − 12
−3y − 12

2. please check my answer for the picture question

Answers

A is right hope this helps you can i get brailylist

2x + y = 8
−x − 3y = −12 → - x = 3.y - 12 → x = -3.y + 12. So I will substitude in the 1st equation, x by -3.y + 12 (2nd answer)

2) you follow the same logic as previously done
and you will find 2x+4y ≥ -16.
Isolate y → 4y ≥ - 2x - 16→→y ≥ - x/2 -4
1st you notice that it's a straight line (and not - - - ), then the equation should have ≥ (and not > )

2nd) It's decreasing that means a<0 (a= - 1/2)
3rd) for x = 0 ; y = -4
All that satisfies the equation y ≥ - x/2 -4 OR 2x+4y ≥ -16 (last answer)

vector is flying his helicopter at 200 miles per hour. how long has he been flying if he has traveled 1,200 miles? A. 2 hours B. 60 hours C. 6 hours D. 10 hours??? please help

Answers

6 hours, because 1,200 divided by 6 is 200. Think about it at 200 mph it will take you 1 hr to go 200 miles two hours will be 400 miles and so on. Does that make sense?

C 6hours because the helicopter can cover 200miles in an hour so if you want to find out 1200 miles all you need to do is divide 1200 by 200 which gives you an answer if 6 xx

Translate this sentence into an equation.

The sum of 14 and holly's age is 55.

Use the variable h to represent holly's age.

Answers

55=h+14
H+14=55
55-14=H

Final answer:

The sentence 'The sum of 14 and Holly's age is 55' can be translated into the equation 14 + h = 55, where h represents Holly's age.

Explanation:

To translate the sentence into an equation, we identify the mathematical operations described by the sentence. The sentence 'The sum of 14 and Holly's age is 55' indicates an addition operation involving Holly's age and the number 14. Using the variable h for Holly's age, we form the equation 14 + h = 55. This is a simple linear equation where h represents an unknown value that can be solved for.

How do you find the median of these numbers $17.49, $11.29, $16.89, $11.79?

Answers

Good morning, kid. It's quite easy.

The median is the middle number in a set after you place them least to greatest:

$11.29, $11.79, $16.89, $17.49

Well, since the numbers in the set are even, meaning there are only 4 numbers, we pick out the 2 middle numbers which would be, $11.79 and $16.89. Find the average (add them and divide by 2) and you'll get the median.

$11.79 + $16.89 = $28.68/2 = $14.34
Thus, the median is: $14.34

n2-14n+49 what’s the answer

Answers

(n-7) (n-7) will be your answer

n x n = n²

n x -7 = -7n
n x - 7 = -7n
-7n +(-7n) = -14n
-7 x -7 = 49

(n-7)² is your answer

hope this helps

and if you are doing the other thing

n = 7, 7

hope this helps

a+b=14 anda*b = 49 The solution to this new system of equations is a=7, b=7. original expression is (n+7)(n+7), or (n+7)^2. *As always meaning when the coefficient of n^2 is 1. When the coefficient is 2+, it's not as simple but the same idea hope this helps

What is the multiplicative inverse of 23/47?

Answers

23 x 47. This is the inverse as X is the opposite of /

What is the scale factor use to create this dilation?

Answers

Given Info: "The dashed triangle is the image of the solid triangle"

So the "before" is the large solid triangle and the "after" is the smaller dashed triangle.

The horizontal side of the solid triangle is 15 units. The corresponding side for the dashed triangle is 3 units. Dividing the two values gives: 3/15 = 1/5 = 0.2

Make this value negative. The reason why is due to the fact that we have a sort of reflection going on as we're scaling down the figure.

So the final answer is -0.2

A graphic designer charges an hourly rate. In July, the only expense is for advertising. The function graphed models the designer's net income, y, for July for x hours of work.

Select True or False to describe each statement.

The x-intercept represents the amount the designer charges for 1 h of work.
The difference between 0 and the y-intercept represents the amount the designer spent on advertising.
The slope represents the designer's hourly rate.

Answers

From the graph shown, the x-axis repredent the time worked while the y-axis represent the net income.

The x-intercept is the value of x when y is zero, thus from the graph, the x-intercept represents the number of hours he has to work to cover for his expenses.

Therefore, the statement "The x-intercept represents the amount the designer charges for 1 h of work." is false.

The y-intercept is the value of y when x is 0, from the graph the y intercept represent the net income when he has not done any work, i.e. the y-intercept represent his expenses.

Therefore, the statement "The difference between 0 and the y-intercept represents the amount the designer spent on advertising." is true.

The slope of a straight line is given by the change in y divided by the corresponding change in x. From the graph, given that the y-axis represent the net income in dollars and the x-axis represent the time worked in hours. Change in y divided by change in x is given by dollars per hour which represent his hourly charge.

Therefore, the statement "The slope represents the designer's hourly rate." is true.

What is 781,407 rounded to the nearest ten thousand What is 781,407 rounded to the nearest ten thousand?

Answers

781,41 is the correct answer

Please help! 20 points!

Answers

12/3 = 4

it was dilated with a scale factor of 4

Two benefits of following the 4 step method of problem solving

Answers

Final Answer:

Following the 4-step method of problem-solving offers the benefits of structured decision-making and enhanced clarity in identifying and addressing core issues. These advantages significantly contribute to effective decision-making and successful implementation of solutions.

Explanation:

The 4-step method, involving identification, planning, execution, and evaluation, provides a structured framework for tackling problems. In the identification phase, _Step 1_, issues are precisely pinpointed, aiding in accurate problem definition, crucial for effective decision-making. For instance, in a business scenario, if sales decline is the issue, this step helps clarify if it's due to product quality, marketing, or market changes, enabling focused decision-making.

Moving to the planning phase, _Step 2_, where strategies and solutions are devised, this structured approach ensures that all potential solutions are thoroughly explored, enhancing the quality of decisions made. This step involves a rigorous evaluation of each potential solution, ensuring a comprehensive understanding of their viability and implications.

During the execution phase, _Step 3_, the structured plan is put into action, benefiting from the earlier clarity and well-thought-out decisions. For example, if a marketing strategy was identified as a solution, this phase would involve implementing the chosen strategy with a clear roadmap, minimizing errors and optimizing resources.

Lastly, the evaluation phase, _Step 4_, allows for the assessment of the implemented solution's effectiveness. By systematically analyzing the outcomes against predefined metrics, this step ensures continuous improvement and learning from the process, contributing to more informed decision-making in the future. This structured approach, therefore, not only facilitates effective decision-making but also ensures successful implementation and ongoing refinement of solutions.

Here is complete question;

"What are two benefits of following the 4-step method of problem-solving, and how do they contribute to effective decision-making and solution implementation?"

Given that we have already tossed a balanced coin ten times and obtained zero heads, what is the probability that we must toss it at least two more times to obtain the first head

Answers

Final answer:

The probability that at least two more coin tosses are required to get the first head, after ten tails in a row with a balanced coin, is 50%.

Explanation:

The student is asking about the probability of a specific outcome in a sequence of coin tosses. Given that we have already tossed a balanced coin ten times and obtained zero heads, we want to calculate the probability of having to toss the coin at least two more times to get the first head. The probability of getting a head on any given coin toss is 0.5. To get the first head in at least two more tosses means we need a tail (T) on the next toss and then any outcome (H or T) after that. Therefore, we calculate the probability as follows:

The probability of getting a tail on the first toss is 0.5.The probability of getting any outcome on the second toss is 1 (since it can be either head or tail).

The combined probability is the product of the two individual probabilities, which is 0.5 * 1 = 0.5 or 50%. Hence, the probability that we must toss the coin at least two more times to obtain the first head is 50%.

On what interval(s) is the graph decreasing? - use interval notation
On what interval(s) is the graph decreasing? - use interval notation
Identify any local maximums values and minimum values. - Algebra 2

Answers

The function is decreasing from -6 to -3, that is, on the interval (-6,-3), and again on the interval (1, infinity).

The function is increasing on (-3,1).

No local or absolute minimum.

(1,4) is an absolute max.

Ronny read for 2.75 hours yesterday. His older brother read for 1.18 hours and his younger brother read for 0.43 hours. How much longer did Ronny read than his two brothers combined? 1.14 hours 1.57 hours 1.61 hours 2.32 hours

Answers

hello there
it is A because add 1.18 and 0.43 to get 1.61 then subtract 2.75-1.61 is 1.14
~hope i help~

The time they read together, is the sum of their individual study time.

Ronny read 1.14 hours longer than her brothers combined

The given parameters are:

[tex]\mathbf{Ronny = 2.75\ hours}[/tex]

[tex]\mathbf{Older\ Brother= 1.18\ hours}[/tex]

[tex]\mathbf{Younger\ Brother= 0.43\ hours}[/tex]

The combined time her brothers studied is:

[tex]\mathbf{Both = Older + Younger}[/tex]

Substitute known values

[tex]\mathbf{Both = 1.18\ hours + 0.43\ hours}[/tex]

Evaluate like terms

[tex]\mathbf{Both = 1.61 \ hours}[/tex]

The time Ronny read longer is calculated as follows:

[tex]\mathbf{Time = Ronny- Both}[/tex]

Substitute known values

[tex]\mathbf{Time = 2.75\ hours - 1.61\ hours}[/tex]

Evaluate like terms

[tex]\mathbf{Time = 1.14\ hours}[/tex]

Hence, Ronny read 1.14 hours longer than her brothers combined

Answers

The total sum of Adriana’s grades are:

sum of grades = 4 * 90

sum of grades = 360

If Adriana and Roberto has similar total sum, therefore the average of Roberto’s grades is:

Roberto average = 360 / 5 = 72

Answer:

write a word phrase for each algebraic expression

1. 100 - 5n

2. 25r + 6

Answers

Problem
Write a word phrase for each algebraic expression

Result
1. Five times a number minus one-hundred
2. Twenty-five times a number plus six

Solution
I recommend watching videos on turning algebraic expressions into word phrases. Try and figure out why the answer is the way it is.

I want to know the answer of this question

Answers

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r\qquad \begin{cases} r=radius\\ -----\\ r=5x^2 \end{cases}\implies C=2\pi 5x^2\implies C=10\pi x^2 \\\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \begin{cases} r=radius\\ -----\\ r=5x^2 \end{cases}\implies A=\pi (5x^2)^2\implies A=\pi (5^2x^{2\cdot 2}) \\\\\\ A=\pi (25x^4)\implies A=25\pi x^4 [/tex]

Which statement best explains whether △PQR is congruent to △XYZ?

△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a rotation of 180° about the origin.

△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a translation 5 units down followed by a reflection across the y-axis.

△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.

△PQR is congruent to △XYZ because △PQR can be mapped to △XYZ by a reflection across the y-axis followed by a reflection across the x-axis.

Answers

Answer:

△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.

Step-by-step explanation:

We can see from the diagram that XYZ is not the same size as PQR. This means there is no series of rigid motions, which preserve segment length, that maps PQR to XYZ.

Answer:

△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.

Step-by-step explanation:

How to get to standard form from slope intercept?

Answers

The slope intercept form of a linear equation is of the kind y = mx + b.

The standard form of a linear equation is Ax + By = C.

So, to get from y = mx + b to Ax + By = C, you follow these steps:

y - mx = b

=> y + (-m)x = b

=> (-m)x + y = b

For example get the standard form from y = 3x + 5

=> (-3)x + y = 5

where =

A = -3

B = 1

C = 5

The three angles of a triangle are in the ratio 3:3:4. What information can you give about the triangle?

Answers

The information tells us that this triangle is an isosceles triangle meaning two sides and two angles are congruent. Also, this is not a right triangle as the only isosceles right triangle has a ratio of 1:1:2

Hope this helps!

let the angles be x.
3x + 4x + 4x = 180 (angle sum property of a triangle is 180 degrees.)
12x = 180
x = 180/12
x= 15
the angles are 45, 60 and 60
it is an isosceles triangle.

What does it mean if the determinant of a matrix is 0?

Answers

It means that it is not invertible. In other words, if a matrix has a determinant of 0, there is no inverse of the matrix.

In linear algebra (university level course), having a determinant of 0 would mean a lot more.

Have an awesome day! :)

Final answer:

The determinant of a matrix is 0 means the matrix is singular, indicating no unique solution for the corresponding system of equations, or in geometry, that space is compressed to a lower dimension.

Explanation:

When the determinant of a matrix is 0, it signals that the matrix does not have an inverse and is considered singular. In practical terms, this means that the system of equations that corresponds to the matrix does not have a unique solution. For instance, in a square matrix, if the determinant is zero, it may indicate that the rows or columns are linearly dependent, meaning that at least one row or column is a scalar multiple of another, resulting in redundant information. In geometry, if we're dealing with transformation matrices, a determinant of zero implies that the transformation compresses the space into a lower dimension, effectively 'flattening' it, and thus, the original geometrical figure loses its volume.

50 POINTS!!

Please show all of your work! Thanks.

Answers

Vertical Angles have equal measure, so set the expressions equal to each other, creating an equation, and solve for x:

mE = mF
9x + 12 = 3x + 24
- 3x - 3x
------------------------------
6x + 12 = 24
- 12 - 12
-------------------------
6x = 12
--- ----
6 6

x = 2

Check this to be sure: mE = 9(2) + 12 = 30 ; mF = 3(2) + 24 = 30 YEP

vertical angles equal each other so you have

angle E = angle F

9x+12 = 3x +24

subtract 12 from each side

9x = 3x +12

subtract 3x from each other

6x =12

divide both sides by 6

x = 12/6 = 2

x = 2

Which of the following is NOT equivalent to the ratio: 12/4 A.6/2 B. 36/12 C.24/16 D.240/80

Answers

12 multiplied by 2 is 24. 4 multiplied by 2 is 8. Therefore 24/16 is not equal to 12/4

The sum of three numbers is 62. The second number is equal to the first number diminished by 4. The third number is four times the first. What are the numbers? Which three expressions could be used to represent the numbers? n; n - 4; 4n n; 4 - n; n + 4 n; n/4; n + 4

Answers

n = first number
2nd number = n diminished by 4.....n - 4
3rd number is 4 times the first.....4n

ur 3 expressions are : n , n - 4, 4n <==

Answer:

Numbers: 11, 7 and 44

Expressions: n, n - 4, 4n

Step-by-step explanation:

We have that A + B + C = 62, where A, B and C represent numbers.

We know that the 2nd number (B) is equal to the first number (A), diminished by 4. This means B = A - 4

We also know that the 3rd number (C) is four times the first (A), that is to say 4*A. This means C = 4*A

If we replace this information in the first expression, we have

A + B + C = A + (A - 4) + (4*A) = 62

We change an equation of 3 variables to an equation of just one. Now we solve it putting together the terms that have the variable A:

A + A - 4 + 4*A = 62

2A + 4A - 4 + 4 = 62 + 4

6A = 66

A = 11

Our first number is 11, now we find B and C:

B = A - 4 = 11 - 4 = 7

C = 4A = 4*11 = 44

So, the numbers are 11, 7 and 44

If we change the A for a "n", the expressions that represent the numbers are n, n - 4 and 4n

If the difference of two numbers is 7 and their product is 60, what are they?

Answers

x - y = 7.....x = y + 7
x * y = 60

y(y + 7) = 60
y^2 + 7y = 60
y^2 + 7y - 60 = 0
(y + 12)(y - 5) = 0

y + 12 = 0
y = -12....not this one because it is negative

y - 5 = 0
y = 5 <===

x - y = 7
x - 5 = 7
x = 7 + 5
x = 12 <==

so ur 2 numbers are 12 and 5

solve for y: 7/9y = 42

Answers

I answered on paper hope that is alright with you. I just find it easier for math problems. That slash means two numbers cancel each other out. What's in the box is the answer and the proof that it's right is underneath.

7/9y=42

Take the denominator and multiply it by the whole. 9*42=378

Then take your answer and divide it by the numerator. 378/7=54

To check your work just simply multiply 7/9 * 54 = 42

Jason started a hat-making business. He spent $750 to purchase supplies to get started and he uses about $3.50 worth of supplies per hat made. Jason charges $15 for each hat. Let h represent the number of hats.

What is the minimum number of hats Jason will need to sell to make a profit?

A. 15h>750+3.5h

B. 3.5h≥750+15h

C. 3.5h>750+15h

D. 15h<750+3.5h

Answers

the answer is 3.5h>750+15h

Please help! Identify the minimum value of the function y=3x^2-12x+10.

A) -2
B) 46
C) 10
D) 2

Answers

the lowest point is at the vertex, or U-turn.

[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llccclll} y = &{{ 3}}x^2&{{ -12}}x&{{ +10}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left( -\cfrac{-12}{2(3)}~~,~~10-\cfrac{(-12)^2}{4(3)} \right)\qquad \textit{so the lowest value is at }10-\cfrac{(-12)^2}{4(3)} [/tex]

The minimum value of the function y=3x^2-12x+10 is found using the vertex form, and it is -2. This value corresponds to the y-coordinate of the vertex of the parabola.

To find the minimum value of the function y=3x^2-12x+10, we can use the vertex form of a quadratic equation, or complete the square method. We also know that a quadratic function with a positive coefficient for the x^2 term opens upwards and has a minimum value at its vertex. To get the vertex form, we complete the square:

y = 3(x^2 - 4x) + 10
y = 3(x^2 - 4x + 4 - 4) + 10
y = 3((x-2)^2 - 4) + 10
y = 3(x-2)^2 -12 + 10
y = 3(x-2)^2 - 2

Now, the vertex of this parabola is at (2, -2). As this is the vertex of a parabola that opens upwards, the y-coordinate of this point gives us the minimum value of the function, which is -2.

Evaluate the expression
-8 X 7 + 33 ÷ (-11)
PLEASE HELP ME ASAP
thanks

Answers

PEMDAS:

1) -8x7= -56
-56 + 33/-11
2) 33/-11
-56 + (-3)
Your answer is -59

Multiply/divide first.
-56 + 33 - 3
Add/subtract left to right.
-26

A line goes through the point (6,–2) and has a slope of –3.
What is the value of a if the point (a,7) lies on the line?

Answers

y = mx + b
slope(m) = -3
(6,-2)...x = 6 and y = -2
sub and find b, the y int
-2 = -3(6) + b
-2 = -18 + b
-2 + 18 = b
16 = b
so ur equation for this line is : y = -3x + 16

(a,7)......so y = 7......" a " is gonna be x

y = -3x + 16
7 = -3x + 16
7 - 16 = -3x
- 9 = -3x
-9/-3 = x
3 = x..........so " a " is gonna be 3 <===

The value of a in the point (a, 7) is 3

The slope intercept equation is as follows:

y = mx + b

where

m = slope

b = y-intercept

Therefore,

Let's find b using (6, -2)

m = -3

y = -3x + b

-2 = -3(6) + b

-2 = -18 + b

b = -2 + 18

b = 16

Therefore,

y = -3x + 16

let's find the value of a in (a, 7)

7 = -3x + 16

7 - 16 = -3x

-9 = -3x

x = -9 / -3

x = 3

Therefore,

a = 3

learn more: https://brainly.com/question/18851803?referrer=searchResults

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