Given a right triangle with sides of length a, b, and c and area a²+b²-c², find c/b, the ratio of the legs of the right triangle.
Answers
Answer:
4
Step-by-step explanation:
Looking at the sketch we can formulate 2 equations:
Pythag: [tex]b^{2} +c^{2} =a^{2}[/tex]
Area of triangle= [tex]\frac{1}{2} bc[/tex]
But area also = [tex]a^{2} +b^{2} -c^{2}[/tex] (from the question)
Therefore [tex]\frac{1}{2} bc[/tex] = [tex]a^{2} +b^{2} -c^{2}[/tex]
But we can sub in the expression for [tex]a^{2}[/tex] from pythag. ([tex]b^{2} +c^{2} =a^{2}[/tex])
[tex]\frac{1}{2} bc= b^{2} +c^{2} +b^{2} -c^{2}[/tex]
[tex]\frac{1}{2} bc=2b^{2}[/tex]
[tex]bc=4b^{2}[/tex]
[tex]c=4b[/tex]
[tex]c/b= 4b/b=4[/tex]
Related Questions
Sharon went bowling with her friends. She paid $3 to rent
her shoes and then $3.75 for each game (x) of bowling. She
spent a total of $18. How many games did she bowl?
WRITE YOUR EQUATION:
SOLVE:
SOLUTION:
Answers
Answer:
3 + 3.75x=18
subtract 3 from both sides
3.75x=15
divide by 3.75 on both sides
x=4
Step-by-step explanation:
Sharee and her two sisters ate 3 5 of a pizza. How much of the pizza did each girl have? A) 1 3 B) 1 5 C) 2 15 D) 3 10
Answers
Sharee and her two sisters ate 3 /5 of a pizza. How much of the pizza did each girl have? A) 1 /3 B) 1/ 5 C) 2 /15 D) 3 /10
Answer:
B) 1/ 5
Step-by-step explanation:
Number of persons = Sharee and her two sisters = 3 persons
Quantity of pizza eaten = 3/5
Each person ate:
3 persons = 3/5 pizza
1 person = x pizza
Cross Multiply
3 × x = 3/5 × 1
x = 3/5 × 1/3
x = 3/5 ÷ 3
x = 3/5 × 1/3
x = 1/5
Hence, each person ate 1/5 pizza.
I need help please and thank you in advance
Answers
write an equation in standard form for the line that is parellel to the graph of -8x=5-4y and has a y-intercept -0.5
A x+.05=0.25
B 10x-5y=2
C 4x-2y=1
D 2x-y=1
Answers
9514 1404 393
Answer:
C 4x -2y = 1
Step-by-step explanation:
The y-intercept of the offered choices can be found by dividing the constant by the y-coefficient.
A: not in standard form (coefficients are not integers)
B: 2/-5 = -2/5 . . . not -1/2
C: 1/-2 = -1/2 . . . a good candidate
D: 1/-1 = -1 . . . not -1/2
PLEASE HELP!!! Chloe is working two summer jobs, landscaping and clearing tables. She must work no less than 12 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours landscaping, l and the number of hours clearing tables, c, that Chloe can work in a given week.
Answers
Answer:
got u homie
Step-by-step explanation:
Answer:
l +c _> 12
Step-by-step explanation:
Help ill give brainliest
Lily begins solving the equation 4(x – 1) – x = 3(x + 5) – 11. Her work is shown below.
4(x – 1) – x = 3(x + 5) – 11
4x – 4 – x = 3x + 15 – 11
3x – 4 = 3x + 4
How can her partial solution be interpreted?
A. The equation has one solution: x = 0.
B. The equation has one solution: x = 8.
C. The equation has no solution.
D. The equation has infinite solutions.
Answers
Answer:
C. no solution
Step-by-step explanation:
3x – 4 = 3x + 4
3x-3x=4+4
0=8
which is not possible.
So, it has no solutions.
w(t) = 3t – 1; t = 5
Answers
A crew of highway workers paved1/4 mile in1//6 a hour. If they work at the same rate, how much will they pave in one hour?
Answers
Answer:
1 1/2 mile
Step-by-step explanation:
In 1 hour they pave 6 times more what they paved in 1/6 of an hour.
6 * 1/4 mile = 6/4 mile = 3/2 mile = 1 1/2 mile
Angelina received 2 discounts on $50. They were taken off one after the other. The first coupon was 20%. She paid $30 for shoes. What is the dollar amount taken off the first coupon.
Answers
Answer:
The dollar amount taken off is $10.
Step-by-step explanation:
I hope i helped.
What is |-24| + |13| =?
Answers
Answer:
37
Step-by-step explanation:
just add the two numbers like they are not negative.
In ΔFGH, the measure of ∠H=90°, the measure of ∠F=18°, and GH = 9.4 feet. Find the length of HF to the nearest tenth of a foot.
Answers
Answer:
28.9
Step-by-step explanation:
tan (18) = 9.4/x times x
x times tan(18) = 9.4 / tan(18)
tan(18)
crosses out.
On a calculator do 9.4/
tan(18).
x = 28.9
Suppose the manager of your local McDonalds tracks the
monthly sales of their new McBurger, Mini McBurger, and
Choco-Latte Shake. The data is listed below.
For January through December, the sales are as follows.
McBurger: 46, 63, 58, 77, 81, 102, 183, 197, 125, 111, 83, 218.
Mini McBurger: 23, 41, 35, 44, 62, 88, 95, 99, 108, 111, 98, 63.
Choco-Latte Shake: 88, 46, 39, 52, 67, 99, 189, 238, 188, 97,
51, 12
Create a matrix to display the data.
Answers
Answer:
Step-by-step explanation:
The question says "Create a matrix to display the data".
The are 3 products:
- McBurger - Mini McBurger - ChocoLatte Shake
The figures represent monthly sales for each product, in a given year. This means 12 figures for each product - represent the 12 months of the year.
These figures will appear on the matrix, with the horizontal arrangement representing each month of the year and the vertical arrangement representing each product's sales.
In that light, you'll have a 12 by 3 matrix.
[tex]\left[\begin{array}{ccc}46&23&88\\63&41&46\\58&35&39\\77&44&52\\81&62&67\\102&88&99\\183&95&189\\197&99&238\\125&108&188\\111&111&97\\83&98&51\\218&63&12\end{array}\right] 12 by 3 matrix[/tex]The first row represents sales in January, the second row represents sales in February, the third row represents sales in March, the fourth row represents sales in April, etcetera.
The first column represents sale of McBurger, the second column represents sale of Mini McBurger, the third column represents sale of Choco-Latte Shake.
Which statement describes how to geometrically divide a complex number, z, by a second complex number, w?
O Scale z by the modulus of w, then rotate clockwise by the argument of w.
O Scale z by the modulus of w, then rotate counterclockwise by the argument of w.
O Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.
O Scale z by the reciprocal of the modulus of w, then rotate counterclockwise by the argument of w.
Answers
Answer: C
Step-by-step explanation:
I just took the quiz and I got it right
Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.
What is Complex number?In mathematics, a complex number is an element of a number system that contains the real numbers and a specific element denoted i, called the imaginary unit
What is Modulus of a complex number?Modulus of the complex number is the distance of the point on the argand plane representing the complex number z from the origin
Given,
Complex number z divides by a second complex number w
To divide a complex number a complex number then multiply the conjugate with the numerator and the denominator of the complex fraction
From the given statements Scale of z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w
Hence, Statement describes how to geometrically divide a complex number z by a second complex number w is Option (C) Scale z by the reciprocal of the modulus of w, then rotate clockwise by the argument of w.
Learn more about Complex number and Modulus of a complex number here
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if 1 apple cost 3 dollars how much would 5 cost?
Answers
Answer:
It would be 15
Step-by-step explanation:
because 5x3 equals 15.
Answer:
15 dollars
Step-by-step explanation:
because you have to multiply how many apples there are to how much each one cost. So the answer would be 5 x 3 equals 15 dollars
Help me with this question pleasee
Answers
Answer:
√23 = a
Step-by-step explanation:
/ab/²= /ac/²+/bc/² (Pythagoras theorem)
12² = a² +11²
144 = a² + 121
144 - 121 = a²
23 = a²
√23 = a
Use the number line to answer the question. Each tick represents 1 unit.
Which of the following points are neither negative nor positive? Select all that apply.
H
M
L
J
P
K
N
Please help
Answers
Answer:
M is niether Negitive or positive
Step-by-step explanation:
Because it is on the zero
mark me brainliest plz
Answer:
Answer:
M is niether Negitive or positive
Step-by-step explanation:
Because it is on the zero
Step-by-step explanation:
Whatbis the slope of a line that is perpendicular to the line y= 2x-6? A. -2
B. 2 C. 1/6 D. -1/2
Answers
Answer:
D. -1/2
Step-by-step explanation:
When a line is perpendicular to another line the slope will be the exact opposite. For example line A = y = 3x + 5 the line perpendicular to it will be -1/3x.
So -1/2 is the slope of your perpendicular line.
The living room of Ann's house is a square with an area of 121 square feet. What is the length of each side of the foyer
Answers
Answer:
30.25
Step-by-step explanation:
121 divided by 4 is 30.25
Read 3 integer numbers from the user; these numbers represent the lengths of 3 straight lines. From the 3 lengths, determine whether a triangle can be formed with the corresponding lines. If it is possible to form a triangle, determine whether the triangle is a right triangle or not. The rules to be used are: 1. To form a triangle where all lines’ ends meet (form vertices), the sum of the lengths of two sides must be greater than the length of the third side. This short video illustrates this concept: How to determine if the three sides make up a triangle. 2. Per the Pythagorean theorem: in a straight triangle, the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides. 3. The user can enter the lengths of each line in any order, i.e.: you may not assume that the first length is the longest or the smallest or the middle value.
Answers
Answer:
Written in Python
print("Enter three sides of a triangle: ")
length = []
for i in range(0,3):
inp = int(input(""))
length.append(inp)
length.sort()
if length[1]+length[2] > length[0] and length[0] + length[2] > length[1] and length[0] + length[1] > length[2]:
print("Triangle")
if length[2]**2 == length[0]**2 + length[1] **2:
print("Right Angled")
else:
print("Not Right Angled")
else:
print("Not Triangle")
Step-by-step explanation:
This line prompts user for sides of triangle
print("Enter three sides of a triangle: ")
This line declares an empty list
length = []
The following iteration gets user input
for i in range(0,3):
inp = int(input(""))
length.append(inp)
This line sorts user input
length.sort()
The following if condition checks if user input is triangle
if length[1]+length[2] > length[0] and length[0] + length[2] > length[1] and length[0] + length[1] > length[2]:
The following is executed is the if condition is true
print("Triangle")
The following if condition checks if user input forms a right angled triangle
if length[2]**2 == length[0]**2 + length[1] **2:
print("Right Angled")
else:
print("Not Right Angled")
This is executed if user input is not a triangle
else:
print("Not Triangle")
what is the Quotient: 3/4divided1/4
Answers
Answer:
3
Step-by-step explanation:
he production of pipes has a mean diameter of 3.25 inches and a standard deviation of .15 inches. The shape of the distribution is approximated by a normal distribution since approximately an equal number of parts are above or below average, and most parts are very close to the mean value. A part will be discarded is it has a diameter of greater than 3.5 inches or less than 3 inches. What proportion of parts are discarded from the production line
Answers
Answer:
The probability that a randomly chosen part has diameter of 3.5 inches or more is 0.9525
Step-by-step explanation:
[tex]Mean = \mu = 3.25 inches[/tex]
Standard deviation = [tex]\sigma = 0.15 inches[/tex]
We are supposed to determine the probability that a randomly chosen part has diameter of 3.5 inches or more
[tex]P(Z \geq 3.5)=1-P(z<\frac{x-\mu}{\sigma})\\P(Z \geq 3.5)=1-P(z<\frac{3.25-3.5}{0.15})\\P(Z \geq 3.5)=1-P(z<-1.67)[/tex]
Refer the z table for p value
[tex]P(Z \geq 3.5)=1-0.0475\\P(Z \geq 3.5)=0.9525[/tex]
Hence the probability that a randomly chosen part has diameter of 3.5 inches or more is 0.9525
I need help with this one
Answers
Answer:
The first three
Step-by-step explanation:
-6(x+4) what this answer simplified.
Answers
Answer:
-6x-24
Step-by-step explanation:
all you have to do is multiply, so -6*x and -6*4 and since -24 is a negative the equation is going to be subtracting
Answer:
Step-by-step explanation:
7th grade math help me plzzz
Answers
Answer:
a. -14
b. -150
c. -51
d. -2
e. 3
f. 5
2+2=4 because 2 fingers and then another 2 fingers
Answers
Answer:
yes
Step-by-step explanation:
Answer:
yes? That's right. ummmm lol
A square is removed from the right hand corner
Answers
Answer:
C im pretty sure
Step-by-step explanation:
Because the square taken out has a 4x4 area which is 16 and the area of the whole square used to be 14x14 which is 196 and if u subtract 16 from that you get 180
The police department of UCR is looking to collect more fines for speeders on campus. (They are turning to speeding because they cannot extract any more money out of people for parking illegally!) They record the speeds on West Campus Drive for a year and find that the average speed is 31.0 miles per hour with a standard deviation of 2.0. The data is approximated by a normal distribution. The top five percent (5%) of speeders will get tickets. What speed must you be going before getting a ticket
Answers
Answer:
≥ 34.29 mph
Step-by-step explanation:
Given that:
Distribution is normal :
Mean(m) = 31 mph
Standard deviation = 2 mph
Speed of top 5%
Top 5% = bottom (100% - 5%) = 95% = 0.95
Zscore which corresponds to 0.95 = 1.645
Using the Z formula:
Zscore = (score - mean) / standard deviation
1.645 = ( score - 31) / 2
Croas multiply:
2 * 1.645 = score - 31
3.29 = score - 31
3.29 + 31 = score
34.29 = score
Hence, speed must be greater than or equal to 34.29 mph
The scatterplot and trend line show a positive correlation between advertising costs and sales.
Which two points can be used to find the slope of the trend line?
Point 1: ?
Point 2: ?
Answers
Answer:
Point 1: (6.4, 117)
Point 2: (6.6, 120)
Step-by-step explanation:
Answer:
Point 1: (6.4, 117)
Point 2: (6.6, 120)
Step-by-step explanation:
A marathon runner travels 9/2 miles in 1/2 hour what is the unit rate
Answers
Answer:
9/2:1/2
Step-by-step explanation:Here's the answer
The Tigers’ first play when they had possession of the ball went for -3 yards. Did the Tigers gain or lose yards on that play? How many yards did they gain or lose?
Answers
Answer:
вы молодец и увас всё получилось