Answer:
48
Step-by-step explanation:
Pythagorean Theorem = h^2=p^2+b^2
We have,
(Hypotenuse)h=50
Let 14 be p, i.e (Perpendicular ,Known side)p=14
(Remaining side ,base)b=?(
Now,
h^2=p^2+b^2
or, 50^2=14^2+b^2
or, 2500-196=b^2
or, √2304=b
b=48
Mathematical induction is:
Answer:
The third option.
Step-by-step explanation:
Mathematical induction is a 2 step mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number.
Step 1 (Base step) - It proves that a statement is true for the initial value.
Step 2 (Inductive step) - It proves that if the statement is true for the nth iteration (or number n), then it is also true for (n + 1)th iteration (or number n + 1)
Hope this helps.
Please mark Brainliest.
Answer:
A method of improving statments
Step-by-step explanation:
"Mathematical Induction is a mathematical technique which is used to prove a statement, a formula or a theorem is true for every natural number."
Compute (3/4)*(8/9)*(15/16)*(24/25)*(35/36)*(48/49)*(63/64)*(80/81)*(99/100) Express your answer in the simplest way possible. (Suggestion: First, try computing 3/4*8/9 then 3/4*8/9*15/16 and so on. Look for patterns.
Answer:
[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}[/tex]
Step-by-step explanation:
Given
[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100})[/tex]
Required
Simplify
For clarity, group the expression in threes
[tex]((\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Evaluate the first group [Divide 8 by 4]
[tex]((\frac{3}{1})*(\frac{2}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 9 by 3]
[tex]((\frac{1}{1})*(\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex]((\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 15 by 3]
[tex]((\frac{2}{1})*(\frac{5}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 16 by 2]
[tex]((\frac{1}{1})*(\frac{5}{8}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](\frac{5}{8})*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Evaluate the second group [Divide 35 and 25 by 5]
[tex](\frac{5}{8})*((\frac{24}{5})*(\frac{7}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 49 by 7]
[tex](\frac{5}{8})*((\frac{24}{5})*(\frac{1}{3})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[Divide 24 by 3]
[tex](\frac{5}{8})*((\frac{8}{5})*(\frac{1}{1})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](\frac{5}{8})*((\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Merge the first and second group
[tex]((\frac{5}{8})*(\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](1*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
[tex](\frac{4}{7})*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]
Evaluate the last group [Divide 99 by 9]
[tex](\frac{4}{7})*((\frac{63}{64})*(\frac{80}{9})*(\frac{11}{100}))[/tex]
[Divide 63 by 9]
[tex](\frac{4}{7})*((\frac{7}{64})*(\frac{80}{1})*(\frac{11}{100}))[/tex]
[Divide 64 and 80 by 8]
[tex](\frac{4}{7})*((\frac{7}{8})*(\frac{10}{1})*(\frac{11}{100}))[/tex]
[Divide 10 and 4 by 2]
[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{5}{1})*(\frac{11}{100}))[/tex]
[Divide 100 by 5]
[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{1}{1})*(\frac{11}{20}))[/tex]
[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{11}{20}))[/tex]
[tex](\frac{4}{7})*(\frac{7}{4})*(\frac{11}{20})[/tex]
[tex]1*(\frac{11}{20})[/tex]
[tex]\frac{11}{20}[/tex]
Hence;
[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}[/tex]
Trisha bought a carton of orange juice. She drank 1/3 of the carton on Monday and 5/12 of the carton on Tuesday. What fraction of the carton did Trisha drink?
Answer:
9/12 or 2/3
Step-by-step explanation:
Make both fractions have the same denominator by finding their least common multiple
1x12 = 12 1x3 = 3
2x6 = 12 3x1 = 3
3x4 = 12
4x3 = 12
6x2 = 12
12x1 = 12
In which case it would be 12.
1/3 would be 4/12
5/12 + 4/12 = 9/12
which is also 2/3 if your teacher wants the simplest answer
A wheel with radius 1 m is rolled in a straight line through one complete revolution on a flat horizontal surface. How many metres did the centre of the wheel travel horizontally from its starting location?
Answer:
6.28 m
Step-by-step explanation:
If a wheel travels with one full revolution, it would have travelled the circumference's distance from it's starting point.
The circumference of a circle is [tex]2\pi r[/tex]
Let's assume [tex]\pi[/tex] is 3.14 and solve for the equation.
[tex]2\cdot3.14\cdot1\\6.28[/tex]
Hope this helped!
Divide write the quotient in lowest term 1 1/3 divided by 1 3/4
Answer:
7/3 or 2 1/3
Step-by-step explanation:
1 1/3 ÷ 1 3/4
Change to improper fractions
(3*1+1)/3 ÷ (4*1+3)/4
4/3 ÷ 7/4
Copy dot flip
4/3 * 7/4
Rewriting
4/4 * 7/3
7/3
As a mixed number
2 1/3
Answer:
11/3÷13/4
11/3×4/13
44/39=
1.1282
Instructions: Determine whether the following polygons are
similar. If yes, type in the similarity statement and scale factor. If
no, type 'None' in the blanks.
Answer:
No they aren't similar different measurements but same angle so they can't be said to be similar
Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = (x - 13)2 + 6
Answer:
Step-by-step explanation:
if we shift 13 units right and 6 units down we get the reqd. graph.
Answer:
see explanation
Step-by-step explanation:
Given the graph of f(x) then f(x + k) is a horizontal translation of f(x)
• If k > 0 then shift left by k units
• If k < 0 then shift right by k units
Thus y = (x - 13)² represents a shift to the right of 13 units
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then shift up by c units
• If c < 0 then shift down by c units
Thus
y = (x - 13)² + 6 is the graph of y = x² translated 13 units right and 6 units up
A cabinet door has a perimeter of 76 inches. Its area is 357 square inches. What are the dimensions of the door?
Answer:
17 by 21 inches
Step-by-step explanation:
The perimeter is twice the sum of the dimensions, and the area is their product, so you have ...
L + W = 38
LW = 357
__
Solution:
W(38 -W) = 357 . . . . . substitute for L
-(W^2 -76W) = 357 . . expand on the left
-(W^2 -38 +19^2) = 357 -19^2 . . . . complete the square
(W -19)^2 = 4 . . . . . . . write as a square
W -19 = ±√4 = ±2 . . . take the square root; next, add 19
W = 19 ±2 = {17, 21} . . . . if width is one of these, length is the other
The dimensions are 17 by 21 inches.
Amy, Hong, and David have a total of $102 in their wallets. Amy has $6 less than Hong. David has 4 times what Hong has. How much does each have?
Answer:
12,18, and 72 respectively
Step-by-step explanation:
102=A+H+D
A+6=H
D=4H=4(A+6)=4A+24
102=A+H+D=A+A+6+4A+24
102=6A+30
6A=72
A=12
H=18
D=72
pls help! I need the answer quickly! thank you!
The perimeter of a triangle is the summation of the three sides of the triangle. Base on the assumed values, the length of side BD is 2.
For [tex]\triangle ACD[/tex], the sides are: AC, AD and CD
So, the perimeter is:
[tex]P_{\triangle ACD} = AC + AD + CD[/tex]
For [tex]\triangle ABD[/tex], the sides are: AB, AD and BD
So, the perimeter is:
[tex]P_{\triangle ABD} = AB + AD + BD[/tex]
The difference in the perimeters is:
[tex]P_{\triangle ACD} - P_{\triangle ABD} =1 + \sqrt 3[/tex]
So, we have:
[tex](AC + AD + CD) - ( AB + AD + BD) =1 + \sqrt 3[/tex]
Open brackets
[tex]AC + AD + CD - AB - AD - BD =1 + \sqrt 3[/tex]
Evaluate like terms
[tex]AC + CD - AB - BD =1 + \sqrt 3[/tex]
Make BD the subject
[tex]BD = AC + CD - AB - (1 + \sqrt 3)[/tex]
The solution cannot be completed because the side lengths of [tex]\triangle ACD[/tex] and [tex]\triangle ABD[/tex] are not given; so, I will assume the following values.
[tex]AC =2; CD = 1; AB = \sqrt 3[/tex]
[tex]BD = AC + CD - AB - (1 + \sqrt 3)[/tex] becomes
[tex]BD = 2 + 1 + \sqrt 3 - (1 + \sqrt 3)[/tex]
Open bracket
[tex]BD = 2 + 1 + \sqrt 3 - 1 - \sqrt 3[/tex]
Evaluate like terms
[tex]BD = 2[/tex]
Base on the assumed values, the length of side BD is 2.
Read more about perimeters at:
https://brainly.com/question/6465134
Lydia has 955 in her account.she withdrew 245 and later 447.How many is left in her account.
Answer:
263
Step-by-step explanation:
with 955 in the account, you subtract all the amount withdrawed from the main money in the account.
955-245-447
=263
HELP! What is the probability of randomly picking a green marble from a bag of 10 green marbles, 10 yellow marbles, and 5 red marbles?
Answer:
2/5
Step-by-step explanation:
For probability, it's the
number of the type you want
_______________________
the total number of items
So the equation for this would be
10/10+10+5
= 10/25
= 2/5
The final answer is 2/5. Keep in mind that probability is a ratio of likeliness between things, so you CANNOT write it as a decimal!
I hope this helped! :D
find inverse of f(x)=- 1/2 x+11
Answer:
-2x + 22
Step-by-step explanation:
We have the function f(x) = -1/2x + 11 and are asked to find the inverse of it.
To find the inverse, we will follow the according steps :
Replacing x with ySolving for yLet's do as followed:
Replacing x with y :
Since f(x) can be also written as y, we can do y = -1/2x + 11, thus making the switch alot easier.
y = -1/2x + 11
x = -1/2y + 11
Solve for y :
We have to get y alone to find the inverse, to do so, get rid of the outlier by subtracting 11 from both sides :
x - 11 = -1/2y
Now divide both sides by -1/2 to get y alone and retrieve our inverse :
-2(x - 11)
Distribute to get the inverse :
-2x + 22
Hey can anyone help me solve this
Answer:
24
Step-by-step explanation:
Answer and Step-by-step explanation:
I think the answer is 48.
We should add the 12 and 4, then multiply by 3. The 16 times 3 is to get the original amount of candies. To check, we go through the process using the number 48.
48 times 1/3 is 16. 4 of them are given to the brother, which leaves us with 12 remaining candies.
#teamtrees #PAW (Plant And Water)
how do I write 1/2 in a from of a decimal?
Answer:
0.5
1 divide by 2 = 0.5
Which property of equality was used to solve this equation? x − 5 = -14 x − 5 + 5 = -14 + 5 x = -9 A. addition property of equality B. subtraction property of equality C. multiplication property of equality D. division property of equality
Answer:
A
Step-by-step explanation:
In the second step, they added 5 to both sides to get rid of the -5 on the left side. Since the same thing was done to both sides (addition), the answer is the addition property of equality.
Answer:
Addition property of equality
Step-by-step explanation:
The equation is like:
=> x - 5 = -14
=> x - 5 + 5 = -14 + 5
=> x = -9
Since, we add 5 to both sides to solve for "x", the answer is "Addition Property of Equality".
Hope this helps.
can someone help me please
Answer:
[tex] {x}^{4} = 2880[/tex]
Step-by-step explanation:
[tex] {y}^{2} = 20 \: (eq . \: 1)[/tex]
[tex] {x}^{2} = {(2 \sqrt{3y)} }^{2} = 12y [/tex]
Putting value of eq. 1 in the following:
[tex] {x}^{4 } = {(12y)}^{2} = 144{y}^{2} = 144 \times 20 = 2880[/tex]
An operator wants to determine the standard deviation for a machine relative to its ability to produce windshield wipers conforming within their specifications. To do this, she wants to create a p-chart. Over a month's time, she tests 100 units every day and records the number of manufacturing defects. The average proportion of non-conforming windshield wipers is found to be 0.042. What is the standard deviation of this sample
Answer:
the standard deviation of the sample is less than 0.1
Step-by-step explanation:
Given that :
The sample size n = 100 units
The average proportion of non-conforming windshield wipers is found to be 0.042 which is the defective rate P-bar
The standard deviation of the machine([tex]S_p[/tex]) can be calculated by using the formula:
[tex]S_p =\dfrac{ \sqrt{ \overline P \times (1 - \overline P)} }{n}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.042 \times (1 -0.042)} }{100}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.042 \times (0.958)} }{100}[/tex]
[tex]S_p =\dfrac{ \sqrt{0.040236} }{100}[/tex]
[tex]S_p =\dfrac{ 0.2005891323 }{100}[/tex]
[tex]S_p =0.002[/tex]
Thus , the standard deviation of the sample is less than 0.1
A.60
B.40
C.24
D.20
Please help me on this
Answer:
The answer is 20
Step-by-step explanation:
3 times 2 is 6, and 120 divided by six is 20%.
Will mark Brainliest! Which point is a vertex of the hyperbola?
A. (1,−15)
B. (1,−2)
C. (1,3)
D. (1,11)
Answer:
So (1,3) is a vertex (out of two) of the hyperbola.
Step-by-step explanation:
The vertices are marked by the dot on the hyperbola.
They are (1,3) and (1,-7).
However, (1,-7) is not on the list of answer choices, but (1,3) is.
So (1,3) is a vertex (out of two) of the hyperbola.
So (1,3) is a vertex (out of two) of the hyperbola.
What is hyperbola?a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant : a curve formed by the intersection of a double right circular cone with a plane that cuts both halves of the cone.
According to the question
The vertices are marked by the dot on the hyperbola.
They are (1,3) and (1,-7).
However, (1,-7) is not on the list of answer choices, but (1,3) is.
Hence , (1,3) is a vertex (out of two) of the hyperbola.
To learn more about hyperbola from here
https://brainly.com/question/13338587
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Helppppp, i dont know how to do this problem
Answer:
(3, -5) (4, -5) (2, -7)
Step-by-step explanation:
An integer is any whole number that is not a fraction, they include -10204, -3, 0, 5, and 8592. (random numbers)
A coordinate with integers can be anything such as (0, 4582) and (547, 42)
However, it can not be (0.45846, 4579) or (54.42, 58).
To determine which points have coordinates that look like they are integers, you just have to select 3 points that lie at the intersection of the y and x value tic marks
You can see that (3, -5) is at the intersection of the x value 3 tic mark and the y value -5 tic mark, while also being on the parabola.
Which of the following is an example of closure? (1 point)
The equation 5 - 5 = 0 is an example of the natural numbers being closed under subtraction
The equation 1.5 +1.6 = 3.1 is an example of the rational numbers being closed under addition
The equation 4 - 6 = -2 is an example of the whole numbers being closed under subtraction
The equation 1+0= 1 is an example of the natural numbers being closed under addition
Answer:
The equation 1+0=1
Step-by-step explanation:
Other options are not eligible because
1 option -Natural numbers cannot be closed under subtraction
2 option-The equation is not having proper rational numbers, they are decimals
3 option-Whole numbers cannot be closed under subtraction
Thank you!
use the given values
9514 1404 393
Answer:
9-1623Step-by-step explanation:
Put the numbers in place of the corresponding variables and do the arithmetic.
√(2a) -b = √(2·8) -(-5) = 4 +5 = 9
-3ac +2b = -3(8)(1/4) +2(-5) = -6 -10 = -16
b² -8c = (-5)² -8(1/4) = 25 -2 = 23
You are rolling a 6-sided number cube with the numbers 1 through 6. Which of the following represents the probability of rolling an even number?
0
1/6
1/2
1
Answer:
1/2
Step-by-step explanation:
The probailty of an event A is:
● P(A) = ( outcomes that give A) / (total number of possible outcomes)
Let A be the event in wich we get an even number.
● The sample space is {2,4,6}
So there are 3 possible outcomes that give A .
The six-sided dice has 6 outcomes
● { 1,2,3,4,5,6}
■■■■■■■■■■■■■■■■■■■■■■■■■■
● P(A) = 3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
i took the test
What is the simplest fraction whose value is equal to the number (red heart) depicted on this number line. (Give your answer as a fraction, not a mixed number. "Simplest fraction" means the numerator and denominator should have no common divisor greater than 1. : Look closely at the numbers on the number line. (red heart) is between 2 and 3. There are 6 tick marks between 2 and 3. How many regions do those tick marks split the number line into?
Answer:
simplest fraction: 2 1/3 the tick marks split the number into 7 regions
Step-by-step explanation:
The red heart is on the 2 tick mark of the 6 ticks between 2 and 3. The answer is 2 2/6 which after simplifying if equal to 2 1/3.
Answer:
16/7
Step-by-step explanation:
2-3 is devided into 7 segments if you make 2 14/7 and 3 21/7 then you have 16/7 with no common devisor other than 1
Find an equation of the tangent plane to the given surface at the specified point. z = ln(x − 8y), (9, 1, 0)
Answer:
x - 8y - z = 1
Step-by-step explanation:
Data provided according to the question is as follows
f(x,y) = z = ln(x - 8y)
Now the equation for the tangent plane to the surface
For z = f (x,y) at the point P [tex](x_0,y_0,z_0)[/tex] is
[tex]z - z_0 = f_x(x_0,y_0)(x-x_0) + f_y(x_0,y_0)(y-y_0)\\[/tex]
Now the partial derivatives of f are
[tex]f_x(x,y) = \frac{1}{x-8y} \\\\f_y(x,y) = \frac{8}{x-8y} \\\\P(x_0,y_0,z_0) = (9,1,0)\\\\f_z(9,1,0) = (\frac{1}{x-8y})_^{(9,1,0)}[/tex]
[tex]\\\\=\frac{1}{9-8}[/tex]
= 1
Now
[tex]f_y(9,1,0)=(\frac{8}{x-8y})_{(9,1,0)}\\\\ = -\frac{8}{9 - 8}[/tex]
= -8
So, the tangent equation is
[tex]z - 0 = 1\times (x - 9) -8\times (y - 1)[/tex]
Now after solving this, the following equation arise
z = x - 9 - 8y + 8
z = x - 8y - 1
Therefore
x - 8y - z = 1
The equation of the tangent plane is [tex]x-8y-z=1[/tex]
Tangent Plane:An equation of the tangent plane to the given surface at the point [tex]P(x_0,y_0,z_0)[/tex] is,
[tex]z-z_0=f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0)[/tex]
The function is,
[tex]z = ln(x-8y)[/tex]
And the point is (9,1,0)
Now, calculating [tex]f_x,f_y[/tex]
[tex]f_x(x,y)=\frac{1}{x-8y}\\ f_y(x,y)=\frac{x-8}{x-8y}[/tex]
Now, substituting the given points into the above functions we get,
[tex]f_x(9,1)=\frac{1}{9-8(1)}=1\\ f_y(x,y)=\frac{-8}{9-8(1)}=-8[/tex]
So, the equation of the tangent plane is,
[tex]z-0=1(x-9)-8(y-1)\\z=x-8y-1\\x-8y-z=1[/tex]
Learn more about the topic tangent plane:
https://brainly.com/question/14850585
Help! Solve equation: xe^2x=0
Answer: x=0
Step-by-step explanation:
For this problem, there are no calculations needed. You just have to know your algebraic properties. Since we are looking for x, we know that x must be 0. The answer is 0. Figuring out e²ˣ can be tricky, but since there is an x multiplying it in front, we know that x must be 0 to make the equation equal to 0.
Find the indicated complement. A certain group of women has a 0.12% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?
Answer:
the probability will be 0.
Step-by-step explanation:
0.12%= 0.0012= 3/2500.
Instructions: Find the missing side. Round your answer to the
nearest tenth
Answer:
49
Step-by-step explanation:
sin(theta) = P/H
sin(28)=23/x, x=23/sin(28)=49
Find the value of x
pls with all solution
Answer:
the value of x is 85
Step-by-step explanation:
x+x+40+2x-20=360
4x=360-20
4x=340
x=340÷4
x=85
Answer:
X+X+40+2x-20=360(being complete angle)
2x+40+2x -20= 360
4x+20=360
4x=360 - 20
4x= 340
X=340÷4
X= 85
now putting the value of X
X+40
85+ 40
125
2x-20
2×85-20
170- 20
150
hope this answer will help you if it did then make me brainliest.