Answer:
Well the correct answer is −4x+28... But I don't
see that as one of your options. :/
Simplify:
18−2(x+x−5)
Distribute:
=18+(−2)(x)+(−2)(x)+(−2)(−5)
=18+−2x+−2x+10
Combine Like Terms:
=18+−2x+−2x+10
=(−2x+−2x)+(18+10)
=−4x+28
Answer:
−4x+28
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{28 - 4x}}}}}[/tex]Option D is the correct option.
Step-by-step explanation:
18 - 2 [ x + ( x - 5 ) ]
Remove the unnecessary Parentheses
⇒18 - 2 [ x + x - 5 ]
Collect like terms
⇒18 - 2 [ 2x - 5 ]
Distribute 2 through the parentheses
⇒18 - 4x + 10
Add the numbers
⇒28 - 4x
Hope I helped!
Best regards!!
Solve. 4x−y−2z=−8 −2x+4z=−4 x+2y=6 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=
Answer:
(-2, 4, 2)
Where x = -2, y = 4, and z = 2.
Step-by-step explanation:
We are given the system of three equations:
[tex]\displaystyle \left\{ \begin{array}{l} 4x -y -2z = -8 \\ -2x + 4z = -4 \\ x + 2y = 6 \end{array}[/tex]
And we want to find the value of each variable.
Note that both the second and third equations have an x.
Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all one variable.
Solve the second equation for z:
[tex]\displaystyle \begin{aligned} -2x+4z&=-4 \\ x - 2 &= 2z \\ z&= \frac{x-2}{2}\end{aligned}[/tex]
Likewise, solve the third equation for y:
[tex]\displaystyle \begin{aligned} x+2y &= 6\\ 2y &= 6-x \\ y &= \frac{6-x}{2} \end{aligned}[/tex]
Substitute the above equations into the first:
[tex]\displaystyle 4x - \left(\frac{6-x}{2}\right) - 2\left(\frac{x-2}{2}\right)=-8[/tex]
And solve for x:
[tex]\displaystyle \begin{aligned} 4x+\left(\frac{x-6}{2}\right)+(2-x) &= -8 \\ \\ 8x +(x-6) +(4-2x) &= -16 \\ \\ 7x-2 &= -16 \\ \\ 7x &= -14 \\ \\ x &= -2\end{aligned}[/tex]
Hence, x = -2.
Find z and y using their respective equations:
Second equation:
[tex]\displaystyle \begin{aligned} z&=\frac{x-2}{2} \\ &= \frac{(-2)-2}{2} \\ &= \frac{-4}{2} \\ &= -2\end{aligned}[/tex]
Third equation:
[tex]\displaystyle \begin{aligned} y &= \frac{6-x}{2}\\ &= \frac{6-(-2)}{2}\\ &= \frac{8}{2}\\ &=4\end{aligned}[/tex]
In conclusion, the solution is (-2, 4, -2)
Answer:
x = -2
y =4
z=-2
Step-by-step explanation:
4x−y−2z=−8
−2x+4z=−4
x+2y=6
Solve the second equation for x
x = 6 -2y
Substitute into the first two equations
4x−y−2z=−8
4(6-2y) -y -2 = 8
24 -8y-y -2z = 8
-9y -2z = -32
−2(6-2y)+4z=−4
-12 +4y +4z = -4
4y+4z = 8
Divide by 4
y+z = 2
z =2-y
Substitute this into -9y -2z = -32
-9y -2(2-y) = -32
-9y -4 +2y = -32
-7y -4 = -32
-7y =-28
y =4
Now find z
z = 2-y
z = 2-4
z = -2
Now find x
x = 6 -2y
x = 6 -2(4)
x =6-8
x = -2
Can you help Jorge organize the results into a two-way frequency table? Please answer this ASAP
Answer:
The table is attached!
Step-by-step explanation:
6 students play both musical instrument and a sport3 students play neither a musical instrument nor a sport14 students in total play a sportGiven: There are 24 students in the class
The number of students that does not play a sport is 24 - 14 = 10
The number of students that does not play a musical instrument but play a sport = 14 - 6 = 8
The frequency table thus is attached below:
Translate the following phrase into an algebraic expression using the variable m. Do not simplify,
the cost of renting a car for one day and driving m miles if the rate is $39 per day plus 45 cents per mile
Answer:
y = 0.45X + 39
how many are 6 raised to 4 ???
Answer:
[tex]\large \boxed{1296}[/tex]
Step-by-step explanation:
6 raised to 4 indicates that the base 6 has an exponent or power of 4.
[tex]6^4[/tex]
6 is multiplied by itself 4 times.
[tex]6 \times 6 \times 6 \times 6[/tex]
[tex]=1296[/tex]
10. Write a word problem for this equation:
n ($25) = $125
Answer:
The word problem is "How many $25 are there in $125?"
Step-by-step explanation:
Given
[tex]n(\$25) = \$125[/tex]
Required
Write a word problem for the expression
We start by solving the given equation
[tex]n(\$25) = \$125[/tex]
Divide both sides by $25
[tex]\frac{n(\$25)}{\$25} = \frac{\$125}{\$25}[/tex]
[tex]n = \frac{\$125}{\$25}[/tex]
[tex]n = 5[/tex]
This implies that there are 5, $25 in $125
Hence; The word problem is "How many $25 are there in $125?"
solve this equation -2x+9=-5x-15
Answer:
x = -8
I hope this helps!
*PLEASE ANSWER TY* What is the volume of a hemisphere-shaped coffee if the width of the coffee cup is about 16.51 centimeters? (Use 3.14)
Answer:
Option (1)
Step-by-step explanation:
By the property of the liquids,
"Liquids have a fixed volume but don't have the fixed shape. If we put a liquid in a bottle or a cup it will acquire the shape of a bottle or cup."
In our question, coffee when kept in a cup will take the shape of the cup which is a hemisphere.
Volume of a hemisphere = [tex]\frac{2}{3}\pi r^{3}[/tex]
Where 'r' = radius of the hemisphere
Radius of the cup = [tex]\frac{16.51}{2}[/tex] cm
Volume of the hemisphere = [tex]\frac{2}{3}\pi (\frac{16.51}{2} )^{3}[/tex]
= [tex]\frac{2}{3}\pi (8.255)^3[/tex]
= 1177.5778
≈ 1177.58 cm³
Therefore, Option (1) will be the answer.
To test the belief that sons are taller than their fathers, a student randomly selects 13 fathers who have adult male children. She records the height of both the father and son in inches and obtains the following data. Are sons taller than their fathers? Use the alphaequals0.10 level of significance. Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
Height of Father Height of Son
72.4 77.5
70.6 74.1
73.1 75.6
69.9 71.7
69.4 70.5
69.4 69.9
68.1 68.2
68.9 68.2
70.5 69.3
69.4 67.7
69.5 67
67.2 63.7
70.4 65.5
Which conditions must be met by the sample for this test? Select all that apply.
A. The sample size is no more than 5% of the population size.
B. The differences are normally distributed or the sample size is large.
C. The sample size must be large.
D. The sampling method results in a dependent sample.
E. The sampling method results in an independent sample.
Write the hypotheses for the test. Upper
H 0 :
H 1 :
Calculate the test statistic. t 0=?
(Round to two decimal places as needed.)
Calculate the P-value. P-value=?
(Round to three decimal places as needed.) Should the null hypothesis be rejected?
▼ Do not reject or Reject Upper H 0 because the P-value is ▼ less than or greater than the level of significance. There ▼ is or is not sufficient evidence to conclude that sons ▼ are the same height or are shorter than or are taller than or are not the same height as their fathers at the 0.10 level of significance. Click to select your answer(s).
Answer:
1) B. The differences are normally distributed or the sample size is large
C. The sample size mus be large
E. The sampling method results in an independent sample
2) The null hypothesis H₀: [tex]\bar x_1[/tex] = [tex]\bar x_2[/tex]
The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] < [tex]\bar x_2[/tex]
Test statistic, t = -0.00693
p- value = 0.498
Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers at 0.10 level of significance
Step-by-step explanation:
1) B. The differences are normally distributed or the sample size is large
C. The sample size mus be large
E. The sampling method results in an independent sample
2) The null hypothesis H₀: [tex]\bar x_1[/tex] = [tex]\bar x_2[/tex]
The alternative hypothesis Hₐ: [tex]\bar x_1[/tex] < [tex]\bar x_2[/tex]
The test statistic for t test is;
[tex]t=\dfrac{(\bar{x}_1-\bar{x}_2)}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}[/tex]
The mean
Height of Father, h₁, Height of Son h₂
72.4, 77.5
70.6, 74.1
73.1, 75.6
69.9, 71.7
69.4, 70.5
69.4, 69.9
68.1, 68.2
68.9, 68.2
70.5, 69.3
69.4, 67.7
69.5, 67
67.2, 63.7
70.4, 65.5
[tex]\bar x_1[/tex] = 69.6
s₁ = 1.58
[tex]\bar x_2[/tex] = 69.9
s₂ = 3.97
n₁ = 13
n₂ = 13
[tex]t=\dfrac{(69.908-69.915)}{\sqrt{\dfrac{3.97^{2}}{13}-\dfrac{1.58^{2} }{13}}}[/tex]
(We reversed the values in the square root of the denominator therefore, the sign reversal)
t = -0.00693
p- value = 0.498 by graphing calculator function
P-value > α Therefore, we do not reject the null hypothesis
Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers at 0.10 lvel of significance
what is the answer to 1/8=s-3/4
Answer:
7/8 =s
Step-by-step explanation:
1/8=s-3/4
Add 3/4
1/8 + 3/4 = s -3/4 +3/4
1/8 + 3/4 = s
Get a common denominator
1/8 + 3/4 *2/2 = s
1/8 + 6/8 =s
7/8 =s
1/8 = s - 3/4
1/8 = s -6/8 ( * 2/2)
7/8 = s
s = 7/8
determine the image of the point p[-3,10) under the translation [5,-7]
[tex](-3+5,10-7)=(2,3)[/tex]
the perimeter of square is 76 cm find are of square
Answer:
Given the information above, the area of the square is 361 cm²
Step-by-step explanation:
A square is a shape with four equal sides. So, in order to find the area of the square, we must find the length of each individual side. We can do this by dividing the perimeter by 4 because a square has 4 equal sides meaning they have the same lengths.
The perimeter of the square is 76. So, let's divide 76 by 4.
76 ÷ 4 = 19
So, the lengths of each sides in the square is 19cm.
In order to find the area, we must multiply the length and the width together. Since a square has equal sides, then we will multiply 19 by 19 to get the area.
19 × 19 = 361
So, the area of the square is 361 cm²
Answer:
361 cm^2
Step-by-step explanation:
The area of a square can be found by squaring the side length.
[tex]A=s^2[/tex]
A square has four equal sides. The perimeter is the sum of all four sides added together. Therefore, we can find one side length by dividing the perimeter by 4.
[tex]s=\frac{p}{4}[/tex]
The perimeter is 76 centimeters.
[tex]s=\frac{76 cm}{4}[/tex]
Divide 76 by 4.
[tex]s=19 cm[/tex]
The side length is 19 centimeters.
Now we know the side length and can plug it into the area formula.
[tex]A=s^2\\s=19cm[/tex]
[tex]A= (19 cm)^2[/tex]
Evaluate the exponent.
(19cm)^2= 19 cm* 19cm=361 cm^2
[tex]A= 361 cm^2[/tex]
The area of the square is 361 square centimeters.
Sandy’s older sister was given $2,400 and was told to keep the balance of the money after sharing with her siblings. Give Sandy exactly $350. Write Sandy’s portion
Sandy got 350 out of 2400.
Her portion is 350/2400 which can be reduced to:
35/240 = 7/48
The portion is 7/48
Joey intends to roll a six-sided number cube 100 times. What probability model can he use to predict whether or not each roll will give a result that is divisible by 3?
Options :
A. Each roll has a 0.117 probability of being divisible by 3.
B. Each roll has a 0.333 probability of being divisible by 3.
C. Each roll has a 0.5 probability of being divisible by 3. D. Each roll has a 0.667 probability of being divisible by 3.
Answer: B. Each roll has a 0.333 probability of being divisible by 3.
Step-by-step explanation:
Sample space for a six-sided number cube :
1, 2, 3, 4, 5, 6
Number of outcomes divisible by 3:
(3, 6) = 2
Probability of an event = Number of required outcomes / total number of possible items
Probability (getting a number divisible by 3):
(Number of outcomes divisible by 3 / total outcomes in sample space)
Probability (getting a number divisible by 3):
2 / 6 = 1/3
= 0.333
A
man paid 15600
for a new
car. He
was given a discount of
7%. Find the marked price
of the car
hope it helps.I was reading the same chapter
One type of fabric costs $31.25 for 5 square yards. Another type of fabric costs $71.50 for 11
square yards. Is the relationship between the number of square yards and the cost
proportional between the two types of fabric?
Answer:
as ratio of two type of fabric is different .
hence, the relationship between the number of square yards and the cost
is not proportional between the two types of fabric
Step-by-step explanation:
For a relation to be proportional
a:b = c:d
in other form
a/b = c/d
______________________________________________
Ratio for first type of fabric
cost of fabric/ area of fabric = 31.25/5 = 6.25
Ratio for other type of fabric
cost of fabric/ area of fabric = 71.50/11 = 6.5
as ratio of two type of fabric is different .
hence, the relationship between the number of square yards and the cost
is not proportional between the two types of fabric
I will give brainliest to the right answer!! Find the vertex and the length of the latus rectum. x= 1/2 (y - 5)² + 7
Answer:
(7, 5)2Step-by-step explanation:
When the quadratic is written in vertex form:
x = a(y -k)^2 +h
the vertex is (x, y) = (h, k), and the length of the latus rectum is 1/a.
For your given equation, ...
x = (1/2)(y -5)^2 +7
you have a=1/2, k = 5, h = 7, so ...
the vertex is (7, 5)
the length of the latus rectum is 1/(1/2) = 2
If 4SINB=3SIN(2A+B) :
Prove that:7COT(A+B)=COTA
Answer:
Step-by-step explanation:
Given the expression 4sinB = 3sin(2A+B), we are to show that the expression 7cot(A+B) = cotA
Starting with the expression
4sinB= 3sin(2A+B)
Let us re write angle B = (A + B) - A
and 2A + B = (A + B) + A
Substituting the derived expression back into the original expression ww will have;
4Sin{(A + B) - A } = 3Sin{(A + B)+ A}
From trigonometry identity;
Sin(D+E) = SinDcosE + CosDSinE
Sin(D-E) = SinDcosE - CosDSinE
Applying this in the expression above;
4{Sin(A+B)CosA - Cos(A+B)SinA} = 3{Sin(A+B)CosA + Cos(A+B)sinA}
Open the bracket
4Sin(A+B)CosA - 4Cos(A+B)SinA = 3Sin(A+B)CosA + 3Cos(A+B)sinA
Collecting like terms
4Sin(A+B)CosA - 3Sin(A+B)cosA = 3Cos(A+B)sinA + 4Cos(A+B)sinA
Sin(A+B)CosA = 7Cos(A+B)sinA
Divide both sides by sinA
Sin(A+B)CosA/sinA= 7Cos(A+B)sinA/sinA
Since cosA/sinA = cotA, the expression becomes;
Sin(A+B)cotA = 7Cos(A+B)
Finally, divide both sides of the resulting equation by sin(A+B)
Sin(A+B)cotA/sin(A+B) = 7Cos(A+B)/sin(A+B)
CotA = 7cot(A+B) Proved!
If sin Θ = 5 over 6, what are the values of cos Θ and tan Θ?
Answer:
Check explanation
Step-by-step explanation:
Sin∅=5/6
Opp=5. Hyp=6
Adj= (√6²+5²)
= √11
Cos∅=(√11)/6
Tan∅=5/(√11)
Latanya buys 5 yard of blue fabric and 8 yards of green fabric. the blue fabric cost $2 dollars more than the green fabric.she pays a total of $ 62. what would be the combined cost of 1 yard of blue fabric and one yard of green fabric?
Answer: $10
Step-by-step explanation:
let x = the price of green fabric, then x+2 = blue fabric price
8x+5(x+2)=62
8x+5x+10=62
13x+10=62
13x=52
x=4
price of green fabric=$4
price of blue fabric=$6
4+6=$10
which transformations can be used to map a triangle with vertices A(2, 2), B(4,1), C(4, 5) to A'(-2,-2), B'(-1.-4). C'(-5, -4)?
Answer:
C!
Step-by-step explanation:
Maggie drew lines of best fit for two scatter plots, as shown. Which statement best describes the placement of the lines Maggie drew?
Answer:
B. Only line B is a well-placed line of best fit.
Step-by-step explanation:
A good line of best fit is a line drawn to represent, as much as possible, all data points. As long as the data points are clustered along the line, and are not farther from each other, the line is a best fit for such data points.
Therefore, from the two lines drawn by Maggie, Line B seems to be the only well-placed line of best fit, as virtually all the data points are clustered along the line, compared to Line A. Line A only runs across 2 data points. The rest data points are scattered far apart from the line.
Therefore, the statement that best describes the placement of the line of best fit drawn by Maggie is: "B. Only line B is a well-placed line of best fit."
Answer:
Only line B
Step-by-step explanation:
Line A is too low on the graph to be best fit for the plot
How can you change a rational number to a decimal? Can you give an exsample?
Answer:
1/2=0.5
Step-by-step explanation:
¼=0.25
¾=0.75
find the perimeter of the quadrant whose radius is 21cm
Answer:
75 cm
Step-by-step explanation:
∅=90° , r = 21 cm
Arc length= (2πr∅)/360
=(2π×21×90)/360
=33 cm
Perimeter= arc length + 2(radius)
=33+2(21)
=33 + 42
= 75 cm
need help will give 5 stars.
Answer:
t=0.64
Step-by-step explanation:
h = -16t^2 +4t +4
We want h =0 since it is hitting the ground
0 = -16t^2 +4t +4
Using the quadratic formula
a = -16 b = 4 c=4
-b ± sqrt( b^2 -4ac)
----------------------------
2a
-4 ± sqrt( 4^2 -4(-16)4)
----------------------------
2(-16)
-4 ± sqrt( 16+ 256)
----------------------------
-32
-4 ± sqrt( 272)
----------------------------
-32
-4 ± sqrt( 16*17)
----------------------------
-32
-4 ± sqrt( 16) sqrt(17)
----------------------------
-32
-4 ± 4 sqrt(17)
----------------------------
-32
Divide by -4
1 ± sqrt(17)
----------------------------
8
To the nearest hundredth
t=-0.39
t=0.64
Since time cannot be negative
t=0.64
Answer:
0.64
Step-by-step explanation:
0 = -16t^2 + 4t + 4
-4(4t^2 - t -1) = 0
t = [-(-1) +/- sqrt (1 - 4*4*-1)] / 8)
t = 0.64, -0.39
answer is 0.64
Manipulate the radius and height of the cone, setting different values for each. Record the radius, height, and exact volume of the cone (in terms of π). The first one has been done for you. Also calculate the decimal value of the volume, and verify that it matches the volume displayed by the tool. (You might see some discrepancies in the tool due to rounding of decimals.)
Answer:
The decimal value of the volume already given= 1885.2 unit³
For radius 11 unit height 12 unit
Volume= 484π unit³
Volume= 1520.73 unit ³
For radius 4 unit height 6 unit
Volume= 32π unit³
Volume= 100.544 unit³
For radius 20 unit height 15 unit
Volume= 2000π unit³
Volume= 6284 unit³
Step-by-step explanation:
The decimal value of the volume already given= 600π
The decimal value of the volume already given= 600*3.142
The decimal value of the volume already given= 1885.2 unit³
For radius 11 unit height 12 unit
Volume= πr²h/3
Volume= 11²*12/3 *π
Volume= 484π unit³
Volume= 1520.73 unit ³
For radius 4 unit height 6 unit
Volume = πr²h/3
Volume= 4²*6/3(π)
Volume= 32π unit³
Volume= 100.544 unit³
For radius 20 unit height 15 unit
Volume= πr²h/3
Volume= 20²*15/3(π)
Volume= 2000π unit³
Volume= 6284 unit³
Here's the right answer.
simplify the equation. (5xE2 - 3x) - (5xE2 - 3x+1)
Answer:
[tex]\huge \boxed{\mathrm{-1}}[/tex]
Step-by-step explanation:
[tex](5xe^2 - 3x) - (5xe^2 - 3x+1)[/tex]
Distribute negative sign.
[tex]5xe^2 - 3x- 5xe^2 +3x-1[/tex]
Combine like terms.
[tex]0xe^2 +0x-1[/tex]
[tex]0-1=-1[/tex]
Solve for x. 3x-91>-87 AND 17x-16>18
Answer & Step-by-step explanation:
For this problem, we have two inequalities to solve for x.
3x - 91 > -87
17x - 16 > 18
Now that we know what our inequalities are, we will solve them as if we are solving for the value of x.
3x - 91 > -87
Add 91 on both sides.
3x > 4
The solution for the first inequality is 3x > 4
Now let's do the second inequality.
17x - 16 > 18
Add 16 on both sides.
17x > 34
Divide by 17 on both sides.
x > 2
The soultion for the second inequality is x > 2
Answer:
The answer is x>2
Step-by-step explanation:
A combination lock uses three numbers between 1 and 46 with repetition, and they must be selected in the correct sequence. Is the name of "combination lock" appropriate? Why or why not? Choose the correct answer below. A. No, because the multiplication counting rule would be used to determine the total number of combinations. B. Yes, because the combinations rule would be used to determine the total number of combinations. C. No, because factorials would be used to determine the total number of combinations. D. No, because the permutations rule would be used to determine the total number of combinations.
The correct answer is D. No because the permutations rule would be used to determine the total number of combinations.
Explanation:
The difference between a combination and a permutation is that in permutations the order is considered. This applies to the numbers in a lock because these need to be in order. Therefore, to analyze the permutations in a lock, the rule for permutations should be used. This includes the general formula P (n,r) =[tex]\frac{n!}{(n-r) !}[/tex]; in this, n is the number of objects and r refers to the objects used in a permutation. Thus, the term "combination" is inappropriate because this is a permutation, and the permutation rule should be used.
Pick out the set of numbers that is not Pythagorean triple
9 40 46
16 30 34
10 24 26
50 120 130
Answer:
[tex]\huge\boxed{9,40,46}[/tex]
Step-by-step explanation:
Let's check it using Pythagorean Theorem:
[tex]c^2 = a^2 + b^2[/tex]
Where c is the longest sides, a and b are rest of the 2 sides
1) 9 , 40 , 46
=> [tex]c^2 = a^2 + b^2[/tex]
=> [tex]46^2 = 9^2 + 40^2[/tex]
=> 2116 = 81 + 1600
=> 2116 ≠ 1681
So, this is not a Pythagorean Triplet
2) 16, 30 and 34
=> [tex]c^2 = a^2 + b^2[/tex]
=> [tex]34^2 = 16^2 + 30^2[/tex]
=> 1156 = 256 + 900
=> 1156 = 1156
No need to check more as we've found the one which is not a Pythagorean Triplet.
Answer:
[tex] \boxed{ \huge{ \boxed{ \sf{ \blue{9 , \: 40 \:, 46 \: }}}}}[/tex]Option A is the correct option.
Step-by-step explanation:
1. Let h , p and b are the hypotenuse , perpendicular and base of a right - angled triangle respectively.
From Pythagoras theorem,
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
Here, we know that the hypotenuse is always greater than perpendicular and base,
h = 46 , p = 40 , b = 9
⇒[tex] \sf{ {46}^{2} = {40}^{2} + {9}^{2} }[/tex]
⇒[tex]2116 = 1600 + 81[/tex]
⇒[tex] \sf{2116 ≠ 1681}[/tex]
Thus , the relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is not satisfied by h = 46 , p = 40 , b = 9
So, The set of numbers 9 , 40 , 46 is not Pythagorean triple.
------------------------------------------------------
2. 16 , 30 , 34
h = 34 , p = 30 , b = 16
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
⇒[tex] \sf{ {34}^{2} = {30}^{2} + {16}^{2} }[/tex]
⇒[tex] \sf{1156 = 900 + 256}[/tex]
⇒[tex] \sf{1156 = 1156}[/tex]
The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and b i.e h = 34 , p = 30 , b = 16
So, the set of numbers 16 , 30 , 34 is a Pythagorean triple.
------------------------------------------------------
3. 10, 24 , 26
h = 26 , p = 24 , b = 10
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
⇒[tex] \sf{ {26}^{2} = {24}^{2} + {10}^{2} }[/tex]
⇒[tex] \sf{676 = 576 + 100}[/tex]
⇒[tex] \sf{676 = 676}[/tex]
The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and h i.e h = 26 , p = 24 , b = 10
So, the set of numbers 10, 24 , 26 is the Pythagorean triple.
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4. 50 , 120 , 130
h = 130 , p = 120 , b = 50
[tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]
⇒[tex] \sf{ {130}^{2} = {120}^{2} + {50}^{2} }[/tex]
⇒[tex] \sf{16900 = 14400 + 2500}[/tex]
⇒[tex] \sf{16900 = 16900}[/tex]
The relation [tex] \sf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex] is satisfied by the particular values of h , p and b i.e h = 130 , p = 120 , b = 50
So, the set of numbers 50, 120 , 130 is the Pythagorean triple.
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In this way, to satisfy the Pythagoras Theorem , the hypotenuse ( h ) , perpendicular ( p ) and the base ( b ) of a right - angles triangle should have the particular values in order. These values of h , p and b are called Pythagorean triple.
Hope I helped!
Best regards!!
simpily 2^3×3^2=6^5
Answer:
2^3×3^2=6^5 equation is wrong because
2×2×2×3×3=72
6^5=6×6×6×6×6=36×36×6=7776
the two numbers are not equal
Mate, I think your question is wrong ! ;(
[tex]Corrected \\ Question...\\[/tex] (2^3)^2*(3^2)^3=6^5
