Coordinates is computed that:
a = 0
b = -0.8
c = 0
d = 0
e = 0
Calculating the missing coordinate in such a way that the three vectors for R3 are orthogonal:
[tex]\left[\begin{array}{ccc}0.6&a&b\\0.8&c&0.6\\1&-1&e\end{array}\right][/tex]
Any two vectors' dot product is zero and their norm is one on an orthogonal basis.
⇒ (-0.6, a, b) (0.8, b, c, -0.6)
⇒ -0.48 + ac - 0.6b = 0 → (1)
Similarly,
(0.8, c, -0.6) (d, -1, e)
⇒ 0.8d - c - 0.6c = 0 → (2)
Similarly,
(-0,6, a, b) (d, -1, e)
⇒ -0.6d - a + be = 0 → (3)
First Norm:
(0.6)² + a² + b² = 1
⇒ 0.36 + a² + b² = 1
⇒ a² + b² = 0.64 → (4)
Second Norm:
(0.8)² + c² + (-0.6)² = 1
⇒ 0.64 + c² + 0.36 = 1
⇒ c² + 1 = 1
⇒ c = 0
Now from equation (1), we can compute that:
(-0.48 + a) * (0 - 0.6b) = 0
⇒ -0.48 - 0.6b = 0
⇒ - (0.48 + 0.6b) = 0
⇒ 0.6b = -0.48
⇒ b = -0.48 / 0.6 = -0.8
∴ b = -0.8
From equation (4) we can compute that:
a² + b² = 0.64
⇒ a² + (-0.8)² = 0.64
⇒ a² = 0
∴ a = 0
Third Norm:
d² + 1 + e² = 1
d² + e² = 0 → (5)
From equation (3) we can infer that:
-0.6d - 0 + (-0.8e) = 0
⇒ -0.6d = 0.8e
⇒ d = -0.8e / 0.6
∴ e = -0.75d
Now we'll put this value in equation (5):
d² + (-0.75d)² = 0
⇒ d² + 0.5625d² = 0
⇒ d² (1 + 0.5625) = 0
⇒ d = 0
∴ e = 0
Therefore,
[tex]\left[\begin{array}{ccc}-0.6&0&-0.8\\0.8&0&-0.6\\0&-1&0\end{array}\right][/tex]
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In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally distributed variable. Find the probability that randomly selected individual would spent between 35 and 48 minutes on the treadmill.
Using the normal distribution, there is a 0.8155 = 81.55% probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation for this problem are given, respectively, by:
[tex]\mu = 42.5, \sigma = 4.8[/tex]
The probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill is the p-value of Z when X = 48 subtracted by the p-value of Z when X = 35, hence:
X = 48:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{48 - 42.5}{4.8}[/tex]
Z = 1.15
Z = 1.15 has a p-value of 0.8749.
X = 35:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 42.5}{4.8}[/tex]
Z = -1.56
Z = -1.56 has a p-value of 0.0594.
0.8749 - 0.0594 = 0.8155.
0.8155 = 81.55% probability that a randomly selected individual would spent between 35 and 48 minutes on the treadmill.
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Will give brainliest
Answer:
Step-by-step explanation:
will give brainiest wrrwrwvrwvr
Country A has an exponential growth rate of 3.8% per year. The population is currently ,000, and the land area of Country A is 35,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
The number of years it would it take for there to be one person for every square yard is 93.6 years.
How many years would it take for there to be one person for every square yard?When there is one person for every square yard, it means that the population and land area are equal in value.
Number of years = (In FV / PV) / r
FV = future population PV = present population r = rate of growth(In 35 billion / 1 billion) / 0.038 = 93.6 years
Here is the complete question:
Country A has an exponential growth rate of 3.8% per year. The population is currently 1,000,000 ,000 and the land area of Country A is 35,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
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the sum of the measures of three angles is 200. these measures are in the ration 3:5:12. Find the measure of the three angles.
Answer:
30, 50, and 120
Step-by-step explanation:
3/20 × 200 = 30
5/20 × 200 = 50
12/20 × 200 = 120
The measures of three angles that are in ratio 3:5:12 are 30 degrees,50 degrees and 120 degrees.
Given that:
The sum of the measures of three angles = 200.
Let the ratios be x.
The ratio of first angle be 3x
The ratio of second angle be 5x
The ratio of third angle be 12x
According to the question,
3x+ 5x+ 12x = 200
20x = 200
Divide both sides by x
x = 200/20
x = 10
The ratio of first angle be 3x = 3(10) = 30 degrees
The ratio of second angle be 5x = 5(10) = 50 degrees
The ratio of third angle be 12x = 12(10) = 120 degrees
The measures of three angles that are in ratio 3:5:12 are 30 degrees,50 degrees and 120 degrees.
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Solve for x in sin xtan x + tan x – 2sin x + cos x = 0 for 0 ≤ x ≤2π rads.
The value of x = 4.71, 0.41, or 5.89 radian value
Specification:
sinxtanx + tanx -2sinx + cosx = 0
tanx = sinx / cosx
sinx (sinx / cosx) + sinx / cosx -2sinx + cosx = Multiply 0
cosx to remove the fraction
sin ^ 2 (x) + sinx -2sinxcosx + cos ^ 2 (x) = 0
sin ^ 2 (x) + cos ^ Replace with 1. 2 (x) = 1
sinx -2sinxcosx + 1 = 0
sinx (1-2cosx) = -1
1-2cosx = -1 / sinx
-2cosx = -1 / sinx -1
2cosx = 1 / sinx + 1
cosx = 1 / 2sinx + 1/2
sqr (1-sin ^ 2 (x)) = 1 / 2sinx + 1/2
Squared on both sides
1-sin ^ 2 (x) = 1 / 4sin ^ 2 (x) + 1 / 2sinx + 1/4
4sin ^ 2 (x) Multiply
4sin ^ 2 (x) -4sin ^ 4 (x) = 1 + 2sinx + sin ^ 2 (X)
4sin ^ 4 (x) -3sin ^ 2 (x) + 2sinx +1 = 0
y = sinx
4y ^ 4 -3y ^ 2 + 2y + 1 = 0
sinx = y = -1 or -0.3478
x = 270, 180-22.61 or -22.61 degrees
x = 270, 157.39 or 337 .39 degrees
or
x = 3pi / 2, 0.13pi or 1.87pi radians
or
x = 4.71, 0.41 Or 5.89 radians
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You randomly select an integer from 0 to 9 (inclusively) and then randomly select and integer from 0 to 7 what is the probability of selecting a 2 both times
Reason:
Set A = {0,1,2,3,4,5,6,7,8,9}
Set B = {0,1,2,3,4,5,6,7}
The probability of getting a "2" from set A is 1/10 since there is one copy of "2" that we want out of ten values total.
The probability of getting a "2" from set B is 1/8 for similar reasoning. This time there are eight numbers in this set.
Multiply those fractions mentioned (1/10)*(1/8) = 1/80
This fraction converts to the exact decimal value of 0.0125, meaning there's exactly a 1.25% chance of getting "2" twice in a row.
a weather balloon is released and reaches a maximum altitude of 5000 meters.A week later, the balloon is recovered at 3750 metwrs. What was the change in altitude between the maximum height and the height at which the balloon was recovered
The change in altitude between the maximum height and the height at which the balloon was recovered is 1300 meters
How to determine the changeIt is important to note that the maximum height is the peak altitude the balloon reached
To find the difference, we use the formula
Change = Maximum height - recovery height
Maximum height = 5000 meters
Recovery height = 3700 meters
Substitute the values
Change = 5000 - 3700
Change = 1300 meters
Thus, the change in altitude between the maximum height and the height at which the balloon was recovered is 1300 meters
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Which graph represents the function f(x) =3(2)*?
I assume you meant [tex]f(x)=3(2)^x[/tex].
What is the missing exponent in the equation 3 TO THE SEVENTH POWER EQUALS 27
Answer: 3 to the 3rd power equals 27
Step-by-step explanation: Because a exponent is the number times itself 3x3 equals 9 that's already 2 then 9x3 equals 27 so anything above is to much
divide 7.39 divide 0.72 rounded quotient of the nearest hundredth
Answer:
10.26 I believe you wanted me to divide 7.39/0.72. If so, you get 10.2638 that rounds to 10.26
Step-by-step explanation:
Can u give me brainliest please
The value of the expression 7.39 ÷ 0.72 is 10.26 to the nearest hundredths.
We have,
Expression:
7.39 ÷ 0.72
Now,
The expression can be written as,
= 7.39 / 0.72 ______(1)
Simplify the numerator and denominator.
Numerator = 7.39 = 739/100 _____(2)
Denominator = 0.72 = 72/100 ______(3)
Now,
From (1), (2), and (3).
7.39 / 0.72
= (739/100) / (72/100)
= 739/100 x 100/72
100 is the common factor so it gets canceled.
= 739/72
= 10.2638888.....
Rounding to the nearest hundredths.
= 10.26
Thus.
The value of the expression 7.39 ÷ 0.72 is 10.26 to the nearest hundredths.
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Deondra has 57 m of fencing to build a three-sided fence around a rectangular plot of
land that sits on a riverbank. (The fourth side of the enclosure would be the river.)
The area of the land is 340 square meters. List each set of possible dimensions
(length and width) of the field.
(L=17m and W=20m) and (L=40m and W=8.5m) are the possible dimensions (length and width) of the field given that the three sided fence has a length of 57m the area of the land is 340 square meters. This can be obtained by forming quadratic equation for the data.
Calculate the set of possible dimensions (length and width) of the field:
Let length be L and width be W.
Given that,
three sided fence has a length of 57m,
⇒ 2W + L = 57 m ⇒ L = 57 - 2W
the area of the land is 340 square meters
length × width = 340 ⇒ L × W = 340
(57 - 2W)W = 340
57W - 2W² = 340
2W² - 57W + 340 = 0
Solve for W using quadratic formula,
a = 2, b = -57, c = 340
W = (-b±√b²-4ac)/2a
= (57±√3249-2720)/4
= (57±√529)/4
= (57±23)/4
W = 20 m and W = 8.5 m
For W=20, L=57-2(20) = 17
For W=8.5, L=57-2(8.5) = 40
Hence (L=17m and W=20m) and (L=40m and W=8.5m) are the possible dimensions (length and width) of the field given that the three sided fence has a length of 57m the area of the land is 340 square meters.
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Which of the following has the least steep graph?
Name a pair of complementary angles in this figure.
a protractor, with segment DEF along the bottom, EH point to the 55 degree on the left, EJ to 90 degrees, EK to the 30 degrees on the right
angles DEH and HEJ
angles DEH and DEJ
angles DEH and DEK
angles DEF and DEH
The answer choice which represents a pair of complementary angles in the task content is; angles DEH and DEJ.
Which pair of angles represent complementary angles?It follows from the concept of angle geometry that two or more angles are said to be complementary when the sum of their measures is 90°.
It follows from the task content therefore that since, DEJ = 90° and the sum of the measures of angles DEH and DEJ amounts to 90°.
Hence, the pair of angles are complementary.
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Which of the following is The function f(x)=2x2−1 is/has
A. order 2 rotational 2 symmetry about the origin
B. symmetry about the y-axis
C. neither symmetric about the y-axis nor has order 2 rotational symmetry about the origin
D. odds a good way to get someone to participate in a group?
The given function has symmetry about the y - axis.
Symmetry of the Function
If we reflect a function's graph about the y-axis, we will get the same graph since if the function is symmetrical about the y-axis. We can reflect a function about the x- and y-axis and obtain the same graph. These two symmetry kinds are known as the even function and odd function.
The given function is,
f(x) = 2x² - 1
It is an even function since the function remains same for both x and -x.
Putting f(x) = 0, we get,
2x² - 1 = 0
2x² = 1
x² = 1/2
x = ±1/2
⇒ Axis of symmetry is, x=0
Hence, the function f(x) is symmetric about y-axis.
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ienes una cuerda que mide 90 cm. Hay que partir la cuerda en 2 segmentos (A y B). La cuerda B debe ser 5 veces más grande que la cuerda A. ¿Cuánto mide la cuerda B?
Basada en el concepto de relación, tenemos que la cuerda B tiene una longitud de 75 centímetros y la cuerda A es de 15 centímetros.
¿Cuánto mide cada segmento de cuerda?
En este problema debemos hallar dos segmentos de cuerda que cumple la siguiente relación, basada en el enunciado citado:
5 = (90 cm - x)/x (1)
5 · x = 90 cm - x
6 · x = 90 cm
x = 15 cm
Basada en el concepto de relación, tenemos que la cuerda B tiene una longitud de 75 centímetros y la cuerda A es de 15 centímetros.
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What is the slope of the line that contains the points (9,-4) and (1,-5)?
OA. 1
OB.1/5
O C.-1/8
O D. -1
Answer:
Step-by-step explanation:
hello .....
note : the slope of the line (AB) is :
m = (YB -YA)/(XB - XA)
given : A(9,-4) and B (1,-5)
m= ((-5)-(-4))/(1-9)
m= 1/8
Se dispone de 800 000 para invertir. Una cuenta paga el 18% de interés anual, y otra paga el 21%. ¿Cuánto debe invertirse en cada cuenta para ganar 150 000 en intereses en un año?
Se debe depositar $ 600 000 en la cuenta con 18 % de interés anual y $ 200 000 en la cuenta con 21 % de interés anual para recibir $ 150 000 en intereses.
¿Cuánto se debe invertir en cada cuenta para alcanzar las ganancias deseadas en un período dado?
En este problema tenemos un depósito repartido en dos cuentas, que adquiere ganancias de manera continua en el tiempo. En consecuencia, tenemos por interés compuesto la siguiente ecuación a resolver:
x · (18/100) + (800 000 - x) · (21/100) = 150 000
168 000 - (3/100) · x = 150 000
(3/100) · x = 18 000
x = 600 000
Se debe depositar $ 600 000 en la cuenta con 18 % de interés anual y $ 200 000 en la cuenta con 21 % de interés anual para recibir $ 150 000 en intereses.
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A ternary string of length n is a sequence of n digits in which only 0, 1, or 2 appear.
For example, (0,1,0,2) and (1,1,2,2) are ternary strings of length 4 and can be seen as: 0102 and 1122.
How many ternary strings of length 2n are there in which the zeros appear only in odd positions?
dunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunnodunno
dunno
Compute the exact value of the height h of the square-based straight pyramid, given that the base is a square with sides 34 feet long, and all other edges are 50 feet long.
Answer:
31√2 feet
Step-by-step explanation:
The height can be found using the Pythagorean theorem. The height of the pyramid will be the height of the right triangle whose sides are half the diagonal of the square base, the distance from the base to the peak, and the edge from the peak back to the corner of the base.
SetupLet h represent the height of the pyramid. The diagonal of the square base will be √2 times the side of the base. So, half the diagonal will be 17√2 ft. The Pythagorean theorem tells us ...
h² +(17√2)² = 50²
SolutionSubtracting the constant on the left gives ...
h² = 2500 -578 = 1992
h = √1992 = 31√2
The height of the square pyramid is exactly 31√2 feet.
__
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Ayayai inc. Has a customer loyalty program that rewards a customer with 1 customer loyalty point for every $10 of purchase. Each point is redeemable for $3 discount on any future purchases . On july 2, 2020 customers purchase pro for $370000 (with a cost of $210900 )and earn 37000 points redeemable for future purchases. Ayayai is expected 31500 points to be redeemed. Ayayai estimates a standalone selling price for $2.50 per point (or $92500 total ) on the basis of the likelihood of redemption . The points provide a material right to customers that they would not receive without entering into a contract. As a result. Ayayai concludes that the points are separate performance obligation. Determine the transaction price for the product and the customer loyalty points. Product purchases, loyalty points, total transaction price
The transaction price for Ayayai's product and the customer loyalty points are $92500 and 37000 points respectively.
How to determine the transaction price?Based on the information provided about Ayayai inc., the transaction price for their product and the customer loyalty points would be allocated as follows:
SSP PA TTP AA____
Product purchases $370,000 80% $370,000 $296,000
Loyalty points $92,500* 20% $370,000 $74,000__
$462,500 $370,000
*37,000 × 2.50 = $92,500
Note:
SSP means Standalone selling prices.PA means Percent allocated.TTP means Total transaction price.AA means Allocated amounts.Read more on transaction price here: https://brainly.com/question/15874481
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Robin can make 8 puppets with the material she already has. For each additional sheet of felt she buys, she can make 5 more puppets. What is an equation that shows how the total number of puppets she can make, y, depends on the number of sheets of felt she buys?
articipation Activity #6
This is similar to Try It #11 in the OpenStax text.
A satellite is rotating around Earth at 0.2 radians per hour at an altitude of 252 km above Earth. If the radius of Earth is 6,378 kilometers, find the linear speed of the satellite in kilometers per hour.
Enter the exact answer.
The linear speed of the satellite is
Number
kilometers per hour.
The linear speed based on the information is 1326 km/h.
How to calculate the speed?The radius will be:
= 6378 + 252
= 6630 km
The angular speed is 0.2. The linear speed will be:
= 6630 × 0.2
= 1326 km/h.
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Q19. When a resistor is placed across 230M supply (de) the
current is 12A. What is the value of resistor that must
De connected in parallel to increase the load current
to 16a
The value of the resistor that must be connected in parallel is 57.47 ohms
How to determine the resistor connected across the 230 V supplyVoltage (V) = 230 VCurrent (I) = 12 AResistor 1 (R₁) =?V = IR
230 = 12 × R₁
Divide both sides by 12
R₁ = 230 / 12
R₁ = 19.17 ohms
How to determine the total resistanceVoltage (V) = 230 VCurrent (I) = 16 ATotal resistance (Rₜ) =?V = IR
230 = 16 × Rₜ
Divide both sides by 12
Rₜ = 230 / 16
Rₜ = 14.375 ohms
How to determine the resistor connected in paralleResistor 1 (R₁) = 19.17 ohms Total resistance (Rₜ) = 14.375 ohmsResistor 2 (R₂) = ?1/Rₜ = 1/R₁ + 1/R₂
Collect like terms
1/R₂ = 1/Rₜ - 1/R₁
R₂ = (Rₜ × R₁) / (R₁ - Rₜ)
R₂ = (14.375 × 19.17) / (19.17 - 14.375)
R₂ = 57.47 ohms
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I need answers please and thank you!
Complete the left-hand column of the table below following the steps indicated in the right-hand column to show that "sin a sin b = 1/2[cos(a-b)-cos(a+b)]" is an identity. Use the definitions of sum and difference formulas for cosine.
The equations which completes the left-hand column of the table are;
[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
cos(a - b) - cos(a + b) = (cos(a)•cos(b) + sin(a)•sin(b)) - (cos(a)•cos(b) - sin(a)•sin(b))sin(a)•sin(b) = (1/2)•(cos(a - b) - cos(a + b))Which equations and identities complete the left-hand column of the table?The given expression on the right is written as follows;
First row;
[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
The definition of the sum and difference of cosine are;
cos(a - b) = cos(a)•cos(b) + sin(a)•sin(b)
cos(a + b) = cos(a)•cos(b) - sin(a)•sin(b)
Therefore;
Second row;
cos(a - b) - cos(a + b) = (cos(a)•cos(b) + sin(a)•sin(b)) - (cos(a)•cos(b) - sin(a)•sin(b))cos(a - b) - cos(a + b) = 2•sin(a)•sin(b)
Which gives;
[tex] sin(a) \cdot sin(b) = \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
Third row;
sin(a)•sin(b) = (1/2)•(cos(a - b) - cos(a + b))Learn more about trigonometric functions here:
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Which of the following is NOT a criterion for making a decision in a hypothesis test?
Choose the correct answer below.
OA. If P-values a, the decision is to reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
OB. If the test statistic falls within the critical region, the decision is to reject the null hypothesis.
OC. If a confidence interval does not include a claimed value of a population parameter, the decision is to reject
the Inull hypothesis.
OD. If the P-value is less than 0.05, the decision is to reject the null hypothesis. Otherwise, we fail to reject the null
hypothesis.
If the p-value less than 0.05, the decision is to reject the Null hypothesis.
What is hypothesis testing?Hypothesis testing is statistical reasoning using information from a sample to draw conclusions about a population parameter or population probability distribution. The parameter or distribution is initially bestguessed. Because it is the underlying assumption, the null hypothesis is often referred to as H0.For instance, you might explore and find that a specific drug effectively manages headaches. But nobody will believe what you find if you can't do that experiment again.A hypothesis seeks to provide an answer to a question. We will be forced to think about the results an experiment should try to achieve by a formulated hypothesis.The independent variable is the first variable. Results with seriousness.The following should NOT be used as a decision-making standard in a hypothesis test.
If the p-value less than 0.05, the decision is to reject the Null hypothesis.
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I need some help on this question
Using slopes, the table that could represent Relationship B is the second table.
What is the slope of a relationship?The slope of a relationship is given by the change in y divided by the change in x.
For relationship A, we have points (2,3) and (4,6), hence the slope is:
mA = (6 - 3)/(4 - 2) = 3/2 = 1.5.
Then, the slopes in the table are given as follows:
m = (8.4 - 6.3)/(4 - 3) = 2.1 > mA, hence the first table cannot be representation B.m = (4.5 - 2.25)/(6 - 3) = 0.75 < mA, hence the second table could represent Relationship B.m = (7.2 - 5.4)/(4 - 3) = 1.8 > mA, hence the third table cannot be representation B.m = (9.6 - 4.8)/(6 - 3) = 1.6 > mA, hence the fourth table cannot be representation B.More can be learned about slopes at https://brainly.com/question/24674549
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slove each problem include a diagram. a. A 6m long wheelchair ramp makes an angle of 15 with the ground. How high abouve the ground does the top end of the ramp reach. b.two treees are 120m apart. From the point halfway between them, then angle of the elevation to the top of the trees is 36 and 52. how much taller is one tree than the other.
The wheelchair ramp must have a height of approximately 1.553 meters. One tree is approximately 310.309 meters taller than the other one.
How to determine measures with trigonometric functions
In this problem we have two cases in which geometric diagrams and trigonometric functions are utilized to determine side lengths. Based on all informations presented in the images attached below, we proceed to find the side lengths:
Case A
h = (6 m) · sin 15°
h ≈ 1.553 m
Case B
Δh = 60 m /cos 36° - 60 m /cos 52°
Δh ≈ 310.309 m
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If (x, 68, 85) form a Pythagorean Triple, what is the value of x?
Answer:
x = 51Step-by-step explanation:
If (x, 68, 85) form a Pythagorean Triple, what is the value of x?
to solve we again use Pythagoras, x is the smallest number, so 68 is a cathetus and 85 the hypotenuse
x = √(85²- 68²)
x = (7225 - 4624)
x = √2601
x = 51
Answer:
x = 51
Step-by-step explanation:
The missing value of the Pythagorean triple can be found using the Pythagorean theorem, or it can be found by comparing the values in the triple to known triples.
What are Pythagorean triples?A Pythagorean triple is a set of integers {a, b, c} that satisfy the equation of the Pythagorean theorem:
a² +b² = c²
The smallest such triple is {3, 4, 5}. It is also the only triple that is an arithmetic sequence. Other triples of small integers are ...
{5, 12, 13}, {7, 24, 25}, {8, 15, 17}
There are an infinite number of "primitive" Pythagorean triples, ones that are not multiples of another triple.
What is this triple?The given values of the triple have the ratio ...
68/85 = (4·17)/(5·17) = 4/5
Only the values in the {3, 4, 5} triple and its multiples will have this ratio.
The value of x is 3·17 = 51, so the triple is {51, 68, 85}.
x = 51
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Additional comments
Any primitive triple will have two odd numbers.
The ratios of numbers in a primitive triple are unique to that triple. That is, the numbers are mutually prime.
For any pair of positive integers m > n, there is a Pythagorean triple {2mn, m²-n², m²+n²}. Such triples will not be primitive if m and n have the same parity.
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The above triple can be verified using the Pythagorean theorem:
51² +68² = 2601 +4624 = 7225 = 85²
You have a job earning $12.50 per hour, and you receive a raise so that you earn $13.25 per hour. What is the percent change in your salary
[tex]increase = 13.25 - 12.50 \\ increase = 0.75 \: dollars[/tex]
[tex]12.50 = 100\% \\ 0.75 = x\%[/tex]
[tex]12.50x = 100(0.75) \\ x = \frac{100(0.75)}{12.50} = \frac{75}{12.5} = 6\%[/tex]