One leg of a right triangle measures 7 feet. If the other leg is 1 foot shorter than the hypotenuse, find the dimensions of the triangle.

The simplified expression is 1/(9a²b⁵).

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

To simplify the given expression, we need to cancel out any common terms in the numerator and denominator. We can do this by dividing both the numerator and denominator by the highest power of a and b that they have in common. Here are the steps:

1. (4a²b₂²)/(15ab³)*(5a³b⁶)/(12a⁴b⁷)
2. Cancel out the common terms in the numerator and denominator:
= (4/15)*(5/12)*(a²/a⁴)*(b²/b⁷)*(a³/a⁴)*(b⁶/b⁷)
3. Simplify the terms:
= (1/9)*(1/a²))*(1/b⁵)
4. Multiply the terms together:
= 1/9a²b⁵

So the simplified expression is1/(9a²b⁵)

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The real number t corresponds to the point P(-2/1, 2/3) on the unit circle. To evaluate the six trigonometric functions of t, we can use the coordinates of point P.

Part 2 of 6:
cost= x-coordinate of point P = -2/1 = -2

Part 5 of 6:
sect= 1/cost= 1/(-2)= -1/2

The other four trigonometric functions can be evaluated similarly using the coordinates of point P:

sint= y-coordinate of point P = 2/3

cott= x-coordinate/y-coordinate = (-2/1)/(2/3) = -3

csc t= 1/sint= 1/(2/3)= 3/2

tant= y-coordinate/x-coordinate = (2/3)/(-2/1) = -1/3

Therefore, the six trigonometric functions of t are:

sint= 2/3
cost= -2
tant= -1/3
csc t= 3/2
sect= -1/2
cott= -3

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In the above problem, note that the percent powdered sugar in mixture B was approximately 25.81%. See table attached.

The last column shows the amount of powdered sugar in each mixture, which we can calculate using the percent powdered sugar and the pounds of mixture.

To find the percent powdered sugar in mixture B, we can use the fact that the total amount of powdered sugar in the final mixture is the sum of the amounts of powdered sugar in each of the original mixtures. So we have:

1 + 0.11x = 3.84

Solving for x, we get:

0.11x = 2.84

x = 25.81

Therefore, the percent powdered sugar in mixture B was approximately 25.81%.

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The answer should be D.

The similarity statements are;

SV/RS = TV/TU

AC/AB = CE/ED

Formally, two triangles ABC and DEF are similar if and only if:

Their corresponding angles are congruent, meaning that angle A is equal to angle D, angle B is equal to angle E, and angle C is equal to angle F.

The corresponding sides are in proportion to each other, meaning that the ratio of the length of side AB to side DE is equal to the ratio of the length of side BC to side EF, which is also equal to the ratio of the length of side AC to side DF.

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Answer:

Option A.

Step-by-step explanation:

We are asked to add these 2 expressions.

First, we should know how to combine like terms.

Combining like terms is adding 2 or more numbers, or variables that are alike.

[tex]-\frac{4}{5} t+\frac{5}{3} s \ + -3 - \frac{7}{5} s+2t=?[/tex]

Let's first begin by combining s and t. We can combine like terms for these two variables.

[tex]-\frac{4}{5} t + 2t = \frac{6}{5} t \ \checkmark[/tex]

[tex]\frac{5}{3} s \ + \frac{7}{5} s \\Which \ can \ also \ be \ represented \ as...\\\frac{25}{15} s \ - \frac{21}{15} s = \frac{4}{15} s \ \checkmark[/tex]

-3 doesn't have any like terms, meaning it'll stay as -3.

[tex]\frac{6}{5} t + \frac{4}{15} s - 3[/tex]

Therefore, our answers matches with Option A.

Answer:

D is not equivalent because 730% is not a rational number.

Length of the side of square is x = 5.7 unit

The Pythagorean theorem states, "In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides." The sides of this triangle were called the perpendicular, the base and the hypotenuse. Here, the hypotenuse is on the opposite side of the 90° angle, so it is the longest side.

Given,

Figure of a rectangle and a right triangle share its hypotenuse with length of rectangle

diagonal of rectangle = 8

length of both sides of right triangle other than hypotenuse = 4

Let length of rectangle be l

By Pythagoras theorem

l² = 4² + 4²

l² = 32

l = 4√2

Now, In the rectangle

8² = l² + x²

64 = 32 + x²

x² = 32

x = 4√2

x = 5.7

rectangle is an square.

Hence value of x, length of the side of square is 5.7 unit.

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Answer:

[tex]18\frac{1}{24}[/tex] ≅ 18.0416667

Step-by-step explanation:

5 7/8 + 4 1/3 + 7 5/6 = [tex]\frac{433}{24}[/tex]

1.Conversion a mixed number 5 7/8

to an improper fraction: 5 7/8 = 5 7/8

= 5 · 8 + 7/8

= 40 + 7/8

= 47/8

To find a new numerator:

a) Multiply the whole number 5 by the denominator 8. Whole number 5 equally 5 * 8/8 = 40/8

b) Add the answer from the previous step 40 to the numerator 7. New numerator is 40 + 7 = 47

c) Write a previous answer (new numerator 47) over the denominator 8.

Five and seven-eighths is forty-seven eighths.

2. Conversion a mixed number 4 1/3

to an improper fraction: 4 1/3 = 4 1/3 = 4 · 3 + 1/3 = 12 + 1/3 = 13/3

To find a new numerator:

a) Multiply the whole number 4 by the denominator 3. Whole number 4 equally 4 * 3/3 = 12/3

b) Add the answer from the previous step 12 to the numerator 1. New numerator is 12 + 1 = 13

c) Write a previous answer (new numerator 13) over the denominator 3.

Four and one-third are thirteen-thirds.

3. Add: 47/8

+ 13/3

= 47 · 3/8 · 3

+ 13 · 8/3 · 8

= 141/24

+ 104/24

= 141 + 104/24

= 245/24

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - is LCM(8, 3) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 3 = 24. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - forty-seven eighths plus thirteen-thirds is two hundred forty-five twenty-fourths.

4. Conversion a mixed number 7 5/6

to an improper fraction: 7 5/6 = 7 5/6 = 7 · 6 + 5/6 = 42 + 5/6= 47/6

To find a new numerator:

a) Multiply the whole number 7 by the denominator 6. Whole number 7 equally 7 * 6/6= 42/6

b) Add the answer from the previous step 42 to the numerator 5. New numerator is 42 + 5 = 47

c) Write a previous answer (new numerator 47) over the denominator 6.

Seven and five-sixths are forty-seven-sixths.

5.Add: the result of step No. 3 + 47/6= 245/24 + 47/6 = 245/24 + 47 · 4/6 · 4 = 245/24 + 188/24 = 245 + 188/24 = 433/24

It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - is LCM(24, 6) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 24 × 6 = 144. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - two hundred forty-five twenty-fourths plus forty-seven sixths are four hundred thirty-three twenty-fourths.

In the given triangle of attached figure , the required value of x and y is given by option d. x=24.0,y=46.4 ( nearest tenth ).

Let us consider triangle name of the attached figure be ABC,

From vertex A perpendicular line intersect BC at point D.

From the attached figure,

Measure of ∠B = 45°

Measure of ∠C = 30°

Side length AC = 34 units

Side length AB = x units

Side length BC = y units

In triangle ADC,

sin C = AD / AC

Substitute the value we have,

⇒ sin 30° = AD / 34

⇒ AD = ( 1/2 )× 34

⇒ AD = 17

And cos C = CD / AC

Substitute the value we have,

⇒ cos 30° = CD / 34

⇒CD = 34 × cos 30°

⇒ CD = 34 × (√3 /2 )

⇒ CD = 29.45 units

In triangle ADB,

sin B = AD/ AB

⇒ sin 45° = 17 / x

⇒ x = 17 / sin 45°

⇒ x = 17 / ( 1/√2)

⇒ x = 17√2

⇒ x= 24.038 units

⇒ x= 24.0 units ( nearest tenth )

Now in triangle ABD,

cos B = BD/ AB

⇒ cos 45° = BD / 24.0

⇒ BD = 24 × cos 45°

⇒ BD = 24× (1/√2)

⇒ BD = 16.97units

y = BD + CD

 = 16.97 + 29.45

 = 46.42

  = 46.4 units ( nearest tenth )

Therefore , the value of x and y from the attached figure is equal to option d. x=24.0,y=46.4.

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The above question is incomplete, the complete question is:

Find the value of x and y to the nearest tenth.

a. x=48.1,y=46.4

b. x=48.1,y=139.3

c. x=24.0,y=139.3

d. x=24.0,y=46.4

Figure is attached.

Answer:

#1 is equivalent

#2 is not equivalent

#3 is not equivalent

#4 is not equivalent

#5 is not equivalent

Hope this helps!

Answer: Supercomputers

Step-by-step explanation: Supercomputers are high-performance computing systems that are designed to perform complex and demanding tasks at incredibly fast speeds.  They are capable of processing massive amounts of data and performing calculations at a rate that far exceeds that of conventional computers.

Supercomputers are used for a variety of purposes, including scientific research, weather forecasting, modeling and simulation, data analysis, and artificial intelligence.  They are especially valuable in fields that require extensive computational power, such as astrophysics, molecular modeling, climate studies, and cryptography.

One key characteristic of supercomputers is their parallel processing capability.  They are designed with multiple processors or cores that work together to execute tasks simultaneously, allowing for faster and more efficient computation. This parallel architecture enables supercomputers to tackle large-scale problems by breaking them down into smaller tasks that can be processed concurrently.

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Answer: The second option

Step-by-step explanation:

To find the total area, add the areas of the shapes together

Area of the cylinder = πr²h

Area of the cone = 1/3(πr²h)

Area of the full shape = πr²h + 1/3(πr²h)

The height of the cylinder is 12.

Hope this helps!

The set of ordered pairs from the given table is: (5.0, 4.20), (6.0, 5.05), (7.0, 5.90), (8.0, 6.75).

When two items are written inside parantheses and are separated by a comma, they create an ordered pair. For instance, the ordered pair (x, y) indicates an ordered pair in which 'x' is referred to as the first element and 'y' is referred to as the second element. These items, which can be either variables or constants, have distinct names depending on the context in which they are used. In an ordered pair, the element order is quite significant. It implies that (x, y) may not always be equivalent to (y, x).

The set of ordered pairs from the given table is:

(5.0, 4.20)

(6.0, 5.05)

(7.0, 5.90)

(8.0, 6.75)

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The complete question is:

To determine the average rate of the speed's increase or decrease from t=2 to t=5, we need to find the slope of the line connecting the points (2,s(2)) and (5,s(5)) on the graph of the equation s(t)=T^2-6T+35. The slope of a line is given by the formula:
slope = (y2-y1)/(x2-x1)

In this case, x1=2, x2=5, y1=s(2), and y2=s(5).
Plugging in the values of x1 and x2 into the equation s(t)=T^2-6T+35, we get:
y1=s(2)=2^2-6(2)+35=4-12+35=27
y2=s(5)=5^2-6(5)+35=25-30+35=30
Now we can plug in the values of x1, x2, y1, and y2 into the slope formula:
slope = (30-27)/(5-2) = 3/3 = 1

Therefore, the average rate of the speed's increase or decrease from t=2 to t=5 is 1. This means that the speed is increasing at a constant rate of 1 unit per unit of time from t=2 to t=5.

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The maximum amount that can be purchased is 84.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, a high school sports team is ordering sports drinks online from a company.

Let the amount of drinks be y and number of drinks be x.

For drink not more than 50.

y=10+0.8x ------(i)

For drinks more than 50

y=15+0.7x ------(ii)

For a purchase of $75, it means that:

y=75

Substitute y=75 in equation (i), we get

y=10+0.8x

75=10+0.8x

0.8x=75-10

0.8x=65

x= 65/0.8

= 81.25

x=81

Substitute y=75 in equation (ii), we get

y=15+0.7x

75=15+0.7x

0.7x=60

x=85.7

x=84

By comparing both values

x=84 and x=81

84>81

Hence, the maximum amount that can be purchased is 84.

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a) Yes, I am skeptical of my friend's claim. The mean score of the class is 80, which means that the average score of all the students is 80.

b) I am also skeptical of my friend's claim that Class 2022 did better than Class 2023 in the Final Test. While the mean score of Class 2022 is higher than the mean score of Class 2023, this does not necessarily mean that Class 2022 did better.

If 50% of the students had a score higher than 80, then the other 50% of the students would have to have a score lower than 80 in order for the mean to be 80. However, my friend's estimation error of 0.07 means that there is a possibility that the true percentage of students with a score higher than 80 is actually between 43% and 57%. Therefore, it is not certain that 50% of the students had a score higher than 80.

It is possible that the distribution of scores for Class 2022 is more spread out, with some students scoring very high and some students scoring very low, while the distribution of scores for Class 2023 is more consistent. Without knowing the standard deviation or the range of the scores for each class, it is not possible to accurately compare the performance of the two classes.

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1). 1/4

2). 11/15x

3). 3x/7

1. To add or subtract the rational expressions 5/8 and 3/8x, we need a common denominator. The smallest common denominator is 8x, so we can rewrite each expression with a denominator of 8x:

5/8 = 5x/8x

3/8x = 3/8 * 1/x = 3x/8x

Now we can combine the numerators and simplify:

5x/8x - 3x/8x = (5x - 3x)/8x = 2x/8x = 1/4

Therefore, 5/8 - 3/8x = 1/4.

2. To add or subtract the rational expressions 9/15x and 2/15x, we again need a common denominator. The smallest common denominator is 15x, so we can rewrite each expression with a denominator of 15x:

9/15x = 3/5x

2/15x = 2/15 * 1/x = 2/15x

Now we can combine the numerators and simplify:

3/5x + 2/15x = (9 + 2)/15x = 11/15x

Therefore, 9/15x + 2/15x = 11/15x.

3. To add or subtract the rational expressions 5x/7 and -2x/7, we already have a common denominator of 7. We can simply combine the numerators:

5x/7 - 2x/7 = (5x - 2x)/7 = 3x/7

Therefore, 5x/7 - 2x/7 = 3x/7.

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The present value of the land is $52,337.28

The worth of an anticipated revenue stream assessed as of the valuation date is known as a present value in the fields of economics and finance.

There are different kinds of PV models including:

How to solve:

We use the formula:

Present value of land= $18,000 + (2,000 * 17.1684)= $52,337.28

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Answer: I speak a little spanish but hopefully this helps:)

Los vectores son muy utilizados en muchos ámbitos de la vida cotidiana porque permiten conocer magnitudes y representarlas a partir de su módulo, sentido y dirección. Suelen usarse para: Marcar recorridos.

Step-by-step explanation:

Answer:

429 m³

Step-by-step explanation:

The volume of right rectangular = Length x Width x Height

The volume of right rectangular prism = 12 x 5 1/2 x 6 1/2

                                                                      = 12 x 11/2 x 13/2

                                                                      = 3 x 11 x 13

                                                                      = 429 m³

The accumulated value is $A = 5000 \times e^{(0.09 \times 4)} = 7,311.12$.

The accumulated value of an investment of $\$ 5,000$ at 9% compounded continuously for 4 years is $7,311.12.

This can be calculated using the compound interest formula

\(A=P e^{\lambda t}\).

In this equation, A is the accumulated value of the investment, P is the principal investment amount (which is $\$ 5,000$), $\lambda$ is the interest rate per compounding period (which is 0.09) and t is the number of compounding periods (which is 4 years).

Therefore, the accumulated value is $A = 5000 \times e^{(0.09 \times 4)} = 7,311.12$.

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Answer:

6

hope this helps! :)

the number that is not in the solution set of x + 8 > 15 is 6

By answering the supplied question, we may infer that the response is trigonometry Cos(2u) = -7/9, Sin(2u) = 4sqrt(2)/9, and Tan(2u) = 3/4.

The area of mathematics called trigonometry examines how triangle side lengths and angles relate to one another. The subject first came to light in the Hellenistic era, about in the third century BC, as a result of the use of geometry in astronomical investigations. The area of mathematics known as exact techniques deals with several trigonometric functions and possible computations using them. There are six common trigonometric functions in trigonometry. These go by the designations sine, cosine, tangent, cotangent, secant, and cosecant, respectively (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. Consequently, studying geometry entails learning about the characteristics of all geometric forms.

The values of sin(2u), cos(2u), and tan(2u) in terms of the given value of u may be determined using the double-angle formulae.

The formulae for double angles are as follows:

[tex]2sin = sin(2u) (u)[/tex]

cos(u)

(2u) = cos(2u)

The formula is 2(u) - sin(u) tan(2u) = (2tan(u)) / (1-tan(u)).

We may use the definition of csc(u) to obtain sin(u) given that csc(u) = 3 and 0 u /2:

[tex]sin(u) = 3 sin(u) = 1/3 csc(u) = 1/sin(u)[/tex]

Now we can calculate sin(2u), cos(2u), and tan(2u) using the double-angle formulas:

[tex]2sin = sin(2u) (u)[/tex]

sqrt(1 - sin2(u)) = 2/3 sqrt(8/9) = 4sqrt(2)/9 cos(u) = 2(1/3)

[tex]cos(2u) = sin - cos2(u)[/tex]

2(u) = (1 - sin 2(u)) sqrt

[tex]a^2 - sin^2(u) = 1/9 - 8/9 = -7/9[/tex]

[tex]tan(2u) = (2tan(u)) / (1-tan(2u)) = (2(1/3)) / (1-(1/3)2) = 6/8 = 3/4[/tex]

Cos(2u) = -7/9, Sin(2u) = 4sqrt(2)/9, and Tan(2u) = 3/4.

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Austin is currently 27 years old.

Explanation:

To find out how old Austin is now, we need to use algebra. Let's start by assigning variables to represent their ages. Let A be Austin's current age and R be Roya's current age.

According to the question, we know that:
A = R + 6 (since Austin is 6 years older than Roya)
In 3 years, their ages will be:
A + 3 (for Austin)
R + 3 (for Roya)
And the sum of their ages in 3 years will be 54:
A + 3 + R + 3 = 54

Simplifying the equation gives us:
A + R = 48
Substituting the first equation into the second equation gives us:
R + 6 + R = 48
Combining like terms gives us:
2R = 42
Dividing both sides by 2 gives us:
R = 21

Now that we know Roya's current age, we can use the first equation to find Austin's current age:
A = R + 6
A = 21 + 6
A = 27

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E|X|n < ∞

Let X and Y be independent random variables satisfying E|X+Y|n < ∞ for some a > 0. We can show that E|X|n < ∞ using the triangle inequality.

Let b = a/2. Since E|X+Y|n < ∞, we know that E|X+Y| < ∞. Then by the triangle inequality, we have E|X| < |X+Y| + |Y| < ∞.

Raising both sides of the inequality to the nth power gives us E|X|n < (|X+Y| + |Y|)n < ∞.

Therefore, E|X|n < ∞.

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Answer:

i do not know

Step-by-step explanation:

mmmmdjfhyhbwsdhsiayjbe

Answer: