y+2=6/5(x+10)

solve for y

Using the rules of exponents, the expression (5 x^−5 y^3)^−2 is equivalent to x^10 / (25 y^6) or "x raised to the tenth power over quantity 25 times y raised to the sixth power end quantity".

Given: (5 x^−5 y^3)^−2

1. Distribute the power of two using the Power of a Power Rule. "When a power is raised to another power, multiply the exponents."

5^−2 x^(−5)(−2) y^(3)(−2) =  5^−2 x^10 y^-6

2. Use Negative Rule of Exponent. "A number with a negative exponent should be put to the denominator, and vice versa."

5^−2 x^10 y^-6 = (x^10) / (5^2 y^6)

3. Simplify the constant term.

(x^10) / (5^2 y^6) = x^10 / 25 y^6

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Answer:

360 cubes

Step-by-step explanation:

Part 1) The value of x is 5

Part 2) The length of line AB is 5 inches

Part 3) The length of BC is 15 inches

Answer:

5

5

15

Step-by-step explanation:

The volume of the rectangular building is 2,731,050 feet³ depending on the given height, base and width.

The volume of the building will be calculated by the formula -

Volume = length × breadth × height

Thus, keeping the value of each component of building in the formula to find the volume of the building.

Volume of building = 255 × 255 × 42

Performing multiplication on Right Hand Side of the equation to find the value of volume

Volume of building = 2,731,050 feet³

Therefore, the volume of the building is 2,731,050 feet³.

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The age of Barbra is 22 years.

The algebraic method for solving simultaneous linear equations is the substitution method. A quantity of one variable through one expression is replaced in the second equation, as the name implies.

Now, according to the question.

Let 'a' be the age of Alice.

Let 'b' be the age of Barbra

Let 'c' be the age of Carol.

The sum of age of all three sisters is 68 years.

Thus,  a + b + c = 68

Now, as Alice is three years younger than Barbra.

a = b - 3

and, Barbra is 5 years younger than Carol.

b = c - 5

c = b + 5

By substitution of values of a and c in total age.

(b - 3) + b + (b + 5) = 68

3b - 3 + 5 = 68

On solving the expression.

b = 22

Therefore, the age of Barbra is 22 years.

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If you want to find out if differences exist between thirty car brands on their average miles per gallon. You should perform ANOVA test. The correct answer is B.

To compare the average miles per gallon across thirty car brands, the appropriate test to perform would be ANOVA (Analysis of Variance). ANOVA is used when comparing the means of three or more groups to determine if there are significant differences between them. In this case, you have thirty car brands, which qualify for an ANOVA analysis.

ANOVA (Analysis of Variance) is a statistical test used to compare the means of three or more groups or treatments to determine if there are significant differences between them. It analyzes the variation between the group means and compares it to the variation within the groups.

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The mean score per game is higher for Central High School than for South County High School because the distribution of Central High School's scores is skewed right and contains large outliers.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

From the data given in the box plot, we can conclude that the mean score per game is higher for Central High School than for South County High School because the distribution of Central High School's scores is skewed right and contains large outliers.

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Answer:

$672

Step-by-step explanation:

First find the area so:

5*4=20ft

2^2*3.14=12.56ft

20+12.56=32.56ft

Second find the price for the area:

32.56*12=$672

Hopefully it's correct!

We can conclude that the amount borrowed at 8% (x) and 10% (y) combined is $10000, and the amount borrowed at 12% (z) is $5000.

Let's denote the amount borrowed at 8% as "x," the amount borrowed at 10% as "y," and the amount borrowed at 12% as "z."

From the given information, we can write the following equations:

x + y + z = 15000 (equation 1) (the total amount borrowed is $15000)

0.08x + 0.10y + 0.12z = 1560 (equation 2) (the annual interest is $1560)

x + y = 2z (equation 3) (the total amount borrowed at 8% and 10% is twice the amount borrowed at 12%)

To solve this system of equations using the elimination method, we'll eliminate one variable at a time.

From equation 3, we can rewrite it as x + y - 2z = 0.

Now, we can eliminate the "x" variable by multiplying equation 3 by -1 and adding it to equation 1:

-(x + y - 2z) + (x + y + z) = 0 + 15000

-x - y + 2z + x + y + z = 15000

3z = 15000

z = 5000

Now, we substitute z = 5000 into equation 3 to find x + y:

x + y = 2z

x + y = 2(5000)

x + y = 10000

We can rewrite this equation as x = 10000 - y and substitute it into equation 1:

10000 - y + y + 5000 = 15000

10000 + 5000 = 15000

15000 = 15000

This equation is always true, which means the system of equations has infinitely many solutions. Therefore, we cannot determine the exact values for x, y, and z.

However, we can conclude that the amount borrowed at 8% (x) and 10% (y) combined is $10000, and the amount borrowed at 12% (z) is $5000.

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Plotting the graph of the inequality we get a line passing through the point x = 5.

A mathematical notion called inequality examines two numbers or expressions to see if they are equal or not. When there is an inequality, one value is either more than or less than the other. "" (less than), ">" (greater than), "" (less than or equal to), and "" are used to denote inequality (greater than or equal to). In algebra and calculus, inequalities are frequently used to explain how variables relate to one another and to solve equations and systems of equations. In the actual world, inequalities are frequently used to compare measurements, quantities, and other variables.

The given function is x² > 25.

Simplifying the given inequality we have:

x > √25

x > 5 or -5

But - 5 is < x

So we have,

-5 < x < 5

Plotting the graph of the inequality we get a line passing through the point -5 < x < 5.

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Answer:

Irrational

Step-by-step explanation:

The square root of 3 is not a perfect square, therefore it is irrational. Another way you could see if it is rational is if it can be put in a fraction, if it can't, then it is irrational.

Answer:

0.6

Step-by-step explanation:

1) 1.4-0.8 (A negative and a positive equals a negative, then you just subtract. On the number line you would start at 1.4 and go back)

hope this helps!

Answer:

(-3,5) (-3,3) (-8,3)

Step-by-step explanation:

Answer:

(-3,5) , (-3,3) , (-8,3)

Step-by-step explanation:

bye, bye!!

To count the number of relations R on set A such that at least one ordered pair in R has element a as its first element, we can consider the total number of relations on A and subtract the number of relations that do not have a as the first element in any ordered pair.

Given:

- Set A has 6 elements.

- Element a is one of the elements in A.

- Element b is also an element in A, and it is distinct from element a.

The total number of relations on set A is given by 2^(n^2), where n is the number of elements in A. In this case, n = 6.

Total number of relations on A = 2^(6^2) = 2^36

Now, let's calculate the number of relations on A that do not have a as the first element in any ordered pair. For any ordered pair in a relation, the first element can be any of the remaining 5 elements in A (excluding a). Similarly, the second element can be any of the 6 elements in A.

Number of relations without a as the first element = 5 * 6^2 = 180

Therefore, the number of relations R on A such that at least one ordered pair in R has a as its first element is:

Number of relations with a as the first element = Total number of relations on A - Number of relations without a as the first element

Number of relations with a as the first element = 2^36 - 180

Please note that the resulting number is an extremely large number.

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Answer:

The answer is c.

I just took the test and got it right

Answer:

275 is a 17.521% increase of 234.

This is the formula:

(y2 - y1) / y1)*100

y1=start value

y2=end value

The percentage increased population is 17.52 % from 234 to 275 during one year.

Percentage is defined as ratio expressed as a fraction of 100.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

Given that,

The population of a village increased from 234 to 275 during one year

So, the difference of population is equal to increased population

The difference of population = 275 - 234

The difference of population = 41

Now , the percentage increased population = 41 of 234

The percentage increased population = (41/234)100

The percentage increased population = (0.1752)100

The percentage increased population = 17.52 %

Hence, the percentage increased population is 17.52 % from 234 to 275 during one year

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The given discrete time system is a linear, causal, memory system.

Let's justify this statement by defining what each of these terms means in the context of a discrete time system:

1. Linear or Non-linear system

A system is said to be linear if it satisfies the property of superposition, i.e.,

if x1(n) -> y1(n) and x2(n) -> y2(n), then a[x1(n)] + b[x2(n)] -> a[y1(n)] + b[y2(n)].

On the other hand, a system is said to be non-linear if it does not satisfy the property of superposition.

Here, y(n) = x(n) + 2x(n+4) - 4x(n-3) + 7

Let's assume that x1(n) -> y1(n) and x2(n) -> y2(n).

Then, let's check if the system satisfies the property of superposition:

x1(n) -> y1(n)

= x(n) + 2x(n+4) - 4x(n-3) + 7x2(n) -> y2(n)

= x(n) + 2x(n+4) - 4x(n-3) + 7a[x1(n)] + b[x2(n)]

= a[x(n) + 2x(n+4) - 4x(n-3) + 7] + b[x(n) + 2x(n+4) - 4x(n-3) + 7]

= [a+b]x(n) + 2[a+b]x(n+4) - 4[a+b]x(n-3) + 7[a+b]

= a[y1(n)] + b[y2(n)]

The system satisfies the property of superposition and hence it is a linear system.

2. Causal or Non-causal system

A system is said to be causal if the output at any given time n depends only on the input at the present and past times, i.e., for any n, y(n) depends only on x(k) where k <= n.

A system is said to be non-causal if the output at any given time n depends on the input at future times.

Here, y(n) = x(n) + 2x(n+4) - 4x(n-3) + 7y(n) depends only on x(n) and the inputs at past times.

Hence, the system is causal.

3. Stable or Unstable system

A system is said to be stable if its output is bounded for any finite input.

A system is said to be unstable if its output is unbounded for a finite input.

Here, y(n) = x(n) + 2x(n+4) - 4x(n-3) + 7

Suppose the input x(n) is a unit step function.

Then, the output y(n) becomes:

y(n) = u(n) + 2u(n+4) - 4u(n-3) + 7

Since the input is a bounded function, the output is also bounded.

Hence, the system is stable.

4. Memory or Memoryless system

A system is said to be memoryless if the output at any given time n depends only on the input at the same time n.

A system is said to be a memory system if the output at any given time n depends on the inputs at past and/or future times.

Here, y(n) = x(n) + 2x(n+4) - 4x(n-3) + 7

Since the output depends on the inputs at past and future times, the system is a memory system.

Therefore, the given discrete time system is a linear, causal, memory system.

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Answer:

The answer to your question is 2

Answer:

An equation of the line that passes through the point (-4, -6) and is perpendicular to the line 2x - y = 6 is y = -2x + 10.

The correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E. Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

Given that a company's vice president's salary n years after becoming vice president is defined by the formula S(n) = 70000(1.2)". We have to determine which of the following statements is true:

She will be receiving a 2% raise per year. Her salary will increase $14,000 every year. The percent increase of her salary is 120% every year. Her salary is always 0.2 times the previous year's salary. The percent increase of her salary is 20% every year.

To calculate the salary of the vice president after n years of becoming a vice president, we use the given formula:

S(n) = 70000(1.2)

S(n) = 84000

The salary of the vice president after one year of becoming a vice president: S(1) = 70000(1.2)

S(1) = 84000

The percent increase of her salary is: S(n) = 70000(1.2)n

S(n) - S(n-1) / S(n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = (70000(1.2)n) - (70000(1.2)n-1) / (70000(1.2)n-1) × 100%

S(n) - S(n-1) / S(n-1) × 100% = 20%

Therefore, the correct statement is the percent increase of her salary is 20% every year. Hence, the answer is option E.

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Answer:

2

Step-by-step explanation:

Answer:

insects adapted for stronger flight may survive in greater numbers.

Answer:

it's actually 28+/-√721/7

Step-by-step explanation:

The required function obtained after solving f(g(x)) will be equal to 15x³ + 16. Hence, option C is correct.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the functions given in the question,

f(x) = 3x² + 16

g(x) = √5x³

Now, find the function f(g(x)).

f(g(x)) = f(√5x³),                     [g(x) = √5x³]

f(g(x)) = 3( √5x³)² + 16           [f(x) = 3x² + 16]

So,

f(g(x)) = 3(5x³) + 16

f(g(x)) = 15x³ + 16

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Answer:

f(g(x)) = 15x^3 + 16 dollars / hour

I answered the quiz and it's correct

1. The integral is (1/2)x - (1/4)sin(2x) + C. 2. The integral becomes -(1/4) cos(2x) - (1/8)cos(4x) + C

1. To compute the integral ∫sin²(x) dx, we can use the power reduction formula. The formula states that sin²(x) = (1/2) - (1/2)cos(2x). Applying this formula, we have:

∫sin²(x) dx = ∫(1/2) - (1/2)cos(2x) dx

Integrating term by term, we get:

= (1/2)∫dx - (1/2)∫cos(2x) dx

The integral of dx is x, and the integral of cos(2x) with respect to x is (1/2)sin(2x). Therefore, the integral becomes:

= (1/2)x - (1/4)sin(2x) + C

where C is the constant of integration.

2. To compute the integral ∫cos²(x) sin(2x) dx, we can use the double-angle formula. The formula states that cos(2x) = 2cos²(x) - 1. Rearranging this equation, we have cos²(x) = (1/2) + (1/2)cos(2x).

Now, we substitute this expression for cos²(x) into the integral:

∫cos²(x) sin(2x) dx = ∫[(1/2) + (1/2)cos(2x)] sin(2x) dx

Expanding the integrand, we have:

= (1/2)∫sin(2x) dx + (1/2)∫cos(2x)sin(2x) dx

The integral of sin(2x) with respect to x is -(1/2)cos(2x), and the integral of cos(2x)sin(2x) with respect to x is -(1/4)cos(4x). Thus, the integral becomes:

= -(1/4)cos(2x) - (1/8)cos(4x) + C

where C is the constant of integration.

The complete question is:

Compute the following: \(\( \int \sin ^{2}(x) d x \)\)

Compute the following: \(( \int \cos ^{2}(x) \sin (2 x) d x \)\)

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The answer is 231 inches.

To understand how we arrive at this answer, let's break down the given measurement step by step. We have 6 yards, 3 feet, and 7 inches.

Starting with yards, we know that 1 yard is equal to 3 feet, so 6 yards would be equivalent to 6 * 3 = 18 feet. Adding the 3 feet given, we have a total of 18 + 3 = 21 feet.

Moving on to inches, we know that 1 foot is equal to 12 inches. So, the 21 feet we calculated earlier would be equal to 21 * 12 = 252 inches. Finally, adding the 7 inches given, we get a total of 252 + 7 = 259 inches.

Therefore, 6 yards 3 feet 7 inches is equal to 259 inches.

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