Rearrange the equation to isolate h:
A = 136h

Answer:

The side length of each square is 2.12 units.

The length ad width of the rectangle are 2.12 and 4.24 units

Step-by-step explanation:

Let the width of the rectangle is x,

So, the length of the rectangle is 2x.

Area of the rectangle = 9 sq. units

\(9 = 2x \times x\) [as area = length x width]

\(\Rightarrow 9 = 2x^2\)

\(\Rightarrow x^2 = \frac{9}{2}=4.5\)

\(\Rightarrow x = 1.5\sqrt{2}=2.12\) units

So, width of the rectangle, x= 2.12 units and

the llengthof the rectangle, 2x= 2 x 2.12= 4.24 units.

After division of the rectangle into two equal square, so, the area of each square will be half of the area of the rectangle.

The area of the rectangle = 9/2=4.5 square units.

Let a be the length of the sides of the square, so

Area \(= a^2\)

\(\Rightarrow a^2=4.5\)

\(\Rightarrow\) \(a = 1.5\sqrt{2}=2.121\)

Hence, the side length of each square = 2.12 units.

Answer:

Blade A : H(θ) = 75 + 50 sin θ

Blade B : H(θ) = 75 + 50 sin(θ + 90° )

Blade C : H(θ) = 75 + 50 sin( θ + 180° )  

Blade D : H(θ) = 75 + 50 sin( θ + 270° )

Step-by-step explanation:

Given data :

Diameter of blade = 50 m

overall height = 125 m

The four blades : Blade A , Blade B, Blade C, Blade D  all moves in same direction hence they make 90° to each other.

Lets assume The blades are standing at  θ with the horizontal

The four equation  modelling the heights :

Blade A : H(θ) = 75 + 50 sin θ

Blade B : H(θ) = 75 + 50 sin(θ + 90° )

Blade C : H(θ) = 75 + 50 sin( θ + 180° )  

Blade D : H(θ) = 75 + 50 sin( θ + 270° )

Answer:

give a heart and 5 stars

Step-by-step explanation:

To find positive integers $a$, $b$, and $2009$ such that $a + b = a \cdot b = 2009$, we observe that $2009$ is a prime number. Since the product of two positive integers is equal to their sum only when they are both equal to $2$, it follows that $a = b = 2$. Thus, the solution is $a = b = 2$.

The problem asks for positive integers $a$, $b$, and $2009$ such that $a + b = a \cdot b = 2009$. First, we note that $2009$ is a prime number. Since the product of two positive integers is equal to their sum only when they are both equal to $2$, we conclude that $a = b = 2$. This can be understood by considering the prime factorization of $2009$, which is $7^2 \cdot 41$. Since $7$ and $41$ are both prime factors, they cannot be expressed as the sum of two positive integers. Therefore, the only solution is $a = b = 2$.

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Answer:

y = 2x - 4

Step-by-step explanation:

First, find the gradient of the line, which is the change in y divided by the change in x. You would get 2. Then, you substitute 2 into your slope equation to get y = 2x + c (c is commonly b in America, but in England we tend to use c instead). Then, substitute the coordinate (4,4) into the equation, and after solving for c, you would get -4.

Therefore, your final answer for the slope would be y = 2x-4

Answer:

2

Step-by-step explanation:

The slope is equal to rise over run, this is the the change in y over the change in x. This is the slope formula: \(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\)

In this case it would look like this: \(\frac{-2 - 4}{1 - 4}\) = -6/-3 = 2

Answer:

90

Step-by-step explanation:

180/2=90

The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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The interval of convergence (I) is (-∞, ∞), as the series converges for all values of x.

To find the radius of convergence (R) of the series, we can apply the ratio test. The ratio test states that for a series ∑a_n*\(x^n\), if the limit of |a_(n+1)/a_n| as n approaches infinity exists, then the series converges if the limit is less than 1 and diverges if the limit is greater than 1.

In this case, we have a_n = \((-1)^n\)* \(x^(n+3)\)/(n+7). Let's apply the ratio test:

|a_(n+1)/a_n| = |\((-1)^(n+1)\) * \(x^(n+4)\)/(n+8) / (\((-1)^n\) * \(x^(n+3)/(n+7\)))|

             = |-x/(n+8) * (n+7)/(n+7)|

             = |(-x)/(n+8)|

As n approaches infinity, the limit of |(-x)/(n+8)| is |x/(n+8)|.

To ensure convergence, we want |x/(n+8)| < 1. Therefore, the limit of |x/(n+8)| must be less than 1. Taking the limit as n approaches infinity, we have: |lim(x/(n+8))| = |x/∞| = 0

For the limit to be less than 1, |x/(n+8)| must approach zero, which occurs when |x| < ∞. Since the limit of |x/(n+8)| is 0, the series converges for all values of x. This means the radius of convergence (R) is ∞.

By applying the ratio test to the series, we find that the limit of |x/(n+8)| is 0. This indicates that the series converges for all values of x. Therefore, the radius of convergence (R) is ∞, indicating that the series converges for all values of x. Consequently, the interval of convergence (I) is (-∞, ∞), representing all real numbers.

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Answer: x is 3

Step-by-step explanation:

6x-5=4x+1

x = 3

The solid has a 62.5 cubic unit volume. Finding the volume of a solid with a circular base of radius 5 units is the task at hand.

The following formula can be used to determine how much of the magical potion is left after a specific period of time:

Let h represent the solid's height. The volume can therefore be stated as follows:

V = (12.5 dh from 0 to h)

Combining, we obtain:

V = 12.5h

The height of the solid is equal to the radius of the circle, which is 5 units, because the slices are perpendicular to the base. Therefore:

V=12.5h=12.5(5)=62.50 cubic metres

Thus, the solid has a 62.5 cubic unit volume.

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a. The sum of 3.7 and 4.888 is 8.6.

b. The product of (4.09 × 10²) and (6.33 × 10⁴) is 2.74 × 10⁷.

c. The result of multiplying 3.376, 23, and 0.123 is 9.95.

d. The result of adding 0.0467 to 23.32 and subtracting 22.8 is 0.099.

a. 3.7 + 4.888

Adding 3.7 and 4.888 gives us a sum of 8.588. Since the least number of decimal places in the given numbers is one, we round the answer to one decimal place, resulting in 8.6.

b. (4.09 × 10²) × (6.33 × 10⁴)

Multiplying the given numbers gives us 259.797 × 10⁶. Since the given numbers have two significant figures each, the answer should have two significant figures as well. Therefore, we round it to 2.7 × 10⁷.

c. 3.376 × 23 × 0.123

Multiplying the given numbers results in 9.984552. The number with the fewest significant figures is 23, which has two significant figures. Therefore, we round the answer to two significant figures, giving us 10.

d. 0.0467 + 23.32 - 22.8

Performing the addition and subtraction operations, we get 0.5667. The given numbers have four decimal places in total. Hence, the answer should also have four decimal places, resulting in 0.099.

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The range of the function f(x) = log5x is (-∞, +∞).The function f(x) = log5x represents the logarithm base 5 of x. To determine the range of this function, we need to consider the possible values that the logarithm can take.

The range of the logarithm function y = log5x consists of all real numbers. The logarithm function is defined for positive real numbers, and as x approaches 0 from the positive side, the logarithm approaches negative infinity. As x increases, the logarithm function approaches positive infinity.

The range of the function is the set of all possible output values. In this case, the range consists of all real numbers that can be obtained by evaluating the logarithm

log5(�)log 5 (x) for �>0 x>0.

Since the base of the logarithm is 5, the function log5x will take on all real values from negative infinity to positive infinity. Therefore, the range of the function f(x) = log5x is (-∞, +∞).

In other words, the function can output any real number, ranging from negative infinity to positive infinity. It does not have any restrictions on the possible values of its output.

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Answer: All real numbers

Step-by-step explanation:

Edge

Answer:

Step-by-step explanation:

it is 100

Answer:

100

Step-by-step explanation:

25 400 10000

----- × ------ = --------- = 100

100 1 100

Hope this helped you- have a good day bro cya)

120 pounds of the cheaper coffee should be use to get a mixture/blend that he would sell for $4 per pound.

An equation is an expression that can be used to show the relationship between variables and numbers.

Let x represent the amount of cheaper coffee.

Jalen has columbian coffee worth $3 per pound that he wishes to mix with 30 pounds of brazilian coffee worth $8 per pound to get a mixture/blend that he would sell for $4 per pound.

Hence:

3x + 8(30) = 4(x + 30)

3x + 240 = 4x + 120

x = 120

120 pounds of the cheaper coffee should be use

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Answer:

x=-5 y=5 (-5,5)

Step-by-step explanation:

(6x-y=-35)-2

5x-2y=-35

-12x+2y=70

5x-2y=-35

-7x=35

x=-5

5(-5)-2y=-35

-25-2y=-35

-2y=-10

y=5

Answer: )Step-by-step explanation:

When you say that the matrices form a basis for the linear space, I assume you mean that they form a basis for the vector space of matrices with the same dimensions.

To write the matrix of the linear transformation relative to the given basis, follow these steps:

1. Identify the basis matrices for the linear space.
2. Apply the linear transformation to each basis matrix.
3. Express the transformed matrices as linear combinations of the basis matrices.
4. Write the coefficients of these linear combinations as columns in the matrix of the linear transformation.

By following these steps, you will have the matrix of the linear transformation relative to the given basis. Note that I cannot provide specific numbers or examples since no specific matrices or transformations were provided in your question.

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Explanation

Let the length be l and width b W, Since the length of the rectangle is 3 m less than twice the width, we will have

Therefore, the area becomes

Logically, the width becomes

Answer: width = 6.5m

Therefore, the length becomes

Answer" lenght =10 m

Answer:

equation: 3h+2.50=13

solution: h=$3.50

each hamburger was $3.50

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

3f-2g

The statement "every composite number greater than 2 can be written as a product of primes in a unique way except for their order" refers to the fundamental theorem of arithmetic.

The fundamental theorem of arithmetic states that every composite number greater than 2 can be expressed as a unique product of prime numbers, regardless of the order in which the primes are multiplied. This means that any composite number can be broken down into a multiplication of prime factors, and this factorization is unique.

For example, the number 12 can be expressed as 2 × 2 × 3, and this is the only way to write 12 as a product of primes (up to the order of the factors). If we were to change the order of the primes, such as writing it as 3 × 2 × 2, it would still represent the same composite number. This property is fundamental in number theory and has various applications in mathematics and cryptography.

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Using the definition of limit, it is shown that for any positive ε, there exists a positive integer N such that the absolute difference between the sequence and 7 is less than ε for all n greater than or equal to N. Therefore, the conjecture is proven.

Conjecture: The limit value of the sequence {\frac{5n}{4n} + 6} as n approaches infinity is 7.

{\frac{5n}{4n} + 6} = {\frac{5}{4}} + 6/n

As n approaches infinity, 6/n approaches 0, so the sequence approaches {\frac{5}{4}} + 0 + 6 = 7.

Proof:

Let ε be a positive number. We want to find a positive integer N such that for all n ≥ N, |{\frac{5n}{4n} + 6} - 7| < ε.

|{\frac{5n}{4n} + 6} - 7| = |{\frac{5n}{4n} - {\frac{4n}{4n}}}|

= |{\frac{n}{4n}}|

= {\frac{1}{4}}

So we want to find N such that {\frac{1}{4}} < ε.

Choose N to be the smallest integer greater than {\frac{1}{4ε}}. Then for all n ≥ N, we have:

|{\frac{5n}{4n} + 6} - 7| = |{\frac{1}{4}}| < ε

Therefore, the limit of the sequence {\frac{5n}{4n} + 6} as n approaches infinity is 7, which proves the conjecture.

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The Z score of the individual with IQ 90 is -0.67.

It is given that the scores are Normally distributed.

The mean given is 100 while the standard deviation is 15.

Let the IQ distribution be X.

Hence X follows a Normal distribution X~N(100, 225)

where

100 = mean

225 = standard deviation

To find the Z score we need to convert the following into the standard normal distribution.

To do that we need to follow

Z = ((x - μ) / σ)

here

μ = mean of the distribution = 100

σ = standard deviation of the distribution = 15

x = 90

Hence the Z score is

Z = (90 - 100) / 15

= -10/15

= -0.67

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The equivalent expression of (2x+2)(3x²-1) is 6x³ + 6x² - 2x -2

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

The given expression,

(2x+2)(3x²-1).

Simplifying,

6x³ + 6x² - 2x -2.

To verify if both of the expressions are equivalent or not:

put x = 1,

The original expression gives, the value = 10

And simplified expression gives , the value = 10.

Similarly, expressions are true for all the values of x.

Therefore, 6x³ + 6x² - 2x -2 is the equivalent expression.

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Answer:

1/6

2/6 or 1/3

Step-by-step explanation:

Answer:

Solution given:

Sin\(\theta_{1}=\frac{1}{4}\)

\(\frac{opposite}{hypotenuse}=\frac{1}{4}\)

equating corresponding value

opposite=1

hypotenuse=4

adjacent=x

By using Pythagoras law

hypotenuse²=opposite²+adjacent²

4²=1²+x²

16=1+x²

x²=16-1

x=\(\sqrt{15}\)

In II quadrant

Cos angle is negative

Cos\(\theta_{1}=\frac{-adjacent}{hypotenuse}\)

Answer:

\(\displaystyle \cos ( \theta _{1} ) = - \frac{ \sqrt{15}}{ 4 }\)

Step-by-step explanation:

on a unit circle there're 4 Quadrant. on Q:I sin and cos both are positive,on Q:II cos is negative and sin positive, on Q:III both sin and cos are negative and on Q:IV cos is positive and sin negative.

actually a unit circle is a coordinate plane but

it'll be required later

well to solve the problem we can consider Pythagorean theorem which states that the square of sin and cos is equal to 1. therefore,

\( \displaystyle \sin ^{2} ( \theta) + \cos ^{2} ( \theta) = 1\)

\( \rm \displaystyle \implies \boxed{\cos ^{} ( \theta) = \sqrt{1 - \sin ^{2} ( \theta) }}\)

in this case,

Thus substitute:

\(\displaystyle \cos ( \theta _{1} ) = \sqrt{1 - \left( \frac{1}{4} \right) ^{2} }\)

simplify square:

\(\displaystyle \cos ( \theta _{1} ) = \sqrt{1 - \frac{1}{16} }\)

simplify substraction:

\(\displaystyle \cos ( \theta _{1} ) = \sqrt{ \frac{16 - 1}{16} }\)

simplify numerator:

\(\displaystyle \cos ( \theta _{1} ) = \sqrt{ \frac{15}{16} }\)

recall redical rule:

\(\displaystyle \cos ( \theta _{1} ) = \frac{ \sqrt{15}}{ \sqrt {16} }\)

simplify square root:

\(\displaystyle \cos ( \theta _{1} ) = \frac{ \sqrt{15}}{ 4 }\)

since cos is negative on Q:II hence,

\(\displaystyle \cos ( \theta _{1} ) = \boxed{- \frac{ \sqrt{15}}{ 4 }}\)

and we're done!

Answer: X²+2x

Step-by-step explanation:

Use FOIL method

Solve:

 x(x+2)

☽------------❀-------------☾

Hi there!

~

What is \(x(x+2)\) expanded?

\(x(x+2)\) in expanded form is :

\(x^2 + 2x\)

Explanation :

Apply the distributive law: \(a( b + c ) = ab + ac\)

\(x(x+2) = xx + x \times 2\)

\(= xx + x \times 2\)

Then you simplify : \(xx + x \times 2 : x^2 + 2x\)

\(= x^2 + 2x\)

❀Hope this helped you!❀

☽------------❀-------------☾

Answer:

D.

Step-by-step explanation:

1) if the points (1;-1) and (4;0) belong to the line, then

2) the equation of this line is 3y-x=-4;

3) the inequality is 3y-x≤-4.

To find the length of a rectangular computer chip, we can use the formula for the area of a rectangle, which is A = l × w, where A is the area, l is the length, and w is the width. We can rearrange the formula to solve for the length, l, by dividing both sides of the equation by the width, w: l = A / w.

Given that the area of the computer chip is 112a3b2 square microns and the width is 8ab microns, we can plug these values into the formula for the length and simplify:

l = A / w
l = 112a3b2 / 8ab
l = (112 / 8) × (a3 / a) × (b2 / b)
l = 14 × a2 × b
l = 14a2b

Therefore, the simplified expression for the length of the computer chip is 14a2b microns.

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Answer: The bag of seeds covers 5656 square feet and is 1/3 pound. To find how many square feet the seeds cover per pound, we can divide the total coverage by the weight of the bag.

Formula: Coverage per pound = Total coverage/weight of the bag

5656 / (1/3) = 5656*3 = 16,968 square feet per pound.

Step-by-step explanation:

Answer:

The present value of $225 received at the end of five years with an interest rate of 5% is $176.29.