Determine which numbers the equations need to be multiplied by to form opposite terms of the y-variable. 3x - 1 4 y = 15 2 3 x - 1 6 y = 6 Which number should the first equation be multiplied by? Which number should the second equation be multiplied by?.

The estimated value of √4.1 using linear approximation is 2.025.

To estimate a number using linear approximation, we use the formula:

f(x + Δx) ≈ f(x) + f'(x)Δx,

where f(x) is the function we want to approximate, f'(x) is its derivative, and Δx is a small increment in x.

For example, if we want to estimate √4.1, we can use the function f(x) = √x and x = 4 as our starting point. We then have:

f'(x) = 1/(2√x)

Δx = 0.1

f(4.1) ≈ f(4) + f'(4)Δx

≈ √4 + (1/(2√4))(0.1)

≈ 2 + 0.025

≈ 2.025

Therefore, the estimated value of √4.1 using linear approximation is 2.025.

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Answer:

560x^3y^4.

Step-by-step explanation:

The (r+1)th term of (a + b)^r = nCr a^(n-r) b^r

We want the fifth term so r = 5 - 1 = 4:

(4 + 1)th term = 7C4 x^(7-4) (-2y)^4

= 35x^3 16y^4

= 560x^3y^4.

Answer:

C. 8 units.

Step-by-step explanation:

The maximum value of the cosine ( cos) function is 1

So, for y = 3cos(2x - 8) + 5

Maximum value  is 3 *1 + 5 = 8.

y = -3cos(2x - 8) + 5 is the above graph reflected in the y axis so the maximum value is also 8.

Answer:

This looks teacher made so i doubt you would be able to find this anywhere

Step-by-step explanation:

by solving this equation, the value of y = (x²+1)/(1-x²)

Equation can be used to represent relationships between variables and to solve problems. They are written using an equal sign (=) and can include numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

To make y the subject of the equation x = √((y-1)/(y+1)),

x = √[(y-1)/(y+1)]

we can square both sides:

x² = (y-1)/(y+1)

Next, we can multiply both sides by (y+1) to get rid of the fraction:

x² × (y+1) = y-1

x²y + x² = y - 1

Rearranging the terms:

x² + 1 = y - x²y

x² + 1 = y(1 - x²)

Divide both side by (1-x²) we get

y = (x²+1)/(1-x²)

So, y is the subject of the equation is y = (x²+1)/(1-x²)

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The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.

To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.

To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.

After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:

(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).

These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.

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To make the system singular, we need the coefficient of one of the variables to be a multiple of the coefficient of the same variable in the other equation. Let's choose b = 4, which makes the first equation a multiple of the second:

2x + 4y = 16

4x + 8y = g

To make the system solvable, we need the two equations to not be parallel, which means the slopes must be different. Let's choose g = 32, which gives the second equation a slope of 1/2:

2x + 4y = 16

4x + 8y = 32

We can solve this system using substitution or elimination. Let's use elimination:

-2(2x + 4y = 16) -> -4x - 8y = -32

4x + 8y = 32

0 = 0

We see that the last equation is always true, which means the system has infinitely many solutions. We can find two solutions by setting x = 0 and solving for y:

2(0) + 4y = 16

y = 4

So one solution is (0,4). Now let's set y = 0 and solve for x:

2x + 4(0) = 16

x = 8

So another solution is (8,0).

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Answer:

37.5=d

Step-by-step explanation:

d+30 = 1.8d

add coefficient 1 to D so it's less confusing

1d +30 = 1.8d

isolate d

-1d

30= .8d

multiply by inverse to make d 1 whole

× 5/4 or 1.25

37.5 = d

The other side lengths of the triangle are 26 and 28 cm

The perimeter (P) is given as:

P = 84 cm

The area is given as:

A = 336

Let the sides be x, y and z.

So, we have:

x + y + z = 84

By herons' formula, we have:

\(Area = \sqrt{s(s-x)(s-y)(s-z)}\)

Where:

s = 0.5(x + y + z)

Multiply by 2

2s = x + y + z

Recall that:

x + y + z = 84

So, we have:

2s = 84

Divide by 2

s = 42

Let x = 30 ---- the given side length

So, we have:

30 + y + z = 84

Subtract 30 from both sides

y + z = 54

Make y the subject

y = 54 - z

Recall that

\(Area = \sqrt{s(s-x)(s-y)(s-z)}\)

The area is 336. So, we have:

\(336 = \sqrt{s(s-x)(s-y)(s-z)}\)

Square both sides

112896 = s(s-x)(s-y)(s-z)

Substitute values for x, y and s

112896 = 42(42-30)(42 - (54 - z))(42 - z)

Divide through by 42

2688 = (42-30)(42 - (54 - z))(42 - z)

Divide through by 12

224 = (42 - (54 - z))(42 - z)

Evaluate the brackets

224 = (z - 12)(42 - z)

Using a graphing calculator, we have:

z =26 or z = 28

Recall that:

y = 54 - z

So, we have

y = 54 - 26 = 28

y = 54 - 28 = 26

Hence, the other side lengths of the triangle are 26 and 28 cm

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The profit is Rs. 200.

The pricing system in which a commodity's (goods or services') price is lower than its listed price is referred to as a "discount." Simply put, "discount" refers to a percentage of the advertised price. A discount is a type of price reduction on products that is seen in consumer transactions. In these transactions, buyers propose a percentage of rebates on various products to increase sales. A discount is the seller's offer of a discount to the buyer.

Given marked price = Rs. 800

discount % = 10%

discount = 10% of 800

discount = 800 x 0.1 = 80

selling price = marked price - discount

selling price = 800 - 80 = Rs. 720

The dealer makes a profit of 20% means is selling the article at 120%.

120%=720

1%=6

Hence, 100%=600

Thus, the cost price of article= 600

profit  = SP - CP = 800 - 600

profit  = Rs. 200

Hence profit is Rs. 200.

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Answer:

Step-by-step explanation:

-9pi/8

23pi/8

-25pi/8

I think its.

The coterminal angles of ( 7π/8 ) are ( 9π/8 ) , ( -9π/8 ) and ( 23π/8 )

Angles with the same starting side and terminal side are said to be coterminal angles. Depending on whether the given angle is in degrees or radians, finding coterminal angles is as easy as adding or subtracting 360° or 2 to each angle. Coterminal angles can be found in an unlimited number of ways.

To find the coterminal angles of angle θ

The measure of coterminal angle is θ ± 360n,  if θ is measured in degrees.

And , measure of coterminal angle isθ ± 2πn,  if θ is measured in radians.

Given data ,

Let the angle be represented as θ

Now , the value of θ = ( 7π/8 )

On simplifying the equation , we get

To find the coterminal angles of angle θ

θ ± 2πn,  if θ is measured in radians.

Substituting the values in the equation , we get

x₁ = ( 7π/8 ) + 2π

x₁ = ( 23π/8 )

And ,

x₂ = 2π - ( 7π/8 )

x₂ = ( 9π/8 )

And ,

x₃ = ( 7π/8 ) - 2π

x₃ = ( -9π/8 )

Hence , the coterminal angles are ( 9π/8 ) , ( -9π/8 ) and ( 23π/8 )

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Hope, Casey, and Daniela are the players in order from lowest to highest points per game average.

To find the points per game for each player, we can divide their total points by the number of games they played:

Casey: 154 points ÷ 8 games = 19.25 points per game

Hope: 132 points ÷ 7 games = 18.86 points per game

Daniela: 101 points ÷ 5 games = 20.2 points per game

Casey mistakenly ordered the players as follows: Hope, Casey, and then Hope. This ordering is incorrect because Casey had a higher point-per-game average than Hope.

The correct ordering from least to greatest points per game average is: Hope, Casey, and then Daniela.

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Complete question:

Daniela scored

101 points in 5 basketball games. Casey scored 154 points in 8 games. Hope scored 132 points in 7 games. Casey tried to order the players by their points per game from least to greatest, but he made a mistake. Here's his work:

The closest correlation of rates of return between stocks a and b is approximately -0.487 (negative), indicating opposite movements.

The relationship coefficient between two stocks an and b can be determined utilizing the equation:

relationship coefficient = covariance/(standard deviation of stock a * standard deviation of stock b)

Considering that the covariance between the profits of stocks an and b is - 0.073, and the standard deviation of the paces of return is 0.5 for stock an and 0.3 for stock b, we can substitute these qualities into the recipe to track down the connection coefficient.

relationship coefficient = - 0.073/(0.5 * 0.3) ≈ - 0.487

Consequently, the nearest worth of the connection of the paces of return between stock an and b is - 0.487. This negative relationship coefficient demonstrates that the profits of the two stocks will generally move in inverse bearings. At the point when one stock's return is high, the other stock's return is probably going to be low, as well as the other way around.

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The maximum number of texts to send or received in next month will be

25.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

Cell phone bill = $24.99 per month

Cost of each text to send or receive = $0.16

Now,

You have at most $29 to spend on your cell phone bill.

Let number of text to send or receive = x

So, We can formulate;

$24.99 + $0.16x < $29

Solve for x as;

$24.99 + $0.16x < $29

Subtract 24.99 we get;

$0.16x < $29 - $24.99

$0.16x < $4.01

Divide by 0.16 we get;

x < 25.06

After rounding we get;

x < 25

Thus, The maximum number of texts to send or received in next month will be 25.

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Answer:

B

Step-by-step explanation:

pic is evidence

The expansion of the Mongol Empire to its height, as depicted on the map, most contributed to the spread of rice-cultivation techniques from East Asia to Europe (option C).

The Mongol Empire's vast territorial expansion had significant implications for cultural exchange and economic interactions across different regions. While the options provided in the question present various possibilities, the spread of rice-cultivation techniques from East Asia to Europe stands out as one of the most significant contributions of the Mongol Empire.

During the Mongol Empire's rule, extensive trade networks were established, connecting the East and West like never before. This facilitated the exchange of goods, technologies, and ideas between different regions. Rice cultivation, a crucial agricultural practice in East Asia, could have been disseminated to other parts of the empire, including Central Asia and the Middle East, and further to Europe through trade routes such as the Silk Road. This diffusion of rice-cultivation techniques would have brought about agricultural advancements, improved food production, and potential changes in dietary patterns in Europe.

It's important to note that the Mongol Empire's expansion also brought about other significant consequences. Constant warfare and the establishment of new cities as administrative centers could have led to deforestation in some areas (option A). However, the question specifically asks for the most significant contribution, which points towards the spread of rice-cultivation techniques. The bubonic plague, often associated with the Mongol Empire due to their extensive trading connections, is not directly linked to their expansion (option B). Although warfare and conquests would have had long-term effects on population decline, attributing it solely to the Mongol Empire's expansion is overly simplistic (option D).

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The row vectors of the matrix are [-2 -3 1 0], and the column vectors are:

In a matrix, row vectors are the elements listed horizontally in a single row, while column vectors are the elements listed vertically in a single column. In this case, the given matrix is a 1x4 matrix, meaning it has 1 row and 4 columns. The row vector is [-2 -3 1 0], which represents the elements in the single row of the matrix. The column vectors, on the other hand, can be obtained by listing the elements vertically. Therefore, the column vectors for this matrix are -2, -3, 1, and 0, each listed in a separate column.

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Answer:

The answer is A I and II

Step-by-step explanation:

The probability that the sampling error would be more than 1.5 hours, obtained from the z-score table is about 39.36%

A z-score is an indication or measure of the number of standard deviations, of a datapoint from the mean of a distribution.

The standard error of the mean = The population standard deviation ÷ (The square root of the sample size)

Therefore; The standard error = $17/√9 ≈ $5.67

The z-score for a value of 1.5 units above the can be found as follows;

z-score = (The value less the mean)/(The standard error)

Therefore; z-score ≈ (76 + 1.5 - 76)/5.67 ≈ 0.265

The z-score table indicates that the probability of obtaining a z-score  larger than 0.265 is; 1 - 0.60642 ≈ 0.3936

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The unknown angles of the right angle triangle is 45 degrees.  

A right angle triangle is a triangle with one angle equals to 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the right triangle has two angle measurements that are equal to each other. The third angle is 90 degrees.

Therefore, let's find the angles measure x, the two other equal angles.

Hence,

x + x + 90 = 180

2x + 90 = 180

subtract 90 from both sides of the equation

2x + 90 = 180

2x + 90 - 90 = 180 - 90

2x = 90

divide both sides by 2

x = 90 / 2

x = 45 degrees

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Geometric series is convergent if the |r|<1 where r is the common ratio.

Let Sn=∑ni=0(−3/4)i then

Sn=(−3/4)n+1−1(−3/4)−1

Now take n→∞ then

Sn→0−1(−3/4)−1=4/7

because |−3/4|<1 and so (−3/4)n→0. Now note that your sum is

lim ∑i=1n+1(−3)i−14i=lim 14∑i=1n+1(−3)i−14i−1=1/4.lim Sn=1/7.

Geometric series: A geometric series is the result of adding together geometric sequences indefinitely. Depending on the sequence given to us, such infinite sums can either be finite or infinite. A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit. In contrast, a divergent series is one whose partial sums do not reach a limit. Divergent series frequently reach, reach, or avoid a particular number.

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Since the selected baby is Hispanic, we can use the probability given for Hispanic babies, which is 1 of 275.

Answer:

The answer is 4cm.

Step-by-step explanation:

Given:

Height= 15cm

The volume of the Cylindrical bottle= 753.6

They have said to use π= 3.14

We are supposed to find r.

-------------------------------------------------------------

Volume of cylinder= πr²h

now substitute teh values given in the formula..we will get:

753.6 = 3.14× r²× 15

After u solve it , you will get

r²= 16

∴r = √16= 4cm

So,  the radius of the bottle is 4cm

Hope it helps!!

Answer:

3r^6

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Slope of AB = 7-5/9-4

=2/5

Answer:

below

Step-by-step explanation:

assuming r=5 and center (0,0)

1.) point at (0,0) for center

2.) point at (5,0)

3.) point at (0,5)

4.) point at (-5,0)

5.) point at (0,-5)

trace around points 2-5 to get the 4pt circle

The inequality to determine how much more money he needs to save so he can buy the shoes is x ≥ $45

Let x be the amount of money Jordan still needs to save to buy the shoes.

The total cost of the shoes is $75, and Jordan has already saved $30. Therefore, the amount of money he still needs to save is:

x = $75 - $30

Simplifying the right side:

x = $45

So, the inequality that represents how much more money Jordan needs to save is:

x ≥ $45

This means that Jordan needs to save at least $45 more to be able to buy the shoes.

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Answer:

X = -14

All you have to do is type in 2(x+5)=(x-4) in to a algebra calculator and you will get -14

The probability to wait more than 15 seconds to connect is 50% and the probability to wait at least 10 more seconds after waiting 10 seconds is 33.33%.

x = old modem establish connection = [0, 30]

Probability density function or PDF is

f(x) = \(\frac{1}{b-a}\); 0 ≤ x ≤ 30

Probability to wait more than 15 seconds to connect is

f(X>5) = \(\int\limits^{30}_{15} {f(x)} \, dx\)

= \(\int\limits^{30}_{15} {\frac{1}{b-a}} \, dx\)

= \(\frac{1}{30-0} \, [x]^{30}_{15}\)

= \(\frac{30-15}{30}\)

= 0.5 or 50%

Probability if already waited 10 seconds and having to wait at least 10 more seconds is equal to wait at least 20 seconds from start. So,

f(X>5) = \(\int\limits^{30}_{20} {f(x)} \, dx\)

= \(\int\limits^{30}_{20} {\frac{1}{b-a}} \, dx\)

= \(\frac{1}{30-0} \, [x]^{30}_{20}\)

= \(\frac{30-20}{30}\)

= 0.3333 or 33.33%

Thus, the 50% probability to wait more than 15 seconds to connect and 33.33% probability to wait at least 20 seconds to connect.

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