What two functions could represent length and width for given values of x based on the combined function? f(x) = x + 7 and g(x) = x + 3 f(x) = x – 7 and g(x) = x – 1 f(x) = x2 + 7 and g(x) = x3 + 3 f(x) = x – 7 and g(x) = x – 3

The linearized equation for the non-linear equation z = x² + 4xy + 6xy² in the region defined by 8 ≤ x ≤ 10, 2 ≤ y ≤ 4 is given by :

z ≈ 244 + 20(x - 8) + 128(y - 2).

When using the linearized equation to calculate the value of z at x = 8, y = 2, the error is 0.

1.1. To linearize the equation in the given region, we need to find the partial derivatives of z with respect to x and y:

∂z/∂x = 2x + 4y

∂z/∂y = 4x + 6xy

At the point (x₀, y₀) = (8, 2), we substitute these values:

∂z/∂x = 2(8) + 4(2) = 16 + 8 = 24

∂z/∂y = 4(8) + 6(8)(2) = 32 + 96 = 128

The linearized equation is given by:

z ≈ z₀ + ∂z/∂x * (x - x₀) + ∂z/∂y * (y - y₀)

Substituting the values, we get:

z ≈ z₀ + 24 * (x - 8) + 128 * (y - 2)

1.2. To find the error when using the linearized equation to calculate the value of z at x = 8, y = 2, we substitute these values:

z ≈ z₀ + 24 * (8 - 8) + 128 * (2 - 2)

= z₀

Therefore, the linearized equation gives the exact value of z at x = 8, y = 2, and the error is 0.

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Answer:

The student didn't fully factorize out the terms to the least factor. He only collected some like terms but there was still more to collect and that's why the Teacher didn't give him full credit

Step-by-step explanation:

The original polynomial is;

4x²y^(5) - 8xy³

Now, if we want to completely factor this properly, we have to do it to the barest minimum.

Thus;

4xy³ is common to both terms so we can bring them out;

4xy³(xy² - 2)

Now this complete factorization is different from the one the student gave which is 2xy³(2xy³ - 4)

Thus, the student at best has factorized but only partly as it has not been reduced to the least of like terms.

Answer:

4 m

Step-by-step explanation:

The formula to find the area of the triangle is:

\(\sf Area = \frac{1}{2} *base*height\)

Given that,

Area = 32m²

Base = 16m

Height =?

Let us use the given formula to find the height of the triangle.

\(\sf Area = \frac{1}{2} *base*height\\\\\sf 32m^2 = \frac{1}{2} *16*h\\\\32= \frac{16h}{2} \\\\32=8h\\\\\frac{32}{8} =\frac{8h}{8} \\\\4m = height\)

\(\longrightarrow{\green{- 9 {x}^{2} + 14x + 16}}\) 

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}\)

\( \sqrt{49} + [ \sqrt{81} - x \: (9x - 14) ] \\ \\ = \sqrt{7 \times 7} + [ \sqrt{9 \times 9} - 9 {x}^{2} + 14x] \\ \\ = \sqrt{( {7})^{2} } + [ \sqrt{ ({9})^{2} } - 9 {x}^{2} + 14x ] \\ \\ (∵ \sqrt{ ({x})^{2} } = x ) \\ \\ = 7 + (9 - 9 {x}^{2} + 14x) \\ \\ = 7 + 9 - 9 {x}^{2} + 14x \\ \\ = - 9 {x}^{2} + 14x + 16\)

\(\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}\)

Answer:

The slope is 2.5

Step-by-step explanation:

7-2=5. 4-2=2

5/2=2.5

The correct answer is d. emergent.

An emergent leader is an individual who grows into the leadership role naturally, often due to circumstances or necessity. They are not appointed or assigned to the position of leadership but rather emerge from the group or organization based on their skills, qualities, or actions.

Emergent leaders may possess certain qualities or demonstrate their competence and ability to guide and influence others. They gain recognition and respect from their peers, leading to their emergence as leaders within the group or organization.

This type of leadership often occurs in situations where formal leadership structures may be absent or ineffective, and individuals step up to take charge based on their capabilities and the needs of the group.

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Answer:

To find the number of degrees the temperature of the oven increases by in one minute, we can use the slope-intercept form of a linear equation, which is written as y = mx + b. In this equation, y represents the dependent variable (in this case, the temperature of the oven), x represents the independent variable (in this case, the time in minutes), m is the slope (which represents the rate of change of y with respect to x), and b is the y-intercept (which represents the starting value of y when x is zero).

To find the slope of the line that represents the temperature of the oven over time, we can use the two points provided in the problem: (4, 158) and (7, 224). The slope is calculated using the following formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the values from the two points, we get:

m = (224 - 158) / (7 - 4) = 66 / 3 = 22

This means that the temperature of the oven increases by 22 degrees for every one minute increase in time.

The y-intercept of the line (the value of y when x is zero) represents the starting temperature of the oven. In this case, the starting temperature is not provided, so we cannot determine the y-intercept. However, we can use the slope and one of the points to find the equation of the line in the form y = mx + b:

y = 22x + b

Substituting one of the points into the equation, we get:

158 = 22 * 4 + b

Solving for b, we get:

b = 158 - 88 = 70

So the equation of the line representing the temperature of the oven over time is:

y = 22x + 70

This equation tells us that for every one minute increase in time, the temperature of the oven increases by 22 degrees, starting from a temperature of 70 degrees.

Since each trait is inherited independently, we can multiply the probabilities together. The probability of obtaining A/a; B/b; C/c; D/d offspring is (1/2) * (1/2) * (1/2) * (1/2) = 1/16.

The probability of obtaining A/a; B/b; C/c; D/d offspring can be calculated by multiplying the probabilities of each individual trait. Since each trait is inherited independently, we can multiply the probabilities together.

The probability of obtaining A/a offspring is 1/2 (A is dominant and a is recessive).

The probability of obtaining B/b offspring is 1/2 (B is dominant and b is recessive).

The probability of obtaining C/c offspring is 1/2 (C is dominant and c is recessive).

The probability of obtaining D/d offspring is 1/2 (D is dominant and d is recessive).

Therefore, the probability of obtaining A/a; B/b; C/c; D/d offspring is (1/2) * (1/2) * (1/2) * (1/2) = 1/16.

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To earn a profit of $10, we need to buy and sell 10 dollars.

The difference between the buying and selling rates is the profit margin for the currency exchange. Here, the profit margin is 116.5 - 115.25 = 1.25 Rs per dollar.

To make a profit of $10, we need to buy and sell enough dollars to earn a profit of 1.25*10 = 12.5 Rs.

Let's assume we buy and sell x dollars. Then the cost of buying x dollars is 115.25x Rs, and the revenue from selling x dollars is 116.5x Rs.

So, the profit from buying and selling x dollars is (116.5x - 115.25x) = 1.25x Rs.

We need to find x such that 1.25x = 12.5, which gives x = 10.

Therefore, we need to buy and sell 10 dollars to earn a profit of $10.

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The exponent of the expression is 6.

Remember that a superscript is a small symbol on the right top of another, then we can write this as:

7⁶

Remember that a general power is:

aⁿ

Where a is the base and n is the exponent.

Comparing that with the given expression, we can see that the base is 7 and the exponent is 6.

So the first option is the correct one.

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Domestic price refers to the price of a product or service within a specific country's domestic market. It is determined by factors such as supply and demand conditions, production costs, and market dynamics within that country.

The autarky domestic price is a price where a country is not involved in any trade with other countries. In this case, the autarky domestic price is \(\(a=7\)\).The free trade world price is a price where all the countries are allowed to trade and there is no restriction on trade.

In this case, the free trade world price is\(\(b=3\)\).The gains from trade refer to the increase in the total welfare of all the countries that trade. The gains from trade are the difference between the autarky price and the free trade price. In this case, the gains from trade for the importing country are:

\(\[gains\ from\ trade =a-b=7-3=4.\]\)

The gains from trade for the exporting country are also:

\(\[gains\ from\ trade =b-a=3-7=-4.\]\)

The total gains from trade are the sum of the gains from trade of both the importing and the exporting countries. In this case, the total gains from trade are:

\(\[total\ gains\ from\ trade =4+(-4)=0.\]\)

Therefore, the total gains from trade for this market are zero.

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The segments AC, BC, and BA forms the Triangle.

Given, AC = 4; BC = 3; BA = 6

The condition if the given segments form a triangle is to use Triangle Inequality Theorem.

Triangle Inequality Theorem states that the sum of the length of two sides of a triangle is always greater than the third side.

Taking AC + BC > BA

4 + 3 > 6

7> 6 which is true.

Now taking BC + BA > AC

3 + 6 > 4

9 > 4, is also true.

Now,  BA + AC > BC

6 + 4 > 3

10 > 3 is true.

Therefore, option A is correct. The segments AC, BC, and BA forms the triangle.

To learn more about, triangle inequality theorem,visit: Option A is correct. The segments AC, BC, and BA forms the Triangle.

Given, AC = 4; BC = 3; BA = 6

The condition if the given segments form a triangle is to use Triangle Inequality Theorem.

Triangle Inequality Theorem states that the sum of the length of two sides of a triangle is always greater than the third side.

Taking AC + BC > BA

4 + 3 > 6

7> 6 which is true.

Now taking BC + BA > AC

3 + 6 > 4

 9 > 4, is also true.

Now,  BA + AC > BC

6 + 4 > 3

10 > 3 is true.

Therefore, option A is correct. The segments AC, BC, and BA forms the triangle.

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All multiple of 6 under 14 are: -12, -6, 0, 6, 12

How do we get 14 here:

√200= 14.142 (Round to thousandth place)

This is how many x we have found.

A multiple in math is the number you get when you multiply a certain number by using an integer. for example, multiples of 5 are: 10, 15, 20, 25, 30…, and so forth. Multiples of 7 are 14, 21, 28, 35, 42, 49…and many others.

In math, the meaning of a multiple is the product result of one number multiplied by another number. Here, 56 is a multiple of the integer 7. Here is an example of multiples: Fun facts. 0 is a multiple of every number as the product of 0 multiplied by any number is 0.

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Answer:

72% are not freshmen.

Step-by-step explanation:

The not freshmen students are,

→ 50 - 14

→ 36 students

Then percent of not freshmen,

→ (36/50) × 100

→ 0.72 × 100

→ 72%

Hence, the answer is 72%.

Answer:

the aswer is 154

Step-by-step explanation:

multiple

Answer:

3 and half

Step-by-step explanation:

half of seven is 3.5

Answer:

a/4b = 0.075

Step-by-step explanation:

a = 30% of b

a = 30/100 × b

a = 0.3b

The value of a/4b is calculated as:

= 0.3b/4b

= 0.075

The dimensions of the box can be represented as (6-2x) inches by (24-2x) inches by "x" inches.

From a 24-inch by 6-inch piece of cardboard, square corners are cut so the sides can fold up to form a box without a top. To determine the dimensions and construct the box, we need to consider the shape of the cardboard and the requirements for folding and creating the box.

The initial piece of cardboard is a rectangle measuring 24 inches by 6 inches. To form the box without a top, we need to remove squares from each corner.

Let's assume the side length of the square cutouts is "x" inches. After cutting out squares from each corner, the remaining cardboard will have dimensions (24-2x) inches by (6-2x) inches.

To create a box, the remaining cardboard should fold up along the edges. The length of the box will be the width of the remaining cardboard, which is (6-2x) inches.

The width of the box will be the length of the remaining cardboard, which is (24-2x) inches. The height of the box will be the size of the square cutouts, which is "x" inches.

Therefore, the dimensions of the box can be represented as (6-2x) inches by (24-2x) inches by "x" inches. To construct the box, the remaining cardboard should be folded along the edges, and the sides should be secured together.

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The right response is B. According to Option B, a data value X is regarded as an outlier if it deviates from the range Q1 - 1.5(IQR) to Q3 + 1.5. (IQR).

The right response is B.

The distance between the first quartile (Q1) and the third quartile in a box plot is known as the interquartile range (IQR) (Q3).

According to Option B, a data value X is regarded as an outlier if it deviates from the range Q1 - 1.5(IQR) to Q3 + 1.5. (IQR).

Although the range given in Option A is erroneous, the idea of an outlier being outside of a specific range based on the IQR is correct.

Option C's range, which is Q2 - 1.5(IQR) to Q2 + 1.5(IQR), is incorrect for locating outliers.

The phrase "TQR," which is uncommon in box plots, is mentioned in Option D. The range of Q2 -1.0(IQR) to Q2 +1.0(IQR) provided is incorrect for either locating outliers.

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The horses' average speeds are approximately:

(a) mi/s: 0.0102 mi/s

(b) mi/h: 58.06 mi/h

To calculate the horses' average speeds, we need to calculate the speed as distance divided by time.

We have:

Distance: 1.50 miles

Time: 147 seconds

(a) To calculate the average speed in mi/s, we divide the distance by the time:

Average speed = Distance / Time

Speed of Fiddle Isle = 1.50 miles / 147 seconds ≈ 0.0102 mi/s

Speed of John Henry = 1.50 miles / 147 seconds ≈ 0.0102 mi/s

(b) To calculate the average speed in mi/h, we need to convert the time from seconds to hours:

Average speed = Distance / Time

Since 1 hour has 3600 seconds, we can convert the time to hours:

Time in hours = 147 seconds / 3600 seconds/hour

Speed of Fiddle Isle = 1.50 miles / (147 seconds / 3600 seconds/hour) ≈ 58.06 mi/h

Speed of John Henry = 1.50 miles / (147 seconds / 3600 seconds/hour) ≈ 58.06 mi/h

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Answer:

28>x

Step-by-step explanation:

7>x/4

remove the denominator by multiplying both sides by 4

4×7>x/4×4

28>x

The required equivalent expression to expression 6.42 x 0.72 ≈ 6.4 x 0.7.

Given that, an expression is given 6.42 x 0.72 we have to determine the equivalent expression.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Given expression,
6.42 x 0.72
Where 6.42 ≈ 6.4 and 0.72 ≈ 0.7
Now,
substitute the values,

6.42 x 0.72 ≈ 6.4 x 0.7

Thus, the required equivalent expression to expression 6.42 x 0.72 ≈ 6.4 x 0.7.

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radius : 3.95 ft

\(\sf volume \ of \ cone: \dfrac{1}{3} \pi r^2h\)

\(\hookrightarrow \sf \dfrac{1}{3} \pi r^2(9) = 147\)

\(\hookrightarrow \sf r^2 = \dfrac{147*3}{\pi (9)}\)

\(\hookrightarrow \sf r = \sqrt{\dfrac{147*3}{\pi (9)}}\)

\(\hookrightarrow \sf r = 3.95 \ ft\)

Answer: 15,600 different choices for initials

Step-by-step explanation:

26 choices for the first, 25 for the second, and 24 for the third. When multipled, this is 15600.

Answer: 17.2

Step-by-step explanation:

You must use the law of sines, which says that sinA/a = sinB/b = sinC/c, where the side is the side across from the angle.

the length of side a = 16m, and the angle A = 25.

the length of side b = x, and the angle B = 27

1. sinA/a = sinB/b

2. sin25/16 = sin27/x

3. x(sin25)/16 = sin27

4. x = 16sin27/sin25

5. x = 17.2

The second-degree Taylor polynomial for the function ()=63 at =0 is simply 63.

To find the Taylor polynomial 2() for the function ()=63 at =0, we need to use the formula for the nth-degree Taylor polynomial:
2() = f(0) + f'(0)() + (1/2!)f''(0)()^2 + (1/3!)f'''(0)()^3 + ... + (1/n!)f^(n)(0)()^n

Since we are only interested in the second-degree Taylor polynomial, we need to calculate f(0), f'(0), and f''(0):
f(0) = 63
f'(x) = 0 (the derivative of a constant function is always 0)
f''(x) = 0 (the second derivative of a constant function is always 0)

Substituting these values into the formula, we get:
2() = 63 + 0() + (1/2!)0()^2
2() = 63

Therefore, the second-degree Taylor polynomial for the function ()=63 at =0 is simply 63.

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the solution of the given system of equations is x=-43/14 and y=-92/21.

Given the system of equations as below: \(\[ \begin{cases}2x-3y=7\\4x+5y=8\end{cases}\]\)

The main answer is the solution for the system of equations. We can solve the system of equations by using the elimination method.

\(\[\begin{aligned}2x-3y&=7\\4x+5y&=8\\\end{aligned}\\)

]Multiplying the first equation by 5, we get,\(\[\begin{aligned}5\cdot (2x-3y)&=5\cdot 7\\10x-15y&=35\\4x+5y&=8\end{aligned}\]\)

Adding both equations, we get,\(\[10x-15y+4x+5y=35+8\][\Rightarrow 14x=-43\]\)

Dividing by 14, we get,\(\[x=-\frac{43}{14}\]\) Putting this value of x in the first equation of the system,\(\[\begin{aligned}2x-3y&=7\\2\left(-\frac{43}{14}\right)-3y&=7\\-\frac{86}{14}-3y&=7\\\Rightarrow -86-42y&=7\cdot 14\\\Rightarrow -86-42y&=98\\\Rightarrow -42y&=98+86=184\\\Rightarrow y&=-\frac{92}{21}\end{aligned}\]\)

in the given system of equations, we have to find the values of x and y. To find these, we used the elimination method. In this method, we multiply one of the equations with a suitable constant to make the coefficient of one variable equal in both the equations and then we add both the equations to eliminate one variable.

Here, we multiplied the first equation by 5 to make the coefficient of y equal in both the equations. After adding both the equations, we got the value of x. We substituted this value of x in one of the given equations and then we got the value of y. Hence, we got the solution for the system of equations.

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Answer:

<BAC=60°

Step-by-step explanation:

THIS IS THE ANSWER

What is 16% of 78? Round to the nearest tenth.

16% = 0.16

so:

0.16 * 78 = 12.48

round:

12.5

Answer:

1/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-4-(-5))/(3-0)

m=(-4+5)/3

m=1/3

Answer:

see explanation

Step-by-step explanation:

To evaluate f(8), substitute x = 8 into f(x) , that is

f(8) = \(\sqrt{2(8)+9}\) = \(\sqrt{16+9}\) = \(\sqrt{25}\) = ± 5

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

Equating

\(\sqrt{2x+9}\) = 3 ( square both sides )

2x + 9 = 9 ( subtract 9 from both sides )

2x = 0 ⇒ x = 0

Thus

f(0) = 3