Solve the following system of equations. Express your answer as an ordered pair in the format (a,b), with no spaces between the numbers or symbols. 3x+4y=17 4x - 3y= -18

The answers contain a. 5  b. [tex]y=-\frac{3}{4} x+\frac{1}{2}[/tex]  c. 148.5 d. 1/7

a. f"(2)

f"(x) = df'(x)/dx = d(sin(πx) + x² +3)/dx = cos(πx) + 2x

f"(2)=cos(π × 2) + 2 × 2

f"(2)=cos(2π) + 4

f"(2)=1 + 4

f"(2)=5

b. Equation for the line tangent to the graph of y = 1/f(x) at x = 0

We first find f(x) by integrating f'(x)

f(x) = ∫f'(x)dx = ∫(sin(πx) + x² +3)dx = -cos(πx)/π + x³/3 +3x + C

f(0) = 2 so,

2 = -cos(π × 0)/π + 0³/3 +3 × 0 + C

2 = -cos(0)/π + 0 + 0 + C

2 = -1/π + C

C = 2 + 1/π

f(x) = -cos(πx)/π + x³/3 +3x + 2 + 1/π

f(x) = [1-cos(πx)]/π + x³/3 +3x + 2

y = 1/f(x) = 1/([1-cos(πx)]/π + x³/3 +3x + 2)

The tangent to y is thus dy/dx

dy/dx = d1/([1-cos(πx)]/π + x³/3 +3x + 2)/dx

dy/dx = -([1-cos(πx)]/π + x³/3 +3x + 2)⁻²(sin(πx) + x² +3)

at x = 0,

dy/dx = -([1-cos(π × 0)]/π + 0³/3 +3 × 0 + 2)⁻²(sin(π × 0) + 0² +3)

dy/dx = -([1-cos(0)]/π + 0 + 0 + 2)⁻²(sin(0) + 0 +3)

dy/dx = -([1 - 1]/π + 0 + 0 + 2)⁻²(0 + 0 +3)

dy/dx = -(0/π + 2)⁻²(3)

dy/dx = -(0 + 2)⁻²(3)

dy/dx = -(2)⁻²(3)

dy/dx = -3/4

At x= 0,

y = 1/([1-cos(π × 0)]/π + 0³/3 +3 × 0 + 2)

y = 1/([1-cos(0)]/π + 0 + 0 + 2)

y = 1/([1 - 1]/π + 2)

y = 1/(0/π + 2)

y = 1/(0 + 2)

y = 1/2

So, the equation of the tangent at (0, 1/2) is

[tex]\frac{y-\frac{1}{2} }{x-0} =-\frac{3}{4} \\\\y-\frac{1}{2} =-\frac{3}{4} x\\\\y=-\frac{3}{4} x+\frac{1}{2}[/tex]

c. If g(x) = f (√(3x² + 4). Find g'(2)

g(x) = f (√(3x² + 4) = [1-cos(π√(3x² + 4)]/π + √(3x² + 4)³/3 +3√(3x² + 4) + 2

g'(x) = [3xsinπ√(3x² + 4) + 18x(3x² + 4) + 9x]/√(3x² + 4)

g'(2) = [3(2)sinπ√(3(2)² + 4) + 18(2)(3(2)² + 4) + 9(2)]/√(3(2)² + 4)

g'(2) = [6sinπ√(12 + 4) + 36(12 + 4) + 18]/√12 + 4)

g'(2) = [6sinπ√(16) + 36(16) + 18]/√16)

g'(2) = [6sin4π + 576 + 18]/4)

g'(2) = [6 × 0 + 576 + 18]/4)

g'(2) = [0 + 576 + 18]/4)

g'(2) = 594/4

g'(2) = 148.5

d. If h is the inverse function of f. Find h' (2)

If h(x) = f⁻¹(x)

then h'(x) = 1/f'(x)

h'(x) = 1/(sin(πx) + x² +3)

h'(2) = 1/(sin(π2) + 2² +3)

h'(2) = 1/(sin(2π) + 4 +3)

h'(2) = 1/(0 + 4 +3)

h'(2) = 1/7

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The most common level of confidence is 95%, however 90% or 99% have also been used on occasion.

A series of observations that are not reliant on any other samples or data constitute an independent random sample. Random samples selected without regard to sequencing. So, choice C is the proper one.

The essential points that are highlighted below are the followings:

Because the difference between the sample proportions G minus H greater population, according to the question. Due to the interval's all-positive values, it seems expected that district G will have more supporters than district H.

Assurance interval A confidence interval (CI) is a range of estimates for an unknown parameter that is determined by a lower bound and an upper bound. At a certain level of confidence, the interval is calculated.

The most typical level of confidence is 95%, however higher levels, such 90% or 99%, are occasionally employed.

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3 of them would not be good, 9-6= 3 non-shiny gold rings.

Using two expressions, a mathematical sentence declares two things. The two expressions either employ variables, numbers, or a combination of the two. Symbols or words like equal, greater than, or less than may also be used in a mathematical sentence.

An accurate arrangement of mathematical symbols that expresses a coherent idea constitutes a mathematical sentence, which is equivalent to an English sentence in meaning. Verbs are used in sentences. The verb "=" is used in the mathematical formula "3+4=7 3 + 4 = 7".

The answer is b c 3 9-6=3

3 of them would not be good

9-6= 3 non shiny gold rings

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Answer: X[tex]\geq[/tex]-4

Step-by-step explanation:

4x-5[tex]\leq[/tex] 6x + 3

-2x [tex]\leq[/tex] 3 + 5

-2x[tex]\leq[/tex] 8

X = [tex]\geq[/tex] - 8/2

There are 4 quarts in a gallon, and a gallon weighs 8.34 pounds, so a quart weighs 2.085 pounds.

The gallon is a volumetric unit that is used in both imperial and American customary measurements. In use right now are three different variations:

the imperial gallon (imp gal), defined as 4.54609 litres, which is or was used in the United Kingdom, Ireland, Canada, Australia, New Zealand, and some Caribbean countries; the US gallon (US gal), defined as 3.785411784 L,[1] (231 cubic inches), which is used in the US and some Latin American and Caribbean countries; and the US dry gallon ("usdrygal"), defined as 18 US bushel (exactly 4.40488377086 L).

gallon equals 4 quarts

2.1*4 =8.4

gallon of water weigh is 8.4

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The kite is 10 meters high

To calculate how high Ana's kite is, you can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the length of the string is one side of the triangle and the distance Ana needs to move to get under the kite is the other side. The height of the kite is the hypotenuse.

Therefore, the height of the kite can be calculated by:

height =  [tex]\sqrt({string^{2} +distance^{2}) }[/tex]

height =  [tex]\sqrt{(8^{2} + 6^{2} )[/tex]

height = √(64 + 36)

             = √100

height = 10

Hence, the kite is 10 meters high.

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There can be one valid triangle created from the given conditions of side a being 5 and angles b and c being 30 and 50 degrees respectively.

To calculate how many triangles can be created from two angles and a side, the user must click the “calculator” tab. Once this is done, it is important to click the “clear” button to begin a new calculation. After this, the user must enter the side (a) under the “sides” section, and the angles (b and c) under the “angles” section. This example used 5 for the side, 30 for angle b, and 50 for angle c. Once the information is entered, the user must click “calculate”. This will result in a valid triangle being created from the given conditions. It is important to note that if the user entered different values, a different result may be obtained. Therefore it is important to ensure that the values entered are the desired ones. Additionally, if the sum of the angles entered are not equal to 180 degrees, then no valid triangle can be created.

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The value of the composite function (f + g)(x) = 14x - 3

From the question, we have the following parameters that can be used in our computation:

f(x) = 2x - 1

g(x) = 12x - 2

The composite function (f + g)(x) is calculated as

(f + g)(x) = f(x) + g(x)

Substitute the known values in the above equation, so, we have the following representation

(f + g)(x) = 2x - 1 + 12x - 2

Evaluate the like terms

(f + g)(x) = 14x - 3

Hence, the composite function is (f + g)(x) = 14x - 3

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Complete question

Consider the functions f(x)=2x−1 g(x)=12x −2

Calculate (f + g)(x)

Answer:5(3+1); 20

Step-by-step explanation:

5x3 is 15 and 5x1 is 5 which is equivalent to 15+5, then add to get 20.

The length of segment CM is equal to the square root of 10. This is determined by dividing the area of the square ABCD, which has sides of length 3, into three equal parts, resulting in a segment of length √10.

The area of square ABCD can be calculated by squaring the length of one side, which is 3, to get 9. To divide this area into three equal parts, each part must have an area of 3. To find the length of segment CM, the square root of this area, 3, must be taken, resulting in a length of √10.

To find the length of segment CM in square ABCD, the area of the square must first be determined. This can be done by squaring the length of one side, which is 3, resulting in an area of 9. To divide this area into three equal parts, each part must have an area of 3. This means the length of segment CM must be the square root of 3, which is equal to √10. Therefore, the length of segment CM is equal to √10. This is the result of dividing the area of the square ABCD into three equal parts.  This process can be used to determine the length of any segment dividing an area into equal parts

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There are 15 possible sums less than 15 that can be made by taking out one to three balls from the chest.

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Answer:

Step-by-step explanation:

If its going by 4 each time then it should be 21 but for n its 6

The amount that Kim Barney spends is $342 for medical expenses.

Given that,

Kim Barney pays a $290.00 yearly premium for a $500.00 deductible insurance plan. 80 percent of the remaining cost is covered by the business. If Kim has medical costs of $2,500.00

To find : The amount that Kim barney spends for the medical expenses.

If the business covers 80% of the remaining balance ($1710), they will be responsible for paying $1368 of it.

10% of 1710 is 171

171x8=1368

The insurance provider covers the $1368.

Kim Barney spends $342.

Consequently, Kim Barney spends the following amount on medical costs $342.

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The expression that represents the length of the rectangle is x + 5

The area of a rectangle is described as follows:

area = lw

where

l = length

w = width

Therefore,

area = x² + 8x + 15

w = x + 3

Therefore,

x² + 8x + 15 = (x + 3)l

divide both sides by x + 3

l =  x² + 8x + 15 / x + 3

l = (x+3)(x+5) / (x + 3)

Finally,

length = x + 5

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Answer:

g(f(- 5)) = - 31

Step-by-step explanation:

to calculate g(f(- 5)), evaluate f(- 5) and substitute the value obtained into g(x)

f(- 5) = (- 5)² + (- 5) - 12 = 25 - 5 - 12 = 25 - 17 = 8 , then

g(8) = - 2(8) - 15 = - 16 - 15 = - 31

Answer:

 -31

Step-by-step explanation:

f(x)=x²+x-12

or,f(-5)=(-5)²+(-5)-12

 =25-5-12

 =25-17

 =8

now, g(x)= -2x-15

 = (-2)×8-15

 = -16-15

 =-31

Congruency is said to be defined on two triangles when they have exact same length of sides and equal angles between them. The shape and size are supposed to be the same even after rotation or flipping of triangles for them to remain congruent.

There are 4 criteria to test the congruency of the triangle and they are as follows:

In this set of triangles, (ABC, def) AB=DE, AC=DF, and ∠ABC= ∠DEF i.e., two sides and one angle are equal but it is not congruent because according to SAS criteria, the angle should be between AB and AC (or DE and DF)

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Option A) The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as 12 divided by 4 gives 3.

One of the four fundamental arithmetic operations, or how numbers are joined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

A quotient is the amount that results from dividing two integers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.

According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0. The same formula may be expressed in writing as follows: If real numbers a, b, and c are present, with a = b and c 0, then a c = b c.

The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as

12 divided by 4 gives 3.

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Option A) The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as 12 divided by 4 gives 3.

One of the four fundamental arithmetic operations, or how numbers are joined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

A quotient is the amount that results from dividing two integers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.

According to the division property of equality, the quotients of an equation remain equal when both sides are divided by a common real integer that is not equal to 0. The same formula may be expressed in writing as follows: If real numbers a, b, and c are present, with a = b and c 0, then a c = b c.

The statement 12 / 3 = 4 can be justified by the equation 4x = 12 as

12 divided by 4 gives 3.

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The height of both trees at the time when they have an equal height will be 48 inches.

Given is that Evelyn planted two trees in her backyard. At the time of planting, Tree A was 32 inches tall and Tree B was 16 inches tall. Each year thereafter, Tree A grew by 4 inches per year and Tree B grew by 8 inches per year.

       Tree {A} : y {A} = 4x + 32

       Tree {B} : y {B} = 8x + 16

Therefore, the height of both trees at the time when they have an equal height will be 48 inches.

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Answer: The missing value is 81.

Step-by-step explanation: In a square, the formula is [tex]y^2 + 2y + y^2[/tex],

where the first y^2 is staying there. 18/2 is 9, and 9 squared is 81.

======================================

Reason:

The 4x and -7x are like terms because they involve the same variable x. This allows us to combine the like terms to end up with -3x

4x-7x = -3x

-------

Another example of like terms is 2x and 5x.

Adding them gets us 2x+5x = 7x

We can think of it like saying "2 boxes + 5 boxes = 7 boxes". Replace each word "boxes" with the single letter "x" and we arrive at 2x+5x = 7x.

Answer:

x = 121°

Step-by-step explanation:

the shape is a heptagon (7 sides). the interior angles in a heptagon will always add up to 900°, so all you need to do is add all the known angles and subtract from 900.

140 + 133 + 145 + 117 + 119 + 125 = 779

900 - 779 = 121

this means that x = 121°

hope this helped, good luck!

The volume of the squared pyramid is 9 cubic yards, so the correct option is D.

For a square pyramid of sidelength S (S is the sidelength of the square base), the volume is given by the formula:

V = (1/3)*S^3

Here we want to find the volume if S = 3 yards, so we just need to replace that in the formula above to get the volume of the sculpture, we will get:

V = (1/3)*(3 yd)^3

V = (1/3)*(27 yd^3)

V = 9 yd^3

The volume is 9 cubic yards, then the correct option is D.

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The Minimum for quadratic function f(x) is smaller than g(x)

and it is -5.

What is a quadratic function?

Quadratic function is also a second-degree polynomial function. The graph of a quadratic function is a parabola. The parabola opens upwards if a graph is made for the quadratic formula.

The point at which the function attains maximum or minimum value is the vertex of the quadratic function. When we say second degree, then the variable is raised to the second power like x^2.

A quadratic function is of the form f(x) = ax^2 + bx + c, where a, b, and c are the numbers with a not equal to zero.

Now,

As the we find minimum value by calculating the value for f(x) or g(x)

and from given values f(x) have minimum value of -5 and g(x) have minimum value of 3.

hence,

          Minimum for quadratic function f(x) is smaller than g(x)

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The area of each of the given shapes is calculated as;

1) 143 sq.in

2) 32 sq.cm

3) 162 sq.yds

4) 150 sq.in

1) The area of a parallelogram is;

Area = base * height

Thus;

Area = 11 * 13

= 143 sq.in

2) Area of a triangle is;

Area = 1/2 * base * height

Area = 1/2 * 8 * 8

Area = 32 sq.cm

3) Area of this will be gotten by the are of the individual triangles;

Area = 2(1/2 * 7 * 8) + 2(1/2 * 12 * 8)

Area = 56 + 96

Area = 162 sq.yds

4) Area = (12 * 12) + (1/2 * 1 * 12)

= 144 + 6

= 150 sq.in

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The length of the pile of the piece of woods put together by Luke would be = 5.8ft

A pile of objects such as wood is defined as the combination of two or more different parts of the object in an orderly form.

The number of woods stacked by Like = 7

The length of each wood = 10/12ft

Therefore the length of the whole pile of wood ;

= 7×10/12

= 70/12

= 5.8ft

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Algorithm 2 is more efficient than Algorithm 1 because it only needs to loop through the numbers up to upper/11 instead of upper. This means that it will take fewer iterations to reach the result, making it more efficient than Algorithm 1.

Algorithm 1 will make upper/11 more checks than Algorithm 2, resulting in a slower runtime. Additionally, Algorithm 2 avoids the need to check the modulus of each number, further reducing the computation time. Algorithm 2 only needs to loop through the multiples of 11, which are always 11 apart from each other, so it can skip over the other numbers between them.

This makes Algorithm 2 much faster than Algorithm 1 because it is only looping through a fraction of the numbers.

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Answer:

The price elasticity of demand measures how responsive the quantity demanded is to a change in price. It can be calculated using the midpoint method, which is (change in quantity demanded / average quantity demanded) / (change in price / average price).

Using the midpoint method to calculate the price elasticity of demand for business travelers and vacationers, you would need more information such as the change in quantity demanded and the average quantity demanded for each group at different prices.

It is not possible to say if the demand is elastic or not for either group based on the information provided.

The value of the function for f(5) is 133

A function can be defined as an equation, law, rule or expression that explains the relationship between two variables.

These variables are known as;

The different types of functions in mathematics are;

From the information given, we have that;

f(x) = 4x² + 2x - 2

To determine the function, f(5), substitute the value of x as 5

f(5) = 4(5)² + 2(5) -2

expand the bracket

f(5) = 125 + 10 -2

Add or subtract the values

f(5) = 133

Hence, the value is 133

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the bicycle has a frame size of 22.04 in.

What is unit conversion?

Units of measure are needed in order to measure these values. Sometimes the units of measurement used may not correspond to the standards required for a particular process or application, as well as the measuring choice and convenience. It's crucial to convert these units in a way that makes sense and can be used effectively. Let's use the example of someone who is only familiar with the metric system to better grasp the statement. The person finds it difficult to determine the height of a 25-foot tree. The person will comprehend the height of the tree better if they convert 25 feet to meters. Let's use a unit conversion table to learn about converting between different units.

A bicycle has a 56 cm frame.

As given 1 in = 2.54cm

so 2.54 cm =1 inc

1 cm = 1/2.54

56 cm for the frame = 56*1/2.54 = 22.04 in

Hence the bicycle has a frame size of 22.04 in.

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The solution set for the inequality -4≤-2(y-1)<2 is the set of all y-values that make the inequality true.

To graph the solution set, we can begin by plotting the inequality as an inequality on the y-axis, and then identifying the solutions that make the inequality true:

First, we can simplify the left side of the inequality: -4≤-2(y-1)

Next, we can solve for y by isolating y: -4/2≤y-1

Then we can add 1 to both sides of the inequality: -2≤y

Now, we can graph the inequality y ≥ -2, which is a line that is equal to or greater than -2.

On the right side, we have -2(y-1)<2

2(y-1)>-2

y-1>-1

y>-1

So we can graph the inequality y>-1, which is a line that is greater than -1.

So the solution set is the region above the line y=-2 and below the line y=-1. The region is a strip between two lines.

It is important to note that the solution set doesn't include the values of the lines, as the inequality is strict, not inclusive.