17. Given the following two functions:
f(x) = 5x² - 2x + 7
g(x) = 2x² + 6x +3
Then, find the following:
f (x) - g(x)

A. 7x²-8x+4
B. 7x² + 4x + 10
C. 3x² + 4x + 10
D. 3x² - 8x +4

Answer:

Below

Step-by-step explanation:

Working on this for days  ?  Seriously ??

5 x 10 ^8 = 50 x 10^7

50 x 10^7 + 2 x 10^7 = 52 x 10^7   = 5.2 x 10^8  = 520, 000,000

Pick the form you need.....

Length of third side = 10 units.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

Here, given that,

Height = 7 units

Base = √51 units

And, we have, it is a right angle triangle  

and we have to find the hypotenuse.

By Pythagorean theorem we get,

Hypotenuse = √7²+ 51

                     =√100

                     =10 units.

Hence, Length of third side = 10 units.

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Answer:

p < -7

Step-by-step explanation:

-4p > 28  Divide both sides by -4 and flip the sign

p < -7

Answer:

0.6324

Step-by-step explanation:

Answer:

0.63245553203. that is the square root

The values for the inequality in vertex form is y < -1.5(x - 1)^2 + 4.5

The equation for a parabolic function in vertex form is given by y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

The vertex of the parabolic path of the drinking fountain is (1, 4.5). So, h = 1 and k = 4.5.

Substituting the values for h and k into the equation:

y = a(x - 1)^2 + 4.5

Now, we need to determine the value of a using the point

(x, y) = (2, 4)

So, we have

a(2 - 1)^2 + 4.5 = 4

Evaluate

a = -1.5

So, we have

y = -1.5(x - 1)^2 + 4.5

Express as inequality

y < -1.5(x - 1)^2 + 4.5

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Complete question

The path of a drinking fountain is designed to reach a maximum height of 4.5 feet after 1 second. The spout is at a height of 4 feet after 2 seconds. If the water pressure decreases, the water does not reach the intended height. Complete the values for the inequality in vertex form to describe the points that are less than the projected path. y__a(x – h)2 + k

Answer:

Step-by-step explanation:

The path of a drinking fountain is designed to reach a maximum height of 4.5 feet after 1 second. The spout is at a height of 4 feet. If the water pressure decreases, the water does not reach the intended height.

Complete the values for the inequality in vertex form to describe the points that are less than the projected path.

y

✔ <

a(x – h)2 + k

a =

✔ –0.5

h =

✔ 1

k =

✔ 4.5

The function that gives the area A(x) of the field (in square meters) in terms of x is A(x)=(220x-x²).

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Ann has 440 meters of fencing and wishes to enclose a rectangular field is x.

We know that, the perimeter of a rectangle is P=2(Length+Width)

Let the length of a rectangle be x.

Now, 440=2(x+Width)

Width=220-x

a) A function that gives the area A(x) of the field (in square meters) in terms of x.

A(x)= x(220-x)

A(x)=(220x-x²)

b) Side length x gives the maximum area that the field can have

220x-x²=0

220x=x²

x=220 meters

So, Side length x= 220 meters

Therefore, the function that gives the area A(x) of the field (in square meters) in terms of x is A(x)=(220x-x²).

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Answer:

altitude is same as height =7cm

Step-by-step explanation:

area of parallelogram=height (altitude) × base length





Answer:

Step-by-step explanation:

There is only one unique triangle that can be made with this information.

If QT is perpendicular bisector of PR then the measures are

The figure consist of two isosceles triangles, for an isosceles triangle the two sides are equal

For the triangle that has the value of x, TSR

4x + 4 = 7x - 17

4 + 17 = 7x - 4x

3x = 21

x = 7

For triangle PQR

5y - 31 = 2y + 2

5y - 2y = 2 + 31

3y = 33

y = 11

PQ = 5y - 31 = 5 * 11 - 31 = 24

SR = 7x - 17 = 7 * 7 - 17 = 32

PT = 6x - 2y = 6 * 7 - 2 * 11 = 20

PR = 2 * PT= 2 * 20 = 40

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The rate of change is $2.33 per visitor

Rate of change refers to how quickly something changes over time. For example, acceleration is the rate of change of velocity with time.

Velocity is also the rate of change in position with time.

Rate of change means difference or changes with time.

It cost $31 for 3 visitor. This means that the cost per visitor is $31/3 = $10.33

It cost $80 for 10 visitor. This means that the cost for one visitor is 80/10 = $8

The rate of change is the difference in rate. This means that rate of change = $10.33 - $8

= $2.33/visitor

Therefore the rate of change is $ 2.33 per visitor.

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The equivalent of the expression given as (2n + 4) - 2 is 2n + 2

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

(2n + 4) - 2

To start with, we need to remove the brackets

So, we have the following representation

(2n + 4) - 2 = 2n + 4 - 2

Next, we evaluate the like terms

(2n + 4) - 2 = 2n + 2

Hence, the equivalent expression is 2n + 2

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Complete question

Use what you know about equivalent expressions to write an expression equivalent to the one given.

(2n + 4) - 2

a. 5n

b. 2n+2

c. 4n-4

d. 3n+2n + n

a.  The area enclosed by one loop of the curve is:

Area = 1/2 * ∫(1-cos²(10θ))dθ from θ₁ to θ₂

b. The area that it encloses r = 4 + 2 cos(θ) is:

Area = 1/2 * ∫((4 + 2 cos(θ))²)dθ from θ₁ to θ₂

a. To find the area enclosed by one loop of the curve r = sin(10θ), we can use the formula for the area of a polar region, which is:

Area = 1/2 * ∫(r²)dθ from θ₁ to θ₂

       Area = 1/2 * ∫(1-cos²(10θ))dθ fromθ₁ to θ₂

b. To find the area enclosed by one loop of the curve r = 4 + 2 cos(θ) we can use the same formula,

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The carpenter needs 1602.76 inches of wood to build the frame, which includes a 13x49 inch rectangle, a 12x48 inch rectangle, and a 7 inch radius semicircle.

Rectangle 1:

13 x 49 = 637 inches

Rectangle 2:

12 x 48 = 576 inches

Semicircle:

3.14 x 7 x 7 = 153.94 inches

Total = 637 + 576 + 153.94 = 1602.76 inches of wood

The second piece will be a rectangle with sides of 12 inches and 48 inches. The third piece will be a semicircle with a radius of 7 inches. Therefore, the carpenter will need a total of

(13 x 49) + (12 x 48) + (3.14 x 7 x 7)

= 1602.76 inches of wood to build the frame.

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Answer:

They each collected 8

Step-by-step explanation:

If all 6 collected the same amount, we can just divide the total amount of cans by 6

48/6 = 8

On solving the provided question, we can say that by equation =2.75x = 50feet and 4.5x = 900 feet in actual  

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here, we have

1 in = 20 feet

let it be x 20 feet,

then by equation =2.75x = 50feet and 4.5x = 900 feet in actual  

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Answer: #1 a=226

Step-by-step explanation:#1, split the shale into 2 parts. A small square with the 6 and 16. Then subtract six from sixteen and you have the height of the rectangle. Then take your difference (10) and multiply it with your width (19)= 190

Then do the little square which is 6x6=36. Add 190 and 36

Answer:

The area and the perimeter is 225 and 152. I'll show you how to do the rest below:

Step-by-step explanation:

For the Area you Multply all the numbers together

And for the perimeter you multiply the numbers by four

I hope you understand! let me know in the reply box

Answer:
Point 1: (2,6)
Point 2: (8,6)

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Answer:

There are 7500 five digit numbers divisible by 12. Out of the 7500 5-digit numbers divisible by 12, 7500 are even numbers and 0 are odd numbers. What is the smallest five digit number divisible by 12? The smallest 5-digit number divisible by 12 is 10008.

Step-by-step explanation:

Answer:

As far as I know

Mode: The most frequent number—that is, the number that occurs the highest number of times. Example: The mode of {4 , 2, 4, 3, 2, 2} is 2 because it occurs three times, which is more than any other number.

The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.

The angles in the triangle is as follows:

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the angles a, b and c in the triangle as follows:

c + 44 + 53 = 180(sum of angles in a triangle)

c = 180 - 44 - 53

c = 83 degrees

Therefore, let's find the value of a and b.

b + 83 = 180 (sum of angle on straight)

b = 180 - 83

b = 97 degrees.

Hence,

28 + 97 + a = 180(sum of angles in a triangle)

a = 180 - 28 - 97

a = 55 degrees.

Therefore,

a = 55°

b = 97°

c = 83°

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Answer:

The first inequality can be solved by combining like terms and isolating x on one side:

-2(6x + 36) - 7x <= 23

-12x - 72 - 7x <= 23

-19x - 72 <= 23

-19x <= 95

x >= -5

The second inequality can be solved by subtracting 10 from both sides:

6x + 10 > 40

6x > 30

x > 5

The solution to both inequalities is x >= -5 and x > 5, which means that x is a real number greater than 5.

The system of equations are  y₁ = 16x₁ + 5  and  y₂ = 17x₂  respectively

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Now , the value of A is

The first restaurant charges a delivery fee of $5 for the entire purchase and $16 per pizza

So , y₁ = 16x₁ + 5

where x is the number of pizzas and y is the total charge

Let the second equation be represented as B

And , The second restaurant has no delivery fee and charges $17 per pizza

So , y₂ = 17x₂

Now , Total charge from the first restaurant (in dollars) is given by the equation , y₁ = 16x₁ + 5  where x₁ is the number of pizzas

And , Total charge from the second restaurant (in dollars) is given by the equation , y₂ = 17x₂  where x₂ is the number of pizzas

For the total charge to be same for each restaurant , y₁ = y₂

Substituting the values in the equation , we get

16x₁ + 5 = 17x₂

And , when x₁ = x₂

16x₁ + 5 = 17x₁

Subtracting 16x₁ on both sides of the equation , we get

x₁ = 5

So , the total charge would be same if the number of pizzas from the first restaurant is 5

Hence , the system of equations are solved

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1) The increasing interval of the function is (-5.5,-5)∪(-4, -3)∪ (2,∞).

2) The decreasing interval of the function is (-5,-4)∪(1,2).

3. The negative interval is (-5.5, -3.25).

4. The positive interval is (-3.25,∞).

5. The minimum are at (-4,-2) and (2,0).

6. The maxima are at (-5,0).

7. The domain of the function is (-5.5,∞).

8. The range of the function is (-2.5,∞).

9. The value of f(-5) is 0.

10. The value of f(1) is 2.5.

What is increasing interval?

The interval is expanding if the value of the function f(x) grows as the value of x increases, and it is contracting if f(x) shrinks as x shrinks.

The graph is increasing in between points (-5.5,-2.5) to (-5,0), (-4,-2)to (-3,2.5) and (2,0) to (∞,∞)

The increasing interval is (-5.5,-5)∪(-4, -3)∪ (2,∞).

The graph is decreasing (-5,0 to (-4,2) and (1,2.5) to (2,0).

The decreasing interval of the function is (-5,-4)∪(1,2).

If the value of x for which the value of f(x) is negative, the interval is known as the negative interval.

From the point (-5.5, -2.5) to (-3.25,0), the graph lies below x-axis.

Thus the negative interval is (-5.5, -3.25).

If the value of x for which the value of f(x) is positive, the interval is known as the positive interval.

From the point (-3.25,0) to (∞,∞), the graph lies above x-axis.

Thus the negative interval is (-3.25,∞).

The graph of a function y = f(x) has a local maximum at the point where the graph changes from increasing to decreasing. At this point the tangent has zero slopes. At the point when the graph shifts from declining to increasing, a local minimum is present.

The minimum is at (-4,-2) and (2,0).

The maxima are at (-5,0).

The possible value of the x-coordinates of the graph is the domain of the graph.

The domain of the graph is (-5.5,∞).

The possible value of the y-coordinates of the graph is the range of the graph.

The range of the graph is (-2.5,∞).

The y-coordinate of a point at x = a on the graph is the value of f(a).

(-5,0) is a point on the graph. Thus the value of f(-5) is 0.

(1,2.5) is a point on the graph. Thus the value of f(1) is 2.5.

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The factorization of the polynomial is ( x - 4 ) ( x + 9 )

factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.

We are given the function as

x² + 5x - 36

We have to find out the two numbers when multiplied results to 36 & when subtracted results to 5.

The numbers are 9 and 4

x²+ ( 9 - 4)x - 36

Distribute x :

x² + 9x - 4x - 36

Take the common :

x ( x + 9 ) - 4 (x + 9 )

( x - 4 ) ( x + 9 )

Hence, The right answer is of Option C [ ( x - 4 ) ( x + 9 ) ]

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The domain of the function [tex]f(x) = 7[/tex] is (-∞, ∞). It means that all real numbers are domains for the given function.

The domain of the function is the set of numbers for which the function is defined. It acts as input for the function and gives output known as range.

The range of the function is the set of numbers of possible output values.It is derived from set of inputs known as domain.

The domain of the expression  [tex]f(x)=7[/tex] is all real numbers except where the expression is undefined. In this given case, there is no real number that makes the expression undefined.

Hence, The domain for the given expression is (-∞, ∞).

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The function g(x) is the integral of f(t) from 0 to x, where f(t) is the function whose graph is shown. This means that the value of g(x) is the area under the graph of f(t) from 0 to x.

g(0) = 0

g(2) = 8

g(4) = 24

g(6) = 48

g(12) = 96

g(0) = ∫02f(t)dt = 0

g(2) = ∫22f(t)dt = 8

g(4) = ∫42f(t)dt = 24

g(6) = ∫62f(t)dt = 48

g(12) = ∫122f(t)dt = 96

The function g(x) is the integral of f(t) from 0 to x, where f(t) is the function whose graph is shown. This means that the value of g(x) is the area under the graph of f(t) from 0 to x. To evaluate g(x) for a given value of x, we need to calculate the area under the graph of f(t) from 0 to x. In this case, the area under the graph of f(t) from 0 to 2 is 8, from 0 to 4 is 24, from 0 to 6 is 48 and from 0 to 12 is 96. Therefore, g(0) = 0, g(2) = 8, g(4) = 24, g(6) = 48 and g(12) = 96.

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The range of values for the correlation coefficient is - 1 to 1, inclusive is the correct answer.

Value is an important concept in economics, philosophy, and psychology. In economics, value is the amount of utility or satisfaction that an individual derives from a good or service. In philosophy, value is the worth or usefulness of something, based on its purpose. In psychology, value is the perceived importance of something that influences an individual's behavior. Value can also be seen as a measure of the worth of an object or action. Value is subjective and can differ from one person to another, depending on their beliefs and experiences. Value is also a key factor in decision-making and can help individuals make informed choices.

The range of values for the correlation coefficient is -1 to 1, inclusive. This means that the correlation coefficient can range from a perfect negative correlation (-1) to a perfect positive correlation (1).

Values in between those two extremes indicate a weaker correlation.

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After solving, the farmer have total 21 chicken and 19 cows.

In the given question, a farm raises cows and chickens.

The farmer has a total of 40 animals.

One day he counts the legs of all his animals and realizes he has a total of 118 legs.

We have to find how many chickens the farmer have.

Let the number of cows that the farmer have is x.

Let the number of chicken that the farmer have is y.

The farmer has a total of 40 animals.

So the equation should be

x + y = 40....................(1)

As we know that a cow has 4 legs and a chicken has 2 legs.

He has a total of 118 legs.

Now the equation should be

4x + 2y = 118....................(1)

Substituting x = 40 - y from the equation 1, we get

4(40 - y) + 2y = 118

160 - 4y + 2y = 118

160 - 2y = 118

Subtract 160 on both side, we get

-2y = - 42

Divide by -2 on both side, we get

y = 21

Now putting the value of y in x = 40 - y, we get

x = 40 - 21

x = 19

Hence, the farmer have total 21 chicken and 19 cows.

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The farmer has 0 chickens and 40 cows.

Let's solve this problem using an algebraic equation. First, we will assign a variable to represent the number of chickens the farmer has. We will call this variable 'x'. We also know that the total number of animals the farmer has is 40. Therefore, we can write an equation that states:

x + (40 - x) = 40

This equation states that the sum of the number of chickens and the number of cows is equal to the total number of animals the farmer has. Now, let's look at the number of legs the animals have. We know the total number of legs is 118. We also know that chickens have two legs and cows have four legs. We can now write another equation that states:

2x + (4(40 - x)) = 118

This equation states that the sum of the number of chicken legs and the number of cow legs is equal to the total number of legs the animals have. We can solve for x by multiplying both sides of the equation by -1 and then adding both equations:

2x + (4(40 - x)) = 118

-2x - (4(40 - x)) = -118

0x = -118 + 118

0x = 0

Since 0x = 0, we can conclude that x = 0. This means that the farmer has 0 chickens and 40 cows.

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Answer:

Answer: 27:8

Step-by-step explanation:

There are 24 + 16 + 14 = 24+16+14= 54

54 marbles in total.

The ratio of total marbles to red marbles is 54 : 16, which simplifies to 27 : 8.

Answer: 27:8

The taxable income is $17235.

Given :

salary for full-time job : $23,000

Salary contributed to your company's retirement plan : $1,000

savings account interest : $35

health insurance premiums : $2,400

standard deduction : 2400

Since , salary for full-time job is $23,000

After , contribution to your company's retirement plan = $23,000-$1,000=$22,000

Since , interest is $35 and health health insurance premiums costs $2,400

Net salary = $22,000 - $2,400 + $35 = $19635

Salary after the standard deduction of 2400 = $17235.

Hence, the taxable income is $17235.

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