F(x)=4x^3+7x^2+8x and g(x)=7x^2-7x, find (f-g)(x) and (f-g)(0)

Both f(x) and g(x) have one x-intercept at x = -1/3.

Theorem A states that for a cubic function of the form f(x) = x^3 + x + b, with b > 1, the function f has exactly one x-intercept. Using Theorem B, we can conclude that for any nonzero real number k, the function g(x) = kf(x) = kx^3 + kx + bk also has exactly one x-intercept.

For example, if f(x) = x^3 + x + 5 and k = 2, then g(x) = 2x^3 + 2x + 10. Both f(x) and g(x) have exactly one x-intercept. This can be shown by solving the quadratic equation formed by setting f(x) = 0 or g(x) = 0. Doing this yields x = -1/3. Therefore, both f(x) and g(x) have one x-intercept at x = -1/3.4

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Answer:

3,2 °C

Step-by-step explanation:

40,2 °C - 37 °C = 3,2 °C

Answer:

  6√2

Step-by-step explanation:

You want one side of a square whose half-diagonal has length 6.

If X is the center point of the square where the diagonals cross at right angles, triangle EXG is an isosceles right triangle with leg length 6. The hypotenuse of an isosceles right triangle is √2 times the leg length, so ...

  EG = 6√2

__

Additional comment

If you like, you can use the Pythagorean theorem to prove that.

  EG² + EX² +GX² = 6² +6² = 72

  EG = √72 = √(36·2) = 6√2

A square is a rhombus, so the diagonals cross at right angles. A square is a rectangle, so the diagonals are the same length. A square is a parallelogram, so the diagonals bisect each other.

Answer:

  G(u+t, s)

Step-by-step explanation:

Given coordinates E(-1, 0), F(0, s), and H(u, 0) of parallelogram EFGH, you want the coordinates of point G.

Segment FG is a horizontal line. Its length will be the same length as horizontal line EH. Since the lines are horizontal, the length is the difference of x-coordinates.

Point H is (u -(-t)) = u+t units to the right of point E. The x-coordinate of point G will be the same number of units to the right of point F.

The x-coordinate of G is 0 +(u+t) = u+t, the length of EH added to the x-coordinate of F.

The y-coordinates of any point on a horizontal line are the same. The y-coordinate of point F is 's'. Point G lies on that same horizontal line, so has the same y-coordinate.

The coordinates of point G are (u+t, s).

__

Additional comment

The midpoints of the diagonals are the same. This means ...

  (E+G)/2 = (F+H)/2

  E+G = F+H . . . . . . multiply by 2

  G = F +H -E . . . . . subtract E

Using the given coordinates:

  G = (0, s) +(u, 0) -(-t, 0) = (0+u+t, s+0+0) = (u+t, s) . . . . as above

All of your "parallelogram" problems are worked the same way. The fourth point has coordinates that are the sum of the coordinates of the end points of the known diagonal, less the known point on the unknown diagonal.

If you work the problem any of several other ways, you get the same answer.

Point E is (u -(-t)) = (u +(-t)) units away from point H. Point G will be located the same amount of units to the right of point F in terms of its x-coordinate.  G(u+t, s)

You need to know the coordinates of point G in the parallelogram EFGH given the coordinates E(-1, 0), F(0, s), and H(u, 0).

FG is a horizontal segment. It will have a length equal to that of a horizontal line, EH. The length is determined by the difference in x-coordinates because the lines are horizontal.

The length of EH multiplied by the x-coordinate of F yields the x-coordinate of G, which is 0 +(u+t) = u+t.

Horizontal line

In a horizontal line, all points have the same y-coordinates. Point F has the y-coordinate of's'. Point G's y-coordinate is the same because it is located on the same horizontal line.

The coordinates of point G are (u+t, s).

__

Additional comment

The midpoints of the diagonals are the same. This means ...

 (E+G)/2 = (F+H)/2

 E+G = F+H . . . . . . Multiply by 2

 G = F +H -E. . . . . Subtract E

Using the given coordinates:

G = (0, s) +(u, 0) (u, 0) (-t, 0) = (u+t, s) + (u+t, s) + (u+t, s) . . . . As mentioned earlier

Your “parallelogram” issues are all solved in the same manner. The fourth point's coordinates are equal to the sum of the coordinates of the known diagonal's end points, minus the known diagonal's known point.

The solution is the same regardless of how you approach the issue.

Vertical line

Any point on a horizontal line has the same y-coordinates. Point F's y-coordinate is's'. Point G has the same y-coordinate since it is located on the same horizontal line.

Point G's coordinates are (u+t, s).

Further commentary

The diagonals' midpoints are identical. This implies...

(E+G)/2 = (F+H)/2

E+G = F+H, multiply by 2, and so on.

G = F + H -E.... Remove E.

Using the coordinates provided:

G = (0, s) +(u, 0) (u, 0) (-t, 0) = (u+t, s) + (u+t, s) + (u+t, s) . . . . as mentioned earlier

Therefore, Your “parallelogram” issues are all solved in the same manner. The fourth point's coordinates are equal to the sum of the coordinates of the known diagonal's end points, minus the known diagonal's known point.

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The numeric value of the function is given as follows:

2x + h + 9.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function in this problem is given as follows:

f(x) = x² + 9x.

At x = x + h, the function is defined as follows:

f(x + h) = (x + h)² + 9(x + h)

f(x + h) = x² + 2xh + h² + 9x + 9h

f(x + h) = x² + 2xh + h² + 9x + 9h.

Subtracting by f(x), we have that:

f(x + h) - f(x) = h² + 2xh + 9h.

f(x + h) - f(x) = h(h + 2x + 9).

Dividing by h, the numeric value is given as follows:

2x + h + 9.

Meaning that the first option is the correct option.

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The answer would be x^-10, since the question asks you to rewrite it with a single variable.

I hope this helps!  o(〃＾▽＾〃)o

The formula for determining the strength of a negative association between two variables is Pearson's Correlation coefficient (r).

This coefficient measures the degree of linear relationship between two variables and ranges from -1 to +1. If two variables have a negative association, the correlation coefficient will be negative.

For example, let's say we are looking at the relationship between daily consumption of donuts (dd) and daily temperature (tt). To calculate the Pearson's Correlation coefficient, we would first calculate the covariance of the two variables using the following formula:

Cov(dd,tt) =  (∑ (dd - dd_mean) * (tt - tt_mean)) / n

Next, we would calculate the standard deviation of both variables using the following formula:

Stdev_dd = √(∑ (dd - dd_mean)^2/n)

Stdev_tt = √(∑ (tt - tt_mean)^2/n)

Finally, we would calculate the Pearson's Correlation coefficient using the following formula:

r = Cov(dd,tt) / (Stdev_dd * Stdev_tt)

If r is close to -1, then this indicates a strong negative association between dd and tt.

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Answer:

Step-by-step explanation:

Answer:

1.91 lb

Step-by-step explanation:

1 3/4 cups of pecans per pie = 1.75 cups.

For 5 pies, 5 × 1.75 cups = 8.75 cups are needed.

1 cup = 99 g

8.75 cup × (99 g) / (1 cup) = 866.25 g

Exact conversion: 453.59237 g = 1 lb

866.25 g × (1 lb)/(453.59237 g) = 1.91 lb

Answer: 1.91 lb

There are 56 students as freshmen. The correct answer would be an option (A).

The percentage is defined as a ratio expressed as a fraction of 100.

A bar graph with the first bar labeled Jaguars, divided into freshmen from 0 to 40 percent and sophomores from 40 to 100 percent.

This can be determined by multiplying the percentage of freshmen who selected Jaguars (40%) by the total number of students surveyed (140).

⇒ 40% × 140 = 56

So there are 56 students as freshmen.

Hence, the correct answer would be option (A).

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The circumference of a circle whose radius is 21 feet, is 132 feet, thus the first option is the correct one.

We know that for a circle of radius R, the circumference is given by:

C = 2*π*R

Where π = 22/7

And here we know that the radius is 21 feet, then we can replace that in the formula above and we will get:

C = 2*(22/7)*21 feet = 132 feet

The circumference of that triangle is 132 feet, thus, the correct option is the first one.

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The expected waiting time in hours until the first call arrived is 0.00045.

The formula for poisson distribution is expressed as

P(x = r) = (e^- µ × µ^r)/r!

Where ,

µ=  represents the mean of the theoretical distribution.

r = represents the number of successes of the event.

According to the question,

µ = 5            

For the probability that there are one in one hour, it is expressed as

P(x = 1) ,

Therefore,

P(x = 1)

= (e^- 10 × 10^1)/1! = 0.00045

Therefore,

P(x = 1)

= 0.00045

Poisson distribution

A Poisson distribution is a discrete probability distribution. It gives the probability of an event happening a certain number of times (k) within a given interval of time or space.

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A graph that represents the solution set of the compound inequality is: graph D.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would solve the given compound inequality by making x the subject of formula as follows;

x + 3 < 1/2(4x - 12) < 20

Multiplying all through by 2, we have the following:

2x + 6 < 4x - 12 < 40

Next, we would solve the compound inequality in parts:

2x + 6 < 4x - 12

4x - 2x < 12 + 6

2x < 18

x < 18/2

x < 9.

4x - 12 < 40

4x < 40 + 12

4x < 52

x < 52/4

x < 13.

In conclusion, the line on a number line (graph) should be open when the inequality symbol is greater than (>) or less than (<).

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As per the given subset, the set T and U are not closed under multiplication.

In math the term subset is defined through the example set A is a subset of another set B if all elements of the set A are elements of the set B.

Here let us consider that S be a subset of R that is closed under multiplication

Here we have also consider that  T and U be disjoint subsets of S whose union is S.

Here we have given that the product of any three elements of T is in T and that the product of any three elements of U is in U, now we have to show that at least one of the two subsets T, U is closed under multiplication.

Here we have to start out with the assumption that neither T nor U is closed under multiplication and use proof by contradiction to prove that at least one of T or U must be closed under multiplication.

Here let us write this as,

=> t1,t2,t3∈T1,2,3 and 

=> u1,u2,u3∈U1,2,3∈,

While it is given by the problem that, then  T and U are disjoint subsets of S and therefore, 

=> T∩U = ∅.

At this time we have take that

=> t3 = u1⋅u2

=> 3 = 1⋅2 and 

=> u3=t1⋅t2

=> 3=1⋅2.

While we looking these statements are valid because T and U are not closed under multiplication, where as the product of u1⋅u21⋅2 must not be in the set U and the product of t1⋅t21⋅2 must not be in set T.

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In the horizontal direction and by 4 units to the left, f(x) should be shifted to match g(x).

The correct option is A.

The function provided by the basic function f(x) and the constant

g(x) = f(x - k),

may be drawn by horizontally moving the f(x) k unit coordinates.

The shift's direction depends on the value of k. Specifically,

The base graph moves k units to the right if k > 0, and

The base graph moves k units to the left if k < 0.

Given:

The quadratic functions f(x) and g(x) are described in the table.

From the table, the functions,

f(x) = x².

And g(x) = (x + 4)².

In the attached image,

the blue curve is the function of f(x).

And red line is the function of g(x).

From the graph,

Left by 4 units, f(x) should be shifted  to match g(x).

Therefore, left by 4 units, f(x) should be shifted to match g(x).

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Answer: A

Step-by-step explanation: took the test

we can conclude that option (A) , (B) and (C) are true.

We know that in a triangle,

• Sum of any to sides is greater than the third side.

• Difference between any two sides is smaller than the third side.

So, in ∆EFG, we have,

• EF + FG > EG

• FG + EG> EF

• EF + EG > FG

and,

• EF - FG <EG or FG - EF <EG

• FG - EG < EF or EG - FG < EF

• EF - EG <FG or EG - EF < FG

From options now we get,

A) EF + FG > EG is true

B)EG + FG > EF is true

C) EG - FG < EF is true

D) EF - FG > EG is false

E) EG + EF < FG is false

Therefore, we can conclude that option () , () and () are true.

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We can conclude that option (A) , (B) and (C) are true.

We know that in a triangle,

• Sum of any to sides is greater than the third side.

• Difference between any two sides is smaller than the third side.

So, in ∆EFG, we have,

• EF + FG > EG

• FG + EG> EF

• EF + EG > FG

and,

• EF - FG <EG or FG - EF <EG

• FG - EG < EF or EG - FG < EF

• EF - EG <FG or EG - EF < FG

From options now we get,

A) EF + FG > EG is true

B)EG + FG > EF is true

C) EG - FG < EF is true

D) EF - FG > EG is false

E) EG + EF < FG is false

Therefore, we can conclude option (A) , (B) and (C) are true.

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Answer: We know that:

x + y = 12 (because he can work at most 12 hours in total)

7x + 10y ≥ 90 (because he must earn no less than $90)

We can graph these inequalities on the coordinate plane.

The equation x + y = 12 represents a line with a slope of -1 and y-intercept of 12. This is the line that separates the region where he works more hours babysitting and the region where he works more hours clearing tables.

The inequality 7x + 10y ≥ 90 represents the region where he earns more than $90.

You can find the solution by finding the intersection of the line and the shaded region. The solution will be a point that lies on both the line and the shaded region.

One possible solution would be for Mason to work 8 hours babysitting and 4 hours clearing tables, earning him $56 from babysitting and $40 from clearing tables, for a total of $96.

Step-by-step explanation:

Answer: 43 because 7 is greater than 5 so you round up. Have a nice day ;)

The correct answer is 43.  0.735 is greater than 0.5, so you round it up to 43

The remaining portions from the three pizzas together make up 13/27 of a large pizza.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Shauntee ate 2/3 of her pizza, so she has 1/3 left.

Carlos ate 8/9 of his pizza, so he has 1/9 left.

Rocco ate 26/27 of his pizza, so he has 1/27 left.

To determine the combined fraction of the remaining portions of the three pizzas, we add the fractions that are left:

1/3 + 1/9 + 1/27 = (1/3) + (1/9) + (1/27)

Simplifying this fraction by finding the least common denominator, which is 27:

(1/3) + (1/9) + (1/27) = (9/27) + (3/27) + (1/27) = 13/27

So they together make up 13/27 of a large pizza.

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The mean and approximate standard deviation of the difference in the total weight of lobster john traps in a day are 2 pounds and 8.32 pounds respectively. Hence, option d is the right answer.

Since the weight of lobsters produced by each trap is independent of the other, we can find the mean and standard deviation of the difference in the total weight of lobsters trapped in a day by subtracting the mean and standard deviation of the west bay trap from the mean and standard deviation of the east bay trap.

Mean = 12 pounds (east bay) - 10 pounds (west bay) = 2 pounds

Standard deviation = √(7^2 + 4.5^2) = √69.25 ≈ 8.32 pounds

So, the mean and approximate standard deviation of the difference in the total weight of lobsters trapped in a day is -

Mean = 2 pounds

Standard deviation = 8.32 pounds

Therefore, the answer is (d) Mean=2; Standard deviation= 8.32.

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The complete question is -

John maintains two separate lines of lobster traps in Penobscot bay. the east bay trap produces a mean of 12 pounds of lobsters per day with a standard deviation of 7 pounds. the west bay trap produces a mean of 10 pounds of lobsters a day with a standard deviation of 4.5 pounds. the weight of lobsters produced by each trap is independent of the other. which of the following are the mean and approximate standard deviation of the difference in the total weight of lobsters john traps in a day?

(a) Mean=11; Standard deviation=2.50

(b) Mean=2; Standard deviation=2.50

(c) Mean=2; Standard deviation= 5.36

(d) Mean=2; Standard deviation =8.32

(e) Mean=2; Standard deviation=11.50

Answer:

We get that x > -5

Step-by-step explanation:

1. Split up the inequality into two parts

We think of it as a > b > c and know that it is the same as a > b and b > c.

Apply this to the compound inequality

3x + 2 > 2x-3 and 2x - 3 > x - 12

2. Start solving 3x + 2 > 2x-3

Subtract 2x from both sides

x + 2 >-3

Subtract 2 from both sides

x > -5

3. Start solving 2x - 3 > x - 12

Subtract x from both sides

x - 3 > -12

Add 3 to both sides

x > -9

4. Finish

Now we have to think how we started with 3x + 2 > 2x-3 and 2x - 3 > x - 12

Since it is an and we need to identify the interval in which it is true on both inequalities which is when the x overlap. In this case is from x > -5.

Answer:

∠ QPT = 59°

Step-by-step explanation:

• the opposite sides are parallel

then

∠ SPT = ∠ QRT ( alternate angles ), that is

16x - 17 = 10x + 1 ( subtract 10x from both sides )

6x - 17 = 1 ( add 17 to both sides )

6x = 18 ( divide both sides by 6 )

x = 3

then

∠ SPT = 16x - 17 = 16(3) - 17 = 48 - 17 = 31°

• the vertices of a rectangle are right

∠ QPS = 90° , so

∠ QPT = 90° - ∠ SPT = 90° - 31° = 59°

Answer:

raised 53%

Step-by-step explanation:

goal = $8,000

raised = $4,200

$4,200/$8,000 = 0.525 = about 53%

The algebraic expression which represents the total cost of buying watermelons and tomatoes as described is; C = 0.68w + 3.25t.

The cost of buying a watermelon that weighs 18.5 pounds and 5 pounds of tomatoes is; $28.83.

It follows from the task content that the cost of buying Tomatoes are $3.25 / lb and Watermelon is $0.68 / lb.

Hence, the algebraic expression which represents the cost of buying a watermelon that weighs, w pounds and tomatoes that weigh t pounds is;

C = 0.68w + 3.25t.

Hence, if the watermelon bought weighs 18.5 pounds and tomatoes weigh 5 pounds,

C = 0.68 (18.5) + 3.25 (5)

C = 12.58 + 16.25

C = $28.83.

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The inequality equation is 8.498 > 8.478

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Let the first number be represented as = p

Let the second number be represented as = q

Now , the value of p = 8.498

The value of q = 8.478

And , the hundredths value in the number 8.498 is greater than the hundredths value in the number 8.478

So , the value of p is greater than q

Therefore , 8.498 > 8.478

Hence , the inequality is 8.498 > 8.478

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Answer:

This is nonsense, if GP = 16 and GH = 12 then HP = 4 (16 - 12 = 4). FP is looking basically the same size as HP, so FP = 4, not 2.

Step-by-step explanation:

These are all lies, your teacher is a liar and EF must be around 12 too.

Answer:

30

Step-by-step explanation: