Question 1 of 40
If f(x) = 4x² - 6 and g(x) = x² - 4x-8, find (f- g)(x).

x+3 is not a factor of f(x)=x^4+6x^3+5x^2-15x-2 because there is a remainder of 7 when we use the long division method to divide x+3 with the given function f(x).

The factors of a quadratic equation are the simplified form of the quadratic equation, that if multiplied together, results in the original quadratic equation.

Given that:

[tex]\mathbf{=\dfrac{x^4+6x^3+5x^2-15x-2}{x+3} }[/tex]

[tex]\mathbf{=x^3+3x^2-4x-3+\dfrac{7}{x+3} }[/tex]

x+3 is not a factor of f(x)=x^4+6x^3+5x^2-15x-2 because there is a remainder of 7 when we use the long division method to divide x+3 with the given function f(x).

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The answer for the fill in the blank is 80

Statistics from 2003 to 2013 indicated that, in the United States, women were earning approximately ___80___ cents for every dollar earned by men.

Answer:

7.76

Step-by-step explanation:

0.22×20=4.4

3.36(base amount ,average of the others)+4.4=7.76

Answer:

300°

Step-by-step explanation:

Given from the diagram:

Angle a° = 180° (Single angle on a straight line)

Angle c° + 60° = 180° (Sum of angles on a straight line)

Angle c° = 180° - 60° = 120°

Angle a° + c° = 180° + 120° = 300°

Answer:

a + c = 300°

Step-by-step explanation:

a = 180°

c = 180° -  60° = 120°

a + c = 180° + 120° = 300°

Answer:

It would be C

Step-by-step explanation:

The fraction equal to 4/5 is 8/10 so closest to 8/10 is 8/11

The graphs show a parabola with a vertex that has Roots are -2 and 4.

We have given that,

vertex of (1,-9) and solutions of (-2,0) and (4,0).

y=k*(x+2)(x-4)

Vertex = (1,-9) is a point of the parabola

-9=k*(1+2)(1-4) implies k=1

Equation of the parabola is y=(x+2)(x-4).

The graphs show a parabola with a vertex that has Roots are -2 and 4.

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Considering the slope of the lines, their relationship is given as follows:

They are not parallel because their slopes are not equal.

The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:

In this problem, their slopes are given as follows:

Different slopes, multiplication different of -1, hence the correct option is given by:

They are not parallel because their slopes are not equal.

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Answer:

C. They are not parallel because their slopes are not equal.

The equation of the parabola which has a vertex at (-2,0) is; y = x² +4x +4.

From the task content, it follows that the vertex of the of the parabola described by the graph in discuss is given by the point; (-2,0).

Hence, the vertex form of the equation is;

y = (x-(-2))² +0

Hence, the equation is; y = x² +4x +4.

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Answer: B

Step-by-step explanation:

Edge 2023

Answer:

x > 0 and y < 2

Step-by-step explanation:

By definition the inverse of a function is simply, when the domain and range are swapped. So if the domain of g(x) is x < 2 and y > 0, then the inverse will have these swapped. So x > 0 and y < 2

Answer:

4f

Step-by-step explanation:

I am using the variable f for fruit. Each pound of fruit costs $4, so the total will be 4 * the number of pounds of fruit.

Answer:

x=7.48 cm, y=6.94

Step-by-step explanation:

Start by finding the value of x.

Using the Pythagorean Theorem, [tex]13^{2}+x^{2} =15^{2}[/tex]

[tex]169+x^{2} =225\\x^2=56\\x=\sqrt{56}\\x=2\sqrt{14}[/tex]

Using this, we can again use the Pythagorean Theorem to find the value of y.

[tex]2.8^{2} +y^{2} =(2\sqrt{14} )^{2} \\7.84+y^{2} =56\\y^{2} =48.16\\y=\sqrt{48.16}[/tex]

(I rounded to two decimal places, not sure what is required here)

x=7.48 cm

y=6.94 cm

In the given diagram, the value of the side labelled x is 10.8 cm

From the question, we are to determine the value of side x

Using the law of sines

In any given triangle XYZ,

[tex]\frac{x}{sinX}=\frac{y}{sinY}=\frac{z}{sinZ}[/tex]

Thus,

In the given triangle,

[tex]\frac{x}{sin81^\circ} =\frac{7}{sin40^\circ}[/tex]

∴ [tex]x=\frac{7 \times sin81^\circ}{sin40^\circ}[/tex]

x = 10.75599

x ≈ 10.8 cm

Hence, the value of the side labelled x is 10.8 cm

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The coordinates of point P along AB so that the ratio of AP to PB is 3 to 1 is (4,13).

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

Given that the ratio of the two lines is 3:1, therefore, we can write,

m:n = 3:1

Also, the coordinate of the endpoints of the line are,

A = (x₁, y₁) = (1, 7)

B = (x₂, y₂) = (5, 15)

Now, Using the Section formula the coordinate of the point P can be written as,

[tex]P = (\dfrac{mx_2+nx_1}{m+n}\ , \dfrac{my_2+yx_1}{m+n})\\\\P = (\dfrac{3(5)+1(1)}{4}\ , \dfrac{3(15)+1(7)}{4})\\\\P = (4, 13)[/tex]

Hence, the coordinates of point P along AB so that the ratio of AP to PB is 3 to 1 is (4,13).

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A transitional matrix answers two questions:

Where did people who are now in each job category come from,

and where did people who were in each job category go?

The term "transition matrix" is used in various contexts of mathematics. In linear algebra, it is sometimes used to represent changes in a coordinate matrix. In Markov chain theory, it is used as an alias for a stochastic matrix, a matrix that describes a transition.

The transition matrix P is regular if there are only positive entries in the power of P. If the transition matrix is ​​regular, a Markov chain is a normal Markov chain. For example, if you take the power of the matrix D in succession, the entry for D will always be (or will be) positive.

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Answer:

0.0256 or 16/625 or 2.56%

Step-by-step explanation:

The problem states that each light bulb operates independently of the other, so the probability doesn't change for each light bulb based on how many other light bulbs are working.

The probability of each light bulb working is 0.6 out of 1. However, we want the probability of it being broken.

1 - 0.6 = 0.4

This is the probability of one light bulb being broken. But there are 4 lightbulbs.

We can multiply 0.4 by itself 4 times, as the probability stacks.

0.4 * 0.4 * 0.4 * 0.4 = 0.0256 (Also achieved by raising 0.4 to the power of 4)

To get the percentage, multiply it by 100. 2.56%

0.4 is equal to 40% or 40/100. If you simply, that fraction is equal to 2/5

2/5 * 2/5 * 2/5 * 2/5 = 16/625 (Also achieved by raising 2/5 to the power of 4)

The equivalent expression for the given expression is 8(d - 2f)

From the question, we are to factor out the GCF

The given expression is

8d - 16f

The GCF of the terms in the expression is 8.

∴ 8d - 16f = 8(d -2f)

The factored form of the expression is 8(d - 2f)

Hence, the equivalent expression for the given expression is 8(d - 2f)

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The shape of the cross section is a square. The correct option is the D. SQUARE

From the question, we are to determine shape of the cross-section formed.

A cross-section is seen when a three-dimensional image is cut by a plane.

The given figure is a square pyramid.

In the given diagram, plane S is a square. The intersection of plane S with the square pyramid gives square cross-section as shown in the figure.

Thus, the shape of the cross section is a square.

A shows a parallelogram

B shows a triangle

C shows a trapezoid

D shows a square

Hence, the shape of the cross section is a square. The correct option is the D. SQUARE

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The width of the rectangle is 10 inches

The given parameters are:

Length = 3x + 6

Width = 3x + 4

Area = 120

The area of a rectangle is

Area = Length * Width

So, we have:

(3x + 6) *(3x + 4) = 120

Expand

9x^2 + 12x + 18x + 24 = 120

Evaluate the like terms

9x^2 + 30x - 96 = 0

Using a graphing calculator, we have:

x = 2

Substitute x = 2 in Width = 3x + 4

Width = 3 * 2 + 4

Evaluate

Width = 10

Hence, the width of the rectangle is 10 inches

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The rate at which the distance from the plane to the station increases is 537 miles/hour. Computed using Pythagoras Theorem and Differentiation.

We assume the station to be at point A.

The plane when directly over the station, takes point C.

As it is flying horizontally continuously at an altitude of 1 mile, AC = b = 1 mile.

The plane flies continuously, and when it is at a distance of 3 miles from the station, it is at point B.

The distance between the plane and the station of 3 miles can be shown as AB = c = 3 miles.

The movement of the plane from C to B can be shown as BC = a.

Now, from the given case, we get a right triangle ABC.

By Pythagoras' Theorem,

a² + b² = c² ... (i).

or, a² + 1² = 3²,

or, a² = 9 - 1 = 8,

or, a = 2√2 miles.

We are told that the plane is moving at a speed of 570 miles/hour.

This can be shown as, da/dt = 570 miles/hour.

As the plane is moving horizontally, the vertical distance between the plane and the station doesn't change, that is, db/dt = 0.

In the question, we are asked to find the rate at which the distance from the plane to the station is increasing, that is, we are asked to find dc/dt.

Differentiating (i), with respect to time t, we get:

2a(da/dt) + 2b(db/dt) = 2c(dc/dt).

Substituting values of a = 2√2 miles, b = 1 mile, c = 3 miles, da/dt = 570 miles/hour, and db/dt = 0, we get:

2(2√2)(570) + 2(1)(0) = 2(3)(dc/dt),

or, 2280√2 + 0 = 6(dc/dt),

or, dc/dt = 380√2 miles/hour = 537.40 miles/hour ≈ 537 miles/hour.

Thus, the rate at which the distance from the plane to the station increases is 537 miles/hour. Computed using Pythagoras Theorem and Differentiation.

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The statement that is true about the estimate is that the number will be less than 1 because when adding the exponents, 11 + (negative 14) = negative 3, and a number in scientific notation with a negative exponent is less than 1 (option D).

According to this question, Bethany wants to estimate the value of (4.296 times 10 Superscript 11) (1.8614 times 10 Superscript negative 14).

This expression can be mathematically written as:

(4.296 × 10¹¹) (1.8614 × 10-¹⁴)

The result of this expression is 7.996 × 10-³, which is value less than 1.

Therefore, the number will be less than 1 because when adding the exponents, 11 + (negative 14) = negative 3, and a number in scientific notation with a negative exponent is less than 1.

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Answer:

The year in which population will be 54000, is 2020.

Step-by-step explanation:

In the question, it is given that the city's population is growing linearly. In 2008 , population was 28200 and in 2012 , it is 36800 .

It is required to identify the year in which population will be 54000 . equation.

Step 1 of 2

The population in 2008 was 28200 and in 2012 it was, 36800 .

The equation relating population and year is,

[tex]$$\begin{aligned}&y-28200=\left(\frac{36800-28200}{2012-2008}\right)(x-2008) \\&y-28200=\left(\frac{8600}{4}\right)(x-2008) \\&y-28200=2150(x-2008)\end{aligned}$$[/tex]

Step 2 of 2

The year in which population will be 54000 , can be determined by substituting 54000 for y,

[tex]54000-28200=2150(x-2008)$\\ $25800=2150(x-2008)$\\ $x-2008=12$\\ $x=2020$[/tex]

Answer:

c=104.1 ft

Step-by-step explanation:

Law of Cosines

c^2 = 66^2 + 120^2 - 2 (66)(120)cos 60

c = 104.1 ft

The area of the circle is 157.14 square unit.

A circle is a round shaped figure , whose all points lie in the same plane and the distance between the center and any point on the circle is same.

It is given that , For Circle

Center is ( 8 , 2)

Point on the circumference is ( 3 , 7)

The distance between these point will give the radius

r = [tex]\rm \sqrt { (3-8)^2 + ( 7-2)^2[/tex]

r = √50 unit

The area of the circle is given by

A = π r²

A = π * (√50 )²

A =  π * 50

A = 50 π

A = 157.14 square unit

Therefore the area of the circle is 157.14 square unit.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Keep in mind:}[/tex]

[tex]\large\textbf{When you hear or see the word \boxed{quotient} in mathematics}\\\large\textbf{usually it means the RESULT/ANSWER of a division}\\\large\textbf{equation.}[/tex]

[tex]\huge\textbf{Assuming:}[/tex]

[tex]\mathbf{\dfrac{1}{3}}[/tex]

[tex]\mathbf{\dfrac{1\leftarrow \boxed{\mathsf{dividend}}}{3\leftarrow \boxed{\mathsf{divisor}}} = result \leftarrow \boxed{\mathsf{quotient}}}[/tex]

[tex]\mathbf{1 \leftarrow \boxed{\rm{dividend}} \div 3 \leftarrow \boxed{\rm{divisor}} = result\leftarrow \boxed{\rm{quotient}}}[/tex]

[tex]\uparrow\huge\textbf{Simplify \& you'll have the quotient}\uparrow[/tex]

[tex]\mathbf{Quotient \rightarrow 0.333333333}[/tex]

[tex]\mathbf{Quotient \approx 0}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{0}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Applying the inscribed angle theorem, the value of x in the circle is: 126°.

According to the inscribed angle theorem, the measure of the inscribed angle, 63° is one-half of the measure of central angle, x, as shown in the circle given.

Therefore, we would have the following equation:

1/2(x) = 63

x = 2(63)

x = 126°

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Answer:

9 sq cm

Step-by-step explanation:

If you join the two triangles it will become a square of side 3cm.

3cm * 3cm = 9cm squared.

Hope you have a nice day :)

Any questions please comment.

Based on quantitative reasoning, Alden should take the classes from Dr. Baeno in his next semester.

Quantitative Reasoning Behind Choosing Dr. Baeno

Alden talked to 17 friends that previously took course from Dr. Alvarez.

Eight out of 17 friends recommended Dr. Alvarez.

∴ The fraction of his friends in favor of Dr. Alvarez = 8/17

Also, Alden talked to 18 friends who took course from Dr. Baeno.

Eleven out of 18 friends recommended Dr. Baeno.

∴ The fraction of his friends in favor of Dr. Baeno = 11/18

Making Comparison

Now, since we know that,

11/18 > 8/17

The capacity for using knowledge and mathematics to address problems in the real world is known as quantitative reasoning.

Hence, applying quantitative reasoning, we can infer that it is more favorable for Alden to take classes from Dr. Baeno.

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Answer:

gradient = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

calculate the gradient m using the gradient formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 2) ← 2 points on the line

m = [tex]\frac{2-0}{0-(-6)}[/tex] = [tex]\frac{2}{0+6}[/tex] = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

Answer: D.  8 cm.

Step-by-step explanation:

[tex]l_{arc}=\frac{26}{9}\pi \ cm\ \ \ \ \Theta=65^0 \ \ \ \ \ r=?\\\boxed {l_{arc}=2\pi r*\frac{\Theta^0}{360^0} }\ \ \ \ \ \Rightarrow\\\boxed {r=\frac{{l_{arc}}*360^0}{2\pi *\Theta} }.\\r=\frac{\frac{26}{9}*\pi *360^0 }{2\pi *65^0} =\frac{13*360^0}{9*65^0} =\frac{40}{5}=8 \ (cm).[/tex]