2) (x+3)
2) Correct the error:
There is an error in the students' work shown below:
Question: Simplify (x-3)(x-7)
Solution: (x-3)(x-7)
x-x-3(x)-7(x) - 21
x²-10x-21
What is the error? Explain how to solve the problem.

The slope is (2/3 - 2/(3+h))/ h and as h is made closer and closer to 0, the slopes of the lines tend toward the derivative of the function f(x) at x = 3.

a) To find the slope of the line between the points (3, f(3)) and (3.1, f(3.1)), we use the formula m = (f(3.1) - f(3)) / (3.1 - 3) = (f(3.1) - f(3)) / 0.1

b) To find the slope of the line between the points (3, f(3)) and (3.01, f(3.01)), we use the formula m = (f(3.01) - f(3)) / (3.01 - 3) = (f(3.01) - f(3)) / 0.01

c) To find the slope of the line between the points (3, f(3)) and (3.001, f(3.001)), we use the formula m = (f(3.001) - f(3)) / (3.001 - 3) = (f(3.001) - f(3)) / 0.001

As h is made closer and closer to 0, the slopes of the lines tend toward the derivative of the function f(x) at x = 3.

Now to find a simplified rational expression for the slope of the line between (3, f(3)) and (3 + h, f(3 +h)), (h 0) :

The slope is equal to (f(3+h) - f(3)) / h

With f(x) = 2/x, we substitute it into the equation above and we get (2/(3+h) - 2/3) / h

The simplified rational expression for the slope is (2/3 - 2/(3+h))/ h

The graph of y = f(x) = 2/x between x = 1/2 and x = 4 :

This is the graph of a hyperbola that is symmetric about the y-axis and passes through the origin (0,0) and as x increases from 1/2 to 4, y decreases from 4 to 1/2.

Read more about the Slope of the points:

brainly.com/question/24907633

#SPJ4

Out of the given statements, statement a. If 4 is a prime number, then 6 is a prime number is the false one. A prime number is a positive integer that has exactly two distinct natural number divisors: 1 and itself.

For example, the number 2 is a prime number because it can only be divided evenly by 1 and 2. 4 is not a prime number because it can be divided evenly by 1, 2, and 4. 6 can be divided evenly by 1, 2, 3, and 6, so it is not a prime number. Therefore, statement a is false because if 4 is a prime number, 6 is not a prime number.

When determining whether a number is a prime number, it is important to remember that 1 is not a prime number. This is because 1 only has one divisor - itself. Any other number that can be divided evenly by more than two distinct natural numbers is not a prime number.

To know more about prime number refer to the link brainly.com/question/4184435

#SPJ4

Answer:

To divide using long division, we first divide the leading term of the dividend (3r³) by the leading term of the divisor (r) to get the first term of the quotient (3r²). Then, we multiply the divisor (r + 4) by the quotient term (3r²) and subtract it from the dividend. We then bring down the next term of the dividend (11r²) and repeat the process. This will give us the quotient and the remainder.

The long division process is as follows:

(r + 4) | (3r³ +11r²-6r-18)

| 3r² (3r²)

|__

| -9r² +11r²-6r-18

|____

| -2r-18

|____

| +12r + 72

|____

| -36

|____

So the quotient is 3r² - 2r + 12 and the remainder is -36

And we can write the division as (3r³ +11r²-6r-18)÷(r + 4) = 3r² - 2r + 12 +(-36)/(r + 4)

When the ellipse has co-vertices at (4,0) and foci at (0,+-4), the equation is y2/32+x2/16=1.

The algebraic equation y=mx+b is known as a linear equation. M serves as the y-intercept, and B serves as the slope. The previous clause has two variables, y and x, and is sometimes referred to as a "linear equation with two variables". Bivariate linear equations are those with two independent variables. The following are a few examples of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation takes the form y=mx+b, with m denoting the slope and b denoting the y-intercept, it is referred to as being linear. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

The center is

=(0,0)

The equation is

y2/a2+x2/b2=1

b=4

c=4

a2=b2+c2

=16+16=32

When the ellipse has co-vertices at (4,0) and foci at (0,+-4), the equation is y2/32+x2/16=1.

To know more about equation visit:

https://brainly.com/question/11897796

#SPJ1

CV stands for standard deviation divided by sample mean multiplied by 100.

CV = (std. deviation*100)/mean = 41.2 %

for SAT score:

CV = (std. deviation*100)/mean = 17.55%

To learn more about standard deviation refer to:

https://brainly.com/question/24298037

#SPJ1

A grid that correctly graphs the points A (3, 1), B (0, 3), and C (1, 3) include the following: B. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 3 units to the right and 1 unit above the origin. Point B is plotted 3 units above the origin. Point C is plotted 1 unit to the right and 3 units above the origin.

In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs (data points) on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis (x-coordinate) and y-axis (y-coordinate) respectively.

Next, we would use an online graphing calculator to plot the above set of data points with a point of intersection at (2, 3) as shown in the graph attached below.

By critically observing graph B of the given set of data points, we can logically deduce that it correctly graphs the points A(3, 1), B(0, 3), and C (1, 3) as shown in the image attached below.

Read more on a graph here: brainly.com/question/4546414

#SPJ1

Complete Question:

Which of the following grids correctly graphs the points A (3, 1), B (0, 3), and C (1, 3)?

A. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 3 units to the right and 1 unit above the origin. Point B is plotted 3 units to the right of the origin. Point C is plotted 1 unit to the right and 3 units above the origin.

B. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 3 units to the right and 1 unit above the origin. Point B is plotted 3 units above the origin. Point C is plotted 1 unit to the right and 3 units above the origin.

C. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 1 unit to the right and 3 units above the origin. Point B is plotted 3 units above the origin. Point C is plotted 3 units to the right and 1 unit above the origin.

D. A coordinate plane has an x-axis from 0 to 5 in increments of 1 and a y-axis from 0 to 5 in increments of 1. Point A is plotted 1 unit to the right and 3 units above the origin. Point B is plotted 3 units to the right of the origin. Point C is plotted 3 units to the right and 1 unit above the origin.

The total volume of glass that makes up the globe to the nearest hundredth is equal to 12,771.71 cubic centimeters.

Mathematically, the volume of a sphere can be calculated by using this mathematical expression:

Volume = 4/3 × πr³

Where:

r represents the radius.

Based on the information provided about the globe, the diameter of the hollow sphere is given by;

Diameter of sphere = 30 cm

Radius = diameter/2 = 30/2 = 15 cm.

Actual radius = 15 cm - 0.5 cm = 14.5 cm.

Substituting the given points into the volume of a sphere formula, we have the following;

Volume of sphere = 4/3 × 3.142 × 14.5³

Volume of sphere = 12,771.71 cubic centimeters.

Read more on volume of a sphere here: brainly.com/question/20394302

#SPJ1

Answer:

Choice B

Step-by-step explanation:

The y increases by 3 every time that the x increases by 1.

Hope this helped! :)

Answer: with ?

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given m = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (- 6, 5 ) into the partial equation

5 = [tex]\frac{1}{3}[/tex] (- 6) + c = - 2 + c ( add 2 to both sides )

7 = c

y = [tex]\frac{1}{3}[/tex] x + 7 ← equation of line

The required function g(x) = 4x² and the related graph is a parabola that is opened upwards on the x-axis  

The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. This means that when we replace x - coordinate with a numerical value in the expression, we get the y-value for the given function f(x).

Here we have

f(x) = x²  

Given that g(x) = f(2x)

To find the g(x) take x = 2x

=> f(2x) = (2x)²

=> g(x) = 4x²  

Therefore,

The required function g(x) = 4x² and the related graph is a parabola that is opened upwards on the x-axis  

Learn more about Graphs at

https://brainly.com/question/16502845

#SPJ1

Answer:

yes

Step-by-step explanation:

a. At the end of the 3 1/2 years, the amount of interest Damian has paid is $4,288.73.

b) When Damian pays off his credit card, the total amount (principal and interest) he has paid will be $14,488.73.

The interest is computed using an online finance calculator, setting the following parameters, based on the compounding interest system.

The calculator also shows the total payments made for the duration of the credit balance.

N (# of periods) = 42 months (3.5 years x 12)

I/Y (Interest per year) = 21%

PV (Present Value) = $10,200

FV (Future Value) = $0

Results:

PMT = $344.97

Sum of all periodic payments = $14,488.73

Total Interest = $4,288.73

Learn more about compound interest at https://brainly.com/question/24274034

#SPJ1

The known quantities are then identified using the visual overview as a guide, and they are q1 q2 q3 x1 and x2. The unknown quantity is then x3

Based on the details provided;

e charge 1 is located at the origin of the x-axis and the positive x-axis points to the right. Let x1, x2, and x3 denote the positions of charge 1, charge 2, and charge 3, respectively

Considering that charge 1 is thought to be at the source;

The known quantities are then identified using the visual overview as a guide, and they are:

q1 q2 q3 x1 and x2

However, given that we are unsure of its precise position x3,

The unknown quantity is then x3

Know more about charge

https://brainly.com/question/18102056

#SPJ4

The simplified form of (f o g)(x) = 8x²  + 8x + 4.

Differentiation is a process in calculus that is used to find the rate of change of a function at a specific point. It is the process of finding the derivative of a function.

To find (f o g)(x), we need to first find g(x) and then substitute that expression into f(x).

Given:

f(x) = 2x + 4

g(x) = 4x²  + 4x

So:

(f o g)(x) = f(g(x)) = f(4x²  + 4x) = 2(4x²  + 4x) + 4

Now we can substitute the expression for g(x) into f(x) and simplify:

= 2(4x²  + 4x) + 4 = 8x²  + 8x + 4

Hence, (f o g)(x) = 8x² + 8x + 4

To learn more about differentiation, Visit

brainly.com/question/954654

#SPJ1

The exact values of the trigonometric functions for an angle are:

The direction of an angle (θ), in degrees, with respect to origin is determine by coordinates on the terminal side. For a point in rectangular format we can determine the exact values of two fundamental trigonometric functions (sine, cosine) and four derivate trigonometric functions (tangent, cotangent, secant, cosecant:

For P(x, y) = (x, y)

Sine

sin θ = y / √(x² + y²)

Cosine

cos θ = x / √(x² + y²)

Tangent

tan θ = sin θ / cos θ

Cotangent

cot θ = 1 / tan θ

Secant

sec θ = 1 / cos θ

Cosecant

csc θ = 1 / sin θ

If we know that x = 2 and y = - 7, then exact values of trigonometric functions are, respectively:

Sine

sin θ = - 7 / √[2² + (- 7)²]

sin θ = - 7 / √53

sin θ = - 7√53 / 53

Cosine

cos θ = 2 / [2² + (- 7)²]

cos θ = 2 / √53

cos θ = 2√53 / 53

Tangent

tan θ = [- 7√53 / 53] / [2√53 / 53]

tan θ = - 7 / 2

Cotangent

cot θ = 1 / (- 7 / 2)

cot θ = - 2 / 7

Secant

sec θ = 1 / (2 / √53)

sec θ = √53 / 2

Cosecant

csc θ = 1 / (- 7 / √53)

csc θ = - √53 / 7

To learn more on trigonometric functions: https://brainly.com/question/14434745

#SPJ1

The statements which are always true in the triangle with interior angles, ∠2, ∠3, and m∠5, and exterior angles, ∠1, ∠4, and ∠5 are;

m∠5 + m∠6 = 180°

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 180°

An exterior angle is an angle that is formed by the extension of a side of the triangle and the side adjacent to the extended side.

The interior angles of the triangle are; angle ∠2, angle ∠3, and angle ∠5

The exterior angles at the interior angles of the triangle ∠2, ∠3, and ∠5 are angles  ∠1, angle ∠4, and angle ∠6 respectively.

Therefore, according to the exterior angle theorem, we get;

m∠1 = m∠3 + m∠5

m∠4 = m∠2 + m∠5

m∠6 = m∠2 + m∠3

The exterior angle and the adjacent internal angle are supplementary angles, therefore;

m∠2 + m∠1 = 180°

m∠3 + m∠4 = 180°

m∠5 + m∠6 = 180°

The angle sum property of a triangle indicates that the sum of the interior angles of a triangle is 180°, therefore;

m∠2 + m∠3 + m∠5 = 180°

The statements that are always true are therefore;

m∠5 + m∠6 = 180°

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

Learn more on the exterior angle theorem here: https://brainly.com/question/1490238

#SPJ1

The figure shows intersecting lines k and m, the measure of angle a is 94 degrees.

What are parallel lines ?

parallel lines can be defined as the lines which are equi distant from each other and which never meet or intersect each other.

Given,

In the figure the lines k and m are intersecting.

so,

by adding 86 degrees with a it should result into 180 degrees.

86+a  = 180

a = 180 - 86

a = 94

Hence, The figure shows intersecting lines k and m,  the measure of angle a is 94 degrees.

To learn more about parallel lines from the given link.

https://brainly.com/question/16701300

#SPJ1

Answer:

[tex]\displaystyle \frac{\sqrt{5}-1}{2}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{2}{1+\sqrt{5}}\\\\=\frac{2}{1+\sqrt{5}}*\frac{1-\sqrt{5}}{1-\sqrt{5}}\\ \\=\frac{2(1-\sqrt{5})}{1-5}\\ \\=\frac{2(1-\sqrt{5})}{-4}\\\\=\frac{\sqrt{5}-1}{2}[/tex]

The value of k from the equation is k = 4

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 equation be represented as A

Now , the value of A is

f ( x ) = ( 2 - k ) / ( 5x + k )   be equation ( 1 )

Now , the equation passes through the point P ( 3 , -2/19 )

On simplifying the equation , we get

Substituting the values of x and y in the equation , we get

y = ( 2 - k ) / ( 5 ( 3 ) + k ) )

-2/19 = ( 2 - k ) / ( 15 + k )

Multiply by ( 15 + k ) on both sides of the equation , we get

-2 ( 15 + k ) / 19 = 2 - k

Multiply by 19 on both sides of the equation , we get

-30 - 2k = 38 - 19k

Adding 2k on both sides of the equation , we get

38 - 17k = -30

Subtracting 38 on both sides of the equation , we get

17k = 68

Divide by 17 on both sides of the equation , we get

k = 4

Hence , the value of k = 4

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

If the mid point of AB is M (-4,-3). and the coordinates of A are (-1,-2), the coordinates of B is solved to be (-7, -4)

The midpoint of a line segment is the centroid of the segment. It is equally distant from both of the ends and hence cuts the section in half.

The formula to determine the center point of a straight line using the coordinates of its endpoints is known as the midpoint formula in coordinate geometry.

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

From the formula the second end point is calculated

-4= (-1 + x₁)/2

-8 = -1 +  x₁

x₁ = -7

-3 = (-2 + y₁)/2

-6 = -2 + y₁

y₁ = -4

The coordinates of B are (-7, -4)

Learn more about midpoint  here:

https://brainly.com/question/30152459

#SPJ1

Answer:

first number= -2 and the second number = 2

Step-by-step explanation:

x= one number and y= the other

your two equations are x+y=4x+8 and  x-y=3y-10

by solving the first one for y, y=3x+8 so plug that in for y in the second equation

x-(3x+8)=3(3x+8)-10

x-3x-8=9x+24-10

-2x-8=9x=14

11x=-22 so x=-2

now plug that in and solve for y

-2+y=4(-2)+8

y=2

Answer:HEYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY TOMATOE TOMATOE TOMATOE BOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

Step-by-step explanation:

Answer: 220

Step-by-step explanation:

Create ratios using fractions, one for the students, and one for the percent

students: [tex]\frac{11}{x}[/tex]  percents: [tex]\frac{5}{100}[/tex]

Then cross multiply 1. [tex]11 *100 = 1100[/tex], 2. [tex]1100 / 5 = 220[/tex]

So [tex]x = 220[/tex], this means there are a total of 220 students in 7th grade

The required order of buttons to press on a scientific calculator to enter 2.8 x 10⁷ is  [2] [.] [8] [EE] [7] . Option A is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
While using the calculator, for the expression 2.8 × 10⁷,
We have to tap on tabs as,  [2] [.] [8] [EE] [7] where [.]  is the multiplication operator and {EE} is the exponential operator.

Thus, the required order of buttons to press on a scientific calculator to enter 2.8 x 10⁷ is  [2] [.] [8] [EE] [7] . Option A is correct.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ1

The area of the mirror is 480 square inches

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

A mirror that has the shape of a parallelogram (see attachment)

From the attachment, we have the following dimensions

Base length = 5 units

Height = 6 units

The area is the product of the dimensions

Since the side length of each square tile is 4 in, then we have

Area = 4 * 4 * 5 * 6

Evaluate

Area = 480

Hence, the area is 480 square inches

Read more about area at

https://brainly.com/question/22972014

#SPJ1