Given that n is an integer and that n>1, prove algebraically that n²-(n-2)²-2 is always an even number

Answer:

The money earn in second week is $ 760 and

The algebraic equation to model the situation is $ x = $ 1240 - $ 480  

Step-by-step explanation:

Given as :

The total money earn by Katelynn in tow weeks = $ 1240

The money earn by Katelynn in first week = $ 480

Let The money earn by Katelynn in second week = $x

Now,

From equation

The total money earn by Katelynn in tow weeks = The money earn by Katelynn in first week  + The money earn by Katelynn in second week

Or,  $ 1240 =  $ 480 + $ x

Or, $ x =  $ 1240 - $ 480

So, x = $ 760

So, The money earn in second week is $ 760

∴ The algebraic equation to model the situation is $ x = $ 1240 - $ 480

Hence ,  The money earn in second week is $ 760 and

The algebraic equation to model the situation is $ x = $ 1240 - $ 480  Answer

Answer:

c then b

Step-by-step explanation:

2 - The elevation at Point E is 50 feet, marked by a contour line, 3 - Point F is at 70 feet elevation, illustrating the informative nature of topographic maps.

On Map 1, Point E is situated at an elevation of 50 feet, as it lies directly on the contour line representing this specific elevation. Contour lines on a topographic map connect points of equal elevation, allowing us to visualize the three-dimensional terrain on a two-dimensional surface.

In this context, every point on the contour line labeled "50 feet" shares the same elevation—50 feet above a reference point, typically sea level. Moving to Point F on Map 1, it is positioned on the contour line corresponding to an elevation of 70 feet.

This indicates that Point F is situated 70 feet above the same reference point. Topographic maps are invaluable tools for understanding the landscape's elevation variations, aiding hikers, geologists, and cartographers in navigating and representing the Earth's surface features accurately.

The contour lines on such maps provide a detailed depiction of the elevation changes, and by closely following them, one can trace the undulations of the terrain.

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The functions f and g that adds up to h(x) are:

f(x) = -2x+3 and g(x) = 7x-9

Step-by-step explanation:

Required output is:

h(x) = 5x-6

In order to find the required f and g functions we will see that which of the two functions add up to h(x)

In order to make our work easier we can see the functions f and g whose coefficients of  add up to 5x

Then we can select from the functions that produce h(x)

So,

Pair 1 whose coefficients of x add up to 5 is:

f(x) = -2x+6 and g(x) = 7x-9

Adding both functions

[tex](f+g)(x) = -2x+6+7x-9\\= 5x-3[/tex]

Pair 2 that adds up to 5x

f(x) = 8x+9 and g(x) = -3x-3

Adding both functions:

[tex](f+g)(x) = 8x+9-3x-3\\= 8x-3x+9-3\\=5x+6[/tex]

Pair 3 is:

f(x) = -2x+3 and g(x) = 7x-9

Adding both functions

[tex](f+g)(x) = -2x+3+7x-9\\= -2x+7x+3-9\\=5x-6[/tex]

Hence,

The functions f and g that adds up to h(x) are:

f(x) = -2x+3 and g(x) = 7x-9

Keywords: Functions, Sum of functions

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The correct answer is A

Answer: B. 239 Square Feet

Step-by-step explanation:

Let y be the size of a kitchen that costs $3,824.00.

Given : The price of tiling a room varies directly as the size of the room.

Equation of direct variation between x and y : [tex]\dfrac{x_1}{x_2}=\dfrac{y_1}{y_2}[/tex]

If the tiling costs 4,224.00 for 264 square feet , to find the  size of a kitchen that costs $3,824.00.

We put [tex]x_1= 4224 \ \ ; \ y_1=264\ ; \x_2=3824\ ; \ y_2=y[/tex] , we get

[tex]\dfrac{4224}{3824}=\dfrac{264}{y}\\\\\Rightarrow\ y=\dfrac{264\times3824}{4224}=239[/tex]

Hence, the size of a kitchen that costs $3,824.00 is 239 Square Feet

The correct answer is B. 239 Square Feet

Answer:

Step-by-step explanation:

[tex]-\dfrac{2}{3}u=-4\qquad\text{change the signs}\\\\\dfrac{2}{3}u=4\qquad\text{multiply both sides by}\ \dfrac{3}{2}\\\\\dfrac{3\!\!\!\!\diagup^1}{2\!\!\!\!\diagup_1}\cdot\dfrac{2\!\!\!\!\diagup^1}{3\!\!\!\!\diagup_1}u=4\!\!\!\!\diagup^2\cdot\dfrac{3}{2\!\!\!\!\diagup_1}\\\\u=(2)(3)\\\\u=6[/tex]

Three other ordered pairs with θ between −360° and 360° that name the same point as (−3, 330°) are (−3, 30°), (−3, 690°), and (−3, -30°).

Given the ordered pair (−3, 330°), we can find three other ordered pairs that name the same point by adding or subtracting 360° from the given angle:

These three ordered pairs have angles between −360° and 360° and represent the same point as the given ordered pair.

Answer: y+3 = 4( x + 1)

Step-by-step explanation:

The equation in point slope form is given as :

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] ) , where m is the slope

slope = 4

point given : (-1,-3)

Using the formula :

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )

and substituting the value , we have

y - (-3) = 4 (x -{-1} )

y+3 = 4( x + 1)

Answer:

I'd say C.60but because of the half units its possibly B. but definitely not A or D.

Step-by-step explanation:

Because the short sides are approximately 6 units long and the long sides are 10 units long. You multiply it to find the area and you get 60.

hope this helps

The area of the graph rectangle is 60 sq. units.

The correct option is D) 60 sq. units.

The area of a rectangle is expressed as:

Area = length × width

First, we use the distance formula to find the length and width of the rectangle.

[tex]Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

From the graph, the length is between the points (-1,1) and (8,-2):

Hence;

[tex]Length = \sqrt{(8-(-1))^2 + (-2 - 1)^2}\\\\Length = \sqrt{(8+1)^2 + (-2 - 1)^2}\\\\Length = \sqrt{(9)^2 + (-3)^2}\\\\Length = \sqrt{81 + 9}\\\\Length = \sqrt{90}\\\\Length = 3\sqrt{10}[/tex]

Next, we find the width which is between the points (-1,1) and (-3,-5):

[tex]Width = \sqrt{(-3 - (-1))^2 + (-5 - 1)^2}\\\\Width = \sqrt{(-3 + 1)^2 + (-5 - 1)^2}\\\\Width = \sqrt{(-2)^2 + (-6)^2}\\\\Width = \sqrt{4 + 36}\\\\Width = \sqrt{40}\\\\Width = 2\sqrt{10}[/tex]

Now, plug the values for the length and width into the above formula and solve for the area:

Area = length × width

Area = 3√10 × 2√10

Area = 3 × 2 × 10

Area = 60 sq. units

Therefore, the area measures 60 sq. units.

Option D) 60 sq. units is the correct answer.

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Answer:

C) –|x| + 3

I got the answer correct!!!

To find the product of 7 and 28 using place value and the distributive property, rewrite the product as 7(20 + 8). Distribute the 7 to both terms inside the parentheses and then add the resulting products.

To find the product of 7 and 28 using place value and the distributive property, we can rewrite the product as 7(20 + 8). This is because 28 can be decomposed into 20 + 8.

Using the distributive property, we can distribute the 7 to both terms inside the parentheses: 7(20) + 7(8).

The product of 7 and 20 is 140 and the product of 7 and 8 is 56. Therefore, the final product is 140 + 56 = 196.

Answer:

The student council from each box of candy will make the profit of $23.50.

Step-by-step explanation:

Given:

Each box of candy costs $50. Profit of 47% from each candy.

Now, to get the amount of how much profit from each box:

Amount of profit (A) = Profit% of cost of candy of each box

A = 47% of $50

[tex]A=\frac{47}{100}\times 50[/tex]

[tex]A=0.47\times 50[/tex]

[tex]A=23.50[/tex]

Amount of profit = $23.50

Therefore, the student council from each box of candy will make the profit of $23.50.

Answer:

Nick gave 3 marbles to each of his 4 friends.

Step-by-step explanation:

Given:

Total Number of Marbles = 12

Number of Friends = 4

Let the number of marbles to be divided in each friend be x

Solution:

To find the number of marbles to be divided in each friend we have to divide Total Number of Marbles by  Number of Friends.

Hence number of marbles to be divided in each friend x = [tex]\frac{\textrm{Total Number of Marbles}}{\textrm{Number of friends}}= \frac{12}{4}=3[/tex]

Hence we can say that Nick gave 3 marbles to each of his 4 friends.

Answer:

7x-2y≤5

7x-2y≤5

Step-by-step explanation: Graph is down below!!

Hope this helps you out!☺

Graph a solid line then shade the area above the boundary line since y is greater than 7/2 x-5/2 as given below.

We need to find the graph which represents the inequality 7x−2y≤5.

In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Now,

Write in y=mx+b form.

y≥7/2x-5/2

Use the slope-intercept form to find the slope and y-intercept.

Slope: 7/2

y-intercept:(0, -5/2)

Graph a solid line then shade the area above the boundary line since y is greater than 7/2 x-5/2 as given below.

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Answer:

2x² + 2x + 3

Step-by-step explanation:

x = 3 is a zero of both the numerator and the denominator, so the denominator will factor completely into the numerator with no remainder.  Using grouping to factor:

(2x³ − 4x² − 3x − 9) / (x − 3)

(2x³ − 4x² − 6x + 3x − 9) / (x − 3)

(2x (x² − 2x − 3) + 3x − 9) / (x − 3)

(2x (x − 3) (x + 1) + 3 (x − 3)) / (x − 3)

2x (x + 1) + 3

2x² + 2x + 3

To use long division instead, see image.

Answer:

21 miles

Step-by-step explanation:

Jeff drove [tex]=\dfrac{1}{2}[/tex] of the trip

Jason Joe drove [tex]=\dfrac{1}{4}[/tex] of the trip

Together Jeff and Jason Joe drove [tex]=\dfrac{1}{2}+\dfrac{1}{4}=\dfrac{2}{4}+\dfrac{1}{4}=\dfrac{3}{4}[/tex] of the trip

All trip [tex]=1[/tex]

Remaining trip [tex]=1-\dfrac{3}{4}=\dfrac{4}{4}-\dfrac{3}{4}=\dfrac{1}{4}[/tex]

Susan and Sharon divided the rest of the drive equally, so

Susan drove = Sharon drove [tex]=\dfrac{1}{4}:2=\dfrac{1}{4}\cdot \dfrac{1}{2}=\dfrac{1}{8}[/tex] of the trip.

The entire trip was 168 miles, then

Sharon drove [tex]=\dfrac{1}{8}\cdot 168=21\ miles[/tex]

Answer:

The valid value of x is x=-2

Step-by-step explanation:

we know that

The sum of the interior angles of any quadrilateral must be equal to 360 degrees

so

[tex](7x^{2}-24x)+100+(24-46x)+(3x^{2}+56)=360[/tex]

solve for x

Combine like terms

[tex]10x^{2}-70x+180=360[/tex]

[tex]10x^{2}-70x-180=0[/tex]

Divide by 10 both sides

[tex]x^{2}-7x-18=0[/tex]

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2}-7x-18=0[/tex]

so

[tex]a=1\\b=-7\\c=-18[/tex]

substitute in the formula

[tex]x=\frac{-(-7)(+/-)\sqrt{-7^{2}-4(1)(-18)}} {2(1)}[/tex]

[tex]x=\frac{7(+/-)\sqrt{121}} {2}[/tex]

[tex]x=\frac{7(+/-)11} {2}[/tex]

[tex]x=\frac{7(+)11} {2}=9[/tex]

[tex]x=\frac{7(-)11} {2}=-2[/tex]

Remember that

The measure of the interior angle cannot be a negative number

For x=9

we have that the measure of one interior angle of quadrilateral  is

[tex]24-46x[/tex]

substitute the value of x

[tex]24-46(9)=-390\°[/tex]

therefore

The value of x=9 cannot be a solution

For x=-2

The measure of the interior angles are

[tex](7(-2)^{2}-24(-2))=76\°\\100\°\\(3(-2)^{2}+56)=68\°\\24-46(-2)=116\°[/tex]

therefore

The valid value of x is x=-2

If the line is parallel to y=2x, the line must have the same slope.

So, the slope of your line is 2.

Now we need to find the y intercept. We should use the point given.

y=mx+b

-3=2(-4)+b

b=5

Equation: y=2x+5

Answer:

See above graph

Step-by-step explanation:

In between those whole numbers, each mark represents ⅕ [or 0,2], therefore you move one-fifth block to the right of 20 with an open circle, then shade everything to the left.

≥, ≤ → Solid Circle [●]

>, < → Blank Circle [○]

I am joyous to assist you anytime.

To graph the solution of the inequality, p < 20.2, one must draw a number line. Mark a point on the number line at 20.2 and shade or draw an arrow pointing to the left of this mark. Ensure to use an open circle at 20.2 to show that it itself is not part of the solution.

To graph the solution of the inequality p < 20.2 on a number line, you need to take the following steps:

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Answer:

not 100% sure of this but I think its a4=192

Answer:

12Pi

Step-by-step explanation:

circumference of a circle can be worked out as Pi x diameter

Diameter = 2 x radius, therefore here d = 12 and circumference = 12 Pi

The circumference of the circle is C = 12π meters

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the radius of the circle be r = 6 meters

Now , circumference of circle = 2πr

On simplifying , we get

C = 2π ( 6 )

C = 12π meters

Hence , the circumference is 12π meters

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Answer:

55/18

Step-by-step explanation:

f(x) = 2/3*12 +3

= 1/18 +3

=55/18

The value of f (12) will be;

⇒ f (12) = 11

What is substitution method?

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The function is,

⇒ f (x) = 2/3x + 3

Now,

Since, The function is,

⇒ f (x) = 2/3x + 3

Substitute x = 12 in above equation, we get;

⇒ f (x) = 2/3x + 3

⇒ f (12) = 2/3 × 12 + 3

⇒ f (12) = 2 × 4 + 3

⇒ f (12) = 11

Thus, The value of f (12) will be;

⇒ f (12) = 11

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Answer:

(A) y+2=3(x-1)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-2)=3(x-1)

y+2=3(x-1)

Answer:

Initial value for Mrs. White is $600 more than Mrs. Brown.

The rate of change is same for both.

Step-by-step explanation:

Cost of car purchased by Mrs. White = $3,000

Rate at which she pays for the car = $300 per month

Cost of car purchased by Mrs. Brown = $2,400

Rate at which she pays for the car = $300 per month

So,

Initial value for Mrs. White was =$3,000

Initial values for Mrs. Brown was =$2,400

difference in initial values  [tex]=3000-2400[/tex]  =$600

∴ Initial value for Mrs. White is $600 more than Mrs. Brown.

Rate of change of payment due for  Mrs. White = $300 per month

Rate of change for payment due for Mrs. Brown = $300 per month

∴ The rate of change is same for both.

Since Mrs White had a higher initial value than Mrs Brown and both having same rates of change, therefore Mrs. White will take a longer time to pay the due.

A 100% increase means a value doubles, a 100% decrease means it drops to zero, and 100% error indicates complete inaccuracy. For increases and decreases, the percentage is calculated based on the ratio of change to the original amount multiplied by 100%. Percent error compares the experimental value with the accepted value to judge accuracy.

An example of a 100% increase would be if you have $50, and this amount doubles to $100. Here the final amount is 100% more than the original, as the increase ($50) is equal to the original value ($50). The formula used is % increase = (Amount of increase/original amount) x 100%. So, % increase = ($50/$50) x 100% = 100%.

A 100% decrease implies that something diminishes completely to zero. For instance, if you have 10 apples and all of them are taken away, the percent decrease is 100% since the decrease (10 apples) equals the original quantity (10 apples). The calculation would be % decrease = (Decrease/original amount) x 100%, which results in % decrease = (10/10) x 100% = 100%.

100% error in a measurement means the measurement is completely inaccurate. For example, if the accepted value of a length is 30 cm and the experimental measurement is 60 cm, then the percent error is calculated as: % error = (Absolute value of (Experimental value - Accepted value)/Accepted value) x 100%, which in this case is % error = (|60 cm - 30 cm|/30 cm) x 100% = 100%. This represents a complete deviation from the actual value.

Answer:

1st and 2nd graph are decreasing functions

Step-by-step explanation:

Increasing function means, as we go from left to right, the function goes "ABOVE" and thus, increases.

Decreasing function means, as we go from left to right, the function goes "DOWN" and thus, decreases.

We will look at all the 4 graphs given. We look from "LEFT-TO-RIGHT".

The first one goes "DOWN", so its decreasing.

The second one also goes "DOWN, so this is decreasing as well.

The third one goes "UP", so it is increasing.

The fourth function stays the same, so it is neither increasing nor decreasing. It is constant.

Thus,

1st and 2nd graph are decreasing functions, only

Answer:

There was 62.23% change in radius as the ion formed.

Step-by-step explanation:

Given

Radius of Aluminium [tex](Al)[/tex] atom  = 143 pm

Radius of Aluminium [tex](Al^{3+})[/tex] atom  = 54 pm

Change is the radius =  Radius of Aluminium [tex](Al)[/tex] atom - Radius of Aluminium [tex](Al^{3+})[/tex] atom = 143 -54 = 89

Now to find % Change is the radius we will divide Change is the radius by Radius of Aluminium [tex](Al)[/tex] atom and multiply by 100 we get

% Change is the radius = [tex]\frac{\textrm{Change is the radius}}{\textrm{Radius of Aluminium (Al) atom}} \times 100 = \frac{89}{143}\times100= 62.23\%[/tex]

Hence there was 62.23% change in radius as the ion formed.

Answer:

B

Step-by-step explanation:

When you dilate a shape you change the size, changing the composition of isometries.

Option B is not a composition of isometries.

The composition of isometries refers to combining multiple isometries (transformations that preserve distance) to create a new transformation. To determine which of the options is not a composition of isometries, we need to verify if each option preserves distance. If any option does not preserve distance, it is not a composition of isometries. Let's analyze each option:

A. Reflection over x=2 then rotation 90 degrees clockwise about the origin: Both reflection and rotation are isometries, as they preserve distance. Therefore, this option is a composition of isometries.

B. Dilation with scale factor 1/2 then rotation 270 degrees clockwise about the origin: Dilation, when the scale factor is not 1, does not preserve distance. Therefore, this option is not a composition of isometries.

C. Translation (x,y)-> (x-2, y+1) then reflection over the y-axis: Both translation and reflection are isometries, as they preserve distance. Therefore, this option is a composition of isometries.

D. Reflection over the x-axis then reflection over the y-axis: Both reflections are isometries, as they preserve distance. Therefore, this option is a composition of isometries.

In summary, option B is the only one that is not a composition of isometries.

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Answer:

The mass of the object if body accelerate at the rate 8 a is [tex]\frac{m}{16}[/tex]

Step-by-step explanation:

Given as :

The net force = F Newton

The mass of the object = m kg

The acceleration = a  m/s²

Now, As The force is define as the product of mass and velocity

So, F = m × a

Now, Again , if the acceleration = 8 a

and The force decrease to [tex]\frac{F}{2}[/tex] = 0.5 F

So, Let The mass = M

∵ F = m × a

∴ mass = [tex]\frac{\textrm Force}{\textrm acceleration}[/tex]

Or. M = [tex]\frac{\textrm 0.5 F}{\textrm 8 a}[/tex]

or, M =0.0625 × [tex]\frac{F}{a}[/tex]

∴ M = 0.0625 × m = [tex]\frac{m}{16}[/tex]

so, The mass =  [tex]\frac{m}{16}[/tex]

Hence The mass of the object if body accelerate at the rate 8 a is [tex]\frac{m}{16}[/tex]  Answer

Final answer:

According to Newton’s second law of motion, the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a). If the force is decreased to F/2, the mass that would accelerate at a rate 8a can be found by rearranging the equation and solving for mass.

Explanation:

According to Newton’s second law of motion, the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a), expressed as F = ma.

If the force is decreased to F/2, the new force is now (F/2). To find the mass (m) that would accelerate at a rate 8a, we need to rearrange the equation as follows:

(F/2) = m * (8a)

To solve for the mass (m), we divide both sides of the equation by (8a), which gives us:

m = (F/2)/(8a)

Therefore, the mass that would accelerate at a rate 8a when the force is decreased to F/2 is (F/2)/(8a).

Answer:

Left box: Outlier in this data set is (57,132)

Right box: because the finish time looks faster than expected for the age.

Step-by-step explanation:

As per the given table shows the [tex]age[/tex] and [tex]finish \ time[/tex] of [tex]10[/tex] runners.

It is clear that people of age around [tex]35[/tex] are finishing at around [tex]142 \ minutes[/tex]

and person with older age takes longer to finish.

One person of age [tex]57[/tex] finishes in [tex]175 \ minutes[/tex] , that looks as expected.

Another person of same age [tex](57)[/tex] finishes it too fast which is unexpected.

Therefore [tex](57,132)[/tex] is an outlier, because it looks a faster finish as per expected.

Answer:

The left box = (57 , 132)

The right box= The finished time is expected for the age.

Step-by-step explanation: