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

The transformations that maps polygon jklm to polygon nopq are described as follows:

C. Reflection across the y-axis, translation 2 units left and 6 units up, dilation with center (0,0) and scale factor 1/2.

The first transformation was a reflection, changing the orientation of the polygon.

Due to the orientation assumed with the equivalent vertices, NL, KO, PJ and MQ, the reflection was over the y-axis, with vertex O assuming coordinates (2,-2).

Since vertex O is at the y-axis, the polygon was translated 2 units left and 6 units up, with O assuming coordinates (0, 4).

The final coordinates of O are (0,2), hence the polygon was dilated with a scale factor of 1/2, as 4 x 1/2 = 2, which is the final y-coordinate of O.

The problem is incomplete, and the complete problem is given by the image at the end of the answer.

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Answer:

10 bags would cost $30

Step-by-step explanation:

We have been given we can get 2 bags for $6

so we need to how many bags we would get for a dollar =

6/2 = 3

now we need the value for 10 bags =

10 times 3 =

$30

I have attached a image which makes the equation much more pleasing to look at, do check it out. :)

(Hi fyi this answer took a lot of time & effort to make sure it was accurate, precise and to the point to be produced, so if you could opt this answer as the brainliest it would mean the world to me,)

Stay positive and Take care,

A fellow mate,

Cheers !

Answer:

x = 30, and the measure of NMO is 64°

Step-by-step explanation:

Since MO bisects LMN, it follows that LMO is congruent to NMO, and the measure of LMN is twice the measure of LMO and of NMO. So we have:

[tex]5x - 22 = 2(x + 34)[/tex]

[tex]5x - 22 = 2x + 68[/tex]

[tex]3x = 90[/tex]

[tex]x = 30[/tex]

So the measure of NMO is equal to the measure of LMO:

[tex]30 + 34 = 64[/tex]

LMO and NMO are 64°.

Answer:

x=30

MO bisects LMN

so LMO = NMO

then LMO+NMO=LMN

The inequality equation is = 15x +10y>=110. This equation represents the possible values for the number of hours lifeguarding and the number of hours washing cars = 15x +10y >= 110

Hourly wage of Cooper working as a lifeguard = $15

Hourly wage of Cooper washing cars = $10

Minimum income required this week = $110

Let x be the number of hours Cooper works as a lifeguard and y be the number of hours Cooper works washing cars

Income from working as a lifeguard based on the number of hours = 15x

Income from working washing cars based on the number of hours = 10y

Formulating the inequality equation we get the following:

15x + 10y >=110

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Answer:

No, 9 is not a factor of 76 and 46.

Step-by-step explanation:

No, 9 is not a factor of 76 and 46. 9 is a factor of 72 and 45.

I hope this helps!

Answer:

See below

Step-by-step explanation:

Given expression

Simplify it as below:

The value of a is 20.

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Given that,

HL is perpendicular to HJ

m ∠2 = (a + 15)°

and

m ∠3 = (a + 35)°

If HL and HJ are perpendicular,

Then,

m ∠2 + m ∠3 = 90°

(a + 15)°  +  (a + 35)° = 90°

Now, solve for a

(a + 15)°  +  (a + 35)° = 90°

a + 15 + a + 35 = 90

a + a = 90 - 15 - 35

2a = 40

a = [tex]\frac{40}{2}[/tex]

a = 20.

Hence, the value of a is 20

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Neither graph in this problem represents a proportional relationship, as they have different rates of change. Examples are as follows:

1. Different rates between days 0-10 and 30-40.

2. Different rates between hours 0 - 1 and 2 - 3.

A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as the rule below shows.

y = kx

Hence, a function will only be proportional if the rate of change is constant for all intervals.

For item 1, we have that:

Hence it is not a proportional relationship, due to the different rates.

For item 2, we have that:

For the same reason as item 1, of the different rates, it does not represent a proportional relationship.

The graphs are missing and are given by the image at the end of the answer.

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Answer:

               Irrational    Rational

7.12              ✔                            

7.122                                ✔        

7.123123                          ✔        

7.123231...                       ✔        

This should be right I apologize if it's not!

Mark me brainiest if it is tho :D

Answer:

$17.58

make sure to mark me as the brainliest

The variance of each random variable is given as follows:

a) Var(2x - y) = 10.4165.

b) Var(x + 3y - 5) = 20.833.

The number that occurs when each dice is thrown is represented by an uniform variable, with bounds a = 1 and b = 6, hence the variance of each variable is calculated as follows:

Var(x) = Var(y) = (6 - 1)²/12 = 2.0833.

When two variables are added, the variance is calculated as follows:

Var(aX + bY) = a²Var(X) + b²Var(Y)

Hence, for item a, the variance is calculated as follows:

Var(2x - y) = 2²Var(x) + (-1)²Var(y) = 4Var(x) + Var(y)

The variances were calculated before, which are both of 2.0833, hence:

4Var(x) + Var(y) = 4 x 2.0833 + 2.0833 = 10.4165.

For item b, the variance is calculated as follows:

Var(x + 3y - 5) = Var(x) + 3²Var(y) + (-1)²Var(-5).

The variance of a constant is of zero, hence Var(-5) = 0, and then:

Var(x + 3y - 5) = Var(x) + 3²Var(y) + (-1)²Var(-5) = 2.0833 + 9(2.0833) = 20.833.

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Answer:

12% commission rate

Step-by-step explanation:

A salesperson earns a commission of $336 for selling $2800 in merchandise find the commission rate:

336 ÷ 2,800 = 0.12

0.12 = 12% commission rate

The surface area of the given pyramid is equivalent to 760 square inches.

The surface area of a figure is the sum of the area of the surfaces of such figure.

The given pyramid is made up of 5 big rectangles and 2 small rectangles

Surface area = Area of 4 large rectangles + 2(area of small rectangles)

Surface area = 2(22 * 10) + 2(22 * 5) + 2(10 * 5)

Surface area = 440 + 220 + 100

Surface area  = 760 square inches

Surface area = 760 square inches

Hence the surface area of the rectangular based pyramid is 760 square inches

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Answer:

4

Step-by-step explanation:

1/2 the bottle is equal to 4/8. giving 1/8 to each sick cat is 4

Answer:8%

Step-by-step explanation:

Answer:

maybe, probably 20mph

Step-by-step explanation:

The average rate of change is equal to 10 miles per hour.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

Given that the function is changing from point (30,2) to (20,1). The average rate of the change will be calculated as,

The average rate of change = ( 30 - 20) / ( 2 - 1)

Average rate of change = 10 miles per hour

Therefore, the average rate of change is equal to 10 miles per hour.

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Answer:

Subtract 8 from both sides

Step-by-step explanation:

You want to isolate the term with the variable you want to solve for.

Answer:

Subtract 8 from both sides.

Given:

prtion D is the correct answer.

[tex]p < 10-4\\p < 6[/tex]

P<6 is the solution

Be reminded <> change direction when you divide or multiply by a negative number.

the area of triangle cod is 6 sq. inch

A trapezoid is also as a trapezium, is a flat closed shape having 4 straight  

sides, with one pair of parallel sides . a trapezium can also a  parallel legs .

Point O (the point of intersection of diagonals )divides two diagonals AC and BD into parts that are proportional:

AO/CO = DO/BO

Then AO x BO = CO xDO

Consider triangle ABO. The area of this triangle is

Aabo  = 1/2 x AO x BO x sin ∠AOB

Consider triangle COD. The area of this triangle is

Acod = 1/2 x CO x DO x sin ∠COD

Since  AO x  BO = CO x DO and angles AOB and COD are congruent as vertical angles

Acod = 1/2 x BO x AO x sin ∠ AOB = Aaob = 6. inc.sq.

hence ,

the area of traiangle cod is 6 sq. inc.

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The Volume of the given Triangular Prism is calculated with the given parameters to be; 63 in³

The formula for Volume of a Triangular Prism is;

V = ¹/₂a*c*h

where;

V is volume

a is height of prism

c is length of shorter side of base

h is length of longer side of base

Now, from the triangular prism we are given, we can see that;

a = 3.5 inches

c = 4 inches

h = 9 inches

Thus;

V = ¹/₂ * 3.5 * 4 * 9

V = 63 in³

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Answer:

[tex]\dfrac{\dfrac{3}{5}x + \dfrac{7}{10}y}{x + y}[/tex]  

where x = number of students in Zankers class and y = number of students in Haynes' class

If the number of students in these classes are equal then the average fraction is 13/20

Step-by-step explanation:

Let x = number of students in Zanker's class

Then number of students who went for the trip is [tex]\dfrac{3}{5}x[/tex]

Let y  be the number of students in Haynes' clas

Number of students who went = [tex]\dfrac{7}{10}y[/tex]

Total number of students who went on the trip = [tex]\dfrac{3}{5}x + \dfrac{7}{10}y[/tex]

Total number of students in both classes = x + y

So average fraction

=
= [tex]\dfrac{\textsf {Total Number of Students On Trip}}{\textsf {Total Number of Students}}\\\\= \dfrac{\dfrac{3}{5}x + \dfrac{7}{10}y}{x + y}[/tex]

Without knowing how many students are in each class we can only come up with an equation

If we assume the same number of students in each class
Then we get total students who went on trip =  [tex]\dfrac{3}{5} N + \dfrac{7}{10}N[/tex][tex]= \left( \dfrac{3}{5} + \dfrac{7}{10}\right)N= \left(\dfrac{13}{10}\right)N[/tex]

where N = total number of students

Since the total in 2 classes is 2N the average fraction

[tex]= \left(\dfrac{13}{10}\right)N \div 2N = \dfrac{13}{20}[/tex]

The coordinates of Z are (-11.5, 5)

When a point on a line segment divides it into two segments, the formula used to determine the coordinates of that point is known as the section formula. Let us say, we have a point P(x,y) that divides the line segment with marked points as A (x1,y1) and B(x2,y2). To find the coordinates, we use the section formula, which is mathematically expressed as:

P(x, y) =  (m[tex]x_2[/tex] + n [tex]x_1[/tex] / m+ n, m [tex]y_2[/tex] +n[tex]y_1[/tex] /m+ n)

Given coordinates:

XY:XZ is 2:3

X is located at (6,10) and Y is located at (-1,8).

let the coordinates of Z(x, y)

using section formula

-1 = (2x + 18)/ 5

-5 = 2x +18

2x = -23

x= -11.5

and, 8 = 2y + 30 /5

40 = 2y + 30

2y= 10

y=5

Hence, the coordinates of Z are (-11.5, 5)

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The derivate of a function f(x) is determinated as:

For the function

First we have to determine de f ( x + h ) as follow:

Then we calculate and simplify the coeficient in the first formula

------------------------------------------------------------------------------------The equation of the tangent:

First you need to know that the derivate of a function is equal to the slope (m) of the tangent of this function

And the equation to thist tangent in a specific point will be find using the next formula:

We have to calculate the slope in the point x =4 using the derivate:

In the point x=4

Calculate the value of f(x0) substituting in the function the given point x:

Knowing that we put the value of m and f(x0) in the equation of the tangent:

---------------------------------------------------------------------------

The normal line

The slope of the normal line is the opposite of the slope of theu tangent in an espesific point:

So in this situation is:

The equation of the normal line is given by the next formula:

Replacing the data we obtain:

We have to evaluate the expressions.

We have to solve each operation in the correct order: first the operations within the parenthesis, and within them, first the powers, then the multiplication/quotients and lastly the adds/subtractions. Then, we apply the same sequence for the terms outside the parenthesis.

a)

b)

c)

Answer: a) 146, b) 4 c) 29

According to the definition of proportion, two ratios are in proportion when they are equal.

A monomial is an expression consisting of a single term.

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. Two ratios or fractions are equal when an equation or a declaration to that effect is utilized.

A polynomial with only one term is called a monomial. An algebraic expression known as a monomial typically has one term, but it can also have several variables and a higher degree. When 9 is the coefficient, x, y, and z are the variables, and 3 is the degree of the monomial, for instance, 9x³yz is a single term.

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Answer:

0

Step-by-step explanation:

You inputted nothing.

Answer:

x=90*

Step-by-step explanation:

t=40