In Exercises 4 and 5. graph the polygon and its image after a reflection in the given line.
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Answer:

5x² ( x² - 2x + 2 ) ( x² + 2x + 2 ) ( x² + 2 ) ( x² - 2 )

Step-by-step explanation:

→ Find the highest common factor from 5 and 80

5

→ Find the highest common factor of x¹⁰ and x²

x²

→ Write the partially factored form

5x² ( x⁸ - 16 )

→ Factor down ( x⁸ - 16 )

( x⁴ + 4 ) ( x⁴ - 4 )

→ Factor down ( x⁴ + 4 ) ( x⁴ - 4 )

( x² - 2x + 2 ) ( x² + 2x + 2 ) ( x² + 2 ) ( x² - 2 )

Answer:

Step-by-step explanation:

The greatest common factor is that factor that includes every prime factor that is found in both expressions. Once that is removed, the formula for the factorization of the difference of squares is needed.

__

Each expression factors as ...

  5x^10 = 5·x^2·x^8

  80x^2 = 5·x^2·16

The common factors in these expressions are 5, x^2, so the expression with the greatest common factor factored out is ...

  5x^2(x^8 -16)

__

The remaining factor is the difference of squares, which factors as ...

  a² -b² = (a -b)(a +b)

Here, we have a=x^4 and b=2^2, so the factors of the difference are ...

  x^8 -16 = (x^4 -4)(x^4 +4)

The first of these factors is also recognizable as a difference of squares, so it can be factored further:

  x^4 -4 = (x^2 -2)(x^2 +2)

The second factor can also be cast as the difference of squares, allowing it to be factored further:

  x^4 +4 = (x^4 +4x^2 +4) -(4x^2) = (x^2 +2)^ -(2x)^2

  = (x^2 +2x +2)(x^2 -2x +2)

So, the complete factorization of the original expression is ...

  5x^10 -80x^2 = 5x^2(x^2 +2x +2)(x^2 -2x +2)(x^2 +2)(x^2 -2)

_____

Additional comment

We could factor to linear terms if we wanted to use radicals and complex numbers. This is the factorization in integers.

Answer: The sample of the survey was 3000 teenagers
               The population of the survey was teenagers across the state

Step-by-step explanation:

"3000 randomly selected teenagers"

"3000 randomly selected teenagers across the state"

Step-by-step explanation:

1 km² = 1km×1km = 1000m × 1000m = 1000000 m²

5 km² = 5000000 m²

so, he has to pay 5000000p as tax.

The amount of tax the farmer must pay is 50000 Rupees.

A compulsory contribution the government has levied on people's income is called the tax , It is of various types and the money accumulated from that is used for the development of the nation.

It is given that the farmer has an area of 5 km²

The farmer must pay 1p tax for each m² of land he owns.

5km² = 5 * (1000)² m²

Area = 5 *10⁶ m²

The amount of tax the farmer needs to pay is

= 1* 5* 10⁶

= 5000000 p

100p = 1 rupees

= 50000 Rupees

Therefore the amount of tax the farmer must pay is 50000 Rupees.

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Answer: (0, –5)

Step-by-step explanation:

Don’t worry the other person is right

Step-by-step explanation:

B) y = 53.8x + 1149.8

C) Total Sales increase from one week to the next by $53.8.

Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.

D) The restaurant's sales for the Monday of the 15th week is expected to be $1956.8

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term.

B) As by scatter plot,

The total sales for week 4 is given as 1,365 while that of week 9 is 1,634.

Therefore, we shall determine the equation for the line of best fit using the points;

( 4, 1365) and ( 9, 1634)

The first step would be to determine the slope of this line;

slope = (1634 - 1365)/ (9 - 4)

       = 53.8

The equation of the line in slope-intercept form is thus;

Sales = 53.8(Week) + c

We need to determine c, the y-intercept. We can use the point ( 4, 1365);

1365= 53.8(4) + c

c = 1365-215.2

c = 1149.8

The equation of the line of best fit is thus;

y = 53.8x + 1149.8

C) The slope of the equation for the lines of best fit was found to be 53.8.  

    This value is positive which implies

    Total Sales increase from one week to the next by $53.8.

    The slope in regression is defined as the change in y for every unit change in x.

Therefore, it is true to say that the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.

D) The equation  for the line of best fit was found to be;

  y = 53.8x+ 1149.8

where y denotes the total sales and x the corresponding week. We are required to determine y when x is 15;

y = 53.8(15) + 1149.8

y = 1956.8

Therefore, the restaurant's sales for the Monday of the 15th week is expected to be $1956.8.

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Answer:

x = 60

Step-by-step explanation:

Discussion

You have 3600 boxes and 60 trucks

The formula you want is

Total Boxes = Number of trucks * number of boxes per truck.

Givens

Total boxes = 3600

Total trucks = 60

Solution

3600 = 60 * x                    Divide by 60

3600/60 = 60x/60

x = 60

Answer:

6

Step-by-step explanation:

[tex]\text{From the question...}\\9x^2 + 4y \div z\\x = \frac{2}{3}\\y = 3\\z = 6\\\\\text{Substitute in values}\\9(\frac{2}{3})^2 + 4(3) \div (6)\\\\\text{Following the rules of BODMAS or PEMDAS}\\9(\frac{4}{9}) + 12 \div 6\\4 + 2\\6[/tex]

Answer:

the answer is 11 because there are so many no. repeating so in this case we count total no of terms and say it n if terms are odd then mode

Step-by-step explanation:

mode = n+1÷2

Answer:

Step-by-step explanation:

sum of first six  terms of given G.P.=1+2+4+8+16+32=63

let d be c.d. of A.P.

first six terms are 1,1+d,1+2d,1+3d,1+4d,1+5d

1+1+d+1+2d+1+3d+1+4d+1+5d=63

6+15d=63

15d=63-6=57

divide by 3

5d=19

d=19/5=3.8

fifth term=1+4d=1+3.8*4=1+15.2=16.2

Answer:

1: The limit doesn't exist

2:

Step-by-step explanation:

Question 1:

f(x) = x + 10 for when x approaches 8

18 = 8 + 10 which is NOT true x < 8             18 < 8

f(x) = 10 - x for when x approaches 8

2 = 10 - 8 which is NOT true x ≥ 8                2 ≥ 8

Question 2:

f(x) = 5 - x for when x approaches 5

0 = 5 - 5 which is TRUE x < 5           0 < 5

f(x) = 8 for when x approaches 5

which is NOT x = 5                          8 = 5

f(x) = x + 3 for when x approaches 5

8 = 5 + 3 which is TRUE x > 5           8 > 5

Answer:

a) 19.63 mm (2 dp)

b) 245.44 mm²  (2 dp)

Step-by-step explanation:

Formula

[tex]\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)[/tex]

[tex]\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]

[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}[/tex]

Calculation

Given:

[tex]\begin{aligned}\implies \textsf{Arc length} &=2 \pi (25)\left(\dfrac{45^{\circ}}{360^{\circ}}\right)\\ & = 50 \pi \left(\dfrac{1}{8}\right)\\ & = \dfrac{25}{4} \pi \\ & = 19.63\: \sf mm \:(2\:dp)\end{aligned}[/tex]

[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{45^{\circ}}{360^{\circ}}\right) \pi (25)^2\\& = \left(\dfrac{1}{8}\right)\pi \cdot 625\\& = \dfrac{625}{8} \pi\\& = 245.44\: \sf mm^2 \:(2\:dp)\end{aligned}[/tex]

Please note:  As you have not specified if π should be approximated, I have not used an approximation for π.

The sides and angles of the right triangle area as follows:

m∠C = 28°

m∠A = 62°

AC = 17 units

Using trigonometric ratios,

cos C = 15 / 17

m∠C = cos⁻¹ 0.88235294117

m∠C = 28.0726015272

m∠C = 28°

m∠A = 180 - 28 - 90 = 62°

AC = 17 units

AC is the hypotenuse of the right angle triangle.

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Step-by-step explanation:

scientific notation is

a.b × 10^c

with a being <> 0.

0.0002 cm = 2.0×10^-4 cm (the "2" moves 4 positions to the right for the actual number).

so, this is between 1.0×10^-4 cm and 1.0×10^-3 cm.

0.02 cm = 2.0×10^-2 cm (the "2" only need to move 2 positions to the right for the actual number).

so, this is between 1.0×10-2 cm and 1.0×10^-1 cm.

200 cm = 2.0×10² cm (now the "2" needs to move 2 positions to the left for the actual number).

so, this is between 1.0×10² cm and 1.0×10³ cm.

20,000 cm = 2.0×10⁴ cm (the "2" has to move 4 positions to the left for the actual number).

so, this is between 1.0×10⁴ cm and 1.0×10⁵ cm.

Answer:

y = x+8

Step-by-step explanation:

You find the difference between the value of y and value of x which is 8 so no matter what x is you always add 8 to get the y value. :)

Answer:

y = x + 8

Step-by-step explanation:

Find the difference between each x and y-value :

Let's take the pair (18, 26)

Answer:

We are given the dimension of the side being 5 inches and it states that we need to determine the surface area.  The first step that we must do is find the area of one side and then we multiply it by 6 because we have 6 same sides.

[tex]A = s^2[/tex]

[tex]A = (5\ in)^2[/tex]

[tex]A = 25\ in^2[/tex]

Now that we have the area of one side we can multiply it by 6 to get the total surface area.

[tex]A = 25\ in^2 * 6[/tex]

[tex]A = 150\ in^2[/tex]

Therefore, our final answer is that the surface area is 150 inches squared

Hope this helps!

Answer:

150 square inches

Step-by-step explanation:

find the area of 1 square face

5*5=25

multiply by 6 faces

25*6=150

To draw a 50 degree angle with a protactor, proceed as follows :

Remember that 50 degree angle cannot be constructed using compass.

0.35x=73.85, comgining moving terms

divide both sides by 0.35

x=211 quarters, which is $52.75 ANSWER

x+5=216 dimes, which is $21.60 ANSWER

That total is $74.35

Answer:

the answer is 210 quarters and 215 dimes

Step-by-step explanation:

Answer:

Sherlyn swam 42 minutes on Saturday

Step-by-step explanation:

danced for 3 2/4 hours on Saturday

3 2/4 hours is equivalent to 3.5 hours

1 / 5 of (that time) 3.5 hours is (1 / 5) * 3.5 = 0.7 hours

Because one hour is equal to sixty minutes, in order to change the units you have to multiply the number of hours, 0.7, by 60.

0.7 x 60 = 42 minutes

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Answer:

The length is 7.3m

Step-by-step explanation:

The end of the ladder touches the top of the tree when kept at 2.8m away from the tree.

The Tree is 4.5m tall

The length of the ladder will be: 2.8+4.5 = 7.3

Answer:

1

Step-by-step explanation:

7^0 = 1

Note : -

( Any number )^0 = 1

The equation of the best fit is y = 16.89x + 134.95 and projected profit is $2700.07

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]

[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

The line of best fit;
y = mx + c

m = 16.89

c = 134.95

y = 16.89x + 134.95

Plug x = 2010 - 2002 = 8

y = 16.89(8) + 134.95

y = $2700.07

Thus, the equation of the best fit is y = 16.89x + 134.95 and projected profit is $2700.07

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Answer:

y=6.4

Step-by-step explanation:

The solution is in the image

The system of equations are solved and the value of y = 32/5

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

Substituting the values in the equation , we get

x + y = 1   be equation (1)

2x - 3y = -30   be equation (2)

Multiply equation (1) by 2 , we get

2x + 2y = 2   be equation (3)

Subtracting equation (2) from equation (3) , we get

5y = 32

Divide by 5 on both sides , we get

y = 32/5

Hence , the equation is solved and y = 32/5

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Answer:

9 sides

Step-by-step explanation:

Formula for finding interior angles of all polygons : 180 ( n - 2) / n = A

(n being the amount of sides it has)

This information is important so you can plug in the numbers that you already know

We know that the interior angle measures to 140 degrees

180 (n - 2) / n = 140

multiply both sides by "n"

(n - 2) x 180 = 140n

Distribute 180 to what's inside the parenthesis

180n - 360 = 140n

Subtract 140n and add 360 to each side (which just moves 360 to the other side of the "="

40n = 360

Divide 40 by both sides

n = 9

hope this helps :)

Answer:

y = - 2x

Step-by-step explanation:

the equation of a line passing through the origin is

y = mx ( m is the slope )

calculate m using the slope formula

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

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 1, 2) ← 2 points on the line

m = [tex]\frac{2-0}{-1-0}[/tex] = [tex]\frac{2}{-1}[/tex] = - 2 , then

y = - 2x ← equation of line

Answer:

b) g(x) = x + 7

it may seem like its x - 7, but it's actually x + 7 since it shifts up the graph 7 units.

As there is the highest degree 4 there are four zeros .

Using calculator

the roots are(attached)

The graph is also attached

Answer:

a) 4 roots

b) x = 1 and x = -3

[tex]\textsf{c)} \quad x=1, \quad x=-3, \quad x=\dfrac{-1 + \sqrt{3}i}{2}, \quad x=\dfrac{-1 - \sqrt{3}i}{2}[/tex]

d) see attached

Step-by-step explanation:

Given function:

[tex]f(x)=x^4+3x^3-x-3[/tex]

Part (a)

From inspection of the function, the highest exponent of the polynomial is 4.  Therefore, it is expected that the polynomial will have 4 roots.

Part (b)

To find the rational roots, find values of x where [tex]f(x)=0[/tex]

[tex]f(1)=(1)^4+3(1)^3-1-3=0[/tex]

[tex]f(-3)=(-3)^4+3(-3)^3-(-3)-3=0[/tex]

Therefore, the rational roots are: x = 1 and x = -3

Part (c)

As there are only 2 rational roots, the other 2 roots must be complex roots. To find these, first factor the polynomial using the 2 rational roots found in part (b):

[tex]\implies f(x)=(x-1)(x+3)(x^2+bx+1)[/tex]

[tex]\implies f(x)=(x^2+2x-3)(x^2+bx+1)[/tex]

[tex]\implies f(x)=x^4+bx^3+x^2+2x^3+2bx^2+2x-3x^2-3bx-3[/tex]

[tex]\implies f(x)=x^4+(2+b)x^3+(2b-2)x^2+(2-3b)-3[/tex]

Compare coefficients to find b:

[tex]\implies (2+b)x^3=3x^3[/tex]

[tex]\implies b=1[/tex]

Therefore the fully factored function is:

[tex]\implies f\:\!(x)=(x-1)(x+3)(x^2+x+1)[/tex]

Therefore:

[tex](x^2+x+1)=0[/tex]

To find the complex roots, use the quadratic formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{1^2-4(1)(1)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{-3}}{2}[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{3}\sqrt{-1}}{2}[/tex]

[tex]\implies x=\dfrac{-1 \pm \sqrt{3}i}{2}[/tex]

Therefore, all the roots of the function are:

[tex]x=1, \quad x=-3, \quad x=\dfrac{-1 + \sqrt{3}i}{2}, \quad x=\dfrac{-1 - \sqrt{3}i}{2}[/tex]

Part (d)

End behaviors:

As the degree of the function is even and the leading coefficient is positive, the end behaviors are:

[tex]\textsf{As } x \rightarrow - \infty, \:\: f(x) \rightarrow + \infty[/tex]

[tex]\textsf{As } x \rightarrow + \infty, \:\: f(x) \rightarrow + \infty[/tex]

y-intercept

Substitute x = 0 into the function:

[tex]f\:\!(0)=(0)^4+3(0)^3-(0)-3=-3[/tex]

Therefore, the y-intercept is (0, -3)

To find the approximate x-coordinates of the turning points (stationary points), differentiate the function, set it to zero, then solve for x:

[tex]f'\:(x)=4x^3+9x^2-1[/tex]

[tex]\implies 4x^3+9x^2-1=0[/tex]

Using a calculator, x ≈ -2.2, x ≈ -0.4, x ≈ 0.3

Therefore the approximate coordinates of the turning points are:

(-2.2, -9.3),  (-0.4, -2.7)  and (0.3, -3.2)

We don't need to plot these points, they merely help us with the approximate shape of the curve.

a =80 vertically oposite angle

a+b=180 angle of the same side of transversal are 180 degree

so b=180-80

=100

c=b vertically oposite angle

b=100=c

c= 100

Answer:

a=80, b=100, c=100

Step-by-step explanation:

Because A is directly across from 80 degrees, A is also 80 degrees. They are alternate angles, and so they equal the same thing. B is 100, because it is on the same line as 80, and a line equals 180 degrees. C is also 100 degrees, because it is across from B and on the same line as A, which is 80 degrees.

Hope this helps!